Using Gradient Flow to Renormalise Matrix Elements for Meson Mixing and Lifetimes

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The gradient-flow formalism proves to be a useful tool in lattice calculations of quantum chromodynamics. For example, it can be used as a scheme to renormalize composite operators by inverting the short-flow-time expansion of the corresponding flowed operators. In this paper, we consider the short-flow-time expansion of five quark bilinear operators, the scalar, pseudoscalar, vector, axialvector, and tensor currents, and compute the matching coefficients through next-to-next-to-leading order QCD. Among other applications, our results constitute one ingredient for calculating bag parameters of mesons within the gradient-flow formalism on the lattice.

Section: Numerical Results For ζ V (T)mentioning

confidence: 99%

“…A first preliminary study, already employing the result for the axialvector current obtained in the present paper, has been published in ref. [34].…”

Section: Discussionmentioning

confidence: 99%

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Short-flow-time expansion of quark bilinears through next-to-next-to-leading order QCD

Borgulat,

Harlander,

Kohnen

et al. 2024

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Two body non-leptonic D0 decays from LCSR and implications for$${\Delta a}_{{\text{CP}}}^{{\text{dir}}}$$

Lenz,

Piscopo,

Rusov

2024

Motivated by the recent measurements of CP violating effects in singly Cabibbo suppressed D0 decays, we revisit the theoretical predictions of these channels. Using up-to-date values for the decay constants and form factors, we find already within naive QCD factorisation, surprisingly good agreement between the central values of the branching ratios and the corresponding experimental data. We further extend the study of these modes by employing the method of light-cone sum rules (LCSR) with light-meson light-cone distribution amplitudes. Using for the first time this framework to compute the leading contribution to the decay amplitude, we can again describe well the experimental branching ratios for the modes D0 → π+K−, D0 → K+K−, D0 → π+π− and D0 → K+π−. The combination of our results with known predictions for the penguin contributions obtained with LCSR, leads to an upper bound for the value of direct CP violation expected in the Standard Model of $$\left|{\Delta a}_{{\text{CP}}}^{{\text{dir}}}\right|\le 2.4\times {10}^{-4}$$, which is approximately a factor six smaller than the current measurement.

Position-space renormalization schemes for four-quark operators in HQET

Lin,

Detmold,

Meinel

2024

X-space schemes are gauge-invariant, regulator-independent renormalization schemes that are defined by requiring position-space correlation functions of gauge-invariant operators to be equal to their noninteracting values at particular kinematic points. These schemes can be used to nonperturbatively renormalize composite operators in Lattice Quantum Chromodynamics (LQCD), and by computing matching coefficients between the X-space scheme and $$ \overline{\textrm{MS}} $$ MS ¯ in the dimensionally-regulated continuum, matrix elements calculated with LQCD can be converted to $$ \overline{\textrm{MS}} $$ MS ¯ -renormalized matrix elements. Using X-space schemes for Heavy Quark Effective Theory (HQET) operators has the additional benefit that appropriate ratios of position-space correlation functions cancel the power-divergent static-quark self-energy of Lattice HQET nonperturbatively. This work presents the O(αS) matching coefficients between X-space renormalized four-quark flavor-nonsinglet HQET operators relevant for the lifetimes of charm- and bottom-hadrons, and four-quark HQET operators relevant for mixing between neutral mesons containing a heavy quark, such as B − $$ \overline{B} $$ B ¯ mixing.