Search results for "operator product expansion"
showing 10 items of 43 documents
ChPT parameters from tau-decay data
2015
Using the updated ALEPH V-A spectral function from tau decays, we determine the lowest spectral moments of the left-right correlator and extract dynamical information on order parameters of the QCD chiral symmetry breaking. Uncertainties associated with violations of quark-hadron duality are estimated from the data, imposing all known short-distance constraints on a resonance-based parametrization. Employing proper pinched weight functions, we obtain an accurate determination of the effective chiral couplings L10 and C87 and the dimension-six and -eight contributions in the Operator Product Expansion.
Operator product expansion coefficients in the exact renormalization group formalism
2020
We study how to compute the operator product expansion coefficients in the exact renormalization group formalism. After discussing possible strategies, we consider some examples explicitly, within the $\epsilon$-expansions, for the Wilson-Fisher fixed points of the real scalar theory in $d=4-\epsilon$ dimensions and the Lee-Yang model in $d=6-\epsilon$ dimensions. Finally we discuss how our formalism may be extended beyond perturbation theory.
Renormalization group analysis of the gluon mass equation
2014
In the present work we carry out a systematic study of the renormalization properties of the integral equation that determines the momentum evolution of the effective gluon mass. A detailed, all-order analysis of the complete kernel appearing in this particular equation reveals that the renormalization procedure may be accomplished through the sole use of ingredients known from the standard perturbative treatment of the theory, with no additional assumptions. However, the subtle interplay of terms operating at the level of the exact equation gets distorted by the approximations usually employed when evaluating the aforementioned kernel. This fact is reflected in the form of the obtained sol…
Vacuum correlators at short distances from lattice QCD
2021
Non-perturbatively computing the hadronic vacuum polarization at large photon virtualities and making contact with perturbation theory enables a precision determination of the electromagnetic coupling at the $Z$ pole, which enters global electroweak fits. In order to achieve this goal ab initio using lattice QCD, one faces the challenge that, at the short distances which dominate the observable, discretization errors are hard to control. Here we address challenges of this type with the help of static screening correlators in the high-temperature phase of QCD, yet without incurring any bias. The idea is motivated by the observations that (a) the cost of high-temperature simulations is typica…
Updated determination of chiral couplings and vacuum condensates from hadronic tau decay data
2016
We analyze the lowest spectral moments of the left-right two-point correlation function, using all known short-distance constraints and the recently updated ALEPH V-A spectral function from tau decays. This information is used to determine the low-energy couplings L10 and C87 of chiral perturbation theory and the lowest-dimensional contributions to the Operator Product Expansion of the left-right correlator. A detailed statistical analysis is implemented to assess the theoretical uncertainties, including violations of quark-hadron duality.
Implications of tau data for CP violation in K decays
2019
The \bm{D=6}𝐃=6 contribution of the Operator Product Expansion (OPE) of the \bm{\mathrm{VV-AA}}VV−AA correlator of quark currents can be related to hadronic matrix elements associated to CP violation in non-leptonic kaon decays. We use those relations to find an updated value for \bm{\langle(\pi\pi)_{I=2}|\mathcal{Q}_{8}|K\rangle}⟨(𝛑𝛑)𝐈=2|𝒬8|𝐊⟩ in the chiral limit using the updated ALEPH spectral function. Taking instead values of the matrix elements from the lattice to obtain the \bm{D=6}𝐃=6 vacuum elements provides a new short-distance constraint that allows for an inclusive determination of \bm{f_{\pi}}𝐟𝛑 and an updated value for the \bm{D=8}𝐃=8 condensate.
〈VAP〉 Green function in the resonance region
2004
Abstract We analyze the 〈 V A P 〉 three-point function of vector, axial-vector and pseudoscalar currents. In the spirit of large N C , a resonance dominated Green function is confronted with the leading high-energy behaviour from the operator product expansion. The matching is shown to be fully compatible with a chiral resonance Lagrangian and it allows to determine some of the chiral low-energy constants of O ( p 6 ) .
A new representation of the Adler function for lattice QCD
2013
We address several aspects of lattice QCD calculations of the hadronic vacuum polarization and the associated Adler function. We implement a representation derived previously which allows one to access these phenomenologically important functions for a continuous set of virtualities, irrespective of the flavor structure of the current. Secondly we present a theoretical analysis of the finite-size effects on our particular representation of the Adler function, based on the operator product expansion at large momenta and on the spectral representation of the Euclidean correlator at small momenta. Finally, an analysis of the flavor structure of the electromagnetic current correlator is perform…
One-loop calculation of the oblique S parameter in higgsless electroweak models
2012
We present a one-loop calculation of the oblique S parameter within Higgsless models of electroweak symmetry breaking and analyze the phenomenological implications of the available electroweak precision data. We use the most general effective Lagrangian with at most two derivatives, implementing the chiral symmetry breaking SU(2)_L x SU(2)_R -> SU(2)_{L+R} with Goldstones, gauge bosons and one multiplet of vector and axial-vector massive resonance states. Using the dispersive representation of Peskin and Takeuchi and imposing the short-distance constraints dictated by the operator product expansion, we obtain S at the NLO in terms of a few resonance parameters. In asymptotically-free gauge …
Lattice Gauge Theory Sum Rule for the Shear Channel
2010
An exact expression is derived for the $(\omega,p)=0$ thermal correlator of shear stress in SU($N_c$) lattice gauge theory. I remove a logarithmic divergence by taking a suitable linear combination of the shear correlator and the correlator of the energy density. The operator product expansion shows that the same linear combination has a finite limit when $\omega\to\infty$. It follows that the vacuum-subtracted shear spectral function vanishes at large frequencies at least as fast as $\alpha_s^2(\omega)$ and obeys a sum rule. The trace anomaly makes a potential contribution to the spectral sum rule which remains to be fully calculated, but which I estimate to be numerically small for $T\gtr…