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Adkins GS, Gomprecht J, Li Y, Shinn E. Recoil Corrections to the Energy Levels of Hydrogenic Atoms. PHYSICAL REVIEW LETTERS 2023; 130:023004. [PMID: 36706415 DOI: 10.1103/physrevlett.130.023004] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/13/2022] [Accepted: 12/14/2022] [Indexed: 06/18/2023]
Abstract
We have completed the calculation of pure-recoil corrections of order (Zα)^{6} to Coulombic bound states of two spin-1/2 fermions without approximation in the particle masses. Our result applies to systems of arbitrary mass ratio such as muonium and positronium, as well as hydrogen and muonic hydrogen (with the neglect of proton structure effects). We have shown how the two-loop master integrals that occur in the relativistic region can be computed in analytic form and suggest that the same method can be applied to the three-loop integrals that would be present in a calculation of order (Zα)^{7} corrections.
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Affiliation(s)
| | | | - Yanxi Li
- Franklin & Marshall College, Lancaster, Pennsylvania 17604, USA
| | - Evan Shinn
- Franklin & Marshall College, Lancaster, Pennsylvania 17604, USA
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2
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Ferenc D, Jeszenszki P, Matyus E. Variational versus perturbative relativistic energies for small and light atomic and molecular systems. J Chem Phys 2022; 157:094113. [DOI: 10.1063/5.0105355] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Variational and perturbative relativistic energies are computed and compared for two-electron atoms and molecules with low nuclear charge numbers. In general, good agreement of the two approaches is observed. Remaining deviations can be attributed to higher-order relativistic, also called non-radiative quantum electrodynamics (QED), corrections of the perturbative approach that are automatically included in the variational solution of the no-pair Dirac--Coulomb--Breit (DCB) equation to all orders of the $\alpha$ fine-structure constant. The analysis of the polynomial $\alpha$ dependence of the DCB energy makes it possible to determine the leading-order relativistic correction to the non-relativistic energy to high precision without regularization. Contributions from the Breit--Pauli Hamiltonian, for which expectation values converge slowly due the singular terms, are implicitly included in the variational procedure. The $\alpha$ dependence of the no-pair DCB energy shows that the higher-order ($\alpha^4 E_\mathrm{h}$) non-radiative QED correction is 5~\% of the leading-order ($\alpha^3 E_\mathrm{h}$) non-radiative QED correction for $Z=2$ (He), but it is 40~\% already for $Z=4$ (Be$^{2+}$), which indicates that resummation provided by the variational procedure is important already for intermediate nuclear charge numbers.
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3
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Berengut JC, Budker D, Delaunay C, Flambaum VV, Frugiuele C, Fuchs E, Grojean C, Harnik R, Ozeri R, Perez G, Soreq Y. Probing New Long-Range Interactions by Isotope Shift Spectroscopy. PHYSICAL REVIEW LETTERS 2018; 120:091801. [PMID: 29547329 DOI: 10.1103/physrevlett.120.091801] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/22/2017] [Revised: 09/20/2017] [Indexed: 06/08/2023]
Abstract
We explore a method to probe new long- and intermediate-range interactions using precision atomic isotope shift spectroscopy. We develop a formalism to interpret linear King plots as bounds on new physics with minimal theory inputs. We focus only on bounding the new physics contributions that can be calculated independently of the standard model nuclear effects. We apply our method to existing Ca^{+} data and project its sensitivity to conjectured new bosons with spin-independent couplings to the electron and the neutron using narrow transitions in other atoms and ions, specifically, Sr and Yb. Future measurements are expected to improve the relative precision by 5 orders of magnitude, and they can potentially lead to an unprecedented sensitivity for bosons within the 0.3 to 10 MeV mass range.
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Affiliation(s)
- Julian C Berengut
- School of Physics, University of New South Wales, Sydney, New South Wales 2052, Australia
| | - Dmitry Budker
- Helmholtz-Institut Mainz, Johannes Gutenberg-Universität Mainz, 55128 Mainz, Germany
- Physics Department, University of California, Berkeley 94720-7300, USA
- Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Cédric Delaunay
- Laboratoire d'Annecy-le-Vieux de Physique Théorique LAPTh, CNRS-Université Savoie Mont Blanc, BP 110, F-74941 Annecy-le-Vieux, France
| | - Victor V Flambaum
- School of Physics, University of New South Wales, Sydney, New South Wales 2052, Australia
| | - Claudia Frugiuele
- Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Elina Fuchs
- Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Christophe Grojean
- DESY, D-22607 Hamburg, Germany
- Institut für Physik, Humboldt-Universität zu Berlin, D-12489 Berlin, Germany
| | - Roni Harnik
- Theoretical Physics Department, Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
| | - Roee Ozeri
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Gilad Perez
- Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Yotam Soreq
- Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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4
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Stanke M, Palikot E, Adamowicz L. Algorithms for calculating mass-velocity and Darwin relativistic corrections with n-electron explicitly correlated Gaussians with shifted centers. J Chem Phys 2016; 144:174101. [PMID: 27155619 DOI: 10.1063/1.4947553] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Algorithms for calculating the leading mass-velocity (MV) and Darwin (D) relativistic corrections are derived for electronic wave functions expanded in terms of n-electron explicitly correlated Gaussian functions with shifted centers and without pre-exponential angular factors. The algorithms are implemented and tested in calculations of MV and D corrections for several points on the ground-state potential energy curves of the H2 and LiH molecules. The algorithms are general and can be applied in calculations of systems with an arbitrary number of electrons.
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Affiliation(s)
- Monika Stanke
- Institute of Physics, Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University, ul. Grudzia̧dzka 5, Toruń, PL 87-100, Poland
| | - Ewa Palikot
- Institute of Physics, Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University, ul. Grudzia̧dzka 5, Toruń, PL 87-100, Poland
| | - Ludwik Adamowicz
- Department of Chemistry and Biochemistry and Department of Physics, University of Arizona, Tucson, Arizona 85721, USA
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5
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Korobov VI, Koelemeij JCJ, Hilico L, Karr JP. Theoretical Hyperfine Structure of the Molecular Hydrogen Ion at the 1 ppm Level. PHYSICAL REVIEW LETTERS 2016; 116:053003. [PMID: 26894709 DOI: 10.1103/physrevlett.116.053003] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/20/2015] [Indexed: 06/05/2023]
Abstract
We revisit the mα^{6}(m/M) order corrections to the hyperfine splitting in the H_{2}^{+} ion and find a hitherto unrecognized second-order relativistic contribution associated with the vibrational motion of the nuclei. Inclusion of this correction term produces theoretical predictions which are in excellent agreement with experimental data [K. B. Jefferts, Phys. Rev. Lett. 23, 1476 (1969)], thereby concluding a nearly 50-year-long theoretical quest to explain the experimental results within their 1-ppm error. The agreement between the theory and experiment corroborates the proton structural properties as derived from the hyperfine structure of atomic hydrogen. Our work furthermore indicates that, for future improvements, a full three-body evaluation of the mα^{6}(m/M) correction term will be mandatory.
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Affiliation(s)
- Vladimir I Korobov
- Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980, Russia
| | - J C J Koelemeij
- LaserLaB and Department of Physics and Astronomy, VU University, De Boelelaan 1081, 1081 HV Amsterdam, Netherlands
| | - L Hilico
- Laboratoire Kastler Brossel, UPMC-Sorbonne Universités, CNRS, ENS-PSL Research University, Collège de France, 4 place Jussieu, F-75005 Paris, France and Université d'Evry-Val d'Essonne, Boulevard François Mitterrand, F-91000 Evry, France
| | - J-Ph Karr
- Laboratoire Kastler Brossel, UPMC-Sorbonne Universités, CNRS, ENS-PSL Research University, Collège de France, 4 place Jussieu, F-75005 Paris, France and Université d'Evry-Val d'Essonne, Boulevard François Mitterrand, F-91000 Evry, France
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6
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Stanke M, Adamowicz L. Non-Born-Oppenheimer calculations of the pure vibrational spectrum of T₂ including relativistic corrections. J Chem Phys 2014; 141:154302. [PMID: 25338891 DOI: 10.1063/1.4897631] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023] Open
Abstract
We report very accurate calculations of the complete pure vibrational spectrum of the T2 molecule with an approach where the Born-Oppenheimer (BO) approximation is not assumed. As the considered states correspond to the zero total angular momentum, their non-BO wave functions are spherically symmetric and are expanded in terms of all-particle, one-center, spherically symmetric explicitly correlated Gaussian functions multiplied by even nonnegative powers of the internuclear distance. The nonrelativistic energies of the states obtained in the non-BO calculations are corrected for the relativistic effects of the order of α(2) (where α is the fine structure constant) calculated as expectation values of the operators representing these effects.
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Affiliation(s)
- Monika Stanke
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudzia̧dzka 5, 87-100 Toruń, Poland
| | - Ludwik Adamowicz
- Department of Chemistry and Biochemistry, University of Arizona, Tucson, Arizona 85721, USA
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7
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Eides MI, Shelyuto VA. Muon loop light-by-light contribution to hyperfine splitting in muonium. PHYSICAL REVIEW LETTERS 2014; 112:173004. [PMID: 24836244 DOI: 10.1103/physrevlett.112.173004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/24/2014] [Indexed: 06/03/2023]
Abstract
Three-loop corrections to hyperfine splitting in muonium, generated by the gauge-invariant sets of diagrams with muon and tauon loop light-by-light scattering blocks, are calculated. These results complete calculations of all light-by-light scattering contributions to hyperfine splitting in muonium.
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Affiliation(s)
- Michael I Eides
- Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 40506, USA and Petersburg Nuclear Physics Institute, Gatchina, St. Petersburg 188300, Russia
| | - Valery A Shelyuto
- D. I. Mendeleyev Institute for Metrology, St. Petersburg 190005, Russia
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8
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Stanke M, Adamowicz L. Molecular Relativistic Corrections Determined in the Framework Where the Born–Oppenheimer Approximation is Not Assumed. J Phys Chem A 2013; 117:10129-37. [DOI: 10.1021/jp4020492] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Monika Stanke
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, ul. Grudzia̧dzka
5, Toruń, PL 87-100, Poland
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9
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Yoder TJ, Adkins GS. Higher order corrections to the hydrogen spectrum from the standard-model extension. Int J Clin Exp Med 2012. [DOI: 10.1103/physrevd.86.116005] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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10
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Bubin S, Pavanello M, Tung WC, Sharkey KL, Adamowicz L. Born–Oppenheimer and Non-Born–Oppenheimer, Atomic and Molecular Calculations with Explicitly Correlated Gaussians. Chem Rev 2012; 113:36-79. [DOI: 10.1021/cr200419d] [Citation(s) in RCA: 115] [Impact Index Per Article: 9.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Sergiy Bubin
- Department
of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235,
United States
| | - Michele Pavanello
- Department
of Chemistry, Rutgers University Newark, Newark, New Jersey 07102,
United States
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11
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Hill RJ, Paz G. Model independent analysis of proton structure for hydrogenic bound states. PHYSICAL REVIEW LETTERS 2011; 107:160402. [PMID: 22107369 DOI: 10.1103/physrevlett.107.160402] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/01/2011] [Indexed: 05/31/2023]
Abstract
Proton structure effects in hydrogenic bound states are analyzed using nonrelativistic QED effective field theory. Implications for the Lamb shift in muonic hydrogen are discussed. Model-dependent assumptions in previous analyses are isolated, and sensitivity to poorly constrained hadronic structure in the two-photon exchange contribution is identified.
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Affiliation(s)
- Richard J Hill
- Enrico Fermi Institute and Department of Physics The University of Chicago, Chicago, Illinois 60637, USA
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12
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Hammant TC, Hart AG, von Hippel GM, Horgan RR, Monahan CJ. Radiative improvement of the lattice nonrelativistic QCD action using the background field method and application to the hyperfine splitting of quarkonium states. PHYSICAL REVIEW LETTERS 2011; 107:112002. [PMID: 22026657 DOI: 10.1103/physrevlett.107.112002] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/27/2011] [Indexed: 05/31/2023]
Abstract
We present the first application of the background field method to nonrelativistic QCD (NRQCD) on the lattice in order to determine the one-loop radiative corrections to the coefficients of the NRQCD action in a manifestly gauge-covariant manner. The coefficients of the σ·B term in the NRQCD action and the four-fermion spin-spin interaction are computed at the one-loop level; the resulting shift of the hyperfine splitting of bottomonium is found to bring the lattice predictions in line with experiment.
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Affiliation(s)
- T C Hammant
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Cambridge CB3 0WA, United Kingdom
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13
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Bubin S, Stanke M, Adamowicz L. Accurate non-Born-Oppenheimer calculations of the complete pure vibrational spectrum of D2 with including relativistic corrections. J Chem Phys 2011; 135:074110. [DOI: 10.1063/1.3625955] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023] Open
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14
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Eides MI, Martin TJS. Universal binding and recoil corrections to bound state g factors in hydrogenlike ions. PHYSICAL REVIEW LETTERS 2010; 105:100402. [PMID: 20867496 DOI: 10.1103/physrevlett.105.100402] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/17/2010] [Indexed: 05/29/2023]
Abstract
The leading relativistic and recoil corrections to bound state g factors of particles with arbitrary spin are calculated. It is shown that these corrections are universal for any spin and depend only on the free particle gyromagnetic ratios. To prove this universality we develop nonrelativistic quantum electrodynamics (NRQED) for charged particles with an arbitrary spin. The coefficients in the NRQED Hamiltonian for higher spin particles are determined only by the requirements of Lorentz invariance and local charge conservation in the respective relativistic theory. For spin one charged particles, the NRQED Hamiltonian follows from the renormalizable QED of the charged vector bosons. We show that universality of the leading relativistic and recoil corrections can be explained with the help of the Bargmann-Michael-Telegdi equation.
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Affiliation(s)
- Michael I Eides
- Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 40506, USA.
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15
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Accurate non-Born–Oppenheimer calculations of the lowest vibrational energies of D2 and T2 with including relativistic corrections. Chem Phys Lett 2010. [DOI: 10.1016/j.cplett.2010.05.081] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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16
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Stanke M, Kȩdziera D, Bubin S, Molski M, Adamowicz L. Orbit-orbit relativistic corrections to the pure vibrational non-Born-Oppenheimer energies of H2. J Chem Phys 2008; 128:114313. [DOI: 10.1063/1.2834926] [Citation(s) in RCA: 36] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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17
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Hill RJ. New value of m(mu)/m(e) from muonium hyperfine splitting. PHYSICAL REVIEW LETTERS 2001; 86:3280-3283. [PMID: 11327950 DOI: 10.1103/physrevlett.86.3280] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/13/2000] [Indexed: 05/23/2023]
Abstract
The complete contribution to the muonium hyperfine splitting of relative order alpha(3)(m(e)/m(mu))lnalpha is calculated. The result is much smaller than suggested by a previous estimate and leads to a 2sigma upward shift of the most precise value for the muon-electron mass ratio. Analogous contributions are calculated for the positronium hyperfine splitting, where a discrepancy with experiment remains.
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Affiliation(s)
- R J Hill
- Newman Laboratory of Nuclear Studies, Cornell University, Ithaca, NY 14853, USA
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18
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Melnikov K, Yelkhovsky A. O(alpha(3) lnalpha) corrections to muonium and positronium hyperfine splitting. PHYSICAL REVIEW LETTERS 2001; 86:1498-1501. [PMID: 11290177 DOI: 10.1103/physrevlett.86.1498] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/18/2000] [Indexed: 05/23/2023]
Abstract
We compute O(alpha(3)lnalpha) relative corrections to the ground-state hyperfine splitting of a QED two-body bound state with different masses of constituents. The general result is then applied to muonium and positronium. In particular, a new value of the muon-to-electron mass ratio is derived from the muonium ground-state hyperfine splitting.
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Affiliation(s)
- K Melnikov
- Stanford Linear Accelerator Center, Stanford University, California 94309, USA.
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19
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Kniehl BA, Penin AA. Order alpha(7)ln(1/alpha) contribution to positronium hyperfine splitting. PHYSICAL REVIEW LETTERS 2000; 85:5094-5097. [PMID: 11102194 DOI: 10.1103/physrevlett.85.5094] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/28/2000] [Revised: 10/16/2000] [Indexed: 05/23/2023]
Abstract
The logarithmically enhanced alpha(7)ln(1/alpha) contribution to the hyperfine splitting of the positronium ground-state energy levels is calculated in the framework of dimensionally regularized nonrelativistic quantum electrodynamics. The correction is negative and amounts to about 1/3 of the leading logarithmic alpha(7)ln (2)(1/alpha) one. The discrepancy between the experimental measurements and the theoretical prediction is reduced.
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Affiliation(s)
- BA Kniehl
- II. Institut fur Theoretische Physik, Universitat Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
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Manohar AV, Stewart IW. Logarithms of alpha in QED bound states from the renormalization group. PHYSICAL REVIEW LETTERS 2000; 85:2248-2251. [PMID: 10977983 DOI: 10.1103/physrevlett.85.2248] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/05/2000] [Indexed: 05/23/2023]
Abstract
The velocity renormalization group is used to determine lnalpha contributions to QED bound state energies. The leading-order anomalous dimension for the potential gives the alpha(5)lnalpha Lamb shift. The next-to-leading-order anomalous dimension determines the alpha(6)lnalpha, alpha(7)ln (2)alpha, and alpha(8)ln (3)alpha corrections to the energy. These are used to obtain the alpha(8)ln (3)alpha Lamb shift and alpha(7)ln (2)alpha hyperfine splitting for hydrogen, muonium, and positronium, as well as the alpha(2)lnalpha and alpha(3)ln (2)alpha corrections to the ortho- and parapositronium lifetimes. This shows for the first time that these logarithms can be computed from the renormalization group.
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Affiliation(s)
- AV Manohar
- Department of Physics, University of California at San Diego, 9500 Gilman Drive, La Jolla, California 92093, USA
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