Inclusion of Isospin Breaking Effects in Lattice Calculations

Rotated twisted-mass: a convenient regularization scheme for isospin breaking QCD and QED lattice calculations

The European Physical Journal A ◽

10.1140/epja/s10050-021-00579-5 ◽

2021 ◽

Vol 57 (9) ◽

Author(s):

R. Frezzotti ◽

G. Gagliardi ◽

V. Lubicz ◽

F. Sanfilippo ◽

S. Simula

Keyword(s):

Correlation Functions ◽

Mass Splitting ◽

Isospin Breaking ◽

Numerical Application ◽

Practical Advantage ◽

Regularization Scheme ◽

Statistical Fluctuations ◽

Twisted Mass ◽

Lattice Calculations

AbstractWe propose a scheme of lattice twisted-mass fermion regularization which is particularly convenient for application to isospin breaking (IB) QCD and QED calculations, based in particular on the so called RM123 approach, in which the IB terms of the action are treated as a perturbation. The main, practical advantage of this scheme is that it allows the calculation of IB effects on some mesonic observables, like e.g. the $$\pi ^+ - \pi ^0$$ π + - π 0 mass splitting, using lattice correlation functions in which the quark and antiquark fields in the meson are regularized with opposite values of the Wilson parameter r. These correlation functions are found to be affected by much smaller statistical fluctuations, with respect to the analogous functions in which quark and antiquark fields are regularized with the same value of r. Two numerical application of this scheme, that we call rotated twisted-mass, within pure QCD and QCD + QED respectively, are also provided for illustration.

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Decay amplitudes to three hadrons from finite-volume matrix elements

Journal of High Energy Physics ◽

10.1007/jhep04(2021)113 ◽

2021 ◽

Vol 2021 (4) ◽

Author(s):

Maxwell T. Hansen ◽

Fernando Romero-López ◽

Stephen R. Sharpe

Keyword(s):

Finite Volume ◽

Decay Amplitude ◽

Weak Decay ◽

Matrix Elements ◽

Isospin Breaking ◽

Final State ◽

Identical Particles ◽

Hadron Decay ◽

Finite State ◽

Particle Decays

Abstract We derive relations between finite-volume matrix elements and infinite-volume decay amplitudes, for processes with three spinless, degenerate and either identical or non-identical particles in the final state. This generalizes the Lellouch-Lüscher relation for two-particle decays and provides a strategy for extracting three-hadron decay amplitudes using lattice QCD. Unlike for two particles, even in the simplest approximation, one must solve integral equations to obtain the physical decay amplitude, a consequence of the nontrivial finite-state interactions. We first derive the result in a simplified theory with three identical particles, and then present the generalizations needed to study phenomenologically relevant three-pion decays. The specific processes we discuss are the CP-violating K → 3π weak decay, the isospin-breaking η → 3π QCD transition, and the electromagnetic γ* → 3π amplitudes that enter the calculation of the hadronic vacuum polarization contribution to muonic g − 2.

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On the influence of spatial discretization in LWR cell- and lattice calculations with HELIOS 1.9

Annals of Nuclear Energy ◽

10.1016/j.anucene.2008.01.022 ◽

2008 ◽

Vol 35 (8) ◽

pp. 1492-1501 ◽

Cited By ~ 9

Author(s):

B. Merk ◽

R. Koch

Keyword(s):

Spatial Discretization ◽

Lattice Calculations

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Another SMEFT story: Z′ facing new results on ε′/ε, ∆MK and K → $$ \pi \nu \overline{\nu} $$

Journal of High Energy Physics ◽

10.1007/jhep12(2020)097 ◽

2020 ◽

Vol 2020 (12) ◽

Author(s):

Jason Aebischer ◽

Andrzej J. Buras ◽

Jacky Kumar

Keyword(s):

Renormalization Group ◽

Mass Difference ◽

Branching Ratios ◽

New Physics ◽

Matrix Elements ◽

Isospin Breaking ◽

Left Handed ◽

The Standard Model ◽

First Time ◽

Group Effects

Abstract Recently the RBC-UKQCD lattice QCD collaboration presented new results for the hadronic matrix elements relevant for the ratio ε′/ε in the Standard Model (SM) albeit with significant uncertainties. With the present knowledge of the Wilson coefficients and isospin breaking effects there is still a sizable room left for new physics (NP) contributions to ε′/ε which could both enhance or suppress this ratio to agree with the data. The new SM value for the K0 − $$ {\overline{K}}^0 $$ K ¯ 0 mass difference ∆MK from RBC-UKQCD is on the other hand by 2σ above the data hinting for NP required to suppress ∆MK. Simultaneously the most recent results for K+ → $$ {\pi}^{+}\nu \overline{\nu} $$ π + ν ν ¯ from NA62 and for KL → $$ {\pi}^0\nu \overline{\nu} $$ π 0 ν ν ¯ from KOTO still allow for significant NP contributions. We point out that the suppression of ∆MK by NP requires the presence of new CP-violating phases with interesting implications for K → $$ \pi \nu \overline{\nu} $$ πν ν ¯ , KS → μ+μ− and KL → π0ℓ+ℓ− decays. Considering a Z′-scenario within the SMEFT we analyze the dependence of all these observables on the size of NP still allowed by the data on ε′/ε. The hinted ∆MK anomaly together with the εK constraint implies in the presence of only left-handed (LH) or right-handed (RH) flavour-violating Z′ couplings strict correlation between K+ → $$ {\pi}^{+}\nu \overline{\nu} $$ π + ν ν ¯ and KL → $$ {\pi}^0\nu \overline{\nu} $$ π 0 ν ν ¯ branching ratios so that they are either simultaneously enhanced or suppressed relative to SM predictions. An anticorrelation can only be obtained in the presence of both LH and RH couplings. Interestingly, the NP QCD penguin scenario for ε′/ε is excluded by SMEFT renormalization group effects in εK so that NP effects in ε′/ε are governed by electroweak penguins. We also investigate for the first time whether the presence of a heavy Z′ with flavour violating couplings could generate through top Yukawa renormalization group effects FCNCs mediated by the SM Z-boson. The outcome turns out to be very interesting.

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