Heavy-to-light transitions on the light cone Zheng-Tao Wei Nankai University Introduction Heavy-to-light form factors Light cone QCD Soft form factors in LC approach Summary 2019/4/10

I. Introduction B physics had been entered into an exciting era → precision flavor physics. CKM angles sin2β=0.687+/-0.032; α=(99+13-8)o; γ=(63+15-12)o Direct CP violation ACP(K+ π-)= -0.108+/-0.017 B->VV polarization puzzle B->ΦK* 2019/4/10

The importance of heavy-to-light form factors in B physics phenomenology: CKM parameter Vub, QCD, perturbative, non-perturbative basic parameters for exclusive decays in QCDF or SCET new physics, 2019/4/10

The study of the heavy-to-light form factors has been a long history. mb The QCD dynamics is complicated: (1) many scales: mb, , ΛQCD; (2) confinement: non-perturbative ΛQCD 2019/4/10

Light cone dominance Light cone vectors close to the light cone. At large recoil region q2<<mb, the light meson moves close to the light cone. 2019/4/10

II. Heavy-to-light form factors Definition 2019/4/10

Hard scattering mechanism Hard gluon exchange: soft spectator quark → collinear quark Perturbative QCD is applicable. 2019/4/10

Endpoint singularity IR divergence ∫01dx/x endpoint singularity Factorization of pertubative contributions from the non-perturbative part is invalid. The soft contribution coming from the endpoint region is necessary. 2019/4/10

PQCD approach Sudakov double logarithm corrections are included. with The transverse momentum are retained, so no endpoint singularity. Sudakov double logarithm corrections are included. with Sudakov factor 2019/4/10

Sudakov suppression effect is about 10-20%. 2019/4/10

Soft mechanism One parton momentum in the light meson is soft. The form factor is dominated by soft interactions. Methods: light cone sum rules, light cone quark model… 2019/4/10

Spin symmetry for soft form factor 2019/4/10

In the large energy limit, The total 10 form factors are reduced to 3 independent factors. There is no flavor symmetry for light mesons. 3→1 impossible! 2019/4/10

Definition 2019/4/10

QCDF and SCET In the heavy quark limit, to all orders of αs and leading order in 1/mb, Sudakov corrections Soft form factors, with singularity and Spin symmetry Perturbative, no singularity The factorization proof is more rigorous than others. The hard contribution ~ (Λ/mb)3/2, soft form factor ~ (Λ/m b)2/3 (?) About the soft form factors, study continues, such as zero-bin method… 2019/4/10

Zero-bin method by Stewart and Manohar (hep-ph/0605001) The soft component of light meson is contained in SCET time-ordered products from collinear fields. ( complete? ) A collinear quark have non-zero energy. The zero-bin contributions should be subtracted out. After subtracting the zero-bin contributions, the remained is finite and can be factorizable. For example, 2019/4/10

III. LC perturbation theory Why light cone framework? The Lagrangian theory is not suitable to describe the bound states. For a relativistic Hamiltonian system, the definition of time is not unique. There are three forms. The LC framework is the most possible way to understand the non-relativistic quark model. Now, most people prefer to use the covariant form. In history, QCD (by Gell-Mann and Fritzsch) and perturbative QCD for exclusive processes (by Brodsky and Lepage) were proposed in the LC form. 2019/4/10

Dirac’s three forms of Hamiltonian dynamics 2019/4/10

LC Fock space expansion LC wave functions LC wave function is the central element in LCQCD. It depends only on the intrinsic variables (xi, k┴i ). In principle, wave functions can be solved if we know the Hamiltonian (T+V). 2019/4/10

Advantage of LC framework LC Fock space expansion provides a convenient description of a hadron in terms of the fundamental quark and gluon degrees of freedom. The LC wave functions is Lorentz invariant. Ψ(xi, k┴i ) is independent of the bound state momentum. The vacuum state is simple, and trivial if no zero-modes. Only dynamical degrees of freedom are remained. for quark: two-component ξ, for gluon: only transverse components A┴. Disadvantage In perturbation theory, LCQCD provides the equivalent results as the covariant form but in a complicated way. It’s difficult to solve the LC wave function from the first principle. 2019/4/10

Instantaneous interaction Kinetic Vertex LC Hamiltonian Instantaneous interaction LCQCD is the full theory compared to SCET. Physical gauge is used A+=0. 2019/4/10

LC time-ordered perturbation theory Diagram are LC time x+-ordered. (old-fashioned) Particles are on-shell. The three-momentum rather than four- is conserved in each vertex. For each internal particle, there are dynamic and instantaneous lines. 2019/4/10

Perturbative contributions: Instantaneous, no singularity break spin symmetry have singularity, conserve spin symmetry Perturbative contributions: Only instantaneous interaction in the quark propagator. The exchanged gluons are transverse polarized. 2019/4/10

III. Soft form factors in LC quark model Soft overlap mechanism The form factor is represented by the convolution of initial and final hadron wave functions. 2019/4/10

Basic assumptions of LC quark model Valence quark contribution dominates. The quark mass is the constitute mass. Constituent quark mass: 2019/4/10

Melosh rotation 2019/4/10

Decay constants 2019/4/10

Form factors 2019/4/10

Power law: ξ(q2)~exp(-ΛQCD/mb) Choose Gaussian-type Power law: ξ(q2)~exp(-ΛQCD/mb) The scaling of the soft form factor depends on the light meson wave function at the endpoint. Only the precise knowledge of the wave function at long distance can solve it. 2019/4/10

Numerical results 2019/4/10

Comparisons with other approaches The predictions of V and A0 in LCSR are larger than other results. 2019/4/10

Summary The heavy-to-light form factors reveal rich QCD dynamics. LC quark model is an appropriate non-perturbative method to study the heavy-to-light form factors. 2019/4/10