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Register a new userForm Factors and Long-Distance Effects in $Bto V(P) ell^+ell^-$ and $Bto V gamma$
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Alexander Khodjamirian
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I overview the hadronic input for the exclusive flavour-changing neutral-current $B$-decays with a vector ($V=K^*,rho$) or pseudoscalar ($P=K,pi$) meson in the final state. After presenting the current status of $Bto P,V$ form factors, I discuss the estimate of the charm-loop effect in $Bto K^{(*)} ell^+ell^-$ and $Bto K^* gamma$.
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We calculate the long-distance effect generated by the four-quark operators with $c$-quarks in the $Bto K^{(*)} ell^+ell^-$ decays. At the lepton-pair invariant masses far below the $bar{c}c$-threshold, $q^2ll 4m_c^2$, we use OPE near the light-cone. The nonfactorizable soft-gluon emission from $c$-quarks is cast in the form of a nonlocal effective operator. The $Bto K^{(*)}$ matrix elements of this operator are calculated from the QCD light-cone sum rules with the $B$-meson distribution amplitudes. As a byproduct, we also predict the charm-loop contribution to $Bto K^*gamma$ beyond the local-operator approximation. To describe the charm-loop effect at large $q^2$, we employ the hadronic dispersion relation with $psi=J/psi,psi (2S), ...$ contributions, where the measured $ Bto K^{(*)}psi $ amplitudes are used as inputs. Matching this relation to the result of QCD calculation reveals a destructive interference between the $J/psi$ and $psi(2S)$ contributions. The resulting charm-loop effect is represented as a $q^2$-dependent correction $Delta C_9(q^2)$ to the Wilson coefficient $C_9$. Within uncertainties of our calculation, at $q^2$ below the charmonium region the predicted ratio $Delta C_9(q^2)/C_9$ is $leq 5% $ for $Bto K ell^+ell^-$, but can reach as much as 20% for $Bto K^*ell^+ell^-$, the difference being mainly caused by the soft-gluon contribution.
In a scenario in which fourth generation fermions exist, we study effects of new physics on the differential decay width, forward-backward asymmetry $A_{text{FB}}$ and integrated branching ratio for $Bto X_s ell^+ ell^-$ decay with $(ell=e,mu)$. Prediction of the new physics on the mentioned quantities essentially differs from the Standard Model results, in certain regions of the parameter space, enhancement of new physics on the above mentioned physical quantities can yield values as large as two times of the SM predictions, whence present limits of experimental measurements of branching ratio is spanned, contraints of the new physics can be extracted. For the fourth generation CKM factor $V_{t^prime b}^ast V_{t^prime s}$ we use $pm 10^{-2}$ and $pm 10^{-3}$ ranges, take into consideration the possibility of a complex phase where it may bring sizable contributions, obtained no significant dependency on the imaginary part of the new CKM factor. For the above mentioned quantities with a new family, deviations from the SM are promising, can be used as a probe of new physics.
We discuss the general properties of the amplitude of the $Bto l^+l^-l u$ decays and calculate the related kinematical distributions $d^2Gamma/dq^2dq^2$, $q$ the momentum of the $l^+l^-$ pair emitted from the electromagnetic vertex and $q$ the momentum of the $l u$ pair emitted from the weak vertex. We emphasize that electromagnetic gauge invariance imposes essential constraints on the $Bto gamma^*l u$ amplitude at small $q^2$ which in the end yield the behaviour of the differential branching fraction as $dGamma(Bto l^+l^-l u)/dq^2propto 1/q^2$ and a mild logarithmic dependence of $Gamma(Bto l^{+}l^{-}l u)$ on the lepton mass $m_l$. Consequently, (i) the main contribution to the decay rate $Gamma(Bto mu^+mu^-e u_e )$ comes from the region of light vector resonances $rho^0$ and $omega$, $q^2simeq M_rho^2, M_omega^2$ and (ii) the decay rate $Gamma(Bto e^{+}e^{-}mu u_mu)$ receives comparable contributions from the region of small $q^2$ and from the resonance region. As the result, the decay rate $Gamma(Bto e^+e^-mu u_mu)$ is only a factor $sim 2$ larger than $Gamma(Bto mu^+mu^-e u_e)$. We perform a detailed analysis of the uncertainties in the theoretical predictions for the decays $Bto l^+l^-l u$ in the Standard Model. We found that the theoretical expectations for such decays in the Standard Model are only marginally compatible with the recent upper limits of the LHCb collaboration.
We comprehensively study the charged-Higgs contributions to the leptonic $B^-_q to ell bar u$ ($q=u,c$) and semileptonic $bar B to X_q ell bar u$ ($X_u=pi, rho; X_c=D,D^*$) decays in the type-III two-Higgs-doublet model (2HDM). We employ the Cheng-Sher ansatz to suppress the tree-level flavor-changing neutral currents (FCNCs) in the quark sector. When the strict constraints from the $Delta B=2$ and $bto s gamma$ processes are considered, parameters $chi^u_{tq}$ from the quark couplings and $chi^ell_ell$ from the lepton couplings dictate the leptonic and semileptonic $B$ decays. It is found that when the measured $B^-_uto tau bar u$ and indirect bound of $B^-_c to tau bar u$ obtained by LEP1 data are taken into account, $R(D)$ and $R(pi)$ can have broadly allowed ranges; however, the values of $R(rho)$ and $R(D^*)$ are limited to approximately the standard model (SM) results. We also find that the same behaviors also occur in the $tau$-lepton polarizations and forward-backward asymmetries ($A^{X_q,tau}_{FB}$) of the semileptonic decays, with the exception of $A^{D^*,tau}_{FB}$, for which the deviation from the SM due to the charged-Higgs effect is still sizable. In addition, the $q^2$-dependent $A^{pi,tau}_{FB}$ and $A^{D,tau}_{FB}$ can be very sensitive to the charged-Higgs effects and have completely different shapes from the SM.
I report here recent measurements of observables from the inclusive decays $Bto X_sgamma$ and $Bto X_sell^+ell^-$. Included are measurements of the branching fractions and CP asymmetries for both channels, as well as the forward-backward lepton asymmetry in inclusive $Bto X_sell^+ell^-$ decays, which is the first measurement of this quantity.
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