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Register a new userMeasurement of Forward-Backward Asymmetry and Wilson Coefficients in $B to K^* ell^+ ell^-$
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We report a measurement of the ratios of Wilson coefficients $A_9/A_7$ and $A_{10}/A_7$ in $B to K^* ell^+ ell^-$. The result is obtained from a data sample containing 386 million $Bbar{B}$ pairs that was collected at the $Upsilon(4S)$ resonance with the Belle detector at the KEKB asymmetric energy $e^+ e^-$ collider.
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We report the first measurement of the lepton forward-backward asymmetry ${cal A}_{rm FB}$ as a function of the squared four-momentum of the dilepton system, $q^2$, for the electroweak penguin process $B rightarrow X_s ell^+ ell^-$ with a sum of exclusive final states, where $ell$ is an electron or a muon and $X_s$ is a hadronic recoil system with an $s$ quark. The results are based on a data sample containing $772times10^6$ $Bbar{B}$ pairs recorded at the $Upsilon(4S)$ resonance with the Belle detector at the KEKB $e^+ e^-$ collider. ${cal A}_{rm FB}$ for the inclusive $B rightarrow X_s ell^+ ell^-$ is extrapolated from the sum of 10 exclusive $X_s$ states whose invariant mass is less than 2 GeV/$c^2$. For $q^2 > 10.2$ GeV$^2$/$c^2$, ${cal A}_{rm FB} < 0$ is excluded at the 2.3$sigma$ level, where $sigma$ is the standard deviation. For $q^2 < 4.3$ GeV$^2$/$c^2$, the result is within 1.8$sigma$ of the Standard Model theoretical expectation.
Using the most general effective Hamiltonian comprising scalar,vector and tensor type interactions, we have written the branching ratio, the forward-backward (FB) asymmetry and the normalized FB asymmetry as functions of the new Wilson coefficients. It is found that the branching ratio depends on all new coefficients,but the dependence of asymmetries on coefficients could be analyzed only for one Wilson coefficient.
A measurement of the ratio of branching fractions of the decays $B^+to K^+mu^+mu^-$ and $B^+to K^+e^+e^-$ is presented. The proton-proton collision data used correspond to an integrated luminosity of $5.0,$fb$^{-1}$ recorded with the LHCb experiment at centre-of-mass energies of $7$, $8$ and $13,$TeV. For the dilepton mass-squared range $1.1 < q^2 < 6.0,$GeV$^2!/c^4$ the ratio of branching fractions is measured to be $R_K = {0.846,^{+,0.060}_{-,0.054},^{+,0.016}_{-,0.014}}$, where the first uncertainty is statistical and the second systematic. This is the most precise measurement of $R_K$ to date and is compatible with the Standard Model at the level of 2.5 standard deviations.
We present a measurement of angular observables, $P_4$, $P_5$, $P_6$, $P_8$, in the decay $B^0 to K^ast(892)^0 ell^+ ell^-$, where $ell^+ell^-$ is either $e^+e^-$ or $mu^+mu^-$. The analysis is performed on a data sample corresponding to an integrated luminosity of $711~mathrm{fb}^{-1}$ containing $772times 10^{6}$ $Bbar B$ pairs, collected at the $Upsilon(4S)$ resonance with the Belle detector at the asymmetric-energy $e^+e^-$ collider KEKB. Four angular observables, $P_{4,5,6,8}$ are extracted in five bins of the invariant mass squared of the lepton system, $q^2$. We compare our results for $P_{4,5,6,8}$ with Standard Model predictions including the $q^2$ region in which the LHCb collaboration reported the so-called $P_5$ anomaly.
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.
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