Gauge invariance at work in FDR: H → γγ

Abstract

We present the first complete calculation performed within the Four Dimensional Regularization scheme (FDR), namely the loop-induced on-shell amplitude for the Higgs boson decay into two photons in an arbitrary R ξ gauge. FDR is a new technique -free of infinities-for addressing multi-loop calculus, which automatically preserves gauge invariance, allowing for a 4-dimensional computation at the same time. We obtained the same result as that assessed in dimensional regularization, thereby explicitly verifying, in a realistic case, that FDR respects gauge invariance.

Theγγdecay of the Higgs boson in FDR

“…The calculation of the amplitude for the Higgs decay into two photons stands as the first test of FDR in the electroweak theory, explicitely verifying -at 1-loop -that the method respects gauge invariance, and providing a detailed example of calculation [20]. We have made it clear that FDR is equivalent to DR at 1-loop, in the sense of a 1-1 correspondence between Feynman diagrams and analytic expressions; the advantage of FDR lies in that there is no need of verifying massive cancellations of unphysical contributions, and -in the case of processes that demand renormalization -that the Lagrangian does not require the addition of counter-terms.…”

“…In a recent work [20], the first application of FDR to a complete calculation in a realistic theory was presented: the 1-loop on-shell amplitude for the Higgs decay into two photons was calculated in arbitrary R ξ -gauge, thereby explicitly verifying that the method respects gauge invariance. Due to its relevance and simplicity, this result, known since a long time [21][22][23][24], has been recently reconsidered in several studies [25][26][27][28][29][30][31][32][33][34][35].…”

Integration‐by‐parts identities in FDR

“…7 Interpreted as the renormalization scale. 8 As an example, when evaluated in n = 4 + ǫ dimensions, Eq. (2.6) reads…”

“…As a two-loop case consider 8) with D i = q 2 i − m 2 i and q 12 = q 1 + q 2 . Differentiating with respect to q α 1 gives…”

“…As a consequence, Feynman diagrams containing counterterms are absent. In [7][8][9] the FDR strategy has been successfully applied to compute several processes at the one-and two-loop accuracy in renormalizable QFTs. 3 1 Acronym of Four Dimensional Regularization/Renormalization.…”