Fierz transformations and renormalization schemes for fourquark operators

Garrón, Nicolas

doi:10.1051/epjconf/201817510005

Cited by 3 publications

(5 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In both schemes, the condition (2.5) is imposed. The conventional definition of the projector P entering the condition (2.6) on the renormalized four-point function is [43]…”

Section: Specifics Of the Ri Schemes And Ward Identitymentioning

confidence: 99%

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

Gorbahn

Jäger

Moretti

et al. 2023

J. High Energ. Phys.

View full text Add to dashboard Cite

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.

show abstract

“…In both schemes, the condition (2.5) is imposed. The conventional definition of the projector P entering the condition (2.6) on the renormalized four-point function is [43]…”

Section: Specifics Of the Ri Schemes And Ward Identitymentioning

confidence: 99%

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

Gorbahn

Jäger

Moretti

et al. 2023

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

“…In our work [24], we show that the conventional definition of the projector P [29] entering the condition (5) on the renormalized four-point function leads, in contrast to what happens in the MS, to a finite renormalization of the semi-leptonic operator even in the case QED is neglected. This can be traced to the violation of the QCD Ward identity (WI) for the quark current and it reflects in a scale dependence of the conversion factor.…”

Section: Specifics Of the Ri Schemes And Ward Identitymentioning

confidence: 73%

Semileptonic weak Hamiltonian to in momentum-space subtraction schemes

Moretti

Gorbahn

Jäger

et al. 2023

J. Phys.: Conf. Ser.

View full text Add to dashboard Cite

The CKM unitarity precision test of the Standard Model requires a systematic treatment of electromagnetic corrections for semi-leptonic decays. Electromagnetic corrections renormalize a semi-leptonic four-fermion operator and we calculate the 𝒪(ααs ) 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 scheme. The conventional projector, that has been used in the literature for MOM kinematics, generates an artificial QCD contribution to the conversion factor, which reflects in an unphysical dependence on the lattice matching scale. This can be traced to the violation of a Ward identity that holds in the case QED is neglected. We show how to remedy this by judicious choices of projector. The resulting Wilson coefficients (and operator matrix elements) have greatly reduced scale dependence.

show abstract

“…[20], RI-SMOM renormalization is expected to have smaller infrared contamination than RI-MOM due to the usage of the non-exceptional momenta. The studies by [17][18][19] confirm such expectation and suggest that for B 4 and B 5 RI-SMOM renormalization should be used to fully control the infrared contamination. In Ref.…”

Section: Neutral-kaon Mixing Parameter B K Based On Standard Model Anmentioning

confidence: 78%

“…For beyond-Standard-Model B i (µ) at the MS scale µ = 3 GeV, the uncertainties of 2+1 flavor lattice results are about 2-5% [1] B 2 = 0.502 (14), B 3 = 0.766 (32), B 4 = 0.926 (19), B 5 = 0.720 (38).…”

Section: Neutral-kaon Mixing Parameter B K Based On Standard Model An...mentioning

confidence: 99%

“…There are clear discrepancies in B 4 and B 5 from different groups. To resolve these discrepancies, RBC-UKQCD collaboration undertakes a study using both RI-MOM and RI-SMOM renormalization [17][18][19]. The calculation is performed using N f = 2 + 1 flavor domain wall fermion at M π ≈ 300 MeV and two lattice spacings a = 0.08 and 0.11 fm.…”

Section: Neutral-kaon Mixing Parameter B K Based On Standard Model An...mentioning

confidence: 99%

See 1 more Smart Citation

Recent progress in applying lattice QCD to kaon physics

Feng

2018

EPJ Web Conf.

View full text Add to dashboard Cite

Abstract. Standard lattice calculations in kaon physics are based on the evaluation of matrix elements of local operators between two single-hadron states or a single-hadron state and the vacuum. Recent progress in lattice QCD has gone beyond these standard observables. I will review the status and prospects of lattice kaon physics with an emphasis on non-leptonic K → ππ decay and long-distance processes including K 0 -K 0 mixing and rare kaon decays.

show abstract

Fierz transformations and renormalization schemes for fourquark operators

Cited by 3 publications

References 13 publications

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

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

Semileptonic weak Hamiltonian to in momentum-space subtraction schemes

Recent progress in applying lattice QCD to kaon physics

Contact Info

Product

Resources

About