M0-M¯0matrix elements in a relativized quark model

Abstract

Matrix elements of the type 〈$M^0$‖${\mathrm{scrO}}_i$‖M¯ ${}_{}{}^0{}_{}{}^{}〉$ are evaluated using a relativized quark model for the $K^0$, $D^0$, $B^0$, and $B_s^0$ systems where ${\mathrm{scrO}}_1$=[q¯${\gamma }^{\mu }$(1-${\gamma }_5$)q][q¯γ ${}_{\mu }{}^{}{}_{}{}^{}$(1-${\gamma }_5$)q], ${\mathrm{scrO}}_2$=[q¯(1-${\gamma }_5$)q] [q¯(1 +${\gamma }_5$)q], ${\mathrm{scrO}}_3$=[q¯${\gamma }_{\mu }$(1-${\gamma }_5$)q][q¯γ ${}_{}{}^{\mu }{}_{}{}^{}$(1+${\gamma }_5$)q], and ${\mathrm{scrO}}_4$=[q¯(1-${\gamma }_5$)q][q¯(1-γ ${}_5{}^{}{}_{}{}^{}$)q]. The pseudoscalar-meson decay constants $f_p$ are first calculated using various approximations to set the scale of the matrix elements’ magnitude and to estimate their accuracy. The matrix elements are then calculated, again using various approximations, and are presented as ratios with respect to the vacuum saturation value of ${\mathrm{scrO}}_1$. When relativistic effects are included we find that significant enhancements are indicated for the ${\mathrm{scrO}}_2$, ${\mathrm{scrO}}_3$, and ${\mathrm{scrO}}_4$ matrix elements which will alter the resulting bounds on new interactions. As an illustration we find that the right-handed W boson of left-right-symmetric theories must have a mass of at least 3.8 TeV.