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Savely G. Karshenboim

Publications and source records attributed to Savely G. Karshenboim.

At least 19 recordsLinked to original sources
arXiv2024

Laboratory constraint on the electric charge of the neutron and the neutrino

We revisit constraints on the electric charge of the neutron and neutrino as well as on e_p+e_e. We consider phenomenological constraints based on laboratory study of the electrical neutrality of subatomic, atomic, and molecular species under assumption of the conservation of the electric charge in the beta decay, that relates e_p+e_e, e_n, and e_nu. Some previously published constraints utilized an additional assumption e_nu=0, which we do not. We dismiss a cosmological constraint at the level of 10^-35 e utilized by PDG in their Review of particle properties as a controversial one which makes the laboratory constraints on e_nu dominant. The phenomenological constraints from the laboratory experiments are obtained as e_p+e_e=(0.2\pm2.6)10^-21 e, e_n=(-0.4\pm1.1)10^-21 e, and e_nu=(0.6\pm3.2)10^{-21} e. The ones on e_p+e_e and e_n are at the same level as the PDG constraints, while our e_nu constraint is several orders of magnitude weaker than the controversial cosmological result dominated in the PDG constraint, but several orders of magnitude stronger than the other individual e_nu constraints considered by PDG. We also consider consistency of the phenomenological constraints and the SM. The SM ignores the neutrino mass term and cannot describe the neutrino oscillations which makes it not a complete theory but a part of it. We demonstrate that the condition of the cancellation of the triangle anomaly within the complete theory does not disagree with the phenomenological constraints since different extensions of the SM may produce different additional contributions to the anomaly. In particular, we consider a minimal extension of the SM, where leptons (nu,e) are treated the same ways as quarks, which sets e_p+e_e=0 and allows for numerical strengthening the constraint on e_n and e_nu, which is e_n=-e_nu=(-0.4\pm1.0)10^-21 e.

hep-ph↗
arXiv2024

A dual concept of the angle in mathematics and practice

We consider the angle in mathematics and arrive at a conclusion that there are two concepts on the issue. One is a descriptive geometrical one, while the other is from functional analysis. They are somewhat different, allow for different options, and both are legitimate and in use. Their difference may cause certain confusions. While the `geometrical angle' allows for different choice of units, the `functional angle' is a purely dimensionless one, being related to the angle in radians. We consider possible options to resolve the problem as it concerns the units.

physics.hist-ph↗
arXiv2019

Virtual Delbrück scattering and the Lamb shift in light hydrogen-like atoms

We return to the problem of evaluation of the light-by-light contribution to the energy levels of the hydrogen atom. We find an additional contribution directly related to the Delbrück scattering amplitude. The new correction is larger than the previously included light-by-light terms at order~$α^2 (Zα)^6\ln(Zα)\, m_e$. We consider the effective potential in position space using an effective field theory approach and evaluate light-by-light corrections to the energy levels of states with non-zero orbital momentum as well as to the weighted difference of $s$ states. We also determine the large distance asymptotic behaviour of the effective potential induced by the light-by-light scattering in muonic atoms.

physics.atom-ph↗
arXiv2019

The Lamb shift of the $1s$ state in hydrogen: two-loop and three-loop contributions

We consider the $1s$ Lamb shift in hydrogen and helium ions, a quantity, required for an accurate determination of the Rydberg constant and the proton charge radius by means of hydrogen spectroscopy, as well as for precision tests of the bound-state QED. The dominant QED contribution to the uncertainty originates from $α^8m$ external-field contributions (i.e., the contributions at the non-recoil limit). We discuss the two- and three-loop cases and in particular, we revisit calculations of the coefficients $B_{61}, B_{60}, C_{50}$ in standard notation. We have found a missing logarithmic contribution of order $α^2(Zα)^6m$. We have also obtained leading pure self-energy logarithmic contributions of order $α^2(Zα)^8m$ and $α^2(Zα)^9m$ and estimated the subleading terms of order $α^2(Zα)^7m$, $α^2(Zα)^8m$, and $α^2(Zα)^9m$. The determination of those higher-order contributions enabled us to improve the overall accuracy of the evaluation of the two-loop self-energy of the electron. We investigated the asymptotic behavior of the integrand related to the next-to-leading three-loop term (order $α^3(Zα)^5m$, coefficient $C_{50}$ in standard notation) and applied it to approximate integration over the loop momentum. Our result for contributions to the $1s$ Lamb shift for the total three loop next-to-leading term is $(-3.3\pm10.5)(α^3/π^3)(Zα)^5m$. Altogether, we have completed the evaluation of the logarithmic contributions to the $1s$ Lamb shift of order $α^8m$ and reduced the overall $α^8m$ uncertainty by approximately a factor of three for H, D, and He$^+$ as compared with the most recent CODATA compilation.

physics.atom-ph↗
arXiv2018

Light-by-light-scattering contributions to the Lamb shift in light muonic atoms

We consider one-loop light-by-light-scattering contributions to the Lamb shift of the $1s, 2s, 2p$ states in light muonic hydrogen like atoms at $Z\leq10$. The contributions are of the order $α^5m_μ$ (with diverse dependence on the nuclear charge $Z$). Those include the contributions of the so-called Wichmann-Kroll potential ($α(Zα)^4m_μ$), the virtual Delbrück scattering ($α^2(Zα)^3m_μ$), etc. The results are obtained in a nonrelativistic approximation. For the calculation of the virtual-Delbrück-scattering contribution, we have constructed an effective potential in the coordinate space which may be applied to other calculations in muonic atoms.

physics.atom-ph↗
arXiv2017

Decay of the dimuonium into a photon and a neutral pion

We compute the decay rate of dimuonium into a neutral pion and a photon. We find that approximately one in 10^5 ortho-dimuonia decays into this channel. We also determine the contribution of the virtual photon-pion loop to the hyperfine splitting in dimuonium and reproduce its leading effect in the anomalous magnetic moment of the muon.

hep-ph↗
arXiv2015

The recoil correction to the proton-finite-size contribution to the Lamb shift in muonic hydrogen

The Lamb shift in muonic hydrogen was measured some time ago to a high accuracy. The theoretical prediction of this value is very sensitive to the proton-finite-size effects. The proton radius extracted from muonic hydrogen is in contradiction with the results extracted from elastic electron-proton scattering. That creates a certain problem for the interpretation of the results from the muonic hydrogen Lamb shift. For the latter we need also to take into account the two-photon-exchange contribution with the proton finite size involved. The only way to describe it relies on the data from the scattering, which may produce an internal inconsistency of theory. Recently the leading proton-finite-size contribution to the two-photon exchange was found within the external field approximation. The recoil part of the two-photon-exchange has not been considered. Here we revisit calculation of the external-field part and take the recoil correction to the finite-size effects into account.

hep-ph↗
arXiv2014

On the accuracy of the optical determination of the proton charge radius

Determination of the proton charge radius by different methods has produced an inconsistency. The most precise value (from spectroscopy of muonic hydrogen) strongly disagrees with three less accurate values (from spectroscopy of ordinary hydrogen and deuterium, from relative measurements of the cross section of the elastic electron-proton scattering at MAMI and from evaluation of the world data on absolute measurements of e-p cross sections). Here, we question the accuracy of the determination of the proton charge radius by means of spectroscopy of ordinary hydrogen and deuterium and demonstrate that its accuracy was probably overestimated. In particular, we revisit determination from each relevant transition and find that the results of two optical experiments, which are the most statistically important, are not perfectly consistent. The inconsistency is rather a `tension' between the results than their discrepancy, however, it implies that a more conservative estimation of the uncertainty is needed. With the more realistic estimation of the uncertainty, the results for the proton charge radius from spectroscopy of ordinary and muonic atoms are rather in fair agreement.

hep-ph↗
arXiv2014

Model-independent determination of the magnetic radius of the proton from spectroscopy of ordinary and muonic hydrogen

To date the magnetic radius of the proton has been determined only by means of electron-proton scattering, which is not free of controversies. Any existing atomic determinations are irrelevant because they are strongly model-dependent. We consider a so-called Zemach contribution to the hyperfine interval in ordinary and muonic hydrogen and derive a self-consistent model-independent value of the magnetic radius of the proton. More accurately, we constrain not a value of the magnetic radius by itself, but its certain combination with the electric-charge radius of the proton, namely, R_E^2+R_M^2. The result from the ordinary hydrogen is found to be R_E^2+R_M^2=1.35(12) fm^2, while the derived muonic value is 1.49(18) fm^2. That allows us to constrain the value of the magnetic radius of proton R_M=0.78(8) fm at the 10% level.

hep-ph↗
arXiv2014

A self-consistent value of the electric radius of the proton from the Lamb shift in muonic hydrogen

Recently a high-precision measurement of the Lamb shift in muonic hydrogen has been performed. An accurate value of the proton charge radius can be extracted from this datum with a high accuracy. To do that a sufficient accuracy should be achieved also on the theoretical side, including an appropriate treatment of higher-order proton-structure effects. Here we consider a higher-order contribution of the finite size of the proton to the Lamb shift in muonic hydrogen. Only model-dependent results for this correction have been known up to date. Meantime, the involved models are not consistent either with the existing experimental data on the electron-proton scattering or with the value for the electric charge radius of the proton extracted from the Lamb shift in muonic hydrogen. We consider the higher-order contribution of the proton finite size in a model-independent way and eventually derive a self-consistent value of the electric radius of the proton. The re-evaluated value of the proton charge radius is found to be R_E=0.84022(56) fm.

hep-ph↗
arXiv2014

Relativistic recoil effects in a muonic atom within a Grotch-type approach: General approach

Recently we calculated relativistic recoil corrections to the energy levels of the low lying states in muonic hydrogen induced by electron vacuum polarization effects. The results were obtained by Breit-type and Grotch-type calculations. The former were described in our previous papers in detail, and here we present the latter. The Grotch equation was originally developed for pure Coulomb systems and allowed to express the relativistic recoil correction in order $(Zα)^4m^2/M$ in terms of the relativistic non-recoil contribution $(Zα)^4m$. Certain attempts to adjust the method to electronic vacuum polarization took place in the past, however, the consideration was incomplete and the results were incorrect. Here we present a Groth-type approach to the problem and in a series of papers consider relativistic recoil effects in order $α(Zα)^4m^2/M$ and $α^2(Zα)^4m^2/M$. That is the first paper of the series and it presents a general approach, while two other papers present results of calculations of the $α(Zα)^4m^2/M$ and $α^2(Zα)^4m^2/M$ contributions in detail. In contrast to our previous calculation, we address now a variety of states in muonic atoms with a certain range of the nuclear charge $Z$.

physics.atom-ph↗
arXiv2014

Relativistic recoil effects for energy levels in a muonic atom within a Grotch-type approach: An application to the one-loop electronic vacuum polarization

We continue our account of relativistic recoil effects in muonic atoms and present explicitly analytic results at first order in electron-vacuum-polarization effects. The results are obtained within a Grotch-type approach based on an effective Dirac equation. Some expressions are cumbersome and we investigate their asymptotic behavior. Previously relativistic two-body effects due to the one-loop electron vacuum polarization were studied by several groups. Our results found here are consistent with the previous result derived within a Breit-type approach (including ours) and disagree with a recent attempt to apply a Grotch-type approach.

physics.atom-ph↗
arXiv2014

Relativistic recoil effects to energy levels in a muonic atom: a Grotch-type calculation of the second-order vacuum-polarization contributions

Adjusting a previously developed Grotch-type approach to a perturbative calculation of the electronic vacuum-polarization effects in muonic atoms, we find here the two-loop vacuum polarization relativistic recoil correction of order $α^2(Zα)^4m^2/M$ in light muonic atoms. The result is in perfect agreement with the one previously obtained within the Breit-type approach. We also discuss here simple approximations of the irreducible part of the two-loop vacuum-polarization dispersion density, which was applied to test our calculations and can be useful for other evaluations with an uncertainty better than 1%.

physics.atom-ph↗
arXiv2014

Constraints on muon-specific dark forces

The recent measurement of the Lamb shift in muonic hydrogen allows for the most precise extraction of the charge radius of the proton which is currently in conflict with other determinations based on $e-p$ scattering and hydrogen spectroscopy. This discrepancy could be the result of some new muon-specific force with O(1-100) MeV force carrier---in this paper we concentrate on vector mediators. Such an explanation faces challenges from the constraints imposed by the $g-2$ of the muon and electron as well as precision spectroscopy of muonic atoms. In this work we complement the family of constraints by calculating the contribution of hypothetical forces to the muonium hyperfine structure. We also compute the two-loop contribution to the electron parity violating amplitude due to a muon loop, which is sensitive to the muon axial-vector coupling. Overall, we find that the combination of low-energy constraints favors the mass of the mediator to be below 10 MeV, and that a certain degree of tuning is required between vector and axial-vector couplings of new vector particles to muons in order to satisfy constraints from muon $g-2$. However, we also observe that in the absence of a consistent standard model embedding, high energy weak-charged processes accompanied by the emission of new vector particles are strongly enhanced by $(E/m_V)^2$, with $E$ a characteristic energy scale and $m_V$ the mass of the mediator. In particular, leptonic $W$ decays impose the strongest constraints on such models completely disfavoring the remainder of the parameter space.

hep-ph↗
arXiv2013

The $α^2(Zα)^4m$ contributions to the Lamb shift and the fine structure in light muonic atoms

Corrections to energy levels in light muonic atoms are investigated in order $α^2(Zα)^4m$. We pay attention to corrections which are specific for muonic atoms and include the electron vacuum polarization loop. In particular, we calculate relativistic and relativistic-recoil two-loop electron vacuum polarization contributions. The results are obtained for the levels with $n=1,2$ and in particular for the Lamb shift ($2p_{1/2}-2s_{1/2}$) and fine-structure intervals ($2p_{3/2}-2p_{1/2}$) in muonic hydrogen, deuterium, and muonic helium ions.

physics.atom-ph↗
arXiv2012

Relativistic recoil corrections to the electron-vacuum-polarization contribution in light muonic atoms

The relativistic recoil contributions to the Uehling corrections are revisited. We consider a controversy in recent calculations based on different approaches including Breit-type and Grotch-type calculations. We have found that calculations of those authors were in fact done in different gauges and in some of those gauges contributions the retardation and two-photon-exchange effects were missed. We have evaluated such effects and obtained a consistent result from those approaches. We present a correct expression for the Grotch-type approach which produces a correct gauge-invariant result. We also consider a finite-nuclear-size correction for the Uehling term. The results are presented for muonic hydrogen and deuterium atoms and for muonic helium-3 and helium-4 ions.

physics.atom-ph↗
arXiv2009

Second-order corrections to the wave function at origin in muonic hydrogen and pionium

Non-relativisitic second-order corrections to the wave function at origin in muonic and exotic atoms are considered. The corrections are due to the electronic vacuum polarization. Such corrections are of interest due to various effective approaches, which take into account QED and hadronic effects. The wave function at origin plays a key role in the calculation of the pionium lifetime, various finite nuclear size effects and the hyperfine splitting. The results are obtained for the $1s$ and $2s$ states in pionic and muonic hydrogen and deuterium and in pionium, a bound system of $π^+$ and $π^-$. Applications to the hyperfine structure and the Lamb shift in muonic hydrogen are also considered.

physics.atom-ph↗