arXiv subjects

Jean-Philippe Karr

Publications and source records attributed to Jean-Philippe Karr.

At least 19 recordsLinked to original sources

arXiv2026

One-loop self-energy using a numerical Green function

We calculate the one-loop self-energy in hydrogenlike atoms using a numerical Green function obtained by solving the radial Dirac equation in an exponential basis set. The self-energy correction in the ground state of hydrogenlike uranium is obtained with about $10^{-5}$ relative uncertainty in the Feynman gauge. Using a convergence acceleration scheme, we extend our calculations to the region of low nuclear charges. Our results allow calculating the self-energy correction for the hydrogen atom with $10^{-4}$ relative uncertainty. Calculations in the Coulomb gauge are also presented, improving the precision to $10^{-5}$. Present limitations and possible improvements of our method are discussed.

physics.atom-ph↗

arXiv2026

Atomic Spectroscopy Probes of New Physics

Precision spectroscopy has long played a central role in testing the foundations of physics, from the early insights that led to the development of quantum mechanics to the validation of quantum electrodynamics and the determination of fundamental constants. Today, advances in atomic and molecular spectroscopy enable sensitive searches for physics beyond the Standard Model. A broad class of well-motivated extensions predicts new light degrees of freedom with feeble couplings to electrons, muons, and nucleons, giving rise to tiny spin-independent interactions that can be probed at low energies. In this review, we present a unified overview of spectroscopic searches for such interactions. We discuss the effective theoretical framework connecting fundamental interactions to atomic and nuclear observables, survey the key experimental and theoretical strategies, and review the atomic and molecular systems providing the strongest sensitivity. We conclude with updated spectroscopic constraints on representative benchmark models, highlighting the unique and complementary role of precision spectroscopy in exploring new fundamental interactions.

hep-ph↗

arXiv2026

High-precision Penning-trap spectroscopy of the ground-state spin structure of HD+

We present high-precision spectroscopy of the ground-state hyperfine structure of HD$^+$ at 4~T. We determine the bound-electron $g$ factor, $g_{e,\mathrm{bound}} = -2.002\,278\,540\,96(40)$, to a relative uncertainty of $2\times$10$^{-10}$, the most precise determination of a bound-electron $g$ factor of a molecular ion to date. The experimental value agrees with recently developed ab initio theory that now includes quantum-electrodynamical effects up to order $\alpha^5$ and has reduced the theoretical uncertainty by three orders of magnitude [O. Kullie \textit{et al.}, Phys. Rev. A 112 052813 (2025)]. In addition, we extract the scalar spin-spin interaction coefficients $E_4$~=~925\,395.758(41)$\,$kHz (electron-proton) and $E_5$~=~142\,287.821(22)$\,$kHz (electron-deuteron), which show a moderate tension with another state-of-the-art theoretical prediction [M. Haidar \textit{et al.}, Phys. Rev. A 106 042815 (2022)].

physics.atom-ph↗

arXiv2026

Photodetachment energy of negative hydrogen ions

We report a high-precision calculation of the photodetachment energy of the hydrogen anion \mathrm{H}^{-}. The nonrelativistic bound-state energy is obtained using an exact three-body approach, and supplemented by leading relativistic, quantum-electrodynamic, finite-nuclear-size, and hyperfine corrections. Our result is 6083$.$06447(68)\mathrm{cm}^{-1} for the detachment to the hydrogen ground-state hyperfine level \mathit{(F=0)}, which is 220 times more precise than the best experimental determination to date, 6082$.$99(15)\mathrm{cm}^{-1}, as reported by Lykke \mathit{et al.} Beyond their intrinsic interest, these results provide critical input for antihydrogen physics, where controlled photodetachment of \bar{\mathrm{H}}^{+} offers a path to producing ultracold antihydrogen (and its isotopes) for precision experiments. Corresponding calculations for the negative deuterium and tritium ions yield 6086$.$70676(68)\mathrm{cm}^{-1} for ^{2}\mathrm{H}^{-}(F=1/2) and 6087$.$87924(68)\mathrm{cm}^{-1} for ^{3}\mathrm{H}(F=0).

physics.atom-ph↗

arXiv2025

Precision calculation of the bound-electron $g$ factor in molecular hydrogen ions

We calculate the bound-electron $g$ factor for a wide range of rovibrational states of the molecular hydrogen ions H$_2^+$ and HD$^+$. Relativistic and QED corrections of orders up to $α^5$ are taken into account. All contributions are calculated in a nonrelativistic QED framework, except for relativistic corrections of order $(Zα)^4$ and above, which are obtained by calculating the relativistic $g$ factor using a precise minmax finite element solution of the two-center Dirac equation. A relative accuracy of $4-5 \times 10^{-11}$ is achieved for the scalar $g$ factor component, which represents an improvement by more than three orders of magnitude over previous calculations. These results are useful for internal state identification and rovibraional spectroscopy of single molecular hydrogen ions in Penning traps, and open a new avenue towards precision tests of QED.

physics.atom-ph↗

arXiv2025

Second-order corrections of orders $mα^6$ and $mα^6(m/M)$ to the spin-averaged energy in the HD$^+$ and H$_2^+$ ions

The relativistic second-order corrections at orders $mα^6$ and $mα^6(m/M)$ in hydrogen molecular ions are calculated. Convergence of numerical results is studied, which allows estimating the relative numerical uncertainty to be less then $10^{-5}$. This accuracy is sufficient to enable future improvement of theoretical predictions beyond the 1 ppt (part-per-trillion) precision level for the ro-vibrational transition frequencies.

physics.atom-ph↗

arXiv2025

Prospects for the determination of fundamental constants with beyond-state-of-the-art uncertainty using molecular hydrogen ion spectroscopy

The proton, deuteron and triton masses can be determined relative to the electron mass via rovibrational spectroscopy of molecular hydrogen ions. This has to occur via comparison of the experimentally measured transition frequencies and the ab initio calculated frequencies, whose dependence on the mass ratios can be calculated precisely. In precision experiments to date (on HD$^+$ and H$_2^+$), the transitions have involved the ground vibrational level $v=0$ and excited vibrational levels with quantum numbers up to $v'=9$. For these transitions, the sensitivity of the ab initio frequency on the high-order-QED contributions is correlated with that on the mass ratios. This prevents an efficient simultaneous determination of these quantities from experimental data, so that the accuracy of the mass ratios is essentially limited by the theoretical uncertainty. Here we analyze how the accuracy of mass ratios may be improved by providing experimental transition frequencies between levels with larger quantum numbers, whose sensitivity on the mass ratio is positive rather than negative, or close to zero. This allows the unknown QED contributions and involved fundamental constants to be much more efficiently determined from a joint analysis of several measurements. We also consider scenarios where transitions of D$_2^+$ are included. We find these to be powerful approaches, allowing in principle to reach uncertainties for the mass ratios approximately three orders smaller than CODATA 2018. Improvements by a factor of 3.5 for the Rydberg constant, and 11 (14) for the proton (deuteron) charge radius, are also projected.

physics.atom-ph↗

arXiv2023

Extraction of spin-averaged rovibrational transition frequencies in HD$^+$ for the determination of fundamental constants

We present a comprehensive analysis of all currently available high-accuracy frequency measurements of rotational and rovibrational transitions in the hydrogen molecular ion HD$^+$. Our analysis utilises the theoretically calculated hyperfine structure to extract the values of three spin-averaged transition frequencies through a global linear least-squares adjustment that takes into account theory-induced correlations between the different transitions. We subsequently use the three spin-averaged transition frequencies as input data in a second adjustment which employs precise theoretical expressions for the transition frequencies, written as a function of the proton, deuteron and electron relative atomic masses, the Rydberg constant, and the proton and deuteron charge radii. Our analysis shows that the HD$^+$ data may significantly improve the value of the electron relative atomic mass and the proton-electron mass ratio, in particular if combined with recent high-precision measurements of particle atomic masses and mass ratios obtained from Penning traps.

physics.atom-ph↗

arXiv2023

High-precision solution of the Dirac Equation for the hydrogen molecular ion using a basis-set expansion

The Dirac equation for H$_2^+$ is solved numerically by expansion in a basis set of two-center exponential functions, using different kinetic balance schemes. Very high precision (27-32 digits) is achieved, either with the dual kinetic balance, which provides the fastest convergence, or without imposing any kinetic balance condition. Application to heavy molecular ions is also illustrated. Calculation of relativistic sum rules shows that this method gives an accurate representation of the complete Dirac spectrum, making it a promising tool for calculations of QED corrections in molecular systems.

physics.atom-ph↗

arXiv2022

Self-consistent extraction of spectroscopic bounds on light new physics

Fundamental physical constants are determined from a collection of precision measurements of elementary particles, atoms and molecules. This is usually done under the assumption of the Standard Model~(SM) of particle physics. Allowing for light new physics~(NP) beyond the SM modifies the extraction of fundamental physical constants. Consequently, setting NP bounds using these data, and at the same time assuming the CODATA recommended values for the fundamental physical constants, is not reliable. As we show in this Letter, both SM and NP parameters can be simultaneously determined in a consistent way from a global fit. For light vectors with QED-like couplings, such as the dark photon, we provide a prescription that recovers the degeneracy with the photon in the massless limit, and requires calculations only at leading order in the small new physics couplings. At present, the data show tensions partially related to the proton charge radius determination. We show that these can be alleviated by including contributions from a light scalar with flavor non-universal couplings.

hep-ph↗

arXiv2022

Higher-order corrections to the spin-orbit and spin-spin tensor interactions in HD$^+$

Improved values of hyperfine coefficients related to the electronic spin-orbit and electron-nucleus spin-spin tensor interactions in the HD$^+$ molecular ion are obtained through numerical calculation of relativistic corrections at the $mα^6$ order and radiative corrections at the $mα^7\ln(α)$ order. The theoretical accuracy is improved by more than one order of magnitude. Some deviations with recent high-precision ro-vibrational spectroscopy experiments are observed, in contrast with the good agreement obtained in H$_2^+$.

physics.atom-ph↗

arXiv2022

Spin-orbit interaction in the HD$^+$ ion

We report on progress in calculation of the spin-orbit interaction for the HD$^+$ molecular ion. This interaction is currently the largest source of theoretical uncertainty in determination of the hyperfine structure of rovibrational transition lines. The corrections of order $mα^7\ln(α)$ are derived and numerically calculated. Theoretical hyperfine intervals are compared with experimental data, and the observed discrepancies are discussed.

physics.atom-ph↗

arXiv2022

Higher-order corrections to spin-orbit and spin-spin tensor interactions in hydrogen molecular ions: theory and application to H$_2^+$

We consider higher-order corrections to hyperfine coefficients related to the spin-orbit and spin-spin tensor interactions in hydrogen molecular ions. The $mα^7 \ln(α)$-order radiative correction is derived in the NRQED framework. We present complete numerical calculations, including as well the $mα^6$-order relativistic correction, for the case of H$_2^+$. The theoretical uncertainty is reduced by more than one order of magnitude with respect to the Breit-Pauli level, down to a few ppm. We also compare our results with available rf spectroscopy data.

physics.atom-ph↗

arXiv2022

High-precision solution of the Dirac Equation for the hydrogen molecular ion by an iterative method

The Dirac equation for H$_2^+$ is solved numerically using an iterative method proposed by Kutzelnigg [Z. Phys. 11, 15 (1989]. The four-component wavefunction is expanded in a newly introduced kinetically balanced exponential basis set. The ground-state relativistic energy is obtained with an accuracy of $10^{-20}$, which represents an improvement by several orders of magnitude, and is shown to be in good agreement with results obtained from perturbation theory.Highly accurate relativistic wavefunctions are obtained, which is a first step towards nonperturbative calculations of the one-loop self-energy correction in hydrogen molecular ions.

physics.atom-ph↗

arXiv2021

Ro-vibrational spin-averaged transitions in the hydrogen molecular ions

We reconsider the calculation of rovibrational transition frequencies in hydrogen molecular ions. Some previously neglected contributions, such as the deuteron polarizability, are included into consideration in comparison with our previous work. In particular, one-loop and two-loop QED corrections at $mα^7$ and $mα^8$ orders are recalculated in the framework of the adiabatic approximation, with systematic inclusion of corrections associated with vibrational motion. Improved theoretical transitions frequencies are obtained and found to be in very good agreement with recent high-precision spectroscopy experiments in HD$^+$. New values for the $m_p/m_e$ and $m_d/m_p$ mass ratios are determined.

physics.atom-ph↗

arXiv2020

Higher-order corrections to spin-spin scalar interactions in HD$^+$ and H$_2^+$

The largest hyperfine interaction coefficients in the hydrogen molecular ion HD$^+$, i.e. the electron-proton and electron-deuteron spin-spin scalar interactions, are calculated with estimated uncertainties slightly below 1~ppm. The $(Zα)^2 E_F$ relativistic correction, for which a detailed derivation is presented, QED corrections up to the order $α^3 \ln^2 (α)$ along with an estimate of higher-order terms, and nuclear structure corrections are taken into account. Improved results are also given for the electron-proton interaction coefficient in H$_2^+$, in excellent agreement with RF spectroscopy experiments. In HD$^+$, a 4$σ$ difference is found in the hyperfine splitting of the $(v,L)=(0,3) \to (9,3)$ two-photon transition that was recently measured with high precision. The origin of this discrepancy is unknown.

physics.atom-ph↗

arXiv2020

Trapping, cooling, and photodissociation analysis of state-selected H$\_2^+$ ions produced by (3+1) multiphoton ionization

We report on the production of cold, state-selected H$_2^+$ molecular ions in a linear RF trap. The ions are produced by (3+1) resonance-enhanced multi-photon ionisation (REMPI) of H$_2$, and sympathetically cooled by laser-cooled Be$^+$ ions. After demonstrating and characterizing the REMPI process, we use photodissociation by a deep UV laser at 213~nm to verify the high vibrational purity of the produced H$_2^+$ ion samples. Moreover, the large difference between the photodissociation efficiencies of ions created in the $v=0$ and $v=1$ levels provides a way to detect a $v=0 \to 1$ transition. These results pave the way towards high-resolution vibrational spectroscopy of H$_2^+$ for fundamental metrology applications.

physics.atom-ph↗

arXiv2020

Hyperfine structure in the H$_2^+$ and HD$^+$ molecular ions at $mα^6$ order

A complete effective Hamiltonian for relativistic corrections at orders $mα^6$ and $mα^6(m/M)$ in a one-electron molecular system is derived from the NRQED Lagrangian. It includes spin-independent corrections to the energy levels and spin-spin scalar interactions contributing to the hyperfine splitting, both of which had been studied previously. In addition, corrections to electron spin-orbit and spin-spin tensor interactions are newly obtained. This allows improving the hyperfine structure theory in the hydrogen molecular ions. Improved values of the spin-orbit hyperfine coefficient are calculated for a few transitions of current experimental interest.

physics.atom-ph↗