QED corrections to leptonic decay rates

Boyle, P. A.; Guelpers, Vera; Juettner, A.; Lehner, Christoph; hÓgáin, Fionn Ó; Portelli, Antonin; Richings, James; Sachrajda, C. T.

doi:10.48550/arxiv.1902.00295

Cited by 2 publications

(2 citation statements)

References 8 publications

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“…A large part of the theoretical uncertainty comes from the statistics and continuum and chiral extrapolation of lattice data, which can be systematically reduced by a more realistic simulation with high statistics. We also note that an independent study of the electromagnetic effects is in progress [242]. Therefore, it is feasible to more precisely determine |V us /V ud | using only lattice-QCD+QED for f K ± / f π ± and the ratio of the experimental values of the K μ2 and π μ2 decay rates.…”

Section: Experimental Information Concerningmentioning

confidence: 99%

FLAG Review 2021

Aoki

Blum²,

Colangelo³

et al. 2022

Eur. Phys. J. C

Self Cite

360

140

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We review lattice results related to pion, kaon, D-meson, B-meson, and nucleon physics with the aim of making them easily accessible to the nuclear and particle physics communities. More specifically, we report on the determination of the light-quark masses, the form factor $$f_+(0)$$ f + ( 0 ) arising in the semileptonic $$K \rightarrow \pi $$ K → π transition at zero momentum transfer, as well as the decay constant ratio $$f_K/f_\pi $$ f K / f π and its consequences for the CKM matrix elements $$V_{us}$$ V us and $$V_{ud}$$ V ud . Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of $$SU(2)_L\times SU(2)_R$$ S U ( 2 ) L × S U ( 2 ) R and $$SU(3)_L\times SU(3)_R$$ S U ( 3 ) L × S U ( 3 ) R Chiral Perturbation Theory. We review the determination of the $$B_K$$ B K parameter of neutral kaon mixing as well as the additional four B parameters that arise in theories of physics beyond the Standard Model. For the heavy-quark sector, we provide results for $$m_c$$ m c and $$m_b$$ m b as well as those for the decay constants, form factors, and mixing parameters of charmed and bottom mesons and baryons. These are the heavy-quark quantities most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. We review the status of lattice determinations of the strong coupling constant $$\alpha _s$$ α s . We consider nucleon matrix elements, and review the determinations of the axial, scalar and tensor bilinears, both isovector and flavor diagonal. Finally, in this review we have added a new section reviewing determinations of scale-setting quantities.

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Section: Experimental Information Concerningmentioning

confidence: 99%

FLAG Review 2021

Aoki

Blum²,

Colangelo³

et al. 2022

Eur. Phys. J. C

Self Cite

360

140

View full text Add to dashboard Cite

show abstract

“…The complete treatment of QED corrections on the lattice is a difficult task and has so far been performed for purely leptonic decays [34][35][36][37]. A novel feature in the semileptonic decay is that the relevant operator renormalizes in the presence of QED corrections.…”

Section: Jhep01(2023)159mentioning

confidence: 99%

Semileptonic weak Hamiltonian to $$ \mathcal{O} $$(ααs) in momentum-space subtraction schemes

Gorbahn

Jäger

Moretti

et al. 2023

J. High Energ. Phys.

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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 $$ \mathcal{O} $$ O (ααs) perturbative scheme conversion between the $$ \overline{\textrm{MS}} $$ 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 α = 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 α = 0 limit. We show how to remedy this by judicious choices of projector, and define two new schemes $$ \overline{\textrm{RI}} $$ RI ¯ -MOM and $$ \overline{\textrm{RI}} $$ 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 $$ \overline{\textrm{MS}} $$ 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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QED corrections to leptonic decay rates

Cited by 2 publications

References 8 publications

FLAG Review 2021

FLAG Review 2021

Semileptonic weak Hamiltonian to $$ \mathcal{O} $$(ααs) in momentum-space subtraction schemes

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