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Radiative μ and τ leptonic decays

  • Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, CH-3012 Bern, Switzerland

Funds:  Supported by the Swiss National Science Foundation.
Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2016.05.005
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  • Author Bio:

    FAEL M., male, born in 1986, PhD. Research field: elementary particle physics. E-mail: fael@itp.unibe.ch

  • Received Date: 14 September 2015
  • Accepted Date: 20 April 2016
  • Rev Recd Date: 20 April 2016
  • Publish Date: 31 May 2016
    Abstract

  • Abstract

    Precise data on radiative leptonic τ decays offer the opportunity to probe the electromagnetic properties of the τ and may allow to determine its anomalous magnetic moment which, in spite of its precise Standard Model prediction, has never been measured. Recently, the branching fractions of the radiative leptonic τ decays (τ→lνγ, with l=e,μ) were measured by the Babar Collaboration. These precise measurements, with a relative error of about 3%, must be compared with the branching ratios at the next-to-leading order in QED. Indeed the radiative corrections are expected to be of order 10%, for l=e, and 3%, for l=μ. Here, we present the prediction of the differential decay rates and branching ratios of the radiative μ and τ leptonic decays in the Standard Model at the next-to-leading order and we compare them with the recent Babar measurements. Moreover, we report on a dedicated feasibility study for the measurements of the τ anomalous magnetic moment at Belle and Belle II.

    Abstract

    Precise data on radiative leptonic τ decays offer the opportunity to probe the electromagnetic properties of the τ and may allow to determine its anomalous magnetic moment which, in spite of its precise Standard Model prediction, has never been measured. Recently, the branching fractions of the radiative leptonic τ decays (τ→lνγ, with l=e,μ) were measured by the Babar Collaboration. These precise measurements, with a relative error of about 3%, must be compared with the branching ratios at the next-to-leading order in QED. Indeed the radiative corrections are expected to be of order 10%, for l=e, and 3%, for l=μ. Here, we present the prediction of the differential decay rates and branching ratios of the radiative μ and τ leptonic decays in the Standard Model at the next-to-leading order and we compare them with the recent Babar measurements. Moreover, we report on a dedicated feasibility study for the measurements of the τ anomalous magnetic moment at Belle and Belle II.
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    • References(60)
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    MICHEL L. Interaction between four half-spin particles and the decay of the μ-meson[J]. Proc Phys Soc A, 1950, 63: 514-531.
    [2]
    BOUCHIAT C, MICHEL L. Theory of μ-meson decay with the hypothesis of nonconservation of parity[J]. Phys Rev, 1957, 106: 170-172.
    [3]
    KINOSHITA T, SIRLIN A. Muon decay with parity nonconserving interactions and radiative corrections in the two-component theory[J]. Phys Rev, 1957, 107: 593-599.
    [4]
    KINOSHITA T, SIRLIN A. Polarization of electrons in muon decay with general parity-nonconserving interactions[J]. Phys Rev, 1957, 108: 844-850.
    [5]
    PRATT R H. Time-reversal invariance and radiative muon decay[J]. Phys Rev, 1958, 111: 649-651.
    [6]
    EICHENBERGER W, ENGFER R, VAN DER SCHAAF A. Measurement of the parameter η in the radiative decay of the muon as a test of the V-A structure of the weak interaction[J]. Nucl Phys A, 1984, 412: 523-533.
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    FETSCHER W, GERBER H J. Precision measurements in muon and tau decays[J]. Adv Ser Direct High Energy Phys, 1995, 14: 657-705.
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    ADAM J, BAO Y, BARACCHINI E, et al (MEG Collaboration). Measurement of the radiative decay of polarized muons in the MEG experiment[DB/OL]. arXiv:1312.3217 [hep-ex].
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    BALDINI A M, CEI F, CERRI C, et al. MEG upgrade proposal[J]. arXiv:1301.7225 [physics.ins-det].
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    BERGER N (for the Mu3e Collaboration). The Mu3e Experiment[J]. Nucl Phys B (Proc Suppl), 2014, 248-250: 35-40.
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    FLORES-TLALPA A, LPEZ CASTRO G, ROIG P. Five-body leptonic decays of muon and tau leptons[DB/OL]. arXiv:1508.01822 [hep-ph].
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    LEES J P, POIREAU V, TISSERAND V, et al (BaBar Collaboration). Measurement of the branching fractions of the radiative leptonic τ decays τ→eγν and τ→μγν at BABAR[J]. Physical Review D, 2015, 91: 051103(R).
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    KINOSHITA T, SIRLIN A. Radiative corrections to Fermi Interactions[J]. Phys Rev, 1959, 113: 1 652-1 660.
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    KINOSHITA T. Mass singularities of Feynman amplitudes [J]. J Math Phys, 1962, 3: 650-677.
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    LEE T D, NAUENBERG M. Degenerate systems and mass singularities[J]. Phys Rev, 1964, 133: B1549.
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    BENNETT G, BOUSQUET B, BROWN H N, et al (Muon (g－2) Collaboration). Final report of the E821 muon anomalous magnetic moment measurement at BNL[J]. Phys Rev D, 2006, 73:072003.
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    [22]
    AOYAMA T, HAYAKAWA M, KINOSHITA T, et al. Tenth-order electron anomalous magnetic moment: Contribution of diagrams without closed lepton loops[J]. Phys Rev D, 2015, 91(3): 033006.
    [23]
    FERROGLIA A, GREUB C, SIRLIN A, et al. Contributions of the W-boson propagator to the μ and τ leptonic decay rates[J]. Phys Rev D, 2013, 88(3):033012.
    [24]
    FAEL M, MERCOLLI L, PASSERA M. W-propagator corrections to μ and τ leptonic decays[J]. Phys Rev D, 2013, 88(9): 093011.
    [25]
    FRONSDAL C, BERALL H. μ-Meson Decay with Inner Bremsstrahlung[J]. Phys Rev, 1959, 113: 654-657.
    [26]
    ECKSTEIN S G, PRATT R H. Radiative muon decay[J]. Ann Phys, 1959, 8: 297-309.
    [27]
    KUNO Y, OKADA Y. Muon decay and physics beyond the standard model[J]. Rev Mod Phys, 2001, 73: 151-202.
    [28]
    FAEL M, MERCOLLI L, PASSERA M. Radiative μ and τ leptonic decays at NLO[J]. JHEP, 2015, 1507: 153.
    [29]
    FISCHER A, KUROSU T, SAVATIER F. QED one-loop corrections to radiative muon decay[J]. Phys Rev D, 1994, 49:3 426-3 433.
    [30]
    ARBUZOV A B, SCHERBAKOVA E S. One-loop corrections to radiative muon decay[J]. Phys Lett B, 2004, 597, 285-290.
    [31]
    KINOSHITA T, SIRLIN A. Radiative decay of the muon[J]. Phys Rev Lett, 1959, 2: 177-178.
    [32]
    FALK B, SEHGAL L M. Helicity-flip bremsstrahlung. An equivalent particle description with applications[J]. Phys Lett B, 1994, 325: 509-516.
    [33]
    SEHGAL L M. Right-handed electrons in radiative muon decay[J]. Phys Lett B, 2003, 569: 25-29.
    [34]
    SCHULZ V S, SEHGAL L M. Wrong-helicity electrons in radiative muon decay[J]. Phys Lett B, 2004, 594: 153-163.
    [35]
    BERGFELD T, EISENSTEIN B I, ERNST J, et al (CLEO Collaboration). Observation of radiative leptonic decay of the tau lepton[J]. Phys Rev Lett, 2000, 84: 830-834.
    [36]
    BUCHMLLER W, WYLER D. Effective lagrangian analysis of new interactions and flavour conservation[J]. Nucl Phys B, 1986, 268: 621-653.
    [37]
    GRZADKOWSKI B, ISKRZYNSKI M, MISIAK M, et al. Dimension-six terms in the Standard Model Lagrangian[J]. JHEP, 2010, 1010: 085.
    [38]
    ABDALLAH J, ABREU P, ADAM W, et al (DELPHI Collaboration). Study of tau-pair production in photon-photon collisions at LEP and limits on the anomalous electromagnetic moments of the tau lepton[J]. Eur Phys J C, 2004, 35: 159-170.
    [39]
    EIDELMAN S, PASSERA M. Theory of the τ lepton anomalous magnetic moment[J]. Mod Phys Lett A, 2007, 22: 159-179.
    [40]
    CORNET F, ILLANA J I. τ-pair production via photon-photon collisions at the CERN e+e- collider LEP[J]. Phys Rev D, 1996, 53: 1 181-1 184.
    [41]
    GONZALEZ-SPRINBERG G A, SANTAMARIA A, Vidal J. Model independent bounds on the tau lepton electromagnetic and weak magnetic moments[J]. Nucl Phys B, 2000, 582: 3-18.
    [42]
    HOOGEVEEN F. The standard model prediction for the electric dipole moment of the electron[J]. Nucl Phys B, 1990, 341: 322-340.
    [43]
    POSPELOV M E, KHRIPLOVICH I B. Electric dipole moment of the W boson and the electron in the Kobayashi-Maskawa model[J]. Sov J Nucl Phys, 1991, 53: 638-640.
    [44]
    COMMINS E D. Electric dipole moments of leptons[J]. Adv At Mol Opt Phys, 1999, 40: 1-55.
    [45]
    BARON J, CAMPBELL W C, DEMILLE D, et al (ACME Collaboration). Order of magnitude smaller limit on the electric dipole moment of the electron[J]. Science, 2014, 343: 269-272.
    [46]
    INAMI K, ABE K, ABE R, et al (Belle Collaboration). Search for the electric dipole moment of the τ lepton[J]. Phys Lett B, 2003, 551: 16-26.
    [47]
    BERNREUTHER W, NACHTMANN O, OVERMANN P. CP -violating electric and weak dipole moments of the τ lepton from threshold to 500 GeV[J]. Phys Rev D, 1993, 48: 78-88.
    [48]
    HAYRETER A, VALENCIA G. Constraining τ-lepton dipole moments and gluon couplings at the LHC[J]. Phys Rev D, 2013, 88(1): 013015 (Erratum: Phys Rev D,2015, 91(9): 099902).
    [49]
    HAYRETER A, VALENCIA G. Spin correlations and New Physics in τ-lepton decays at the LHC[J]. JHEP, 2015, 1507: 174.
    [50]
    ATAGˇ S, BILLUR A A. Possibility of determining τ lepton electromagnetic moments in γγ→τ+τ- process at the CERN-LHC[J]. JHEP, 2010, 1011: 060.
    [51]
    SAMUEL M A, LI G. How to measure the magnetic moment of the tau lepton[J]. Int J Theor Phys, 1994, 33: 1 471-1 477.
    [52]
    DEL AGUILA F, CORNET F, ILLANA J I. The possibility of using a large heavy-ion collider for measuring the electromagnetic properties of the tau lepton[J]. Phys Lett B, 1991, 271: 256-260.
    [53]
    AUSHEV T, BARTEL W, BONDAR A, et al. Physics at Super B factory[DB/OL]. arXiv:1002.5012 [hep-ex].
    [54]
    BERNABEU J, GONZALEZ-SPRINBERG G A, PAPAVASSILIOU J, et al. Tau anomalous magnetic moment form factor at Super B/Flavor factories[J]. Nucl Phys B, 2008, 790: 160-174.
    [55]
    OHNISHI Y, ABE T, ADACHI T, et al. Accelerator design at SuperKEKB[J]. PTEP, 2013: 03A011.
    [56]
    KOISO H, MORITA A, OHNISHI Y. Lattice of the KEKB colliding rings[J]. Prog Theor Exp Phys, 2013: 03A009.
    [57]
    LAURSEN M L, SAMUEL M A, Sen A. Radiation zeros and a test for the g value of the τ lepton[J]. Phys Rev D, 1984, 29: 2 652-2 654 (Erratum: Phys Rev D, 1997, 56: 3 155).
    [58]
    EIDELMAN S, EPIFANOV D, FAEL M, et al. Tau dipole moments via radiative leptonic tau decays[J].
    JHEP, 2016,1603:140.
    [59]
    FAEL M. Electromagnetic dipole moments of fermions[D/OL]. http://opac.nebis.ch/ediss/20142170.pdf
    [60]
    TSAI Y S. Decay correlations of heavy leptons in e++e-→l++l-[J]. Phys Rev D, 1971, 4: 2 821-2 837(Erratum: Phys Rev D, 1976, 13: 771).
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    [1]
    MICHEL L. Interaction between four half-spin particles and the decay of the μ-meson[J]. Proc Phys Soc A, 1950, 63: 514-531.
    [2]
    BOUCHIAT C, MICHEL L. Theory of μ-meson decay with the hypothesis of nonconservation of parity[J]. Phys Rev, 1957, 106: 170-172.
    [3]
    KINOSHITA T, SIRLIN A. Muon decay with parity nonconserving interactions and radiative corrections in the two-component theory[J]. Phys Rev, 1957, 107: 593-599.
    [4]
    KINOSHITA T, SIRLIN A. Polarization of electrons in muon decay with general parity-nonconserving interactions[J]. Phys Rev, 1957, 108: 844-850.
    [5]
    PRATT R H. Time-reversal invariance and radiative muon decay[J]. Phys Rev, 1958, 111: 649-651.
    [6]
    EICHENBERGER W, ENGFER R, VAN DER SCHAAF A. Measurement of the parameter η in the radiative decay of the muon as a test of the V-A structure of the weak interaction[J]. Nucl Phys A, 1984, 412: 523-533.
    [7]
    FETSCHER W, GERBER H J. Precision measurements in muon and tau decays[J]. Adv Ser Direct High Energy Phys, 1995, 14: 657-705.
    [8]
    ADAM J, BAO Y, BARACCHINI E, et al (MEG Collaboration). Measurement of the radiative decay of polarized muons in the MEG experiment[DB/OL]. arXiv:1312.3217 [hep-ex].
    [9]
    BALDINI A M, CEI F, CERRI C, et al. MEG upgrade proposal[J]. arXiv:1301.7225 [physics.ins-det].
    [10]
    BERGER N (for the Mu3e Collaboration). The Mu3e Experiment[J]. Nucl Phys B (Proc Suppl), 2014, 248-250: 35-40.
    [11]
    FLORES-TLALPA A, LPEZ CASTRO G, ROIG P. Five-body leptonic decays of muon and tau leptons[DB/OL]. arXiv:1508.01822 [hep-ph].
    [12]
    LEES J P, POIREAU V, TISSERAND V, et al (BaBar Collaboration). Measurement of the branching fractions of the radiative leptonic τ decays τ→eγν and τ→μγν at BABAR[J]. Physical Review D, 2015, 91: 051103(R).
    [13]
    KINOSHITA T, SIRLIN A. Radiative corrections to Fermi Interactions[J]. Phys Rev, 1959, 113: 1 652-1 660.
    [14]
    KINOSHITA T. Mass singularities of Feynman amplitudes [J]. J Math Phys, 1962, 3: 650-677.
    [15]
    LEE T D, NAUENBERG M. Degenerate systems and mass singularities[J]. Phys Rev, 1964, 133: B1549.
    [16]
    CRITTENDEN R R, WALKER W D, BALLAM J. Radiative decay modes of the muon[J]. Phys Rev, 1961, 121: 1 823-1 832.
    [17]
    POCANIC D, MUNYANGABE E, BYCHKOV M, et al. New results in rare allowed muon and pion decays[J]. Int J Mod Phys Conf Ser, 2014, 35: 1460437.
    [18]
    HANNEKE D, FOGWELL S, GABRIELSE G. New measurement of the electron magnetic moment and the fine structure constant[J]. Phys Rev Lett, 2008, 100: 120801.
    [19]
    BENNETT G, BOUSQUET B, BROWN H N, et al (Muon (g－2) Collaboration). Final report of the E821 muon anomalous magnetic moment measurement at BNL[J]. Phys Rev D, 2006, 73:072003.
    [20]
    OLIVE K A, AGASHE K, AMSLER C, et al (Particle Data Group). Review of particle physics[J]. Chinese Physics C, 2014, 38: 090001.
    [21]
    AOYAMA T, HAYAKAWA M, KINOSHITA T, et al. Tenth-order QED contribution to the electron g-2 and an improved value of the fine structure constant[J]. Phys Rev Lett, 2012, 109: 111807.
    [22]
    AOYAMA T, HAYAKAWA M, KINOSHITA T, et al. Tenth-order electron anomalous magnetic moment: Contribution of diagrams without closed lepton loops[J]. Phys Rev D, 2015, 91(3): 033006.
    [23]
    FERROGLIA A, GREUB C, SIRLIN A, et al. Contributions of the W-boson propagator to the μ and τ leptonic decay rates[J]. Phys Rev D, 2013, 88(3):033012.
    [24]
    FAEL M, MERCOLLI L, PASSERA M. W-propagator corrections to μ and τ leptonic decays[J]. Phys Rev D, 2013, 88(9): 093011.
    [25]
    FRONSDAL C, BERALL H. μ-Meson Decay with Inner Bremsstrahlung[J]. Phys Rev, 1959, 113: 654-657.
    [26]
    ECKSTEIN S G, PRATT R H. Radiative muon decay[J]. Ann Phys, 1959, 8: 297-309.
    [27]
    KUNO Y, OKADA Y. Muon decay and physics beyond the standard model[J]. Rev Mod Phys, 2001, 73: 151-202.
    [28]
    FAEL M, MERCOLLI L, PASSERA M. Radiative μ and τ leptonic decays at NLO[J]. JHEP, 2015, 1507: 153.
    [29]
    FISCHER A, KUROSU T, SAVATIER F. QED one-loop corrections to radiative muon decay[J]. Phys Rev D, 1994, 49:3 426-3 433.
    [30]
    ARBUZOV A B, SCHERBAKOVA E S. One-loop corrections to radiative muon decay[J]. Phys Lett B, 2004, 597, 285-290.
    [31]
    KINOSHITA T, SIRLIN A. Radiative decay of the muon[J]. Phys Rev Lett, 1959, 2: 177-178.
    [32]
    FALK B, SEHGAL L M. Helicity-flip bremsstrahlung. An equivalent particle description with applications[J]. Phys Lett B, 1994, 325: 509-516.
    [33]
    SEHGAL L M. Right-handed electrons in radiative muon decay[J]. Phys Lett B, 2003, 569: 25-29.
    [34]
    SCHULZ V S, SEHGAL L M. Wrong-helicity electrons in radiative muon decay[J]. Phys Lett B, 2004, 594: 153-163.
    [35]
    BERGFELD T, EISENSTEIN B I, ERNST J, et al (CLEO Collaboration). Observation of radiative leptonic decay of the tau lepton[J]. Phys Rev Lett, 2000, 84: 830-834.
    [36]
    BUCHMLLER W, WYLER D. Effective lagrangian analysis of new interactions and flavour conservation[J]. Nucl Phys B, 1986, 268: 621-653.
    [37]
    GRZADKOWSKI B, ISKRZYNSKI M, MISIAK M, et al. Dimension-six terms in the Standard Model Lagrangian[J]. JHEP, 2010, 1010: 085.
    [38]
    ABDALLAH J, ABREU P, ADAM W, et al (DELPHI Collaboration). Study of tau-pair production in photon-photon collisions at LEP and limits on the anomalous electromagnetic moments of the tau lepton[J]. Eur Phys J C, 2004, 35: 159-170.
    [39]
    EIDELMAN S, PASSERA M. Theory of the τ lepton anomalous magnetic moment[J]. Mod Phys Lett A, 2007, 22: 159-179.
    [40]
    CORNET F, ILLANA J I. τ-pair production via photon-photon collisions at the CERN e+e- collider LEP[J]. Phys Rev D, 1996, 53: 1 181-1 184.
    [41]
    GONZALEZ-SPRINBERG G A, SANTAMARIA A, Vidal J. Model independent bounds on the tau lepton electromagnetic and weak magnetic moments[J]. Nucl Phys B, 2000, 582: 3-18.
    [42]
    HOOGEVEEN F. The standard model prediction for the electric dipole moment of the electron[J]. Nucl Phys B, 1990, 341: 322-340.
    [43]
    POSPELOV M E, KHRIPLOVICH I B. Electric dipole moment of the W boson and the electron in the Kobayashi-Maskawa model[J]. Sov J Nucl Phys, 1991, 53: 638-640.
    [44]
    COMMINS E D. Electric dipole moments of leptons[J]. Adv At Mol Opt Phys, 1999, 40: 1-55.
    [45]
    BARON J, CAMPBELL W C, DEMILLE D, et al (ACME Collaboration). Order of magnitude smaller limit on the electric dipole moment of the electron[J]. Science, 2014, 343: 269-272.
    [46]
    INAMI K, ABE K, ABE R, et al (Belle Collaboration). Search for the electric dipole moment of the τ lepton[J]. Phys Lett B, 2003, 551: 16-26.
    [47]
    BERNREUTHER W, NACHTMANN O, OVERMANN P. CP -violating electric and weak dipole moments of the τ lepton from threshold to 500 GeV[J]. Phys Rev D, 1993, 48: 78-88.
    [48]
    HAYRETER A, VALENCIA G. Constraining τ-lepton dipole moments and gluon couplings at the LHC[J]. Phys Rev D, 2013, 88(1): 013015 (Erratum: Phys Rev D,2015, 91(9): 099902).
    [49]
    HAYRETER A, VALENCIA G. Spin correlations and New Physics in τ-lepton decays at the LHC[J]. JHEP, 2015, 1507: 174.
    [50]
    ATAGˇ S, BILLUR A A. Possibility of determining τ lepton electromagnetic moments in γγ→τ+τ- process at the CERN-LHC[J]. JHEP, 2010, 1011: 060.
    [51]
    SAMUEL M A, LI G. How to measure the magnetic moment of the tau lepton[J]. Int J Theor Phys, 1994, 33: 1 471-1 477.
    [52]
    DEL AGUILA F, CORNET F, ILLANA J I. The possibility of using a large heavy-ion collider for measuring the electromagnetic properties of the tau lepton[J]. Phys Lett B, 1991, 271: 256-260.
    [53]
    AUSHEV T, BARTEL W, BONDAR A, et al. Physics at Super B factory[DB/OL]. arXiv:1002.5012 [hep-ex].
    [54]
    BERNABEU J, GONZALEZ-SPRINBERG G A, PAPAVASSILIOU J, et al. Tau anomalous magnetic moment form factor at Super B/Flavor factories[J]. Nucl Phys B, 2008, 790: 160-174.
    [55]
    OHNISHI Y, ABE T, ADACHI T, et al. Accelerator design at SuperKEKB[J]. PTEP, 2013: 03A011.
    [56]
    KOISO H, MORITA A, OHNISHI Y. Lattice of the KEKB colliding rings[J]. Prog Theor Exp Phys, 2013: 03A009.
    [57]
    LAURSEN M L, SAMUEL M A, Sen A. Radiation zeros and a test for the g value of the τ lepton[J]. Phys Rev D, 1984, 29: 2 652-2 654 (Erratum: Phys Rev D, 1997, 56: 3 155).
    [58]
    EIDELMAN S, EPIFANOV D, FAEL M, et al. Tau dipole moments via radiative leptonic tau decays[J].
    JHEP, 2016,1603:140.
    [59]
    FAEL M. Electromagnetic dipole moments of fermions[D/OL]. http://opac.nebis.ch/ediss/20142170.pdf
    [60]
    TSAI Y S. Decay correlations of heavy leptons in e++e-→l++l-[J]. Phys Rev D, 1971, 4: 2 821-2 837(Erratum: Phys Rev D, 1976, 13: 771).
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