Search

For an accurate theoretical description of muonic bound systems, it is crucial to consistently treat relativistic and recoil corrections to vacuum polarization. The one-loop vacuum-polarization effect is by far the dominant quantum electrodynamic (QED) energy correction for bound muons, being of order $\alpha (Z\alpha)^2 m_r$, where $\alpha$ is the fine-structure constant, $Z$ is the nuclear charge number, and $m_r$ is the reduced mass. Gauge invariance of the relativistic and recoil corrections to vacuum polarization of order $\alpha (Z\alpha)^4 m_r$ is investigated with respect to nonretarded and standard, renormalized variants of Coulomb gauge. The invariance is shown after including three-photon exchange diagrams. Our derivation is based on an adapted form of Nonrelativistic Quantum Electrodynamics for bound muon systems (NRQED$_\mu$), which is a version of NRQED where the hard scale is set at the muon mass instead of the electron mass. Updated values for the gauge-independent corrections for one-muon ions with nuclear charge numbers $Z = 1,2,6$ are presented., Comment: 15 pages, 1 figure

We discuss numerical aspects of instantons in two- and three-dimensional $\phi^4$ theories with an internal $O(N)$ symmetry group, the so-called $N$-vector model. Combining asymptotic transseries expansions for large argument with convergence acceleration techniques, we obtain high-precision values for certain integrals of the instanton that naturally occur in loop corrections around instanton configurations. Knowledge of these numerical properties are necessary in order to evaluate corrections to the large-order factorial growth of perturbation theory in $\phi^4$ theories. The results contribute to the understanding of the mathematical structures underlying the instanton configurations., Comment: 11 pages; RevTeX

The calculation of higher-order binding corrections to bound systems is a fundamental problem of theoretical physics. For any nonrelativistic expansion, one needs the Foldy-Wouthuysen Transformation which disentangles the particle and the antiparticle degrees of freedom. This transformation is carried out here to eighth order in the momenta, or, to eighth order in the momentum operators, which is equivalent to the eighth order of the fine-structure constant. Matrix elements of the eighth-order terms are evaluated for F_5/2 and F_7/2 states in hydrogenlike ions and compared with the Dirac-Coulomb energy levels., Comment: 9 pages; RevTeX; discussion in Appendix A enhanced; accepted for publication by Physical Review A

The so-called proton radius puzzle (the current discrepancy of proton radii determined from spectroscopic measurements in ordinary versus muonic hydrogen) could be addressed via an accurate measurement of the Rydberg constant, because the proton radius and the Rydberg constant values are linked through high-precision optical spectroscopy. We argue that, with manageable additional experimental effort, it might be possible to improve circular Rydberg state spectroscopy, potentially leading to an important contribution to the clarification of the puzzle. Our proposal involves circular and near-circular Rydberg states of hydrogen with principal quantum number around $n=18$, whose classical velocity on a Bohr orbit is slower than that of the fastest macroscopic man-made object, the Parker Solar Probe. We obtain improved estimates for the quality factor of pertinent transitions, and illustrate a few recent improvements in instrumentation which facilitate pertinent experiments., Comment: 8 pages; RevTeX

We revisit the derivation of multipole contributions to the atom-wall interaction previously presented in [G. Lach et al., Phys. Rev. A 81, 052507 (2010)]. A careful reconsideration of the angular-momentum decomposition of the second-, third- and fourth-rank tensors composed of the derivatives of the electric-field modes leads to a modification for the results for the quadrupole, octupole and hexadecupole contributions to the atom-wall interaction. Asymptotic results are given for the asymptotic long-range forms of the multipole terms, in both the short-range and long-range limits. Calculations are carried out for hydrogen and positronium in contact with $\alpha$-quartz; a reanalysis of analytic models of the dielectric function of alpha-quartz is performed. Analytic results are provided for the multipole polarizabilities of hydrogen and positronium. The quadrupole correction is shown to be numerically significant for atom-surface interactions. The expansion into multipoles is shown to constitute a divergent, asymptotic series. Connections to van-der-Waals corrected density-functional theory and applications to physisorption are decribed., Comment: 13 pages; RevTeX

We analyze the leading and higher-order quantum electrodynamic corrections to the energy levels for a single electron bound in a Penning trap, including the Bethe logarithm correction due to virtual excitations of the reference quantum cyclotron state. The effective coupling parameter alpha_c in the Penning trap is identified as the square root of the ratio of the cyclotron frequency, converted to an energy via multiplication by the Planck constant, to the electron rest mass energy. We find a large, state-independent, logarithmic one-loop self-energy correction of order alpha alpha_c^4 m c^2 ln(alpha_c^(-2)), where m is the electron rest mass and c is the speed of light. Furthermore, we find a state-independent "trapped" Bethe logarithm. We also obtain a state-dependent higher-order logarithmic self-energy correction of order alpha alpha_c^6 m c^2 ln(alpha_c^(-2)). In the high-energy part of the bound-state self energy, we need to consider terms with up to six magnetic interaction vertices inside the virtual photon loop., Comment: 11 pages; RevTeX

We use an algebraic approach to the calculation of Landau levels for a uniform magnetic field in the symmetric gauge with a vector potential A = (1/2) (B x r), where B is assumed to be constant. The magnetron quantum number constitutes the degeneracy index. An overall complex phase of the wave function, given in terms of Laguerre polynomials, is a consequence of the algebraic structure. The relativistic generalization of the treatment leads to fully relativistic bispinor Landau levels in the symmetric gauge, in a representation which writes the relativistic states in terms of their nonrelativistic limit, and an algebraically accessible lower bispinor component. Negative-energy states and the massless limit are discussed. The relativistic states can be used for a number of applications, including the calculation of higher-order quantum electrodynamic binding corrections to the energies of quantum cyclotron levels., Comment: 7 pages; RevTeX

The proton radius puzzle is known as the discrepancy of the proton radius, obtained from muonic hydrogen spectroscopy (obtained as being roughly equal to 0.84fm), and the proton radius obtained from (ordinary) hydrogen spectroscopy where a number of measurements involving highly excited states have traditionally favored a value of about 0.88fm. Recently, a number of measurements of hydrogen transitions by the Munich (Garching) groups (notably, several hyperfine-resolved sublevels of the 2S-4P) and by the group at the University of Toronto (2S-2P_1/2) have led to transition frequency data consistent with the smaller proton radius of about 0.84fm. A recent measurement of the 2S-8D transition by a group at Colorado State University leads to a proton radius of about $0.86$\,fm, in between the two aforementioned results. The current situation points to a possible, purely experimental, resolution of the proton radius puzzle. However, a closer look at the situation reveals that the situation may be somewhat less clear, raising the question of whether or not the proton radius puzzle has been conclusively solved, and opening up interesting experimental possiblities at TRIUMF/ARIEL., Comment: 4 pages; RevTeX

We investigate the time propagation of tachyonic (superluminal) and tardyonic (subluminal, ordinary) massive wave packets on cosmic scales. A normalizable wave packet cannot be monochromatic in momentum space and thus acquires a positional uncertainty (or packet width) that increases with travel distance. We investigate the question of how this positional uncertainty affects the uncertainty in the detection time for cosmic radiation on Earth. In the ultrarelativistic limit, we find a unified result, $\delta x(t)/c^3 = m^2 \delta p t /p_0^3$, where $\delta x(t)$ is the positional uncertainty, $m$ is the mass parameter, $\delta p$ is the initial momentum spread of the wave function, and $p_0$ is the central momentum of the wave packet, which, in the ultrarelativistic limit, is equal to its energy. This result is valid for tachyons and tardyons; its interpretation is being discussed., Comment: Published in journal "Symmetry" in the special issue on "Tachyons and Fundamental Symmetries"

Recently, the large-order behavior of correlation functions of the $O(N)$-anharmonic oscillator has been analyzed by us in [L. T. Giorgini et el., Phys. Rev. D 101, 125001 (2020)]. Two-loop corrections about the instanton configurations were obtained for the partition function, and the two-point and four-point functions, and the derivative of the two-point function at zero momentum transfer. Here, we attempt to verify the obtained analytic results against numerical calculations of higher-order coefficients for the $O(1)$, $O(2)$, and $O(3)$ oscillators, and demonstrate the drastic improvement of the agreement of the large-order asymptotic estimates and perturbation theory upon the inclusion of the two-loop corrections to the large-order behavior., Comment: 18 pages, 4 figures

Current precision scattering experiments and even more so many experiments planed for the Electron Ion Collider will be limited by systematics. From the theory side, a fundamental source of systematic uncertainty is the correct treatment of radiative effects. To gauge the current state of technique and knowledge, help the cross-pollination between different direction of nuclear physics, and to give input to the yellow report process, the community met in an ad-hoc workshop hosted by the Center for Frontiers in Nuclear Science, Stony Brook University. This whitepaper is a collection of contributions to this workshop.

The hypothesis of Lorentz violation in the neutrino sector has intrigued scientists for the last two to three decades. A number of theoretical arguments support the emergence of such violations first and foremost for neutrinos, which constitute the "most elusive" and "least interacting" particles known to mankind. It is of obvious interest to place stringent bounds on the Lorentz-violating parameters in the neutrino sector. In the past, the most stringent bounds have been placed by calculating the probability of neutrino decay into a lepton pair, a process made kinematically feasible by Lorentz violation in the neutrino sector, above a certain threshold. However, even more stringent bounds can be placed on the Lorentz-violating parameters if one takes into account, additionally, the possibility of neutrino splitting, i.e., of neutrino decay into a neutrino of lower energy, accompanied by "neutrino-pair Cerenkov radiation". This process has negligible threshold and can be used to improve the bounds on Lorentz-violating parameters in the neutrino sector. Finally, we take the opportunity to discuss the relation of Lorentz and gauge symmetry breaking, with a special emphasis on the theoretical models employed in our calculations., Comment: 16 pages; LaTeX

Two recent experimental observations at the ATOMKI Institute of the Hungarian Academy of Sciences (regarding the angular emission pattern of electron-positron pairs from nuclear transitions from excited states in 8Be and 4He) indicate the possible existence of a particle of a rest mass energy of roughly 17 MeV. The so-called X17 particle constitutes a virtual state in the process, preceding the emission of the electron-positron pair. Based on the symmetry of the nuclear transitions ($1^+$ to $0^+$ and $0^-$ to $0^+$), the X17 could either be a vector, or a pseudoscalar particle. Here, we calculate the effective potentials generated by the X17, for hyperfine interactions in simple atomic systems, for both the pseudoscalar as well as the vector X17 hypotheses. The effective Hamiltonians are obtained in a general form which is applicable to both electronic as well as muonic bound systems. The effect of virtual annihilation and its contribution to the hyperfine splitting also is considered. Because of the short range of the X17-generated potentials, the most promising pathway for the observation of the X17-mediated effects in bound systems concerns hyperfine interactions, which, for $S$ states, are given by modifications of short-range (Dirac-delta) potentials in coordinate space. For the pseudoscalar hypothesis, the exchange of one virtual X17 quantum between the bound lepton and the nucleus exclusively leads to hyperfine effects, but does not affect the Lamb shift. Effects due to the X17 are shown to be drastically enhanced for muonic bound systems. Prospects for the detection of hyperfine effects mediated by X17 exchange are analyzed for muonic deuterium, muonic hydrogen, muonium, true muonium ($\mu^+\mu^-$ bound system), and positronium., Comment: 14 pages; RevTeX

The application of the CPT theorem to an apple falling on Earth leads to the description of an anti-apple falling on anti-Earth (not on Earth). On the microscopic level, the Dirac equation in curved space-time simultaneously describes spin-1/2 particles and their antiparticles coupled to the same curved space-time metric (e.g., the metric describing the gravitational field of the Earth). On the macroscopic level, the electromagnetically and gravitationally coupled Dirac equation therefore describes apples and anti-apples, falling on Earth, simultaneously. A particle-to-antiparticle transformation of the gravitationally coupled Dirac equation therefore yields information on the behavior of "anti-apples on Earth". However, the problem is exacerbated by the fact that the operation of charge conjugation is much more complicated in curved as opposed to flat space-time. Our treatment is based on second-quantized field operators and uses the Lagrangian formalism. As an additional helpful result, prerequisite to our calculations, we establish the general form of the Dirac adjoint in curved space-time. On the basis of a theorem, we refute the existence of tiny, but potentially important, particle-antiparticle symmetry breaking terms whose possible existence has been investigated in the literature. Consequences for antimatter gravity experiments are discussed., Comment: 19 pages; LaTeX

We study the interplay of general relativity, the equivalence principle, and high-precision experiments involving atomic transitions and g factor measurements. In particular, we derive a generalized Dirac Hamiltonian, which describes both the gravitational coupling for weak fields, as well as the electromagnetic coupling, e.g., to a central Coulomb field. An approximate form of this Hamiltonian is used to derive the leading gravitational corrections to transition frequencies and g factors. The position-dependence of atomic transitions is shown to be compatible with the equivalence principle, up to a very good approximation. The compatibility of g factor measurements requires a deeper, subtle analysis, in order to eventually restore the compliance of g factor measurements with the equivalence principle. Finally, we analyze small, but important limitations of Einstein's equivalence principle due to quantum effects, within high-precision experiments. We also study the relation of these effects to a conceivable gravitationally induced collapse of a quantum mechanical wave function (Penrose conjecture), and space-time noncommutativity, and find that the competing effects should not preclude the measurability of the higher-order gravitational corrections. Surprisingly large higher-order gravitational effects are obtained for transitions in diatomic molecules., Comment: 19 pages; RevTeX; some typographical errors corrected

Theoretical and experimental resonance strengths for KLL dielectronic recombination (DR) into He-, Li-, Be-, and B-like mercury ions are presented, based on state-resolved DR x-ray spectra recorded at the Heidelberg electron beam ion trap. The DR resonance strengths were experimentally extracted by normalizing them to simultaneously recorded radiative recombination signals. The results are compared to state-of-the-art atomic calculations that include relativistic electron-electron correlation and configuration mixing effects. Combining the present data with other existing ones, we derive an improved semi-empirical $Z$-scaling law for DR resonance strength as a function of the atomic number, taking into account higher-order relativistic corrections, which are especially relevant for heavy highly charged ions., Comment: 11 pages, 4 figures, accepted to Phys. Rev. A

Recently, a peak in the light fermion pair spectrum at invariant q^2 approximately equal to 16.7 Me^2. has been observed in the bombardment of Li-7 by protons. This peak has been interpreted in terms of a protophobic interaction of fermions with a gauge boson (X boson) of invariant mass of approximately 16.7 MeV which couples mainly to neutrons. High-precision atomic physics experiments aimed at observing the protophobic interaction need to separate the X boson effect from the nuclear-size effect, which is a problem because of the short range of the interaction 11.8 fm, which is commensurate with a "nuclear halo". Here, we analyze the X boson in terms of its consequences for both electronic atoms as well as muonic hydrogen and deuterium. We find that the most promising atomic systems where the X boson has an appreciable effect, distinguishable from a finite-nuclear-size effect, are muonic atoms of low and intermediate nuclear charge numbers., Comment: 8 pages; RevTeX

The emission of a charged light lepton pair by a superluminal neutrino has been identified as a major factor in the energy loss of highly energetic neutrinos. The observation of PeV neutrinos by IceCube implies their stability against lepton pair Cerenkov radiation. Under the assumption of a Lorentz-violating dispersion relation for highly energetic superluminal neutrinos, one may thus constrain the Lorentz-violating parameters. A kinematically different situation arises when one assumes a Lorentz-covariant, space-like dispersion relation for hypothetical tachyonic neutrinos, as an alternative to Lorentz-violating theories. We here discuss a hitherto neglected decay process, where a highly energetic tachyonic neutrinos may emit other (space-like, tachyonic) neutrino pairs. We find that the space-like dispersion relation implies the absence of a q^2 threshold for the production of a tachyonic neutrino-antineutrino pair, thus leading to the dominant additional energy loss mechanism for an oncoming tachyonic neutrino in the medium-energy domain. Surprisingly, the small absolute value of the decay rate and energy loss rate in the tachyonic model imply that these models, in contrast to the Lorentz-violating theories, are not pressured by the cosmic PeV neutrinos registered by the IceCube collaboration., Comment: 7 pages; RevTeX; accepted for publication for Advances in High Energy Physics

We consider in detail the calculation of the decay rate of high-energy superluminal neutrinos against (charged) lepton pair Cerenkov radiation (LPCR), and neutrino pair Cerenkov radiation (NPCR), i.e., against the decay channels nu -> nu e+ e- and nu -> nu nubar nu. Under the hypothesis of a tachyonic nature of neutrinos, these decay channels put constraints on the lifetime of high-energy neutrinos for terrestrial experiments as well as on cosmic scales. For the oncoming neutrino, we use the Lorentz-covariant tachyonic relation E_nu = (p^2 - m_nu^2)^(1/2), where m_nu is the tachyonic mass parameter. We derive both threshold conditions as well as decay and energy loss rates, using the plane-wave fundamental bispinor solutions of the tachyonic Dirac equation. Various intricacies of rest frame versus lab frame calculations are highlighted. The results are compared to the observations of high-energy IceCube neutrinos of cosmological origin., Comment: 29 pages; RevTeX

Current experiments do not exclude the possibility that one or more neutrinos are very slightly superluminal or that they have a very small tachyonic mass. Important bounds on the size of a hypothetical tachyonic neutrino mass term are set by lepton pair Cerenkov radiation (LPCR), i.e., by the decay channel nu -> e^+ e^- nu which proceeds via a virtual Z0 boson. Here, we use a Lorentz-invariant dispersion relation which leads to very tight constraints on the tachyonic mass of neutrinos; we also calculate decay and energy loss rates. A possible cutoff seen in the IceCube neutrino spectrum for E_nu > 2 PeV, due to the potential onset of LPCR, is discussed., Comment: 7 pages; accepted for publication in the Advances of High-Energy Physics

The attractive branch of the interaction potentials with the surface of gold have been computed for a large variety of atomic systems: the hydrogen atom, noble gases (He, Ne, Ar, Kr, Xe), alkali atoms (Li, Na, K, Rb, Cs) and alkaline atoms (Be, Mg, Ca, Sr, Ba). The results include highly accurate dynamic polarizabilities for the helium atom calculated using a variational method and explicitly correlated wavefunctions. For other atoms considered we used the data available in the literature. The interaction potentials include both the effects of retardation of the electromagnetic interactions and a realistic representation of the optical response function of gold (beyond the approximation of a perfect conductor). An explicit comparison of our result to the interaction between an atom and a perfect conductor is given., Comment: 8 pages, 1 figure

The energy levels of quantum systems are determined by quantization conditions. For one-dimensional anharmonic oscillators, one can transform the Schrodinger equation into a Riccati form, i.e., in terms of the logarithmic derivative of the wave function. A perturbative expansion of the logarithmic derivative of the wave function can easily be obtained. The Bohr-Sommerfeld quantization condition can be expressed in terms of a contour integral around the poles of the logarithmic derivative. Its functional form is B_m(E,g) = n + 1/2, where B is a characteristic function of the anharmonic oscillator of degree m, E is the resonance energy, and g is the coupling constant. A recursive scheme can be devised which facilitates the evaluation of higher-order Wentzel-Kramers-Brioullin (WKB) approximants. The WKB expansion of the logarithmic derivative of the wave function has a cut in the tunneling region. The contour integral about the tunneling region yields the instanton action plus corrections, summarized in a second characteristic function A_m(E,g). The evaluation of A_m(E,g) by the method of asymptotic matching is discussed for the case of the cubic oscillator of degree m=3., Comment: 11 pages, LaTeX; three further typographical errors corrected

The hyperfine structure (hfs) and the g factor of a bound electron are caused by external magnetic fields. For the hfs, the magnetic field is due to the nuclear spin. A uniform-in-space and constant-in-time magnetic field is used to probe the bound-electron g factor. The self-energy corrections to these effects are more difficult to evaluate than those to the Lamb shift. Here, we describe a numerical approach for both effects in the notoriously problematic regime of hydrogen-like bound systems with low nuclear charge numbers. The calculation is nonperturbative in the binding Coulomb field. Accurate numerical values for the remainder functions are provided for 2P states and for nS states with n=1,2,3., Comment: 17 pages, 6 tables

In the relativistic and the nonrelativistic theoretical treatment of moderate and high-power laser-matter interaction, the generalized Bessel function occurs naturally when a Schr\"odinger-Volkov and Dirac-Volkov solution is expanded into plane waves. For the evaluation of cross sections of quantum electrodynamic processes in a linearly polarized laser field, it is often necessary to evaluate large arrays of generalized Bessel functions, of arbitrary index but with fixed arguments. We show that the generalized Bessel function can be evaluated, in a numerically stable way, by utilizing a recurrence relation and a normalization condition only, without having to compute any initial value. We demonstrate the utility of the method by illustrating the quantum-classical correspondence of the Dirac-Volkov solutions via numerical calculations., Comment: 14 pages, 5 figures

The concept of a generalized nonanalytic expansion which involves nonanalytic combinations of exponentials, logarithms and powers of a coupling is introduced and its use illustrated in various areas of physics. Dispersion relations for the resonance energies of odd anharmonic oscillators are discussed, and higher-order formulas are presented for cubic and quartic potentials.