Violation of the Kluberg-Stern-Zuber theorem in SCET

Abstract

A classic result, originally due to Kluberg-Stern and Zuber, states that operators that vanish by the classical equation of motion (eom) do not mix into "physical" operators. Here we show that and explain why this result does not hold in soft-collinear effective theory (SCET) for the renormalization of power-suppressed operators. We calculate the non-vanishing mixing of eom operators for the simplest case of N -jet operators with a single collinear field in every direction. The result implies that-for the computation of the anomalous dimension but not for on-shell matrix elements-there exists a preferred set of fields that must be used to reproduce the infrared singularities of QCD scattering amplitudes. We identify these fields and explain their relation to the gauge-invariant SCET Lagrangian. Further checks reveal another generic property of SCET beyond leading power, which will be relevant to resummation at the next-to-leading logarithmic level, the divergence of convolution integrals with the hard matching coefficients. We propose an operator solution that allows to consistently renormalize such divergences. arXiv:1907.05463v1 [hep-ph]

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

“…The refactorization theorem for the bare operator O 25) suggests that this result closely resembles the structure of (5.18). We would thus like to establish a similar relation that holds after renormalization.…”

“…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 ).…”

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

“…However, a rearrangement is necessary due to the factorization anomaly as discussed below. The renormalization of SCET II operators then proceeds similarly to the SCET I case, see [26,34,37]. We next discuss the renormalization of each sector separately and then present the combined result for the SCET II operators.…”

Next-to-leading power threshold factorization for Drell-Yan production

“…The systematic expansion in powers of λ which is built into the SCET framework means that this effective field theory is ideally suited to the study of power corrections. The formalism we use here was developed in [3,14,15,16]. 2 A generic, N-jet, operator has the following form…”