Effective field theory after a new-physics discovery

153

144

We provide a systematic treatment of the previously discovered power-enhanced QED corrections to the leptonic decay B q → µ + µ − (q = d, s) in the framework of soft-collinear effective theory (SCET). Employing two-step matching on SCET I and SCET II , and the respective renormalization group equations, we sum the leadinglogarithmic QED corrections and the mixed QED-QCD corrections to all orders in the couplings for the matrix element of the semileptonic weak effective operator Q 9 . We propose a treatment of the B-meson decay constant and light-cone distribution amplitude in the presence of process-specific QED corrections. Finally we include ultrasoft photon radiation and provide updated values of the non-radiative and radiative branching fractions of B q → µ + µ − decay that include the double-logarithmic QED and QCD corrections.

mentioning

confidence: 84%

“…In this application, the insertion of an external Higgs field operator corresponds to the lepton mass factor. The off-diagonal anomalous dimension in[33] misses the factor w, because the one-particle reducible diagram with the Higgs insertion on the external leg was not included.…”

mentioning

confidence: 99%

Power-enhanced leading-logarithmic QED corrections to Bq→ μ+μ−

Beneke

Bobeth

Szafron

2019

153

144

“…Note that both the matching coefficient H 2 (z) contain terms that are singular for z = 0, 1 and the two subtraction terms properly remove the singularities of the product of these two quantities. This generalizes a simple "plus-type" subtraction prescription for the bare operator proposed in [24,25], which works only for cases where the relevant matching coefficient approaches a constant plus power-suppressed terms as z → 0. Removing the endpoint divergences in the way described above comes at the price of introducing hard upper limits on the integrals over + and − in the last term of the factorization formula (2.9), which originally have power counting ± = O(m b ).…”

Section: Factorization Formula In Terms Of Bare Objectsmentioning

confidence: 87%

Factorization at subleading power and endpoint-divergent convolutions in h → γγ decay

Liu

Neubert

2020

Self Cite

148

It is by now well known that, at subleading power in scale ratios, factorization theorems for high-energy cross sections and decay amplitudes contain endpoint-divergent convolution integrals. The presence of endpoint divergences hints at a violation of simple scale separation. At the technical level, they indicate an unexpected failure of dimensional regularization and the MS subtraction scheme. In this paper we start a detailed discussion of factorization at subleading power within the framework of soft-collinear effective theory. As a concrete example, we factorize the decay amplitude for the radiative Higgs-boson decay h → γγ mediated by a b-quark loop, for which endpoint-divergent convolution integrals require both dimensional and rapidity regulators. We derive a factorization theorem for the decay amplitude in terms of bare Wilson coefficients and operator matrix elements. We show that endpoint divergences caused by rapidity divergences cancel to all orders of perturbation theory, while endpoint divergences that are regularized dimensionally can be removed by rearranging the terms in the factorization theorem. We use our result to resum the leading double-logarithmic corrections of order α n s ln 2n+2 (−M 2 h /m 2 b ) to the decay amplitude to all orders of perturbation theory.

“…2 (z) contain terms that are singular for z = 0, 1 and the two subtraction terms properly remove the singularities of the product of these two quantities. This generalizes a simple "plus-type" subtraction prescription for the bare operator proposed in [12,29], which works only for cases where the relevant matching coefficient approaches a constant plus power-suppressed terms as z → 0. Figure 2.…”

Section: Factorization Formula In Terms Of Bare Objectsmentioning

confidence: 87%

Factorization at subleading power and endpoint divergences in h → γγ decay. Part II. Renormalization and scale evolution

Liu

Mecaj

Neubert

et al. 2021

Self Cite

Building on the recent derivation of a bare factorization theorem for the b-quark induced contribution to the h → γγ decay amplitude based on soft-collinear effective theory, we derive the first renormalized factorization theorem for a process described at subleading power in scale ratios, where λ = mb/Mh « 1 in our case. We prove two refactorization conditions for a matching coefficient and an operator matrix element in the endpoint region, where they exhibit singularities giving rise to divergent convolution integrals. The refactorization conditions ensure that the dependence of the decay amplitude on the rapidity regulator, which regularizes the endpoint singularities, cancels out to all orders of perturbation theory. We establish the renormalized form of the factorization formula, proving that extra contributions arising from the fact that “endpoint regularization” does not commute with renormalization can be absorbed, to all orders, by a redefinition of one of the matching coefficients. We derive the renormalization-group evolution equation satisfied by all quantities in the factorization formula and use them to predict the large logarithms of order $$ {\alpha \alpha}_s^2{L}^k $$ αα s 2 L k in the three-loop decay amplitude, where $$ L=\ln \left(-{M}_h^2/{m}_b^2\right) $$ L = ln − M h 2 / m b 2 and k = 6, 5, 4, 3. We find perfect agreement with existing numerical results for the amplitude and analytical results for the three-loop contributions involving a massless quark loop. On the other hand, we disagree with the results of previous attempts to predict the series of subleading logarithms $$ \sim {\alpha \alpha}_s^n{L}^{2n+1} $$ ∼ αα s n L 2 n + 1 .