Longitudinal Lepton Polarization Research Articles

Symmetry breaking radiative corrections to B to tensor meson form factors at large recoil

In heavy-to-light B decays, the heavy-quark/large-energy symmetry reduces the number of QCD form factors. At large final state meson energy, these form factors receive sizeable perturbative corrections. The hard-gluon vertex corrections are absorbed in the coefficients of soft-form factors, while the hard-spectator interactions generate symmetry-breaking corrections and end-point singularities. At an order of 1/m b, using the heavy-quark/large-energy symmetry, the end-point singularities can also be absorbed in the soft form factors, whereas the symmetry breaking corrections add separately to the form factors. In this work, we calculate these perturbative corrections for B → Tμ + μ − decays, with T representing the tensor mesons all having J P = 2+. We find that the values of the branching ratio (Br) and the zero-position of the forward–backward asymmetry of decay receive nearly 5% and 14% contributions, respectively, from these radiative corrections. Compared to these observables, the radiative corrections change the averaged longitudinal lepton polarization asymmetry (⟨P L⟩) by 13%. Therefore, prior to attributing any deviation from the SM predictions of these asymmetries as a hint of NP, one has to take into account the contributions of vertex and hard-spectator corrections.

Semileptonic Bs→K0*(1430) transitions with the light-cone sum rules

In the $\rm SU(3)_F$ symmetry limit, using two- and three-particle distribution amplitudes of $B^{\pm}$-meson for $B_s$, the transition form factors of semileptonic $B_{s}\to K_{0}^*(1430)$ decays are calculated in the framework of the light-cone sum rules. The two-particle distribution amplitudes, $\varphi_{_{+}}(\omega)$ and $\varphi_{_{-}}(\omega)$ have the most important contribution in estimation of the form factors $f_{+}(q^2)$, $f_{-}(q^2)$ and $f_{T}(q^2)$. The knowledge of the behavior of $\varphi_{_+}(\omega)$ is still rather limited. Therefore, we consider three different parametrizations for the shapes of $\varphi_{_+}(\omega)$ that are derived from the phenomenological models. Using the form factors $f_{+}$, $f_{-}$ and $f_{T}$, the semileptonic $B_s \to K_0^*(1430) l \bar{\nu_{l}}$ and $B_s \to K_0^*(1430) l \bar{l}/\nu \bar{\nu}$, $l=e, \mu, \tau$ decays are analyzed. The branching fractions for the aforementioned decays, in addition the longitudinal lepton polarization asymmetries are calculated. A comparison between our results with predictions of other approaches is provided.

Vertex renormalization and hard scattering symmetry breaking corrections to B to axial vector meson form factors at large recoil

The symmetries arise due to heavy quark and large energy limit help us to reduce the number of independent form factors in the heavy-to-light $B$-meson decays. It is expected that these symmetry relations are not exact and are broken by the perturbative effects, namely, the vertex corrections and the hard-spectator scatterings. The former are included in the form factors via vertex renormalization whereas the later are calculated through light-cone distribution amplitudes. We first calculate these symmetry breaking corrections to the form factors involved in semileptonic $B$-meson to an axial-vector $(K_{1})$-meson decay. Later, by using these form factors we see their effect on the physical observables such as the zero-position of the forward-backward $(\mathcal{A}_{FB})$ asymmetry and the longitudinal lepton polarization ($P_L$) asymmetry in $B\rightarrow K_1(1270) \mu^+\mu^-$ decay. We find that as a result of these corrections to the form factors, the zero-position of the forward-backward asymmetry is shifted by $10\%$ from its SM value while the effects on $P_L$ are rather insignificant.

Exclusive Rare B (s,c) Decays in Light-Front Quark Model

We investigate the exclusive rare \({B_s\to (K,\eta^{(\prime)})(\nu_{\ell}\bar{\nu_{\ell}}, \ell^+\ell^-)}\) and \({B_c\to D_{(s)}(\nu_{\ell}\bar{\nu_{\ell}}, \ell^+\ell^-)}\) (l = e, μ, τ) decays within the standard model and the light-front quark model constrained by the variational principle for the QCD motivated effective Hamiltonian. The branching ratios and the longitudinal lepton polarization asymmetries are calculated and compared with other theoretical model predictions.

B c meson rare decays in the light-cone quark model

We investigate the rare decays $B_c \rightarrow D_s(1968) \ell \bar{\ell}$ and $B_c\rightarrow D_s^*(2317) \ell \bar{\ell}$ in the framework of the light-cone quark model (LCQM). The transition form factors are calculated in the space-like region and then analytically continued to the time-like region via exponential parametrization. The branching ratios and longitudinal lepton polarization asymmetries (LPAs) for the two decays are given and compared with each other. The results are helpful to investigating the structure of $B_c$ meson and to testing the unitarity of CKM quark mixing matrix. All these results can be tested in the future experiments at the LHC.

Rare semileptonicBsdecays toηandη′mesons in QCD

We analyze the rare semileptonic $B_s \to (\eta, \eta') l^+ l^-$, $(l=e, \mu, \tau)$ and $B_s \to (\eta, \eta') \nu \bar{\nu}$ transitions probing the $\bar s s$ content of the $\eta$ and $\eta'$ mesons via three--point QCD sum rules. We calculate responsible form factors for these transitions in full theory. Using the obtained form factors, we also estimate the related branching fractions and longitudinal lepton polarization asymmetries. Our results are in a good consistency with the predictions of the other existing nonperturbative approaches.

Exclusive rare Bs → (K, η, η′)ℓ+ℓ− decays in the light-front quark model

Using the light-front quark model, we calculate the transition form factors, decay rates and longitudinal lepton polarization asymmetries for the exclusive rare ) (ℓ = e, μ, τ) decays within the standard model, taking into account the η − η′ mixing angle. For the mixing angle θ = −20° (−10°) in the octet-singlet basis, we obtain , BR(Bs → ημ+μ−) = 1.5(2.4) × 10−7, BR(Bs → ητ+τ−) = 3.8(5.8) × 10−8, , BR(Bs → η′μ+μ−) = 2.4(1.8) × 10−7 and BR(Bs → η′τ+τ−) = 3.4(2.6) × 10−8, respectively. The branching ratios for the decays are at least an order of magnitude smaller than those for the decays. The averaged values of the lepton polarization asymmetries for Bs → (K, η(′))ℓ+ℓ− are obtained as , ⟨PKL⟩τ = −0.24, ⟨PηL⟩τ = −0.20 and , respectively.

Light-front quark model analysis of the exclusive rareBc→D(s)(ℓ+ℓ−,νℓν¯ℓ)decays

We investigate the exclusive rare ${B}_{c}\ensuremath{\rightarrow}{D}_{(s)}{\ensuremath{\nu}}_{\ensuremath{\ell}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\ell}}$ and $B\ensuremath{\rightarrow}{D}_{(s)}{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ ($\ensuremath{\ell}=e$, $\ensuremath{\mu}$, $\ensuremath{\tau}$) decays within the standard model and the light-front quark model constrained by the variational principle for the QCD-motivated effective Hamiltonian. The form factors ${f}_{\ifmmode\pm\else\textpm\fi{}}({q}^{2})$ and ${f}_{T}({q}^{2})$ are obtained from the analytic continuation method in the ${q}^{+}=0$ frame. While the form factors ${f}_{+}({q}^{2})$ and ${f}_{T}({q}^{2})$ are free from the zero mode, the form factor ${f}_{\ensuremath{-}}({q}^{2})$ is not free from the zero mode in the ${q}^{+}=0$ frame. We discuss the covariance (i.e. frame independence) of our model calculation and quantify the zero-mode contributions to ${f}_{\ensuremath{-}}({q}^{2})$ for ${B}_{c}\ensuremath{\rightarrow}{D}_{(s)}$ decays. The branching ratios and the longitudinal lepton polarization asymmetries are calculated with and without the long-distance contributions. Our numerical results for the nonresonant branching ratios for ${B}_{c}\ensuremath{\rightarrow}D({D}_{s})\ensuremath{\sum}_{}^{}{\ensuremath{\nu}}_{\ensuremath{\ell}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\ell}}$ and ${B}_{c}\ensuremath{\rightarrow}D({D}_{s}){\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ are in the order of ${10}^{\ensuremath{-}8}$ (${10}^{\ensuremath{-}7}$) and ${10}^{\ensuremath{-}9}$ (${10}^{\ensuremath{-}8}$), respectively. The averaged values of the lepton polarization asymmetries obtained from the linear (harmonic oscillator) potential parameters are found to be $\ensuremath{-}0.99$ ($\ensuremath{-}0.99$) for ${B}_{c}\ensuremath{\rightarrow}D{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ and $\ensuremath{-}0.16$ ($\ensuremath{-}0.15$) for ${B}_{c}\ensuremath{\rightarrow}D{\ensuremath{\tau}}^{+}{\ensuremath{\tau}}^{\ensuremath{-}}$, and $\ensuremath{-}0.98$ ($\ensuremath{-}0.98$) for ${B}_{c}\ensuremath{\rightarrow}{D}_{s}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ and $\ensuremath{-}0.14$ ($\ensuremath{-}0.12$) for ${B}_{c}\ensuremath{\rightarrow}{D}_{s}{\ensuremath{\tau}}^{+}{\ensuremath{\tau}}^{\ensuremath{-}}$, respectively.

Analysis of rare semileptonicBc→Ds0*(2317)l+l−decays

We analyze the rare semileptonic B{sub c{yields}}D{sub s0}*l{sup +}l{sup -}, (l=e, {mu}, {tau}) and B{sub c{yields}}D{sub s0}*{nu}{nu} decays in the framework of the three-point QCD sum rules. D{sub s0}* is a scalar meson with total spin 0 and even parity. Taking into account the gluon condensate contributions as the important correction of the nonperturbative parts of the correlation function and the large effects of Coulombic corrections, the relevant form factors of these transitions have been calculated. The branching fractions and longitudinal lepton polarization asymmetry are also investigated.

Analysis of the rare semileptonic decays ofBstof0(980)andK0*(1430)scalar mesons in QCD sum rules

We investigate the rare semileptonic decays ${B}_{s}\ensuremath{\rightarrow}[{f}_{0}(980),{K}_{0}^{*}(1430)]{l}^{+}{l}^{\ensuremath{-}}$, ($l=e$, $\ensuremath{\mu}$, $\ensuremath{\tau}$), and ${B}_{s}\ensuremath{\rightarrow}[{f}_{0}(980),{K}_{0}^{*}(1430)]\ensuremath{\nu}\overline{\ensuremath{\nu}}$ in the framework of the three-point QCD sum rules. These decays are important to study because the ${f}_{0}(980)$ and ${K}_{0}^{*}(1430)$ are the scalar mesons with total spin 0 and even parity and the quark content of them are still controversial in high energy physics. These rare decays occur at loop level by electroweak penguin and weak box diagrams in the standard model via the flavor changing neutral current transitions of $b\ensuremath{\rightarrow}d$, $s$, and not allowed by tree level. Considering the effective contributions of the nonperturbative parts of the correlation function, we calculate the relevant form factors of these transitions. The branching fractions and longitudinal lepton polarization asymmetry are also investigated.

Scalar mesons in weak semileptonic decays ofB(s)

The transition form factors of ${B}_{(s)}\ensuremath{\rightarrow}S$, with $S$ denoting a scalar meson, are investigated in the light-cone sum rules approach. The numerical values are approximately twice the number estimated in the light-front quark model and QCD sum rules approach. Using these form factors, we present the analysis of the decay rates for $B\ensuremath{\rightarrow}{a}_{0}(1450)l{\overline{\ensuremath{\nu}}}_{l}$, $B\ensuremath{\rightarrow}{K}_{0}^{*}(1430)l\overline{l}$, ${B}_{s}\ensuremath{\rightarrow}{K}_{0}^{*}(1430)l{\overline{\ensuremath{\nu}}}_{l}$, and ${B}_{s}\ensuremath{\rightarrow}{f}_{0}(1500)l\overline{l}$ with $l=e$, $\ensuremath{\mu}$, $\ensuremath{\tau}$. The results indicate that magnitudes of $BR({\overline{B}}_{0}\ensuremath{\rightarrow}{a}_{0}(1450)l{\overline{\ensuremath{\nu}}}_{l})$ and $BR({B}_{s}\ensuremath{\rightarrow}{K}_{0}^{*}(1430)l{\overline{\ensuremath{\nu}}}_{l})$ arrive at the order of ${10}^{\ensuremath{-}4}$, which can be measured in future experiments to clarify the inner structure of scalar mesons. It is also observed that $BR(B\ensuremath{\rightarrow}{K}_{0}^{*}(1430){\ensuremath{\tau}}^{+}{\ensuremath{\tau}}^{\ensuremath{-}})$ and $BR({B}_{s}\ensuremath{\rightarrow}{f}_{0}(1500){\ensuremath{\tau}}^{+}{\ensuremath{\tau}}^{\ensuremath{-}})$ are an order of magnitude smaller than the corresponding channels of ${e}^{+}{e}^{\ensuremath{-}}$ and ${\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ final states due to the heavily suppressed phase space. Moreover, the longitudinal lepton polarization asymmetry for $B\ensuremath{\rightarrow}{K}_{0}^{*}(1430)l\overline{l}$ and ${B}_{s}\ensuremath{\rightarrow}{f}_{0}(1500)l\overline{l}$ are also investigated, whose values are close to $\ensuremath{-}1$ for the ${e}^{+}{e}^{\ensuremath{-}}$ and ${\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ pair except for the region close to the endpoints.

Study ofB→K0*(1430)ll¯decays

We examine the exclusive rare decays of B{yields}K{sub 0}*(1430)ll with K{sub 0}*(1430) being the p-wave scalar meson and l={nu}, e, {mu}, {tau} in the standard model. The form factors for the B{yields}K{sub 0}* transition matrix elements are evaluated in the light-front quark model. For the decays of B{yields}K{sub 0}*ll, the branching ratios are found to be (11.6,1.63,1.62,0.029)x10{sup -7} with l=({nu},e,{mu},{tau}) and the integrated longitudinal lepton polarization asymmetries (-0.97,-0.95,-0.03) with l=(e,{mu},{tau}), respectively.

Study of decays

We study the rare decays of Bs → Msℓ (Ms = η, η′, ϕ and ℓ = ν, e, μ, τ) in the standard model. With the hadronic form factors evaluated in the light front and constituent quark models, we estimate the decay branching ratios, respectively. We also discuss the longitudinal lepton polarization and forward-backward asymmetries.

Light-front quark model analysis of rareB→Kl+l−decays

Using the light-front quark model, we calculate the transition form factors, decay rates, and longitudinal lepton polarization asymmetries for the exclusive rare $B\to K\ell^+\ell^-(\ell=e,\mu,\tau$) decays within the standard model. Evaluating the timelike form factors, we use the analytic continuation method in $q^+=0$ frame to obtain the form factors $F_+$ and $F_T$, which are free from zero-mode. The form factor $F_-$ which is not free from zero-mode in $q^+ = 0$ frame and contaminated by the higher(or nonvalence) Fock states in $q^+ \neq 0$ frame is obtained from an effective treatment for handling the nonvalence contribution based on the Bethe-Salpeter formalism. The covariance(i.e. frame-independence) of our model calculation is discussed. We obtain the branching ratios for ${\rm BR}(B\to K\ell^+\ell^-)$ as $4.96\times10^{-7}|V_{ts}/V_{cb}|^2$ for $\ell=e,\mu$ and $1.27\times 10^{-7}|V_{ts}/V_{cb}|^2$ for $\ell=\tau$.

Longitudinal polarization in KL→ μ+μ− in MSSM with large tan β

A complete experiment on decay K L → l + l − will not only consist of measurement of the decay rates but also lepton polarization etc. These additional observations will yield tests of CP invariance in these decays. In K L and K S decays, the e mode is slower than the μ mode by roughly ( m e / m μ ) 2 [4]. As well discussed in literature [5]the Standard Model contribution to the lepton polarization is of order 2×∼10 −3. We show that in MSSM with large tan β and light higgs masses (∼2 M W ), the longitudinal lepton polarization in K L → μ + μ − can be enhanced to a higher value, of about 10 −2.

Formula omitted] decay in the two Higgs doublet model with flavor changing neutral currents

We study the decay width, forward–backward asymmetry and the longitudinal lepton polarization for the exclusive decay B→K ∗l +l − in the two Higgs doublet model with three level flavor changing neutral currents (model III) and analyse the dependencies of these quantities on the the selected parameters, ξ U, D , of model III including the next to leading QCD corrections. It is found that to look for charged Higgs effects, the measurements of the branching ratio, forward–backward asymmetry and the longitudinal lepton polarization for the decay B→K ∗l +l − are promising.

Probing the standard model and its extensions in rare exclusive b → sℓ + ℓ − decays

Long-distance effects on the forward-backward and longitudinal lepton polarization asymmetries in rare B → (K, K*)l+l- decays are investigated. The lepton asymmetries are found to be largely unaffected by the theoretical uncertainties in the long-distance contributions, induced both by the long-range charming penguins in the l+ l− channel and by the transition form factors in the meson channels, while they are mainly determined by the short-distance Wilson coefficients, providing in this way a test of the possible presence of New Physics. We also show that within left-right models one can expect a strong enhancement of the right-handed K* production in B → K*l+ l− decays compared to models including only left-handed quark currents. Hence an experimental study of the transverse asymmetry of the produced K* mesons provides a clean possibility to discriminate between the MSSM and LR extensions of the SM.

Probing right-handed currents in [formula omitted] transitions

We discuss a possibility to probe right-handed weak hadronic currents in rare semileptonic b→ s transitions. It is shown that within models involving right-handed as well as left-handed quark currents (LR models) one can expect a strong enhancement of the right-handed K ∗ production in B→K ∗ℓ +ℓ − decays compared with models including only left-handed quark currents (SM, MSSM). Hence an experimental study of the transverse asymmetry of the produced K ∗ mesons provides a clear test of the presence of the right-handed quark currents and a possibiltity to discriminate between the MSSM and LR extentions of the SM. At the same time, MSSM and LR models are found to yield qualitatively the same type of deviations from the SM in the forward-backward and the longitudinal lepton polarization asymmetries.

Lepton asymmetries in exclusive b→ sℓ +ℓ − decays as a test of the standard model

We argue that the longitudinal lepton polarization and the forward-backward asymmetries in exclusive B→(K,K ∗)ℓ +ℓ − decays are largely unaffected by the theoretical uncertainties in the long-distance contributions both induced by the long-range charming penguins in the ℓ +ℓ − channel and those in the meson channels encoded in the meson transition form factors, and are mainly determined by the short-distance Wilson coefficients at the low-energy scale μ≃ m b . Thus, the abovementioned asymmetries provide a powerful probe of the Standard Model and its extensions.

Rare exclusive semileptonicb→stransitions in the standard model

We study long-distance effects in rare exclusive semileptonic decays $\stackrel{\ensuremath{\rightarrow}}{B}{(K,K}^{*})({\mathcal{l}}^{+}{\mathcal{l}}^{\ensuremath{-}},\ensuremath{\nu}\overline{\ensuremath{\nu}})$ and analyze dilepton spectra and asymmetries within the framework of the standard model. The form factors, describing the meson transition amplitudes of the effective Hamiltonian, are calculated within the lattice-constrained dispersion quark model: the form factors are given by dispersion representations through the wave functions of the initial and final mesons, and these wave functions are chosen such that the $\stackrel{\ensuremath{\rightarrow}}{B}{K}^{*}$ transition form factors agree with the lattice results at large ${q}^{2}$. We calculate branching ratios of semileptonic $\stackrel{\ensuremath{\rightarrow}}{B}{K,K}^{*}$ transition modes and study the sensitivity of observables to the long-distance contributions. The shape of the forward-backward asymmetry and the longitudinal lepton polarization asymmetry are found to be independent of the long-distance effects and mainly determined by the values of the Wilson coefficients in the standard model.