# H→γγ: a comment on the indeterminacy of non-gauge-invariant integrals

• We reanalyze the recent computation of the amplitude of the Higgs boson decay into two photons presented by Gastmans et al. [1, 2]. The reasons for why this result cannot be the correct one have been discussed in some recent papers. We address here the general issue of the indeterminacy of integrals with four-dimensional gauge-breaking regulators and to which extent it might eventually be solved by imposing physical constraints. Imposing gauge invariance as the last step upon Rξ-gauge calculations with four-dimensional gauge-breaking regulators, allows us to recover the well known H→γγ result. However we show that in the particular case of the unitary gauge, the indeterminacy cannot be tackled in the same way. The combination of the unitary gauge with a cutoff regularization scheme turns out to be non-predictive.
PCAS:
•  [1] Gastmans R, WU S L, WU T T. arXiv:1108.5322[hep-ph][2] Gastmans R, WU S L, WU T T. arXiv:1108.5872[hep-ph][3] Ellis J R, Gaillard M K, Nanopoulos D V. Nucl. Phys. B, 1976, 106: 292[4] Shifman M A et al. Sov. J. Nucl. Phys., 1979, 30: 711-716 [Yad.Fiz.30:1368-1378,1979][5] Dyson F. Phys. Rev., 1949, 75: 486; 1736[6] Shifman M et al. Phys. Rev. D, 2012, 85: 013015[7] HUANG D, TANG Y, WU Y L. Commun. Theor. Phys., 2012, 57: 427[8] Marciano W, ZHANG C, Willenbrock S. Phys. Rev. D, 2012, 85: 013002[9] Jegerlehner F. arXiv:1110.0869[hep-ph][10] Cornwall J M, Levin D N, Tiktopoulos G. Phys. Rev. D, 1974, 10: 1145; Chanowitz M S, Gaillard M K. Nucl. Phys. B, 1985, 261: 379; Bagger J, Schmidt C. Phys. Rev. D, 1990, 41: 264; Veltman H. Phys. Rev. D, 1990, 41: 2294; HE H J. KUANG Y P, LI X. Phys. Rev. Lett., 1992, 69: 2619[11] SHAO H S, ZHANG Y J, CHAO K T. JHEP, 2012, 1201: 053[12] LIANG Y, Czarnecki A. Can. J. Phys., 2012, 90: 11[13] Bursa F et al. arXiv:1112.2135 [hep-ph][14] Appelquist T, Carazzone J. Phys. Rev. D, 1975, 11: 2856[15] WU Y L. Int. J. Mod. Phys. A, 2003, 18: 5363; Mod. Phys. Lett. A, 2004, 19: 2191, [arXiv:hep-th/0311082v2][16] Jackiw R. Int. J. Mod. Phys. B, 2000, 14: 2011 [arXiv:hep-th/9903044v1][17] Apostol T M. Calculus, John Wiley Sons, 1967, 1: 413-414[18] Schwinger J S. Particles, Sources, and Fields. Vol. 2, Reading, USA: Addison-Wesley, 1989. 306 (Advanced book classics series)

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A. Pilloni and A. D. Polosa. H→γγ: a comment on the indeterminacy of non-gauge-invariant integrals[J]. Chinese Physics C, 2013, 37(4): 043102. doi: 10.1088/1674-1137/37/4/043102
A. Pilloni and A. D. Polosa. H→γγ: a comment on the indeterminacy of non-gauge-invariant integrals[J]. Chinese Physics C, 2013, 37(4): 043102.
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Revised: 2012-06-22
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## H→γγ: a comment on the indeterminacy of non-gauge-invariant integrals

Abstract: We reanalyze the recent computation of the amplitude of the Higgs boson decay into two photons presented by Gastmans et al. [1, 2]. The reasons for why this result cannot be the correct one have been discussed in some recent papers. We address here the general issue of the indeterminacy of integrals with four-dimensional gauge-breaking regulators and to which extent it might eventually be solved by imposing physical constraints. Imposing gauge invariance as the last step upon Rξ-gauge calculations with four-dimensional gauge-breaking regulators, allows us to recover the well known H→γγ result. However we show that in the particular case of the unitary gauge, the indeterminacy cannot be tackled in the same way. The combination of the unitary gauge with a cutoff regularization scheme turns out to be non-predictive.

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