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Register a new user$bar B_sto K$ semileptonic decay from an Omn`es improved constituent quark model
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We study the $f^+$ form factor for the semileptonic $bar B_sto K^+ell^-bar u_ell$ decay in a constituent quark model. The valence quark estimate is supplemented with the contribution from the $bar B^*$ pole that dominates the high $q^2$ region. We use a multiply-subtracted Omn`es dispersion relation to extend the quark model predictions from its region of applicability near $q^2_{rm max}=(M_{B_s}-M_K)^2sim 23.75$ GeV$^2$ to all $q^2$ values accessible in the physical decay. To better constrain the dependence of $f^+$ on $q^2$, we fit the subtraction constants to a combined input from previous light cone sum rule [Phys. Rev. D 78 (2008) 054015] and the present quark model results. From this analysis, we obtain $Gamma(bar B_sto K^+ell^-bar u_ell)=(5.45^{+0.83}_{-0.80})|V_{ub}|^2times 10^{-9},{rm MeV}$, which is about 20% higher than the prediction based only on QCD light cone sum rule estimates. Differences are much larger for the $f^+$ form factor in the region above $q^2=15$ GeV$^2$.
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We study the $f^+$ form factor for the $bar B_sto K^+ell^-bar u_ell$ semileptonic decay in a nonrelativistic quark model. The valence quark contribution is supplemented with a $bar B^*$-pole term that dominates the high $q^2$ region. To extend the quark model predictions from its region of applicability near $q^2_{rm max}=(M_{B_s}-M_K)^2$, we use a multiply-subtracted Omn`es dispersion relation. We fit the subtraction constants to a combined input from previous light cone sum rule results in the low $q^2$ region and the quark model results (valence plus $bar B^*$-pole) in the high $q^2$ region. From this analysis, we obtain $Gamma(bar B_sto K^+ell^-bar u_ell)=(5.47^{+0.54}_{-0.46})|V_{ub}|^2times 10^{-9},{rm MeV}$, which is about 10% and 20% higher than predictions based on Lattice QCD and QCD light cone sum rules respectively.
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A simple analysis of time-dependent $B_sto K^+K^-$ transitions, based on recent results from the LHCb experiment, is presented. The benefits of adopting a fully consistent theoretical description of the $B^0_s$--$bar B^0_s$ mixing are stressed. It is shown that bounds on CPT violation in the $B^0_s$--$bar B^0_s$ system can be consistently obtained and that direct CP violation in $B_sto K^+K^-$ can be robustly established, even in the presence of CPT violation in the mixing.
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