JHEP01(2023)159.pdf (513.58 kB)
Semileptonic weak Hamiltonian to O(aas) in momentum-space subtraction schemes
journal contribution
posted on 2023-06-10, 06:21 authored by M Gorbahn, S Jager, F Moretti, Eric Van Der MerweEric Van Der MerweThe 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.
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Publication status
- Published
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- Published version
Journal
Journal of High Energy PhysicsISSN
1126-6708Publisher
Springer Science and Business Media LLCExternal DOI
Volume
2023Page range
a159 1-24Department affiliated with
- Physics and Astronomy Publications
Institution
University of SussexFull text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2023-03-01First Open Access (FOA) Date
2023-03-01First Compliant Deposit (FCD) Date
2023-03-01Usage metrics
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