Discovery of Violations of Fundamental Symmetry Principles

IntroductionThe neutral kaon system

The Cronin-Fitch-experimentTheoretical description and the search for direct CPV

Discovery of Violations of FundamentalSymmetry Principles in the Decay of Neutral

K-mesons

Stefan Paul

Seminar on Nobel Prizes in Particle Physics

15.01.2016

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Table of contents

Introduction

The neutral kaon system

The Cronin-Fitch-experiment

Theoretical description and the search for direct CPV

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SymmetriesThe path to the discovery of CP violation (CPV)

Symmetries

I symmetries play an important role in physics:I enabled postulation of undiscovered particlesI deep connection to conservation laws

I continuous symmetries (Noether’s theorem)

I discrete symmetries (represented by operators in QM)

I charge conjugation C: X → X

I parity transformation P: ~r → −~rI time reversal symmetry T: t → −tI Pauli & Luders 1955:

CPT-theorem

Physical phenomena are invariant under combined action ofC, P & T.

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The path to the discovery of CP violation

I for a long time also separate C-, P- & T-symmetry wereassumed to be valid

I Until 1956: Lee & Yang postulated C- & P-violation in theweak interaction

I Experimental confirmation for C- & P-violation by Wu in 1957I Nobel Prize 1957 awarded to Lee and Yang

I Landau 1957: violations of C and P compensate each other→ apparent CP-invariance

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The path to the discovery of CP violation

I for a long time also separate C-, P- & T-symmetry wereassumed to be valid

I Until 1956: Lee & Yang postulated C- & P-violation in theweak interaction

I Experimental confirmation for C- & P-violation by Wu in 1957I Nobel Prize 1957 awarded to Lee and Yang

I Landau 1957: violations of C and P compensate each other→ apparent CP-invariance

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I Evidence for CP violation in the decay of neutral K-mesonsobserved by James Cronin & Val Fitch in 1964

I CP violation implies T violation if CPT invariance is assumedI Sakharov 1967: Conditions for the baryon asymmetry in the

early universe (baryogenesis) include CP violationI 1980 Cronin and Fitch received the Nobel Prize “for the

discovery of violations of fundamental symmetry principles inthe decays of neutral K-mesons”

James Cronin (left)and

Val Fitch (right)

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CP eigenstatesMeson oscillationsRegeneration

The neutral kaon system

I strong eigenstates: |K0〉 = |ds〉 & |K0〉 = |sd〉I generated in strong interactions, typical production channels:

π− + p→ Λ + K0

p + p → K+ + K0 + π−

I neutral kaons decay to hadronic and semi-leptonic final statesvia weak interaction

I mixing of K0 & K0 via weak interactionI physical states are superposition of K0 & K0

I K0 & K0 are no eigenstates of CP:

CP |K0〉 = − |K0〉CP |K0〉 = − |K0〉

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CP eigenstates

I CP eigenstates are linear combinations of the strong eigenstates:

|K1〉 =1√2

(|K0〉 − |K0〉

), CP |K1〉 = + |K1〉 ”CP even”

|K2〉 =1√2

(|K0〉+ |K0〉

), CP |K2〉 = − |K2〉 ”CP odd”

I for the final states of neutral kaon decays to pions one finds:

e.g. for K0 → π0π0 JP : 0− → 0−0− ⇒ L = 0

CP |π0π0〉 = P |π0π0〉 = (−1)2(−1)L = + |π0π0〉

From similar arguments: CP |ππ〉 = + |ππ〉 CP even

CP |πππ〉 = − |πππ〉 CP odd

I assuming CP invariance in the decays thus yields:

CP even: K1 → ππ , K1 6→ πππ

CP odd: K2 → πππ , K2 6→ ππ

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I expect large difference in lifetimes:

mK−2mπ ≈ 220MeV � mK−3mπ ≈ 80MeV ⇒ τ1 � τ2

I indeed a short-lived and a long-lived particle KS & KL wereobserved in experiment, before the discovery of CPV it wasthus natural to identify:

|KS〉 = |K1〉 =1√2

(|K0〉 − |K0〉

)|KL〉 = |K2〉 =

1√2

(|K0〉+ |K0〉

)τS = 0.9 · 10−10s, τL = 0.5 · 10−7s

tiny mass difference: mS ≈ mL ≈ 498MeV , ∆mm ≈ 7 · 10−15

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(Angelopoulos et. al. 2001)




Meson oscillations (assuming CP invariance)

I K0 ↔ K0-mixing arises frombox-diagrams

I WF for production of a K0 at t = 0:

|ψ(t)〉 =1√2

(e− t

2τS+imS t |KS〉+ e

− t2τL

+imLt |KL〉)

I probabilities to be in state K0 or K0 after time t:

P(K0t=0 → K0) = | 〈K0|ψ(t)〉 |2 =

1

4

[e−t/τS + e−t/τL + 2cos(∆mt)e−t/2(τS+τL)

]P(K0

t=0 → K0) = | 〈K0|ψ(t)〉 |2 =1

4

[e−t/τS + e−t/τL − 2cos(∆mt)e−t/2(τS+τL)

]Stefan Paul 9 / 23




Meson oscillations (assuming CP invariance)

I K0 ↔ K0-mixing arises frombox-diagrams

I WF for production of a K0 at t = 0:

|ψ(t)〉 =1√2

(e− t

2τS+imS t |KS〉+ e

− t2τL

+imLt |KL〉)

I probabilities to be in state K0 or K0 after time t:

P(K0t=0 → K0) = | 〈K0|ψ(t)〉 |2 =

1

4

[e−t/τS + e−t/τL + 2cos(∆mt)e−t/2(τS+τL)

]P(K0

t=0 → K0) = | 〈K0|ψ(t)〉 |2 =1

4

[e−t/τS + e−t/τL − 2cos(∆mt)e−t/2(τS+τL)

]Stefan Paul 9 / 23




Regeneration

I K0(S = +1) and K0(S = −1) interact differently with nuclearmatter due to their opposite strangeness

I K0 only scatters (quasi-)elastically with nucleons:

K0 + N → K0 + N(∗)

I K0 can also excite hyperons orresonances thereof:

K0[sd ] + N[uud/udd ]→ π0[dd ] + Λ/Σ/Y ∗[suu/sud ]

⇒ much stronger absorption of K0

Regeneration

Production of KS as a KL-beam traverses nuclear matter.

I coherent regeneration: KS generated in forward direction haveidentical momentum and phase as incident KL

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Experimental setupRegeneration measurementsResultsCP violation

The Cronin-Fitch-experiment

I located at the Alternating Gradient Synchrotron (AGS) atBrookhaven National Laboratory

I mainly intended for study of regeneration in neutral kaons

I advent of spark chamber detectors enabled a new level ofprecision

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Experimental setup

I K0 beam produced by bombarding a Be-target with 30GeV-protonsfrom AGS

I after freely propagating 57 feet (∼17.4m) the initial K0-beam hasbecome purely KL

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Experimental Setup

I 2 modes of operation

I detection of charged decayproducts in 2 spectrometers

I spark chambers triggeredon coincidence betweenboth spectrometer arms

I analysis program yields3-momenta ~p1 and ~p2 ofdetected particles

I identification of 2π decays:

1. via 3-momentum sum~p1 + ~p2

2. by invariant massm∗ = mK?

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Experimental Setup

I 2 modes of operation

I detection of charged decayproducts in 2 spectrometers

I spark chambers triggeredon coincidence betweenboth spectrometer arms

I analysis program yields3-momenta ~p1 and ~p2 ofdetected particles

I identification of 2π decays:1. via 3-momentum sum~p1 + ~p2

2. by invariant massm∗ = mK?

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Regeneration measurements

I coherent KS regenerationmeasurements

1. calibration for rare CPviolating decaysKL → ππ as these aresimulated by the rapidKS → ππ decays

2. important observation:number of detectedKS → ππ eventsnegligible in He gas

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Results - mass distribution of all KL decays in He gas

I broad peak due to 3-body-decays:

KL → π+ `− ν`

KL → π− `+ ν `

KL → π+π−π0

I no signature of decays to two pionsrecognizable (i.e. no sharp peakaround m∗ = mK ≈ 498MeV )

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Results - angular distribution for different mass ranges

I data from 22700 KL decays

I uniform background from3-body-decays

I after background correction: 45±9events in forward peak(cosθ > 0.9999) at m∗ ≈ mK

I as coherent regeneration of KS

negligible in He, these 45 eventscorrespond to KL → π+π− decays

BR =Γ(KL → π+π−)

Γ(KL → all charged modes)

= (2.0± 0.4) · 10−3

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CP violation

I we identified |KS〉 = |K1〉 & |KL〉 = |K2〉

I conclusion: observation of KL → π+π− events implies that KL

is not a pure CP-eigenstate ⇒ (indirect) CP violation!I The actual physical states are then given by:

|KL〉 =1√

1 + |ε|2(|K2〉+ ε |K1〉) ≈ |K2〉

|KS〉 =1√

1 + |ε|2(|K1〉+ ε |K2〉) ≈ |K1〉

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Assuming CP invariancein decay, we only have:K1 → ππ (CP = +1)K2 → πππ (CP = −1)

with ε ≈ 2.3 · 10−3




CP violation

I 2nd possibility: CP is violated in the decay (direct CPV)

|KL〉 = |K2〉 → |ππ〉CP=-1→ CP=+1

I also both effects can be realized at the same time:

I direct CPV is quantified by the parameter ε′

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Theoretical description of CPVSearch for direct CPV violationRecent studies of CPV

Theoretical description of CPV

1. superweak theory proposed by Wolfenstein (1964)I predicts fifth fundamental interaction: “superweak force”

transforming KL into KSI includes only indirect but no direct CPV (ε′ = 0)

2. Cabbibo-Kobayashi-Maskawa(CKM)-matrix (1973)I describes quark mixing due to weak interactionI CPV enters via a complex phase factor in CKM-matrixI complex phase requires matrix of rank ≥ 3 ⇒ postulation of

3rd quark generation (NP 2008)I indirect and direct CPV postulated

VCKM =

1 0 00 c23 s23

0 −s23 c23

c13 0 s13e−iδ13

0 1 0−s13e

iδ13 0 c13

c12 s12 0−s12 c12 0

0 0 1

where c12 = cos(θ12), s12 = sin(θ12), ...

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Search for direct CP violation

<(ε′

ε

)≈ 1

6

1−| Γ(KL→π0π0)

Γ(KS→π0π0)|2

| Γ(KL→π+π−)Γ(KS→π+π−) |2

I two generations of experiments gave

definite results:I at CERN: NA31 followed by NA48I at FNAL: E731 followed by KTeV

I first proof of direct CPV by NA31

in 1993: <(ε′

ε

)= (23± 6.5) · 10−4

I average from these experiments: <(ε′

ε

)= (16.7± 1.6) · 10−4

I these measurements ruled out the superweak theory ascomplete description of CPV while confirming the predictionsof the CKM-formalism!

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Recent studies of CPV

I current PDG values for CPV parameters in K-system:

|ε| = (2.228± 0.011) · 10−3

<(ε′

ε

)= (1.65± 0.26) · 10−3

I CPV was also observed for D- & B-mesons

I current research mainly focused on CPV in B-system as thelarge mass difference between B0 & B0 yields stronginterference effects between direct and indirect CP violation

I huge experimental efforts at B-factories and LHCb

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Sources

I J. H. Christenson, J. W. Cronin, V. L. Fitch, and R. Turlay, Phys. Rev. Lett. 13, 138 - Published 27 July1964

I J. H. Christenson, J. W. Cronin, V. L. Fitch, and R. Turlay, Phys. Rev. 140, B74 - Published 11 October1965

I Val L. Fitch - The Discovery of Charge-Conjugation Parity Asymmetry, Nobel Lecture, 1980,http://www.nobelprize.org/nobel prizes/physics/laureates/1980/fitch-lecture.pdf

I James W. Cronin - CP Symmetry Violation - The Search For Its Origin, Nobel Lecture, 1980,http:/www.nobelprize.org/nobel prizes/physics/laureates/1980/cronin-lecture.pdf

I Mark Thomson - Modern Particle Physics, Cambridge University Press, August 31, 2013I Mark Thomson - Handout 12: The CKM Matrix and CP Violation, Lecture Slides, 2009,

http://www.hep.phy.cam.ac.uk/ thomson/lectures/partIIIparticles/Handout12 2009.pdfI Angelopoulos, A. et al. 2001. Eur. Phys. J., C22, 5579.I I. I. Bigi, A. I. Sanda - CP Violation, Cambridge University Press, April 30, 2009, Publisher: Cambridge

University Press, April 30, 2009I K. Kleinknecht - CP Violation and K Decays, Annual Review of Nuclear Science, Vol. 26: 1-50 (Volume

publication date December 1976)I A. Kellerbauer - 50 Jahre CP-Verletzung, Physik in unserer Zeit Volume 45, Issue 4, pages 168-175, Juli

2014I L. Wolfenstein, Phys. Rev. Lett. 13, 562 - Published 2 November 1964I M. Kobayashi, T. Maskawa, Prog. Theor. Phys. (1973) 49 (2), 652-657.I W. Wislicki - Direct CP Violation In Neutral Kaon Decays, 2003, http://arxiv.org/abs/hep-ex/0303037v1I Gianluca Lamanna - Search for Direct CP violation in charged Kaons with NA48/2 experiment (PhD

Thesis), 2006, http://inspirehep.net/record/1186241/files/tesidott2311.pdfI Particle Data Group - CP Violation in Meson Decays, 2012,

http://pdg.lbl.gov/2012/reviews/rpp2012-rev-cp-violation.pdfI https://en.wikipedia.org/wiki/Neutral particle oscillation

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Figure sources

I Gianluca Lamanna - Search for Direct CP violation in charged Kaons with NA48/2 experiment (PhDThesis), 2006, http://inspirehep.net/record/1186241/files/tesidott2311.pdf

I J. H. Christenson, J. W. Cronin, V. L. Fitch, and R. Turlay Phys. Rev. Lett. 13, 138 Published 27 July1964

I J. H. Christenson, J. W. Cronin, V. L. Fitch, and R. Turlay Phys. Rev. 140, B74 Published 11 October1965

I http://www.nobelprize.org/nobel prizes/physics/laureates/1980/cronin-facts.html

I http://www.nobelprize.org/nobel prizes/physics/laureates/1980/fitch-facts.html

I Mark Thomson - Modern Particle Physics, Cambridge University Press, August 31, 2013

I https://en.wikipedia.org/wiki/Kaon#/media/File:Kaon-box-diagram-with-bar.svg

I I. I. Bigi, A. I. Sanda - CP Violation, Cambridge University Press, April 30, 2009, Publisher: CambridgeUniversity Press, April 30, 2009

I J. H. Christenson, J. W. Cronin, V. L. Fitch, and R. Turlay Phys. Rev. 140, B74 Published 11 October1965

I https://universe-review.ca/I15-25-CPviolation2.jpg

I W. Wislicki - Direct CP Violation In Neutral Kaon Decays, 2003, http://arxiv.org/abs/hep-ex/0303037v1

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Discovery of Violations of Fundamental Symmetry Principles