<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi></mml:math>parameter in QCD from domain wall fermions

Abstract

We have computed the $SU(2)$ low-energy constant ${l}_{5}$ and the mass splitting between charged and neutral pions from a lattice QCD simulation of ${n}_{f}=2+1$ flavors of domain wall fermions at a scale of ${a}^{\ensuremath{-}1}=2.33\text{ }\text{ }\mathrm{GeV}$. Relating ${l}_{5}$ to the $S$ parameter in QCD we obtain a value of $S({m}_{H}=120\text{ }\text{ }\mathrm{GeV})=0.42(7)$, in agreement with previous determinations. Our result can be compared with the value of $S$ from electroweak precision data which constrains strongly interacting models of new physics like technicolor. This work in QCD serves as a test for the methods to compute the $S$ parameter with domain wall fermions in theories beyond the standard model. We also infer a value for the pion mass splitting in agreement with experiment.