Nuclear charge radii and polarizabilities from laser spectroscopy of light muonic atoms

• Randolf POHL (Johannes Gutenberg Universität Mainz, Germany)

Room: Amphi Charpak

The proton radius from electron scattering measurements (and other thoughts about form factors)

• Jan C. BERNAUER (Stony Brook University and RIKEN-BNL Research Center)

Room: Amphi Charpak In the talk, I will review the scattering side of the proton radius puzzle, starting from the original Mainz experiment. I will discuss the results from recent experiments and describe my view of the current situation with regard to the electric and magnetic radii of the proton. The talk will close with an outlook of planned scattering experiments.

Hydrogen atom spectroscopy at Colorado State University

• Dylan YOST (Colorado State University, CO, USA)

Room: Amphi Charpak In this talk, I will discuss a new measurement of the hydrogen 2S1/2-8D5/2 two-photon transition performed in our group, which produces additional tension within the global dataset of precision hydrogen spectroscopy. In addition, I will present new results where we load a metastable hydrogen beam into a moving optical lattice, which we then decelerate to control the motion of the atoms. This technique offers a robust means to slow atomic hydrogen with visible lasers, which could provide a platform for increased precision.

Precision spectroscopy of atomic hydrogen and deuterium at Max-Planck-Institute for Quantum Optics (MPQ), Garching

• Vitaly WIRTHL (Max-Planck-Institute for Quantum Optics, Garching)

Room: Amphi Charpak

1S-3S spectroscopy of deuterium atoms

• Pauline YZOMBARD (Laboratoire Kastler Brossel, Sorbonne Université, ENS, Collège de France)

Room: Amphi Charpak I will present the 1S-3S spectroscopy campaign we carried on Deuterium atoms during the winter 2020, using our home-made CW 205 nm laser. I will show for the first time a new systematic effect that we have recently lifted concerning our old atomic beam. I will present the latest analysis results that are still ongoing.

The present and future of the PRad experiment at Jefferson Lab

• Ashot GASPARIAN (North Carolina Agricultural and Technical State University, Greensboro, NC, USA)

Room: Amphi Charpak

Elastic electron-proton scattering and proton radius

• Egle TOMASI-GUSTAFSSON (CEA Saclay / Irfu / DPhN - Université Paris-Saclay)

Room: Amphi Charpak Recent electron-proton elastic scattering data are reanalyzed in terms of discrete derivatives. The pertinence of elastic scattering process is discussed in view of a very precise extraction of the proton radius.

Theory of light hydrogenlike atoms: status and perspectives

• Krzysztof PACHUCKI (University of Warsaw, Poland)

Room: Amphi Charpak

Dispersive analysis of the nucleon electromagnetic form factors

• Ulf-G. MEISSNER (Universität Bonn & Forschungszentrum Jülich, Germany)

Room: Amphi Charpak

Radiative corrections for proton radius measurements

• Andrei AFANASEV (George Washington University, USA)

Room: Amphi Charpak

Nucleon radial density moments

• Mostafa HOBALLAH (IJCLab Orsay, CNRS/IN2P3, Université Paris-Saclay, France)

Room: Amphi Charpak

Muonic hydrogen ground-state hyperfine splitting: CREMA status report

• Aldo ANTOGNINI (ETH Zurich and Paul Scherrer Institut (PSI), Switzerland)

Room: Amphi Charpak The CREMA collaboration at the Paul Scherrer Institute is aiming at the measurement of the ground-state hyperfine splitting in muonic hydrogen (μp) with an accuracy of 1 ppm to extract the two-photon- exchange contribution with a relative accuracy of 10−4. From this both the Zemach radius and the inelastic contribution can be obtained. The principle of the μp HFS experiment is presented together with the progress of the development needed to perform this experiment.

The FAMU experiment: present status (amid Brexit, pandemic, accelerator long shutdown, and war)

• Emiliano MOCCHIUTTI (INFN Trieste, Italy)

Room: Amphi Charpak The main goal of the FAMU experiment is a high precision laser spectroscopy measurement of the ground state of the muonic hydrogen. From the measurement of the muonic hydrogen ground state hyperfine splitting, precise information about the magnetic structure of the proton can be extracted. Even though we are passing through hard times, the preparation work did not stop. In this contribution, the status of the FAMU experiment will be presented, spanning from the data analysis of the transfer rate measurements to the present setup of the whole experiment. Finally, an overview of the analysis planned for the data taking, scheduled by the end of this year, will be given.

Muonic atom spectroscopy at J-PARC: the Zemach radius measurement and studies on related dynamical processes.

• Sohtaro KANDA (KEK, Japan)

Room: Amphi Charpak The muonic atom, a bound state of negative muon and nucleus, has a small orbital radius compared to an ordinary atom. Therefore, muonic atoms are a highly sensitive probe for the interaction between muon and nucleus. While the discrepancy between the charge radii of protons measured by several independent methods has received much attention, knowledge of what happens to the Zemach radius has been relatively limited. In particular, the determination of the proton Zemach radius by spectroscopy of the muon hydrogen's hyperfine structure is an exciting attempt to shed light on the "puzzle" from a different angle. At J-PARC MLF MUSE, a laser spectroscopy experiment of muonic hydrogen HFS is under preparation. Understanding various dynamical processes involving muonic atoms is essential in successful spectroscopy. In this talk, We will introduce the preparation status of the experiment and the surrounding topics.

Nuclear structure corrections in muonic atoms

• Simone Salvatore LI MULI (Johannes Gutenberg Universität Mainz, Germany)

Room: Amphi Charpak Abstract: Nuclear polarizability effects account for the largest source of the uncertainty in the calculation of the Lamb-shift in muonic atoms. Combining advanced few-body techniques and effective field theories developed for studies of nuclear structures and reactions, we are able to provide precise determinations of these effects and to reliably quantify the associated uncertainties. I will review our recent calculations and present an outlook for the future.

The proton radius from effective field theories

• Clara PESET (Universidad Complutense de Madrid, Spain)

Room: Amphi Charpak Effective field theories (EFTs) are exceptionally suited to define and determine the proton radius and its relatives from low energy observables. They not only provide a unified and unambiguous definition of the low energy constants that naturally includes electromagnetic corrections, but they also yield a robust determination of the theoretical uncertainty. In this talk, I will present the effective field theory that allows us to extract the proton charge radius from spectroscopic measurements. As an application, I will review the determination of the proton radius from measurements of the Lamb shift in regular and muonic hydrogen, emphasizing the importance of the EFT framework.

Theoretical status of scattering and spectroscopy measurements of Rp

• Vladimir PASCALUTSA (Johannes Gutenberg Universität Mainz, Germany)

Room: Amphi Charpak

Towards High-Precision Spectroscopy of the 1S–2S Transition in He+

• Akira OZAWA (Max-Planck-Institute of Quantum Optics, Garching, Germany)

Room: Amphi Charpak The energy levels of hydrogen-like atoms can be precisely described by bound-state quantum electrodynamics (QED). The frequency of the narrow 1s-2s transition of atomic hydrogen has been measured with a relative uncertainty below 10−14. When combined with other spectroscopic measurements of hydrogen and hydrogen-like atoms, the Rydberg constant and the proton charge radius can be determined. Comparing the physical constants extracted from different combinations of measurements serves as a consistency check for the theory [1]. Hydrogen-like He+ ion is yet another interesting spectroscopy target for testing QED. Due to their charge, He+ ions can be held near-motionless in the field-free environment of a Paul trap, providing ideal conditions for high precision measurement. Interesting higher-order QED corrections scale with large exponents of the nuclear charge, which makes this measurement much more sensitive to these corrections compared to the hydrogen case. We are currently setting up an experiment to perform precise spectroscopy of the He+ 1S–2S transition [2]. The main challenge of the experiment is that driving the 1S–2S transition in He+ requires narrow-band radiation at 61 nm. This lies in the extreme ultraviolet (XUV) spectral range where no continuous wave laser sources exist. Our approach is to use two-photon direct frequency comb spectroscopy with an XUV frequency comb. The XUV comb is generated from an infrared high power frequency comb using intracavity high harmonic generation. The spectroscopy target will be a small number of He+ ions, which are trapped in a linear Paul trap and sympathetically cooled by co-trapped Be+ ions. In this talk, we will present our recent progress in developing XUV frequency comb and Paul-trap for high-precision spectroscopy of He+ 1S–2S transition. [1] Th. Udem. Nat. Phys. 14, 632 (2018). [2] M. Herrmann et al., Phys. Rev. A 79, 052505 (2009).

Towards Ramsey-Comb Spectroscopy of the 1S-2S Transition in He+

• Elmer GRÜNDEMAN

Room: Amphi Charpak Simple systems are an ideal probe to test fundamental physics. At the LaserLaB at the Vrije Universiteit Amsterdam we study several of these systems. One of our goals is to measure the 1S-2S transition in singly-ionized helium with 1 kHz accuracy. Since He+ has twice the nuclear charge of hydrogen, some interesting QED contributions are strongly enhanced and can therefore be tested more precisely. Furthermore nuclear properties such as e.g. the alpha particle charge radius or nuclear polarizability contributions can also be probed. We want to measure the extreme ultraviolet (XUV) 2-photon 1S-2S transition in He+ via Ramsey-comb spectroscopy (RCS). RCS uses two amplified and up-converted pulses from a frequency comb to perform a Ramsey-like excitation. We will excite the two-photon transition with a fundamental photon at 790nm and its 25th harmonic at 32nm. In this talk I will give an update on the status of the He+ experiment, and I will show some of the latest results on the isotope shift measurements in neutral helium.

High-precision spectroscopy of hydrogen molecules

• Maximilian BEYER (Amsterdam VU, The Netherlands)

Room: Amphi Charpak Molecular hydrogen and its ion are the simplest of all molecules and as such are important systems for the development of molecular quantum mechanics. The rovibrational energy level structure of these one- and two-electron systems can be calculated extremely precisely by quantum-chemical methods which include the determination of relativistic and QED effects. By comparison with the results of laser precision measurements of rovibronic intervals, fundamental constants or particle properties, such as the proton-to-electron mass ratio or the proton size, could be determined. I will give an overview of various precision measurements involving the ground and excited electronic states of molecular hydrogen and its isotopologues, leading to the determination of the dissociation and ionization energy and the H+H scattering length. Moreover, I will show how highly excited electronic states of molecular hydrogen can be used to selectively prepare the molecular ions in exotic states, which show an enhanced sensitivity to the proton-to-electron mass ratio and ortho-para mixing.

Measuring Charge Radii with High-Energy Particle Beams

• Stephan PAUL (Technische Universität München, Germany)

Room: Amphi Charpak The determination of the proton charge radius has so far been the domain of low energy experiments. The radius has been extracted from either elastic electron scattering or through line shifts measured by atomic laser spectroscopy. With the persistent mismatch of experimental results originating from various techniques and experiments, new probes have been advertised. The AMBER experiment at CERN is set to study elastic muon proton scattering at very high energies. This offers very different scattering kinematics, and such a measurement can charm through small distortions owing to both multiple scattering and radiative corrections. High energy particle beams, however, can also be used to access the charge radius of unstable particles. The scattering of kaons and pions on electrons follows inverse kinematics and the sensitivity to the charge distributions is limited by the beam energy. With a modern spectrometer we can much improve on previous measurements. We will discuss the different measurement strategies and also project to a possible experiment with high energy protons.

Status of the MUSE experiment

• Tigran ROSTOMYAN (Paul Scherrer Instute (PSI), Switzerland)

Room: Amphi Charpak The Paul Scherrer Institute MUSE experiment was created a decade ago in response to the Proton Radius Puzzle, the difference observed between muonic hydrogen measurements of the proton radius and the existing electronic measurements. MUSE simultaneously scatters electrons and muons from hydrogen, alternating between beam polarities, to directly compare the cross sections and form factors with each probe, and to determine the proton radius for each reaction. The comparison of the + and - beam polarities probes Two-Photon Exchange (TPE). MUSE aims to measure sub-percent-level cross sections, providing electron scattering data at a level similar to other high-precision experiments, muon scattering data an order of magnitude better than previous measurements, and two-photon exchange measurements several times better than any others up to now. To date, MUSE has commissioned its experimental systems to the level needed for the measurements and performed a careful studies of the electron and muon beam properties in the PiM1 channel. In 2021 we obtained a high statistics scattering data set at +/-115 MeV/c. We are currently working on some technical upgrades, analysis, and preparing to obtain production data this fall.

Proton Radius experiment at MESA

• Sören SCHLIMME (Johannes Gutenberg Universität Mainz, Germany)

Room: Amphi Charpak The MAGIX spectrometer setup at the high-intensity electron accelerator MESA will be ideally suited to perform precision measurements of the proton form factors at small four-momentum transfers, reaching below Q^2=0.0001 GeV^2. The key element to the success of this type of experiment, aimed at a precise determination of the proton charge radius, is the absence of a target cell and the very low target density compared to a liquid target, minimizing the irreducible background and the effects of energy loss and multiple scattering. In this talk, I will present the basic concept as well as the status of preparations for this proton radius experiment at MESA.

Current status of the ULQ2 experiment

• Yuki HONDA (Research Center for Electron Photon Science, Tohoku University, Japan)

Room: Amphi Charpak The ULQ2 (Ultra Low Q2) experiment at ELPH is aiming at determining the proton charge radius with the electron scattering. The features of the ULQ2 experiment are as follows: absolute cross section measurement with very high accuracy of 0.001 using relative measurement of e+p and e+C, measurement at extremely low momentum transfer region of 0.0003 ≤ Q2 ≤ 0.008 (GeV/c)2 with lowest-ever beam energies of 10 - 60 MeV, and experimental separation of charge and magnetic form factor (Rosenbluth separation). Such measurements can remove model dependence as much as possible and obtain the most reliable proton radius for electron scattering. A new beam line and spectrometers specially designed for the low-energy electrons scattering have been constructed, and commissioning is ongoing for physics run starting in FY2022. In this talk, the details and preparation status of the ULQ2 experiments will be presented.

Precision spectroscopy at York University, Canada

• Eric HESSELS (York University, Toronto, Canada)

Room: !!! New room: LPNHE Seminar room The n=2 atomic hydrogen Lamb shift has been measured [1]. An update on this measurement (since it was first announced at the proton radius meeting in Mainz) will be given, including an explanation of the published uncertainty -- which is smaller than that announced in Mainz. Continuing measurements at York of helium fine-structure and of the electron electric dipole moment will also be discussed. [1] N Bezginov, T Valdez, M Horbatsch, A Marsman, AC Vutha and EA Hessels, A measurement of the atomic hydrogen Lamb shift and the proton charge radius, Science 365, 1007 (2019).

Precision spectroscopy of molecular hydrogen ions: Relevance to determination of nuclear properties

• Stephan SCHILLER (Heinrich Heine Universität, Düsseldorf)

Room: LPNHE Seminar room Molecular hydrogen ions (MHI), the simplest molecules, are three-body quantum systems composed of two simple nuclei and one electron. They are of high interest for fundamental physics and metrology because they provide the missing link between the fields of mass and g-factor measurements with Penning traps and spectroscopy of hydrogen-like atoms. Similar to s-states in the hydrogen atom, the rovibrational energy levels of the MHI are shifted by the interaction between the sole electron and the finite-size nuclei because the electron's wavefunction is nonzero at the nuclei's positions. The shift can be calculated accurately [1]. Additionally, in states with nonzero rotational angular momentum, there occurs a shift due to the finite electric quadrupole moment of the deuteron. This shift is embedded in the hyperfine structure of rovibrational transitions. Both above shifts cannot be measured directly in a simply way; they may be extracted from experimental data with the help of highly precise calculations of QED corrections to the rovibrational energies and of a precise theory of the hyperfine structure [2,3], respectively. Moreover, the results of precision experiments on other systems are required [4,5,6]. We discuss some of our results on this topic as well as the potential and the challenges for increased precision of the determination of charge radii and quadrupole moments in the coming years. [1] D. T. Aznabayev et al., Phys. Rev. A 99, 012501 (2019) [2] D. Bakalov et al., Phys. Rev. Lett. 97, 243001 (2006) [3] S. Alighanbari et al., Nature 581, 152 (2020) [4] M. Germann et al., Phys. Rev. Research 3 L022028 (2021) [5] I. V. Kortunov et al., Nat. Phys. 17, 569 (2021) [6] S. Alighanbari et al., subm.

Precision measurements of the ionization energies of the two-electron systems He and H2

• Frédéric MERKT (ETH Zürich, Switzerland)

Room: LPNHE Seminar room Recently, considerable progress has been made in the calculation of the energy level structures of the two-electron systems He and H2. Patkóš, Yerokhin, and Pachucki have performed the first complete calculation of the Lamb shift of the helium 2 3S1 and 2 3PJ triplet states up to the term in a7m [1]. Whereas their theoretical result for the frequency of the 2 3P - 2 3S transition perfectly agrees with the experimental value, a more than 10sigma discrepancy was identified for the 3 3D - 2 3S and 3 3D - 2 3P transitions, which hinders the determination of the He2+ charge radius from atomic spectroscopy that would complement the recent determination using muonic helium [2]. We report on the determination of the ionization energy of the metastable 2 1S0 state of helium by Rydberg-series extrapolation through the measurement of the frequencies of np - 2 1S0 transitions in the range of principal quantum number n between 24 to 102 [3]. The experiments are carried out by single-photon excitation in a doubly-skimmed supersonic beam of metastable helium atoms. Combining the ionization energy of the 2 1S0 state of helium with earlier measurements of the 2 3S1 - 2 1S0 [4] and the 2 3P - 2 3S1 interval [5,6], we derive new experimental values for the ionization energies of the 2 3S1 state (1 152 842 742.640(32) MHz) and the 2 3P centroid energy (876 106 247.025(39) MHz). These values reveal disagreements with the a7m Lamb shift predictions by 6.5sigma and 11sigma, respectively, and support the suggestion by Patkóš et al. [1] of an unknown theoretical contribution to the Lamb shifts of the 2 3S1 and 2 3P states of He. A new experiment aiming at the direct determination of the ionization energy of 2 3S1 state will also be presented, in which multistage Zeeman deceleration and transverse laser cooling is used to generate a slow, highly collimated beam of metastable 2 3S1 He. If time permits, new measurements of the ionization energy of H2 and of the level structure of H2+ will be presented. Starting from the GK 1Sg+ (v=0, N=0) level of H2, we record transitions to Rydberg-Stark states belonging to series converging on different rotational and vibrational levels of H2+ in the presence of weak electric fields. From the analysis of the Stark effect, we determine the positions of zero quantum defect for different series, which we then use to extract rotational and vibrational energy intervals in H2+. [1] V. Patkóš, V. A. Yerokhin, and K. Pachucki, Phys. Rev. A 103, 042809 (2021). [2] J. J. Krauth et al., Nature (London) 589, 527 (2021). [3] G. Clausen, P. Jansen, S. Scheidegger, J. A. Agner, H. Schmutz and F. Merkt, Phys. Rev. Lett. 127, 093001 (2021) [4] R. J. Rengelink, Y. van der Werf, R. P. M. J.W. Notermans, R. Jannin, K. S. E. Eikema, M. D. Hoogerland, and W. Vassen, Nat. Phys. 14, 1132 (2018). [5] P. Cancio Pastor, G. Giusfredi, P. De Natale, G. Hagel, C. de Mauro, and M. Inguscio, Phys. Rev. Lett. 92, 023001 (2004); 97, 139903(E) (2006). [6] X. Zheng, Y. R. Sun, J.-J. Chen, W. Jiang, K. Pachucki, and S.-M. Hu, Phys. Rev. Lett. 119, 263002 (2017)

Latest results and status of the Mu-MASS experiment at PSI

• Paolo CRIVELLI (ETH Zürich, Institute for Particle Physics and Astrophysics, Switzerland)

Room: LPNHE Seminar room Being purely leptonic, i.e. made of constituents which have (to the best of our knowledge) no internal structure, Muonium (M) is an excellent candidate to probe b-QED. I will present our recent measurement of the n=2 M Lamb Shift of 1047.2(2.5) MHz, which comprises an order of magnitude improvement upon the last determinations and matches with theory within one sigma. This allows us to set limits on Lorentz and CPT violation in the muonic sector, as well as on new physics coupled to muons and electrons which could provide an explanation of the muon g-2 anomaly. I will discuss the future prospects of such a measurement and the current status of the 1S-2S experiment.

Microwave spectroscopy of the positronium n = 2 fine structure

• Tamara BABIJ (University College London, United Kingdom)

Room: LPNHE Seminar room Recent measurements of the positronium (Ps) 23S1 → 23PJ fine-structure intervals, for νJ (J = 0, 1, 2), are presented. This experiment used slow Ps atoms, which were optically excited to the metastable 23S1 level. This metastable beam then passed through a microwave guide, which produced a radiation field tuned to drive the transition to the short-lived 23PJ levels. These short-lived Ps atoms were then detected via their subsequent annihilation radiation. For the ν0 transition, a discrepancy of 4.5 σ from QED theory was measured [1]. While the ν1, and ν2 transitions exhibited asymmetric lineshapes [2]. Simulations seem to suggest that this asymmetry was due to reflections of the RF field in the chamber [3]. Recent improvements have been made to the experiment, with asymmetry no longer observed. [1] L. Gurung, T. J. Babij, S. D. Hogan, and D. B. Cassidy.Precision microwave spectroscopy of the positronium n = 2 fine structure. Phys. Rev. Lett, 125, 073002 (2020). [2] L. Gurung, T. J. Babij, J. Pérez-Ríos, S. D. Hogan, and D. B. Cassidy. Observation of asymmetric line shapes in precision microwave spectroscopy of the positronium 23S1  23PJ (J = 1, 2) fine-structure intervals. Phys. Rev. A, 103, 02805 (2021). [3]L. A. Akopyan, T. J. Babij, K. Lakhmanskiy, D. B. Cassidy, and A. Matveev. Line-shape modeling in microwave spectroscopy of the positronium n = 2 fine-structure intervals. Phys. Rev. A., 104, 062810 (2021).

Determining the charge radius of the neutron through electron-nucleon scattering experiments.

• Michael PAOLONE (New Mexico State University, NM, USA)

Room: LPNHE Seminar room The neutron charge radius can be extracted by determining the slope of Sachs form factor GEn as Q2 -> 0. One can combine global neutron and proton GE data and exploit charge symmetry to perform a flavor dependent decomposition of the nucleon's Dirac form factors and simultaneously extract the proton and neutron charge radii. The resulting proton charge radius using this method is consistent with results obtained from muonic hydrogen spectroscopy. The neutron charge radius extraction compliments previous measurements that relied solely on neutron-electron scattering data which appears to have underlying systematic discrepancies. Additional leverage in the low Q2 region of GEn may be obtained through N-Delta transition form factor data. A discussion of the methodology behind the extraction of the radii and the impact of including N-Delta TFFs will be presented.

Low-energy electron scattering: beyond proton radius

• Toshimi SUDA (Research Center for Electron Photon Science, Tohoku University, Japan)

Room: LPNHE Seminar room I will introduce low-energy electron scattering facilities for nuclear physics that we have constructed in Japan. 1) the ULQ2 facility at Tohoku for the proton radius Ee = 10 - 60 MeV, \theta_e = 30 - 150 deg.. high-resolution twin spectrometers with 4k-ch silicon strip detectors. 2) the SCRIT facility in RIKEN/RIBF for short-lived exotic nuclei. the world’s first electron scattering facility dedicated to short- lived exotic nuclei. Ee = 150 - 300 MeV, q = 80 - 300 MeV/c. Luminosity ~ 10^{27} /cm2/s with N_RI ~ 10^8/s. ISOL (Photofission), electron storage ring, large-acceptance spectrometer. After introducing the facility details and current status, I will discuss a new physics case, recently we pointed out, at such low-energy electron-scattering facilities.

Two photon exchange at Jefferson Lab

• Tyler KUTZ (Massachusetts Institute of Technology, MA, USA)

Room: LPNHE Seminar room Two photon exchange (TPE) and the larger class of hadronic box diagrams can be a significant radiative correction to lepton scattering and beta decay measurements. Notably, it has been hypothesized that TPE could be responsible for the proton form factor ratio discrepancy. However, these diagrams remain difficult to calculate without large uncertainty and model-dependence, and theoretical calculations of some observables sensitive to TPE are in disagreement with experimental results. Extending experimental measurements of complementary TPE observables can provide critical benchmarks for these calculations. I will summarize recent and future TPE measurements at Jefferson Lab, including those that would be made possible by the proposed addition of a positron source to Jefferson Lab’s accelerator facility.

Closing session Room: LPNHE Seminar room