Final state interactions in Kaon decays

Pallante, Elisabetta; Pich, Antonio

doi:10.1016/s0550-3213(00)00601-5

Cited by 84 publications

(114 citation statements)

References 111 publications

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“…Although it has been known for more than a decade that the rescattering of the two final pions induces a large correction to the isospin-zero decay amplitude, this effect was not taken properly into account in the theoretical predictions. From the measured π-π phase shifts one can easily infer that FSI generate a strong enhancement of the predicted ε ′ /ε value, by roughly the needed factor of two [1,2]. A detailed analysis of the corrections induced by FSI has been already given in ref.…”

Section: Introductionmentioning

confidence: 93%

“…Moreover, as shown in refs. [1,2] they can be exponentiated to all orders in the momentum expansion. Since this is a 1/N C suppressed (but numerically large) effect, it generates an important correction, not included in the previous leading-order determination of chiral couplings.…”

Section: Fieldsmentioning

confidence: 99%

“…One-loop corrections to K → ππ have been extensively analyzed in ref. [2], with the aim of identifying and resum FSI effects. Those effects, subleading in 1/N C but numerically relevant, will be taken into account in sections 6 and 7.…”

Section: Chiral Perturbation Theory Descriptionmentioning

confidence: 99%

“…[1] and [2]. The relevant hadronic matrix elements are fixed at leading order in the 1/N C expansion, through a matching procedure between the effective short-distance Lagrangian and its corresponding low-energy description in Chiral Perturbation Theory.…”

Section: Introductionmentioning

confidence: 99%

“…A detailed analysis of the corrections induced by FSI has been already given in ref. [2], where the low-energy (infrared) physics involved has been investigated and the size of the FSI enhancement and the associated uncertainties have been quantified.…”

Section: Introductionmentioning

confidence: 99%

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The Standard Model prediction for ε′/ε

2001

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We present a detailed analysis of ε ′ /ε within the Standard Model, taking into account the strong enhancement through final-state interactions identified in refs. [1] and [2]. The relevant hadronic matrix elements are fixed at leading order in the 1/N C expansion, through a matching procedure between the effective short-distance Lagrangian and its corresponding low-energy description in Chiral Perturbation Theory. All large logarithms are summed up, both at short and long distances. Two different numerical analyses are performed, using either the experimental or the theoretical value for ε, with compatible results. We obtain Re (ε ′ /ε) = (1.7 ± 0.9) · 10 −3 . The error is dominated by the uncertainty in the value of the strange quark mass and the estimated corrections from unknown 1/N C -suppressed local contributions. A better estimate of the strange quark mass would reduce the uncertainty to about 30%. The Standard Model prediction agrees with the present experimental world average Re (ε ′ /ε) = (1.93 ± 0.24) · 10 −3 .

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Section: Introductionmentioning

confidence: 93%

Section: Fieldsmentioning

confidence: 99%

Section: Chiral Perturbation Theory Descriptionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The Standard Model prediction for ε′/ε

2001

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Lattice matrix elements and CP violation inB andK physics: Status and outlook

Soni

2004

Pramana - J Phys

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Status of lattice calculations of hadron matrix elements along with CP violation in B and in K systems is reviewed. Lattice has provided useful input which, in conjunction with experimenatl data, leads to the conclusion that CP-odd phase in the CKM matrix plays the dominant role in the observed asymmetry in B → ψK s . It is now quite likely that any beyond the SM, CP-odd, phase will cause only small deviations in B-physics. Search for the effects of the new phase(s) will consequently require very large data samples as well as very precise theoretical predictions. Clean determination of all the angles of the unitarity triangle therefore becomes essential. In this regard B → KD 0 processes play a unique role. Regarding K-decays, remarkable progress made by theory with regard to maintenance of chiral symmetry on the lattice is briefly discussed. First application already provide quantitaive information on B K and the ∆I = 1/2 rule. The enhancement in ReA 0 appears to arise solely from tree operators, esp. Q 2 ; penguin contribution to ReA 0 appears to be very small. However, improved calculations are necessary for ǫ ′ /ǫ as there the contributions of QCD penguins and electroweak penguins largely seem to cancel. There are good reasons, though, to believe that these cancellations will not survive improvements that are now underway. Importance of determining the unitarity triangle purely from K-decays is also emphasized. I IntroductionWith important input from the lattice along with the classic results of indirect CP violation in K L → ππ, the asymmetric B-factories with measurements of CP asymmetry in B → ψK s are providing valuable support to the CKM paradigm of CP violation [1]. It is now clear that the CP-odd phase in the CKM matrix is the dominant source of CP violation in B → ψK s . However, as is well known essentially compelling theoretical arguements suggest that new CP-odd phase(s) 0

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Implementing the three-particle quantization condition including higher partial waves

Blanton

Romero-López

Sharpe

2019

J. High Energ. Phys.

102

193

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We present an implementation of the relativistic three-particle quantization condition including both sand d-wave two-particle channels. For this, we develop a systematic expansion of the three-particle K matrix, K df,3 , about threshold, which is the generalization of the effective range expansion of the two-particle K matrix, K 2 . Relativistic invariance plays an important role in this expansion. We find that d-wave two-particle channels enter first at quadratic order. We explain how to implement the resulting multichannel quantization condition, and present several examples of its application. We derive the leading dependence of the threshold three-particle state on the two-particle d-wave scattering amplitude, and use this to test our implementation. We show how strong twoparticle d-wave interactions can lead to significant effects on the finite-volume three-particle spectrum, including the possibility of a generalized three-particle Efimov-like bound state. We also explore the application to the 3π + system, which is accessible to lattice QCD simulations, where we study the sensitivity of the spectrum to the components of K df,3 . Finally, we investigate the circumstances under which the quantization condition has unphysical solutions.F Properties of the isotropic approximation 50 G Failure of Eq. (4.34) for quadratic and cubic terms in the threshold expansion 53There is also an induced three-particle interaction due to the exchange of a virtual particle between a pair of two-particle interactions. This is included in all approaches.2 The p wave is absent due to Bose symmetry. 3 It is expected, however, that there is no barrier to extending to higher waves.-3 -Z 2 symmetry that forbids 2 ↔ 3 transitions. Another important feature of this approach is that it can be made relativistic [5], which turns out to simplify the expansion about threshold. Although we use the RFT approach, we expect that many of the technical considerations and general conclusions will apply to all three approaches to the quantization condition.The formalism of Ref.[1] is restricted to two-particle interactions that do not lead to poles in K 2 , the two-particle K matrix. If there are such poles, then one should use the generalized, and more complicated, formalism derived in Ref. [7]. For simplicity, we consider here only examples in which there are no K-matrix poles.Since our main goal is to show how the formalism works when including higher waves, our numerical examples are mainly chosen for illustrative purposes and do not represent physical systems. However, there is one case in nature for which our simplified setting applies, namely the 3π + system. Thus, in one of our examples, we set the two-particle scattering parameters to those measured experimentally for two charged pions, and illustrate the dependence of the resulting three-pion spectrum on the three-particle scattering parameters. This is similar to the study made in Ref.[15] using the FVU approach, except here we include d-wave dimers.All three-particle quantization condi...

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Final state interactions in Kaon decays

Cited by 84 publications

References 111 publications

The Standard Model prediction for ε′/ε

The Standard Model prediction for ε′/ε

Lattice matrix elements and CP violation inB andK physics: Status and outlook

Implementing the three-particle quantization condition including higher partial waves

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