In this paper we present a new derivation of the QCD factorization. We deduce the k_T- and collinear factorizations for the DIS structure functions by consecutive reductions of a more general theoretical construction. We begin by studying the amplitude of the forward Compton scattering off a hadron target, representing this amplitude as a set of convolutions of two blobs connected by the simplest, two-parton intermediate states. Each blob in the convolutions can contain both the perturbative and non-perturbative contributions. We formulate conditions for separating the perturbative and non-perturbative contributions and attributing them to the different blobs. After that the convolutions correspond to the QCD factorization. Then we reduce this totally unintegrated (basic) factorization first to the k_T- factorization and finally to the collinear factorization. In order to yield a finite expression for the Compton amplitude, the integration over the loop momentum in the basic factorization must be free of both ultraviolet and infrared singularities. This obvious mathematical requirement leads to theoretical restrictions on the non-perturbative contributions (parton distributions) to the Compton amplitude and the DIS structure functions related to the Compton amplitude through the Optical theorem. In particular, our analysis excludes the use of the singular factors x^{-a} (with a > 0) in the fits for the quark and gluon distributions because such factors contradict to the integrability of the basic convolutions for the Compton amplitude. This restriction is valid for all DIS structure functions in the framework of both the k_T- factorization and the collinear factorization if we attribute the perturbative contributions only to the upper blob.
In this paper, we firstly varify that the factorization hypothesis is valid for the exclusive process $ργ^{\star} \to π$ at the next-to-leading order (NLO) with the collinear factorization approach, and then extend this proof to the case of the $k_T$ factorization approach. We particularly show that at the NLO level, the soft divergences in the full quark level calculation could be canceled completely as for the $πγ^{\star} \to π$ process where only the pseudoscalar $π$ meson involved, and the remaining collinear divergences can be absorbed into the NLO hadron wave functions. The full amplitud…
I review the basic idea of $k_{\perp}$-factorization and its relation to collinear factorization. Theoretical results in resummed perturbation theory are summarized and the example of the heavy-flavour structure functions is explicitly considered. Using these results one can investigate the small-$x$ behaviour of quantities that are independent of the non-perturbative parton densities. In particular, one can introduce physical anomalous dimensions that relate the scaling violations in different hadronic observables.
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 show that both the k_T- and collinear factorization for the DIS structure functions can be obtained by consecutive reductions of the Compton scattering amplitude. Each of these reductions is an approximation valid under certain assumptions. In particular, the transitions to the k_T- factorization is possible when the virtualities of the partons connecting the perturbative and non-perturbative blobs are space-like. Then, if the parton distribution has a sharp maximum in k_T, the k_T factorization can be reduced to the collinear factorization.
In this paper, we study the $B \to D^{(*)} l^- \barν_{\rm l}$ semileptonic decays and calculate the branching ratios ${\cal B}(B \to D^{(*)} l^- \barν_{\rm l})$ and the ratios $R(D^{(*)})$ and $R_{\rm D}^{\rm l,τ}$ by employing the perturbative QCD (pQCD) factorization approach. We find that (a) for $R(D)$ and $R(D^*)$ ratios, the pQCD predictions are $R(D)=0.430^{+0.021}_{-0.026}$, $R(D^*)=0.301 \pm 0.013$ and agree well with BaBar's measurements of $R(D^{(*)})$; (b) for the newly defined $R_{\rm D}^{\rm l}$ and $R_{\rm D}^{\rm τ}$ ratios, the pQCD predictions are $R_{\rm D}^{\rm l} = 0.450^{…
We discuss factorization of the Dyson--Schwinger equations using the Lie- and Hopf algebra of graphs. The structure of those equations allows to introduce a commutative associative product on 1PI graphs. In scalar field theories, this product vanishes if and only if one of the factors vanishes. Gauge theories are more subtle: integrality relates to gauge symmetries.
Color transparency is a prediction of perturbative QCD. Yet detailed calculations have been lacking, and aspects of the required factorization have been controversial. We report on the first complete calculations entirely within a perturbative QCD framework. We also comment on the underlying factorization method and assumptions.
We define the collinear factorization scheme, which absorbs only the collinear physics into the parton distribution functions. In order to isolate the collinear physics, we introduce a procedure to combine real and virtual corrections, canceling infrared singularities prior to integration. In the collinear scheme, the factorization scale $μ$ has a simple physical interpretation as a collinear cutoff. We present a method for choosing the factorization scale and apply it to the Drell-Yan process; we find $μ\approx Q/2$, where $Q$ is the vector-boson invariant mass. We show that, for a wide varie…
The possibility of an improvement of current NLO Monte Carlo event generators by means of choosing a suitable factorization scheme is studied. The optimal factorization scheme for combining initial state parton showers and NLO hard scattering cross-sections is the ZERO factorization scheme, in which all NLO splitting functions vanish. However, it has turned out that the ZERO factorization scheme has a limited range of practical applicability. Hence, this paper is focused on searching for a factorization scheme which is applicable at the NLO in the full range of x relevant for QCD phenomenology…
Description of hadronic reactions at high energies is conventionally done on basis of QCD factoriza- tion so that factorization convolutions involve non-perturbative inputs mimicking non-perturbative contributions and perturbative evolution of those inputs. We construct the inputs for the gluon- hadron scattering amplitudes in the forward kinematics and, using the Optical theorem, convert them into inputs for gluon distributions in the both polarized and unpolarized hadrons. Firstly, we derive general mathematical criteria which any model for the inputs should obey and then suggest a Resonance…
Current all-orders proofs of factorization of hard processes are made by extracting the leading power behavior of Feynman graphs, i.e., by extracting asymptotics strictly order-by-order in perturbation theory. The resulting parton densities and fragmentation functions include non-perturbative effects. I show how there are missing elements in the proofs; these are related to and exemplified by string and cluster models of hadronization. The proofs rely on large rapidity differences between different parts of graphs for the process; but in reality large rapidity gaps are filled in
We use results for the structure functions $F_L$ for a gluon target having nonzero transverse momentum square at order $α_s$, obtained in our previous paper, to compare with recent H1 experimental data for $F_L$ at fixwd W values and with collinear GRV predictions at LO and NLO approximation.
In this paper, we studied the $ργ^* \to π$ and $ργ^*\to ρ$ transition processes and made the calculations for the $ρπ$ transition form factor $Q^4 F_{ρπ}(Q^2)$ and the $ρ$ meson electromagnetic form factors, $F_{\rm LL, LT,TT}(Q^2)$ and $F_{1,2,3}(Q^2)$, by employing the perturbative QCD (PQCD) factorization approach. For the $ργ^* \to π$ transition, we found that the contribution to form factor $Q^4 F_{ρπ}(Q)$ from the term proportional to the distribution amplitude combination $ϕ^T_ρ(x_1)ϕ^P_π(x_2)$ is absolutely dominant, and the PQCD predictions for both the size and the $Q^2$-dependence o…
In this paper we argue for existence of an intrinsic mass scale in QCD factorization and present a possible origin of it. Values of this scale are within the Non-Perturbative QCD mass range. It differs from the known factorization scale which is within the perturbative mass range and dependence on which vanishes in the factorization convolutions. We show that the intrinsic mass scale plays the key part in reduction of KT Factorization to Collinear Factorization: such a reduction can be done provided that dependence of the non-perturbative inputs in KT Factorization on invariant energy has a sh…
We prove a factorization theorem in QCD for the color suppressed decays B0-> D0 M0 and B0-> D*0 M0 where M is a light meson. Both the color-suppressed and W-exchange/annihilation amplitudes contribute at lowest order in LambdaQCD/Q where Q={mb, mc, Epi}, so no power suppression of annihilation contributions is found. A new mechanism is given for generating non-perturbative strong phases in the factorization framework. Model independent predictions that follow from our results include the equality of the B0 -> D0 M0 and B0 -> D*0 M0 rates, and equality of non-perturbative strong phases between …
The freedom associated with the definition of parton distribution functions is analyzed and formulae governing the dependence of parton distribution functions and hard scattering cross-sections on unphysical quantities associated with the renormalization and factorization procedure are derived. The issue of the specification of factorization schemes via the corresponding higher order splitting functions is discussed in detail. A numerical analysis of the practical applicability of the so called ZERO factorization scheme, which could be useful for the construction of consistent NLO Monte Carlo …
I discuss the systematic modifications to the perturbative QCD factorization approach in high energy l+A, p+A and A+A reactions. These include transverse momentum diffusion manifest in the Cronin effect and a small increase in the dijet acoplanarity; nuclear size enhanced power corrections that lead to shadowing in deeply inelastic scattering and suppression of single and double inclusive hadron production at forward rapidity at RHIC but disappear as a function of the transverse momentum; inelastic attenuation of the jet cross sections or jet quenching that persists to much higher pT.
We evaluate in the framework of QCD factorization the two-loop vertex corrections to the decays $\bar{B}_{(s)}\to D_{(s)}^{(\ast)+} \, L^-$ and $Λ_b \to Λ_c^+ \, L^-$, where $L$ is a light meson from the set $\{π,ρ,K^{(\ast)},a_1\}$. These decays are paradigms of the QCD factorization approach since only the colour-allowed tree amplitude contributes at leading power. Hence they are sensitive to the size of power corrections once their leading-power perturbative expansion is under control. Here we compute the two-loop ${\cal O}(α_s^2)$ correction to the leading-power hard scattering kernels, an…
We calculate the branching ratios and CP asymmetries of the $B\to ϕK$ decays using perturbative QCD approach, which includes $k_T$ and threshold resummations. Our results of branching ratios are consistent with the experimental data and larger than those obtained from the naive factorization assumption and the QCD-improved factorization approach.
We prove factorization theorem for the processes $πγ^*\toγ$ and $πγ^*\toπ$ to leading twist in the covariant gauge by means of the Ward identity. Soft divergences cancel and collinear divergences are grouped into a pion wave function defined by a nonlocal matrix element. The gauge invariance and universality of the pion wave function are confirmed. The proof is then extended to the exclusive $B$ meson decays $B\toγl\barν$ and $B\toπl\barν$ in the heavy quark limit. It is shown that a light-cone $B$ meson wave function, though absorbing soft dynamics, can be defined in an appropriate frame. Fac…
By employing the perturbative QCD (PQCD) factorization approach, we calculated the branching ratios, CP-violating asymmetries, the longitudinal and transverse polarization fractions and other physical observables of the thirteen charmless hadronic $\bar{B}^0_s \to V V $ decays with the inclusion of all currently known next-to-leading order (NLO) contributions. We focused on the examination of the effects of all those currently known NLO contributions and found that: (a) for the measured decays $\bar{ B}_s^0 \to ϕϕ, K^{*0} ϕ,\bar K^{*0} K^{*0}$ and $ρ^0 ϕ$, the NLO contributions can provide $\s…
I review the basics of the collinear factorization theorem applied primarily to deep inelastic scattering (DIS) involving forward parton distributions (PDFs) and the extensions of this theorem for exclusive processes probing non-forward parton distributions (GPDs), the generalized distribution amplitudes (GDAs) and the transition distribution amplitudes (TDAs). These QCD factorization theorem is an important tool in the description of hard processes in QCD. Whenever valid, it permits to represent the cross section or the scattering amplitude for such a process as a convolution in partonic mome…
We prove collinear factorization theorem for the process $πγ^*\toπ$ at the twist-3 level in the covariant gauge by means of the Ward identity, concentrating on the two-parton case. It is shown that soft divergences cancel and collinear divergences are grouped into the pseudo-scalar and pseudo-tensor two-parton twist-3 pion distribution amplitudes. The delicate summation of a complete set of diagrams for achieving factorization in momentum, spin, and color spaces is emphasized. The proof is then extended to the exclusive semileptonic decay $B\toπl\barν$, assuming the hard scale to be of $O(\sqr…
We present a factorization formula for valence quark distributions in a hadron in x-->1 limit. For the example of pion, we arrive at the form of factorization by analyzing momentum flow in the leading and high-order Feynman diagrams. The result confirms the well-known 1-x scaling rule to all orders in perturbation theory, providing the non-perturbative matrix elements for the infrared-divergence factors. We comment on re-summation of perturbative single and double logarithms in 1-x.
Reported is a factorization theorem for large-s behavior of total cross sections obtained in a straightforward fashion from ordinary perturbation theory. The theorem extends the standard factorization results for the Bjorken and Drell-Yan processes. The obtaining of useful evolution equations is found to be problematic. A by-product is a direct method for systematic calculations of the parton evolution kernels.
In the original Collins-Soper-Sterman (CSS) presentation of the results of transverse-momentum-dependent (TMD) factorization for the Drell-Yan process, results for perturbative coefficients can be obtained from calculations for collinear factorization. Here we show how to use these results, plus known results for the quark form factor, to obtain coefficients for TMD factorization in more recent formulations, e.g., that due to Collins, and apply them to known results at order $α_s^2$ and $α_s^3$. We also show that the "non-perturbative" functions as obtained from fits to data are equal in the t…
In this paper we firstly demonstrate step by step that the factorization hypothesis is valid at the next-to-leading order (NLO) for the exclusive process $ργ^{\star} \to ρ$ by employing the collinear factorization approach, and then extend this proof to the case of the $k_T$ factorization by taking into account the transversal momentum of the light external quark (anti-quark) lines in the $ρ$ meson. At the NLO level, we then show that the soft divergences from different sub-diagrams will be canceled each other in the quark level, while the remaining collinear divergences can be absorbed into t…
We study O(alpha^2 beta_0) perturbative corrections to matrix elements entering two-body exclusive decays of the form B -> pi pi, pi K in the QCD factorization formalism, including chirally enhanced power corrections, and discuss the effect of these corrections on direct CP asymmetries, which receive their first contribution at O(alpha). We find that the O(alpha^2 beta_0) corrections are often as large as the O(alpha) corrections. We find large uncertainties due to renormalization scale dependence as well as poor knowledge of the non-perturbative parameters. We assess the effect of the perturb…
We study the normalization of perturbative QCD corrections to the inclusive $B \rightarrow X_s γ$ decay. We propose to set the renormalization scale using the Brodsky-Lepage-Mackenzie (BLM) method. In the proposed method the scale is determined by absorbing the vacuum polarization correction from light fermions to renormalization scale but not including the anomalous dimensions. The BLM scale depends in general on the renormalization scheme and the factorization scale. We find that the BLM scale is insensitive to the factorization scale. In the heavy-quark potential scheme, we find that the BL…
We consider semi-inclusive deep inelastic scattering (SIDIS) and Drell-Yan events within transverse momentum dependent (TMD) factorization. Based on the simultaneous fit of multiple data points, we extract the unpolarized TMD distributions and the non-perturbative evolution kernel. The high quality of the fit confirms a complete universality of TMD non-perturbative distributions. The extraction is supplemented by phenomenological analyses of various parts of the TMD factorization, such as sensitivity to non-perturbative parameterizations, perturbative orders, collinear distributions, correlati…
The perturbative QCD (PQCD) approach based on $k_T$ factorization has made a great achievement for the QCD calculation of the hadronic B decays. Regulating the endpoint divergence by the transverse momentum of quarks in the propagators, one can do the perturbation calculation for kinds of diagrams including the annihilation type diagrams. In this paper, we review the current status of PQCD factorization calculation of two-body charmless $B\to PP, PV, VV$ decays up to the next-to-leading order (NLO) QCD corrections. two new power suppressed terms in decaying amplitudes are also taken into accou…
We show that the factorization formula for non-leptonic B decays to two light flavor non-singlet mesons derived by Bauer et al. in the context of soft-collinear effective theory is equivalent to the corresponding formula in the QCD factorization approach. The apparent numerical differences in the analysis of B->pi+pi data performed by these authors, as compared to previous QCD factorization analyses, can largely be attributed to the neglect of known perturbative and power corrections.
The charmless bottom meson decays are systematically investigated based on an approximate six quark operator effective Hamiltonian from perturbative QCD. It is shown that within this framework the naive QCD factorization method provides a simple way to evaluate the hadronic matrix elements of two body mesonic decays. The singularities caused by on mass-shell quark propagator and gluon exchanging interaction are appropriately treated. Such a simple framework allows us to make theoretical predictions for the decay amplitudes with reasonable input parameters. The resulting theoretical predictions…
We study the one-loop correction in Transverse-Momentum-Dependent(TMD) factorization for Drell-Yan processes at small transverse momentum of the lepton pair. We adopt the so-called subtractive approach, in which one can systematically construct contributions for subtracting long-distance effects represented by diagrams. The perturbative parts are obtained after the subtraction. We find that the perturbative coefficients of all structure functions in TMD factorization at leading twist are the same. The perturbative parts can also be studied with scattering of partons instead of hadrons. In this…
Using a modified perturbative approach that includes the Sudakov resummation and transverse degrees of freedom we analyze the penguin-induced $B^{-} \to π^{-}ϕ$ decay by applying the next-to-leading order effective weak Hamiltonian. The modified perturbative method enables us to include nonfactorizable contributions and to control virtual momenta appearing in the process. Besides, we apply the three-scale factorization theorem for nonleptonic processes that offers the possibility of having the scale-independent product of short- and long-distance parts in the amplitude of the weak Hamiltonian.…
In this paper, we will make systematic calculations for the branching ratios and the CP-violating asymmetries of the twenty one $\bar{B}^0_s \to PV $ decays by employing the perturbative QCD (PQCD) factorization approach. Besides the full leading-order (LO) contributions, all currently known next-to-leading order (NLO) contributions are taken into account. We found numerically that: (a) the NLO contributions can provide $\sim 40\%$ enhancement to the LO PQCD predictions for ${\cal B}(\bar{B}_s^0 \to K^0 \bar{K}^{*0})$ and $ {\cal B}(\bar{B}_s^0 \to K^{\pm}K^{*\mp})$, or a $\sim 37\% $ reductio…
High-energy virtual photon-virtual photon scattering can be viewed as interaction of small size color dipoles from the beam and target photons, which makes $γ^{*}γ^{*}, γ^{*}γ$ scattering at high energies (LEP, LEP200 & NLC) an indispensable probe of short distance properties of the QCD pomeron exchange. Based on the color dipole representation, we investigate consequences for the $γ^{*}γ^{*},γ^{*}γ$ scattering of the incorporation of asymptotic freedom into the BFKL equation which makes the QCD pomeron a series of isolated poles in the angular momentum plane. The emerging color dipole BFKL-Re…
With a consistent definition of transverse-momentum-dependent(TMD) light-cone wave function of $B$-meson, we show that the amplitude of the radiative leptonic B-decay can be factorized at one-loop level as a convolution with the wave function and a perturbative coefficient function, combined with a soft factor. In this TMD factorization, the transverse momenta of partons in the $B$-meson are taken into account and all soft divergences are contained in the wave function and the soft factor. The coefficient function is infrared-safe. The factorization works on a diagram-by-diagram basis and is p…
By employing the perturbative QCD (PQCD) factorization approach, we study the quasi-two-body $B^0_{(s)}\to η_c{(2S)}π^+π^-$ decays, where the pion pair comes from the $S$-wave resonance $f_0(X)$. The Breit$-$Wigner formula for the $f_0(500)$ and $f_0(1500)$ resonances, and the Flatté model for the $f_0(980)$ resonance are adopted to parameterize the time-like scalar form factors in the two-pion distribution amplitudes. As a comparison, Bugg's model is also used for the wide $f_0(500)$ in this work. For decay rates, we found the following PQCD predictions: (a) $ {\cal B}(B^0_s\to η_c(2S) f_0(X)…
We construct non-perturbative inputs for the elastic gluon-hadron scattering amplitudes in the forward kinematic region for both polarized and non-polarized hadrons. We use the optical theorem to relate invariant scattering amplitudes to the gluon distributions in the hadrons. By analyzing the structure of the UV and IR divergences, we can determine theoretical conditions on the non-perturbative inputs, and use these to construct the results in a generalized Basic Factorization framework using a simple Resonance Model. These results can then be related to the K_T and Collinear Factorization ex…
We extend the framework of QCD factorization to non-leptonic $B$ decays into three light mesons, taking as an example the decay $B^+ \to π^+ π^+ π^-$. We discuss the factorization properties of this decay in different regions of phase space. We argue that, in the limit of very large $b$-quark mass, the central region of the Dalitz plot can be described in terms of the $B \to π$ form factor and the $B$ and $π$ light-cone distribution amplitudes. The edges of the Dalitz plot, on the other hand, require different non-perturbative input: the $B \to ππ$ form factor and the two-pion distribution amp…
Using a modified perturbative approach that includes the Sudakov resummation and transverse degrees of freedom we analyze the penguin-induced B -> pi phi decay. The perturbative method enables us to include nonfactorizable contributions and to control virtual momenta appearing in the process. The calculation supports the results obtained in the standard BSW factorization approach, illustrating the electroweak penguin dominance and the branching ratio of order O(10^{-8}). However, the estimated prediction of 16% for CP asymmetry is much larger than that obtained in the factorization approach.
The annihilation type diagrams are difficult to calculate in any kind of models or method. Encouraged by the the successful calculation of pure annihilation type B decays in the perturbative QCD factorization approach, we calculate the pure annihilation type $D\to PP(V)$ decays in the perturbative QCD approach based on the $k_T$ factorization. Although the expansion parameter $1/m_D$ is not very small, our leading order numerical results agree with the existing experiment data for most channels. We expect the more accurate observation from experiments, which can help us learn about the dynamic…
The perturbative QCD description of high-energy hadroproduction of two hard jets separated by a large rapidity gap void of emission (also called Mueller-Tang jets) is based on a factorization formula of BFKL type that represents exchanges of colour-singlet objects among the external particles. This formula resums to all perturbative orders a certain class of Feynman diagrams that are supposed to dominate the cross-section in the Regge limit. However, the explicit calculations at next-to-leading logarithmic order questions the validity of such factorization when an IR safe jet algorithm is used…
By employing a framework for the quasi-two-body decays in the perturbative QCD (PQCD) factorization approach, we calculate the branching ratios of the decays $B_{(s)} \to D (ρ(1450),ρ(1700))\to D ππ$ with $D=(D_{(s)}, \bar{D}_{(s)})$. The pion vector form factor $F_π$, acquired from a {\it BABAR} Collaboration analysis of $e^+ e^- \to π^+ π^-(γ)$ data, is involved in the two-pion distribution amplitudes $Φ^{I=1}_{ππ}$. The PQCD predictions for the branching ratios of the considered quasi-two-body decays are in the range of $10^{-10} \sim 10^{-4}$. The PQCD predictions for ${\cal B}(B^0\to \bar…
We propose a QCD-based model for calculation of the non-perturbative corrections to the factorization approximation in the decays of heavy mesons. In the framework of the model, factorization in pseudoscalar transitions holds exactly at the leading order leaving the opportunity to calculate non-leading corrections consistently.
This is a brief introduction to two of the central concepts in perturbative quantum chromodynamics, jets and factorization, which serve as windows into the short-distance behavior of quantum fields.
We consider distributions of unpolarized (polarized) quarks in unpolarized (polarized) hadrons. Our approach is based on QCD factorization. We begin with study of Basic factorization for the parton-hadron scattering amplitudes in the forward kinematics and suggest a model for non-perturbative contributions to such amplitudes. This model is based on the simple observation: after emitting an active quark by the initial hadron, the remaining set quarks and gluons becomes unstable, so description of this colored state can approximately be done in terms of resonances, which leads to expressions of …
We calculate the lowest order QCD amplitude, i.e. the quark exchange contribution, to the forward production amplitude of a pair of longitudinally polarized $ρ$ mesons in the scattering of two virtual photons $γ^*(Q_1) γ^*(Q_2) \to ρ^0_L ρ^0_L$. We show that the scattering amplitude simultaneously factorizes in two quite different ways: the part with transverse photons is described by the QCD factorization formula involving the generalized distribution amplitude of two final $ρ$ mesons, whereas the part with longitudinally polarized photons takes the QCD factorized form with the $γ^*_L \to ρ^0…
Using $e^+e^-\rightarrowγ+ X$ as an example, we show that the conventional factorization theorem in perturbative quantum chromodynamics breaks down for isolated photon cross sections in a well defined part of phase space. Implications and physical consequences are discussed.
We compute radiative corrections to $Λ_b \to Λ$ from factors, at next-to-leading logarithmic accuracy, from QCD light-cone sum rules with $Λ_b$-baryon distribution amplitudes. Employing the diagrammatic approach factorization of the vacuum-to-$Λ_b$-baryon correlation function is justified at leading power in $Λ/m_b$, with the aid of the method of regions. Hard functions entering the factorization formulae are identical to the corresponding matching coefficients of heavy-to-light currents from QCD onto soft-collinear effective theory. The universal jet function from integrating out the hard-col…
We study the scattering of a single parton state with a multi-parton state to derive the complete results of perturbative coefficient functions at leading order, which appear in the collinear factorization for Single transverse-Spin Asymmetry(SSA) in Drell-Yan processes with a transversely polarized hadron in the initial state. We find that the factorization formula of SSA contains hard-pole-, soft-quark-pole- and soft-gluon-pole contributions. It is interesting to note that the leading order perturbative coefficient functions of soft-quark-pole- and soft-gluon-pole contributions are extracted…
We present an all-order generalized factorization formula for QCD scattering amplitudes in kinematical configurations where two or more momenta of the external partons become collinear. The singular behaviour of the scattering amplitudes in the collinear limit is encoded by collinear splitting matrices. In the space-like region and beyond the tree level, the collinear splitting matrices depend also on the momenta and quantum numbers of the non-collinear partons, thus breaking strict collinear factorization. Although the factorization breaking contribution partly cancels for squared amplitudes,…
I review recent progress on exclusive $B$ meson decays made in the perturbative QCD approach, concentrating on the evolution of the $B$ meson wave function in $k_T$ factorization, radiative decays, polarizations in $VV$ modes, and new physics effect in $B\to ϕK_S$.
The next to leading order (NLO) quarkonium-hadron cross section is calculated in perturbative QCD. The corresponding leading order (LO) result was performed by Peskin more than 20 years ago using the operator product expansion (OPE). In this work, the calculation is performed using the Bethe-Salpeter amplitude and the factorization formula. The soft divergence appearing in the intermediate stages of the calculations are shown to vanish after adding all possible crossed terms, while the collinear divergences are eliminated by mass factorization. Applying the result to the Upsilon system, one fi…
The extension of the factorization theorems of perturbative QCD to power corrections associated with re-scattering in nuclear collisions is reviewed. The importance of hadron-nucleus collisions is discussed.
