arXiv subjects
Publications and source records attributed to Hsiang-nan Li.
I review important aspects of the perturbative QCD approach to exclusive $B$ meson decays, concentrating on factorization theorem, gauge invariance, end-point singularities, $k_T$ and threshold resummations, power counting, penguin enhancement, and CP asymmetries.
I review theoretical progresses on $B$ physics and CP violation which were made in Taiwan recently. I concentrate on the approaches to exclusive $B$ meson decays based on factorization assumption, SU(3) symmetry, perturbative QCD factorization theorem, QCD factorization, and light-front QCD formalism.
We evaluate $B\to Kπ$ decay amplitudes in perturbative QCD picture. It is found that penguin contributions are dynamically enhanced by nearly 50% compared to those assumed in the factorization approximation. It is also shown that annihilation diagrams are not negligible, and give large strong phases. Our results for branching ratios of $B\to Kπ$ decays for a representative parameter set are consistent with data. We evaluate $B\to Kπ$ decay amplitudes in perturbative QCD picture. It is found that penguin contributions are dynamically enhanced by nearly 50% compared to those assumed in the factorization approximation. It is also shown that annihilation diagrams are not negligible, and give large strong phases. Our results for branching ratios of $B\to Kπ$ decays for a representative parameter set are consistent with data.
We predict branching ratios and CP asymmetries of the $B\to KK$ decays using perturbative QCD factorization theorem, in which tree, penguin, and annihilation contributions, including both factorizable and nonfactorizable ones, are expressed as convolutions of hard six-quark amplitudes with universal meson wave functions. The unitarity angle $ϕ_3= 90^o$ and the $B$ and $K$ meson wave functions extracted from experimental data of the $B\to Kπ$ and $ππ$ decays are employed. Since the $B\to KK$ decays are sensitive to final-state-interaction effects, the comparision of our predictions with future data can test the neglect of these effects in the above formalism. The CP asymmetry in the $B^\pm\to K^\pm K^0$ modes and the $B_d^0\to K^\pm K^\mp$ branching ratios depend on annihilation and nonfactorizable amplitudes. The $B\to KK$ data can also verify the evaluation of these contributions.
We study the polarized $Λ_b$ baryon semileptonic decay $Λ_b \to Λ_cl{\barν}$ using perturbative QCD factorization theorem. In this approach heavy baryon transition form factors are expressed as the convolutions of hard $b$ quark decay amplitudes with universal $Λ_b$ and $Λ_c$ baryon wave functions. With the heavy baryon wave functions determined in our previous work, we predict the asymmetry parameter $α({\hat e})\equiv (N_+-N_-)/(N_++N_-)=-0.31 {\bf P}\cdot{\hat e}$, where ${\bf P}$ is the $Λ_b$ baryon polarization, ${\hat e}$ a unit vector perpendicular to the $Λ_b$ baryon momentum, $N_+$ ($N_-$) the number of leptons whose momenta possess positive (negative) components along ${\hat e}$. This result is useful for extracting the transverse polarization of a $Λ_b$ baryon from data of exclusive semileptonic decays.
We compare the factorization approach, the perturbative QCD approach and the Beneke-Buchalla-Neubert-Sachrajda approach to nonleptonic charmless $B$ meson decays. We discuss their treatments of factorizable, nonfactorizable, and annihilation contributions, infrared-cutoff and scale dependences, and strong phases. It is proposed that measurement of CP asymmetries in two-body $B$ meson decays provides an appropriate test of the these approaches.
We develop perturbative QCD factorization theorem for the semileptonic heavy baryon decay $Λ_b \to Λ_c l\barν$, whose form factors are expressed as the convolutions of hard $b$ quark decay amplitudes with universal $Λ_b$ and $Λ_c$ baryon wave functions. Large logarithmic corrections are organized to all orders by the Sudakov resummation, which renders perturbative expansions more reliable. It is observed that perturbative QCD is applicable to $Λ_b \to Λ_c$ decays for velocity transfer greater than 1.2. Under requirement of heavy quark symmetry, we predict the branching ratio $B(Λ_b \to Λ_c l{\barν})\sim 2%$, and determine the $Λ_b$ and $Λ_c$ baryon wave functions.
We propose a new unified evolution equation for parton distribution functions appropriate for both large and small Bjorken variables $x$, which is an improved version of the Ciafaloni-Catani-Fiorani-Marchesini equation. In this new equation the cancellation of soft divergences between virtual and real gluon emissions is explicit without introducing infrared cutoffs, next-to-leading contributions to the Sudakov resummation can be included systematically. It is shown that the new equation reduces to the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi equation at large $x$, to the Balitsky-Fadin-Kuraev-Lipatov (BFKL) equation at small $x$, and to the modified BFKL equations with a dependence on momentum transfer $Q$ and with unitarity, if hard virtual gluon contributions and correction to strong rapidity ordering are retained, respectively.
We review the current status of perturbative QCD calculation of hadronic electromagnetic form factors.
We demonstrate that both the $k_T$ and threshold resummations can be performed in the Collins-Soper resummation formalism by evaluating soft gluon emissions with infrared cutoffs for the longitudinal and transverse loop momenta, respectively. The reason the $k_T$ resummation for a parton distribution function leads to suppression in the large $b$ region, $b$ being the conjugate variable of parton transverse momentum $k_T$, and the threshold resummation leads to enhancement in the large $N$ limit, $N$ being the moment of a distribution function, is a consequence of opposite directions of double-logarithm evolutions. The $k_T$ and threshold resummations for an energetic final-state jet give suppression. The switch of the threshold resummation from enhancement to suppression is attributed to a nonvanishing jet invariant mass. In the same framework we derive a unification of the $k_T$ and threshold resummations for a parton distribution function by requiring infrared cutoffs for both longitudinal and transverse loop momenta. This unified resummation exhibits suppression at large $b$, similar to the $k_T$ resummation, and exhibits enhancement at small $b$, similar to the threshold resummation.
We investigate effects of threshold resummation of logarithmic corrections $\ln N$ in Mellin space quantitatively. Threshold resummation leads to enhancement of next-to-leading-order QCD predictions for jet production at large jet transverse energy, which is in the trend indicated by experimental data. We show that this enhancement is completely determined by the behavior of threshold resummation at small $N$, the region where hierachy among different powers of $\ln N$ is lost and current next-to-leading-logarithm resummation is not reliable. Our analysis indicates that more accurate threshold resummation formalism should be developed in order to obtain convincing predictions.
We extract the B, D, and D* meson wave functions from the CLEO data of the decays B -> K*γand B -> D^(*)πin the perturbative QCD framework. In this formalism, various logarithmic corrections are organized to give the Wilson evolution from the W boson mass down to the characteristic scale of a decay process, which is of order of the b quark mass, and the Sudakov evolution from the characteristic scale to a lower factorization scale of order Lambda_{QCD}. With large logarithms organized, the b quark decay amplitudes are evaluated reliably in perturbation theory. Below the factorization scale, QCD dynamics is regarded as being nonperturbative, and absorbed into meson wave functions. Because of their universality, the heavy-meson wave functions determined in this work, can be employed to make predictions of other decay modes. We also observe that the dependence of heavy meson wave functions on intrinsic parton transverse momenta plays an important role in the explanation of data.
We show that the controversies on the gauge dependence and the infrared singularity emerged in the generalized factorization approach for nonleptonic heavy meson decays within the framework of the operator product expansion can be resolved by perturbative QCD factorization theorem. Gauge invariance of the decay amplitude is maintained under radiative corrections by assuming on-shell external quarks. For on-shell external quarks, infrared poles in radiative corrections have to be extracted using the dimensional regularization. These poles, signifying nonperturbative dynamics of a decay process, are absorbed into bound-state wave functions. Various large logarithms produced in radiative corrections are summed to all orders into the Wilson and Sudakov evolution factors. The remaining finite part gives a hard subamplitude. A decay rate is then factorized into a convolution of the hard subamplitude, the Wilson coefficient, and the Sudakov factor with the bound-state wave functions, all of which are well-defined and gauge invariant.
We apply the perturbative QCD factorization theorem developed recently for nonleptonic heavy meson decays to the radiative decay $B\to K^*γ$. In this formalism the evolution of the Wilson coefficients from the $W$ boson mass down to the characteristic scale of the decay process is governed by the effective weak Hamiltonian. The evolution from the characteristic scale to a lower hadronic scale is formulated by the Sudakov resummation. Besides computing the dominant contribution arising from the magnetic-penguin operator $O_7$, we also calculate the contributions of four-quark operators. By fitting our prediction for the branching ratio of the $B\to K^*γ$ decay to the CLEO data, we determine the $B$ meson wave function, that possesses a sharp peak at a low momentum fraction.
We develop perturbative QCD factorization theorems for inclusive b-hadron decays, in which radiative corrections characterized by the hadronic scale, the b-hadron mass, and the W boson mass are absorbed into a heavy hadron distribution function, a hard b quark decay amplitude, and a "harder" function, respectively. Double logarithmic corrections associated with a light energetic final-state quark, which appear at kinematic end points, are absorbed into a jet function. Various large logarithms contained in the above functions are summed to all orders, leading to the evolution factors among the three characteristic scales. The heavy hadron distribution function is identical to the one constructed in the framework of heavy quark effective theory. It is shown that hadron kinematics must be employed in factorization theorems, and that perturbative contributions, depending on hadron kinematics, distinguish the lifetimes of the b-hadrons $B_d, B_s$ and $Λ_b$. Assuming the same heavy-quark-effective-theory parametesr $λ_1$ for these hadrons, we predict the lifetimes $τ(B_d)=1.56$ ps, $τ(B_s)=1.46$ ps and $τ(Λ_b)=1.22$ ps. We also predict the $B_u$ meson lifetime $τ(B_u)=1.62$ ps by varying the B meson distribution function slightly. All the above results are consistent with experimental data.
The perturbative QCD formalism for exclusive heavy meson decays, especially the three-scale factorization theorem for nonleptonic modes is reviewed and compared to the conventional Bauer-Stech-Wirbel model.
We demonstrate that all the known single- and double-logarithm summations for a parton distribution function can be unified in the Collins-Soper resummation technique by applying soft approximations appropriate in different kinematic regions to real gluon emissions. Neglecting the gluon longitudinal momentum, we obtain the $k_T$ (double-logarithm) resummation for two-scale QCD processes, and the Balitsky-Fadin-Kuraev-Lipatov (single-logarithm) equation for one-scale processes. Neglecting the transverse momentum, we obtain the threshold (double-logarithm) resummation for two-scale processes, and the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (single-logarithm) equation for one-scale processes. If keeping the longitudinal and transverse momenta simultaneously, we derive a unified resummation for large Bjorken variable $x$, and a unified evolution equation appropriate for both intermediate and small $x$.
We apply perturbative QCD factorization theorems to inclusive heavy hadron decays, and obtain simultaneously a low semileptonic branching ratio $B(B\to Xl\barν)=10.16%$, the average charm yield $ =1.17$ per $B$ decay, a small lifetime ratio $τ(Λ_b)/τ(B_d)=0.78$, and the correct absolute decay widths of the $B$ meson and of the $Λ_b$ baryon.