Abstract
We perform a systematic study of the correlation functions of two quark currents in a pion using lattice QCD. We obtain good signals for all but one of the relevant Wick contractions of quark fields. We investigate the quark mass dependence of our results and test the importance of correlations between the quark and the antiquark in the pion. Our lattice data are compared with predictions from chiral perturbation theory.
Highlights
Hadronic matrix elements of one or two currents can be calculated in lattice QCD
At large distances between the two currents, the correlation functions we consider can be evaluated in chiral perturbation theory, which describes the low-energy limit of QCD in terms of mesons and their interactions
We focus on the current combinations V 0V 0 and A0A0 and on graph C1, which can be interpreted as a physical matrix element in the sense discussed at the end of section 3.2
Summary
The object of our study are correlation functions of two currents in a pion, πk(p)| Oiq1q2 (y)Ojq3q4 (0) |πk (p) ,. In a pion at rest, these currents are associated with the vector, axial, scalar or pseudoscalar charges. We can compute the matrix elements for y0 = 0 and for different pion momenta. The rotation to Euclidean time and the method to extract hadronic matrix elements from a lattice calculation single out a particular reference frame. It is a valuable check for lattice artefacts to verify that for a given y 2, the matrix elements with scalar and pseudoscalar currents are independent of the pion momentum when y · p = 0, a condition that can be achieved for both zero and nonzero p.
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