Abstract.
We focus on the chiral Lagrangian couplings describing radiative corrections to weak semi-leptonic decays and relate them to the decay amplitude of a lepton, computed by Braaten and Li at one loop in the standard model. For this purpose, we follow a two-step procedure. A first matching, from the standard model to Fermi theory, yields a relevant set of counterterms. The latter are related to chiral couplings thanks to a second matching, from Fermi theory to the chiral Lagrangian, which is performed using the spurion method. We show that the chiral couplings of physical relevance obey integral representations in a closed form, expressed in terms of QCD chiral correlators and vertex functions. We deduce exact relations among the couplings, as well as numerical estimates which go beyond the usual \(\log(M_Z/M_\rho)\) approximation.
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References
V. Cirigliano, H. Neufeld, H. Pichl, Eur. Phys. J. C 35, 53 (2004) [hep-ph/0401173]
A. Sher et al. , Phys. Rev. Lett. 91, 261802 (2003) [hep-ex/0305042]
O.P. Yushchenko et al. , Phys. Lett. B 589, 111 (2004) [hep-ex/0404030]
A. Lai et al. [NA48 Collaboration], Phys. Lett. B 602, 41 (2004) [hep-ex/0410059]; B 604, 1 (2004) [hep-ex/0410065]
T. Alexopoulos et al. [KTeV Collaboration], Phys. Rev. Lett. 93, 181802 (2004) [hep-ex/0406001]; Phys. Rev. D 70, 092007 (2004) [hep-ex/0406003]
P. Franzini, hep-ex/0408150
V. Cirigliano, M. Knecht, H. Neufeld, H. Rupertsberger, P. Talavera, Eur. Phys. J. C 23, 121 (2002) [hep-ph/0110153]
T.C. Andre, hep-ph/0406006; V. Bytev, E. Kuraev, A. Baratt, J. Thompson, Eur. Phys. J. C 27, 57 (2003) [Erratum C 34, 523 (2004)] [hep-ph/0210049]
S.M. Berman, Phys. Rev. Lett. 1, 468 (1958); T. Kinoshita, Phys. Rev. Lett. 2, 477 (1959)
A. Sirlin, Rev. Mod. Phys. 50, 573 (1978) [Erratum 50, 905 (1978)]
A. Sirlin, Nucl. Phys. B 196, 83 (1982)
S. Weinberg, Physica A 96, 327 (1979)
J. Gasser, H. Leutwyler, Annals Phys. 158, 142 (1984)
J. Gasser, H. Leutwyler, Nucl. Phys. B 250, 465 (1985)
J.F. Donoghue, E. Golowich, B.H. Holstein, Dynamics of the standard model (Cambridge University Press)
R. Urech, Nucl. Phys. B 433, 234 (1995) [hep-ph/9405341]
M. Knecht, H. Neufeld, H. Rupertsberger, P. Talavera, Eur. Phys. J. C 12, 469 (2000) [hep-ph/9909284]
B. Moussallam, Nucl. Phys. B 504, 381 (1997) [hep-ph/9701400]
T. Das, G.S. Guralnik, V.S. Mathur, F.E. Low, J.E. Young, Phys. Rev. Lett. 18, 759 (1967)
J. Gasser, A. Rusetsky, I. Scimemi, Eur. Phys. J. C 32, 97 (2003) [hep-ph/0305260]
E. Braaten, C.S. Li, Phys. Rev. D 42, 3888 (1990)
C. Itzykson, J.B. Zuber, Quantum field theory (McGraw-Hill 1980), Sect. 5-1-3
G. Ecker, J. Gasser, A. Pich, E. de Rafael, Nucl. Phys. B 321, 311 (1989)
M.J. Savage, M.E. Luke, M.B. Wise, Phys. Lett. B 291, 481 (1992) [hep-ph/9207233]
M. Knecht, A. Nyffeler, Eur. Phys. J. C 21, 659 (2001) [hep-ph/0106034]
S. Weinberg, The quantum theory of fields (Cambridge University Press 1996), vol. 2, Sect. 20.5
T. Das, V.S. Mathur, S. Okubo, Phys. Rev. Lett. 19, 859 (1967)
V. Cuplov, A. Nehme, hep-ph/0311274
S. Weinberg, Phys. Rev. Lett. 18, 507 (1967)
J. Bijnens, E. Gamiz, E. Lipartia, J. Prades, JHEP 0304, 055 (2003) [hep-ph/0304222]
V. Cirigliano, G. Ecker, M. Eidemuller, A. Pich, J. Portoles, Phys. Lett. B 596, 96 (2004) [hep-ph/0404004]
J. Wess, B. Zumino, Phys. Lett. B 37, 95 (1971); E. Witten, Nucl. Phys. B 223, 422 (1983)
G. ‘t Hooft, Nucl. Phys. B 72, 461 (1974)
W.J. Marciano, A. Sirlin, Phys. Rev. Lett. 71, 3629 (1993)
A. Czarnecki, W.J. Marciano, A. Sirlin, Phys. Rev. D 70, 093006 (2004) [hep-ph/0406324]
H. Neufeld, Proceedings of the 337th WE-Heraeus seminar, Bad Honnef, Germany, December 13-17 2004, Effective field theories in nuclear, particle and atomic physics, edited by J. Bijnens, U.G. Meissner, A. Wirzba, hep-ph/0502008
B. Ananthanarayan, B. Moussallam, JHEP 0406, 047 (2004) [hep-ph/0405206]
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Received: 16 May 2005, Published online: 19 July 2005
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Descotes-Genon, S., Moussallam, B. Radiative corrections in weak semi-leptonic processes at low energy: a two-step matching determination*. Eur. Phys. J. C 42, 403–417 (2005). https://doi.org/10.1140/epjc/s2005-02316-8
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DOI: https://doi.org/10.1140/epjc/s2005-02316-8