Renormalization group evolution for the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Δ</mml:mi><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:math>effective Hamiltonian with<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>N</mml:mi><mml:mi>f</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:math>

Adams, David H.; Lee, Weonjong

doi:10.1103/physrevd.75.074502

Cited by 6 publications

(14 citation statements)

References 16 publications

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“…We find that this result is consistent with Eq. (40) of Ref [25],. where, in order to regulate the singularity, a small regulator is introduced in the eigenvalues ofγ EM /α s ) part we obtain the following term,…”

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confidence: 95%

Singularity-free next-to-leading order ΔS = 1 renormalization group evolution and ϵ K ′ /ϵK in the Standard Model and beyond

Kitahara

Nierste

Tremper

2016

J. High Energ. Phys.

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Abstract:The standard analytic solution of the renormalization group (RG) evolution for the ∆S = 1 Wilson coefficients involves several singularities, which complicate analytic solutions. In this paper we derive a singularity-free solution of the next-to-leading order (NLO) RG equations, which greatly facilitates the calculation of K , the measure of direct CP violation in K → ππ decays. Using our new RG evolution and the latest lattice results for the hadronic matrix elements, we calculate the ratio K / K (with K quantifying indirect CP violation) in the Standard Model (SM) at NLO to K / K = (1.06 ± 5.07) × 10 −4 , which is 2.8 σ below the experimental value. We also present the evolution matrix in the high-energy regime for calculations of new physics contributions and derive easy-to-use approximate formulae. We find that the RG amplification of new-physics contributions to Wilson coefficients of the electroweak penguin operators is further enhanced by the NLO corrections: if the new contribution is generated at the scale of 1-10 TeV, the RG evolution between the new-physics scale and the electroweak scale enhances these coefficients by 50-100%. Our solution contains a term of order α 2 EM /α 2 s , which is numerically unimportant for the SM case but should be included in studies of high-scale new-physics.

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confidence: 95%

Singularity-free next-to-leading order ΔS = 1 renormalization group evolution and ϵ K ′ /ϵK in the Standard Model and beyond

Kitahara

Nierste

Tremper

2016

J. High Energ. Phys.

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“…It turns out that the standard form of solution is singular, but this can be removed by the analytic continuation method proposed in Ref. [23]. Details will be given in Ref.…”

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confidence: 99%

Neutral kaon mixing from new physics: Matrix elements inNf=2+1lattice QCD

et al. 2013

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We present results for matrix elements of ∆S = 2 four-fermion operators arising generically in models of new physics. These are needed to constrain such models using the measured values of εK and ∆MK . We use lattice QCD with 2 + 1 flavors of improved staggered fermions on lattices generated by the MILC collaboration. We extrapolate to the continuum from three lattice spacings ranging down to a ≈ 0.045 fm. Total errors are ∼ 5 − 6%, arising primarily from our use of one-loop matching between lattice and continuum operators. For two of the matrix elements, our results disagree significantly from those obtained using different fermion discretizations.

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“…For the evolution of the coefficients from µ = M S to µ = µ h , we use a new analytical solution of the RG equations which avoids the problem of a singularity in the NLO terms discussed in Refs. [4,34]. For H |∆S|=1 eff, SUSY , we employ proper threshold matching at the scales µ t,b,c set by the top, bottom, and charm quark masses with the usual threshold matching matrices [9].…”

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confidence: 99%

Supersymmetric Explanation of CP Violation in $K\to ππ$ Decays

Kitahara,

Nierste,

Tremper

2016

Preprint

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Recent progress in the determination of hadronic matrix elements has revealed a tension between the measured value of K / K , which quantifies direct CP violation in K → ππ decays, and the Standard-Model prediction. The well-understood indirect CP violation encoded in the quantity K typically precludes large new-physics contributions to K / K and challenges such an explanation of the discrepancy. We show that it is possible to cure the K / K anomaly in the Minimal Supersymmetric Standard Model with squark masses above 3 TeV without overshooting K . This solution exploits two features of supersymmetry: the possibility of large isospin-breaking contributions (enhancing K ) and the Majorana nature of gluinos (permitting a suppression of K ). Our solution involves no fine-tuning of CP phases or other parameters.

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Renormalization group evolution for theΔS=1effective Hamiltonian withNf=2+1

Cited by 6 publications

References 16 publications

Singularity-free next-to-leading order ΔS = 1 renormalization group evolution and ϵ K ′ /ϵK in the Standard Model and beyond

Singularity-free next-to-leading order ΔS = 1 renormalization group evolution and ϵ K ′ /ϵK in the Standard Model and beyond

Neutral kaon mixing from new physics: Matrix elements inNf=2+1lattice QCD

Supersymmetric Explanation of CP Violation in $K\to ππ$ Decays

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