arXiv subjects
Publications and source records attributed to Hsiang-nan Li.
We combine the resummations for radiative corrections and for the heavy quark expansion to study the inclusive radiative decay $B \to X_sγ$. The infrared renormalon ambiguity is also taken into account. Including both theoretical and experimental uncertainties, we determine the allowed domain for the HQET parameters ${\bar Λ}$ and $λ_1$ centered at ${\bar Λ}=0.65$ GeV and $λ_1=-0.71$ GeV$^2$.
We propose a unified and simple viewpoint to various evolution equations appropriate in different kinematic regions. We show that the resummation technique reduces to the Altarelli-Parisi equation, if the transverse degrees of freedom of a parton are ignored, to the Balitskii-Fadin-Kuraev-Lipatov equation, if the momentum fraction of a parton vanishes, and to the Gribov-Levin-Ryskin equation, if the recombination of gluons is included.
We develop a perturbative QCD factorization theorem which is compatible with effective field theory. The factorization involves three scales: an infrared cutoff of order $Λ_{\rm QCD}$, a hard scale of order the $B$ meson mass, and an ultraviolet cutoff of order the $W$ boson mass. Our approach is renormalization group invariant and moderates the scale-dependence problem in effective field theory. Applying this formalism to exclusive nonleptonic $B$ meson decays, we clarify the controversy over the Bauer-Stech-Wirbel parameters $a_2/a_1$ for charm and bottom decays. It is found that the nonfactorizable contribution plays an important role in the explanation of the sign and magnitude of $a_2/a_1$.
We show that the resummation of large radiative corrections in QCD processes can be performed both in covariant gauge and in axial gauge. We extend the resummation technique to inclusive processes, concentrating on deeply inelastic scattering, Drell-Yan production, and inclusive heavy meson decays in end-point regions. Leading and next-to-leading logarithms produced by radiative corrections are organized into Sudakov factors, whose expressions are the same as those derived from the conventional Wilson-loop approach. The gauge invariance of the resummation in the end-point region is demonstrated explicitly.
We evaluate external $W$-emission, internal $W$-emission and $W$-exchange contributions to nonleptonic $B\to D^{(*)}$ decays based on the perturbative QCD formalism including Sudakov effects, whose ratio is found to be $1:+0.2:0.03i$ at the amplitude level. We observe that the internal $W$-emission contribution is additive to the external $W$-emission contribution, and that the $W$-exchange contribution is negligible and mainly imaginary, its real part being at least one order of magnitude smaller than the imaginary part. Our predictions are consistent with the CLEO data and with those obtained by the Bauer-Stech-Wirbel method.
We develop the perturbative QCD formalism for inclusive semileptonic $B$ meson decays, which includes Sudakov suppression from the resummation of large radiative corrections near the high end of charged lepton energy. Transverse degrees of freedom of partons are introduced to facilitate the factorization of $B$ meson decays. Ambiguities appearing in the quark-level analysis are then avoided. A universal distribution function, arising from the nonperturbative Fermi motion of the $b$ quark, is constructed according to the heavy quark effective field theory based operator product expansion, through which the mean and the width of the distribution function are related to hadronic matrix elements of local operators. Charged lepton spectra of the $B\to X_u\ellν$ decay are presented. We find 50\% suppression near the end point of the spectrum. The overall suppression on the total decay rate is 8\% for the free quark model, and is less than 7\% for the use of smooth distribution functions. With our predictions, it is then possible to extract the Cabibbo-Kobayashi-Maskawa matrix element $|V_{ub}|$ from experimental data. We also discuss possible implications of our analysis when confronted with the rather small observed semileptonic branching ratio in $B$ meson decays.
We show that the resummation technique developed recently for heavy-light systems and the conventional approach based on the factorization of Wilson loops are equivalent. The two methods lead to the same results of the resummation of large corrections in inclusive $B$ meson decays.
We compute various form factors involved in $B\to D^{(*)}$ transitions based on the perturbative QCD formalism, which includes Sudakov effects from the resummation of large radiative corrections in a heavy-light system. A two-parameter model wave function for $D^{(*)}$ mesons is fixed using data of the nonleptonic decays $B\to D^{(*)}π$, from which the ratio of the decay constants $f_{D^*}/f_D=0.92$ is obtained. We then derive the spectrum of the semileptonic decay $B\to D^{*}\ellν$ in the fast recoil region of the $D^*$ meson, and extract the CKM matrix element $|V_{cb}|=0.043\times(0.12 {\rm GeV}/f_B)\times(0.14 {\rm GeV}/f_D)$, $f_B$ and $f_D$ being the $B$ and $D$ meson decay constants, respectively. Here we adopt the convention with the pion decay constant $f_π=93$ MeV. With these outcomes, we evaluate the decay rate of $B\to DD_s$, and estimate the ratio $f_{D_s}/f_D=0.98$ from data. Contributions of internal $W$-emission and $W$-exchange diagrams are briefly discussed.
We examine the applicability of perturbative QCD to $B$ meson decays into $D$ mesons. We find that the perturbative QCD formalism, which includes Sudakov effects at intermediate energy scales, is applicable to the semi-leptonic decay $B\to D lν$, when the $D$ meson recoils fast. Following this conclusion, we analyze the two-body non-leptonic decays $B\to Dπ$ and $B\to DD_s$. By comparing our predictions with experimental data, we extract the matrix element $|V_{cb}|=0.044$.
Resummation of large QCD radiative corrections, including leading and next-to-leading logarithms, in pion electromagnetic form factor is reviewed. Similar formalism is applied to exclusive processes involving heavy mesons, and leads to Sudakov suppression for the semi-leptonic decay $B\toπlν$. It is found that, with the inclusion of Sudakov effects, perturbative QCD analysis of this decay is possible for the energy fraction of the pion above 0.3. By combining predictions from the soft pion theorems, we estimate that the upper limit of the KM matrix element $|V_{ub}|$ is roughly 0.003.
We develop the perturbative QCD formalism including Sudakov effects for semi-leptonic $B$ meson decays. We evaluate the differential decay rate of $B\to πl ν$, and find that the perturbative calculation is reliable for the energy fraction of the pion above 0.3. Combining predictions from the soft pion theorems, we extract the value of the matrix element $|V_{ub}|$ which is roughly $2.7\times 10^{-3}$.
We investigate the transition to perturbative QCD in Compton processes, by concentrating on the specific reactions $πγ\to πγ$ and pion photoproduction at moderate energy scales. New sum rules for each of the helicities involved in the scattering and the cross section are given, together with a detailed stability analysis. Our results are then compared with those derived from higher-power factorization, incorporating Sudakov suppression for quark elastic scattering. An overlap of predictions obtained by the two approaches is observed at a momentum transfer as low as 4 GeV$^2$ and at a photon scattering angle around 40$^o$. Our work shows that factorization theorems and sum rule methods complement each other in the description of Compton scattering at moderate energy scales, and give information on the transition to perturbative QCD in these processes. The sum rule formalism is further applied to the crossed reaction $γγ\to π^+ π^-$, and is in very good agreement with the experimental data."
We perform a stability analysis of a recently proposed sum rule for pion Compton scattering at fixed angle and moderate Mandelstam invariants. The sum rule is found to be sensitive to the parameter $λ^2$, the contour radius of a generalized Borel transform. A modified phenomenological model for the continuum contribution is proposed to remove this dependence. It is shown that the best value of the quark-hadron duality interval $s_0=0.6$ GeV$^2$ is close to that in the form factor case ($s_0=0.7$ GeV$^2$). The application of this new model to the pion form factor is examined. A comparison of our predictions with those derived from a modified perturbative calculation including Sudakov suppression is also briefly considered.
We compare two approaches to the description of pion Compton scattering at moderate momentum transfer, one being based on local duality QCD sum rules for the invariant amplitudes of the process, which have been derived recently, and the other on the modified factorization formula with Sudakov effects included. We find that perturbative QCD predictions are dominant over those from QCD sum rules only for the scattering angle greater than 90$^o$.