Correlators of left charges and weak operators in finite volume chiral perturbation theory

Hernández, P.; Laine, M.

doi:10.1088/1126-6708/2003/01/063

Cited by 31 publications

(53 citation statements)

References 72 publications

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“…Given that our results for [C 27 ] ab norm (x 0 , y 0 ) are completely independent of N f and of the function E(x; M 2 ), however, there is no change with respect to the unquenched theory for this observable [19].…”

Section: Further Remarksmentioning

confidence: 69%

“…The purpose of the present paper is to extend the results of Ref. [19] in two ways. First of all, we compute the same observables as before, but also at larger quark masses, corresponding to the p-regime of chiral perturbation theory.…”

Section: Introductionmentioning

confidence: 66%

“…The two-point correlation function C(x 0 ) is defined (apart from contact terms) by 19) and the three-point correlation function we are interested in, reads (again apart from contact terms)…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…In a previous paper [19], we have already computed the NLO ǫ-regime predictions for the correlators of left-handed flavour currents and the ∆I = 3/2 weak operator, whose coefficient determines the kaon mixing parameterB K in the chiral limit. The purpose of the present paper is to extend the results of Ref.…”

Section: Introductionmentioning

confidence: 99%

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Probing the chiral weak Hamiltonian at finite volumes

Hernández¹,

Laine²

2006

J. High Energy Phys.

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Non-leptonic kaon decays are often described through an effective chiral weak Hamiltonian, whose couplings ("low-energy constants") encode all non-perturbative QCD physics. It has recently been suggested that these low-energy constants could be determined at finite volumes by matching the non-perturbatively measured three-point correlation functions between the weak Hamiltonian and two left-handed flavour currents, to analytic predictions following from chiral perturbation theory. Here we complete the analytic side in two respects: by inspecting how small ("ǫ-regime") and intermediate or large ("p-regime") quark masses connect to each other, and by including in the discussion the two leading ∆I = 1/2 operators. We show that the ǫ-regime offers a straightforward strategy for disentangling the coefficients of the ∆I = 1/2 operators, and that in the p-regime finite-volume effects are significant in these observables once the pseudoscalar mass M and the box length L are in the regime M L < ∼ 5.0. July 20061 pilar.hernandez@ific.uv.es 2

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Section: Further Remarksmentioning

confidence: 69%

Section: Introductionmentioning

confidence: 66%

Section: Formulation Of the Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Probing the chiral weak Hamiltonian at finite volumes

Hernández¹,

Laine²

2006

J. High Energy Phys.

Self Cite

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“…3 For this purpose, we define correlators involving left-handed flavour currents (this choice is well suited also for a practical implementation of matching computations on the lattice [19,20] …”

Section: Basic Setupmentioning

confidence: 99%

Charm mass dependence of the weak Hamiltonian in chiral perturbation theory

Hernández¹,

Laine

2004

J. High Energy Phys.

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Suppose that the weak interaction Hamiltonian of four-flavour SU(4) chiral effective theory is known, for a small charm quark mass m c . We study how the weak Hamiltonian changes as the charm quark mass increases, by integrating it out within chiral perturbation theory to obtain a three-flavour SU(3) chiral theory. We find that the ratio of the SU(3) low-energy constants which mediate ∆I = 1/2 and ∆I = 3/2 transitions, increases rather rapidly with m c , as ∼ m c ln(1/m c ). The logarithmic effect originates from "penguin-type" charm loops, and could represent one of the reasons for the ∆I = 1/2 rule.

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Factorization of correlation functions and the replica limit of the Toda lattice equation

2004

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Exact microscopic spectral correlation functions are derived by means of the replica limit of the Toda lattice equation. We consider both Hermitian and non-Hermitian theories in the WignerDyson universality class (class A) and in the chiral universality class (class AIII). In the Hermitian case we rederive two-point correlation functions for class A and class AIII as well as several onepoint correlation functions in class AIII. In the non-Hermitian case the average spectral density of non-Hermitian complex random matrices in the weak non-Hermiticity limit is obtained directly from the replica limit of the Toda lattice equation. In the case of class A, this result describes the spectral density of a disordered system in a constant imaginary vector potential (the Hatano-Nelson model) which is known from earlier work. New results are obtained for the average spectral density in the weak non-Hermiticity limit of a quenched chiral random matrix model at nonzero chemical potential. These results apply to the ergodic or ǫ domain of the quenched QCD partition function at nonzero chemical potential. Our results have been checked against numerical results obtained from a large ensemble of random matrices. The spectral density obtained is different from the result derived by Akemann for a closely related model, which is given by the leading order asymptotic expansion of our result. In all cases, the replica limit of the Toda lattice equation explains the factorization of spectral one-and two-point functions into a product of a bosonic (noncompact integral) and a fermionic (compact integral) partition function. We conclude that the fermionic partition functions, the bosonic partition functions and the supersymmetric partition function are all part of a single integrable hierarchy. This is the reason that it is possible to obtain the supersymmetric partition function, and its derivatives, from the replica limit of the Toda lattice equation.

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Correlators of left charges and weak operators in finite volume chiral perturbation theory

Cited by 31 publications

References 72 publications

Probing the chiral weak Hamiltonian at finite volumes

Probing the chiral weak Hamiltonian at finite volumes

Charm mass dependence of the weak Hamiltonian in chiral perturbation theory

Factorization of correlation functions and the replica limit of the Toda lattice equation

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