In this work, we present expressions for the full effective potential corresponding to the one-photon exchange interaction within the framework of an effective Schrödinger-like equation, which is derived exactly from the Bethe-Salpeter equation in quantum electrodynamics. The final effective potential is expressed in terms of eight scalar functions. When these eight scalar functions are expanded in terms of velocities order by order, we can return to the non-relativistic effective potential systematically organized by velocities. By retaining the exact momentum dependence in the effective potential, we estimate its corrections to the energy spectrum of hydrogen using a highly precise numerical method. The comparison of the numerical results with those obtained using conventional bound-state perturbative theory is discussed. Our calculations suggest that it is possible to accurately account for all relativistic contributions using this method. It would be interesting to extend these calculations to positronium, muonic hydrogen, and scenarios involving nuclear structure and radiative corrections.
We illustrate how to apply modern effective field theory techniques and dimensional regularization to factorize the various scales which appear in non-relativistic bound states at finite temperature. We focus here on the simplest case: the hydrogen atom. We discuss in detail the interplay of the hard, soft and ultrasoft scales of the non-relativistic system at zero temperature with the additional scales induced at finite temperature. We also comment on the implications of our results for heavy quarkonium bound states in the quark gluon plasma.
We obtain a model-independent prediction for the two-photon exchange contribution to the hyperfine splitting in muonic hydrogen. We use the relation of the Wilson coefficients of the spin-dependent dimension-six four-fermion operator of NRQED applied to the electron-proton and to the muon-proton sectors. Their difference can be reliably computed using chiral perturbation theory, whereas the Wilson coefficient of the electron-proton sector can be determined from the hyperfine splitting in hydrogen. This allows us to give a precise model-independent determination of the Wilson coefficient for th…
We compute the spin-dependent and spin-independent structure functions of the forward virtual-photon Compton tensor of the proton at one loop using heavy baryon effective theory including the Delta particle. We compare with previous results when existing. Using these results we obtain the leading hadronic contributions, associated to the pion and Delta particles, to the Wilson coefficients of the lepton-proton four fermion operators in NRQED. The spin-independent coefficient yields a pure prediction for the two-photon exchange contribution to the muonic hydrogen Lamb shift, $ΔE_{\rm TPE}(π\&Δ)…
We illustrate how to apply modern effective field theory techniques and dimensional regularization to factorise the various scales which appear in QED bound states at finite temperature. We focus here on the muonic hydrogen atom. Vacuum polarization effects make the physics of this atom at finite temperature very close to that of heavy quarkonium states. We comment on the implications of our results for these states in the quark gluon plasma. In particular, we estimate the effects of a finite charm quark mass in the dissociation temperature of bottomonium.
We reevaluate the Zemach, recoil and polarizability corrections to the hyperfine splitting in muonic hydrogen expressing them through the low-energy proton structure constants and obtain the precise values of the Zemach radius and two-photon exchange (TPE) contribution. The uncertainty of TPE correction to S energy levels in muonic hydrogen of 105 ppm exceeds the ppm accuracy level of the forthcoming 1S hyperfine splitting measurements at PSI, J-PARC and RIKEN-RAL.
Based on the simple phenomenological $σππ$, $σN N$ and $ππγ$ interactions, we estimate the $σ$ exchange effect in the Lamb shift of muonic hydrogen. We at first calculate the effective couplings of $σμμ$ by two photons and two pions exchange, then calculate the corresponding corrections to the energy shift of the 2S/2P states of muonic hydrogen. We find the correction to the energy shift of 2S state is about -14$μ$eV by the current used parameters, which is about $44\%$ of the usual two photons exchange contribution, and is larger than the current experimental precision, and should be consider…
We study kaonic hydrogen, the bound K^-p state A_(Kp). Within a quantum field theoretic and relativistic covariant approach we derive the energy level displacement of the ground state of kaonic hydrogen in terms of the amplitude of K^-p scattering for arbitrary relative momenta. The amplitude of low-energy K^-p scattering near threshold is defined by the contributions of three resonances Lambda(1405), Lambda(1800) and Sigma^0(1750) and a smooth elastic background. The amplitudes of inelastic channels of low-energy K^-p scattering fit experimental data on near threshold behaviour of the cross s…
We investigate the muonic hydrogen 2P^{F=2}_{3/2} to 2S^{F=1}_{1/2} transition through a precise, non-perturbative numerical solution of the Dirac equation including the finite-size Coulomb force and finite size vacuum polarization. The results are compared with earlier perturbative calculations of (primarily) Borie, Martynenko, and Pachucki; and experimental results recently presented by Pohl et al., in which this very comparison is interpreted as requiring a modification of the proton charge radius from that obtained in electron scattering and electronic hydrogen analyses. We find no signifi…
We consider pionic hydrogen A_(pi p), the bound pi^- p state. Within the quantum field theoretic and relativistic covariant approach we calculate the shift and width of the energy level of the ground state of pionic hydrogen caused by strong low-energy interactions treated perturbatively. The generalization of the Deser-Goldberger-Baumann-Thirring (DGBT) formulas (Phys. Rev. 96, 774 (1954)) is given. The generalized DGBT formulas for the energy level displacement of the ground state of pionic hydrogen contain the non-perturbative and model-independent correction about 1%, caused by the relativ…
We develop a method for lattice QCD calculation of the two-photon exchange (TPE) contribution to the muonic-hydrogen Lamb shift. To demonstrate the feasibility of this method, we also present an exploratory study with a gauge ensemble at $m_π= 142$ MeV. By adopting the infinite-volume reconstruction (IVR) method along with an optimized subtraction scheme, we obtain a preliminary result of the TPE contribution which agrees well with previous calculation using other methods and one magnitude smaller compare to the large $\sim300~μ$eV discrepancy for the proton radius puzzle.
We develop a method for lattice QCD calculation of the two-photon exchange contribution to the muonic-hydrogen Lamb shift. To demonstrate its feasibility, we present the first lattice calculation with a gauge ensemble at $m_π= 142$ MeV. By adopting the infinite-volume reconstruction method along with an optimized subtraction scheme, we obtain $ΔE_{\text{TPE}} = -28.9(4.9)~μ\text{eV} + 93.72~μ\text{eV}/\text{fm}^2 \cdot\langle r_p^2 \rangle$, or $ΔE_{\text{TPE}} = 37.4(4.9)~μ$eV, which is consistent with the previous theoretical results in a range of 20-50 $μ$eV.
We evaluate the two-photon exchange corrections to the Lamb shift and hyperfine splitting of S states in electronic hydrogen relying on modern experimental data and present the two-photon exchange on a neutron inside the electronic and muonic atoms. These results are relevant for the precise extraction of the isotope shift as well as in the analysis of the ground state hyperfine splitting in usual and muonic hydrogen.
A set of fully relativistic one-pion-exchange electromagnetic operators is developed for use in one-particle emission reactions induced by electrons. To preserve the gauge invariance of the theory additional pionic correlation operators are required beyond the usual meson-exchange current operators. Of these, in the present work emphasis is placed on the self-energy current which is infinite and needs to be renormalized. The renormalized current is expanded to first order to obtain a genuine one-pion-exchange contribution to the inclusive responses.
The relativistic interacting quark-diquark model, constructed in the framework of point form dynamics, is extended to strange baryons. The strange and nonstrange baryon spectra are calculated and compared with the experimental data.
It is shown that, in the relativistic hydrogenic approximation, expectation values of the type $\langle n\ell j|r^k|n\ell j\rangle$ can be expressed in terms of Clebsch-Gordan coefficients or $3jm$ symbols. This generalizes the results obtained by Varshalovich and Karpova [Opt. Spectrosc. 118, 1-5 (2015); Opt. Spektrosk. 118, 3-7] in the non-relativistic hydrogenic case.
It is shown that the dynamical observables calculated with the point form relativistic quantum mechanics incorporate effects of particle-antiparticle creation from the vacuum by interactions. The electromagnetic observables obtained with the point form impulse approximation include contributions from the ``pair'' exchange currents that are associated with the interactions between particles. This implies that the recently calculated nucleon electromagnetic formfactors with the chiral constituent quark model automatically take into account effects of ``pair'' exchange currents that are associate…
Relativistic effects and the role of heavy meson exchange in deuteron photodisintegration are studied systematically for photon energies below the pion production threshold. In a (p/M)-expansion, all leading order relativistic one-body and pi-exchange as well as all static heavy meson exchange currents consistent with the Bonn OBEPQ model are included. In addition, one- and two-body boost effects have been investigated. Sizeable effects from the various two-body contributions beyond pi-exchange have been found in almost every observable considered, i.e., differential cross section and single p…
The one-pion exchange current corrections to isoscalar and isovector magnetic moments of double-closed shell nuclei plus and minus one nucleon with $A=15,17,39$ and 41 have been studied in the relativistic mean field (RMF) theory and compared with previous relativistic and non-relativistic results. It has been found that the one-pion exchange current gives a negligible contribution to the isoscalar magnetic moments but a significant correction to the isovector ones. However, the one-pion exchange current doesn't improve the description of nuclear isovector magnetic moments for the concerned nu…
The chiral two-pion exchange nucleon-nucleon interaction has nowadays a rather firm conceptual basis, but depends on low-energy constants, which may be extracted from fits to data. In order to facilitate this kind of application, we present here a parametrized version of our relativistic expansion of this component of the force to $O(q^4)$, performed recently.
A model of two-component relativistic fluid is considered, and the thermal nature of coupling between the fluid constituents is outlined. This thermal coupling is responsible for non-ideality of the fluid composite where the components are not fully independent. The interaction between particles is reflected only in the equation of state of each component, but it deals nothing with the coupling between the fluid components and does not influence the hydrodynamic motion. A general form of two-fluid decomposition is formulated for arbitrary interacting system.
The renormalization of the NN interaction with the Chiral Two Pion Exchange Potential computed using relativistic baryon chiral perturbation theory is considered. The short distance singularity reduces the number of counter-terms to about a half as those in the heavy-baryon expansion. Phase shifts and deuteron properties are evaluated and a general overall agreement is observed.
Treating the quark and diquark as elementary particles, the Bethe-Salpeter equation for the nucleon is solved numerically. The dependence of the mass on the diquark mass and on the coupling constants is investigated. The resulting relativistic quark-diquark-nucleon vertex is presented and discussed.
The energy density functional (EDF) method is very widely used in nuclear physics, and among the various existing functionals those based on the relativistic Hartree (RH) approximation are very popular because the exchange contributions (Fock terms) are numerically rather onerous to calculate. Although it is possible to somehow 'mock up' the effects of meson-induced exchange terms by adjusting the meson-nucleon couplings, the lack of Coulomb exchange contributions hampers the accuracy of predictions. In this note, we show that the Coulomb exchange effects can be easily included with a good acc…
We examine the effect of adding pion exchange between quarks and pion self-energy corrections to the Los Alamos Relativistic Quark model with a short distance cutoff of the Bethe form. The contributions to the nucleon and the Delta-baryon are small. We conclude that the model is stable under this change in the sense that significant changes to the model parameters are not required.
Electron-induced one-nucleon knock-out observables are computed for moderate to high momentum transfer making use of semi-relativistic expressions for the one-body and two-body meson-exchange current matrix elements. Emphasis is placed on the semi-relativistic form of the $Δ$-isobar exchange current and several prescriptions for the dynamical-equivalent form of the $Δ$-propagator are analyzed. To this end, the inclusive transverse response function, evaluated within the context of the semi-relativistic approach and using different prescriptions for the $Δ$-propagator, is compared with the full…
We show that formally for the standard ansatz relativistic point-coupling mean-field (RMF-PC) model a lagrangian density L is not equivalent in Hartree and Hartree-Fock approximations. The equivalency can be achieved only if we use a ``complete'' ansatz at the cost of introducing new parameters in the model. An approximate treatment of the exchange terms from standard RMF-PC indicates that these effects cannot be easily, if at all, absorbed by a Dirac-Hartree approximation.
A consistent analysis of relativistic pionic correlations and meson-exchange currents for electroweak quasielastic electron scattering from nuclei is carried out. Fully-relativistic one-pion-exchange electromagnetic operators are developed for use in one-particle emission electronuclear reactions within the context of the relativistic Fermi gas model. Then the exchange and pionic correlation currents are set up fully respecting the gauge invariance of the theory. Emphasis is placed on the self-energy current which, being infinite, needs to be renormalized. This is achieved starting in the Hart…
The relativistic local density approximation (LDA) for the Coulomb exchange functional in nuclear systems is presented. This approximation is composed of the well-known Slater approximation in the non-relativistic scheme and the corrections due to the relativistic effects. Its validity in finite nuclei is examined by comparing with the exact treatment of the Coulomb exchange term in the relativistic Hartree-Fock-Bogoliubov theory. The relativistic effects are found to be important and the exact Coulomb exchange energies can be reproduced by the relativistic LDA within 5% demonstrated by the se…
Elastic charge-exchange in relativistic heavy ion collisions is responsible for the non-disruptive change of the charge state of the nuclei. We show that it can be reliably calculated within the eikonal approximation for the reaction part. The formalism is applied to the charge-pickup cross sections of 158 GeV/nucleon Pb projectiles on several targets. The relative contributions of pion- and rho-exchange are determined, using a single-particle model for the internal structure of the nuclei. The calculated cross sections are non-negligible for heavy targets. It is shown that these cross section…
We analyze the role of meson exchange currents (MEC) in photon- and electron-induced one nucleon emission reactions in a fully relativistic model. The relativistic mean field theory is used for the bound state and the Pauli reduction for the scattering state. Direct 1-body and exchange 2-body terms in the nuclear current are considered. Results for the 12C(gamma,p) and 16O(gamma,p) differential cross sections and photon asymmetries are displayed in an energy range between 60 and 196 MeV. The 2-body seagull current affects the cross section less than in nonrelativistic analyses. In the case of …
We calculate in baryon chiral perturbation theory the relativistic $1/M^2$-corrections to the leading order two-pion exchange diagrams. We give explicit expressions for the corresponding one-loop NN-amplitudes in momentum space. The resulting isovector central and isoscalar spin-spin and tensor NN-amplitudes involve non-static terms proportional to the squared nucleon center-of-mass momentum $p^2$. From the two-pion exchange box diagrams we obtain an isoscalar quadratic spin-orbit NN-amplitude. We give also analytical expressions for the corresponding NN-potentials in coordinate space. The dia…
Using a three-dimensional formalism that includes relativistic kinematics, the effects of negative-energy states, approximate boosts of the two-body system, and current conservation we calculate the electromagnetic form factors of the deuteron up to $Q^2=6$ GeV$^2$. This is done both in impulse approximation and with a $ρπγ$ meson-exchange current included. The experimentally-measured quantities $A$, $B$, and $T_{20}$ are calculated over the kinematic range probed in recent Jefferson Laboratory experiments. The meson-exchange current provides significant strength in $A$ at large $Q^2$, but has…
The N-quantum approach (NQA) to quantum field theory uses the complete and irreducible set of in or out fields, including in or out fields for bound states, as standard building blocks to construct solutions to quantum field theories. In particular, introducing in (or out) fields for the bound states allows a new way to calculate energy levels and wave functions for the bound states that is both covariant and effectively 3-dimensional. This method is independent of the Bethe-Salpeter equation. In contrast to the Bethe-Salpeter equation, all solutions of the NQA are normalizable and correspond …
