arXiv subjects

Vladimir Pascalutsa

Publications and source records attributed to Vladimir Pascalutsa.

At least 19 recordsLinked to original sources

arXiv2026

Hadronic vacuum polarization in hydrogen-like atoms and ions amid the interplay of recoil and finite-size effects

Hadronic vacuum polarization (hVP) enters simple atomic systems at a level that is small yet decisive for the precision spectroscopy now underway. We evaluate the hVP contributions to the Lamb shift and the hyperfine splitting (HFS) in ordinary and muonic hydrogen (H and $\mu$H) and hydrogen-like helium-3 ions ($^3$He$^+$ and $\mu^3$He$^+$), using the dispersive data-driven approach and state-of-the-art empirical parametrizations of the $R$ ratio. At the centre of the analysis is the interplay of recoil and finite-size effects: the recoil corrections that dominate the HFS in muonium (Mu), where both constituents are pointlike, are shown to be suppressed by the nuclear elastic form factors (FFs). Our results for the leading hVP contribution to the Lamb shift agree with the literature within uncertainties. Furthermore, we present a first evaluation of the subleading $O(Z^5\alpha^6)$ hVP-finite-size correction, which is by no means negligible in $\mu^3$He$^+$. Our results for the hVP contribution to the HFS deviate significantly from all previous evaluations. For the ground-state HFS, we obtain $2.153(11)~\mu$eV in $\mu$H and $-15.19(57)~\mu$eV in $\mu^3$He$^+$, as well as $0.0860(4)~$kHz and $-0.476(17)~$kHz in ordinary H and $^3$He$^+$, respectively. Notably, our result for $\mu$H differs from previous evaluations by roughly ten times the experimental precision anticipated by the upcoming CREMA and FAMU measurements.

physics.atom-ph↗

arXiv2026

Lepton $g-2$ non-universality of hadronic contributions and a sub-GeV window to New Physics

We propose the linear combination of the anomalous magnetic moments of the muon and electron, $a_{\mu-e} \equiv a_\mu - (m_\mu/m_e)^2 a_e$, as a natural low-energy window quantity that may directly probe the current discrepancy between the data-driven and lattice-QCD evaluations of hadronic contributions. The rescaling ensures an exact cancellation of the short-range effects, thereby improving the UV behavior and bypassing a number of issues that arise in $a_\mu$ or $a_e$ separately. The hadronic-vacuum-polarization effect in $a^{\rm HVP}_{\mu-e}$, together with its uncertainty, is reduced as compared to $a^{\rm HVP}_{\mu}$ by $\sim 85\%$. This is promising for tests of New Physics, conditional to significant improvements in experimental measurements of $a_e$ and $\alpha$. One can foresee the improvements in tests of New Physics with some degree of flavor non-universality, as well as for the flavor-universal sub-GeV states.

hep-ph↗

arXiv2025

Field-theoretic versus data-driven evaluations of electromagnetic corrections to hadronic vacuum polarization in $(g-2)_\mu$

The Standard Model prediction of the muon $g-2$ increasingly depends on lattice QCD computations of the hadronic vacuum polarization (HVP), where the isospin-breaking (IB) effects remain a significant source of uncertainty. To complement the lattice QCD evaluations, the data-driven approach to HVP has been used to assess some of the electromagnetic IB effects, in particular from the channels with a photon in the final state, e.g., $e^+e^-\to\pi^0 \gamma$. Here we argue that such contributions are largely canceled by virtual electromagnetic corrections to the purely hadronic channels: $\pi^+ \pi^-$, $\pi^+ \pi^- \pi^0$, etc. We identify these leading corrections by performing a field-theoretical calculation in a vector-meson dominance model, thereby reconciling the timelike and spacelike approaches to electromagnetic effects. Although these virtual corrections are more difficult to extract in a systematic manner, addressing them is essential for the data-driven method to consistently complement the lattice QCD program.

hep-ph↗

arXiv2025

New superconvergence relations for spin and tensor structure functions of $\gamma\gamma$ fusion

The Burkhardt--Cottingham sum rule is an exact superconvergence relation for a spin-structure function, derived from general principles of light absorption and scattering, and valid at any momentum transfer $Q^2$. I illustrate how a class of such relations emerges from the Siegert point, an unphysical kinematical point where both the probe and the target are at rest. From light-by-light scattering, new sum rules for $\gamma^\ast \gamma^\ast$ fusion are emerging, valid for arbitrary photon virtualities. Regarding the convergence of these relations, there is a simple argument for the suppression of longitudinal photon polarizations at high energy. Among its consequences is the prediction of $\sigma_L/ \sigma_T \to 0$ at high energy, for the ratio of unpolarized nucleon photoabsorption cross sections.

hep-ph↗

arXiv2025

Isospin-violating vacuum polarization in the muon $(g-2)$ with SU(3) flavour symmetry from lattice QCD

We compute the isospin-violating part $a_\mu^{\text{HVP}, 38}$ of the hadronic-vacuum-polarization (HVP) contribution to the muon $(g-2)$ in lattice QCD at the SU$(3)_{\rm f}$-symmetric point where $M_\pi=M_K\simeq 416$ MeV. All diagrams involving internal photons are evaluated in coordinate space, employing a Pauli-Villars-regulated photon propagator with a cutoff scale $\Lambda$ well below the lattice cutoff. The counterterm $(m_u-m_d)$, whose $\Lambda$ dependence is consistent with the expected logarithmic behaviour, is calibrated using the experimental kaon mass splitting as input. The bare electromagnetic contribution at fixed $\Lambda$ is compared to a phenomenological estimate based on the kaon-loop and pseudoscalar-pole contributions to the forward light-by-light amplitude. An extension of these calculations to physical pion and kaon masses appears promising.

hep-lat↗

arXiv2025

Computing the UV-finite electromagnetic corrections to the hadronic vacuum polarization in the muon $(g-2)$ from lattice QCD

In order to reach a precision of $0.2\%$ on the hadronic vacuum polarization (HVP) contribution to the anomalous magnetic moment of the muon, $(g-2)_\mu$, such that the full Standard-Model prediction matches in precision the direct experimental measurement, it is crucial to include the leading, O($\alpha$) electromagnetic corrections to HVP. In this work, we determine an important contribution to the latter from a diagram comprised of two two-point quark-loops, connected by the internal photon and gluons. This ultraviolet-finite correction is calculated from lattice QCD using a coordinate-space formalism, where photons are treated in the continuum and infinite volume. Our result amounts to a $(-0.89\pm 0.18)\%$ correction to the leading-order HVP contribution to $(g-2)_\mu$. To overcome the worsening statistical noise at large distances, our analysis is combined with phenomenological models featuring light pseudoscalar mesons with masses below 1 GeV. In particular, our data show a very steep mass dependence as dictated by the charged pion loop. Similarly, the other diagrams appearing in the O$(\alpha)$-corrections to the HVP with the internal photon connecting two separate quark loops are also ultraviolet-finite and can be computed with the same formalism.

hep-lat↗

arXiv2024

The isospin-violating part of the hadronic vacuum polarisation

We present our calculation of the isospin-violating part of the hadronic vacuum polarisation (HVP) contribution to muon $(g-2)$ in lattice QCD at the $SU(3)_{\mathrm{f}}$ symmetric point. The computation of the contributing fully connected diagrams with one internal photon as well as the computation of the only (mass) counterterm are shown. The latter is determined from the charged-neutral kaon mass splitting. We employ coordinate-space methods and a photon propagator which is regulated \`a la Pauli-Villars with a cutoff scale $\Lambda$ well below the lattice cutoff. This regularization makes it possible for us to do crosschecks of individual contributions with calculations in the continuum. Our continuum extrapolated results show little to no dependence on $\Lambda$. This makes our final limit $\Lambda \rightarrow \infty$ straightforward.

hep-lat↗

arXiv2024

New Spin Structure Constraints on Hyperfine Splitting and Proton Size

The 1S hyperfine splitting in hydrogen is measured to an impressive ppt precision and will soon be measured to ppm precision in muonic hydrogen. The latter measurement will rely on theoretical predictions, which are limited by knowledge of the proton polarizability effect $\Delta_\text{pol}$. Data-driven evaluations of $\Delta_\text{pol}$ have long been in significant tension with baryon chiral perturbation theory. Here we present improved results for $\Delta_\text{pol}$ driven by new spin structure data, reducing the long-standing tension between theory and experiment and halving the dominating uncertainty in hyperfine splitting calculations.

nucl-ex↗

arXiv2023

Chiral perturbation theory of the hyperfine splitting in (muonic) hydrogen

The ongoing experimental efforts to measure the hyperfine transition in muonic hydrogen prompt an accurate evaluation of the proton-structure effects. At the leading order in $\alpha$, which is $O(\alpha^5)$ in the hyperfine splitting (hfs), these effects are usually evaluated in a data-driven fashion, using the empirical information on the proton electromagnetic form factors and spin structure functions. Here we perform a first calculation based on the baryon chiral perturbation theory (B$\chi$PT). At leading orders it provides a prediction for the proton polarizability effects in hydrogen (H) and muonic hydrogen ($\mu$H). We find large cancellations among the various contributions leading to, within the uncertainties, a zero polarizability effect at leading order in the B$\chi$PT expansion. This result is in significant disagreement with the current data-driven evaluations. The small polarizability effect implies a smaller Zemach radius $R_\mathrm{Z}$, if one uses the well-known experimental $1S$ hfs in H or the $2S$ hfs in $\mu$H. We, respectively, obtain $R_\mathrm{Z}(\mathrm{H}) = 1.010(9)$ fm, $R_\mathrm{Z}(\mu\mathrm{H}) = 1.040(33)$ fm. The total proton-structure effect to the hfs at $O(\alpha^5)$ is then consistent with previous evaluations; the discrepancy in the polarizability is compensated by the smaller Zemach radius. Our recommended value for the $1S$ hfs in $\mu\text{H}$ is $182.640(18)\,\mathrm{meV}.$

nucl-th↗

arXiv2023

The QED of Bernab\'eu-Tarrach sumrule for electric polarizability and its implication for the Lamb shift

We attempt to rehabilitate a sum rule (proposed long ago by Bernab\'eu and Tarrach) which relates the electric polarizability of a particle to the total photoabsorption of quasi-real longitudinally polarized photons by that particle. We discuss its perturbative verification in QED, which is largely responsible for the scepticism about its validity. The failure of the QED test can be understood via the Sugawara-Kanazawa theorem and is due to the non-vanishing contour contribution in the pertinent dispersion relation. We show another example where this contribution is absent and the perturbative test works exactly. On the empirical side, we show that the sum rule gives a reasonable estimate of the $\pi N$-channel contribution to the proton electric polarizability. If this sum rule is valid indeed, there should be a sum rule for the so-called ``subtraction function'' entering the data-driven calculations of the polarizability effects in the Lamb shift. We have written down a possible sum rule for the subtraction function and verified it in a perturbative calculation.

hep-ph↗

arXiv2022

Two-photon decay of fully-charmed tetraquarks from light-by-light scattering at the LHC

The LHC newly-discovered resonant structures around 7 GeV, such as the $X(6900)$, could be responsible for the observed excess in light-by-light scattering between 5 and 10 GeV. We show that the ATLAS data for light-by-light scattering may indeed be explained by such a state with the $\gamma \gamma$ branching ratio of order of $10^{-4}$. This is much larger than the value inferred by the vector-meson dominance, but agrees quite well with the tetraquark expectation for the nature of this state. Further light-by-light scattering data in this region, obtained during the ongoing Run-3 and future Run-4 of the LHC, are required to pin down these states in $\gamma\gamma$ channel.

hep-ph↗

arXiv2022

Muonic-Atom Spectroscopy and Impact on Nuclear Structure and Precision QED Theory

Recent progress in laser and x-ray spectroscopy of muonic atoms offers promising long-term possibilities at the intersection of atomic, nuclear and particle physics. In muonic hydrogen, laser spectroscopy measurements will determine the ground-state hyperfine splitting (HFS) and additionally improve the Lamb shift by a factor of 5. Precision spectroscopy with cryogenic microcalorimeters has the potential to significantly improve the charge radii of the light nuclei in the $Z=3-8$ range. Complementary progress in precision should be achieved on the theory of nucleon- and nuclear-structure effects. The impact of this muonic-atom spectroscopy program will be amplified by the upcoming results from H and He$^+$ spectroscopy, simple molecules such as HD$^+$ and Penning trap measurements. In this broader context, one can test ab-initio nuclear theories, bound-state QED for two- or three-body systems, and determine fundamental constants, such as the Rydberg ($R_\infty$) and the fine-structure ($\alpha$) constants.

nucl-th↗

arXiv2022

Theoretical discrepancies in the nucleon spin structure and the hyperfine splitting of muonic hydrogen

Two groups, ours (Mainz) and Bochum, have recently been re-evaluating the spin polarizabilities and spin structure functions at low $Q$, using the baryon chiral perturbation theory (B$\chi$PT), the manifestly-covariant counterpart of the heavy-baryon chiral perturbation theory (HB$\chi$PT). Whilst the two groups agree that the B$\chi$PT framework works better than HB$\chi$PT in this sector, their quantitative results disagree in some of the quantities; most notably, the proton spin polarizabilities $\gamma_0$ and $\delta_{LT}$. These discrepancies are especially intriguing in light of new experimental data coming from the Jefferson Lab "Spin Physics Program". The preliminary data on the proton are reported by Karl Slifer in a plenary session of this workshop. Another theoretical discrepancy is emerging in the proton-polarizability contribution to the hyperfine splitting (hfs) in hydrogen and muonic hydrogen. Our B$\chi$PT calculation shows a significantly smaller effect than the state-of-the-art data-driven evaluations based on empirical spin structure functions. The smaller polarizability contribution leads to a smaller Zemach radius of the proton. This discrepancy could be relevant for the planned first-ever measurement of the ground-state hfs in muonic hydrogen.

hep-ph↗

arXiv2022

Forward light-by-light scattering and electromagnetic correction to hadronic vacuum polarization

Lattice QCD calculations of the hadronic vacuum polarization (HVP) have reached a precision where the electromagnetic (e.m.) correction can no longer be neglected. This correction is both computationally challenging and hard to validate, as it leads to ultraviolet (UV) divergences and to sizeable infrared (IR) effects associated with the massless photon. While we precisely determine the UV divergence using the operator-product expansion, we propose to introduce a separation scale $\Lambda\sim400\;$MeV into the internal photon propagator, whereby the calculation splits into a short-distance part, regulated in the UV by the lattice and in the IR by the scale $\Lambda$, and a UV-finite long-distance part to be treated with coordinate-space methods, thereby avoiding power-law finite-size effects altogether. In order to predict the long-distance part, we express the UV-regulated e.m. correction to the HVP via the forward hadronic light-by-light (HLbL) scattering amplitude and relate the latter via a dispersive sum rule to $\gamma^*\gamma^*$ fusion cross-sections. Having tested the relation by reproducing the two-loop QED vacuum polarization (VP) from the tree-level $\gamma^*\gamma^*\to e^+e^-$ cross-section, we predict the expected lattice-QCD integrand resulting from the $\gamma^*\gamma^*\to\pi^0$ process.

hep-lat↗

arXiv2022

The two-photon decay of X(6900) from light-by-light scattering at the LHC

The LHCb Collaboration has recently discovered a structure around 6.9 GeV in the double-$J/\psi$ mass distribution, possibly a first fully-charmed tetraquark state $X(6900)$. Based on vector-meson dominance (VMD) such a state should have a significant branching ratio for decaying into two photons. We show that the recorded LHC data for the light-by-light scattering may indeed accommodate for such a state, with a $\gamma \gamma$ branching ratio of order of $10^{-4}$, which is larger even than the value inferred by the VMD. The spin-parity assignment $0^{-+}$ is in better agreement with the VMD prediction than $0^{++}$, albeit not significantly at the current precision. Further light-by-light scattering data in this region, clarifying the nature of this state, should be obtained in the Run 3 and probably in the high-luminosity phase of the LHC (Run 4 etc.).

hep-ph↗

arXiv2022

Two-photon exchange in (muonic) deuterium at N3LO in pionless effective field theory

We present a study of the two-photon-exchange ($2\gamma$-exchange) corrections to the $S$-levels in muonic ($\mu$D) and ordinary (D) deuterium within the pionless effective field theory (pionless EFT). Our calculation proceeds up to next-to-next-to-next-to-leading order (N3LO) in the pionless EFT expansion. The only unknown low-energy constant entering the calculation at this order corresponds to the coupling of a longitudinal photon to the nucleon-nucleon system. To minimise its correlation with the deuteron charge radius, it is extracted using the information about the hydrogen-deuterium isotope shift. We find the elastic $2\gamma$-exchange contribution in $\mu$D larger by several standard deviations than obtained in other recent calculations. This discrepancy ameliorates the mismatch between theory and experiment on the size of $2\gamma$-exchange effects, and is attributed to the properties of the deuteron elastic charge form factor parametrisation used to evaluate the elastic contribution. We identify a correlation between the deuteron charge and Friar radii, which can help one to judge how well a form factor parametrisation describes the low-virtuality properties of the deuteron. We also evaluate the higher-order $2\gamma$-exchange contributions in $\mu$D, generated by the single-nucleon structure and expected to be the most important terms beyond N3LO. The uncertainty of the theoretical result is dominated by the truncation of the pionless EFT series and is quantified using a Bayesian approach. The resulting extractions of the deuteron charge radius from the $\mu$D Lamb shift, the $2S-1S$ transition in D, and the $2S-1S$ hydrogen-deuterium isotope shift, with the respective $2\gamma$-exchange effects evaluated in a unified pionless EFT approach, are in perfect agreement.

nucl-th↗

arXiv2022

A reassessment of nuclear effects in muonic deuterium using pionless effective field theory at N3LO

We provide a systematic assessment of the order-$\alpha^5$ nuclear contributions to the Lamb shift of muonic deuterium, including the accompanying radiative corrections due to vacuum polarization, up to next-to-next-to-next-to-leading order (N3LO) within the pionless effective field theory (EFT). We also evaluate higher-order corrections due to the single-nucleon structure, which are expected to be the most important corrections beyond N3LO. We find a correlation between the deuteron charge and Friar radii, which can be useful to judge the quality of charge form factor parametrisations. We refine the theoretical description of the $2\gamma$-exchange contribution, especially in the elastic contribution and the radiative corrections, ameliorating the original discrepancy between theory and experiment in the size of $2\gamma$-exchange effects. Based on the experimental Lamb shift of muonic deuterium, we obtain the deuteron charge radius, $r_d(\mu\text{D})=2.12763(13)_\text{exp}(77)_\text{theory}$~fm, which is consistent with (but less precise than) the value obtained by combining the H-D isotope shift with the muonic hydrogen Lamb shift. The theory uncertainty is evaluated using a Bayesian procedure and is dominated by the truncation of the pionless EFT series.

nucl-th↗

arXiv2022

The proton structure in and out of muonic hydrogen

Laser spectroscopy of muonic atoms has been recently used to probe properties of light nuclei with unprecedented precision. We introduce nuclear effects in hydrogen-like atoms, nucleon structure quantities (form factors, structure functions, polarizabilities) and their effects in the Lamb shift and hyperfine splitting (HFS) of muonic hydrogen ($\mu$H). Updated theory predictions for the Lamb shift and HFS in $\mu$H are presented. We review the challenges of the ongoing effort to measure the ground-state HFS in $\mu$H and its impact on our understanding of the nucleon spin structure. To narrow down this search, we present a novel theory prediction obtained by scaling the measured HFS in hydrogen leveraging radiative corrections. We also summarize recent developments in the spectroscopy of simple atomic and molecular systems and emphasize how they allow for precise determinations of fundamental constants, bound-state QED tests and New Physics searches.

nucl-th↗