Johan Bijnens, Karim Ghorbani
A general formula is derived for the finite volume dependence of vacuum expectation values analogous to Luscher's formula for the masses. The result involves no integrals over kinematic quantities and depends only on the matrix element between pions at zero momentum transfer thus presenting a new way to calculate the latter, i.e. pion sigma terms. The full order $p^6$ correction to the vacuum condensate $<\bar q q>$ is evaluated and compared with the result from the Luscher formula. Due to the size of the $p^6$ result no conclusion about the accuracy of the Luscher formula can be drawn. LU TP 06-11, hep-lat/0602019 |