The exclusive vision of rare K and B decays and of the quark mixing in the standard model

Abstract

AbstractThe most common predictions for rareKandBdecay branching ratios in the Standard Model in the literature are based on the CKM elements$$|V_{cb}|$$|Vcb|and$$|V_{ub}|$$|Vub|resulting from global fits, that are in the ballpark of their inclusive and exclusive determinations, respectively. In the present paper we follow another route, which to our knowledge has not been explored for$$\Delta M_{s,d}$$ΔMs,dand rareKandBdecays by anybody to date. We assume, in contrast to the prevailinginclusiveexpectations for$$|V_{cb}|$$|Vcb|, that the future true values of$$|V_{cb}|$$|Vcb|and$$|V_{ub}|$$|Vub|will be both fromexclusivedeterminations; in practice we use the most recent averages from FLAG. With the precisely known$$|V_{us}|$$|Vus|the resulting rare decay branching ratios,$$\varepsilon _K$$εK,$$\Delta M_d$$ΔMd,$$\Delta M_s$$ΔMsand$$S_{\psi K_S}$$SψKSdepend then only on the angles$$\beta $$βand$$\gamma $$γin the unitarity triangle that moreover are correlated through the CKM unitarity. An unusual pattern of SM predictions results from this study with some existing tensions being dwarfed and new tensions being born. In particular using HPQCD$$B^0_{s,d}-{{\bar{B}}}^0_{s,d}$$Bs,d0-B¯s,d0hadronic matrix elements a$$3.1\sigma $$3.1σtension in$$\Delta M_s$$ΔMsindependently of$$\gamma $$γis found. For$$60^\circ \le \gamma \le 75^\circ $$60∘≤γ≤75∘the tension in$$\Delta M_d$$ΔMdbetween$$4.0\sigma $$4.0σand$$1.1\sigma $$1.1σis found and in the case of$$\varepsilon _K$$εKbetween$$5.2\sigma $$5.2σand$$2.1\sigma $$2.1σ. Moreover, the room for new physics in$$K^+\rightarrow \pi ^+\nu {\bar{\nu }}$$K+→π+νν¯,$$K_L\rightarrow \pi ^0\nu {\bar{\nu }}$$KL→π0νν¯and$$B\rightarrow K(K^*)\nu {\bar{\nu }}$$B→K(K∗)νν¯decays is significantly increased. We compare the results in this EXCLUSIVE scenario with the HYBRID one in which$$|V_{cb}|$$|Vcb|in the former scenario is replaced by the most recent inclusive$$|V_{cb}|$$|Vcb|and present the dependence of all observables considered by us in both scenarios as functions of$$\gamma $$γ. As a byproduct we compare the determination of$$|V_{cb}|$$|Vcb|from$$\Delta M_s$$ΔMs,$$\Delta M_d$$ΔMd,$$\varepsilon _K$$εKand$$S_{\psi K_S}$$SψKSusing$$B^0_{s,d}-{{\bar{B}}}^0_{s,d}$$Bs,d0-B¯s,d0hadronic matrix elements from LQCD with$$2+1+1$$2+1+1flavours,$$2+1$$2+1flavours and their average. Only for the$$2+1+1$$2+1+1case values for$$\beta $$βand$$\gamma $$γexist for which the same value of$$|V_{cb}|$$|Vcb|is found:$$|V_{cb}|=42.6(4)\times 10^{-3}$$|Vcb|=42.6(4)×10-3,$$\gamma =64.6(16)^\circ $$γ=64.6(16)∘and$$\beta =22.2(7)^\circ $$β=22.2(7)∘. This in turn implies a$$2.7\sigma $$2.7σanomaly in$$B_s\rightarrow \mu ^+\mu ^-$$Bs→μ+μ-.