Effective Hamiltonian for $B \ra X_s e^+ e^-$ Beyond Leading Logarithms in the NDR and HV Schemes

Abstract

We calculate the next-to-leading QCD corrections to the effective Hamiltonian for \Bsee in the NDR and HV schemes. We give for the first time analytic expressions for the Wilson Coefficient of the operator $Q_9=(\bar{s}b{)}_{V-A}(\bar{e}e{)}_V$ in the NDR and HV schemes. Calculating the relevant matrix elements of local operators in the spectator model we demonstrate the scheme independence of the resulting short distance contribution to the physical amplitude. Keeping consistently only leading and next-to-leading terms, we find an analytic formula for the differential dilepton invariant mass distribution in the spectator model. Numerical analysis of the $\mt$, $\Lms$ and $μ\approx {\cal O}(\mb)$ dependences of this formula is presented. We compare our results with those given in the literature.

18 pages, LaTeX, 5 postscript figures included

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• Explaining the $R_K$ and $R_{K^{\ast }}$ Anomalies With Right-handed Sneutrino
• Double-Lepton Polarization Asymmetries and Branching Ratio in $B \rar K_{0}^{*}(1430) l^+ l^- $ transition from Universal Extra Dimension Model
• The Forward Backward asymmetries of $B\to X_s{\tau }^{+}{\tau }^{-}$ in the MSSM
• General analysis of the rare Bc->D^*_s l^+ l^- decay beyond the standard model
• Imprints of CP violation asymmetries in rare ${\Lambda }_b\to \Lambda {\ell }^{+}{\ell }^{-}$ decay in family non-universal $Z^{\prime }$ model
• Comparative analysis of the ${\Lambda }_b\to \Lambda {\ell }^{+}{\ell }^{-}$ decay in the SM, SUSY and RS model with custodial protection
• Rare Semileptonic $B_s$ Decays to $\eta$ and ${\eta }^{\prime }$ mesons in QCD
• On the Impact of Soft Photons on $B\to K{\ell }^{+}{\ell }^{-}$
• Forward-backward Asymmetry and Branching Ratio of $B \rar K_1 \ell^+ \ell^-$ Transition in Supersymmetric Models
• Constraining four generation SM with b\to s γand b\to s g decays
• Exclusive B --> K^* l^+ l^-$ decay in the three Higgs doublet model
• Transition form factors and angular distributions of the ${\mathbf{\Lambda }}_{\mathbf{b}}\to \mathbf{\Lambda }(1520)(\to \mathbf{N}\bar{\mathbf{K}}){\mathbf{\ell }}^{+}{\mathbf{\ell }}^{-}$ decay supported by baryon spectroscopy
• B_c meson rare decays in the light-cone quark model
• Complementarity of Semileptonic $B$ to $K_2^{\ast }(1430)$ and $K^{\ast }(892)$ Decays in the Standard Model with Fourth Generation
• The Effects of Fourth Generation on the double Lepton Polarization in B \rar K \ell^+ \ell^- decay
• Semileptonic $B_s\to K_0^{\ast }(1430)$ transitions with the light-cone sum rules
• Analysis of ${\Lambda }_b\to \Lambda l^{+}{l}^{-}$ rare decays in a non-universal $Z^{\prime }$ model
• Determination of the CKM unitarity triangle by B -> X_d l^+ l^- decay
• Double Lepton Polarization Forward--Backward Asymmetries in B \rar K^\ast \ell^+ \ell^- Decay in the SM4
• The sensitivity of the zero position of the forward--backward asymmetry to new physics effects in the B -> K^\ast μ^+ μ^- decay
• CP-Conserving Unparticle Phase Effects on the Unpolarized and Polarized Direct CP Asymmetry in $b\to d{\ell }^{+}{\ell }^{-}$ Transition
• The Semileptonic $B$ to $K_1(1270,1400)$ Decays in QCD Sum Rules
• Double-Lepton Polarization Asymmetries and Polarized Forward Backward Asymmetries in the Rare b \to s \ell^+ \ell^- Decays in a Single Universal Extra Dimension Scenario
• Probing anomalous right-handed top quark couplings in rare B decays
• Study Standard Model and Majorana Neutrino Contributions to $B^{+}\to K^{(\ast )\pm }{\mu }^{+}{\mu }^{\mp }$
• Subleading corrections to the V_ub determination from exclusive B decays
• b -> s Decays in a model with Z-mediated flavor changing neutral current
• Implications of light $Z^{\prime }$ on semileptonic $B(B_s)\to T\{K_2^{\ast }(1430)$ $(f_2^{\prime }(1525))\}{\ell }^{+}{\ell }^{-}$ decays at large recoil
• Application of HQET to $B\to K^{(\ast )}$ Transitions
• Systematic analysis of the $B_s\to f_0{\ell }^{+}{\ell }^{-}$ in the universal extra dimension
• A study on the radiative dileptonic decays $B^0(B_s)\to \gamma {\ell }^{+}{\ell }^{-}$
• Study of Bc-> D_s^* \ell^+ \ell^- in Single Universal Extra Dimension
• Semi-leptonic $B\to S$ decays in the standard model and in the universal extra dimension model
• The CP asymmetry for B--> K^* l^+ l^- decay in the general two Higgs doublet model
• Vertex renormalization and hard scattering symmetry breaking corrections to $B$ to axial vector meson form factors at large recoil
• Polarized forward-backward asymmetries of lepton pair in $B\to K_1{\ell }^{+}{\ell }^{-}$ decay in the presence of New physics
• Fourth-generation SM imprints in B -> K^*l^+l^- decays with polarized K^*
• Asymmetry Parameter of the $K_1(1270,1400)$ by Analyzing the $B\to K_1\nu \bar{\nu }$ Transition Form Factors within QCD
• Form Factors and Differential Branching Ratio of $B\to K{\mu }^{+}{\mu }^{-}$ in AdS/QCD
• Subleading Shape-Function Effects and the Extraction of |V_ub|
• Looking for forward backward asymmetries in $B\to K{\mu }^{+}{\mu }^{-}$ and $K^{+}\to {\pi }^{+}{\mu }^{+}{\mu }^{-}$
• Custodial bulk Randall-Sundrum model and B->K* l+ l'-
• Exclusive $B \rar ρ\ell^+ \ell^-$ Decay in the Standard Model with Fourth--Generation
• Rare baryonic decays ${\Lambda }_b\to \Lambda l^{+}{l}^{-}$ in the TTM model
• The Study of Rare $B_c\to D_{s,d}^{(\ast )}l\bar{l}$ Decays
• Double-Lepton Polarization Asymmetries and Branching Ratio of the $B\rar γl^+ l^- $ transition in Universal Extra Dimension
• Investigation of rare semileptonic $B_c$ decays into $(D_{(}s,d{)}^{(}(\ast ))){\mu }^{+}{\mu }^{-}$ decays with non-universal $Z^{\prime }$ effect
• Analysis of the B --> π\ell^+ \ell^- Decay in the Standard Model with Fourth Generation
• $B\to X_{{}_S}{l}^{+}{l}^{-}$ in the minimal gauged $(B-L)$ supersymmetry
• Tension between scalar/pseudoscalar new physics contribution to B_s --> mu+ mu- and B --> K mu+ mu-
• Effects of neutral $Z^{\prime }$ boson in $B_s\to \varphi {\ell }^{+}{\ell }^{-}$ decay with polarized $\varphi$ and the unpolarized and polarized $CP$ violation asymmetry
• Rare ${\Lambda }_b\to \Lambda {\ell }^{+}{\ell }^{-}$ decay in the two-Higgs doublet model of type-III
• Rare radiative leptonic B-decays
• On the effective lifetime of $B_s\to \mu \mu \gamma$
• CP violation in the $B\to K{\ell }^{+}{\ell }^{-}$ decay
• Search for the $B_s^0\to {\mu }^{+}{\mu }^{-}\gamma$ decay
• CP-Violation in b \to s \ell^{+} \ell^{-} transition Beyond the Standard Model
• Double-Lepton Polarization Asymmetries in $B_s \rar ϕ\ell^+ \ell^-$ Decay in the Fourth-Generation Standard Model
• Investigation of the $D_{s1}$ structure via $B_c$ to $D_{s1}{l}^{+}{l}^{-}/\nu \bar{\nu }$ transitions in QCD
• The effects of enhanced Z penguins on lepton polarizations in $B\to X_s{\ell }^{+}{\ell }^{-}$
• B-meson signatures of a Supersymmetric U(2) flavor model
• Implication of the Fourth Generation Standard Model to the Lepton Polarization asymmetries in the $B\to K^{\ast }{\ell }^{+}{\ell }^{-}$ Decay
• A Method For Extracting cosα
• Longitudinal Polarization in $K_L\to {\mu }^{+}{\mu }^{-}$ in MSSM with large $tan\beta$
• Semileptonic $B_{(s)}\to a_1(K_1){\ell }^{+}{\ell }^{-}$ decays via the light-cone sum rules with $B$-meson distribution amplitudes
• Magnetic-dipole corrections to $R_K$ and $R_{K^{\ast }}$ in the Standard Model and Dark Photon scenarios
• Constraints on the anomalous $Wtb$ couplings from $B$-physics experiments
• Charming-loop contribution to $B_s\to \gamma \gamma$ decay
• Implication of Z-mediated FCNC on semileptonic decays $B_s\to \varphi l^{+}{l}^{-}$ and $B^{+}\to K^{+}{l}^{+}{l}^{-}$
• 1/m_b^2 correction to the left-right lepton polarization asymmetry in the decay B -> X_s mu^+ mu^-
• $B\to K_1(1270)(\to \rho K){\ell }^{+}{\ell }^{-}$ in LEET
• 2004 Review of Light Cone Field Theory
• B_s ---> γγdecay in the model III and 3HDM(O_2) with CP violating effects
• Scrutinizing $B^0$-meson flavor changing neutral current decay into scalar $K_0^{\ast }(1430)$ meson with $b\to s{\ell }^{+}{\ell }^{-}(\nu \bar{\nu })$ transition
• Flavor Changing Neutral Currents Transition of the ${\Sigma }_Q$ to Nucleon in Full QCD and Heavy Quark Effective Theory
• CP Asymmetry of $B\to X_s{l}^{+}{l}^{-}$ in Low Invariant Mass Region
• CP violation in the radiative dileptonic B-meson decays
• Analysis of the lepton polarisation asymmetries of $\bar{B}\to {\bar{K}}_2(1430){\ell }^{+}{\ell }^{-}$ decay
• Analysis of Various Polarization Asymmetries In The Inclusive $b\to s{\ell }^{+}{\ell }^{-}$ Decay In The Fourth-Generation Standard Model
• Rare decays of the $B_s-$meson into four charged leptons in the framework of the Standard Model
• Lepton polarization and CP-violating effects in $\overline{B}\to {\overline{K}}_0^{\ast }(1430){\ell }^{+}{\ell }^{-}$ Decay in Standard and Two Higgs Doublet Model
• Study of $B_s^0\to l^{+}{l}^{-}\gamma$ decays in the nonuniversal Z' model
• Implications of new physics in $B\to K_1{\mu }^{+}{\mu }^{-}$ decay processes
• Form factors of $B_{(s)}$ to light scalar mesons with the $B$-meson LCSR
• Decay $B_c^{+}\to D_{(s)}^{(\ast )+}{\ell }^{+}{\ell }^{-}$ within covariant confined quark model
• Polarized and Unpolarized Lepton Pair Forward-backward Asymmetries in $\overline{B}\to {\overline{K}}_0^{\ast }(1430){\ell }^{+}{\ell }^{-}$ and $\overline{B}\to \overline{K}{\ell }^{+}{\ell }^{-}$ Decays in Two Higgs Doublet Model
• B_s -> τ^+ τ^- decay in the general two Higgs Doublet model
• Reappraisal of the minimal flavoured $Z^{\prime }$ scenario
• ${\bar{B}}_s\to {\mu }^{+}{\mu }^{-}$ decay in the Randall-Sundrum model
• Constraints on new physics from decays of polarized ${\Lambda }_b^0$ baryons at the FCC-ee
• Semileptonic B to Scalar meson Decays in the Standard Model with Fourth Generation
• Long-distance QCD effects in FCNC $B\to \gamma l^{+}{l}^{-}$ decays
• Standard Model CP violation in B->X_d \ell^+\ell^- decays
• Rare Bc->Ds l^+ l^- decay beyond the standard model
• General analysis of time evolution of decay spectrum in B^0 -> pi^+ pi^- l^+ l^-
• Baryons and baryoniums in the perspective of QCD sum rules
• Form factors and differential distributions in rare radiative leptonic B-decays
• The Forward-Backward Asymmetry in the $B\to \pi {\ell }^{+}{\ell }^{-}$ Decay
• Combined analysis of $B_c\to D_s^{(\ast )}{\mu }^{+}{\mu }^{-}$ and $B_c\to D_s^{(\ast )}\nu \bar{\nu }$ decays within $Z^{\prime }$ and leptoquark new physics models
• Probing new physics through B->K l+ l- decays in R-parity violating minimal supersymmetric standard model
• Flavour anomalies in supersymmetric scenarios with non-minimal flavour violation
• Implications of lepton nonuniversality in the beauty sector
• Reexamination of the resonance contributions in B->X_s e^+ e^-
• $B_{(s)}\to S(a_0(1450),K_0^{\ast }(1430),f_0(1500))$ helicity form factors within QCD light-cone sum rules
• Implication of the HyperCP boson $X^0$ (214 MeV) in the flavour changing neutral current processes
• Effects of a Single Universal Extra Dimension in $B_c\to (D_s,D){\ell }^{+}{\ell }^{-}$ Decays