The NLO twist-3 contributions to $B\to \pi$ form factors in $k_T$ factorization

Abstract

In this paper, we calculate the next-to-leading-order (NLO) twist-3 contribution to the form factors of $B\to \pi$ transitions by employing the $k_T$ factorization theorem. All the infrared divergences regulated by the logarithms $\ln (k_{iT}^2)$ cancel between those from the quark diagrams and from the effective diagrams for the initial $B$ meson wave function and the final pion meson wave function. An infrared finite NLO hard kernel is therefore obtained, which confirms the application of the $k_T$ factorization theorem to $B$ meson semileptonic decays at twist-3 level. From our analytical and numerical evaluations, we find that the NLO twist-3 contributions to the form factors $f^{+,0}(q^2)$ of $B\to \pi$ transition are similar in size, but have an opposite sign with the NLO twist-2 contribution, which leads to a large cancelation between these two NLO parts. For the case of $f^{+}(0)$, for example, the $24\%$ NLO twist-2 enhancement to the full LO prediction is largely canceled by the negative ( about $-17\%$ ) NLO twist-3 contribution, leaving a small and stable $7\%$ enhancement to the full LO prediction in the whole range of $0\le q^2\le 12$ GeV${}^2$. At the full NLO level, the perturbative QCD prediction is $F^{B\to \pi }(0)=0.269_{-0.050}^{+0.054}$. We also studied the possible effects on the pQCD predictions when different sets of the B meson and pion distribution amplitudes are used in the numerical evaluation.

25 pages, 12 figures, 5 Tables. More discussions, several new references are added. The version to be published in Phys.Rev.D

References in corpus (6)

• Modelling light-cone distribution amplitudes from non-relativistic bound states
• Next-to-leading-order corrections to exclusive processes in $k_T$ factorization
• Joint resummation for pion wave function and pion transition form factor
• The NLO twist-3 contribution to the pion electromagnetic form factors in $k_T$ factorization
• Three-particle contributions to the renormalisation of B-meson light-cone distribution amplitudes
• On Transverse-Momentum Dependent Light-Cone Wave Functions of Light Mesons

Cited by in corpus (37)

• QCD corrections to $B\to \pi$ form factors from light-cone sum rules
• ${\bar{B}}_s\to f_0(980)$ form factors and the width effect from light-cone sum rules
• Charmless two-body $B$ meson decays in perturbative QCD factorization approach
• Hochschild homology, trace map and $\zeta$-cycles
• $B\to \pi \pi$ decays and effects of the next-to-leading order contributions
• Branching Fractions and CP Asymmetries of the Quasi-Two-Body Decays in $B_s\to K^0({\overline{K}}^0)K^{\pm }{\pi }^{\mp }$ within PQCD Approach
• Time-like pion electromagnetic form factors in $k_T$ factorization with the Next-to-leading-order twist-3 contribution
• Subleading power corrections to $B\to \gamma l\nu$ decay in PQCD approach
• Transverse-momentum-dependent wave functions with Glauber gluons in $B\to \pi \pi$, $\rho \rho$ decays
• Reinvestigating the $B$ $\to$ $PP$ decays by including the contributions from ${\varphi }_{B2}$
• Anatomy of $B_s\to PV$ decays and effects of next-to-leading order contributions in the perturbative QCD factorization approach
• Recent Developments on the CKM Matrix
• The PQCD approach towards to next-to-leading order: a short review
• The $\rho {\gamma }^{\ast }\to \pi (\rho )$ transition form factors in the Perturbative QCD factorization approach
• The NLO contributions to the scalar pion form factors and the $\mathcal{O}({\alpha }_s^2)$ annihilation corrections to the $B\to \pi \pi$ decays
• Nonleptonic decays of $B\to (f_1(1285),f_1(1420))V$ in the perturbative QCD approach
• ${\bar{B}}_s^0\to ({\pi }^0{\eta }^{(\ast )},{\eta }^{(\ast )}{\eta }^{(\ast )})$ decays and the effects of next-to-leading order contributions in the perturbative QCD approach
• Perturbative QCD Analysis of Exclusive Processes $e^{+}{e}^{-}\to VP$ and $e^{+}{e}^{-}\to TP$
• The perturbative QCD factorization of $\rho {\gamma }^{\star }\to \pi$
• Rapidity resummation for $B$-meson wave functions
• Reinvestigating the $B$ $\to$ $PV$ decays by including the contributions from ${\varphi }_{B2}$ with the perturbative QCD approach
• Determination of pion distribution amplitudes from the electromagnetic form factor with the data-driven dispersion relation
• Perturbative QCD analysis of neutral $B$-meson decays into $\sigma \sigma ,\sigma f_0$ and $f_0{f}_0$
• The perturbative QCD factorization of $\rho {\gamma }^{\star }\to \rho$
• Non-dipolar gauge links for transverse-momentum-dependent pion wave functions
• $B_{(s)}\to {\eta }_c(P,V)$ decays and effects of the next-to-leading order contributions in the perturbative QCD approach
• $B_{d,s}^0\to f_1{f}_1$ decays with $f_1(1285)-f_1(1420)$ mixing in the perturbative QCD approach
• Anatomy of $B_s\to PP$ decays and effects of the next-to-leading order contributions in the perturbative QCD approach
• Charmless hadronic $B\to (f_1(1285),f_1(1420))P$ decays in the perturbative QCD approach
• The next-to-leading order corrections to $B\to \rho$ transition in the $k_T$ factorization
• Revisiting $B_s\to PP$ and $PV$ Decays with Contributions from ${\varphi }_{B2}$ with perturbativen QCD approach
• Searching a systematics for nonfactorizable contribution to B-and B0 mesons
• P wave mesons emitting weak decays of bottom mesons
• The semileptonic decays of $B/B_s$ meson in the perturbative QCD approach: A short review
• Constrain the UT angle $\gamma$ by CP violation parameters in $B^0\to {\pi }^{+}{\pi }^{-}$
• Study of Form Factors and Observables in $B_c^{-}\to {\bar{D}}^{(\ast )0}{\ell }^{-}{\bar{\nu }}_{\ell }$ and $B_c^{-}\to D^{(\ast )-}{\ell }^{+}{\ell }^{-}$ decays
• Next-to-leading-order QCD calculations of $B\to A$ form factors with higher-twist corrections