THE EXPERIMENTAL FOUNDATIONS OF PARTICLE · PDF fileTHEEXPERIMENTALFOUNDATIONS OF PARTICLE PHYSICS Robert N. Cahn Senior Physicist, Lawrence Berkeley Laboratory University of California,

THE EXPERIMENTAL FOUNDATIONS

OF PARTICLE PHYSICS

ii

THE EXPERIMENTAL FOUNDATIONS

OF PARTICLE PHYSICS

Robert N. Cahn

Senior Physicist,

Lawrence Berkeley Laboratory

University of California, Berkeley

and

Gerson Goldhaber

Professor of Physics,

Physics Department and

Lawrence Berkeley Laboratory

University of California at Berkeley

CAMBRIDGE UNIVERSITY PRESS

Cambridge New York New Rochelle Melbourne Sydney

Published by the Press Syndicate of the University of CambridgeThe Pitt Building, Trumpington Street, Cambridge CB2 1RP32 East 57th Street, New York, NY 10022, USA10 Stamford Road, Oakleigh, Melbourne 3166, Australia

c© Cambridge University Press 1989

First published 1989

Printed in the United States of America

Library of Congress Cataloging in Publication DataCahn, Robert N.

The experimental foundations of particle physics1. Particles (Nuclear physics) I. GoldhaberGerson. II. Title.QC793.2.C34 1988 539.7’21 87-36751

British Library Cataloging in Publication DataCahn, Robert N.

The experimental foundations of particle physics.1. Elementary particlesI. Title II. Goldhaber, Gerson539.7’21

ISBN 0 521 33255 9

Articles and Figures reprinted by permission of the authors and the publishers:American Institute of Physics: all articles from Physical Review and PhysicalReview LettersElsevier Science Publishers B. V.: all articles from Nuclear Physics and PhysicsLettersComptes Rendus de l’Academie des Sciences de Paris: C. R. Acad. Sciences,seance du 13 dec. 1944, p. 618Nature, copyright Macmillan Journals Limited: Vol. 129, No. 3252, p. 312;Vol.159, No. 4030, pp. 126-7; Vol. 160, No. 4066, pp. 453-6; Vol. 160, No. 4077, pp.855-7; Vol. 163, No. 4133, p. 82Il Nuovo CimentoPhilosophical MagazineSpringer Verlag: Zeitschrift fur Physik

For

Fran, Deborah, and Sarah

and for

Judy, Nat, Marilyn, Michaela, and Shaya

vi

Contents

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

1 The atom completed and a new particle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2 The muon and the pion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3 Strangeness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4 Antibaryons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

5 The resonances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

6 Weak interactions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .154

7 The neutral kaon system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193

8 The structure of the nucleon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217

9 The J/ψ, the τ , and charm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257

10 Quarks, gluons, and jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306

11 The fifth quark . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337

12 From neutral currents to weak vector bosons . . . . . . . . . . . . . . . . . . . . . . . . . . . 377

13 Epilogue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 420

vii

viii

Preface

Fifty years of particle physics research has produced an elegant and concisetheory of particle interactions at the subnuclear level. This book presents theexperimental foundations of that theory. A collection of reprints alone would,perhaps, have been adequate were the audience simply practicing particle physi-cists, but we wished to make this material accessible to advanced undergraduates,graduate students, and physicists with other fields of specialization. The text thataccompanies each selection of reprints is designed to introduce the fundamentalconcepts pertinent to the articles and to provide the necessary background infor-mation. A good undergraduate training in physics is adequate for understandingthe material, except perhaps some of the more theoretical material presented insmaller print and some portions of Chapters 6, 7, 8, and 12, which can be skippedby the less advanced reader.

Each of the chapters treats a particular aspect of particle physics, with thetopics given basically in historical order. The first chapter summarizes the de-velopment of atomic and nuclear physics during the first third of the twentiethcentury and concludes with the discoveries of the neutron and the positron. Thetwo succeeding chapters present weakly-decaying non-strange and strange parti-cles, and the next two the antibaryons and the resonances. Chapters 6 and 7deal with weak interactions, parity and CP violation. The contemporary pictureof elementary particles emerges from deep inelastic lepton scattering in Chapter8, the discovery of charm and the tau lepton in Chapter 9, quark and gluon jetsin Chapter 10, and the discovery of the b-quark in Chapter 11. The synthesis ofall this is given in Chapter 12, beginning with neutral current interactions andculminating in the discovery of the W and Z.

A more efficient presentation can be achieved by working in reverse, startingfrom the standard model of QCD and electroweak interactions and concludingwith the hadrons. This, however, leaves the reader with the fundamentally falseimpression that particle physics is somehow derived from an a priori theory. Itfails, too, to convey the standard model’s real achievement, which is to encompassthe enormous wealth of data accumulated over the last fifty years.

Our approach, too, has its limitations. Devoting pages to reprinting articleshas forced sacrifices in the written text. The result cannot be considered a com-plete textbook. The reader should consult some of the additional references listedat the end of each chapter. The text by D. H. Perkins provides an excellent supple-ment. A more fundamental problem is that, quite naturally, we have reprinted (webelieve) correct experiments and provided (we hope!) the correct interpretations.However, at any time there are many contending theories and sometimes contra-dictory experiments. By selecting those experiments that have stood the test oftime and ignoring contemporaneous results that were later disproved, this bookinevitably presents a smoother view of the subject than would a more historically

ix

complete treatment. Despite this distortion, the basic historical outline is clear.In the reprinted papers the reader will see the growth of the field, from modestexperiments performed by a few individuals at cosmic ray laboratories high atopmountains, to monumental undertakings of hundreds of physicists using apparatusweighing thousands of tons to measure millions of particle collisions. The readerwill see as well the development of a description of nature at the most fundamentallevel so far, a description of elegance and economy based on great achievements inexperimental physics.

Selecting articles to be reprinted was difficult. The sixty or so experimentalpapers ultimately selected all played important roles in the history of the field.Many other important articles have not been reprinted, especially when there weretwo nearly simultaneous discoveries of the same particle or effect. In two instances,for the sake of brevity, we chose to reprint just the first page of an article. Bychoosing to present usually the first paper on a subject often a later paper that mayhave been more complete has been neglected. In some cases, through oversight orignorance we may simply have failed to include a paper that ought to be present.Some papers were not selected simply because they were too long. We extendour apologies to our colleagues whose papers have not been included for any ofthese reasons. The reprinted papers are referred to in boldface, while other papersare listed in ordinary type. The reprinted papers are supplemented by numerousfigures taken from articles that have not been reprinted and which sometimesrepresent more recent results. Additional references, reviews or textbooks, arelisted at the end of each chapter.

Exercises have been provided for the student or assiduous reader. They areof varying difficulty; the most difficult and those requiring more background aremarked with an asterisk. In addition to a good standard text book, the readerwill find it helpful to have a copy of the most recent Review of Particle Properties,which may be obtained as described at the end of Chapter 2.

G. G. would like to acknowledge 15 years of collaboration in particle physicswith Sulamith Goldhaber (1923 - 1965).

We would like to thank the many particle physicists who allowed us to repro-duce their papers, completely or in part, that provide the basis for this book. Weare indebted, as well, to our many colleagues who have provided extensive criticismof the written text. These include F. J. Gilman, J. D. Jackson, P. V. Landshoff, V.Luth, M. Suzuki, and G. H. Trilling. The help of Richard Robinson and ChristinaF. Dieterle is also acknowledged. Of course, the omissions and inaccuracies areours alone.

R. N. C.G. G.

Berkeley, California, 1988

5

The Resonances

A pattern evolves, 1952 – 1964

Most of the particles whose discoveries are described in the preceeding chaptershave lifetimes of 10−10 s or more. They travel a perceptible distance in a bubblechamber or emulsion before decaying. The development of particle acceleratorsand the measurement of scattering cross sections revealed new particles in theform of resonances. The resonances corresponded to particles with extremely smalllifetimes as measured through the uncertainty relation ∆t∆E = h. The energyuncertainty, ∆E, was reflected in the width of the resonance, usually 10 to 200MeV, so the implied lifetimes were roughly h/100MeV ≈ 10−25s. As more andmore particles and resonances were found, patterns appeared. Ultimately thesepatterns revealed a deeper level of particles, the quarks.

The first resonance in particle physics was discovered by H. Anderson, E. Fermi,E. A. Long, and D. E. Nagle, working at the Chicago Cyclotron in 1952. (Ref.5.1) They observed a striking difference between the π+p and π−p total crosssections. The π−p cross section rose sharply from a few millibarns and came up toa peak of about 60 mb for an incident pion kinetic energy of 180 MeV. The π+pcross section behaved similarly except that for any given energy, its cross sectionwas about three times as large as that for π−p.

In two companion papers they investigated the three scattering processes:

(1) π+p→ π+p elastic π+ scattering

(2) π−p→ π0n charge exchange scattering

(3) π−p→ π−p elastic π− scattering

They found that of the three cross sections, (1) was largest and (3) was thesmallest. The data were very suggestive of the first half of a resonance shape. Theπ+ cross section rose sharply but the data stopped at too low an energy to showconclusively a resonance shape. K. A. Brueckner, who had heard of these results,

104

5.The Resonances 105

suggested that a resonance in the πp system was being observed and noted that aspin-3/2, isospin-3/2 πp resonance would give the three processes in the ratio 9:2:1,compatible with the experimental result. Furthermore, the spin-3/2 state wouldproduce an angular distribution of the form 1 + 3 cos2 θ for each of the processes,while a spin-1/2 state would give an isotropic distribution. The π+p state musthave total isospin I = 3/2 since it has Iz = 3/2. If the resonance were not in theI = 3/2 channel, the π+p state would not participate. Fermi proceeded to showthat a phase shift analysis gave the J = 3/2, I = 3/2 resonance. C. N. Yang,then a student of Fermi’s, showed, however, that the phase shift analysis hadambiguities and that the resonant hypothesis was not unique. It took another twoyears to settle fully the matter with many measurements and phase shift analyses.Especially important was the careful work of J. Ashkin et al. at the Rochestercyclotron which showed that there is indeed a resonance, what is now called the∆(1232) (Ref. 5.2). A contemporary analysis of the J = 3/2, I = 3/2 pion–nucleonchannel is shown in Figure 5.1.

The canonical form for a resonance is associated with the names of G. Breit and E.Wigner. A heuristic derivation of a resonance amplitude is obtained by recalling that fors-wave potential scattering, the scattering amplitude is given by

f =exp(2iδ) − 1

2ik

where δ is the phase shift and k is the center-of-mass momentum. For elastic scatteringthe phase shift is real. If there is inelastic scattering δ has a positive imaginary part. Forthe purely elastic case it follows that

Im(1/f) = −k

which is satisfied by

1/f = (r − i)k

where r is any real function of the energy. Clearly, the amplitude is biggest when rvanishes. Suppose this occurs at an energy E0 and that r has only a linear dependence onE, the total center-of-mass energy. Then we can introduce a constant Γ that determineshow rapidly r passes through zero:

f =1

2k(E0 −E)/Γ − ik=

1

k· Γ/2

(E0 −E) − iΓ/2

The differential cross section is

dσ/dΩ = |f |2

and the total cross section is

σ = 4π|f |2 =4π

k2

Γ2/4

(E −E0)2 + Γ2/4

106 5.The Resonances

Figure 5.1: An analysis of the J = 3/2, I = 3/2 channel of pion–nucleon scattering.Scattering data have been analyzed and fits made to the various angular momentum andisospin channels. For each channel there is an amplitude, aIJ = (eiδIJ − 1)/2i, where δIJ

is real for elastic scattering and ImδIJ > 0 if there is inelasticity. Elastic scattering givesan amplitude on the boundary of the Argand circle, with a resonance occurring when theamplitude reaches the top of the circle. In the Figure, the elastic resonance at 1232 MeVis visible, as well as two inelastic resonances. Tick marks indicate 50 MeV intervals. Theprojections of the imaginary and real parts of the J = 3/2, I = 3/2 partial wave amplitudeare shown to the right and below the Argand circle [Results of R. E. Cutkosky as presentedin Review of Particle Properties, Phys. Lett. 170B, 1 (1986)].


The quantity Γ is called the the full width at half maximum or, more simply, the width.This formula can be generalized to include spin for the resonance (J), the spin of twoincident particles (S1, S2), and multichannel effects. The total width receives contributionsfrom various channels, Γ =

∑

n Γn, where Γn is the partial decay rate into the final staten. If the partial width for the incident channel is Γin and the partial width for the finalchannel is Γout, the Breit-Wigner formula is

σ =4π

k2

2J + 1

(2S1 + 1)(2S2 + 1)

ΓinΓout/4

(E −E0)2 + Γ2/4

In this formula, k is the center-of-mass momentum for the collision.

As higher pion energies became available at the Brookhaven Cosmotron, moreπp resonances (this time in the I = 1/2 channel and hence seen only in π−p) wereobserved, as shown in Figure 5.2. Improved measurements of these resonancescame from photoproduction experiments, γN → πN , carried out at Caltech andat Cornell (Ref. 5.4).

The full importance and wide-spread nature of resonances only became clear in1960 when Luis Alvarez and a team that was to include A. Rosenfeld, F. Solmitz,and L. Stevenson began their work with separated K− beams in hydrogen bubblechambers exposed at the Bevatron. The first resonance observed (Ref. 5.5) wasthe I = 1 Λπ resonance originally called the Y ∗

1 , but now known as the Σ(1385).The reaction studied in the Lawrence Radiation Laboratory’s 15-inch hydrogenbubble chamber was K−p → Λπ+π− at 1.15 GeV/c. The tracks in the bubblechamber pictures were measured on semiautomatic measuring machines and themomenta were determined from the curvature and the known magnetic field. Themeasurements were refined by requiring that the fitted values conserve momentumand energy. The invariant masses of the pairs of particles,

M212 = (p1 + p2)

2 = (E1 +E2)2 − (p1 + p2)2

were calculated. For three-particle final states a Dalitz plot was used, with eitherthe center-of-mass frame kinetic energies, or equivalently, two invariant massessquared, as variables. As for the τ -meson decay originally studied by Dalitz, in theabsence of dynamical correlations, purely s-wave decays would lead to a uniformdistribution over the Dalitz plot. The most surprising result found by the Alvarezgroup was a band of high event density at fixed invariant mass, indicating thepresence of a resonance.

The data showed resonance bands for both the Y ∗+ → Λπ+ and the Y ∗− →Λπ− processes. Since the isospins for Λ and π are 0 and 1 respectively, the Y ∗ hadto be an isospin-1 resonance. The Alvarez group also tried to determine the spinand parity of the Y ∗, but with only 141 events this was not possible.

This first result was followed rapidly by the observation of the first meson

resonance, the K∗(890), observed in the reaction K−p→ K0π−p, measured in the

same bubble chamber exposure (Ref. 5.6). This result was based on 48 identified


Figure 5.2: Data from the Brookhaven Cosmotron for π+p and π−p scattering. The crosssection peak present for π−p and absent for π+p demonstrates the existence of an I = 1/2resonance (N∗) near 900 MeV kinetic energy (center of mass energy 1685 MeV). A peaknear 1350 MeV kinetic energy (center of mass energy 1925 MeV) is apparent in the π+pchannel, indicating an I = 3/2 resonance, as shown in Figure 5.1. Ultimately, severalresonances were found in this region. (Ref. 5.3)

events, of which 21 lay in the K∗ resonance peak. The data were adequate todemonstrate the existence of the resonance, but provided only the limit J < 2for the spin. The isospin was determined to be 1/2 on the basis of the decaysK∗− → K−π0 and K∗0 → K−π+.

A very important J = 1 resonance had been predicted first by Y. Nambu andlater by W. Frazer and J. Fulco. This ππ resonance, the ρ, was observed by A. R.Erwin et al. using the 14-inch hydrogen bubble chamber of Adair and Leipunerat the Cosmotron (Ref. 5.7). The reactions studied were π−p → π−π0p,π−p → π−π+n, and π−p → π0π0n. Events were selected so that the momentumtransfer between the initial and final nucleons was small. For these events, therewas a clear peak in the ππ mass distribution. From the ratio of the rates for thethree processes, the I = 1 assignment was indicated, as required for a J = 1 ππ


resonance (J = 1 makes the spatial wave function odd, so bose statistics requirethat the isospin wave function be odd, as well).

By requiring that the momentum transfer be small, events were selected thatcorresponded to the “peripheral” interactions, that is, those where the closestapproach (classically) of the incident particles was largest. In these circumstances,the uncertainty principle dictates the reaction be described by the virtual exchangeof the lightest particle available, in this instance, a pion. Thus the interactioncould be viewed as a collision of an incident pion with a virtual pion emitted bythe nucleon. The subsequent interaction was simply ππ scattering. This fruitfulmethod of analysis was developed by G. Chew and F. Low. For the Erwin et al.experiment, the analysis showed that the ππ scattering near 770 MeV center-of-mass energy was dominated by a spin-1 resonance.

Shortly after the discovery of the ρ, a second vector (spin-1) resonance wasfound, this time in the I = 0 channel. B. Maglich, together with other mem-bers of the Alvarez group, studied the reaction pp → π+π−π+π−π0 using a 1.61GeV/c separated antiproton beam (Ref. 5.8). After scanning, measurement, andkinematic fitting, distributions of the πππ masses were examined. A clean, verynarrow resonance was observed with a width Γ < 30 MeV. The peak occurred inthe π+π−π0 combination, but not in the combinations with total charges otherthan 0. This established that the resonance had I = 0. A Dalitz plot analysisshowed that JP = 1− was preferred, but was not a unique solution. The re-maining uncertainty was eliminated in a subsequent paper (Ref. 5.9). The Dalitzplot proved an especially powerful tool in the analysis of resonance decays, espe-cially of those into three pions. This was studied systematically by Zemach, whodetermined where zeros should occur for various spins and isospins, as shown inFigure 5.3.

The discovery of the meson resonances took place in “production” reactions.The resonance was produced along with other final-state particles. The term“formation” is used to describe processes in which the resonance is formed fromthe two incident particles with nothing left over, as in the ∆ resonance formed inπN collisions (N = p or n).

The term “resonance” is applied when the produced state decays strongly, asin the ρ or K∗. States such as the Λ, which decay weakly, are termed particles.The distinction is, however, somewhat artificial. Which states decay weakly andwhich decay strongly is determined by the masses of the particles involved. Theordering of particles by mass may not be fundamental. Geoffrey Chew proposedthe concept of “nuclear democracy”, that all particles and resonances were on anequal footing. This view has survived and a resonance like K ∗ is regarded as noless fundamental than the K itself, even though its lifetime is shorter by a factorof 1014.

The proliferation of particles and resonances called for an organizing principlemore powerful than the Gell-Mann – Nishijima relation and one was found as a


Figure 5.3: Zemach’s result for the location of zeros in decays into three pions. The darkspots and lines mark the location of zeros. C. Zemach, Phys. Rev. 133, B1201 (1964).

generalization of isospin. One way to picture isospin is to regard the proton andneutron as fundamental objects. The pion can then be thought of as a combinationof a nucleon and an antinucleon, for example, np→ π+. This is called the Fermi-Yang model. S. Sakata proposed to extend this by taking the n, p, and Λ asfundamental. In this way the strange mesons could be accommodated: Λp→ K+.The hyperons like Σ could also be represented: nΛp→ Σ+. Isospin, which can berepresented by the n and p, has the mathematical structure of SU(2). Sakata’ssymmetry, based on n, p, and Λ, is SU(3). Ultimately, Murray Gell-Mann andindependently, Yuval Ne’eman proposed a similar but much more successful model.

Each isospin or SU(3) multiplet must be made of particles sharing a commonvalue of spin and parity. Without knowing the spins and parities of the particlesit is impossible to group them into multiplets. Because the decays Λ → π−p andΛ → π0n are weak and, as we shall learn in the next chapter, do not conserveparity, it is necessary to fix the parity of the Λ by convention. This is done bytaking it to have P = +1 just like the nucleon. With this chosen, the parity of theK is an experimental issue.


The work of M. Block et al. (Ref. 5.10) studying hyperfragments produced byK− interactions in a helium bubble chamber showed the parity of the K− to benegative. The process observed was K−He4 → π−He4

Λ. The He4Λ hyperfragment

consists of ppnΛ bound together. It was assumed that the hyperfragment hadspin-zero and positive parity, as was subsequently confirmed. The reaction thenhad only spin-zero particles and the parity of the K− had to be the same as thatof the π− since any parity due to orbital motion would have to be identical in theinitial and final states.

The parity of the Σ was determined by Tripp, Watson, and Ferro-Luzzi (Ref.5.11) by studying K−p → Σπ at a center of mass energy of 1520 MeV. At thisenergy there is an isosinglet resonance with JP = 3/2+. The angular distributionof the produced particles showed that the parity of the Σ was positive. Thusit could fit together with the nucleon and Λ in a single multiplet. The Ξ waspresumed to have the same JP .

In the Sakata model the baryons p, n, and Λ formed a 3 of SU(3), while thepseudoscalars formed an octet. In the version of Gell-Mann and Ne’eman thebaryons were in an octet, not a triplet. The baryon octet included the isotripletΣ and the isodoublet Ξ in addition to the nucleons and the Λ. The basic entity ofthe model of Gell-Mann and Ne’eman was the octet. All particles and resonanceswere to belong either to octets, or to multiplets that could be made by combiningoctets. The rule for combining isospin multiplets is the familiar law of additionof angular momentum. For SU(3), the rule for combining two octets gives 1 +8 + 8 + 10 + 10∗ + 27. (Here the 10 and 10∗ are two distinct ten-dimensionalrepresentations.) The “eightfold way” postulated that only these multiplets wouldoccur. The baryon octet is displayed in Figure 5.4.

The pseudoscalar mesons known in 1962 were the π+, π0, π−, the K+, K0,

K0, and the K−. Thus, there was one more to be found according to SU(3). A.

Pevsner of Johns Hopkins University and M. Block of Northwestern University,together with their co-workers found this particle, now called the η, by studyingbubble chamber film from Alvarez’s 72-inch bubble chamber filled with deuterium.The exposure was made with a π+ beam of 1.23 GeV/c at the Bevatron (Ref.5.12). The particle was found in the π+π−π0 channel at a mass of 546 MeV.No charged partner was found, in accordance with the SU(3) prediction that thenew particle would be an isosinglet. The full pseudoscalar octet is displayed inFigure 5.5 in the conventional fashion.

The η was established irrefutably as a pseudoscalar by M. Chretien et al. (Ref.5.13) who studied π−p → ηn at 1.72 GeV using a heavy liquid bubble chamber.The heavy liquid improved the detection of photons by increasing the probabilityof conversion. This enabled the group to identify the two photon decay of the η.See Figure 5.6. By Yang’s theorem, this excluded spin-one as a possibility. Theabsence of the two pion decay mode excluded the the natural spin-parity sequence0+, 1−, 2+,.. . If the possibility of spin two or higher is discounted, only 0− remains.


Σ0, Λ Σ+Σ−

n p

Ξ− Ξ0

−1 0 1

1

0

−1

- Iz

6

Y

Figure 5.4: The baryon JP = 1/2+ octet containing the proton and the neutron. The hor-izontal direction measures Iz , the third component of isospin. The vertical axis measuresthe hypercharge, Y = B + S, the sum of baryon number and strangeness.

Surprisingly the decay of the η into three pions is an electromagnetic decay.The η has three prominent decay modes : π+π−π0, π0π0π0, and γγ. The last issurely electromagnetic, and since it is comparable in rate to the others, they cannotbe strong decays. The absence of a strong decay is most easily understood in termsof G-parity, a concept introduced by R. Jost and A. Pais, and independently, byL. Michel.

G-parity is defined to be the product of charge conjugation, C, with the ro-tation in isospin space e−iπIy . Since the strong interactions respect both chargeconjugation and isospin invariance, G-parity is conserved in strong interactions.The nonstrange mesons are eigenstates of G-parity and for the neutral memberslike ρ0 (I = 1, C = +1), ω0 (I = 0, C = −1), η0 (I = 0, C = +1), and π0

(I = 1, C = +1), the G-parity is simply C(−1)I . All members of the multiplethave the same G-parity even though the charged particles are not eigenstates ofC. Thus the pions all have G = −1. The ρ has even G-parity and decays into aneven number of pions. The ω has odd G-parity and decays into an odd number ofpions.

The η has G = +1 and cannot decay strongly into an odd number of pions. Onthe other hand, it cannot decay strongly into two pions since the J = 0 state of twopions must have even parity, while the η is pseudoscalar. Thus the strong decayof the η must be into four pions. Now this is at the edge of kinematic possibility


π0, η π+π−

K0 K+

K− K0

−1 0 1

1

0

−1

- Iz

6

Y

Figure 5.5: The pseudoscalar octet. The horizontal direction measures Iz while the verticalmeasures the hypercharge, Y = B + S

(if two of the pions are neutral), but to obtain JP = 0−, the pions must havesome orbital angular momentum. This is scarcely possible given the very smallmomenta the pions would have in such a decay. As a result, the 3π decay, whichviolates G-parity and thus must be electromagnetic, is a dominant mode.

The SU(3) symmetry is not exact. Just as the small violations of isospinsymmetry lead the proton–neutron mass difference, the larger deviations fromSU(3) symmetry break the mass degeneracy among the particles in the mesonand baryon octets. By postulating a simple form for the symmetry breaking,Gell-Mann and subsequently, S. Okubo were able to predict the mass relations

1

2(mp +mΞ) =

1

4(mΣ + 3mΛ)

m2K =

1

4(m2

π + 3m2η)

The use of m for the baryons and m2 for the mesons relies on dynamical con-siderations and does not follow from SU(3) alone. The relations are quite wellsatisfied.

The baryon and pseudoscalar octets are composed of particles that are stable,that is, decay weakly or electromagnetically, if at all. In addition, the resonanceswere also found to fall into SU(3) multiplets in which each particle had the samespin and parity. The vector meson multiplet consists of the ρ+, ρ0, ρ−,K∗+,K∗0,


Figure 5.6: A histogram of the openingangle between the two photons in thedecay η → γγ. The solid curve is thetheoretical expectation correspondingthe mass of the η (Ref. 5.13).

K∗0,K∗−, and ω. The spin of the K∗(890) was determined in an experiment by W.

Chinowsky et al. (Ref. 5.14) who observed the production of a pair of resonances,K+p → K∗∆. They found that J > 0 for the K∗, while Alston et al. foundJ < 2. The result was JP = 1−. An independent method, due to M. Schwartz,was applied by R. Armenteros et al. (Ref. 5.15) who reached the same conclusion.

An additional vector meson, φ, decaying predominantly into KK was discov-ered by two groups, a UCLA team under H. Ticho (Ref. 5.16) and a Brookhaven-Syracuse group, P. L. Connolly et al. (Ref. 5.17), the former using an exposureof the 72-inch hydrogen bubble chamber to K− mesons at the Bevatron, the lat-ter using the 20-inch hydrogen bubble chamber at the Cosmotron. The reactionsstudied were

(1) K−p→ ΛK0K0

(2) K−p→ ΛK+K−

A sharp peak very near the KK threshold was observed and it was demon-strated that the spin of the resonance was odd, and most likely J = 1.


The analysis relies on the combination of charge conjugation and parity, CP . From

the decay φ→ K+K− we know that if the spin of the φ is J , then C = (−1)J , P = (−1)J ,

and so it has CP = +1. As discussed in Chapter 7, the neutral kaon system has very

special properties. The K0 and K0

mix to produce a short-lived state, K0S and a longer-

lived K0L. These are very nearly eigenstates of CP with CP (K0

S) = +1, CP (K0L) = −1.

M. Goldhaber, T. D. Lee, and C. N. Yang. noted that a state of angular momentum J

composed of a K0S and a K0

L thus has CP = −(−1)J . Thus the observation of the K0SK

0L

in the decay of the CP even φ would show the spin to be odd. Conversely, the observation

of K0LK

0L or K0

SK0S would, because of Bose statistics, show the state to have even angular

momentum. The long-lived K is hard to observe because it exits from the bubble chamber

before decaying. Thus when the experiment of Connolly et al. observed 23 ΛK0S, but no

events ΛK0SK

0S, it was concluded that the spin was odd, and probably J = 1.

With the addition of the φ there were nine vector mesons. This filled anoctet multiplet and a singlet (a one-member multiplet). The isosinglet membersof these two multiplets have the same quantum numbers, except for their SU(3)designation. Since SU(3) is an approximate rather than an exact symmetry, thesestates can mix, that is, neither the ω nor the φ is completely singlet or completelyoctet. The same situation arises for the pseudoscalars, where there is in additionan η′ meson, which mixes with the η.

The octet of spin-1/2 baryons including the nucleons consisted of the p, n,Λ,Σ+, Σ0, Σ−, Ξ0, Ξ−. This multiplet was complete. The ∆ had spin 3/2 and couldnot be part of this multiplet. An additional spin-3/2 baryon resonance was known,the Y ∗(1385) or Σ(1385). Furthermore, another baryon resonance was found bythe UCLA group (Ref. 5.18) and the Brookhaven–Syracuse collaboration (Ref.5.19) that discovered the φ. They observed the reactions

K−p→ Ξ−π0K+

K−p→ Ξ−π+K0

and found a resonance in the Ξπ system with a mass of about 1530 MeV. Itsisospin must be 3/2 or 1/2. If it is the former, the first reaction should be twiceas common as the first, while experiment found the second dominated. The spinand parity were subsequently determined to be JP = (3/2)+.

The JP = (3/2)+ baryon multiplet thus contained 4∆s, 3Σ∗s, and 2Ξ∗s. Thesituation came to a head at the 1962 Rochester Conference. According to the rulesof the eightfold way, this multiplet could only be a 10 or a 27. The 27 would involvebaryons of positive strangeness. None had been found. Gell-Mann, in a commentfrom the floor, declared the multiplet was a 10 and that the tenth member hadto be an S = −3, I = 0, JP = (3/2)+ state with a mass of about 1680 MeV.It was possible to predict the mass from the pattern of the masses of the knownmembers of the multiplet. For the 10, it turns out that there should be equalspacing between the multiplets. From the known differences 1385 − 1232 = 153,


∆− ∆0 ∆+ ∆++

Σ∗− Σ∗0 Σ∗+

Ξ∗− Ξ∗0

Ω−−2

−1 0 1

1

0

−1

- Iz

6

Y

Figure 5.7: The JP = 3/2+ decuplet completed by the discovery of the Ω−.

1530 − 1385 = 145, the mass was predicted to be near 1680. The startling aspectof the prediction was that the particle would decay weakly, not strongly since the

lightest S = −3 state otherwise available is ΛK0K− with a mass of more than

2100 MeV. Thus the new state would be a particle, not a resonance. The sameconclusion had been reached independently by Y. Ne’eman, who was also in theaudience.

Bubble chamber physicists came home from the conference and started lookingfor the Ω−, as it was called. Two years later, a group including Nick Samios andRalph Shutt working with the 80-inch hydrogen bubble chamber at Brookhavenfound one particle with precisely the predicted properties (Ref. 5.20). The decaysequence they observed was

K−p→ Ω−K+K0

Ω− → Ξ0π−

Ξ0 → Λπ0

Λ → pπ−

The π0 was observed through the conversion of its photons. The complete J P =3/2+ decuplet is shown in Figure 5.7.


This was a tremendous triumph for both theory and experiment. With theestablishment of SU(3) pseudoscalar and vector octets, a spin-1/2 baryon octet,and finally a spin 3/2 baryon decuplet, the evidence for the eightfold way wasoverwhelming. Other multiplets were discovered, the tensor meson J PC = 2++,octet [ f2(1270), K2(1420), a2(1320), f

′

2(1525)], JPC = 1++ and JPC = 1+−

meson octets, and numerous baryon octets and decuplets. The discoveries filledthe ever-growing editions of the Review of Particle Properties.

A clearer understanding of SU(3) emerged when Gell-Mann and independently,G. Zweig proposed that hadrons were built from three basic constituents, “quarks”in Gell-Mann’s nomenclature. Now called u (“up”), d (“down”), and s (“strange”),these could explain the eightfold way. The mesons were composed of a quark(generically, q) and an antiquark (q). The Sakata model was resurrected in a newand elegant form. The SU(3) rules dictate that the nine combinations formedfrom qq produce an octet and a singlet. This can be displayed graphically in“weight diagrams,” where the horizontal distance is Iz, while the vertical distanceis√

3Y/2 =√

3(B+S)/2. The combinations qq, which make an octet and a singletof mesons, are represented as sums of vectors, one from q and one from q.

>Z

ZZ

?

ud

s

ZZ

Z~

=

6

u d

s

6

ZZ

Z~

=

6

=Z

ZZ~

ZZ

Z~

=

6

us

ud

ds

du

su sd

In the qq diagram there are three states at the origin (uu, dd, ss) and one state


at each of the other points. The state (uu+ dd+ ss)/√

3 is completely symmetricand forms the singlet representation. The eight other states form an octet. For

the pseudoscalar mesons the octet is π+, π0, π−, K+, K0, K0, K−, η and the

singlet is η′. Actually, since SU(3) is not an exact symmetry, it turns out thatthere is some mixing of the η and η′, as mentioned earlier.

Baryons are produced from three quarks. The SU(3) multiplication rules give3×3×3 = 10+8+8+1, so only decuplets, octets, and singlets are expected. TheJP = (3/2)+ decuplet shown in Figure 5.7 contains states like ∆++ = uuu andΩ− = sss. The JP = (1/2)+ octet contains the proton (uud), the neutron (udd),etc. There are baryons that are primarily SU(3) singlets, like the Λ(1405), whichhas JP = (1/2)−, and the Λ(1520), with JP = (3/2)−.

The simplicity and elegance of the quark description of the fundamental parti-cles was most impressive. Still, the quarks seemed even to their enthusiasts moreshorthand notation than dynamical objects. After all, no one had observed aquark. Indeed, no convincing evidence was found for the existence of free quarksduring the 20 years following their introduction by Gell-Mann and Zweig. Theirlater acceptance as the physical building blocks of hadrons came as the result of agreat variety of experiments described in Chapters 8 – 11.

EXERCISES

5.1 Predict the value of the π+p cross section at the peak of the ∆(1232) reso-nance and compare with the data.

5.2 Show that for an I = 3/2 resonance the differential cross sections for π+p→π+p, π−p → π0n, and π−p → π−p are in the ratio 9:2:1. Show that the∆(1232) produced in πp scattering yields a 1 + 3 cos2 θ angular distributionin the center-of-mass frame.

5.3 For the ∆++(1232) and the Y ∗+(1385), make Argand plots of the elasticamplitudes for π+p → π+p and π+Λ → π+Λ using the resonance energiesand widths given in Table II of Alston, et al. (Ref. 5.5).

5.4 Verify the ratios expected for I(ππ) = 0, 1, 2 in Table I of Erwin, et al., (Ref.5.7).

5.5 Verify that isospin invariance precludes the decay ω → 3π0.

5.6 What is the width of the η? How is it measured? Check the Review ofParticle Properties.

5.7 Verify the estimate of Connolly, et al. (Ref. 5.17) that if J(φ) = 1, then

BR(φ→ K0SK

0L)

BR(φ→ K0SK

0L) +BR(φ→ K+K−)

= 0.39


5.8 How was the parity of the Σ determined? See (Ref. 5.11).

BIBLIOGRAPHY

The authoritative compilation of resonances is compiled by the Particle DataGroup working at the Lawrence Berkeley Laboratory and CERN. A newReview of Particle Properties is published in even numbered years.

S. Gasiorowicz, Elementary Particle Physics, Wiley, New York, 1966 containsextensive coverage of the material covered in this chapter. See especiallyChapters 14 – 20.

D. H. Perkins, Introduction to High Energy Physics, Addison–Wesley, Menlo Park,Calif., 1987, provides a very accessible treatment of related topics in Chapters4 and 5.

REFERENCES

5.1 H. L. Anderson, E. Fermi, E. A. Long, and D. E. Nagle, “Total Cross Sectionsof Positive Pions in Hydrogen.” Phys. Rev., 85, 936 (1952). and ibid. p.934.

5.2 J. Ashkin et al., “ Pion Proton Scattering at 150 and 170 MeV.” Phys. Rev.,101, 1149 (1956).

5.3 R. Cool, O. Piccioni, and D. Clark, “Pion-Proton Total Cross Sections from0.45 to 1.9 BeV.” Phys. Rev., 103, 1082 (1956).

5.4 H. Heinberg et al., “Photoproduction of π+ Mesons from Hydrogen in theRegion 350 - 900 MeV.” Phys. Rev., 110, 1211 (1958). Also F. P. Dixonand R. L. Walker, “Photoproduction of Single Positive Pions from Hydrogenin the 500 – 1000 MeV Region.” Phys. Rev. Lett., 1, 142 (1958).

5.5 M. Alston et al., “Resonance in the Λπ System.” Phys. Rev. Lett., 5, 520(1960).

5.6 M. Alston et al., “Resonance in the Kπ System.” Phys. Rev. Lett., 6, 300(1961).

5.7 A. R. Erwin, R. March, W. D. Walker, and E. West, “Evidence for a π − πResonance in the I = 1, J = 1 State.” Phys. Rev. Lett., 6, 628 (1961).

5.8 B. C. Maglic, L. W. Alvarez, A. H. Rosenfeld, and M. L. Stevenson, “Evi-dence for a T = 0 Three Pion Resonance.” Phys. Rev. Lett., 7, 178 (1961).


5.9 M. L. Stevenson, L. W. Alvarez, B. C. Maglic and A. H. Rosenfeld, “Spinand Parity of the ω Meson.” Phys. Rev., 125, 687 (1962).

5.10 M. M. Block et al., “Observation of He4 Hyperfragments from K−−He In-teractions; the K− − Λ Relative Parity.” Phys. Rev. Lett., 3, 291 (1959).

5.11 R. D. Tripp, M. B. Watson, and M. Ferro-Luzzi, “Determination of the ΣParity.” Phys. Rev. Lett., 8, 175 ( 1962).

5.12 A. Pevsner et al., “Evidence for a Three Pion Resonance Near 550 MeV.”Phys. Rev. Lett., 7, 421 (1961).

5.13 M. Chretien et al., “Evidence for Spin Zero of the η from the Two GammaRay Decay Mode.” Phys. Rev. Lett., 9, 127 (1962).

5.14 W. Chinowsky, G. Goldhaber, S. Goldhaber, W. Lee, and T. O’Halloran,“On the Spin of the K∗ Resonance.” Phys. Rev. Lett., 9, 330 (1962).

5.15 R. Armenteros et al., “Study of the K∗ Resonance in pp Annihilations atRest.” Proc. Int. Conf. on High Energy Nuclear Physics, Geneva, 1962, p.295 (CERN Scientific Information Service)

5.16 P. Schlein et al., “Quantum Numbers of a 1020-MeV KK Resonance.” Phys.Rev. Lett., 10, 368 (1963).

5.17 P. L. Connolly et al., “Existence and Properties of the φ Meson.” Phys. Rev.Lett., 10, 371 (1963).

5.18 G. M. Pjerrou et al., “Resonance in the Ξπ System at 1.53 GeV.” Phys. Rev.Lett., 9, 114 (1962).

5.19 L. Bertanza et al., “Possible Resonances in the Ξπ and KK Systems.” Phys.Rev. Lett., 9, 180 (1962).

5.20 V. E. Barnes et al., “Observation of a Hyperon with Strangeness MinusThree.” Phys. Rev. Lett., 12, 204 (1964).

Ref. 5.1: The first Baryonic Resonance 121

122 M. Alston et al.

Ref. 5.5: The first strange resonance 123


Ref. 5.5: The first strange resonance 125


Ref. 5.6: The first meson resonance 127


Ref. 5.6: The first meson resonance 129

130 A. R. Erwin et al.

Ref. 5.7: The discovery of the ρ 131

132 A. R. Erwin et al.

Ref. 5.8: The discovery of the ω 133

134 B. C. Maglic et al.


136 B. C. Maglic et al.


138 A. Pevsner et al.

Ref. 5.12: The discovery of the η 139

140 A. Pevsner et al.

Ref. 5.17: Co-discovery of the φ 141

142 P. L. Connolly et al.





Ref. 5.18: Co-discovery of the Ξ∗ 147

148 G. M. Pjerrou et al.

Ref. 5.18: Co-discovery of the Ξ∗ 149

150 G. M. Pjerrou et al.

Ref. 5.20: The discovery of the Ω− 151

152 V. E. Barnes et al.

Ref. 5.20: The discovery of the Ω− 153

9

The J/ψ, the τ , and charm

New forms of matter, 1974–1976

In November 1974, Burton Richter at SLAC and Samuel Ting at Brookhavenwere leading two very different experiments, one studying e+e− annihilation, theother the e+e− pairs produced in proton–beryllium collisions. Their simultaneousdiscovery of a new resonance with a mass of 3.1 GeV so profoundly altered particlephysics that the period is often referred to as the “November Revolution.” Word ofthe discoveries spread throughout the high energy physics community on November11 and soon much of its research was directed towards the new particles.

Ting led a group from MIT and Brookhaven measuring the rate of productionof e+e− pairs in collisions of protons on a beryllium target. The experiment wasable to measure quite accurately the invariant mass of the e+e− pair. This madethe experiment much more sensitive than an earlier one at Brookhaven led by LeonLederman. That experiment differed in that µ+µ− pairs were observed rather thane+e− pairs. Both these experiments investigated the Drell–Yan process whosemotivation lay in the quark–parton model.

The Drell–Yan process is the production of e+e− or µ+µ− pairs in hadroniccollisions. Within the parton model, this can be understood as the annihilation of aquark from one hadron with an antiquark from the other to form a virtual photon.The virtual photon materializes some fraction of the time as a charged-lepton pair.

The e-pair and µ-pair approaches to measuring lepton-pair production eachhave advantages and disadvantages. Because high-energy muons are more pene-trating than high-energy hadrons, muon pairs can be studied by placing absorbingmaterial directly behind the interaction region. The absorbing material stops thestrongly interacting π s, K s, and protons, but not the muons. This technique per-mits a very high counting rate since the muons can be separated from the hadronsover a large solid angle if enough absorber is available. The momenta of the muonscan be determined by measuring their ranges. Together with the angle betweenthe muons, this yields the invariant mass of the pair. Of course, the muons aresubject to multiple Coulomb scattering in the absorber, so the resolution of the

257

258 9.The J/ψ,the τ , and charm

technique is limited by this effect. The spectrum observed by Lederman’s groupfell with increasing invariant mass of the lepton pair. There was, however, a shoul-der in the spectrum between 3 and 4 GeV that attracted some notice, but whosereal significance was obscured by the inadequate resolution.

By contrast, electrons can be separated from hadrons by the nature of theshowers they cause or by measuring directly their velocity (using Cerenkov coun-ters), which is much nearer the speed of light than that of a hadron of comparablemomentum. The Cerenkov-counter approach is very effective in rejecting hadrons,but can be implemented easily only over a small solid angle. As a result, thecounting rate is reduced. Ting’s experiment used two magnetic spectrometers tomeasure separately the e+ and e−. The beryllium target was selected to mini-mize multiple Coulomb scattering. The achieved resolution was about 20 MeV forthe e+e− pair, a great improvement over the earlier µ-pair experiment. The elec-trons and positrons were, in fact, identified using Cerenkov counters, time-of-flightinformation, and pulse height measurements.

In the early 1970s Richter, together with his co-workers, fulfilled his long-timeambition of constructing an e+e− ring, SPEAR, at SLAC to study collisions in the2.5 to 7.5 GeV center-of-mass energy region. Lower energy machines had alreadybeen built at Novosibirsk, Orsay, Frascati, and Cambridge, Mass. Richter himselfhad worked as early as 1958 with Gerard O’Neill and others on the pioneeringe−e− colliding-ring experiments at Stanford.

To exploit the new ring, SPEAR, the SLAC team, led by Richter and MartinPerl, and their LBL collaborators, led by William Chinowsky, Gerson Goldhaber,and George Trilling built a multipurpose large-solid-angle magnetic detector, theSLAC-LBL Mark I. The heart of this detector was a cylindrical magnetostrictivespark chamber inside a solenoidal magnet of 4.6 kG. This was surrounded by time-of-flight counters for particle velocity measurements, shower counters for photondetection and electron identification, and by proportional counters embedded iniron absorber slabs for muon identification.

What could the Mark I Collaboration expect to find in e+e− annihilations?In the quark-parton model, since interactions between the quarks are ignored, theprocess e+e− → qq is precisely analogous to e+e−→µ+µ−, except that the chargeof the quarks is either 2/3 or −1/3 and that the quarks come in three colors, as morefully discussed in Chapter 10. Thus the ratio of the cross section for annihilationinto hadrons to the cross section for the annihilation into muon pairs should simplybe three times the sum of the squares of the charges of the quarks. This ratio,conventionally called R, was in 1974 expected to be 3[(−1/3)2+(2/3)2+(−1/3)2] =2 counting the u, d, and s quarks. In fact, measurements made at the CambridgeElectron Accelerator (CEA) found that R was not constant in the center-of-massregion to be studied at SPEAR, but instead seemed to grow to a rather large value,perhaps 6. The first results from the Mark I detector confirmed this puzzling result.

In 1974, Ting, Ulrich Becker, Min Chen and co-workers were taking data

9.The J/ψ,the τ , and charm 259

with their pair spectrometer at the Brookhaven AGS. By October of that yearthey found an e+e− spectrum consistent with expectations, except for a possiblepeak at 3.1 GeV. In view of the as-yet-untested nature of their new equipment,they proceeded to check and recheck this effect under a variety of experimentalconditions and to collect more data.

During this same period, the Mark I experiment continued measurements ofthe annihilation cross section into hadrons with an energy scan with steps of 200MeV. Since no abrupt structure was anticipated, these steps seemed small enough.The data confirming and extending the CEA results were presented at the LondonConference in June 1974.

The data seemed to show a constant cross section rather than the 1/s behavioranticipated. (In the quark-parton model, there is no dimensionful constant, so thetotal cross section should vary as 1/s on dimensional grounds.) In addition, thevalue at center-of-mass energy 3.2 GeV appeared to be a little high. It was decidedin June 1974 to check this by taking additional data at 3.1 and 3.3 GeV. Furtherirregularities at 3.1 GeV made it imperative in early November, 1974, before across section paper could be published, to remeasure this region. Scanning thisregion in very small energy steps revealed an enormous, narrow resonance. Theincrease in the cross section noticed at 3.2 GeV was the due to the tail of theresonance and the anomalies at 3.1 GeV were caused by variations in the preciseenergy of the beam near the lower edge of the resonance, where the cross sectionwas rising rapidly.

By Monday, November 11 (at which time the first draft of the ψ paper wasalready written) Richter learned from Sam Ting (who too had a draft of a paperannouncing the new particle) about the MIT-BNL results on the resonance (namedJ by Ting ), and vice versa. Clearly, both experiments had observed the sameresonance. Word quickly reached Frascati, where Giorgio Bellettini and co-workersmanaged to push the storage ring beyond the designed maximum of 3 GeV andconfirmed the discovery. Papers reporting the results at Brookhaven, SLAC, andFrascati all appeared in the same issue of Physical Review Letters (Refs. 9.1,9.2, 9.3).

That the resonance was extremely narrow was apparent from the e+e− data,which showed an experimental width of 2 MeV. This was not the intrinsic width,but the result of the spread in energy of the electron and positron beams due tosynchrotron radiation in the SPEAR ring. Additionally, the shape was spreadasymmetrically by radiative corrections. If the natural width is much less than thebeam spread, the area under the cross section curve

Area =

∫

dE σ

is nearly the same as it would be in the absence of the beam spread and radiativecorrections. The intrinsic resonance cross section is of the usual Breit–Wigner formgiven in Chapter 5


σ =2J + 1

(2S1 + 1)(2S2 + 1)

π

p2cm

ΓinΓout(E −E0)2 + Γ2

tot/4

where the incident particles have spin S1, S2 = 1/2 and momentumpcm ≈ Mψ/2 = E0/2. If the observed cross section is that for annihilation intohadrons, then Γout = Γhad, the partial width for the resonance to decay intohadrons, while Γin = Γee is the electronic width. Assuming that the observedresonance has spin J = 1, we find by integrating the above,

Area =6π2ΓeeΓhadM2ψΓtot

The area under of the resonance curve measured at SPEAR is about10 nb GeV. If we assume Γhad ≈ Γtot and use the measured mass, Mψ = 3.1GeV, we find Γee ≈ 4.2 keV. The accepted value is 4.7 keV. Subsequent measure-ments of the branching ratio into electron pairs (≈ 7%) led to a determinationof the total width of between 60 and 70 keV, an astonishingly small value for aparticle with a mass of 3 GeV.

Spurred by these results and theoretical predictions of a series of excited stateslike those in atomic physics, the SLAC–LBL Mark I group began a methodicalsearch for other narrow states. It turned out to be feasible to modify the machineoperation of SPEAR so that the energy could be stepped up by 1 MeV everyminute. Ten days after the first discovery, a second narrow resonance was found(Ref. 9.4). The search continued, but no comparable resonances were found upto the maximum SPEAR energy of 7.4 GeV. The next such discovery had to waituntil Lederman’s group, this time at Fermilab and with much-improved resolution,continued their study of muon pairs into the 10 GeV region, as discussed in Chapter11.

The discovery of the ψ(3096) and its partner, ψ ′ or ψ(3685) was the beginningof a period of intense spectroscopic work, which still continues. The spin and parityof the ψ s were established to be JP = 1− by observing the interference betweenthe ψ and the virtual photon intermediate states in e+e− → µ+µ−. The G-paritywas found to be odd when the predominance of states with odd numbers of pionswas demonstrated. Since C was known to be odd from the photon interference, theisospin had to be even and was shown to be nearly certainly I = 0. Two remarkabledecays were observed quite soon after, ψ ′ → ψππ and ψ′ → ψη. Figure 9.8 showsa particularly clean ψ′ → ψππ decay with ψ → e+e−.

Prior to the announcement of the ψ, Tom Appelquist and David Politzer wereinvestigating theoretically the binding of a charmed and an anticharmed quark,which is described later in the chapter. They found that QCD predicted thatthere would be a series of bound states with very small widths, analogous tothe e+e− bound states known as positronium. The cc bound states immediatelybecame the leading explanation for the ψ and this interpretation was strengthened


Figure 9.8: An example of the decayψ′ → ψπ+π− observed by the SLAC–LBL Mark I Collaboration. Thecrosses indicate spark chamber hits.The outer dark rectangles show hits inthe time-of-flight counters. Ref. 9.5.

by the discovery of the ψ′. The ψ was seen as the lowest s-wave state with totalspin equal to one. In spectroscopic notation it was the 13S1. The ψ′ was the nextlowest spin-triplet, the s-wave state 23S1.

The analogy between the cc bound states and positronium was striking. Thetwo lowest energy states of positronium are the 3S1 and the 1S0. The formerhas C = −1 and the latter C = +1. It is this difference that first enabled Mar-tin Deutsch to find experimental evidence for positronium in 1951. Because thetriplet state has odd charge conjugation, it cannot decay into two photons likethe charge-conjugation-even singlet state. As a consequence it decays into threephotons and has a much longer lifetime. With detailed lifetime studies, Deutschwas able to find evidence for a long-lived species. QCD required that the tripletstate of cc decay into three gluons, the quanta that bind the quarks together, whilethe singlet state could decay into two gluons. Again, this meant that the tripletstate should be longer lived, that is, should have a narrow width.

In the nonrelativistic approximation, we can describe the cc system by a wavefunction, φ(r), satisfying a Schrodinger equation for some appropriate potential.The partial width, Γ(ψ → e+e−), is related to the wave function at zero separation,φ(0). The relation is obtained from the general prescription for a reaction rate,Γ = σρv, where Γ is the reaction rate, σ the cross section, v is the relative velocityof the colliding particles and ρ is the target density. In this application ρ = |φ(0)|2.For the cross section we use the low energy limit of the process cc→ e+e−,

σ = 3 ×2πα2e2qβs


where α is the fine-structure constant (≈ 1/137), β is the velocity of the quarkor antiquark in the center-of-mass frame, s is the center-of-mass energy squared(≈M2

ψ), and eq is the charge of the quark measured in units of the proton’s charge.A factor of 3 has been included to account for the three colors. The above crosssection is averaged over the quark spins. The ψ is in fact a spin-triplet. Thespin-singlet state has C = +1 and cannot annihilate through a virtual photon intoe+e−. Since the cross section in the spin-singlet state is zero, the cross section inthe spin-triplet state is actually 4/3 times the spin-averaged cross section. Notingthat the relative velocity, v, is 2β, we have

Γ(ψ → e+e−) =4

3× 3 ×

2πα2e2qβM2

ψ

· 2β|φ(0)|2

=16πα2e2qM2ψ

|φ(0)|2

The nonrelativistic model predicted that between the s-wave ψ and ψ ′ therewould be a set of p-wave states. The spin-triplet states, 3P , would have totalangular momentum J =2, 1, or 0. The spin-singlet state, 1P , would have totalangular momentum J = 1. For a fermion–antifermion system the charge conju-gation quantum number is C = (−1)L+S , while the parity is P = (−1)L+1. Thusthe 3P2,1,0 states would have JPC = 2++, 1++, 0++, while the 1P1 state wouldhave JPC = 1+−. The ψ′ was expected to decay radiatively to the C-even states,which are now denoted χ (thus ψ′ → γχ). Such a transition was first observed atthe PETRA storage ring at DESY in Hamburg by the Double Arm Spectrometer(DASP) group (Ref. 9.6). Evidence for all three χ states was then observedby the SLAC–LBL group with the Mark I detector, both by measuring the twophotons in ψ′ → χγ, χ → ψγ and by detecting the first photon and a subsequenthadronic decay of the χ that was fully reconstructed.

The complete unraveling of these states took several years and was culminatedin the definitive work of the Crystal Ball Collaboration, led by Elliott Bloom (Ref9.7). Their detector was designed to provide high spatial and energy resolution forphotons using 672 NaI crystals. A particularly difficult problem was the detectionof the anticipated s-wave, spin singlet states, 11S0 and 21S0 (denoted ηc and η′c)that were expected to lie just below the corresponding spin-triplet states, 13S1

and 23S1. Since these states have C = +1 and J = 0, they cannot be produceddirectly by e+e− annihilation through a virtual photon. Instead, they must beobserved in the same way as the χ states, through radiative decays of the ψ andψ′. The transitions are suppressed by kinematical and dynamical factors. Theywere identified only after a long effort.

In the simplest nonrelativistic model for the interaction between the charmedand anticharmed quarks, the potential is taken to be spin independent. In this


approximation, the four p-states are degenerate, with identical radial wave func-tions. The E1 transitions, ψ′ → γχ thus would occur with rates proportional tothe statistical weights of the final states, 3P0,1,2, i.e., 1 : 3 : 5. In fact, as a resultof spin-dependent forces, the splittings between the p-states are significant, so abetter approximation is obtained by noting that the E1 rates are proportional toω3, where ω is the photon energy in the ψ ′ rest frame,

ω =M2ψ′ −M2

χ

2Mψ′

If, for the masses of the ψ′ , χ2, χ1, χ0 we take the measured values, 3.686,3.556, 3.510, and 3.415 GeV, respectively, we find ω2 = 0.128 GeV, ω1 = 0.172GeV, and ω0 = 0.261 GeV and the ratios

5 × (0.128)3 : 3 × (0.172)3 : 1 × (0.261)3 = 1 : 1.46 : 1.70

The 1988 edition of the Review of Particle Properties gives branching ratiosfor ψ′ → γχ2,1,0 of 7.8 ± 0.8%, 8.7 ± 0.8%, and 9.3 ± 0.8%, in fair agreement withthe above estimates.

It was during the exciting period of investigation of the ψ,ψ ′, and χ statesthat Martin Perl and co-workers of the SLAC–LBL group made a discovery nearlyas dramatic as that of the ψ. Carefully sifting through 35,000 events, they found24 with a µ and an opposite sign e, and no additional hadrons or photons. Theyinterpreted these events as the pair production of a new lepton, τ , followed by itsleptonic decay (Ref. 9.8). The leptonic decays were τ → eνν and τ → µνν.Figure 9.9 shows results obtained by the DASP Collaboration, using a double armspectrometer, and by the DESY-Heidelberg Collaboration at the DORIS storagering at DESY. Figure 9.10 show results from DELCO, the Direct Electron Counterat SPEAR. These established the spin and mass of the τ .

The decay τ → eνν is exactly analogous to the decay µ → eνν. In bothcases we can ignore the mass of the final state leptons. The decay rate for theµ is proportional to the square of the Fermi constant, G2

F , which has dimension[mass]−4. The decay rate for the µ must then be proportional to m5

µ. We concludethat

Γ(τ → eνν) = (mτ/mµ)5Γ(µ→ eνν) = 6 × 1011 s−1

The measured lifetime of the τ is about 3.0× 10−13 s and the branching ratio intoeνν is near 18%. Combining these gives a partial rate for τ → eνν of roughly6 × 1011 s−1, in good agreement with the expectation.

Within a very short time, two new fundamental fermions had been discov-ered. The interpretation of the ψ as a bound state of a charmed quark andan charmed antiquark was backed by strong circumstantial evidence. What was


Figure 9.9: Left: The cross section from e+e− annihilation into candidates for τ leptons,as a function of center-of-mass energy, as measured by the DASP Collaboration. Thethreshold was determined to be very near 2× 1800 MeV, that is, below the ψ(3685) (Ref.9.9). Right: Similar results from the DESY-Heidelberg group which give 1787+10

−18 MeV forthe mass of the τ . The curves shown are for a spin-1/2 particle [W. Bartel et al., Phys.Lett. B77, 331 (1978)].

Figure 9.10: The production of anomalous two-prong events as a function of the center-of-mass energy, as determined by DELCO. These candidates for τ s yielded a thresholdof 3564+4

−14 MeV, i.e. a mass of 1782+2−7. The threshold behavior confirmed the spin-1/2

assignment. (Ref. 9.10)


d

s

d

s

µ−

µ+

µ−

µ+

W−

W+

W−

W+

u

c

νµ

νµ

cos θc

sin θc

− sin θc

cos θc

Figure 9.11: Two contributionsto the decayK0

L → µ+µ− show-ing the factors present at thequark vertices. If only the up-per contribution were present,the decay rate would be farin excess of the observed rate.The second contribution cancelsmost of the first. The can-cellation would be exact if thec quark and u quark had thesame mass. This cancellationis an example of the Glashow–Iliopoulos–Maiani mechanism.

lacking was proof that its constituents were indeed the charmed quarks first pro-posed by Bjorken and Glashow. As Glashow, Iliopoulos, and Maiani showed in1970, charmed quarks were the simplest way to explain the absence of neutralstrangeness-changing weak currents.

Until 1973 only weak currents that change charge had been observed. Forexample, in µ decay, the µ turns into νµ, and its charge changes by one unit.The neutral weak current, which can cause reactions like νp → νp, as discussedin Chapter 12, does not change strangeness. If strangeness could be changedby a neutral current, then the decays K0 → µ+µ− and K+ → π+e+e− wouldbe possible. However, very stringent limits existed on these decays and othersrequiring strangeness-changing neutral weak currents. So restrictive were theselimits that even second order weak processes would violate them in the usualCabibbo scheme of weak interactions. Glashow, Iliopoulos, and Maiani showedthat if in addition to the charged weak current changing an s quark into a uquark, there were another changing an s quark into a c quark, there would be acancellation of the second order terms.

Consider the decay K0L → µ+µ− for which the rate was known to be extremely

small. The decay can proceed through the diagrams shown in Figure 9.11. Asidefrom other factors, the first diagram is proportional to sin θC from the usW vertexand to cos θC from the udW vertex. Here, W stands for the carrier of the weakinteraction mentioned in Chapter 6 and discussed at length in Chapter 12.


The result given by this diagram alone would imply a decay rate that is notsuppressed relative to normal K decay, in gross violation of the experimental facts.The proposal of Glashow, Iliopoulos, and Maiani was to add a fourth quark andcorrespondingly a second contribution to the charged weak current, which wouldbecome, symbolically,

u(cos θCd+sin θCs)+c(−sin θCd+cos θCs) =(

u c)

(

cos θC sin θC−sin θC cos θC

)(

ds

)

Thus the Cabibbo angle would be simply a rotation, mixing the quarks d and s.Now when the K0

L → µ+µ− is calculated, there is a second diagram in which a cquark appears in place of the u quark. This amplitude has a term proportional to−sin θCcos θC , just cancelling the previous term. The surviving amplitude is higherorder in GF and does not conflict with experiment. The seminal quantitativetreatment of this and related processes was given by M. K. Gaillard and B. W.Lee, who predicted the mass of the charmed quark to be about 1.5 - 2 GeV, inadvance of the discovery of the ψ!

As is described in Chapter 12, the discovery of strangeness non-changing neu-tral weak currents in 1973 made much more compelling the case for a unified theoryof electromagnetism and weak interactions. The charmed quark was essential tothis theoretical structure and the properties of the new quark were well specifiedby the theory. If the ψ was a bound state of a charmed quark and a charmedantiquark, there would have to be mesons with the composition cu and cd, etc.,that were stable against strong decays. The weak decay of a particle containing ac quark would yield an s quark. Thus the decay of a D+ (= cd) could produce aK− (= su) but not a K+ (= su).

There were a number of hints of charm already in the literature. K. Niu andcollaborators working in Japan observed several cosmic ray events in emulsion inwhich a secondary vertex was observed 10 to 100 µm from the primary vertex.These may have been decays of a particle with a lifetime in the 10−12 to 10−13 srange, just the lifetime expected for charmed particles. Nicolas Samios and RobertPalmer and co-workers, in a neutrino exposure of a hydrogen bubble chamber atBrookhaven, observed a single event that could have been a charmed baryon. SeeFigure 9.12. In other neutrino experiments, events with a pair of muons in the finalstate had been observed (Figure 9.13). These would be expected from processesin which the incident neutrino changed into a muon through the usual chargedweak current and a strange quark was transformed into a charmed quark, again bythe charged weak current. For that fraction in which the charmed particle decayproduced a muon, two muons would be observed in the final state, and they wouldhave opposite charges. The evidence for a new phenomenon, perhaps charm, wasaccumulating.

The SLAC-LBL Mark I detector at SPEAR and the corresponding


Figure 9.12: The event obtained in a neutrino exposure of the 7-ft hydrogen bubble cham-ber at Brookhaven that gave evidence for a charmed baryon. The overall reaction wasmost likely νp → µ−Λ0π+π+π+π−. The most probable assignments are shown in thesketch on the right. This violates the ∆S = ∆Q rule. Such a violation can be understoodif the process were really νp → Σ++

c µ−, followed by the strong decay Σ++c → Λ+

c π+. In

the quark model Σ++c = uuc and Λ+

c = udc. The decay of the Λ+c to Λ0π+π+π− accounts

for the violation of the ∆S = ∆Q rule and is in accord with the pattern expected forcharm decay. The mass of the Σ++

c was measured to be 2426± 12 MeV. There were threepossible choices for the pions to be joined to the Λ0. Of these, one gave a mass splittingbetween the Σ++

c and the Λ+c of about 166 MeV, which agreed with the theoretical expec-

tations [E. G. Cazzoli et al., Phys. Rev. Lett. 34, 1125 (1975), Figure courtesy N. Samios,Brookhaven National Laboratory].


Figure 9.13: Early evidence for charm from opposite-sign dileptons observed in neutrinoexperiments at Fermilab. Left, one of fourteen events observed by the Harvard-Penn-Wisconsin Collaboration [A. Benvenuti et al., Phys. Rev. Lett. 34, 419 (1975)]. Right,a similar event, one of eight seen by the Caltech-Fermilab Collaboration [B. C. Barishet al., Phys. Rev. Lett. 36, 939 (1976)]. In addition, four events containing µ−e+K0

S

were observed in the 15-ft bubble chamber at Fermilab [J. von Krogh et al., Phys. Rev.Lett. 36, 710 (1976)] and two such events were seen in the Gargamelle bubble chamber atCERN [J. Blietschau et al., Phys. Lett. 60B, 207 (1976)].

PLUTO and DASP at DESY were the leading candidates to produce convinc-ing evidence for charmed particles. The rise in the e+e− annihilation cross sectionnear a center-of-mass energy of 4 GeV strongly suggested that the threshold mustbe in that vicinity. The narrowness of the ψ ′ indicated that the threshold must beabove that mass since the ψ′ would be expected to decay rapidly into states likecu and uc if that were kinematically possible.

Despite advance knowledge of the approximate mass of the charmed particlesand their likely decay characteristics, it took nearly two years before irrefutableevidence for them was obtained. The task turned out to be quite difficult becausethere were many different decay modes, with each having a branching ratio of justa few percent.

Ultimately, the SLAC-LBL Mark I group did succeed in isolating decays likeD0 → K−π+ and D0 → K−π−π+π+ (Ref. 9.11), and soon after,D+ → K−π+π+ (Ref. 9.12). See Figure 9.14. Overwhelming evidence wasamassed identifying these new particles with the proposed charmed particles. Theirmasses were large enough to forbid the decay of the ψ ′ into a DD pair. The par-


Figure 9.14: Invariant mass spectrafor (a) K∓π±π± and (b) K∓π+π−.Only the former figure shows a peak,in agreement with the prediction thatD+ decays to K−π+π+, but notK+π−π+. (Ref 9.12)

ticles came in two doublets, (D+, D0) and (D0, D−), corresponding to cd, cu and

cu, cd. The decay mode D+ → K−π+π+ was seen, but D+ → K+π−π+ was not.It was possible to infer decay widths of less than 2 MeV, indicating that the decayswere unlikely to be strong. The D s shared some properties of the K s. They werepair-produced with a particle of equal or greater mass, indicating the existence ofa quantum number conserved in strong and electromagnetic interactions. In addi-tion, their decays were shown to violate parity. Both nonleptonic and semileptonicdecays were observed. The Cabibbo mixing in the four-quark model called fordecays c → d, suppressed by a factor roughly sin2 θc ≈ 5%. These, too, wereobserved in D0 → π+π− and D0 → K+K−. See Figure 9.15.

Further discoveries conformed to the charmed quark hypothesis. A set of part-ners about 140 MeV above the first states was found, with decays likeD∗+ → D0π+

(Ref. 9.13). See Figure 9.16. These decays were strong, the analogs of K ∗ → Kπ.Moreover, the spins of the D and D∗ were consistent with the expected assign-ments, pseudoscalar and vector, respectively. Detailed studies of the charmedmesons were aided enormously by the discovery by the Lead Glass Wall collabo-ration of a resonance just above the charm threshold (Ref. 9.14), shown in Fig-ure 9.17. The resonance, ψ(3772), is primarily a d-wave bound state of cc withsome mixture of 3S1. The bound state decays entirely to DD. The ψ(3772) is thus


Figure 9.15: Examples of Cabibbo-suppressed decay modes of charmed mesons observedat the ψ′′. Left: D0 → π+π− and D0 → K+K− as well as the Cabibbo-allowed decay toK∓π±. The data are from the Mark II experiment [G. S. Abrams et al., Phys. Rev. Lett.

43, 481 (1979)]. Right: D+ → K0K+ as well as the Cabibbo-allowed mode D+ → Kπ+

from the Mark III experiment [R. M. Baltrusaitis et al., Phys. Rev. Lett. 55, 150 (1985)].For the suppressed modes, two peaks are observed. The one near 1865 MeV is the signalwhile the other is due to K/π misidentification.

a D-meson “factory” and has been the basis for a continuing study of charmedmesons.

The quark model requires that in addition to charmed mesons, there must becharmed baryons, in which one or more of the first three quarks are replaced bycharmed quarks. Evidence for charmed baryons accumulated from a variety ofexperiments including neutrino bubble chamber experiments at Brookhaven andFermilab, a photoproduction experiment at Fermilab, a spectrometer experimentat the CERN Intersecting Storage Ring (ISR), and the work of the Mark II group atSPEAR. The lowest mass charmed baryon has the composition udc and is denotedΛ+c . It has been identified in decays to Λπ+π+π−,Λπ+, pK0

S , and pK−π+. Inagreement with the results for meson decays, the decay of the charmed baryonyielded negative strangeness.


Figure 9.16: Data for D0π+ withD0 → K−π+. The abscissa isthe difference between the Dπ massand the D mass. There is a clearenhancement near 145 MeV (G. J.Feldman et al. Ref. 9.13). Thevery small Q value for the D∗+ de-cay, 5.88 ± 0.07 MeV, has becomean important means of identifyingthe presence of a D∗+ in high en-ergy interactions. The data for

D0π+, a combination with the wrong

quantum numbers to be a quark–antiquark state, show no enhance-ment.

The strange-charmed meson with quark composition cs was even harder tofind than the D. At first called the F+ and now indicated D+

s , it was observedby the CLEO detector at Cornell, by the ARGUS detector at DORIS (located atDESY), and by the TPC and HRS at PEP (located at SLAC). Evidence for thisparticle is shown in Figure 9.18. The F ∗ or D∗

s was also identified by TASSOat PETRA and the TPC, as well as the Mark III detector at SPEAR. It decayselectromagnetically, D∗

s → Dsγ. While the mass splitting is possibly large enoughto permit D∗

s → Dsπ0, this decay is forbidden by isospin conservation.

The lifetimes of the charmed mesons D0, D+, and D+s as well as the charmed

baryon Λc and the τ lepton are all in the region 10−13 s to 10−12 s and hencesusceptible to direct measurement. The earliest measurements used photographicemulsions, with cosmic rays or beams at Fermilab or CERN providing the incidentparticles. This ‘ancient’ technique is well suited to the few micron scale dictatedby the small lifetimes. Studies were also conducted using special high resolutionbubble chambers at CERN and SLAC. The required resolution was also achievedwith electronic detectors at e+e− machines with the development of high precisionvertex chambers pioneered by Mark II and later by MAC and DELCO at PEP,and TASSO, CELLO, and JADE at PETRA. The latest stage of development


Figure 9.17: The ψ(3772) resonance isbroader than the ψ(3096) and ψ(3684)because it can decay into DD. P. A.Rapidis et al., (Ref. 9.14).

returned the focus to hadronic machines where the production rate of charmedparticles far exceeds that possible at e+e− machines. The detection with therequisite precision is achieved with silicon microstrips. Experiments carried out atCERN and Fermilab have achieved remarkable results, which required the analysisof 108 events in order to isolate several thousand charm decays.

Some of the lifetime measurements have relied on reconstructed vertices, otherson impact parameters of individual tracks, as first employed in π0 lifetime studies(Ref. 2.7). Figure 9.19 shows the photoproduction of a pair of charmed mesonsfrom the SLAC Hybrid Facility Photon Collaboration. Both decay vertices areplainly visible. In the same figure a computer reconstruction of a digitized bubblechamber picture from LEBC at CERN, with an exaggerated transverse magnifi-cation, is shown. Again, pair production of charmed particles is demonstrated.Exponential decay distributions for charmed mesons obtained using a tagged pho-ton beam at Fermilab are displayed in Figure 9.20.

The discoveries of the ψ, τ, and charm were pivotal events. They establishedthe reality of the quark structure of matter and provided enormous circumstantialevidence for the theoretical view dubbed “The Standard Model,” to be discussedin Chapter 12. The τ pointed the way to the third generation of matter, which isdiscussed in Chapter 11.


Figure 9.18: On the left, observation of the decay D+s → φπ+ by CLEO. In (a) only events

in which the K+K− invariant mass is consistent with the mass of the φ are plotted. In(b) only K+K−π events not containing a φ are shown [A. Chen et al., Phys. Rev. Lett.,51, 634 (1983)]. On the right, observation of the decay D+

s → K∗0K+ by ARGUS. In (a)only events with K−π+ in the K∗0 band are shown. In (b) only events without a K∗0 areshown [ARGUS Collaboration, Phys. Lett. 179B, 398 (1986)].


Figure 9.19: Left: A bubble chamber picture of the production and decay of a chargedcharmed particle and a neutral charmed particle. The charged particle decays into threetracks at 0.86 mm and the neutral decays after 1.8 mm. The quantities dmax and d2, thelargest and second largest impact distances were used in the lifetime calculations. Theincident photon beam (Emax = 20 GeV) was obtained by Compton scattering of laserlight off high energy electrons at SLAC [K. Abe et al., Phys. Rev. Lett. 48, 1526 (1982)].Right: A computer reconstruction of a digitized bubble chamber picture. The transversescale is exaggerated. The production vertex is at A. A charged charmed particle decays atC3 and a neutral charmed particle at V 2. The picture was obtained with LEBC (LexanBubble Chamber) at CERN using a 360-GeV π− beam [M. Aguilar-Benitez et al., Zeit.Phys. C31, 491 (1986)].


Figure 9.20: Proper time distributions for D0, D+, and D+s mesons and Λc baryons

from the Tagged Photon Spectrometer Collaboration at Fermilab, using silicon microstripdetectors [J. R. Raab et al., Phys. Rev. D37, 2391 (1988), J. C. Anjos et al., Phys. Rev.Lett. 60, 1379 (1988)]. For the D0, a corresponds to D∗+ → D0π+, D0 → K−π+, b toD∗+ → D0π+, D0 → K−π+π+π−, and c to D0 → K−π+. For the D+, the decay mode

is D+ → K−π+π+. For the D+s , a corresponds to D+

s → φπ+ and b to D+s → K

∗0K+,

K∗0 → K−π+. The observed lifetimes are τD0 = (0.422 ± 0.008 ± 0.010) × 10−12 s,

τD+ = (1.090 ± 0.030 ± 0.025) × 10−12 s, τDs= (0.47 ± 0.04 ± 0.02) × 10−12 s and τΛc

=0.22± 0.03± 0.02× 10−12 s.


EXERCISES

9.1 Estimate the lifetime of theD-meson. Do you expect the neutral and chargedD’s to have the same lifetime? What do the data say?

9.2 Describe the baryons containing one or more charmed quarks that extend thelowest lying multiplets, the octet and decuplet. How many of these particleshave been found? Compare with Review of Particle Properties. What doyou expect their decay modes to be?

9.3 How have the most precise measurements of the mass of the ψ been made?See Ref.(9.15).

9.4 * Calculate the branching ratio for τ → πν. See Y. S. Tsai, Phys. Rev. D4,2821 (1971); M. L. Perl, Ann. Rev. Nucl. Part. Sci. 30, 229 (1980).

9.5 * Calculate the expected widths for ψ ′ → γχ2,1,0 in terms of the s- and p-statewave functions. Evaluate the results for a harmonic oscillator potential withthe charmed quark mass set to 1.5 GeV and the spring constant adjusted togive the level splitting between the ψ and ψ ′ correctly. Calculate the partialwidth for ψ → γηc. Why is the transition ψ′ → γηc suppressed? Compareyour results with the data given in the Review of Particle Properties. [Seethe lecture by J. D. Jackson listed in the Bibliography.]

9.6 * Show that the ψs produced in e+e− annihilation have their spins’ compo-nents along the beam axis equal either to +1 or −1, but not 0. (Use thecoupling of the ψ to e+e− : eγµeψ

µ)

9.7 * What is the angular distribution of the γ’s relative to the beam directionin e+e−→ ψ′ → γχ0? What is the answer for χ1 and χ2 assuming that thetransitions are pure E1? ( See E. Eichten et al., Phys. Rev. Lett. 34, 369(1975); G. J. Feldman and F. J. Gilman, Phys. Rev. D12, 2161 (1975); L.S. Brown and R. N. Cahn, Phys. Rev. D13, 1195 (1975).)

BIBLIOGRAPHY

e+e− Annihilation: New Quarks and Leptons, Benjamin/Cummings, Menlo Park,CA 1984, R. N. Cahn, ed. ( A collection of articles from Annual Review ofNuclear and Particle Science.)

J. D. Jackson, “Lectures on the New Particles” in Proc. of Summer Institute onParticle Physics, Stanford, CA, Aug. 2-13, 1976, M. Zipf, ed.

G. J. Feldman and M. L. Perl, “Electron-Positron Annihilation above 2 GeV andthe New Particles,”Phys. Rep. 19, 233 (1975) and 33, 285 (1977).


G. H. Trilling, “The Properties of Charmed Particles,” Phys. Rep. 75, 57 (1981).

S. C. C. Ting, “Discovery of the J Particle: a Personal Recollection,” Rev. Mod.Phys. 44(2), 235 (1977).

B. Richter, “From the Psi to Charm: the Experiments of 1975 and 1976,” Rev.Mod. Phys. 44(2), 251 (1977).

A popular account of much of the historical material in the chapter is containedin contributions by S. C. C. Ting, G. Goldhaber, and B. Richter in Adven-tures in Experimental Physics, ε, B. Maglich ed., World Science Education,Princeton, N.J., 1976. See also M. Riordan The Hunting of the Quark, Simon& Schuster, 1987.

REFERENCES

9.1 J. J. Aubert et al., “Experimental observation of a heavy particle J.” Phys.Rev. Lett., 33, 1404 (1974).

9.2 J.-E. Augustin et al., “Discovery of a narrow resonance in e+e− annihilation.”Phys. Rev. Lett., 33, 1406 (1974).

9.3 C. Bacci et al., “Preliminary result of Frascati (ADONE) on the nature ofa new 3.1 GeV Particle Produced in e+e− Annihilation.” Phys. Rev. Lett.,33, 1408 (1974).

9.4 G. S. Abrams et al., “Discovery of a Second Narrow Resonance in e+e−

Annihilation.” Phys. Rev. Lett., 33, 1453 (1974).

9.5 G. S. Abrams et al., “Decay of ψ(3684) into ψ(3095).” Phys. Rev. Lett., 34,1181 (1974).

9.6 W. Braunschweig et al., “Observation of the Two Photon Cascade 3.7 →3.1 + γγ via an Intermediate State Pc.” Phys. Lett., B57, 407 (1975).

9.7 R. Partridge et al., “Observation of an ηc Candidate State with Mass 2978±9MeV.” Phys. Rev. Lett., 45, 1150 (1980).; See also E. D. Bloom and C. W.Peck, Ann. Rev. Nucl. Part. Sci. 30, 229 (1983). “Physics with theCrystal Ball Detector” and J. E. Gaiser et al., “Charmonium Spectroscopyfrom Inclusive ψ′ and J/ψ Radiative Decays.” Phys. Rev., D34, 711 (1986).

9.8 M. L. Perl et al., “Evidence for Anomalous Lepton Production in e+e− An-nihilation.” Phys. Rev. Lett., 35, 1489 (1975).

9.9 R. Brandelik et al., “Measurements of Tau Decay Modes and a Precise De-termination of the Mass.” Phys. Lett., 73B, 109 (1978).


9.10 W. Bacino et al., “Measurement of the threshold Behavior of τ+τ− Produc-tion in e+e− Annihilation.” Phys. Rev. Lett., 41, 13 (1978).

9.11 G. Goldhaber et al., “Observation in e+e− Annihilation of a Narrow Stateat 1865 Mev/c2 Decaying to Kπ and Kπππ.” Phys. Rev. Lett., 37, 255(1976).

9.12 I. Peruzzi et al., “Observation of a Narrow Charged State at 1876 MeV/c2

Decaying to an Exotic Combination of Kππ.” Phys. Rev. Lett., 37, 569(1976).

9.13 G. J. Feldman et al., “Observation of the Decay D∗+ → D0π+.” Phys. Rev.Lett., 38, 1313 (1977).

9.14 P. A. Rapidis et al., “Observation of a Resonance in e+e− Annihilation Justabove Charm Threshold.” Phys. Rev. Lett., 39, 526 (1977).

9.15 A. A. Zholentz et al., “High Precision Measurement of the ψ and ψ ′ MesonMasses.” Phys. Lett., 96B, 214 (1980).

Ref. 9.1: Discovery of the J 279

280 J. J. Aubert et al.

Ref. 9.2: Discovery of the ψ 281

282 J.-E. Augustin et al.

Ref. 9.2: Discovery of the ψ 283

284 G. Abrams et al.

Ref. 9.4: Discovery of the ψ′ 285

286 G. Abrams et al.

Ref. 9.6: Discovery of a χ state 287

288 W. Braunschweig et al.





Ref. 9.7: Co-discovery of the ηc 293

294 R. Partridge et al.

Ref. 9.7: Co-discovery of the ηc 295

296 R. Partridge et al.

Ref. 9.8: Discovery of the τ lepton 297

298 M. L. Perl et al.

Ref. 9.8: Discovery of the τ lepton 299

300 M. L. Perl et al.

Ref. 9.11: Discovery of charmed mesons 301

302 G. Goldhaber et al.


304 G. Goldhaber et al.


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THE EXPERIMENTAL FOUNDATIONS OF PARTICLE · PDF fileTHEEXPERIMENTALFOUNDATIONS OF PARTICLE PHYSICS Robert N. Cahn Senior Physicist, Lawrence Berkeley Laboratory University of California,