Feng Feng, Saadi Ishaq, Yu Jia, Jia-Yue Zhang
Following the operator definition of the fragmentation function developed by Collins and Soper, we compute the gluon-to-$h_c$ fragmentation function at the lowest order in the velocity expansion in NRQCD factorization approach. Utilizing some modern technique developed in the area of multi-loop calculation, we are able to analytically deduce the infrared-finite color-singlet short-distance coefficient associated with the fragmentation function. The fragmentation probability for gluon into $h_c$ is estimated to be order $10^{-6}$.
Saadi Ishaq, Sajawal Zafar, Abdur Rehman, Ishtiaq Ahmed
Motivated by the study of heavy-light meson production within the framework of heavy quark effective theory (HQET) factorization, we extend the factorization formalism for a rather complicated process $W^+\to B^+\ell^+\ell^-$ in the limit of a non-zero invariant squared-mass of dilepton, $q^2$, at the lowest order in $1/m_b$ up to $\mathcal{O}(α_s)$. The purpose of the current study is to extend the HQET factorization formula for the $W^+\to B^+\ell^+\ell^-$ process and subsequently compute the form factors for this channel up to next-to-leading-order corrections in $α_s$. We explicitly show the amplitude of the $W^+\to B^+\ell^+\ell^-$ process can also be factorized into a convolution between the perturbatively calculable hard-scattering kernel and the non-perturbative yet universal light-cone distribution amplitude (LCDA) defined in HQET. The validity of HQET factorization depends on the assumed scale hierarchy $m_W \sim m_b \gg Λ_{\mathrm{QCD}}$. Within the HQET framework, we evaluate the form factors associated with the $W^+ \rightarrow B^+\ell^+\ell^-$ process, providing insights into its phenomenology. In addition, we also perform an exploratory phenomenological study on $W^+ \rightarrow B^+\ell^+\ell^-$ by employing an exponential model for the LCDAs for $B^+$ meson. Our findings reveal that the branching ratio for $W^+ \rightarrow B^+\ell^+\ell^-$ is below $10^{-10}$. Although the branching ratios are small, this channel in high luminosity LHC experiments may serve to further constraints the value of $λ_B$.
Faisal Munir Bhutta, Abdur Rehman, M. Jamil Aslam, Ishtiaq Ahmed, Saadi Ishaq
Recent measurements of the lepton flavor universality ratios $R^{μe}_{K}$ and $R^{μe}_{K^*}$ in $B\to \left(K, K^*\right)μ^{+}μ^{-}\left(e^+e^-\right)$ at LHCb align with the Standard Model predictions, necessitating search for the complementary decay modes. In this context, we derive the angular decay distributions of the four-fold $B \to K_{1}(1270,1400)(\to V P) μ^{+}μ^{-}$ decays, where $K_1 $ is an axial-vector meson, $V=ρ, K^{\ast}$, and $P=K, π$. Considering the weak effective Hamiltonian with vector and axial-vector new physics operators, and employing the helicity formalism, we obtain the four-dimensional differential decay distributions and extract various physical observables. These include differential branching ratios, lepton forward-backward asymmetry, forward-backward asymmetry for transversely polarized $K_1$ meson, longitudinal and transverse polarization fractions of the $K_1$ meson, and the normalized angular coefficients with longitudinally and transversely polarized final state vector meson $V$, in the cascade decay $K_1\to VP$. Based on the latest global fit analysis data for all $b\to s$ transitions, we predict the results of these observables in various bins of the square of the momentum transfer, $q^2$. Our findings indicate that these physical observables are not only sensitive to new physics but can also differentiate between various new physics scenarios in certain kinematical regions. The precise measurements of these observables in $B \to K_{1}(1270,1400)(\to V P) μ^{+}μ^{-}$ decays at current and future experiments will provide opportunities for the complementary searches for physics beyond the Standard Model in $b\to s\ell^+\ell^-$ decays.
Faisal Munir, Saadi Ishaq, Ishtiaq Ahmed
Double polarized forward-backward asymmetries in $B\rightarrow K_{1}(1270,1400)\ell^{+}\ell^{-}$ with $\ell=μ, τ$ decays are studied, using most general non-standard local four-fermi interactions, where the mass eigenstates $K_{1}(1270)$ and $K_{1}(1400)$ are the mixture of $^{1}{P}_{1}$ and $^{3}{P}_{1}$ states with the mixing angle $θ_{K}$. We have calculated the expressions of nine doubly polarized forward-backward asymmetries and it is presented that the polarized lepton pair forward-backward asymmetries are greatly influenced by the new physics. Therefore, these asymmetries are interesting tool to explore the status of new physics in near future, specially at LHC.
Ishtiaq Ahmed, Saba Shafaq, M. Jamil Aslam, Saadi Ishaq
The Standard Model (SM) is lepton flavor universal, and the recent measurements of lepton flavor universality in $B \to (K,K^*)\ell^{+}\ell^{-}$, for $\ell = μ, \; e$, decays now lie close to the SM predictions. However, this is not the case for the $τ$ to $μ$ ratios in these decays, where there is still some window open for the new physics (NP), and to accommodate them various extensions to the SM are proposed. It will be interesting to identify some observables which are not only sensitive on the parametric space of such NP models but also have some discriminatory power. We find that the polarization of the $K^{*}$ may play an important role, therefore, we have computed the unpolarized and polarized lepton flavor universality ratios of $τ$ to $μ$ in $B\to K^{*}\ell^{+}\ell^{+}$, $\ell= μ, τ$ decays. The calculation shows that in most of the cases, the values of the various proposed observables fall within the current experimental sensitivity, and their study at some on going and future experiments will serve as a tool to segregate the variants of the NP models.
Saadi Ishaq, Yu Jia, Xiaonu Xiong, De-Shan Yang
The light-cone distribution amplitude (LCDA) of a heavy-light meson defined in heavy quark effective theory (HQET), is a fundamental nonperturbative input to account for innumerable $B$ meson exclusive decay and production processes. On the other hand, the conventional heavy-flavored meson LCDA defined in QCD, also ubiquitously enters the factorization formula for hard exclusive $B$ production processes. Inspired by the observation that these two LCDAs exhibit the identical infrared behaviors, yet differ in the ultraviolet scale of order $m_b$ or greater, we propose a novel factorization theorem for the heavy-light mesons, that the LCDA defined in QCD can be further expressed as a convolution between the LCDA in HQET and a perturbatively calculable coefficient function thanks to asymptotic freedom. This refactorization program can be invoked to fully disentangle the effects from three disparate scales $Q$, $m_b$ and $Λ_{\rm QCD}$ for a hard exclusive $B$ production process, particularly to facilitate the resummation of logarithms of type $\ln Q/m_b$ and $\ln m_b/Λ_{\rm QCD}$ in a systematic fashion.
Saadi Ishaq, Yu Jia, Xiaonu Xiong, De-Shan Yang
Analogous to NRQCD factorization for heavy quarkonium exclusive production, in this work we propose to employ the heavy-quark-effective-theory (HQET) factorization, which has been predominantly applied to account for exclusive $B$ decays, to study the exclusive production of the heavy-flavored mesons. We take $W\to B(D_s)+γ$ as a prototype process. The validity of the HQET factorization rests upon the presumed scale hierarchy: $m_W\sim m_b\gg Λ_{\rm QCD}$. Through an explicit analysis at next-to-leading order in $α_s$ yet at leading order in $1/m_b$, we verify that the decay form factors can indeed be expressed as the convolution between perturbatively calculable hard-scattering kernel and the $B$ meson light-cone distribution amplitude (LCDA) defined in HQET. It is observed that the factorization scale dependence becomes reduced after incorporating the NLO perturbative correction. An interesting future investigation is to identify and resum large collinear logarithms of $m_W/m_b$ that arise ubiquitously in the fixed-order expressions of the hard-scattering kernel in HQET factorization.