Towards a nonperturbative calculation of weak Hamiltonian Wilson coefficients

Bruno, Mattia; Lehner, Christoph; Soni, Amarjit

doi:10.1103/physrevd.97.074509

Cited by 2 publications

(4 citation statements)

References 45 publications

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“…As previously mentioned, the Wilson coefficients that incorporate the short distance physics "integrated out" from the Standard Model are known in perturbation theory in the ten-operator basis to NLO in the MS scheme. Partial calculations at NNLO are available in the literature [49][50][51][52][53], together with a preliminary study on a direct lattice determination [54]; in this manuscript we utilize the complete NLO results of Ref. [7] in the MS-naive dimensional regularization scheme for our central values and the LO predictions to assign a systematic error due to the truncation of the perturbative series.…”

Section: Results For a 0 And εmentioning

confidence: 99%

Direct CP violation and the ΔI=1/2 rule in K→<

et al. 2020

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We present a lattice QCD calculation of the ΔI ¼ 1=2, K → ππ decay amplitude A 0 and ε 0 , the measure of direct CP violation in K → ππ decay, improving our 2015 calculation [1] of these quantities. Both calculations were performed with physical kinematics on a 32 3 × 64 lattice with an inverse lattice spacing of a −1 ¼ 1.3784ð68Þ GeV. However, the current calculation includes nearly 4 times the statistics and numerous technical improvements allowing us to more reliably isolate the ππ ground state and more accurately relate the lattice operators to those defined in the standard model. We find ReðA 0 Þ ¼ 2.99ð0.32Þð0.59Þ × 10 −7 GeV and ImðA 0 Þ ¼ −6.98ð0.62Þð1.44Þ × 10 −11 GeV, where the errors are statistical and systematic, respectively. The former agrees well with the experimental result ReðA 0 Þ ¼ 3.3201ð18Þ × 10 −7 GeV. These results for A 0 can be combined with our earlier lattice calculation of A 2 [2] to obtain Reðε 0 =εÞ ¼ 21.7ð2.6Þð6.2Þð5.0Þ × 10 −4 , where the third error represents omitted isospin breaking effects, and ReðA 0 Þ=ReðA 2 Þ ¼ 19.9ð2.3Þð4.4Þ. The first agrees well with the experimental result of Reðε 0 =εÞ ¼ 16.6ð2.3Þ × 10 −4. A comparison of the second with the observed ratio ReðA 0 Þ=ReðA 2 Þ ¼ 22.45ð6Þ, demonstrates the standard model origin of this "ΔI ¼ 1=2 rule" enhancement.

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Section: Results For a 0 And εmentioning

confidence: 99%

Direct CP violation and the ΔI=1/2 rule in K→<

et al. 2020

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“…Already at this preliminary stage, without properly accounting for the differences in the renormalization schemes, we observe a relative good agreement with the known perturbative predictions. In a second publication we further advance this calculation by properly addressing all the systematic errors, with a more detailed and comprehensive study [18].…”

Section: Discussionmentioning

confidence: 99%

“…Note that the conversion factor Z RI→MS is currently missing from the calculation, an issue which we address in Ref. [18] for both γ and / q intermediate schemes. For a qualitative comparison we present in Figure 3 the results from the γ scheme where we expect the conversion matrix Z RI→MS to be very close to the identity [11].…”

Section: Renormalization and Continuum Limitmentioning

confidence: 99%