Virtual- and bremsstrahlung corrections to b -> d l+ l- in the standard model

Abstract

We present the calculation of the virtual- and bremsstrahlung corrections of O(alpha_s) to the matrix elements <d l+ l-|O_i|b>. This is the missing piece in the NNLL results for various observables associated with the process B-> X_d l+ l-, like the branching ratio, the CP-rate asymmetry and the forward-backward asymmetry. This paper is an extension of analogous calculations done by some of us for the process B-> X_s l+ l-. As the contributions of the diagrams induced by the operators O_1^u and O_2^u with a u-quark running in the quark loop are strongly CKM suppressed, they were omitted in the analysis of B->X_s l+ l-. This is no longer possible for B-> X_d l+ l-, as the corresponding contributions are not suppressed. The main new work therefore consists of calculating the O(alpha_s) corrections to <d l+ l-|O_{1,2}^u|b>. In this paper we restrict ourselves to the range 0.05 < s/m_b^2 < 0.25 (s is the invariant mass of the lepton pair), which lies above the rho- and omega-resonances and below the J/psi-resonance. We present the analytic results for the mentioned observables related to the process B-> X_d l+ l- as expansions in the small parameters s/m_b^2, z = m_c^2/m_b^2 and s/(4 m_c^2). In the phenomenological analysis at the end of the paper we discuss the impact of the NNLL corrections on the observables mentioned above.

43 pages including 5 postscript figures; Added three references, corrected some typos

References in corpus (6)

• Anomalous Dimension Matrix for Radiative and Rare Semileptonic B Decays up to Three Loops
• Present Status of Inclusive Rare B Decays
• Forward--Backward Asymmetry in B -> X_s l^+ l^- at the NNLL Level
• NNLL corrections to the angular distribution and to the forward-backward asymmetries in b -> X_s l+ l-
• Measurement of the Electroweak Penguin Process B --> X(s) l+ l-
• NNLL QCD Corrections to the Decay $B\to X_s{\ell }^{+}{\ell }^{-}$

Cited by in corpus (29)

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• Exclusive radiative and electroweak b->d and b->s penguin decays at NLO
• The Benefits of B ---> K* l+ l- Decays at Low Recoil
• Charm Quark Contribution to K+ -> pi+ nu anti-nu at Next-to-Next-to-Leading Order
• Complete NNLO QCD Analysis of B -> X_s l^+ l^- and Higher Order Electroweak Effects
• The Rare Decay K^+ -> pi^+ nu nubar at the Next-to-Next-to-Leading Order in QCD
• Precise Calculation of the Dilepton Invariant-Mass Spectrum and the Decay Rate in $B^{\pm }\to {\pi }^{\pm }{\mu }^{+}{\mu }^{-}$ in the SM
• Three-Loop Mixing of Dipole Operators
• Phenomenology of semileptonic B-meson decays with form factors from lattice QCD
• Radiative and Electroweak Penguin Decays of B Mesons
• Standard Model predictions for $B\to K{\ell }^{+}{\ell }^{-}$, $B\to K{\ell }_1^{-}{\ell }_2^{+}$ and $B\to K\nu \bar{\nu }$ using form factors from $N_f=2+1+1$ lattice QCD
• $B\to \pi \ell \ell$ form factors for new-physics searches from lattice QCD
• Hadronic effects and observables in $B\to \pi {\ell }^{+}{\ell }^{-}$ decay at large recoil
• Analytic two-loop virtual corrections to $b-->d{l}^{+}{l}^{-}$
• The rare decays $B_u^{+}\to {\pi }^{+}{\ell }^{+}{\ell }^{-}$, ${\rho }^{+}{\ell }^{+}{\ell }^{-}$ and $B_d^0\to {\ell }^{+}{\ell }^{-}$ in the R-parity violating supersymmetry
• Model-independent analysis of $b\to d$ processes
• Two loop virtual corrections to $b\to (d,s){\ell }^{+}{\ell }^{-}$ and $c\to u{\ell }^{+}{\ell }^{-}$ for arbitrary momentum transfer
• Reduction of Charm Quark Mass Scheme Dependence in $\bar{B}\to X_s\gamma$ at the NNLL Level
• Probing flavor constrained SMEFT operators through $tc$ production at the Muon collider
• Long distance effects in inclusive rare $B$ decays and phenomenology of $\bar{B}\to X_d{\ell }^{+}{\ell }^{-}$
• Implication of family non-universal $Z^{\prime }$ model to rare exclusive $b\to s(l\bar{l},\nu \bar{\nu })$ transitions
• Predictions of Angular Observables for ${\bar{B}}_s\to K^{\ast }\ell \ell$ and $\bar{B}\to \rho \ell \ell$ in Standard Model
• Predictions for $B_s\to {\bar{K}}^{\ast }\ell \ell$ in non-universal $Z^{\prime }$ models
• Study of the $b\to d\ell \ell$ transitions in the Standard Model and test of New Physics sensitivities
• Five-particle contributions to the inclusive rare $\bar{B}\to X_{s(d)}{\ell }^{+}{\ell }^{-}$ decays
• Renormalisation group evolution for the $\Delta S=1$ effective Hamiltonian with $N_f=2+1$
• CP violation in polarized B-> pi ell+ ell- and B-> rho ell+ ell- decays
• Branching Fraction of the Decay $B^{+}\to {\pi }^{+}{\tau }^{+}{\tau }^{-}$ and Lepton Flavor Universality Test via the Ratio $R_{\pi }(\tau /\mu )$
• Searches for $B^0\to K^{+}{\pi }^{-}{\tau }^{+}{\tau }^{-}$ and $B_s^0\to K^{+}{K}^{-}{\tau }^{+}{\tau }^{-}$ decays