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Nonperturbative True Muonium on the Light Front with TMSWIFT

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Abstract

The true muonium \({(\mu\bar{\mu})}\) bound state presents an interesting test of light-cone quantization techniques. In addition to exhibiting the standard problems of handling non-perturbative calculations, true muonium requires correct treatment of \({e\bar{e}}\) Fock-state contributions. Having previously produced a crude model of true muonium using the method of iterated resolvents, our current work has focused on the inclusion of the box diagrams to improve the cutoff-dependent issues of the model. Further, a parallel computer code, TMSWIFT, allowing for smaller numerical uncertainties, has been developed. This work focuses on the current state of these efforts to develop a model of true muonium that is testable at near-term experiments.

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References

  1. Antognini A., Nez F., Schuhmann K., Amaro F.D., Biraben F. et al.: Proton structure from the measurement of 2S−2P transition frequencies of muonic hydrogen. Science 339, 417–420 (2013)

    Article  ADS  Google Scholar 

  2. Arteaga-Romero N., Carimalo C., Serbo V.: Production of bound triplet \({\mu^+\mu^-}\) system in collisions of electrons with atoms. Phys. Rev. A 62, 032501 (2000)

    Article  ADS  Google Scholar 

  3. Banburski A., Schuster P.: The production and discovery of true muonium in fixed-target experiments. Phys. Rev. D 86, 093007 (2012)

    Article  ADS  Google Scholar 

  4. Benelli A.: DIRAC experiment at CERN. EPJ Web Conf. 37, 01011 (2012)

    Article  Google Scholar 

  5. Bennett G. et al.: Final report of the muon E821 anomalous magnetic moment measurement at BNL. Phys. Rev. D 73, 072003 (2006)

    Article  ADS  Google Scholar 

  6. Brodsky S.J., Lebed R.F.: Production of the smallest QED atom: true muonium (\({\mu^+\mu^-}\)). Phys. Rev. Lett. 102, 213401 (2009)

    Article  ADS  Google Scholar 

  7. Brodsky S.J., Pauli H.C., Pinsky S.S.: Quantum chromodynamics and other field theories on the light cone. Phys. Rep. 301, 299–486 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  8. Celentano A.: The heavy photon search experiment at Jefferson laboratory. J. Phys. Conf. Ser. 556(1), 012064 (2014)

    Article  ADS  Google Scholar 

  9. Chabysheva S.S., Hiller J.R.: Nonperturbative Pauli-Villars regularization of vacuum polarization in light-front QED. Phys. Rev. D 82, 034004 (2010)

    Article  ADS  Google Scholar 

  10. Chabysheva S.S., Hiller J.R.: Basis of symmetric polynomials for many-boson light-front wave functions. Phys. Rev. E 90(6), 063,310 (2014)

    Article  Google Scholar 

  11. Chen, Y., Zhuang, P.: Dimuonium \({(\mu^+\mu^-)}\) Production in a Quark-Gluon Plasma. arXiv:1204.4389. (2012)

  12. Chliapnikov, P.: Numbers of \({\mu^\pm\pi\mp}\), \({\mu^+\mu^-}\) and K + K atoms and Coulomb pairs in the DIRAC experiment. DIRAC-NOTE-2014-05

  13. Dirac P.A.M.: Forms of Relativistic Dynamics. Rev. Mod. Phys. 21, 392–399 (1949)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  14. Ginzburg I., Jentschura U., Karshenboim S.G., Krauss F., Serbo V. et al.: Production of bound \({\mu^+\mu^-}\) systems in relativistic heavy ion collisions. Phys. Rev. C 58, 3565–3573 (1998)

    Article  ADS  Google Scholar 

  15. Hernandez V., Roman J.E., Vidal V.: SLEPc: a scalable and flexible toolkit for the solution of eigenvalue problems. ACM Trans. Math. Softw. 31(3), 351–362 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  16. Holvik E., Olsen H.A.: Creation of relativistic fermionium in collisions of electrons with atoms. Phys. Rev. D 35, 2124 (1987)

    Article  ADS  Google Scholar 

  17. Hughes V., Maglic B.: True Muonium. Bull. Am. Phys. Soc. 16, 65 (1971)

    Google Scholar 

  18. Kaluza, M., Pauli, H.C.: Discretized light cone quantization: \({e^+e^-(\gamma)}\) model for positronium. Phys. Rev. D 45, 2968–2981 (1992)

  19. Karmanov V.A., Mathiot J.F., Smirnov A.V.: Systematic renormalization scheme in light-front dynamics with Fock space truncation. Phys. Rev. D 77, 085028 (2008)

    Article  ADS  Google Scholar 

  20. Karmanov V.A., Mathiot J.F., Smirnov A.V.: Ab initio nonperturbative calculation of physical observables in light-front dynamics Application to the Yukawa model. Phys. Rev. D 86, 085006 (2012)

    Article  ADS  Google Scholar 

  21. Kozlov G.: On the problem of production of relativistics lepton bound states in the decays of light mesons. Sov. J. Nucl. Phys. 48, 167–171 (1988)

    Google Scholar 

  22. Krautgartner M., Pauli H.C., Wolz F.: Positronium and heavy quarkonia as testing case for discretized light cone quantization. Phys. Rev. D 45, 3755–3774 (1992)

    Article  ADS  Google Scholar 

  23. Lamm H.: Can Galileons solve the muon problem?. Phys. Rev. D 92(5), 055007 (2015a)

    Article  ADS  Google Scholar 

  24. Lamm H.: Electroweak corrections to the true muonium hyperfine splitting. Phys. Rev. D 91, 073008 (2015b)

    Article  ADS  Google Scholar 

  25. Lamm, H.: True muonium: the atom that has it all. In: CIPANP 2015 Vail, Colorado, USA, 19–24 May 2015. arXiv:1509.09306

  26. Lamm H., Lebed R.F.: True muonium \({(\mu^+ \mu^-)}\) on the light front. J. Phys. G 41(12), 125003 (2014)

    Article  Google Scholar 

  27. Lepage G.P., Brodsky S.J.: Exclusive processes in perturbative quantum chromodynamics. Phys. Rev. D 22, 2157 (1980)

    Article  ADS  Google Scholar 

  28. Li, Y., Maris, P., Zhao, X., Vary, J.P.: Heavy Quarkonium in a Holographic Basis. arXiv:1509.07212 (2015)

  29. Malyshev M.Y., Paston S.A., Prokhvatilov E.V., Zubov R.A.: Renormalized light front Hamiltonian in the Pauli-Villars regularization. Int. J. Theor. Phys. 54(1), 169–184 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  30. Moffat J.: Does a heavy positronium atom exist?. Phys. Rev. Lett. 35, 1605 (1975)

    Article  ADS  Google Scholar 

  31. Nemenov L.: Atomic decays of elementary particles. Yad Fiz 15, 1047–1050 (1972)

    Google Scholar 

  32. Nemenov L.L., Ovsyannikov V.D.: DC field control of decay processes in a (\({\pi^+\pi^-}\)) atom: A possibility to measure the energy splitting between 2s- and 2p-states. Phys. Lett. B 514, 247–252 (2001). doi:10.1016/S0370-2693(01)00802-4

    Article  ADS  Google Scholar 

  33. Pauli, H.C.: Solving gauge field theory by discretized light cone quantization. hep-th/9706036. (1997)

  34. Pauli H.C., Brodsky S.J.: Discretized light cone quantization: solution to a field theory in one space one time dimensions. Phys. Rev. D 32, 2001 (1985)

    Article  ADS  MathSciNet  Google Scholar 

  35. Tang A.C., Brodsky S.J., Pauli H.C.: Discretized light cone quantization: formalism for quantum electrodynamics. Phys. Rev. D 44, 1842–1865 (1991)

    Article  ADS  MathSciNet  Google Scholar 

  36. Trittmann, U., Pauli, H.C.: Quantum electrodynamics at strong couplings. hep-th/9704215. (1997)

  37. Tucker-Smith D., Yavin I.: Muonic hydrogen and MeV forces. Phys. Rev. D 83, 101702 (2011)

    Article  ADS  Google Scholar 

  38. Wiecki P., Li Y., Zhao X., Maris P., Vary J.P.: Basis light-front quantization approach to positronium. Phys. Rev. D 91(10), 105009 (2015)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, Arizona State University, P.O. Box 871504, Tempe, AZ, 85287-1504, USA

    Henry Lamm & Richard F. Lebed

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  1. Henry Lamm
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  2. Richard F. Lebed
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Correspondence to Henry Lamm.

Additional information

Work supported by the National Science Foundation under Grant Nos. PHY-1068286 and PHY-1403891 and by the International Light Cone Advisory Committee under the McCartor Fellowship program.

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Lamm, H., Lebed, R.F. Nonperturbative True Muonium on the Light Front with TMSWIFT. Few-Body Syst 57, 663–667 (2016). https://doi.org/10.1007/s00601-016-1075-3

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