Studying ε′/ε in the chiral quark model: γ5-scheme independence and NLO hadronic matrix elements

We present preliminary results of the first lattice QCD calculation of the K → π matrix elements of the chromomagnetic operator O CM = gs σ µν G µν d, which appears in the effective Hamiltonian describing ∆S = 1 transitions in and beyond the Standard Model. Having dimension 5, the chromomagnetic operator is characterized by a rich pattern of mixing with operators of equal and lower dimensionality. The multiplicative renormalization factor as well as the mixing coefficients with the operators of equal dimension have been computed at one-loop in perturbation theory. The power divergent coefficients controlling the mixing with operators of lower dimension have been computed non-perturbatively, by imposing suitable subtraction conditions. The numerical simulations have been carried out using the gauge field configurations produced by the European Twisted Mass Collaboration with N f = 2 + 1 + 1 dynamical quarks at three values of the lattice spacing. Our preliminary result for the B-parameter of the chromomagnetic operator is B CMO = 0.29(11), which can be compared with the estimate B CMO ∼ 1 − 4 currently used in phenomenological analyses. K → π matrix elements of the chromagnetic operator on the lattice V. Lubicz

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“…At leading order (LO) in chiral perturbation theory (ChPT), the CMO has a single representation in terms of pseudo-Goldstone boson fields [6],…”

Section: Introductionmentioning

confidence: 99%

Renormalization of the chromomagnetic operator on the lattice

Constantinou

Costa

Frezzotti³

et al. 2015

Phys. Rev. D

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“…The second term describes the interactions of light quarks with light (Goldstone) mesons in terms of the chiral quark model (χQM) [15,16,24,25,26]:…”

Section: The Heavy Light Chiral Quark Model (Hlχqm)mentioning

confidence: 99%

“…The covariant derivative D µ in (21) contains the soft gluon field forming the gluon condensates. The effects based on (21) can be calculated by Feynman diagram techniques as in [11,12,13,24,25] or by the means of heat kernel techniques as in [16,21,26].…”

Section: The Heavy Light Chiral Quark Model (Hlχqm)mentioning

confidence: 99%

“…Performing the bosonization of the HLχQM, one encounters divergent loop integrals which will in general be quadraticly, linearly and logarithmicly divergent [13]. The quadraticly and logarithmicly divergent integrals are related to the quark condensate and the bare pion decay constant f [25], respectively. The linearly divergent integral (which is finite within dimensional regularization) is related to the axial coupling g A in (8).…”

Section: The Heavy Light Chiral Quark Model (Hlχqm)mentioning

confidence: 99%

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Color suppressed contributions to the decay modes $B_{d,s} \to D_{s,d} D_{s,d} $ , $B_{d,s} \to D_{s,d} D^_{s,d}$ , and $B_{d,s} \to D^_{s,d} D^*_{s,d} $

2005

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The amplitudes for decays of the typehave relatively small factorizable contributions through the annihilation mechanism. The dominant contributions to the decay amplitudes arise from chiral loop contributions and tree level amplitudes which can be obtained in terms of soft gluon emissions forming a gluon condensate. We predict that the branching ratios for the processesB. We obtain branching ratios for two D * 's in the final state of order two times bigger.

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“…(15) and (16). By taking the real part of the amplitudes from experimental data, s expt = 3.3 × 10 −7 , p expt = 1.2 × 10 −7 [17], and using m s + m d = 0.110GeV, mg ∼ 500GeV [1,18], m K = 0.495GeV , we get the phase of S-wave and P -wave…”

mentioning

confidence: 99%

CP-violating asymmetry in p in the Skyrme model

Jiang¹,

Yan²

2004

J. Phys. G: Nucl. Part. Phys.

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We study the CP -violating asymmetry in nonleptonic decay Λ → pπ. By employing the Skyrme model to calculate this decay amplitude contributed by the gluonic diploe operator, we find a possible large CP -violating asymmetry could be expected, which is consistent with the previous study.11.30. Er, 12.60.Jv, 13.30.Eg, 14.20.Jn Typeset using REVT E X 1 CP -violating asymmetry in Λ → pπ in the Skyrme model where α is hyperon decays parameter of Λ 0 − → pπ − andᾱ corresponds toΛ 0 − →pπ + , δ s = 6 o and δ p = −1.1 o are the final state πN strong interaction phases for S and P wave amplitudes with ∆I = 1/2 respectively [5], and φ s,p are the corresponding CP −violating weak phases. The standard model prediction for A(Λ 0 − ) is around 3 × 10 −5 , and the recent study in Ref. [2] showsA model independent study of new CP −violating interactions has shown that A(Λ 0 − ) could be larger than that predicted within the standard model [6]. An example of an operator is precisely the gluonic dipole operator [1,6], in which A(Λ 0 − ) would be enhanced and could reach around O(10 −3 ) [1]. *

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Studying ε′/ε in the chiral quark model: γ5-scheme independence and NLO hadronic matrix elements

Cited by 74 publications

References 63 publications

Renormalization of the chromomagnetic operator on the lattice

Renormalization of the chromomagnetic operator on the lattice

Color suppressed contributions to the decay modes $B_{d,s} \to D_{s,d} D_{s,d} $ , $B_{d,s} \to D_{s,d} D^_{s,d}$ , and $B_{d,s} \to D^_{s,d} D^*_{s,d} $

CP-violating asymmetry in p in the Skyrme model

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Studying ε′/ε in the chiral quark model: γ5-scheme independence and NLO hadronic matrix elements

Cited by 74 publications

References 63 publications

Renormalization of the chromomagnetic operator on the lattice

Renormalization of the chromomagnetic operator on the lattice

Color suppressed contributions to the decay modes $B_{d,s} \to D_{s,d} D_{s,d} $ , $B_{d,s} \to D_{s,d} D^*_{s,d}$ , and $B_{d,s} \to D^*_{s,d} D^*_{s,d} $

CP-violating asymmetry in p in the Skyrme model

Contact Info

Product

Resources

About

Color suppressed contributions to the decay modes $B_{d,s} \to D_{s,d} D_{s,d} $ , $B_{d,s} \to D_{s,d} D^_{s,d}$ , and $B_{d,s} \to D^_{s,d} D^*_{s,d} $