Gravitational Effects in g Factor Measurements and High-Precision Spectroscopy: Limits of Einstein's Equivalence Principle

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 correcte

Non-uniform convergence of two-photon decay rates for excited atomic states

Two-photon decay rates in simple atoms such as hydrogenlike systems represent rather interesting fundamental problems in atomic physics. The sum of the energies of the two emitted photons has to fulfill an energy conservation condition, the decay takes place via intermediate virtual states, and the total decay rate is obtained after an integration over the energy of one of the emitted photons. Here, we investigate cases with a virtual state having an energy intermediate between the initial and the final state of the decay process, and we show that due to non-uniform convergence, only a careful treatment of the singularities infinitesimally displaced from the photon integration contour leads to consistent and convergent results.Comment: 3 pages; LaTe

Neutrino Pair Cerenkov Radiation for Tachyonic Neutrinos

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 Physic

Lepton-pair Cerenkov radiation emitted by tachyonic neutrinos: Lorentz-covariant approach and IceCube data

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 Physic

Relativistic calculation of the two-photon decay rate of highly-excited ionic states

Based on quantum electrodynamics, we reexamine the two-photon decay of one-electron atoms. Special attention is paid to the calculation of the (two-photon) total decay rates which can be viewed as the imaginary part of the two-loop self-energy. We argue that our approach can easily be applied to the cases with a virtual state having an intermediate energy between the initial and the final state of the decay process leading, thus, to the resonance peaks in the two-photon energy distribution. In order to illustrate our approach, we obtain fully relativistic results, resolved into electric and magnetic multipole components, for the two-photon decay rates of the 3S_{1/2} -> 1S_{1/2} transition in neutral hydrogen as well as in various hydrogen-like ions.Comment: 11 pages, LaTe

Recursive algorithm for arrays of generalized Bessel functions: Numerical access to Dirac-Volkov solutions

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 figure

Calculation of Hydrogenic Bethe Logarithms for Rydberg States

We describe the calculation of hydrogenic (one-loop) Bethe logarithms for all states with principal quantum numbers n <= 200. While, in principle, the calculation of the Bethe logarithm is a rather easy computational problem involving only the nonrelativistic (Schroedinger) theory of the hydrogen atom, certain calculational difficulties affect highly excited states, and in particular states for which the principal quantum number is much larger than the orbital angular momentum quantum number. Two evaluation methods are contrasted. One of these is based on the calculation of the principal value of a specific integral over a virtual photon energy. The other method relies directly on the spectral representation of the Schroedinger-Coulomb propagator. Selected numerical results are presented. The full set of values is available at quant-ph/0504002.Comment: 10 pages, RevTe

Squeezing the Parameter Space for Lorentz Violation in the Neutrino Sector by Additional Decay Channels

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; LaTe

Proton Radius: A Puzzle or a Solution!?

The proton radius puzzle is known as the discrepancy of the proton radius, obtained from muonic hydrogen spectroscopy (obtained as being roughly equal to 0.84 fm), 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 0.88 fm. 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 0.84 fm. 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 possibilities at TRIUMF/ARIEL