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Hsiang-nan Li

Publications and source records attributed to Hsiang-nan Li.

At least 91 records · Page 5Linked to original sources
arXiv2013

Resummation of rapidity logarithms in $B$ meson wave functions

We construct an evolution equation for the $B$ meson wave functions in the $k_T$ factorization theorem, whose solutions sum the double logarithms associated with the light-cone singularities, namely, the rapidity logarithms. The derivation is subtler than that of the Sudakov resummation for an energetic light hadron, due to the involvement of the effective heavy-quark field. The renormalization-group evolution in the factorization scale needs to be included in order to derive an ultraviolet-finite and scale-invariant kernel for resumming the rapidity logarithms. It is observed that this kernel is similar to that of the joint resummation for QCD processes in extreme kinematic regions, which combines the threshold and $k_T$ resummations. We show that the resummation effect maintains the normalization of the $B$ meson wave functions, and strengths their convergent behavior at small spectator momentum. The resummation improved $B$ meson wave functions are then employed in the leading-order analysis of the $B\toπ$ transition form factors, which lead to approximately 25% deduction in the large recoil region.

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arXiv2012

Branching ratios and direct CP asymmetries in $D\to PP$ decays

We propose a theoretical framework for analyzing two-body nonleptonic $D$ meson decays, based on the factorization of short-distance (long-distance) dynamics into Wilson coefficients (hadronic matrix elements of four-fermion operators). The parametrization of hadronic matrix elements in terms of several nonperturbative quantities is demonstrated for the $D\to PP$ decays, $P$ denoting a pseudoscalar meson. We consider the evolution of Wilson coefficients with energy release in individual decay modes, and the Glauber strong phase associated with the pion in nonfactorizable annihilation amplitudes, that is attributed to the unique role of the pion as a Nambu-Goldstone boson and a quark-anti-quark bound state simultaneously. The above inputs improve the global fit to the branching ratios involving the $η'$ meson, and resolves the long-standing puzzle from the $D^0\toπ^+π^-$ and $D^0\to K^+K^-$ branching ratios, respectively. Combining short-distance dynamics associated with penguin operators and the hadronic parameters determined from the global fit to branching ratios, we predict direct CP asymmetries, to which the quark loops and the scalar penguin annihilation give dominant contributions. In particular, we predict $ΔA_{\rm CP}\equiv A_{\rm CP}(K^+K^-)-A_{\rm CP}(π^+π^-)=-1.00\times 10^{-3}$, lower than the LHCb and CDF data.

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arXiv2012

Implications on $η$-$η'$-glueball mixing from $B_{d/s} \to J/Ψη^{(')}$ Decays

We point out that the recent Belle measurements of the $B_{d/s} \to J/Ψη^{(')}$ decays imply large pseudoscalar glueball contents in the $η^{(\prime)}$ meson. These decays are studied in the perturbative QCD (PQCD) approach, considering the $η$-$η'$-$G$ mixing, where $G$ represents the pseudoscalar glueball. It is shown that the PQCD predictions for the $B_{d/s} \to J/Ψη^{(')}$ branching ratios agree well with the data for the mixing angle $ϕ_G\approx 30^\circ$ between the flavor-singlet state and the pure pseudoscalar glueball. Extending the formalism to the $η$-$η'$-$G$-$η_c$ tetramixing, the abnormally large observed $B_d\to Kη'$ branching ratios are also explained. The proposed mixing formalism is applicable to other heavy meson decays into $η^{(\prime)}$ mesons, and could be tested by future LHCb and Super-$B$ factory data.

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arXiv2012

Next-to-leading-order corrections to $B \to π$ form factors in $k_T$ factorization

We calculate next-to-leading-order (NLO) corrections to the $B\toπ$ transition form factors at leading twist in the $k_T$ factorization theorem. Light partons off-shell by $k_T^2$ are considered in the quark diagrams, in the effective diagrams for the $B$ meson wave function defined with the effective heavy-quark field, and in the effective diagrams for the pion wave function. It is explicitly demonstrated that the infrared logarithms $\ln k_T^2$ cancel between the above sets of diagrams, as deriving the $k_T$-dependent NLO hard kernel from their difference. The infrared finiteness of the hard kernel confirms the application of the $k_T$ factorization theorem to $B$ meson semileptonic decays. The NLO pion wave function is identical to those constructed from the pion transition and electromagnetic form factors, consistent with its universality. Choosing the renormalization and factorization scales lower than the $B$ meson mass, the NLO corrections are under control: they amount only up to 30% of the form factors at large recoil of the pion, when varying models for the meson wave functions.

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arXiv2012

$η_c$ mixing effects on charmonium and $B$ meson decays

We include the $η_c$ meson into the $η$-$η'$-$G$ mixing formalism constructed in our previous work, where $G$ represents the pseudoscalar gluball. The mixing angles in this tetramixing matrix are constrained by theoretical and experimental implications from relevant hadronic processes. Especially, the angle between $η_c$ and $G$ is found to be about $11^\circ$ from the measured decay widths of the $η_c$ meson. The pseudoscalar glueball mass $m_G$, the pseudoscalar densities $m_{qq,ss,cc}$ and the U(1) anomaly matrix elements associated with the mixed states are solved from the anomalous Ward identities. The solution $m_G\approx 1.4$ GeV obtained from the $η$-$η'$-$G$ mixing is confirmed, while $m_{qq}$ grows to above the pion mass, and thus increases perturbative QCD predictions for the branching ratios $Br(B\toη'K)$. We then analyze the $η_c$-mixing effects on charmonium magnetic dipole transitions, and on the $B\toη^{(\prime)}K_S$ branching ratios and CP asymmetries, which further improve the consistency between theoretical predictions and data. A predominant observation is that the $η_c$ mixing enhances the perturbative QCD predictions for $Br(B\toη'K)$ by 18%, but does not alter those for $Br(B\toηK)$. The puzzle due to the large $Br(B\toη'K)$ data is then resolved.

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arXiv2011

Three-parton contribution to the $B\toπ$ form factors in $k_T$ factorization

We calculate the three-parton twist-3 contribution to the $B\toπ$ transition form factors in the $k_T$ factorization theorem. Since different mesons are involved in the initial and final states, two(three)-parton-to-three(two)-parton amplitudes do not vanish. It is found that the dominant contribution arises from the diagrams with the additional valence gluon attaching to the leading-order hard gluon. Employing the three-parton meson distribution amplitudes from QCD sum rules, we show that this subleading piece amounts only up to few percents of the form factors at large recoil of the pion. The framework for analyzing three-parton contributions to $B$ meson decays in the $k_T$ factorization is established.

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arXiv2011

QCD resummation for jet substructures

We provide a novel development in jet physics by predicting the energy profiles of light-quark and gluon jets in the framework of perturbative QCD. Resumming large logarithmic contributions to all orders in the coupling constant, our predictions are shown to agree well with Tevatron CDF and Large-Hadron-Collider CMS data. We also extend our resummation formalism to the invariant mass distributions of light-quark and gluon jets produced in hadron collisions. The predicted peak positions and heights in jet mass distributions are consistent with CDF data within uncertainties induced by parton distribution functions.

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arXiv2011

Three-parton contribution to pion form factor in kT factorization

We set up a framework for the study of the power-suppressed three-parton contribution to the pion electromagnetic form factor in the $k_T$ factorization theorem. It is first shown that the gauge dependence proportional to parton transverse momenta from the two-parton Fock state and the gauge dependence associated with the three-parton Fock state cancel each other. After verifying the gauge invariance, we derive the three-parton-to-three-parton $k_T$-dependent hard kernel at leading order of the coupling constant, and find that it leads to about 5% correction to the pion electromagnetic form factor in the whole range of experimentally accessible momentum transfer squared. This subleading contribution is much smaller than the leading-order twist-2, next-to-leading-order twist-2 and leading-order two-parton twist-3 ones, which have been calculated in the literature.

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arXiv2011

Restoration of $k_T$ factorization for low $p_T$ hadron hadroproduction

We discuss the applicability of the $k_T$ factorization theorem to low-$p_T$ hadron production in hadron-hadron collision in a simple toy model, which involves only scalar particles and gluons. It has been shown that the $k_T$ factorization for high-$p_T$ hadron hadroproduction is broken by soft gluons in the Glauber region, which are exchanged among a transverse-momentum-dependent (TMD) parton density and other subprocesses of the collision. We explain that the contour of a loop momentum can be deformed away from the Glauber region at low $p_T$, so the above residual infrared divergence is factorized by means of the standard eikonal approximation. The $k_T$ factorization is then restored in the sense that a TMD parton density maintains its universality. Because the resultant Glauber factor is independent of hadron flavors, experimental constraints on its behavior are possible. The $k_T$ factorization can also be restored for the transverse single-spin asymmetry in hadron-hadron collision at low $p_T$ in a similar way, with the residual infrared divergence being factorized into the same Glauber factor.

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arXiv2011

Nonlocal Condensate Model for QCD Sum Rules

We include effects of nonlocal quark condensates into QCD sum rules (QSR) via the K$\ddot{\mathrm{a}}$ll$\acute{\mathrm{e}}$n-Lehmann representation for a dressed fermion propagator, in which a negative spectral density function manifests their nonperturbative nature. Applying our formalism to the pion form factor as an example, QSR results are in good agreement with data for momentum transfer squared up to $Q^2 \approx 10 $ GeV$^2$. It is observed that the nonlocal quark condensate contribution descends like $1/Q^2$, different from the exponential decrease in $Q^2$ obtained in the literature, and contrary to the linear rise in the local-condensate approximation.

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arXiv2011

Next-to-leading-order correction to pion form factor in $k_T$ factorization

We calculate next-to-leading-order (NLO) correction to the pion electromagnetic form factor at leading twist in the $k_T$ factorization theorem. Partons off-shell by $k_T^2$ are considered in both quark diagrams and effective diagrams for the transverse-momentum-dependent (TMD) pion wave function. The light-cone singularities in the TMD pion wave function are regularized by rotating the Wilson lines away from the light cone. The soft divergences from gluon exchanges among initial- and final-state partons cancel exactly. We derive the infrared-finite $k_T$-dependent NLO hard kernel for the pion electromagnetic form factor by taking the difference of the above two sets of diagrams. Varying the renormalization and factorization scales, we find that the NLO correction is smaller, when both the scales are set to the invariant masses of internal particles: it becomes lower than 40% of the leading-order (LO) contribution for momentum transfer squared $Q^2>7$ GeV$^2$. It is observed that the NLO leading-twist correction does not play an essential role in explaining the experimental data, but the LO higher-twist contribution does.

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arXiv2011

Possible resolution of the B -> pi pi, pi K puzzles

We show that there exist uncanceled soft divergences in the k_T factorization for nonfactorizable amplitudes of two-body nonleptonic B meson decays, similar to those identified in hadron hadroproduction. These divergences can be grouped into a soft factor using the eikonal approximation, which is then treated as an additional nonperturbative input in the perturbative QCD formalism. Viewing the special role of the pion as a q-qbar bound state and as a pseudo Nambu-Goldstone boson, we postulate that the soft effect associated with it is significant. This soft factor enhances the nonfactorizable color-suppressed tree amplitudes, such that the branching ratios B(pi^0 pi^0) and B(pi^0 rho^0) are increased under the constraint of the B(rho^0 rho^0) data, the difference between the direct CP asymmetries A_{CP}(pi^\mp K^\pm) and A_{CP}(pi^0 K^\pm) is enlarged, and the mixing-induced CP asymmetry S_{pi^0 K_S} is reduced. Namely, the known pi pi and pi K puzzles can be resolved simultaneously.

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arXiv2010

Comment on "Nonuniversality of Transverse Momentum Dependent Parton Distributions at Small x"

We point out that the analysis in arXiv:1003.0482 actually verifies the universality of transverse momentum dependent quark distributions at small $x$, which supports the observation in our earlier work arXiv:0904.4150. Once the gluon exchanges responsible for the additional infrared divergences are factorized and summed into an exponential factor, it can be expressed as a matrix element of Wilson line operators, and treated as a nonperturbative input to the $k_T$ factorization of $pA$ collisions. The same exponential factor has been extracted from $pp$ collisions in arXiv:0904.4150, rendering possible experimental constraints on its behavior from $pp$ processes, and predictions for $pA$ processes.

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arXiv2009

General Theoretical Introduction to Hadronic $B$ Decays

I briefly introduce the theoretical frameworks for studies of two-body hadronic $B$ meson decays, which include the factorization assumption, the QCD-improved factorization, the perturbative QCD, the soft-collinear effective theory, the light-cone QCD sum rules, and the quark-diagram parametrization.

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arXiv2009

Pion transition form factor in k_T factorization

It has been pointed out that the recent BaBar data on the pi gamma^* -> gamma transition form factor F_{pi gamma}(Q^2) at low (high) momentum transfer squared Q^2 indicate an asymptotic (flat) pion distribution amplitude. These seemingly contradictory observations can be reconciled in the k_T factorization theorem: the increase of the measured Q^2F_{pi gamma}(Q^2) for Q^2 > 10 GeV^2 is explained by convoluting a k_T dependent hard kernel with a flat pion distribution amplitude, k_T being a parton transverse momentum. The low Q^2 data are accommodated by including the resummation of alpha_s ln^2x, x being a parton momentum fraction, which provides a stronger suppression at the endpoints of x. The next-to-leading-order correction to the pion transition form factor is found to be less than 20% in the considered range of Q^2.

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arXiv2009

Comment on "Gauge Invariance and $k_T$-Factorization of Exclusive Processes"

We point out mistakes made in the one-loop calculation of some diagrams for the process $πγ^* \to γ$ in the preprint arXiv:0807.0296, and present correct results. Especially, we have difficulty to understand their argument that a highly off-shell gluon generates a light-cone (infrared) singularity. It is shown by means of the Ward identity that the gauge-dependent light-cone singularity found in arXiv:0807.0296 does not exist. It is then shown that a hard kernel derived in the $k_T$ factorization of exclusive processes is gauge invariant and free of the light-cone singularity.

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arXiv2009

Pseudoscalar glueball mass from $η$-$η'$-$G$ mixing

We deduce the mass of the pseudoscalar glueball $G$ from an $η$-$η'$-$G$ mixing formalism based on the anomalous Ward identity for transition matrix elements. With the inputs from the recent KLOE experiment, we find a solution for the pseudoscalar glueball mass around $(1.4\pm 0.1)$ GeV, which is fairly insensitive to a range of inputs with or without Okubo-Zweig-Iizuka-rule violating effects. This affirms that $η(1405)$, having a large production rate in the radiative $J/Ψ$ decay and not seen in $γγ$ reactions, is indeed a leading candidate for the pseudoscalar glueball. Other relevant quantities including the anomaly and pseudoscalar density matrix elements are obtained. The decay widths for $G\to γγ$, $\ell^+\ell^-$ are also predicted.

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