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

We 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.

Decay amplitudes to three hadrons from finite-volume matrix elements

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.

A phenomenological analysis on isospin-violating decay of X(3872)

In a molecular scenario, we investigate the isospin-breaking hidden charm decay processes of X(3872), i.e., $$X(3872) \rightarrow \pi ^+ \pi ^- J/\psi $$ X ( 3872 ) → π + π - J / ψ , $$X(3872) \rightarrow \pi ^+ \pi ^- \pi ^0 J/\psi $$ X ( 3872 ) → π + π - π 0 J / ψ , and $$X(3872)\rightarrow \pi ^0\chi _{cJ}$$ X ( 3872 ) → π 0 χ cJ . We assume that the source of the strong isospin violation comes from the different coupling strengths of X(3872) to its charged components $$D^{*+} D^-$$ D ∗ + D - and neutral components $$D^{*0 } {\bar{D}}^0$$ D ∗ 0 D ¯ 0 as well as the interference between the charged meson loops and neutral meson loops. The former effect could fix our parameters by using the measurement of the ratio $$\Gamma [X(3872) \rightarrow \pi ^+ \pi ^- \pi ^0 J/\psi ]/\Gamma [X(3872) \rightarrow \pi ^+ \pi ^- J/\psi ]$$ Γ [ X ( 3872 ) → π + π - π 0 J / ψ ] / Γ [ X ( 3872 ) → π + π - J / ψ ] . With the determined parameter range, we find that the estimated ratio $$\Gamma [X(3872) \rightarrow \pi ^0 \chi _{c1}/\Gamma [X(3872) \rightarrow \pi ^+ \pi ^- J/\psi ]$$ Γ [ X ( 3872 ) → π 0 χ c 1 / Γ [ X ( 3872 ) → π + π - J / ψ ] is well consistent with the experimental measurement from the BESIII collaboration. Moreover, the partial width ratio of $$\pi ^0 \chi _{cJ}$$ π 0 χ cJ for $$J=0,1,2$$ J = 0 , 1 , 2 is estimated to be $$1.77{-}1.65:1:1.09{-}1.43$$ 1.77 - 1.65 : 1 : 1.09 - 1.43 , which could be tested by further precise measurements of BESIII and Belle II.

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

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.

Hadronic vacuum polarization and vector-meson resonance parameters from $$\varvec{e^+e^-\rightarrow \pi ^0\gamma }$$

We study the reaction $$e^+e^-\rightarrow \pi ^0\gamma $$ e + e - → π 0 γ based on a dispersive representation of the underlying $$\pi ^0\rightarrow \gamma \gamma ^*$$ π 0 → γ γ ∗ transition form factor. As a first application, we evaluate the contribution of the $$\pi ^0\gamma $$ π 0 γ channel to the hadronic-vacuum-polarization correction to the anomalous magnetic moment of the muon. We find $$a_\mu ^{\pi ^0\gamma }\big |_{\le 1.35\,\text {GeV}}=43.8(6)\times 10^{-11}$$ a μ π 0 γ | ≤ 1.35 GeV = 43.8 ( 6 ) × 10 - 11 , in line with evaluations from the direct integration of the data. Second, our fit determines the resonance parameters of $$\omega $$ ω and $$\phi $$ ϕ . We observe good agreement with the $$e^+e^-\rightarrow 3\pi $$ e + e - → 3 π channel, explaining a previous tension in the $$\omega $$ ω mass between $$\pi ^0\gamma $$ π 0 γ and $$3\pi $$ 3 π by an unphysical phase in the fit function. Combining both channels we find $${\bar{M}}_\omega =782.736(24)\,\text {MeV}$$ M ¯ ω = 782.736 ( 24 ) MeV and $${\bar{M}}_\phi =1019.457(20)\,\text {MeV}$$ M ¯ ϕ = 1019.457 ( 20 ) MeV for the masses including vacuum-polarization corrections. The $$\phi $$ ϕ mass agrees perfectly with the PDG average, which is dominated by determinations from the $${\bar{K}} K$$ K ¯ K channel, demonstrating consistency with $$3\pi $$ 3 π and $$\pi ^0\gamma $$ π 0 γ . For the $$\omega $$ ω mass, our result is consistent but more precise, exacerbating tensions with the $$\omega $$ ω mass extracted via isospin-breaking effects from the $$2\pi $$ 2 π channel.