Prospects for the Calculation of Rare Kaon Decay Amplitudes from Lattice Simulations

Sachrajda, Christopher

doi:10.22323/1.181.0019

“…already encountered in B s,d → µ + µ − decays and given in (124). We note the minus sign in front of Y R as opposed to X R in (202) that results from the fact that only the γ µ γ 5 part contributes.…”

Section: Preliminariesmentioning

confidence: 79%

Towards the identification of new physics through quark flavour violating processes

Buras

¹

,

Girrbach

²

2014

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We outline a systematic strategy which should help in this decade to identify New Physics (NP) beyond the Standard Model (SM) by means of quark flavour violating processes and thereby to extend the picture of short distance physics down to the scales as short as 10 −20 m and even shorter distance scales corresponding to energies of 100 TeV. Rather than using all possible flavour violating observables that will be measured in the coming years at the LHC, SuperKEKB and in Kaon physics dedicated experiments at CERN, J-PARC and Fermilab, we concentrate on those observables that are theoretically clean and very sensitive to NP. Assuming that the data on the selected observables by us will be very precise, we stress the importance of correlations between these observables as well as of future precise calculations of non-perturbative parameters by means of lattice QCD simulations with dynamical fermions. Our strategy consists of twelve steps which we will discuss in detail illustrating possible outcomes with the help of the SM, models with constrained Minimal Flavour Violation (CMFV), MFV at large and models with tree-level FCNCs mediated by neutral gauge bosons and scalars. We also briefly summarize the status of a number of concrete models. We propose DNA-charts that exhibit correlations between flavour observables in different NP scenarios. The models with new left-handed and/or right-handed currents and non-MFV interactions can be distinguished transparently in this manner. We emphasize the important role of the stringent CMFV relations between various observables as standard candles of flavour physics. The pattern of deviations from these relations may help in identifying the correct NP scenario. The success of this program will be very much facilitated through direct signals of NP at the LHC even if LHC will not be able to probe the physics at scales shorter than 4×10 −20 m. We also emphasize the importance of lepton flavour violation, electric dipole moments and (g − 2) e,µ in these studies.

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“…already encountered in B s,d → µ + µ − decays and given in (124). We note the minus sign in front of Y R as opposed to X R in (202) that results from the fact that only the γ µ γ 5 part contributes.…”

Section: Experimentally We Have [295]mentioning

confidence: 79%

“…which are not yet included in the FLAG average but having smaller errors are consistent with the latter Evidently there is a big progress in determining all these relevant parameters but one would like to decrease the errors further and it appears that this should be possible in the coming years. Selected reviews about the status and prospects can be found in [62,[121][122][123][124][125].…”

Section: Step 2: Improved Lattice Calculations Of Hadronic Parametersmentioning

confidence: 99%

Towards the Identification of New Physics through Quark Flavour Violating Processes

Buras,

Girrbach

2013

Preprint

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We outline a systematic strategy which should help in this decade to identify New Physics (NP) beyond the Standard Model (SM) by means of quark flavour violating processes and thereby to extend the picture of short distance physics down to the scales as short as 10 −20 m and even shorter distance scales corresponding to energies of 100 TeV. Rather than using all possible flavour violating observables that will be measured in the coming years at the LHC, SuperKEKB and in Kaon physics dedicated experiments at CERN, J-PARC and Fermilab, we concentrate on those observables that are theoretically clean and very sensitive to NP. Assuming that the data on the selected observables by us will be very precise, we stress the importance of correlations between these observables as well as of future precise calculations of non-perturbative parameters by means of lattice QCD simulations with dynamical fermions. Our strategy consists of twelve steps which we will discuss in detail illustrating possible outcomes with the help of the SM, models with constrained Minimal Flavour Violation (CMFV), MFV at large and models with tree-level FCNCs mediated by neutral gauge bosons and scalars. We also briefly summarize the status of a number of concrete models. We propose DNA-charts that exhibit correlations between flavour observables in different NP scenarios. The models with new left-handed and/or right-handed currents and non-MFV interactions can be distinguished transparently in this manner. We emphasize the important role of the stringent CMFV relations between various observables as standard candles of flavour physics. The pattern of deviations from these relations may help in identifying the correct NP scenario. The success of this program will be very much facilitated through direct signals of NP at the LHC even if LHC will not be able to probe the physics at scales shorter than 4×10 −20 m. We also emphasize the importance of lepton flavour violation, electric dipole moments and (g − 2) e,µ in these studies.

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“…As far as the meson matrix elements are concerned, the ultimate goal is to compute them in a nonperturbative quark-gluon picture where mesons occur as bound states. This route is followed by lattice computations and in fact since our work appeared in 1986 impressive progress has been made in this manner [41][42][43]. Yet this numerical route is very demanding as even after more than a quarter of a century of hard work by lattice community the present results for K → ππ amplitudes are still not fully satisfactory and the matrix element ππ|Q 6 (µ)|K from lattice QCD is presently unknown.…”

Section: General Structurementioning

confidence: 99%

Large $$N$$ N approach to Kaon decays and mixing 28 years later: $$\Delta I=1/2$$ Δ I = 1 / 2 rule, $$\hat{B}_K$$ B ^ K , and $$\Delta M_K$$ Δ M K

Buras

¹

,

Gérard

²

,

Bardeen

³

2014

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We review and update our results for K → ππ decays and K 0 -K 0 mixing obtained by us in the 1980s within an analytic approximate approach based on the dual representation of QCD as a theory of weakly interacting mesons for large N , where N is the number of colors. In our analytic approach the Standard Model dynamics behind the enhancement of ReA 0 and suppression of ReA 2 , the socalled I = 1/2 rule for K → ππ decays, has a simple structure: the usual octet enhancement through the long but slow quark-gluon renormalization group evolution down to the scales O(1 GeV) is continued as a short but fast meson evolution down to zero momentum scales at which the factorization of hadronic matrix elements is at work. The inclusion of lowest-lying vector meson contributions in addition to the pseudoscalar ones and of Wilson coefficients in a momentum scheme improves significantly the matching between quarkgluon and meson evolutions. In particular, the anomalous dimension matrix governing the meson evolution exhibits the structure of the known anomalous dimension matrix in the quark-gluon evolution. While this physical picture did not yet emerge from lattice simulations, the recent results on Re A 2 and ReA 0 from the RBC-UKQCD collaboration give support for its correctness. In particular, the signs of the two main contractions found numerically by these authors follow uniquely from our analytic approach. Though the current-current operators dominate the I = 1/2 rule, working with matching scales O(1 GeV) we find that the presence of QCD-penguin operator Q 6 is required to obtain satisfactory result for Re A 0 . At NLO in 1/N we obtain R = ReA 0 /Re A 2 = 16.0 ± 1.5 which amounts to an order of magnitude enhancement over the strict large N limit value √ 2. We also update our results for the parameterB K , finding a e-mail: aburas@ph.tum.deB K = 0.73 ± 0.02. The smallness of 1/N corrections to the large N valueB K = 3/4 results within our approach from an approximate cancelation between pseudoscalar and vector meson one-loop contributions. We also summarize the status of M K in this approach.

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Prospects for the Calculation of Rare Kaon Decay Amplitudes from Lattice Simulations

Cited by 5 publications

References 16 publications

Towards the identification of new physics through quark flavour violating processes

Towards the identification of new physics through quark flavour violating processes

Towards the Identification of New Physics through Quark Flavour Violating Processes

Large $$N$$ N approach to Kaon decays and mixing 28 years later: $$\Delta I=1/2$$ Δ I = 1 / 2 rule, $$\hat{B}_K$$ B ^ K , and $$\Delta M_K$$ Δ M K

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