On the importance of NNLO QCD and isospin-breaking corrections in $$\varepsilon '/\varepsilon $$

Aebischer, Jason; Bobeth, Christoph; Buras, Andrzej J.

doi:10.1140/epjc/s10052-019-7549-y

Cited by 152 publications

(61 citation statements)

References 74 publications

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“…The role of isospin breaking contributions in the lattice calculations has been further scrutinized in[80] 5. A very recent update based on a detailed reassessment of the isospin breaking effects leads to ε /ε = 14 ± 5 × 10 −4[81].…”

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confidence: 99%

Kaon CP violation and neutron EDM in the minimal left-right symmetric model

2020

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Within the minimal Left-Right (LR) symmetric model we revisit the predictions for the kaon CP violating observables ε and ε in correlation with the neutron electric dipole moment. We perform a complete study of the cross constraints on the model parameters, phases and the MW R scale, considering the two cases of extended parity or charge conjugation as LR discrete symmetries, together with the possible presence of a Peccei-Quinn symmetry. We discuss in particular two scenarios: whether the Standard Model saturates the experimental value of ε /ε or whether new physics is needed, still an open issue after the recent lattice results on the QCD penguin matrix elements. Within the first scenario, we find no constraints on the LR scale in the charge-conjugation case while in the parity case we show that MW R can be as low as 13 TeV. On the other side, the request that new physics contributes dominantly to ε implies strong correlations among the model parameters, with an upper bound of MW R < 8-100 TeV depending on tan β in the case of charge conjugation and a range of MW R 7-45 TeV in the parity setup. Both scenarios may be probed directly at future colliders and only indirectly at the LHC. * stefano.bertolini@sissa.it † Alessio.Maiezza@irb.hr ‡ fabrizio.nesti@aquila.infn.it Right (LR) symmetric theories, based on the gauge groupA particular role is played by the minimal version of the Left-Right symmetric models (LRSM) [9]. Besides being predictive, the model provides a natural rationale for the origin and smallness of the neutrino mass [10,11], a setup for the restoration of parity at high scale [12], and a novel source for neutrinoless double-beta decay [13,14]. The LRSM has aroused a renewed interest in the era of LHC, because of the possibility of a direct detection via the Keung-Senjanovic (KS) process [15], which violates lepton number in full analogy with the low energy neutrinoless double-beta decay.

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confidence: 99%

Kaon CP violation and neutron EDM in the minimal left-right symmetric model

2020

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“…which is now more than 2σ above the central value (9) of ChPT. We emphasize that the lower numerical result obtained in [19] and recalled in (11) mostly originates from the input values available at that time for the parameters in (17) and (20), namely R = 45.5 and θ = −22 • , respectively. In this phenomenological approach, uncertainties on (22) are basically due to our assumption expressed at the begining of this section and seem difficult to assess.…”

Section: Update Of a Simple η − η Pole Modelmentioning

confidence: 87%

“…Meanwhile we note that the excited-state contamination seen at 1.5 GeV in LQCD data might be residual effects of the scalar resonance at O( p 2 , 0) and meson evolution at O( p 0 , 1/N ), those being essential for the estimate of the Q 6 hadronic matrix elements around 1 GeV in DQCD. Now isospin-breaking effects as well as NNLO QCD corrections to Wilson coefficients of penguin operators, all absent in the RBC-UKQCD result quoted above, lower the SM predition for ε /ε [17]. Extracting the hadronic matrix elements from [16], using the estimate of the isospinbreaking effects from [11] and including the missing NNLO QCD corrections to electroweak penguin contributions, the authors in [18] find…”

Section: Introductionmentioning

confidence: 99%

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Isospin-breaking in $$\varepsilon '/\varepsilon $$: impact of $$\eta _0$$ at the dawn of the 2020s

Buras

Gérard

2020

Eur. Phys. J. C

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For direct CP-violation in $$K\rightarrow \pi \pi $$K→ππ decays, the usual isospin-breaking effects at the percent level are amplified by the dynamics behind the $$\Delta I=1/2$$ΔI=1/2 rule and conventionally encoded in $$\Omega _\mathrm{IB}$$ΩIB parameters. The updated prediction $$\Omega _\mathrm{IB}^{(8)}=(15.9\pm 8.2)\times 10^{-2}$$ΩIB(8)=(15.9±8.2)×10-2 of the Chiral Perturbation Theory for the strong isospin-breaking due to $$\pi _3-\eta _8$$π3-η8 mixing confirms such a tendency but is quite sensitive to the theoretical input value of the low-energy constant corresponding to the flavour-singlet $$\eta _0$$η0 exchange contribution in this truncated octet scheme. We rather exploit the phenomenological $$\eta _8-\eta _0$$η8-η0 mixing as a probe for the non-negligible flavour-singlet component of the physical $$\eta $$η pole to find $$\Omega _\mathrm{IB}^{(9)}=(35\pm 7)\times 10^{-2}$$ΩIB(9)=(35±7)×10-2 in a complete nonet scheme. A large central value in the nonet scheme is thus substituted for a large uncertainty in the octet one. Including the experimental $$\pi ^+-\pi ^0$$π+-π0 mass difference as the dominant electromagnetic isospin-breaking, we obtain for the effective parameter entering the ratio $$\varepsilon '/\varepsilon $$ε′/ε an improved result $$\hat{\Omega }_\mathrm{eff}^{(9)}=(29\pm 7)\times 10^{-2}$$Ω^eff(9)=(29±7)×10-2 to be compared with $$\hat{\Omega }_\mathrm{eff}^{(8)}=(17\pm 9)\times 10^{-2}$$Ω^eff(8)=(17±9)×10-2 used in recent analyses of $$\varepsilon '/\varepsilon $$ε′/ε. Accordingly, we get a reduction from $$(\varepsilon '/\varepsilon )_\text {SM}^{(8)}=(17.4\pm 6.1)\times 10^{-4}$$(ε′/ε)SM(8)=(17.4±6.1)×10-4 to $$(\varepsilon '/\varepsilon )_\text {SM}^{(9)}=(13.9\pm 5.2)\times 10^{-4}$$(ε′/ε)SM(9)=(13.9±5.2)×10-4 and thereby an effective suppression of $$(\varepsilon '/\varepsilon )_\text {SM}$$(ε′/ε)SM by isospin-breaking corrections as large as $$40\%$$40% relative to the recent RBC-UKQCD value.

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“…On the other hand, Kaon physics has still a lot to offer. In particular the ratio ε /ε [19], that describes the amount of direct CP violation in K L → ππ decays relative to the indirect one, still allows for significant NP contributions and this also applies to rare Kaon decays K + → π + νν and K L → π 0 νν.…”

Section: Introductionmentioning

confidence: 99%

Quark-lepton connections in Z′ mediated FCNC processes: gauge anomaly cancellations at work

Aebischer

Buras

Cerdà-Sevilla

et al. 2020

J. High Energ. Phys.

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We consider scenarios with a heavy Z gauge boson with flavour non-universal quark and lepton couplings with the goal to illustrate how the cancellation of gauge anomalies generated by the presence of an additional U(1) gauge symmetry would imply correlations between FCNC processes within the quark sector, within the lepton sector and most interestingly between quark flavour and lepton flavour violating processes. To this end we present simple scenarios with only left-handed flavour-violating Z couplings and those in which also right-handed flavour-violating couplings are present. The considered scenarios are characterized by a small number of free parameters but in contrast to gauge anomaly cancellation in the Standard Model, in which it takes place separately within each generation, in our scenarios anomaly cancellation involves simultaneously quarks and leptons of all three generations. Our models involve, beyond the ordinary quarks and leptons, three heavy right-handed neutrinos. The models with only left-handed FCNCs of Z involve beyond g Z and M Z two real parameters characterizing the charges of all fermions under the U(1) gauge symmetry and the CKM and PMNS ones in the quark and lepton sectors, respectively. The models with the right-handed FCNCs of Z involve few additional parameters. Imposing constraints from well measured ∆F = 2 observables we identify a number of interesting correlations that involve e.g. ε /ε, B s,d → µ + µ − , B → K(K * ) + − , K + → π + νν, K L → π 0 νν and purely lepton flavour violating decays like µ → eγ, µ → 3e, τ → 3µ and µ − e conversion among others. Also (g − 2) µ,e are considered. The impact of the experimental µ → eγ, µ → 3e and in particular µ − e conversion bounds on rare K and B decays is emphasized.

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On the importance of NNLO QCD and isospin-breaking corrections in $$\varepsilon '/\varepsilon $$

Cited by 152 publications

References 74 publications

Kaon CP violation and neutron EDM in the minimal left-right symmetric model

Kaon CP violation and neutron EDM in the minimal left-right symmetric model

Isospin-breaking in $$\varepsilon '/\varepsilon $$: impact of $$\eta _0$$ at the dawn of the 2020s

Quark-lepton connections in Z′ mediated FCNC processes: gauge anomaly cancellations at work

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