ECT* Workshop on the Proton Radius Puzzle

Home , Polarizability

Book of Abstracts

October 29 - November 2, 2012

Trento, Italy

October 8, 2012

A. Afanasev R.J. Hill

J. Arrington M. Kohl

J.C. Bernauer I.T. Lorenz

A. Beyer J.A. McGovern E. Borie G.A. Miller M.C. Birse K. Pachucki P. Brax G. Paz J.D. Carroll R. Pohl C.E. Carlson M. Pospelov M.O. Distler B.A. Raue M.I. Eides S.S. Schlesser K.S.E. Eikema I. Sick A. Gasparian R. Gilman K.J. Slifer M. Gorchtein D. Solovyev K. Griffioen V. Sulkosky N.D. Guise A. Vacchi E.A. Hessels I. Yavin A. Afanasev Radiative corrections and two-photon effects for lepton-nucleon scattering J. Arrington Extracting the proton radius from low Q2 electron/muon scattering J.C. Bernauer The Mainz high-precision proton form factor measurement I. Overview and 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 scattering 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. Basic principles 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 Radius via 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 Howwellcananuclearchargeradiusbemeasuredwith low-Q2 electron scattering data? N.D. Guise Towards One-electron Ions in Rydberg States for a Rydberg Constant Determination Independent of the Proton Radius E.A. Hessels Progress towards a new separated-oscillatory-field microwave measurement of the atomic hydrogen n=2 Lamb shift R.J. Hill Model independent analysis of proton structure for hydrogenic bound states M.Kohl TheOLYMPUSexperimentatDESY 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 hydrogen at fourth order in chiral perturbation theory G.A. Miller Proton Polarizability Contribution: Muonic Hydrogen Lamb Shift and Elastic Scattering K. Pachucki Directions toward the resolution of the proton charge radius puzzle G. Paz Model independent extraction of the proton charge radius from electron 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 elastic scattering S.S. Schlesser Nuclear polarizability contribution to the Lamb shift in muonic helium I.Sick Protonrms-radiusandtailofdensity p K.J.Slifer TheJeffersonLab g2 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 hydrogen I. Yavin Muonic hydrogen and MeVforces 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 factor measurement I. Overview and results Jan 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 like the radius and charge distribution. In the talk, precise results from a measurement of the elastic electron-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 to Q2 = 1(GeV/c)2 with statistical errors below 0.2%. The electric and magnetic form factors of the proton 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

1 2 2 rE = 0.879(5)stat.(4)syst.(2)model(4)group fm,

1 2 2 rM = 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 experiments, which were updated to the same level of radiative corrections. A phenomenological model for two-photon-exchange contributions is used to account for the discrepancy between the results from unpolarized and polarized scattering experiments. A continuous, simultaneous ﬁt up to Q2 = 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. H¨anscha,b a Max Planck Institute of Quantum Optics, 85748 Garching b Ludwig Maximilian University, 80799 Munich ∗ [email protected]

The ’proton size puzzle’, i.e. the discrepancy between the values for the proton charge radius extracted from precision spectroscopy of atomic hydrogen and electron-proton- scattering on the one hand [1] and the 2S Lamb shift measurement in muonic hydrogen on the other [2], attracted great interest both of experimentalists and theoreticians for the last two years. Still, no convincing argument to explain or resolve this discrepancy could be found so far. Transition frequency measurements in atomic hydrogen with improved accuracy can help to solve this puzzle or at least to rule out hydrogen experiments as a possible source for the discrepancy. Furthermore, as soon as the puzzle will be resolved and a more accurate value for rp will be available, these measurements can provide stringent tests 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 of the one-photon 2S-4P transition frequency in atomic hydrogen: In contrast to previous measurements of 2S-nl transitions in other groups, our experiment is based on a cold thermal beam of hydrogen atoms optically excited to the metastable 2S state. The setup for the 2S excitation is the same as has successfully been used for the measurement of the 1S-2S transition frequency in our group and provides a reliable and well controlled source of 2S atoms [3]. In addition, the experiment benefits from technical advances, such as subhertz line width diode lasers both for 1S-2S and 2S-4P spectroscopy [4] or direct measurement of the absolute transition frequency via a frequency comb, which have not been available for older measurements. During 13 measurements days a total number of 11,652 individual line profiles for the 2S1/2-4P1/2 transition have been recorded, including 6 different velocity distributions of 2S atoms. The resulting statistical uncertainty of 0.8 kHz is more than one order of magnitude smaller than the one of the previous best measurement of this transition [5]. The study of systematic effects is underway and will be discussed in this talk.

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[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 accurately. 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 Scattering E. Borie Karlsruhe Institute of Technology, Institut für 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 proton radius puzzle. The proposal will directly test whether or not − p and e − p scattering are the same and will perform measurements with ± and e± at low Q2 in order to study the two-photon exchange contributions in greater detail. Since the muon is about 206.7 times heavier than the electron for the energies mentioned in the proposal, the muons are neither ultrarelativistic nor nonrelativistic. For the muon 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 for v/c very close to 1. Thus, the standard kinematics assumptions made in the analysis of e-p scattering will not all be valid in the case of an experiment on mu-p scattering at the proposed energies. A calculation of 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◦ to ◦ 2 2 2 2 2 100 , corresponding to Q in the range (0.01-0.1) (GeV/c) . For comparison, mµc = 0.01116(GeV/c) . 2 2 The radiative corrections to the scattering cross section are functions of Q /mµ, which is in the range of approximately 0.9-9.0. The usual formulas [3, 4], which assume that Q2/m2 ≫ 1, will not be accurate. This will be discussed. 2 Here m is the lepton rest mass, M is the target rest mass, and α = e /4π. p1 and p3 are the incoming and outgoing muon four-momenta, and p2 and p4 are the incoming and outgoing proton four-momenta. In ′ ′ the lab system we have p1 = (E, p) p3 = (E , p ), p2 = (M, 0), p4 = (M +ω, q). Here q = p1−p3 = p4−p2, ′ 2 2 2 and ω = q0 = E − E . It is useful to observe that q = 2m − 2p1 p3 = 2M − 2p2 p4 = −2Mω. The proton current is taken to have the usual on-shell form, characterized by

ν 2 2 iσµν q Γ = F1(q )γ + κF2(q ) µ µ 2M Here κ is the anomalous magnetic moment of the proton. The so-called Sachs form factors are related to Q2 F1 and F2 by G = F1 + κF2, G = F1 − κF2. M E 4M 2 The ﬁnal result for the cross section is given by

dσ α2 p′/p (4EE′ + q2) = G2 dΩ′ q4 1 + (E − pE′/p′ cos θ)/M h E 1 − q2/4M 2 4 2 2 (1) 2 ′ 2 1 q q m + G (4EE + q ) 1 − + + M 1 − q2/4M 2 2M 2 M 2 i

2 In the limit of very high lepton energies, one has p ≈ E, p′ ≈ E′, q2 ≈−4EE′ sin (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 Théorique, CEA, IPhT, CNRS, URA2306, F-91191 Gif-sur-Yvette cédex, France 2 Départment de Physique Théorique, Universitéde Genève, 24 Quai E. Ansermet, CH-1211, Genève, Switzerland 3 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 measurements 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 energy 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.

∗[email protected] †[email protected] New Physics and the Proton Radius Problem

Carl E. Carlson Physics Department College of William and Mary Williamsburg, VA 23187, USA

The recent disagreement between the proton charge radius extracted from Lamb shift measurements of muonic and electronic hydrogen invites speculation that new physics may be to blame. Several proposals have been made for new particles that account for both the Lamb shift and the muon anomalous moment discrepancies. We explore the possibility that new particles’ couplings to the muon can be fine-tuned to account for all experimental constraints. We consider two fine-tuned models, the first involving new particles with scalar and pseudoscalar couplings, and the second involving new particles with vector and axial couplings. The couplings are constrained by the Lamb shift and muon magnetic moments measurements while mass constraints are obtained by kaon decay rate data. For the scalar-pseudoscalar model, masses between 100 to 200 MeV are not allowed. For the vector model, masses below about 200 MeV are not allowed. The strength of the couplings for both models approach that of electrodynamics for particle masses of about 2 GeV. New physics with fine tuned couplings may be entertained 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; Källen-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: [email protected] The Mainz high-precision proton form factor measurement II. Basic principles and spin-offs

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

An unprecedented amount of more than 1400 cross section data points have been collected in the course of the Mainz high-precision proton form factor measurement [1]. For the first time this allowed the super Rosenbluth method to be applied to the data where a selection of different form factor models were directly fitted to the measured cross sections in order to extract the electric and magnetic form factors. In the talk a number of details of the Mainz analysis will be discussed, like the importance of the Rosenbluth formula, the relevance of the normalization parameters, and the choice of the form factor models used. Also, the interpretation of the Mainz data requires a deeper insight of the statistical methods involved. To this end the basic concepts of estimation and the construction of confidence intervals and error bands will be reviewed. A number of suggestions have been made to resolve the proton radius puzzle by using exotic form factor models. Those proposals will be discussed regarding their implications for the charge distribution [2]. The Mainz collaboration will continue to investigate the proton radius discrepancy. New proposals will be presented to measure the charge form factor of the proton at very low q2 using the initial state radiation (ISR) method and to measure the charge (C0) form factor of the deuteron at low q2.

References

[1] J. C. Bernauer et al. [A1 Collaboration], “High-precision determination of the electric 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 the Proton and Zemach Moments,” Phys. Lett. B 696 (2011) 343 [arXiv:1011.1861 [nucl-th]]. Weak Interaction Contributions in Light Muonic Atoms

Michael I. Eides Department of Physics and Astronomy, University of Kentucky Lexington, KY 40506, USA

Weak interaction contributions to hyperﬁne splitting and Lamb shift in light electronic and muonic atoms are calculated. We notice that correction to hyperﬁne splitting turns into zero for deuterium. Weak correction to the Lamb shift in hydrogen is additionally 2 suppressed in comparison with other cases by a small factor (1 − 4 sin 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: [email protected]

In view of the "proton radius puzzle"1,2 it is very interesting to perform precision spectroscopic 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 developed 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 1 absolute frequency measurements at the shortest wavelength to date (51 nm, on the 1 S0 - 4,5 1 P1 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 ep Scattering Method

A. Gasparian1 North Carolina A&T State University, USA

Abstract

We are preparing a novel high precision magnetic-spectrometer-free experiment to measure the proton charge radius via ep elastic cross sections at very low four-momentum transfer squared, Q2, from 10−4 to 10−2 (GeV/c)2 range at Jefferson Laboratory. This experiment will use a high resolution crystal calorimeter to reach the extreme forward scattering angles together 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 QED process, 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 allow for a sub-percent and essentially model independent extraction of the proton charge radius for the first time in ep scattering experiments. This experiment, with its independent novel approach and projected precision, will have a direct potential to either significantly shift the current value of the proton radius, or question the sufficiency of QED calculations in the muonic hydrogen experiment, or probe new physics beyond the Standard Model. Thereby, this experiment will have a direct impact on the “proton charge radius puzzle” currently developing in hadronic and atomic physics. The description and the current status of the experiment 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 f¨ur Kernphysik, Johannes Gutenberg-Universit¨at, 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 deuterium 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 [email protected] †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 Fig. 1. Time-of-flight signal of ions ejected from a compact interest is the fact that the Rydberg constant is the leading Penning trap, for two ion storage times after capturing bare neon source of uncertainty in this regime—about a factor of 100 nuclei: (a) 1 ms storage time; and (b) 2 s storage time, showing larger than the uncertainty due to other constants. production of lower charge states by electron capture from residual Consequently, one-electron ions in Rydberg states can background gas. enable a Rydberg constant determination that is independent ACKNOWLEDGEMENT of the proton radius if sufficiently precise measurements can The work of N. D. Guise at NIST was supported in part be realized for comparison with prediction. Such effort by a Research Associateship Award from the U.S. National could potentially provide useful information to help resolve Research Council. the proton radius puzzle [5]. REFERENCES We report on progress made at NIST towards the goal of [1] R. Pohl, et. al. , “The size of the proton,” Nature , vol. 466, pp. 213-218, July 2010. forming one-electron ions in Rydberg states that can be [2] P. J. Mohr, B. N. Taylor and D. B. Newell, “CODATA probed accurately using optical frequency metrology. Bare recommended values of the fundamental physical constants,” nuclei created in an EBIT were recently extracted and Rev. Mod. Phys. , vol. 80, pp. 633-730, June 2008. captured in a novel compact Penning trap [6], as illustrated [3] U. D. Jentschura, P. J. Mohr, J. N. Tan and B. J. Wundt, in Figure 1. The architecture of this ion trap was designed to “Fundamental constants and tests of theory in Rydberg states of hydrogenlike ions,” Phys. Rev. Lett. , vol. 100, p. 160404, facilitate experiments with controlled recombination and April 2008. laser spectroscopy. To produce one-electron ions in [4] U. D. Jentschura, P. J. Mohr and J. N. Tan, “Fundamental Rydberg states, the experimental apparatus will allow constants and tests of theory in Rydberg states of one-electron electron transfer from an excited atom to a bare nucleus ions,” J. Phys. B: At. Mol. Opt. Phys ., vol. 43, p. 074002, stored in an ion trap. For nuclear charge in the range 1 < Z < March 2010. [5] U. D. Jentschura, “Lamb shift in muonic hydrogen—II. 11, it is possible to find many E1 transitions between Analysis of the discrepancy of theory and experiment,” Rydberg states in the optical domain accessible to an optical Annals Phys. , vol. 326, p. 516-533, February 2011. frequency comb synthesizer [3]. Other applications include [6] J. N. Tan, S. M. Brewer and N. D. Guise, “Penning traps with spectroscopic studies of highly-charged ions of special unitary architecture for storage of highly charged ions,” Rev. Sci. Instrum. 83 , 023103 (2012). 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.

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 of low-energy lepton-hadron interactions. Using this motivation we develop modern effective field theory tools to systematically analyze nuclear structure effects in atomic bound states. The NRQED Lagrangian is constructed through order 1/M 4. Model independent relations between lepton-nucleon scattering measurements and bound state observables are derived. Model-dependent assumptions in previous analyses of the muonic hydrogen Lamb shift are isolated and sensitivity to poorly constrained hadronic structure parameters 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/M 4”, in preparation . The OLYMPUS experiment at DESY 1 Michael Kohl Hampton University and Jeﬀerson Lab for the OLYMPUS Collaboration

Abstract Two-photon exchange is believed to be responsible for the different findings for the proton electric to magnetic form factor ratio with the Rosenbluth and polarization transfer methods. If this explanation is cor- rect, one expects significant differences in the lepton-proton cross sections between positrons and electrons. The OLYMPUS experiment at DESY in Hamburg, Germany was designed to measure the ratio of unpolarized positron-proton and electron-proton elastic scattering cross sections over a wide kinematic range with high precision, in order to quantify the effect of two-photon exchange. The experiment uses intense beams of electrons and positrons stored in the DORIS ring at 2.0 GeV interacting with an internal windowless hydrogen gas target. The current status of OLYMPUS will 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 respects the constraints from analyticity and unitarity on the nucleon structure [1]. We also perform a continued fraction p +0.01 analysis of these data. We ﬁnd a small electric proton charge radius, rE = 0.84−0.01 fm, consistent with the recent determination from muonic hydrogen measurements and earlier dispersive analyses. We also extract p +0.01 the proton magnetic radius, rM = 0.86−0.02 fm, consistent with earlier determinations based on dispersion relations and continued fractions. p Making use of a conformal mapping combined with the recent Mainz data we conﬁrm our small rE -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 hydrogen at fourth order in chiral perturbation theory

Michael C. Birse and Judith A. McGovern School 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 value that differs by about 5 standard deviations from the CODATA value [2] and from the results of recent electron scattering experiments [3]. However before concluding that new physics is required, it is essential to examine carefully any possible conventional explanations. One place where some theoretical uncertainty remains is the contribution 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 the spin-averaged amplitude for forward doubly-virtual Compton scattering (V2CS) [4]. This comprises two tensor structures: qµqν 1 p · q p · q T µν = −gµν + T (ω, Q2) + pµ − qµ pν − qν T (ω, Q2), (1) q2 1 M 2 q2 q2 2 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 amplitudes 2 T1,2(ω, Q ) from the corresponding structure functions measured in inelastic electron scattering. These parts of the 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 a 2 2 dependence on the unmeasured amplitude T1(0,Q ). The slope of this term at Q = 0 is given by a low-energy theorem (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 using the 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 the 2 slope of T1(0,Q ) and suggested that off-shell form-factors of the proton could generate new large polarisability contributions to V2CS. In this work [18] we re-examine the derivation of the LET to clarify that β does indeed govern the slope of the “structure” part, and we discuss how the LET is embodied in nonrelativistic effective field theories such as heavy-baryon chiral perturbation theory (HBChPT). To obtain a model-independent result for the form of 2 2 T1(0,Q ) at low Q , we calculate it within HBChPT to fourth order, including effects of the ∆ up to fifth order in “δ-counting” [13]. Since the contribution ∆Esub of this amplitude to the Lamb shift is dominated by the low-momentum region, this can significantly reduce the theoretical uncertainty in this quantity. This extends work 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 no room for any large additional polarisability eﬀect arising from oﬀ-shell form factors, and we see no sign of any rapid 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. Bernab´euand R. Tarrach, Ann. Phys. 102, 323 (1976) [5] J. Bernab´euand 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 unexplained. It looks that the muon-proton and the electron-proton interactions have a diﬀerent low energy limit, in contradiction to the universality of electromagnetic interactions. 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 Physics The University of Chicago, Chicago, Illinois, 60637, USA bDepartment of Physics and Astronomy Wayne State University, Detroit, MI 48201, USA

Abstract

Scattering data allows us to directly extract the charge radius of the proton from the slope of the proton electric form factor. Over the last 50 years there has been many such extractions with values almost anywhere in the range of 0.8−0.9 fm. Since the functional form of the form factor is unknown, all of these extractions rely on model dependent assumptions on the shape of the form factor. In [1], we have shown how to address this problem. By using analyticity constraints we provide a systematic procedure for analyzing arbitrary data without model-dependent assumptions. It also allows us to include electron-neutron scattering data, and ππ → NN¯ data to improve the precision on the charge radius while maintaining model-dependence. p Using representative datasets we ﬁnd rE = 0.870 ± 0.023 ± 0.012 fm using just proton p +0.017 p scattering data; rE = 0.880−0.020 ± 0.007 fm adding neutron data; and rE = 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 of the same method to the extraction of the magnetic radius of the proton, whose value also 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 determined the Lamb shift [1] and the 2S hyperfine splitting [2] in muonic hydrogen. The 2nd transition in µp confirms the proton charge radius obtained in [1] and reinforces the “proton radius puzzle”. In addition, a value of the Zemach radius is extracted from the 2S hyperfine splitting in µp which is in agreement with previous values.

In muonic deuterium µd, we have measured three 2S-2P transitions. Both, Lamb shift and 2S hyperﬁne splitting are determined from experiment. Large deuteron polarizability contributions 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 to manifest itself in the Lamb shift of the muonic atoms. I attempt to build a self-consistent model of muon-specific forces and show that the chiral structure of the Standard Model makes it an exceedingly difficult task. The scalar force mediator is in immediate trouble due to the constraints from the meson decay. The vector force has to avoid coupling to neutrino fields, and thus almost inevitably would have to be coupled to the right-handed muon currents. I demonstrate that the gauged µR model with O(10 MeV) mediator, despite a number of theoretical issues within its structure, is nevertheless not excluded by any of the existing experiments. The parameters of the model that suit the muonic hydrogen Lamb shift measurement are determined. If taken seriously, the model implies the existence of large parity-violating effects in neutral currents for muons that imply the strength of the interaction much larger than Fermi constant GF . Incidentally, there are no tests of parity in neutral currents perfmored with muons at low energy. I show that one possible avenue for testing large parity violation for muons is the investigation of angular asymmetry in 2S −1S transition for Z ∼ 30 muonic atoms that are obtained through the process of atomic radiative capture (ARC) of muons directly into low-lying atomic S states. Neither the ARC process nor the 2S − 1S was ever observed in any muonic atom. The existing facilities at TRIUMF, PSI and J-PARC are well suited for observing the in-flight capture, the 2S − 1S transition and for directly testing the gauged 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. Raue Department of Physics, Florida International University, Miami, United States of America

Two photon exchange (TPE) has been proposed as the primary source of the discrepancy between Rosenbluth and polarization-transfer methods of determining the electric- to-magnetic form-factor ratio of the proton. A direct measurement of the TPE contribution to elastic scattering can be determined by measuring the lepton-proton elastic σ(e+p) scattering ratio R = 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 E08-007 Proton Electromagnetic Form Factor Ratio at Low Q2

G. Ron Hebrew University of Jerusalem

Electromagnetic form factors of the nucleon are model-independent observables which encode our ignorance of its complex internal structure. In recent years significant attention has been drawn to these observables due to the discovery of unexplained deviations from previously measured results as well as a striking discrepancy between the proton charge radius as measured by electron scattering and atomic hydrogen Lamb shift with that measured by muonic hydrogen Lamb shift. Recoil polarization measurements and high precision cross section measurements are allowing the electric to magnetic form factors ratios be determined with unprecedented precision, a recent set of measurement was by Jefferson Lab experiment E08-007. While these measurements provide important insight into the proton form factors at low Q2 they cannot extend to very low Q2 since the recoil proton cannot be detected at this range of momentum transfer. An alternative technique, using beam-target asymmetry promises to allow measurement to extremely low Q2 values since it does not require detection of the proton. The second part of JLab experiment E08-007, using beam-target asymmetry 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 uncertainties. I will discuss the current status of the proton form factor measurements, with emphasis on the new E08-007 results under analysis and their potential to 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 µ3He. 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 developed 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 Sick Dept. of Physics, University of Basel, Basel, Switzerland Email: [email protected]

The proton rms-radius R is extracted in general from a fit of the e-p scattering data using suitable parameterizations of the electric Sachs form factor 2 Ge(q), with the slope at q = 0 yielding the radius R. A generic difficulty results from the fact that the slope is not measured at q2 =0 but extrapolated from q ∼ 1fm−1 where the finite-size effect 1 − G(q2) ∼ q2R2/6+ ... is large enough to be measured with satisfactory precision and where higher moments of the density still give a small contribution. The ’extrapolation’ to q2 =0 via the parameterization of Ge(q) then causes a model dependence, and can lead to erroneous results if the parameterization implies an unphysical behavior of ρ(r) at large radii r leading to structure of the fitted Ge(q) at q

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 experimental program, the inclusive nucleon structure functions have been well p determined, with the exception being g2 which is relatively unknown. p The Jefferson Lab E08-027 experiment measured g2 in the resonance region 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 p nucleon spin polarizabilities, but a precise determination of g2 is also important 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, Russia b St. Petersburg Branch of Special Astrophysical Observatory, Russian Academy of Sciences, 196140, St. Petersburg, Russia c 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) properties via the space telescopes require a significant increase in the accuracy of theoretical research. For the precise astrophysical calculations the detailed description of multiphoton emission/absorption processes is required [1]-[3]. The problem of the evaluation of the two-photon decay width of excited states in hydrogen is considered [4]. As application the two-photon decay channels for the 3s level of the hydrogen atom are evaluated, including the cascade transition probability 3s − 2p − 1s. The dependence on the principal quantum number (n) of the initial state is investigated. The E1E1, E2E2, M1M1 and E1M2 decay 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 studied also the hydrogen atom in an external photon fields. Field characteristics are defined from conditions which correspond to the recombination era of universe. Approximation of three-level atom is used for the description of ”atom - fields” interaction. It is found that the electromagnetically induced transparancy phenomena take a place in hydrogen recombination epoch in early universe.The additional terms to the optical depth in definition of Sobolev escape probability on the level about 1% are found [7], [8].

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[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 of µp and ep scattering. The puzzle is the difference between the proton radius measurements from atomic hydrogen and electron scattering vs. radius measurements using muonic hydrogen. While measurements of µp scattering have been done, there are no high-precision low-Q2 µp scattering data that would allow a reliable extraction of the 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 generally accepted. One general issue in ﬁnding an explanation is that the muonic hydrogen measurement should be much more precise and reliable, but the various independent ep radius measurements get consistent results. It is an odd, though possible, situation if the different types of ep 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 most interesting possible explanation is that novel physics violates lepton universality so that the µp and ep interactions are not equivalent. MUSE tests this possibility with simultaneous measurements with a mixed µ and e beam of the scattering cross sections, leading to precise relative cross sections. This will also allow a precise comparison of the relative radius from the scattering measurements. A second possible explanation is that two-photon exchange (TPE) processes might differentiate between electrons and muons. MUSE tests this possibility with measurements using both positive and negative beam polarities. The difference between the two beam polarities directly gives (the real part of) the two-photon exchange correction. Conventional estimates of TPE indicate these effects will be small; these estimates will be tested. A third possible explanation is that structure in the electromagnetic form factors lead to incorrect extractions of the proton radius from scattering experiments, as well as corrections to the formulas that are used to extract the proton radius from atomic physics measurements. MUSE tests this possibility with measurements that go to low Q2, as low as 0.002 GeV2, with uncorrelated point-to-point uncertainties perhaps as small as as few tenths of a percent. The talk will include a description of the MUSE experimental goals and techniques and will report on the test measurements planned for fall 2012 at PSI. This work has been supported in part by the U.S. Department of Energy and National Science Foundation via grants to the MIT Laboratory for Nuclear Science. Towards a measurement of the 1S hyperﬁne splitting in muonic hydrogen

Andrea Vacchi National Institute of Nuclear Physics (INFN), Trieste, Italy

Determining the Zemach radius of the proton by means of hyperfine spectroscopy of muonic hydrogen and comparing it to the value, obtained from hydrogen, though not in position to resolve the ”proton size puzzle”, may be very helpful for its deeper understanding. The Zemach radius - i.e. the first moment of the convolution of the charge and magnetic moment distributions of the proton - is related to the hyperfine splitting in a S-state of a hydrogen-like atom through a linear relation similar to the relation between the charge r.m.s radius and the Lamb shift. The fact that the former involves the less well known proton polarizability only sets restrictions on the accuracy of the Zemach radius value. A few relevant steps have recently neared the realization of the long lasting effort to measure the hyperfine splitting in the ground state of muonic hydrogen and extract the Zemach radius of the proton. Laser sources in the 6 micron range have been constructed and successfully used in spectroscopy, new approaches are under development. The feasibility and the achievable precision of the proposed experiment have been analyzed in details. Present days pulsed muon sources are shown to have sufficient intensity to obtain an independent and improved accuracy value of the Zemach radius. The method consists in comparing the time distribution of muon transfer events with and without laser pulse at 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.