Dispersive calculation of B_7^{3/2} and B_8^{3/2} in the chiral limit

TL;DR

This paper uses spectral functions from tau decay data and dispersive analysis to calculate low energy constants B_7^{3/2} and B_8^{3/2} in the chiral limit, updating previous phenomenological results.

Contribution

It introduces a dispersive method combined with spectral function data to determine B_7^{3/2} and B_8^{3/2} in the chiral limit, refining earlier estimates.

Findings

B_7^{3/2} = 0.55 +- 0.07 +- 0.10

B_8^{3/2} = 1.11 +- 0.16 +- 0.23

Updated phenomenological determination using ALEPH data.

Abstract

We show how the isospin vector and axialvector current spectral functions rho_V and rho_A can be used to determine in leading chiral order the low energy constants B_7^{3/2} and B_8^{3/2}. This is accomplished by matching the Operator Product Expansion to the dispersive analysis of vacuum polarization functions. The data for the evaluation of these dispersive integrals has been recently enhanced by the ALEPH measurement of spectral functions in tau decay, and we update our previous phenomenological determination. Our calculation yields in the NDR renormalization scheme and at renormalization scale mu = 2 GeV the values B_7^{3/2} = 0.55 +- 0.07 +- 0.10 and B_8^{3/2} = 1.11 +- 0.16 +- 0.23 for the quark mass values m_s + m = 0.1 GeV.