<span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>O</mi><mo>(</mo><mrow><msup><mrow><mi>α</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mi mathvariant="normal">ln</mi><mrow><msub><mrow><mo>(</mo><mi>m</mi></mrow><mrow><mi>μ</mi></mrow></msub></mrow><mrow><msub><mrow><mo>/</mo><mi>m</mi></mrow><mrow><mi>e</mi></mrow></msub></mrow><mo>)</mo><mo>)</mo></math></span> corrections to the electron energy spectrum in muon decay

Andrej Arbuzov; Kirill Melnikov

doi:10.1103/PhysRevD.66.093003

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$O (α^{2} \ln {(m}_{μ} {/ m}_{e}))$ corrections to the electron energy spectrum in muon decay

Andrej Arbuzov^*

Kirill Melnikov^†

Department of Physics, University of Alberta, Edmonton, Alberta, Canada T6G 2J1

Stanford Linear Accelerator Center, Stanford University, Stanford, California 94309

^*On leave of absence from JINR, Dubna. Electronic address: aarbuzov@phys.ualberta.ca
^†Electronic address: melnikov@slac.stanford.edu

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Phys. Rev. D 66, 093003 – Published 6 November, 2002

DOI: https://doi.org/10.1103/PhysRevD.66.093003

Abstract

The $O (α^{2} \ln {(m}_{μ} {/ m}_{e}))$ corrections to the electron energy spectrum in muon decay are computed using the perturbative fragmentation function approach. The magnitude of these corrections is comparable to the anticipated precision of the TWIST experiment where the Michel parameters will be extracted from the measurement of the electron energy spectrum in muon decay.

References (20)

See, e.g., Y. Kuno and Y. Okada, Rev. Mod. Phys. 73, 151 (2001), and references therein.
N.L. Rodning et al., Nucl. Phys. B (Proc. Suppl.) 98, 247 (2001).
M. Quraan et al., Nucl. Phys. A663, 903 (2000).
C. Bouchiat and L. Michel, Phys. Rev. 106, 170 (1957); ibid.T. Kinoshita and A. Sirlin, 107, 593 (1957); ibid.108, 844 (1957); ibid.S. Larsen, E. Lubkin, and M. Tausner, 107, 856 (1957).
Some peculiarities of the standard definition of the Michel parameters, in case when radiative corrections are included, are discussed, e.g., in R. Sachs and A. Sirlin, in Muon Physics, Vol. II, Weak Interactions, edited by C. S. Wu (Academic, New York, 1975).
T. Kinoshita, hep-ph/0101197.
T. van Ritbergen and R.G. Stuart, Phys. Rev. Lett. 82, 488 (1999).
A. Arbuzov, A. Czarnecki, and A. Gaponenko, Phys. Rev. D 65, 113006 (2002).
R. K. Ellis, W. J. Stirling, and B. R. Webber, QCD and Collider Physics (Cambridge University Press, Cambridge, England, 1996) and references therein.
B. Mele and P. Nason, Nucl. Phys. B361, 626 (1991).
M. Cacciari and S. Catani, Nucl. Phys. B617, 253 (2001).
G. Corcella and A.D. Mitov, Nucl. Phys. B623, 247 (2002).
T. Kinoshita and A. Sirlin, Phys. Rev. 113, 1652 (1959).
A.B. Arbuzov, Phys. Lett. B 524, 99 (2002).
G. Curci, W. Furmanski, and R. Petronzio, Nucl. Phys. B175, 27 (1980).
E.G. Floratos, C. Kounnas, and R. Lacaze, Nucl. Phys. B192, 417 (1981).
W. Furmanski and R. Petronzio, Phys. Lett. 97B, 437 (1980).
R.K. Ellis and W. Vogelsang, hep-ph/9602356.
F.A. Berends, W.L. van Neerven, and G.J. Burgers, Nucl. Phys. B297, 429 (1988); ibid.B304, 921(E) (1988).
A. Arbuzov, hep-ph/0206036.

[c1] See, e.g., Y. Kuno and Y. Okada, Rev. Mod. Phys. 73, 151 (2001), and references therein.

[c2] N.L. Rodning et al., Nucl. Phys. B (Proc. Suppl.) 98, 247 (2001).

[c3] M. Quraan et al., Nucl. Phys. A663, 903 (2000).

[c4] C. Bouchiat and L. Michel, Phys. Rev. 106, 170 (1957); ibid.T. Kinoshita and A. Sirlin, 107, 593 (1957); ibid.108, 844 (1957); ibid.S. Larsen, E. Lubkin, and M. Tausner, 107, 856 (1957).

[c5] Some peculiarities of the standard definition of the Michel parameters, in case when radiative corrections are included, are discussed, e.g., in R. Sachs and A. Sirlin, in Muon Physics, Vol. II, Weak Interactions, edited by C. S. Wu (Academic, New York, 1975).

[c6] T. Kinoshita, hep-ph/0101197.

[c7] T. van Ritbergen and R.G. Stuart, Phys. Rev. Lett. 82, 488 (1999).

[c8] A. Arbuzov, A. Czarnecki, and A. Gaponenko, Phys. Rev. D 65, 113006 (2002).

[c9] R. K. Ellis, W. J. Stirling, and B. R. Webber, QCD and Collider Physics (Cambridge University Press, Cambridge, England, 1996) and references therein.

[c10] B. Mele and P. Nason, Nucl. Phys. B361, 626 (1991).

[c11] M. Cacciari and S. Catani, Nucl. Phys. B617, 253 (2001).

[c12] G. Corcella and A.D. Mitov, Nucl. Phys. B623, 247 (2002).

[c13] T. Kinoshita and A. Sirlin, Phys. Rev. 113, 1652 (1959).

[c14] A.B. Arbuzov, Phys. Lett. B 524, 99 (2002).

[c15] G. Curci, W. Furmanski, and R. Petronzio, Nucl. Phys. B175, 27 (1980).

[c16] E.G. Floratos, C. Kounnas, and R. Lacaze, Nucl. Phys. B192, 417 (1981).

[c17] W. Furmanski and R. Petronzio, Phys. Lett. 97B, 437 (1980).

[c18] R.K. Ellis and W. Vogelsang, hep-ph/9602356.

[c19] F.A. Berends, W.L. van Neerven, and G.J. Burgers, Nucl. Phys. B297, 429 (1988); ibid.B304, 921(E) (1988).

[c20] A. Arbuzov, hep-ph/0206036.

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$O (α^{2} \ln {(m}_{μ} {/ m}_{e}))$ corrections to the electron energy spectrum in muon decay

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O(α2ln(mμ/me)) corrections to the electron energy spectrum in muon decay

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$O (α^{2} \ln {(m}_{μ} {/ m}_{e}))$ corrections to the electron energy spectrum in muon decay