ECT* Workshop on the Proton Radius

Puzzle

Book of Abstracts

October 29 - November 2, 2012

Trento, Italy

October 8, 2012

A. Afanasev

J. Arrington

J.C. Bernauer

A. Beyer

E. Borie

M.C. Birse

P. Brax

J.D. Carroll

C.E. Carlson

M.O. Distler

M.I. Eides

K.S.E. Eikema

A. Gasparian

R. Gilman

M. Gorchtein

K. Griffioen

N.D. Guise

E.A. Hessels

R.J. Hill

M. Kohl

I.T. Lorenz

J.A. McGovern

G.A. Miller

K. Pachucki

G. Paz

R. Pohl

M. Pospelov

B.A. Raue

S.S. Schlesser

I. Sick

K.J. Slifer

D. Solovyev

V. Sulkosky

A. Vacchi

I. Yavin

A. Afanasev Radiative corrections and two-photon effects for lepton-nucleon scat-tering

J. Arrington Extracting the proton radius from low Q2 electron/muon scattering

J.C. Bernauer The Mainz high-precision proton form factor measurement I. Overviewand results

A. Beyer Atomic Hydrogen 2S-nP Transitions and the Proton Size

E. Borie Muon-proton Scattering

M.C. Birse Issues with determining the proton radius from elastic electron scat-tering

P. Brax Atomic Precision Tests and Light Scalar Couplings

C.E. Carlson New Physics and the Proton Radius Problem

J.D. Carroll Non-perturbative QED spectrum of Muonic Hydrogen

M.O. Distler The Mainz high-precision proton form factor measurement II. Basicprinciples and spin-offs

M.I. Eides Weak Interaction Contributions in Light Muonic Atoms

K.S.E. Eikema XUV frequency comb spectroscopy of helium and helium+ ions

A. Gasparian A Novel High Precision Measurement of the Proton Charge Radiusvia ep Scattering Method

R. Gilman JLab Experiment E08-007: Proton Electromagnetic Form Factor Ra-tio at Low Q2

M. Gorchtein Hadronic contributions to Lamb shift in muonic deuterium

K. Griffioen How well can a nuclear charge radius be measured with low-Q2 electronscattering data?

N.D. Guise Towards One-electron Ions in Rydberg States for a Rydberg ConstantDetermination Independent of the Proton Radius

E.A. Hessels Progress towards a new separated-oscillatory-field microwave measure-ment of the atomic hydrogen n=2 Lamb shift

R.J. Hill Model independent analysis of proton structure for hydrogenic boundstates

M. Kohl The OLYMPUS experiment at DESY

I.T. Lorenz The size of the proton - closing in on the radius puzzle

J.A. McGovern Proton polarisability contribution to the Lamb shift in muonic hydro-gen at fourth order in chiral perturbation theory

G.A. Miller Proton Polarizability Contribution: Muonic Hydrogen Lamb Shift andElastic Scattering

K. Pachucki Directions toward the resolution of the proton charge radius puzzle

G. Paz Model independent extraction of the proton charge radius from elec-tron scattering

R. Pohl Lamb shift and hyperfine splitting in muonic hydrogen and deuterium

M. Pospelov Extension of the Standard Model by muon-specic forces

B.A. Raue Measurement of Two Photon Exchange effects in electron-proton elas-tic scattering

S.S. Schlesser Nuclear polarizability contribution to the Lamb shift in muonic helium

I. Sick Proton rms-radius and tail of density

K.J. Slifer The Jefferson Lab gp

2 Experiment

D. Solovyev Multiphoton processes in atomic physics and astrophysics

V. Sulkosky Elastic µp Scattering at the Paul Scherrer Institute

A. Vacchi Towards a measurement of the 1S hyperfine splitting in muonic hy-drogen

I. Yavin Muonic hydrogen and MeV forces

Extracting the proton radius from low Q2

electron/muon scattering

John Arrington

Physics Division, Argonne National Lab

While electron scattering is the tool of choice for extracting nucleon form factors,

there are several things which must be accounted for in extracting the form factors from

scattering cross sections or asymmetry measurements. Further issues arise in obtaining

charge and magnetic radii from the extracted form factors.

I will discuss some these issues, focusing on experimental uncertainties, fitting proce-

dures, and the impact of two-photon exchange and Coulomb distortion. These will be

discussed in the context of the recent JLab extraction of the proton charge and magnetic

radii, the differences between various electron scattering extractions, and projections for

future measurements. In addition, I will present some new investigations into the impact

of two-photon exchange and Coulomb corrections on the extraction of the charge radius.

The Mainz high-precision proton form factormeasurement

I. Overview and resultsJan C. Bernauer for the A1 Collaboration

Institut für Kernphysik, Johannes Gutenberg-Universität Mainz, 55099 Mainz, Germany.Present address: Laboratory for Nuclear Science, MIT, Cambridge, MA 02139, USA.

Abstract. Form factors offer a direct approach to fundamental properties of the nucleons likethe radius and charge distribution. In the talk, precise results from a measurement of the elasticelectron-proton scattering cross section performed at the Mainz Microtron MAMI will be presented.About 1400 cross sections were measured with negative four-momentum transfers squared up toQ2 = 1(GeV/c)2 with statistical errors below 0.2%. The electric and magnetic form factors of theproton were extracted with fits of a large variety of form factor models directly to the cross sections.

The charge and magnetic radii are determined to be

⟨r2

E⟩ 1

2 = 0.879(5)stat.(4)syst.(2)model(4)group fm,

⟨r2

M⟩ 1

2 = 0.777(13)stat.(9)syst.(5)model(2)group fm,

strengthening the discrepancy between determinations using electronic and muonic systems.We extended the data set with the world data from unpolarized and polarized scattering ex-

periments, which were updated to the same level of radiative corrections. A phenomenologicalmodel for two-photon-exchange contributions is used to account for the discrepancy between theresults from unpolarized and polarized scattering experiments. A continuous, simultaneous fit up toQ2 = 10(GeV/c)2 is achieved.

Atomic Hydrogen 2S-nP Transitions and the Proton Size

Axel Beyera,∗, Arthur Matveeva, Christian G. Partheya, Janis Alnisa,Randolf Pohla, Nikolai Kolachevskya, Thomas Udema

and Theodor W. Hanscha,b

a Max Planck Institute of Quantum Optics, 85748 Garchingb Ludwig Maximilian University, 80799 Munich

∗ Axel.Beyer@mpq.mpg.de

The ’proton size puzzle’, i.e. the discrepancy between the values for the proton chargeradius extracted from precision spectroscopy of atomic hydrogen and electron-proton-scattering on the one hand [1] and the 2S Lamb shift measurement in muonic hydrogenon the other [2], attracted great interest both of experimentalists and theoreticians for thelast two years. Still, no convincing argument to explain or resolve this discrepancy couldbe found so far. Transition frequency measurements in atomic hydrogen with improvedaccuracy can help to solve this puzzle or at least to rule out hydrogen experiments as apossible source for the discrepancy. Furthermore, as soon as the puzzle will be resolved anda more accurate value for rp will be available, these measurements can provide stringenttests to bound state QED calculations utilizing the new rp value.

In this talk we report on the setup which has been developed for the measurement ofthe one-photon 2S-4P transition frequency in atomic hydrogen: In contrast to previousmeasurements of 2S-nl transitions in other groups, our experiment is based on a coldthermal beam of hydrogen atoms optically excited to the metastable 2S state. The setupfor the 2S excitation is the same as has successfully been used for the measurement ofthe 1S-2S transition frequency in our group and provides a reliable and well controlledsource of 2S atoms [3]. In addition, the experiment benefits from technical advances, suchas subhertz line width diode lasers both for 1S-2S and 2S-4P spectroscopy [4] or directmeasurement of the absolute transition frequency via a frequency comb, which have notbeen available for older measurements. During 13 measurements days a total number of11,652 individual line profiles for the 2S1/2-4P1/2 transition have been recorded, including6 different velocity distributions of 2S atoms. The resulting statistical uncertainty of0.8 kHz is more than one order of magnitude smaller than the one of the previous bestmeasurement of this transition [5]. The study of systematic effects is underway and willbe discussed in this talk.

————————

[1] Mohr et al., arXiv:1203.5425

[2] Pohl et al., Nature 466 (7303), 2010

[3] Parthey et al., Phys. Rev. Lett. 107.203001, 2011

[4] Kolachevsky et al., Opt. Lett. 36.004299, 2011

[5] Berkeland et al., Phys. Rev. Lett. 75.2470, 1995

Issues with determining the proton radius from elastic

electron scattering

Michael C. Birse

Theoretical Physics Division, School of Physics and Astronomy,

The University of Manchester, Manchester, M13 9PL, UK

The charge radius of the proton has proved remarkably hard to pin down accu-

rately. There is a long history of determinations from elastic ep scattering but recent

values still range between 0.84 and 0.9 fm, and even fits by different groups to the

same data can be in disagreement. This range spans the values extracted from the

Lamb shifts in muonic and electronic hydrogen and so the “proton radius puzzle”

remains.

Underlying this is the need to extrapolate the available data to Q2 = 0 in order

to determine the slope of the form factor there. This extrapolation can be sensitive

to corrections applied to the data and to assumptions about low-momentum physics

that are built in to the parametrisation used to fit the data. I explore some of these

issues and the sensitivity of the extracted charge radius to them.

Muon-proton ScatteringE. Borie

Karlsruhe Institute of Technology,Institut fur Hochleistungsimpuls and Mikrowellentechnik (IHM),Hermann-von-Helmholtzplatz 1,D-76344 Eggenstein-Leopoldshafen, Germany

A proposal for muon-proton scattering at PSI [1] has been made in an attempt to help resolve the protonradius puzzle. The proposal will directly test whether or not µ − p and e − p scattering are the sameand will perform measurements with µ± and e± at low Q2 in order to study the two-photon exchangecontributions in greater detail. Since the muon is about 206.7 times heavier than the electron for theenergies mentioned in the proposal, the muons are neither ultrarelativistic nor nonrelativistic. For themuon momenta given in the proposal the value of v/c for the incoming lepton is between 0.7 and 0.9,while the standard expressions for the scattering cross section of high energy leptons are valid only forv/c very close to 1. Thus, the standard kinematics assumptions made in the analysis of e-p scattering willnot all be valid in the case of an experiment on mu-p scattering at the proposed energies. A calculationof the basic cross section without such approximations is presented here.

According to the proposal, scattering of negative and positive muons (and electrons) will be studied.The muon momenta will be in the range (115-210)MeV/c with scattering angles in the range 20 to100, corresponding to Q2 in the range (0.01-0.1) (GeV/c)2. For comparison, m2

µc2 =0.01116 (GeV/c)2.

The radiative corrections to the scattering cross section are functions of Q2/m2

µ, which is in the range ofapproximately 0.9-9.0. The usual formulas [3, 4], which assume that Q2/m2

≫ 1, will not be accurate.This will be discussed.

Here m is the lepton rest mass, M is the target rest mass, and α = e2/4π. p1 and p3 are the incomingand outgoing muon four-momenta, and p2 and p4 are the incoming and outgoing proton four-momenta. Inthe lab system we have p1 = (E, ~p) p3 = (E′, ~p′), p2 = (M, 0), p4 = (M+ω, ~q). Here q = p1−p3 = p4−p2,and ω = q0 = E − E′. It is useful to observe that q2 = 2m2

− 2p1 · p3 = 2M2− 2p2 · p4 = −2Mω.

The proton current is taken to have the usual on-shell form, characterized by

Γµ = F1(q2)γµ + κF2(q

2)iσµνq

ν

2M

Here κ is the anomalous magnetic moment of the proton. The so-called Sachs form factors are related to

F1 and F2 by GM = F1 + κF2, GE = F1 −Q2

4M2κF2.

The final result for the cross section is given by

dσ

dΩ′=

α2

q4p′/p

1 + (E − pE′/p′ cos θ)/M

[

G2

E

(4EE′ + q2)

1− q2/4M2

+G2

M

(

(4EE′ + q2)(

1−1

1− q2/4M2

)

+q4

2M2+

q2m2

M2

)]

(1)

In the limit of very high lepton energies, one has p ≈ E, p′ ≈ E′, q2 ≈ −4EE′ sin2(θ/2)In this case, the cross section given in Eq. 1 reduces to the standard expression found in the literature.

Acknowledgments

The author wishes to thank R. Gilman for extensive email correspondence regarding this work.

References[1] A. Afanasev et al., Paul Scherrer Institute Proposal R-12-01.1.

[2] J.D. Bjorken, S.D. Drell, Relativistic Quantum Mechanics, McGraw-Hill, New York, 1964.

[3] L.W. Mo, Y.S. Tsai Rev. Mod. Phys., 41, 205 (1969)

[4] L.C. Maximon, J.A. Tjon, Phys.Rev. C76, 035205 (2007)

1

Atomic Precision Tests and Light Scalar Couplings

Philippe Brax1∗, and Clare Burrage2,3†

1 Institut de Physique Theorique, CEA, IPhT, CNRS, URA2306, F-91191

Gif-sur-Yvette cedex, France

2 Department de Physique Theorique, Universite de Geneve, 24 Quai E. Ansermet,

CH-1211, Geneve, Switzerland3 Theory Group, Deutsches Elektronen-Synchrotron DESY, D-22603, Hamburg,

Germany

We calculate the shift in the atomic energy levels induced by the presence of a scalar

field which couples to matter and photons. We find that a combination of atomic mea-

surements can be used to probe both these couplings independently. A new and stringent

bound on the matter coupling springs from the precise measurement of the 1s to 2s en-

ergy level difference in the hydrogen atom, while the coupling to photons is essentially

constrained by the Lamb shift. Combining these constraints with current particle physics

bounds we find that the contribution of a scalar field to the recently claimed discrepancy

in the proton radius measured using electronic and muonic atoms is negligible.

∗philippe.brax@cea.fr†clare.burrage@unige.ch

New Physics and the Proton Radius Problem

Carl E. CarlsonPhysics Department

College of William and MaryWilliamsburg, VA 23187, USA

The recent disagreement between the proton charge radius extractedfrom Lamb shift measurements of muonic and electronic hydrogen invitesspeculation that new physics may be to blame. Several proposals have beenmade for new particles that account for both the Lamb shift and the muonanomalous moment discrepancies. We explore the possibility that new parti-cles’ couplings to the muon can be fine-tuned to account for all experimentalconstraints. We consider two fine-tuned models, the first involving new par-ticles with scalar and pseudoscalar couplings, and the second involving newparticles with vector and axial couplings. The couplings are constrained bythe Lamb shift and muon magnetic moments measurements while mass con-straints are obtained by kaon decay rate data. For the scalar-pseudoscalarmodel, masses between 100 to 200 MeV are not allowed. For the vectormodel, masses below about 200 MeV are not allowed. The strength ofthe couplings for both models approach that of electrodynamics for parti-cle masses of about 2 GeV. New physics with fine tuned couplings may beentertained as a possible explanation for the Lamb shift discrepancy.

(Reference: Carl E. Carlson and Benjamin C. Rislow, Phys. Rev. D 86,035013 (2012); e-Print arXiv: 1206.3587 [hep-ph])

1

Non-perturbative QED spectrum of Muonic Hydrogen

J. D. Carroll∗ and A. W. Thomas

Centre for the Subatomic Structure of Matter (CSSM),School of Chemistry and Physics, University of Adelaide, SA 5005, Australia

J. Rafelski

Departments of Physics, University of Arizona, Tucson, Arizona, 85721 USA

G. A. Miller

University of Washington, Seattle, WA 98195-1560 USA

The exact solution of the single particle Dirac equation for Hydrogen has been a distant eventuality

for much of the past few decades—able to provide a fully relativistic, non-perturbative description

of the bound lepton wavefunction in the presence of a proton, including many QED effects to all

orders self-consistently—yet computational complexity has until now prevented such a solution from

feasibility.

Through careful control of very high-precision numerical processing, we demonstrate that the

solution is obtainable; that currently explored QED contributions are calculable; and that for the

first time, quantifiable testing of the perturbation theory contributions is available.

With relevance to the muonic hydrogen proton radius problem, we calculate the relativistic Dirac;

first-order vacuum polarization; Kallen-Sabry; Wichmann-Kroll; and muon-VP contributions to

the 2P -2S Lamb shift, fine-, and hyperfine-structures in order to provide a fully non-perturbative

component of a theory estimate of the experimental transitions obtained at PSI.

In this talk I will detail the specifics of these calculations, some of the difficulties in performing a

comparison to the experiment and earlier perturbative estimates, and our results.

∗ Electronic address: jonathan.carroll@adelaide.edu.au

The Mainz high-precision proton form factormeasurement

II. Basic principles and spin-offs

Michael O. Distler for the A1 CollaborationInstitut für Kernphysik, Johannes Gutenberg-Universität Mainz, Germany

An unprecedented amount of more than 1400 cross section data points havebeen collected in the course of the Mainz high-precision proton form factor mea-surement [1]. For the first time this allowed the super Rosenbluth method to beapplied to the data where a selection of different form factor models were directlyfitted to the measured cross sections in order to extract the electric and magneticform factors.

In the talk a number of details of the Mainz analysis will be discussed, like theimportance of the Rosenbluth formula, the relevance of the normalization parame-ters, and the choice of the form factor models used. Also, the interpretation of theMainz data requires a deeper insight of the statistical methods involved. To this endthe basic concepts of estimation and the construction of confidence intervals anderror bands will be reviewed. A number of suggestions have been made to resolvethe proton radius puzzle by using exotic form factor models. Those proposals willbe discussed regarding their implications for the charge distribution [2].

The Mainz collaboration will continue to investigate the proton radius discrep-ancy. New proposals will be presented to measure the charge form factor of theproton at very low q2 using the initial state radiation (ISR) method and to measurethe charge (C0) form factor of the deuteron at low q2.

References

[1] J. C. Bernauer et al. [A1 Collaboration], “High-precision determination of theelectric and magnetic form factors of the proton,” Phys. Rev. Lett. 105 (2010)242001 [arXiv:1007.5076 [nucl-ex]].

[2] M. O. Distler, J. C. Bernauer and T. Walcher, “The RMS Charge Radius of theProton and Zemach Moments,” Phys. Lett. B 696 (2011) 343 [arXiv:1011.1861[nucl-th]].

Weak Interaction Contributions in Light Muonic Atoms

Michael I. EidesDepartment of Physics and Astronomy, University of Kentucky

Lexington, KY 40506, USA

Weak interaction contributions to hyperfine splitting and Lamb shift in light electronicand muonic atoms are calculated. We notice that correction to hyperfine splitting turnsinto zero for deuterium. Weak correction to the Lamb shift in hydrogen is additionallysuppressed in comparison with other cases by a small factor (1 − 4 sin2 θW ).

This work was supported by the NSF grant PHY-1066054.

XUV frequency comb spectroscopy of helium and helium+ ions

J. Morgenweg, I. Barmes, T.J. Pinkert, D. Z. Kandula*, G. Gohle+, K.S.E. Eikema

LaserLaB Amsterdam, VU University, De Boelelaan 1081, Amsterdam, The Netherlands *Present address: Max Born Institute, Max-Born Str. 2A, Berlin, Germany

+Present address: Physics Department, Ludwig-Maximilians-University, Schellingstrasse 4, München, Germany

Email: k.s.e.eikema@vu.nl

In view of the "proton radius puzzle"1,2 it is very interesting to perform precision spectroscop-ic measurements in helium and helium+ ions (and their muonic counterparts) to investigate the radius of the alpha particle. Especially transitions from the ground state are sensitive to the size of the nucleus, but it does require extreme ultraviolet (XUV, λ < 100 nm). We devel-oped a method3,4 to perform high-accuracy frequency comb measurements in this wavelength region. It is based on amplification of two pulses from a near-infrared frequency comb laser, and subsequent high-harmonic upconversion (HHG) to the XUV. The resulting highly coherent XUV pulses have been used in a Ramsey scheme to perform absolute frequency measurements at the shortest wavelength to date (51 nm, on the 1 1S0 - 4,5 1P1 transitions). A modulation depth of up to 61% was observed when the "broad XUV comb" was scanned over the transitions. For helium, the ground state ionization energy3,4 was determined from this signal with an accuracy of 6 MHz, which constitutes an 8-fold im-provement over previous experiments. Efforts are now focused on the realization of kHz-level accuracy in the XUV using several improvements. Up to now, a fixed optical delay line was used in the pump laser for the non-collinear parametric amplifier (NOPCPA) of the comb pulses. This method restricts the prac-tical pulse delay to <20 ns, which in turn restricts the attainable resolution. Moreover, small alignment and wavefront errors in the pump pulses for the NOPCPA imparted phase shifts on the amplified frequency comb pulses, which requires careful characterization. We have now developed a new pump laser system, without a delay line, which overcomes these issues. It can produce near-identical pump laser pulses (under computer control) matched to the timing of the frequency comb laser pulses over a time span exceeding micro-seconds. In a new measurement scheme based on discrete Fourier-transform spectroscopy, this strongly reduces or even eliminates the influence of phase errors in the NOCPCPA and HHG, which should enable kHz-level frequency measurements in the XUV on helium and helium+ ions.

References

1. R. Pohl et al., Nature 466, 213 (2010) 2. C.G. Parthey et al., Phys. Rev. Lett. 107, 203001 (2011) 3. D.Z. Kandula et al., Phys. Rev. Lett. 105, 063001 (2010) 4. D.Z. Kandula et al., Phys. Rev. A 84, 062512 (2011)

A Novel High Precision Measurement of the Proton Charge Radius via epScattering Method

A. Gasparian1

North Carolina A&T State University, USA

Abstract

We are preparing a novel high precision magnetic-spectrometer-free experiment to measurethe proton charge radius via ep elastic cross sections at very low four-momentum transfersquared, Q2, from 10−4 to 10−2 (GeV/c)2 range at Jefferson Laboratory. This experimentwill use a high resolution crystal calorimeter to reach the extreme forward scattering anglestogether with a windowless hydrogen gas flow target to minimize the experimental back-grounds. The absolute value of the ep cross sections will be normalized to a well known QEDprocess, the Møller scattering from the atomic electrons, which will be measured continu-ously in this experiment within similar kinematics and the same experimental acceptances.The high precision differential cross sections, measured in this very low Q2 range, will allowfor a sub-percent and essentially model independent extraction of the proton charge radiusfor the first time in ep scattering experiments. This experiment, with its independent novelapproach and projected precision, will have a direct potential to either significantly shift thecurrent value of the proton radius, or question the sufficiency of QED calculations in themuonic hydrogen experiment, or probe new physics beyond the Standard Model. Thereby,this experiment will have a direct impact on the “proton charge radius puzzle” currentlydeveloping in hadronic and atomic physics. The description and the current status of theexperiment will be presented in this talk.

1For the Proton Charge Radius Collaboration E12-11-106 at JLab

Hadronic contributions to Lamb shift in muonic

deuterium

Misha Gorchtein and Marc Vanderhaeghen

Institut fur Kernphysik, Johannes Gutenberg-Universitat,

Mainz, Germany

We revisit the two-photon exchange contribution to Lamb shift in muonic deuterium.

We capitalize on recent high quality data from JLab on virtual photoabsorption on deu-

terium to constrain the size of hadronic contributions to the Lamb shift. These include

both inelastic and quasi-elastic contributions.

How well can a nuclear charge radius be measured

with low-Q2 electron scattering data?

Keith Griffioen

Dept. of Physics

College of William & Mary

Williamsburg, VA, USA

Although the slope of the nucleon’s electric form factor at Q2=0 is proportional to its

squared charge radius, extracting this radius from imperfect data, which do not extend to

zero and have contributing curvature at small Q2, is difficult. The assumptions built into

a fitting scheme can bias the value of the extracted slope. The limitations of this fitting

approach and the accuracy of possible future measurements will be discussed.

Towards One-electron Ions in Rydberg States for a Rydberg Constant Determination Independent of the Proton Radius

Nicholas D. Guise*†, Samuel M. Brewer†, and Joseph N. Tan*

*National Institute of Standards and Technology, 100 Bureau Drive, Gaithersburg, MD 20899, USA Joseph.Tan@nist.gov

†University of Maryland, College Park, MD 20742 , USA The large discrepancy in the proton radius measurements [1] has significant impact upon the determination of the Rydberg constant, when taken together with precise measurements of various transitions in hydrogen and deuterium [2]. This has renewed interest in alternative systems capable of providing a Rydberg constant measurement that is independent of the proton radius. Earlier theoretical work at NIST considered the possibility of testing theory with one-electron ions in high angular momentum states [3][4]. The energy levels for high-angular momentum states can be calculated much more accurately than for low-angular momentum states, in part because the nuclear size correction is vanishingly small. In the high-L regime, theoretical uncertainties are smaller than the uncertainties of fundamental constants [3]. Of particular interest is the fact that the Rydberg constant is the leading source of uncertainty in this regime—about a factor of 100 larger than the uncertainty due to other constants. Consequently, one-electron ions in Rydberg states can enable a Rydberg constant determination that is independent of the proton radius if sufficiently precise measurements can be realized for comparison with prediction. Such effort could potentially provide useful information to help resolve the proton radius puzzle [5]. We report on progress made at NIST towards the goal of forming one-electron ions in Rydberg states that can be probed accurately using optical frequency metrology. Bare nuclei created in an EBIT were recently extracted and captured in a novel compact Penning trap [6], as illustrated in Figure 1. The architecture of this ion trap was designed to facilitate experiments with controlled recombination and laser spectroscopy. To produce one-electron ions in Rydberg states, the experimental apparatus will allow electron transfer from an excited atom to a bare nucleus stored in an ion trap. For nuclear charge in the range 1 < Z < 11, it is possible to find many E1 transitions between Rydberg states in the optical domain accessible to an optical frequency comb synthesizer [3]. Other applications include spectroscopic studies of highly-charged ions of special interest in atomic physics, astrophysics and metrology; for example, fluorescence from metastable states of highly-charged ions isolated in a compact Penning trap has recently been observed.

Fig. 1. Time-of-flight signal of ions ejected from a compact Penning trap, for two ion storage times after capturing bare neon nuclei: (a) 1 ms storage time; and (b) 2 s storage time, showing production of lower charge states by electron capture from residual background gas.

ACKNOWLEDGEMENT The work of N. D. Guise at NIST was supported in part

by a Research Associateship Award from the U.S. National Research Council.

REFERENCES

[1] R. Pohl, et. al., “The size of the proton,” Nature, vol. 466, pp. 213-218, July 2010.

[2] P. J. Mohr, B. N. Taylor and D. B. Newell, “CODATA recommended values of the fundamental physical constants,” Rev. Mod. Phys., vol. 80, pp. 633-730, June 2008.

[3] U. D. Jentschura, P. J. Mohr, J. N. Tan and B. J. Wundt, “Fundamental constants and tests of theory in Rydberg states of hydrogenlike ions,” Phys. Rev. Lett., vol. 100, p. 160404, April 2008.

[4] U. D. Jentschura, P. J. Mohr and J. N. Tan, “Fundamental constants and tests of theory in Rydberg states of one-electron ions,” J. Phys. B: At. Mol. Opt. Phys., vol. 43, p. 074002, March 2010.

[5] U. D. Jentschura, “Lamb shift in muonic hydrogen—II. Analysis of the discrepancy of theory and experiment,” Annals Phys., vol. 326, p. 516-533, February 2011.

[6] J. N. Tan, S. M. Brewer and N. D. Guise, “Penning traps with unitary architecture for storage of highly charged ions,” Rev. Sci. Instrum.83, 023103 (2012).

Progress towards a new separated-oscillatory-field

microwave measurement of the atomic hydrogen n=2 Lamb shift

E.A. Hessels, A.C. Vutha, N. Bezginov, I. Ferchichi, M.C. George,

V. Isaac, C.H. Storry, M. Weel

York University, Toronto, Canada We propose to make a more precise microwave measurement of the atomic hydrogen n=2 Lamb shift using the Ramsey method of separated oscillatory fields. This new measurement (with an anticipated uncertainty of 2 kHz (5 times more accurate than the 1981 measurement of Lundeen and Pipkin [1]), along with existing precise atomic theory calculations [2], will allow for a new determination of the proton charge radius to an accuracy of 0.6 percent. The measurement will shed light on the 7-standard-deviation discrepancy between proton radius recently obtained from muonic hydrogen [3] and the CODATA value [2]. The talk will give an outline of the experimental method to be used for the measurement and review progress to date. This work is supported by NSERC, CRC and CFI of Canada and by a NIST Precision Measurements Grant.

[1] S.R. Lundeen and F. M. Pipkin, Phys. Rev. Lett. 46, 232 (1981).

[2] CODATA 2010, arXiv:1203.5425 (2012).

[3] R. Pohl, et al, Nature 466, 213 (2010)

Model independent analysis of proton structure for

hydrogenic bound states

Richard J. Hill

Enrico Fermi Institute and Department of Physics

The University of Chicago, Chicago, Illinois, 60637, USA

Abstract

I describe work done in collaboration with G. Paz, J. Heinonen, G. Lee and M.Solon [1,2,3].

Recent results in muonic hydrogen spectroscopy have challenged our understanding oflow-energy lepton-hadron interactions. Using this motivation we develop modern effec-tive field theory tools to systematically analyze nuclear structure effects in atomic boundstates. The NRQED Lagrangian is constructed through order 1/M4. Model independentrelations between lepton-nucleon scattering measurements and bound state observablesare derived. Model-dependent assumptions in previous analyses of the muonic hydrogenLamb shift are isolated and sensitivity to poorly constrained hadronic structure param-eters is discussed.

References:

[1] R.J. Hill and G. Paz Phys. Rev. Lett. 107 (2011) 160402 .[2] J. Heinonen, R.J. Hill and M.P. Solon, arXiv:1208.0601 .[3] R.J. Hill, G. Lee, G. Paz and M.P. Solon, ”The NRQED lagrangian at order 1/M4”,in preparation .

The OLYMPUS experiment at DESY 1

Michael Kohl <kohlm@jlab.org>Hampton University and Jefferson Lab

for the OLYMPUS Collaboration

Abstract

Two-photon exchange is believed to be responsible for the differentfindings for the proton electric to magnetic form factor ratio with theRosenbluth and polarization transfer methods. If this explanation is cor-rect, one expects significant differences in the lepton-proton cross sectionsbetween positrons and electrons. The OLYMPUS experiment at DESYin Hamburg, Germany was designed to measure the ratio of unpolarizedpositron-proton and electron-proton elastic scattering cross sections overa wide kinematic range with high precision, in order to quantify the effectof two-photon exchange. The experiment uses intense beams of electronsand positrons stored in the DORIS ring at 2.0 GeV interacting with an in-ternal windowless hydrogen gas target. The current status of OLYMPUSwill be discussed.

1supported by NSF grants PHY-0855473, PHY-0959521, and PHY-1207672

1

The size of the proton - closing in on the radius puzzle

I. T. Lorenz,1 H.-W. Hammer,1 and Ulf-G. Meißner1, 2

1Helmholtz-Institut fur Strahlen- und Kernphysik and Bethe Center for Theoretical Physics,Universitat Bonn, D–53115 Bonn, Germany

2Institute for Advanced Simulation, Institut fur Kernphysik and Julich Center for Hadron Physics,Forschungszentrum Julich, D–52425 Julich, Germany

We analyze the recent electron-proton scattering data from Mainz using a dispersive framework that respectsthe constraints from analyticity and unitarity on the nucleon structure [1]. We also perform a continued fractionanalysis of these data. We find a small electric proton charge radius, rpE = 0.84+0.01

−0.01 fm, consistent withthe recent determination from muonic hydrogen measurements and earlier dispersive analyses. We also extractthe proton magnetic radius, rpM = 0.86+0.01

−0.02 fm, consistent with earlier determinations based on dispersionrelations and continued fractions.Making use of a conformal mapping combined with the recent Mainz data we confirm our small rpE-value [2].

[1] I.T. Lorenz, H.-W. Hammer, U.-G. Meißner, [hep-ph/1205.6628],[2] I.T. Lorenz, H.-W. Hammer, U.-G. Meißner, in preparation.

Proton polarisability contribution to the Lamb shift in muonic hydrogenat fourth order in chiral perturbation theory

Michael C. Birse and Judith A. McGovernSchool of Physics and Astronomy, The University of Manchester, Manchester, M13 9PL, UK

The recent determination of the proton charge radius from the Lamb shift in muonic hydrogen [1] gives a valuethat differs by about 5 standard deviations from the CODATA value [2] and from the results of recent electronscattering experiments [3]. However before concluding that new physics is required, it is essential to examinecarefully any possible conventional explanations. One place where some theoretical uncertainty remains is thecontribution of proton structure to two-photon exchange, specifically through the polarisability of the proton.

The energy shift of an S-wave hydrogenic state due to two-photon exchange can be expressed in terms of thespin-averaged amplitude for forward doubly-virtual Compton scattering (V2CS) [4]. This comprises two tensorstructures:

Tµν =(−gµν +

qµqν

q2

)T1(ω,Q2) +

1M2

(pµ − p · q

q2qµ

) (pν − p · q

q2qν

)T2(ω,Q2), (1)

where p and q are the four-momenta of the proton and photon, respectively, M is the nucleon mass, Q2 = −q2,and ω = p · q/M . Dispersion relations [5, 6] can be used to estimate the inelastic parts of the amplitudesT1,2(ω,Q2) from the corresponding structure functions measured in inelastic electron scattering. These parts ofthe contribution of proton structure are well determined from the available data, with one important exception:the dispersion relation for T1 does not converge and so it requires a subtraction at ω = 0, introducing adependence on the unmeasured amplitude T1(0, Q2). The slope of this term at Q2 = 0 is given by a low-energytheorem (LET) in terms of the magnetic polarisability of the proton, β [7–9]. Otherwise its form is unknown.

This approach to determining the amplitude for forward V2CS has been questioned in several recent papers.On the one hand Pachucki’s division into “Born” and “structure” contributions, with the former calculated usingthe Dirac equation with on-shell form factors [6], has been called into question by Carlson and Vanderhaeghen[10] and Hill and Paz [11]. On the other hand Miller et al. [12] have questioned the validity of the LET for theslope of T1(0, Q2) and suggested that off-shell form-factors of the proton could generate new large polarisabilitycontributions to V2CS.

In this work [18] we re-examine the derivation of the LET to clarify that β does indeed govern the slope ofthe “structure” part, and we discuss how the LET is embodied in nonrelativistic effective field theories suchas heavy-baryon chiral perturbation theory (HBChPT). To obtain a model-independent result for the form ofT1(0, Q2) at low Q2, we calculate it within HBChPT to fourth order, including effects of the ∆ up to fifth orderin “δ-counting” [13]. Since the contribution ∆Esub of this amplitude to the Lamb shift is dominated by thelow-momentum region, this can significantly reduce the theoretical uncertainty in this quantity. This extendswork previously done to third order in HBChPT by Nevado and Pineda [14, 15].

When the chiral amplitude is matched smoothly onto the high-Q2 behaviour expected in the partonic regime[11, 16], and using the value for β obtained in Ref. [19], we find the contribution to the Lamb shift to be

∆Esub = 4.2± 1.0 µeV. (2)

This is similar in magnitude to previous, more model-dependent determinations [6, 10]. Our results leave noroom for any large additional polarisability effect arising from off-shell form factors, and we see no sign of anyrapid growth of the form factor at low Q2 that could lead to a large contribution to the Lamb shift.

[1] R. Pohl et al., Nature 466, 213 (2010).[2] P. J. Mohr, B. N. Taylor and D. B. Newell, Rev. Mod. Phys. 80, 633 (2008) [arXiv:0801.0028].[3] J. C. Bernauer et al. (A1 Collaboration), Phys. Rev. Lett. 105, 242001 (2010) [arXiv:1007.5076].[4] J. Bernabeu and R. Tarrach, Ann. Phys. 102, 323 (1976)[5] J. Bernabeu and C. Jarlskog, Nucl. Phys. B 60, 347 (1973).[6] K. Pachucki, Phys. Rev. A 60, 3593 (1999) [arXiv:physics/9906002].[7] S. Scherer, A. Yu. Korchin and J. H. Koch, Phys. rev. C 54, 904 (1996) [arXiv:nucl-th/9605030].[8] D. Drechsel, G. Knoechlein, A. Metz and S. Scherer, Phys. Rev. C 55, 424 (1997) [arXiv:nucl-th/9608061].[9] H. W. Fearing and S. Scherer, Few-Body Syst. 23, 111 (1998) [arXiv:nucl-th/9607056].

[10] C. E. Carlson and M. Vanderhaeghen, Phys. Rev. A 84, 020102 (2011) [arXiv:1101.5965].[11] R. J. Hill and G. Paz, Phys. Rev. Lett. 107, 160402 (2011) [arXiv:1103.4617].[12] G. A. Miller, A. W. Thomas, J. D. Carroll and J. Rafelski, Phys. Rev. A 84, 020101 (2011) [arXiv:1101.4073].[13] V. Pascalutsa and D. R. Phillips, Phys. Rev. C 67, 055202 (2003) [arXiv:nucl-th/0212024].[14] A. Pineda, Phys. Rev. C 71, 065205 (2005) [arXiv:hep-ph/0412142].[15] D. Nevado and A. Pineda, Phys. Rev. C 77, 035202 (2008) [arXiv:0712.1294].[16] J. C. Collins, Nucl. Phys. B 149, 90 (1979).[17] V. Bernard, N. Kaiser, A. Schmidt and U.-G. Meissner. Phys. Lett. B 319, 269 (1993) [arXiv:hep-ph/9309211].[18] M. C. Birse and J. A. McGovern, Eur. Phys. J. A 48 120 (2012) [arXiv:1206.3030].[19] H. W. Griesshammer, J. A. McGovern, D. R. Phillips and G. Feldman, Prog. Part. Nucl. Phys. 67, 841 (2012)

[arXiv:1203.6834].

Proton Polarizability Contribution: Muonic Hydrogen

Lamb Shift and Elastic Scattering

Gerald A. Miller

Department of Physics

Univ. of Washington

Seattle, WA 98195-3560

The uncertainty in the computed contribution to the Lamb shift in muonic hydrogen,

∆Esubt arising from proton polarizability effects entering in the two-photon exchange

diagram at large virtual photon momenta is shown to be large enough to account for

the proton radius puzzle. This is because the integral that determines ∆Esubt contains a

logarithmic divergence. We evaluate this integral using a chosen form factor and also by

using the dimensional regularization procedure which makes explicit the need for a low

energy constant. The consequences of this new contribution to two photon exchange are

approximately independent of the method of calculation and should be observable in a

planned low energy lepton-proton scattering experiment planned to run at PSI.

Directions toward the resolution of the proton charge

radius puzzle

Krzysztof Pachucki

Institute of Theoretical Physics

University of Warsaw

Hoza 69, 00-681 Warsaw, Poland

Inspite of many attempts, the discrepancy in the proton charge radius remains un-

explained. It looks that the muon-proton and the electron-proton interactions have a

different low energy limit, in contradiction to the universality of electromagnetic interac-

tions. I will analyze main paradigms in the description of the lepton-proton interactions

and possible ways of their experimental verification.

Model independent extraction of the proton charge

radius from electron scattering

Richard J. Hilla and Gil Pazb

aEnrico Fermi Institute and Department of PhysicsThe University of Chicago, Chicago, Illinois, 60637, USA

bDepartment of Physics and AstronomyWayne State University, Detroit, MI 48201, USA

Abstract

Scattering data allows us to directly extract the charge radius of the proton from theslope of the proton electric form factor. Over the last 50 years there has been manysuch extractions with values almost anywhere in the range of 0.8−0.9 fm. Since thefunctional form of the form factor is unknown, all of these extractions rely on modeldependent assumptions on the shape of the form factor.

In [1], we have shown how to address this problem. By using analyticity constraintswe provide a systematic procedure for analyzing arbitrary data without model-dependentassumptions. It also allows us to include electron-neutron scattering data, and ππ → NNdata to improve the precision on the charge radius while maintaining model-dependence.Using representative datasets we find rpE = 0.870 ± 0.023 ± 0.012 fm using just protonscattering data; rpE = 0.880+0.017

−0.020 ± 0.007 fm adding neutron data; and rpE = 0.871 ±0.009± 0.002± 0.002 fm adding ππ data.

In this talk we review this work as well a preliminary results on the application ofthe same method to the extraction of the magnetic radius of the proton, whose valuealso shows large variations between different extractions.

References:

[1] R.J. Hill, G. Paz, PRD 82, 113005 (2010)

Lamb shift and hyperfine splitting in muonic hydrogen

and deuterium

News from experiment

Randolf Pohl for the CREMA collaboration

Max-Planck-Institute of Quantum Optics

Garching, Germany

We have measured two transisions [1,2] in muonic hydrogen from which we determinedthe Lamb shift [1] and the 2S hyperfine splitting [2] in muonic hydrogen. The 2nd tran-sition in µp confirms the proton charge radius obtained in [1] and reinforces the “protonradius puzzle”. In addition, a value of the Zemach radius is extracted from the 2S hyper-fine splitting in µp which is in agreement with previous values.

In muonic deuterium µd, we have measured three 2S-2P transitions. Both, Lamb shiftand 2S hyperfine splitting are determined from experiment. Large deuteron polarizabilitycontributions to both the Lamb shift and the 2s hyperfine splitting are seen.

[1] R. Pohl et al., ”The size of the proton”, Nature 466, 213 (2010)

[2] A. Antognini et al, ”Proton structure from muonic hydrogen spectroscopy”,submitted (2012)

Extension of the Standard Model by muon-specific forces

Maxim Pospelov (a,b)

(a)Perimeter Institute for Theoretical Physics, Waterloo, ON, N2J 2W9, Canada(b)Department of Physics and Astronomy, University of Victoria,

Victoria, BC, V8P 1A1 Canada

Abstract

I report the results of joint work with Drs. B. Batell and D. McKeen [1, 2].Among possible resolutions of the ”proton charge radius puzzle” is an [unlikely] possibility

of new physics that somehow eluded all previous attempts to detect it, but found its way tomanifest itself in the Lamb shift of the muonic atoms. I attempt to build a self-consistentmodel of muon-specific forces and show that the chiral structure of the Standard Modelmakes it an exceedingly difficult task. The scalar force mediator is in immediate troubledue to the constraints from the meson decay. The vector force has to avoid coupling toneutrino fields, and thus almost inevitably would have to be coupled to the right-handedmuon currents.

I demonstrate that the gauged µR model with O(10 MeV) mediator, despite a numberof theoretical issues within its structure, is nevertheless not excluded by any of the exist-ing experiments. The parameters of the model that suit the muonic hydrogen Lamb shiftmeasurement are determined.

If taken seriously, the model implies the existence of large parity-violating effects inneutral currents for muons that imply the strength of the interaction much larger thanFermi constant GF . Incidentally, there are no tests of parity in neutral currents perfmoredwith muons at low energy. I show that one possible avenue for testing large parity violationfor muons is the investigation of angular asymmetry in 2S−1S transition for Z ∼ 30 muonicatoms that are obtained through the process of atomic radiative capture (ARC) of muonsdirectly into low-lying atomic S states. Neither the ARC process nor the 2S − 1S was everobserved in any muonic atom. The existing facilities at TRIUMF, PSI and J-PARC are wellsuited for observing the in-flight capture, the 2S − 1S transition and for directly testing thegauged µR model.

References

[1] B. Batell, D. McKeen and M. Pospelov, Phys. Rev. Lett. 107, 011803 (2011)[arXiv:1103.0721 [hep-ph]].

[2] D. McKeen and M. Pospelov, Phys. Rev. Lett. 108, 263401 (2012) [arXiv:1205.6525[hep-ph]].

1

Measurement of Two Photon Exchange effects in

electron-proton elastic scattering

Brian A. RaueDepartment of Physics, Florida International University,

Miami, United States of America

Two photon exchange (TPE) has been proposed as the primary source of the discrep-ancy between Rosenbluth and polarization-transfer methods of determining the electric-to-magnetic form-factor ratio of the proton. A direct measurement of the TPE contri-bution to elastic scattering can be determined by measuring the lepton-proton elastic

scattering ratio R = σ(e+p)σ(e−p)

. We have measured R using the CLAS spectrometer at Jeffer-

son for Q2 < 2.5 GeV2 over most of range of ǫ. Preliminary results will be presented.

JLab Experiment E08-007Proton Electromagnetic Form Factor Ratio at Low Q2

G. RonHebrew University of Jerusalem

Electromagnetic form factors of the nucleon are model-independent ob-servables which encode our ignorance of its complex internal structure. Inrecent years significant attention has been drawn to these observables due tothe discovery of unexplained deviations from previously measured results aswell as a striking discrepancy between the proton charge radius as measuredby electron scattering and atomic hydrogen Lamb shift with that measuredby muonic hydrogen Lamb shift.

Recoil polarization measurements and high precision cross section mea-surements are allowing the electric to magnetic form factors ratios be de-termined with unprecedented precision, a recent set of measurement was byJefferson Lab experiment E08-007. While these measurements provide im-portant insight into the proton form factors at low Q2 they cannot extendto very low Q2 since the recoil proton cannot be detected at this range ofmomentum transfer. An alternative technique, using beam-target asymme-try promises to allow measurement to extremely low Q2 values since it doesnot require detection of the proton.

The second part of JLab experiment E08-007, using beam-target asym-metry has recently concluded data taking in the Q2 range 0.01–0.05 GeV2

with ∼1% statistical uncertainty. The combination of both Hall A spec-trometers promises to allow a significant reduction in the systematic uncer-tainties.

I will discuss the current status of the proton form factor measurements,with emphasis on the new E08-007 results under analysis and their potentialto improve the current status of the proton form factor extraction.

Nuclear polarizability contribution to the Lamb shift

in muonic helium

S.S. Schlesser

Theoretical Nuclear Physics Dept.

KVI Groningen

The Netherlands

The largest uncertainty in theoretical predictions for the muonic helium Lamb shift

comes from the nuclear polarizability. This effect will substantially limit the accuracy for

the nuclear charge radii as obtained from the measurements of the 2S-2P transition in

µ4He and µ

3He.

The nuclear polarizability correction cannot be calculated from first principles, as all

the other QED corrections, and requires precise knowledge on the low-energy interactions

between nucleons. Our computational method employs very efficient techniques devel-

oped previously in the quantum chemistry area. We calculate the wave function of the

nucleus using a variational approach with explicitly correlated Gaussian functions. The

minimization with respect to all nonlinear parameters is not a limitation to the accuracy

of the result. To properly account for the low-energy nucleonic interactions, we use the

pionless effective field theory. We have already obtained an effective potential for the

two-nucleon interaction at next-to-leading-order through a fit to the known scattering

data. The three-nucleon force will be obtained by a fit to the triton binding energy.

Proton rms-radius and tail of density

Ingo SickDept. of Physics, University of Basel, Basel, Switzerland

Email: ingo.sick@unibas.ch

The proton rms-radius R is extracted in general from a fit of the e-p scat-tering data using suitable parameterizations of the electric Sachs form factorGe(q), with the slope at q2 = 0 yielding the radius R. A generic difficultyresults from the fact that the slope is not measured at q2 = 0 but extrapolatedfrom q ∼ 1fm−1 where the finite-size effect 1−G(q2) ∼ q2R2/6 + ... is largeenough to be measured with satisfactory precision and where higher momentsof the density still give a small contribution. The ’extrapolation’ to q2 = 0 viathe parameterization of Ge(q) then causes a model dependence, and can leadto erroneous results if the parameterization implies an unphysical behavior ofρ(r) at large radii r leading to structure of the fitted Ge(q) at q < qmin.

We show by two examples why recent fits to the e-p data yield radii that arequite different from the ’standard’ radii extracted from electron scattering, andexplain why this is linked to an unphysical behavior at large r of the densitycalculated from the Fourier transform of the Ge(q) that was fitted to the data.We also demonstrate that good fits with extremely different values of R canbe found.

In order to improve upon this unsatisfactory situation, several approachesprovide a partial improvement: (absolute) measurements of cross sections tomuch lower momentum transfers, more careful selection of the type of param-eterization employed, or fits that include data to the largest q’s available. Asatisfactory solution, however, is possible only when considering, simultane-ously with the fit of the cross section data, the behavior of the charge densityρ(r) at large r.

In particular, a stable and reliable value forR can be obtained when imposingduring the fit of the e-p data the known large-r behavior of the tail density,resulting from the least-bound Fock component n+ π+ of the proton.

The Jefferson Lab gp2 Experiment

Karl J. Slifer

Department of Physics

University of New Hampshire

Durham, New Hampshire, USA

Proton structure contributes a significant correction to atomic energy

levels. These corrections are dominated by the contribution from very low

Q2, and affect a range of Q.E.D. calculations; from hyperfine splitting to

extractions of the proton charge radius. As the result of a dedicated exper-

imental program, the inclusive nucleon structure functions have been well

determined, with the exception being gp

2 which is relatively unknown.

The Jefferson Lab E08-027 experiment measured gp

2 in the resonance re-

gion for 0.02 < Q2 < 0.20 GeV2. This was a large installation involving many

novel upgrades to the Hall A beamline and detector packages. This data is

needed to clarify the failure of chiral perturbation theory to reproduce the

nucleon spin polarizabilities, but a precise determination of gp

2 is also impor-

tant for a full understanding of the simplest bound atomic systems. We will

show some preliminary results and discuss the significance of this data to the

proton radius puzzle.

Multiphoton processes in atomic physics and astrophysics

D. A. Solovyeva, L. N. Labzowskya, and V. K. Dubrovichb,c

a St. Petersburg State University, St. Petersburg, Russiab St. Petersburg Branch of Special Astrophysical Observatory, Russian Academy of

Sciences, 196140, St. Petersburg, Russiac Nizhny Novgorod State Technical University n. a. R. E Alekseev, GSP-41, N.

Novgorod, Minin str., 24, 603950

The recent accurate measurements of the cosmic microwave background (CMB) prop-erties via the space telescopes require a significant increase in the accuracy of theoreticalresearch. For the precise astrophysical calculations the detailed description of multipho-ton emission/absorption processes is required [1]-[3]. The problem of the evaluation of thetwo-photon decay width of excited states in hydrogen is considered [4]. As application thetwo-photon decay channels for the 3s level of the hydrogen atom are evaluated, includingthe cascade transition probability 3s − 2p − 1s. The dependence on the principal quan-tum number (n) of the initial state is investigated. The E1E1, E2E2, M1M1 and E1M2decay rates of the ns, nd states (up to n = 100) are evaluated [5]. The ”two-photon”approximation was formulated for the multiphoton cascade emission [6]. We have stud-ied also the hydrogen atom in an external photon fields. Field characteristics are definedfrom conditions which correspond to the recombination era of universe. Approximation ofthree-level atom is used for the description of ”atom - fields” interaction. It is found thatthe electromagnetically induced transparancy phenomena take a place in hydrogen recom-bination epoch in early universe.The additional terms to the optical depth in definitionof Sobolev escape probability on the level about 1% are found [7], [8].

————————

[1] Ya. B. Zeldovich, V. G. Kurt and R. A. Sunyaev, Zh. Exsp. Teor. Fiz. 55 (1968) 278[Engl. Transl. Sov. Phys. - JETP Lett. 28 (1969) 146]

[2] J. Chluba and R. A. Sunyaev, Astronomy&Astrophysics 480, 3, pp. 629-645 (2008)

[3] V. K. Dubrovich and S. I. Grachev, Astronomy Letters 31 (2006) 359

[4] L. Labzowsky, D. Solovyev and G. Plunien, Phys. Rev. A 80 (2009) 062514

[5] D. Solovyev, V. Dubrovich, A. Volotka, L. Labzowsky and G. Plunien, J. Phys. B 43(2010) 175001

[6] D. Solovyev and L. Labzowsky, Phys. Rev. A 81 (2010) 062509

[7] D. Solovyev, V. Dubrovich and G. Plunien,J. Phys. B: At. Mol. Opt. Phys. 45 (2012)215001

[8] D. Solovyev, V. Dubrovich, arXiv:1209.5194 [physics.atom-ph], 24 Sep. 2012

ELASTIC µP SCATTERING AT THE PAUL SCHERRER INSTITUT

V. Sulkosky1, for the MUSE Collaboration

1Massachussetts Institute of Technology, Cambridge, MA 02139

The MUon proton Scattering Experiment (MUSE) at the Paul Scherrer Institut (PSI), Villigen, Switzer-land, intends to study the proton radius puzzle through simultaneous measurements ofµp andep scattering.The puzzle is the difference between the proton radius measurements from atomic hydrogen and electronscattering vs. radius measurements using muonic hydrogen.While measurements ofµp scattering havebeen done, there are no high-precision low-Q2 µp scattering data that would allow a reliable extraction ofthe proton radius. The MUSE experiment is being designed to do this measurement.

There are several possible explanations for the proton radius puzzle, but at present none are generallyaccepted. One general issue in finding an explanation is thatthe muonic hydrogen measurement should bemuch more precise and reliable, but the various independentep radius measurements get consistent results.It is an odd, though possible, situation if the different types ofep measurements get the same wrong answer.The resolution of the puzzle might require multiple explanations.

The MUSE experiment is designed to test several possible explanations of the puzzle. Perhaps the mostinteresting possible explanation is that novel physics violates lepton universality so that theµp and ep

interactions are not equivalent. MUSE tests this possibility with simultaneous measurements with a mixedµ ande beam of the scattering cross sections, leading to precise relative cross sections. This will also allowa precise comparison of the relative radius from the scattering measurements.

A second possible explanation is that two-photon exchange (TPE) processes might differentiate betweenelectrons and muons. MUSE tests this possibility with measurements using both positive and negative beampolarities. The difference between the two beam polaritiesdirectly gives (the real part of) the two-photonexchange correction. Conventional estimates of TPE indicate these effects will be small; these estimates willbe tested.

A third possible explanation is that structure in the electromagnetic form factors lead to incorrect extrac-tions of the proton radius from scattering experiments, as well as corrections to the formulas that are usedto extract the proton radius from atomic physics measurements. MUSE tests this possibility with measure-ments that go to lowQ2, as low as 0.002 GeV2, with uncorrelated point-to-point uncertainties perhapsassmall as as few tenths of a percent.

The talk will include a description of the MUSE experimentalgoals and techniques and will report onthe test measurements planned for fall 2012 at PSI.

This work has been supported in part by the U.S. Department ofEnergy and National Science Foundation viagrants to the MIT Laboratory for Nuclear Science.

Towards a measurement of the 1S hyperfine splitting

in muonic hydrogen

Andrea VacchiNational Institute of Nuclear Physics (INFN), Trieste, Italy

Determining the Zemach radius of the proton by means of hyperfine spectroscopyof muonic hydrogen and comparing it to the value, obtained from hydrogen, thoughnot in position to resolve the ”proton size puzzle”, may be very helpful for its deeperunderstanding. The Zemach radius - i.e. the first moment of the convolution of thecharge and magnetic moment distributions of the proton - is related to the hyperfinesplitting in a S-state of a hydrogen-like atom through a linear relation similar to therelation between the charge r.m.s radius and the Lamb shift. The fact that the formerinvolves the less well known proton polarizability only sets restrictions on the accuracy ofthe Zemach radius value.

A few relevant steps have recently neared the realization of the long lasting effort tomeasure the hyperfine splitting in the ground state of muonic hydrogen and extract theZemach radius of the proton. Laser sources in the 6 micron range have been constructedand successfully used in spectroscopy, new approaches are under development. The fea-sibility and the achievable precision of the proposed experiment have been analyzed indetails. Present days pulsed muon sources are shown to have sufficient intensity to obtainan independent and improved accuracy value of the Zemach radius. The method consistsin comparing the time distribution of muon transfer events with and without laser pulseat resonance frequency.

Muonic hydrogen and MeV forces

Itay Yavin

Center for Cosmology and Particle Physics, Department of Physics,

New York University, New York, New York 10003, USA

In this talk I will discuss the possibility that a new interaction between muons and

protons is responsible for the discrepancy between the CODATA value of the proton radius

and the value deduced from the measurement of the Lamb shift in muonic hydrogen. A

new force carrier with roughly MeV mass can account for the observed energy shift as well

as the discrepancy in the muon anomalous magnetic moment. However, measurements in

other systems constrain the couplings to electrons and neutrons to be suppressed relative

to the couplings to muons and protons, which seems challenging from a theoretical point

of view. One can nevertheless make predictions for energy shifts in muonic deuterium,

muonic helium, and true muonium under the assumption that the new particle couples

dominantly to muons and protons.