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Howard Grotch

Publications and source records attributed to Howard Grotch.

15 recordsLinked to original sources
arXiv2004

Three-Loop Radiative-Recoil Corrections to Hyperfine Splitting in Muonium

We consider three-loop radiative-recoil corrections to hyperfine splitting in muonium. These corrections are enhanced by the large logarithm of the electron-muon mass ratio. The leading logarithm cubed and logarithm squared contributions were obtained a long time ago. We calculate the single-logarithmic and nonlogarithmic contributions of order $α^3(m/M)E_F$ generated by gauge invariant sets of diagrams with one- and two-loop polarization insertions in diagrams with two exchanged photons and radiative photons, and by diagrams with one-loop radiative photon insertions both in the electron and muon lines. The results of this paper constitute a next step in the implementation of the program of reduction of the theoretical uncertainty of hyperfine splitting below 10 Hz. They improve the theory of hyperfine splitting, and affect the value of the electron-muon mass ratio extracted from experimental data on the muonium hyperfine splitting.

hep-ph↗
arXiv2004

Three-Loop Radiative-Recoil Corrections to Hyperfine Splitting Generated by One-Loop Fermion Factors

We consider three-loop radiative-recoil corrections to hyperfine splitting in muonium generated by diagrams with one-loop radiative photon insertions both in the electron and muon lines. An analytic result for these nonlogarithmic corrections of order $α(Z^2α)(Zα)(m/M)\widetilde E_F$ is obtained. This result constitutes a next step in the implementation of the program of reduction of the theoretical uncertainty of hyperfine splitting below 10 Hz.

hep-ph↗
arXiv2003

Three-Loop Radiative-Recoil Corrections to Hyperfine Splitting in Muonium

We calculate three-loop radiative-recoil corrections to hyperfine splitting in muonium generated by the diagrams with the first order electron and muon polarization loop insertions in graphs with two exchanged photons. These corrections are enhanced by the large logarithm of the electron-muon mass ratio. The leading logarithm squared contribution was obtained a long time ago. Here we calculate the single-logarithmic and nonlogarithmic contributions. We previously calculated the three-loop radiative-recoil corrections generated by two-loop polarization insertions in the exchanged photons. The current paper therefore concludes calculation of all three-loop radiative-recoil corrections to hyperfine splitting in muonium generated by diagrams with closed fermion loop insertions in the exchanged photons. The new results obtained here improve the theory of hyperfine splitting, and affect the value of the electron-muon mass ratio extracted from experimental data on the muonium hyperfine splitting.

hep-ph↗
arXiv2001

Two-Loop Polarization Contributions to Radiative-Recoil Corrections to Hyperfine Splitting in Muonium

We calculate radiative-recoil corrections of order $α^2(Zα)(m/M)E_F$ to hyperfine splitting in muonium generated by the diagrams with electron and muon polarization loops. These corrections are enhanced by the large logarithm of the electron-muon mass ratio. The leading logarithm cubed and logarithm squared contributions were obtained a long time ago. The single-logarithmic and nonlogarithmic contributions calculated here improve the theory of hyperfine splitting, and affect the value of the electron-muon mass ratio extracted from the experimental data on the muonium hyperfine splitting.

hep-ph↗
arXiv2000

Radiative-Recoil Corrections of Order $α(Zα)^5(m/M)m$ to Lamb Shift Revisited

The results and main steps of an analytic calculation of radiative-recoil corrections of order $α(Zα)^5(m/M)m$ to the Lamb shift in hydrogen are presented. The calculations are performed in the infrared safe Yennie gauge. The discrepancy between two previous numerical calculations of these corrections existing in the literature is resolved. Our new result eliminates the largest source of the theoretical uncertainty in the magnitude of the deuterium-hydrogen isotope shift.

hep-ph↗
arXiv2000

Theory of Light Hydrogenlike Atoms

The present status and recent developments in the theory of light hydrogenic atoms, electronic and muonic, are extensively reviewed. The discussion is based on the quantum field theoretical approach to loosely bound composite systems. The basics of the quantum field theoretical approach, which provide the framework needed for a systematic derivation of all higher order corrections to the energy levels, are briefly discussed. The main physical ideas behind the derivation of all binding, recoil, radiative, radiative-recoil, and nonelectromagnetic spin-dependent and spin-independent corrections to energy levels of hydrogenic atoms are discussed and, wherever possible, the fundamental elements of the derivations of these corrections are provided. The emphasis is on new theoretical results which were not available in earlier reviews. An up-to-date set of all theoretical contributions to the energy levels is contained in the paper. The status of modern theory is tested by comparing the theoretical results for the energy levels with the most precise experimental results for the Lamb shifts and gross structure intervals in hydrogen, deuterium, and helium ion $He^+$, and with the experimental data on the hyperfine splitting in muonium, hydrogen and deuterium.

hep-ph↗
arXiv1998

Second Order in Mass Ratio Radiative-Recoil Corrections to Hyperfine Splitting in Muonium

Radiative-recoil corrections to hyperfine splitting in muonium of orders $α(Zα)(m/M)^2E_F$ and $(Z^2α)(Zα)(m/M)^2E_F$ are calculated. These corrections are of the second order in the small electron-muon mass ratio. An analytic expression $[(-6 \ln2- \frac{3}{4})α(Zα) - \frac{17}{12} (Z^2 α) (Zα)](\frac{m}{M})^2 E_F$ is obtained. Numerically the correction is equal to $-0.0351\:\mbox{kHz}$ and is of the same order of magnitude as the expected accuracy of the current Los Alamos experiment to measure the hyperfine splitting.

hep-ph↗
arXiv1997

Gyromagnetic Ratios of Bound Particles

A new approach to calculation of the binding corrections to the magnetic moments of the constituents in a loosely bound system, based on the Bargmann-Michel-Telegdi equation, is suggested. Binding corrections are calculated in this framework, and the results confirm earlier calculations performed by other methods. Our method clearly demonstrates independence of the binding corrections on the magnitude of the spin of the constituents.

hep-ph↗
arXiv1996

One More Analytic Result for $α^{2}(Zα)^{5}m$ Correction to the Lamb Shift

The analytic result for the radiative correction of order $α^{2}(Zα)^{5}m$ to the Lamb shift connected with a polarization insertion in one of the two external Coulomb lines is obtained. This correction arises from a gauge invariant set of diagrams which contain, besides the polarization insertion in the Coulomb leg, all one-loop radiative photon insertions in the electron line with two external Coulomb lines.

hep-ph↗
arXiv1996

Corrections of Order $α^6m$ to $S$-Levels of Helium

Several new corrections of order $mα^6$ to the energy levels of $S$ states in helium are obtained from radiative corrections to the Breit potential and from the polarization insertions in the two photon exchange graphs. While individual gauge invariant contributions are comparable to current experimental errors, the sum of these corrections is an order of magnitude smaller due to mutual cancellations.

hep-ph↗
arXiv1994

New Corrections of Order $α^6$ to $s$-Levels of Two-Body Systems

New corrections to the energy of $S$-levels of positronium of order $mα^6$ which are as large as several hundred kilohertz are obtained. A new recoil correction of order $α(Zα)^5(m/M)m$ to the Lamb shift in hydrogen is calculated. This correction turns out to be too small from the phenomenological point of view.

hep-ph↗
arXiv1994

An $α^{2}(Z α)^{5}m$ Contribution to the Hydrogen Lamb Shift from Virtual Light by Light Scattering

The radiative correction to the Lamb shift of order $α^{2}(Zα)^5m$ induced by the light by light scattering insertion in external photons is obtained. The new contribution turns out to be equal to $-0.122(2)α^2(Zα)^5/(πn^3)(m_r/m)^3m$. Combining this contribution with our previous results we obtain the complete correction of order $α^{2}(Zα)^5m$ induced by all diagrams with closed electron loops. This correction is $37.3(1)$ kHz and $4.67(1)$ kHz for the $1S$- and $2S$-states in hydrogen, respectively.

hep-ph↗