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Semileptonic weak Hamiltonian to O(aas) in momentum-space subtraction schemes

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posted on 2023-06-10, 06:21 authored by M Gorbahn, S Jager, F Moretti, Eric Van Der MerweEric Van Der Merwe
The CKM unitarity precision test of the Standard Model requires a systematic treatment of electromagnetic and strong corrections for semi-leptonic decays. Electromagnetic corrections require the renormalization of a semileptonic four-fermion operator. In this work we calculate the O(aas) perturbative scheme conversion between the MS¯ scheme and several momentum-space subtraction schemes, which can also be implemented on the lattice. We consider schemes defined by MOM and SMOM kinematics and emphasize the importance of the choice of projector for each case. The conventional projector, that has been used in the literature for MOM kinematics, generates QCD corrections to the conversion factor that do not vanish for a = 0 and which generate an artificial dependence on the lattice matching scale that would only disappear after summing all orders of perturbation theory. This can be traced to the violation of a Ward identity that holds in the a = 0 limit. We show how to remedy this by judicious choices of projector, and define two new schemes RI¯ -MOM and RI¯ -SMOM. We prove that the Wilson coefficients in the new schemes are free from pure QCD contributions, and find that the Wilson coefficients (and operator matrix elements) have greatly reduced scale dependence. Our choice of the MS¯ scheme over the traditional W-mass scheme is motivated by the fact that, besides being more tractable at higher orders, unlike the latter it allows for a transparent separation of scales. We exploit this to obtain renormalization-group-improved leading-log and next-to-leading-log strong corrections to the electromagnetic contributions and study the (QED-induced) dependence on the lattice matching scale.

History

Publication status

  • Published

File Version

  • Published version

Journal

Journal of High Energy Physics

ISSN

1126-6708

Publisher

Springer Science and Business Media LLC

Volume

2023

Page range

a159 1-24

Department affiliated with

  • Physics and Astronomy Publications

Institution

University of Sussex

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2023-03-01

First Open Access (FOA) Date

2023-03-01

First Compliant Deposit (FCD) Date

2023-03-01

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