We use a new approach to color evaporation model (CEM) for quarkonium production. The production of $c\bar c$ pairs is performed within $k_T$-factorization approach using different unintegrated gluon distribution functions (UGDF) from the literature. We include all recent improvements to color evaporation model. We cannot describe simultaneously mid and forward rapidity data measured at the LHC when using the KMR UGDF with the same normalization parameter. Furthermore we get somewhat too hard distribution in $J/ψ$ transverse momentum. Correcting the standard KMR distributions for saturation effects at small values of $x$ improves $J/ψ$ rapidity distributions, while taking correction for emissions hidden in the KMR UGDF in the evaluation of $x$ values improves a bit $J/ψ$ transverse momentum distributions. The modifications improve also description of the LHCb $D$-meson data.
We calculate the production and polarization of direct $J/ψ$ in the improved color evaporation model at $\mathcal{O}(α_s^3)$ in the collinear factorization approach. We present the first calculation of polarization parameters $λ_\vartheta$, $λ_ϕ$, and $λ_{\vartheta ϕ}$ in the helicity and the Collins-Soper frames, as well as the frame-invariant polarization parameter $\tildeλ$ as a function of transverse momentum. We find agreement with both $J/ψ$ cross sections and the invariant polarization parameters at small and moderate $p_T$.
We use a new approach to color evaporation model (CEM) for quarkonium production. The production of $c\bar c$ pairs is performed within $k_T$-factorization approach using different unintegrated gluon distribution functions (UGDF) from the literature. We include all recent improvements to color evaporation model. We get poor description of the large transverse momentum distributions of $J/ψ$ with the JH-2013 CCFM-based UGDF. Here explicit inclusion of $2 \to 3$ processes considerably improves the situation. Similar effects are discussed in the context of the KMR UGDF.
We calculate the polarization of prompt $J/ψ$ production in the improved color evaporation model at leading order employing the $k_T$-factorization approach. In this paper, we present the polarization parameter $λ_\vartheta$ of prompt $J/ψ$ as a function of transverse momentum in $p+p$ and $p$ + A collisions to compare with data in the helicity, Collins-Soper and Gottfried-Jackson frames. We also present calculations of the charmonium production cross sections as a function of rapidity and transverse momentum. This is the first $p_T$-dependent calculation of charmonium polarization in the impr…
We calculate the polarization of prompt $\varUpsilon$($n$S) production in the improved color evaporation model at leading order employing the $k_T$-factorization approach. We present the polarization parameter $λ_\vartheta$ of prompt $\varUpsilon$($n$S) as a function of transverse momentum in $p+p$ and $p+\bar{p}$ collisions to compare with data in the helicity, Collins-Soper and Gottfried-Jackson frames. We also present calculations of the bottomonium production cross sections as a function of transverse momentum and rapidity. This is the first $p_T$-dependent calculation of bottomonium produ…
We compare the color-evaporation model (CEM) and nonrelativistic QCD (NRQCD) factorization predictions for inclusive quarkonium production. Using the NRQCD factorization formulas for quarkonium production and for perturbative QQ-bar production, we deduce relationships that are implied by the CEM between the nonperturbative NRQCD matrix elements that appear in the factorization formula for quarkonium production. These relationships are at odds with the phenomenological values of the matrix elements that have been extracted from the Tevatron data for charmonium production at large transverse mom…
We apply our calculation of direct $J/ψ$ production in the improved color evaporation mode at ${\mathcal O}(α_s^3)$ in collinear factorization to Pb+Pb collisions. The cold nuclear matter effects of nuclear modifications of the parton densities and intrinsic transverse momentum broadening are included. We find that the polarization is independent of these effects. Our calculations are compared to the Pb+Pb polarization parameters extracted by the ALICE Collaboration at $\sqrt{s_{NN}} = 5.02$ TeV.
Measurements by the Belle Collaboration of the cross section for inclusive J/psi production in e^+e^- annihilation have been a serious challenge to current heavy-quarkonium theory. Especially, the measured cross sections for exclusive J/psi+eta_c and inclusive J/psi+cc-bar+X differ from nonrelativistic QCD predictions by an order of magnitude. In order to check if other available alternative theory can resolve such a large discrepancy, we calculate the cross section for inclusive J/psi+cc-bar+X based on the color-evaporation model. As a phenomenological model, the color-evaporation model is st…
In the article, we study single and pair $J/ψ$ hadroproduction in the Improved Color Evaporation Model via the Parton Reggeization Approach. The last one is based on $k_T$-factorization of hard processes in multi-Regge kinematics, the Kimber-Martin-Ryskin-Watt model for unintegrated parton distribution functions, and the effective field theory of Reggezied gluons and quarks, suggested by L.N. Lipatov. We compare contributions from the single and double parton scattering mechanisms in the pair $J/ψ$ production. The numerical calculations are realized using the Monte-Carlo event generator KaTie.
The production of the $f_{0}(980)$ meson at high energies is not well understood. We investigate two different potential mechanisms for inclusive scalar meson production in the $k_t$-factorization approach: color-singlet gluon-gluon fusion and color evaporation model. The $γ^* γ^* \to f_0(980)$ form factor(s) can be constraint from the $f_0(980)$ radiative decay width. The $g^* g^* \to f_0(980)$ form factors are obtained by a replacement of $α_{\rm{em}}$ electromagnetic coupling constant by $α_{\rm{s}}$ strong coupling constant and appropriate color factors. The form factors for the two coupli…
The color evaporation model simply states that charmonium production is described by the same dynamics as $D \bar D$ production, {\em i.e.}, by the formation of a colored $c \bar c$ pair. Its color happens to be bleached by soft final-state interactions. We show that the model gives a complete picture of charmonium production including low-energy production by proton, photon and antiproton beams, and high-energy production at the Tevatron and HERA. Our analysis includes the first next-to-leading-order calculation in the color evaporation model.
The H1 Collaboration recently reported a new analysis on the inelastic photo- production of J/ψmesons at DESY HERA ep collider. We show that these new experimental results are well described by the Color Evaporation Model for quarkonium production. Moreover, this new data requires the introduction of resolved photon contributions in order to explain the results on small charmonium energy fraction, indicating that colored c \bar{c} pairs also contribute to the process.
We present the estimate of the branching ratio for the rare decay $\bar B^0\to D^*γ$. We use QCD factorization approach in order to compute the amplitude of the process. The calculation is carried out with the leading order accuracy. % Our consideration is based on the % factorization for the amplitude of the process which % has been derived with the leading order accuracy. The appearing non-perturbative matrix elements have been estimated using the large$-N_c$ limit and QCD sum rule approach. We obtained that $\mathcal{B}(\bar B^0\to D^*γ)\simeq 1.52\times 10^{-7}$. Such value of the branchin…
We discuss charm production at LHC. The production of single $c \bar c$ pairs is calculated in the $k_t$-factorization approach. We use several unintegrated gluon distributions from the literature. Differential distributions for several charmed mesons are presented and compared to recent results of the ALICE and LHCb collaborations. Some missing strength can be observed. Furthermore we discuss production of two $c \bar c$ pairs within a simple formalism of double-parton scattering (DPS). Surprisingly large cross sections, comparable to single-parton scattering (SPS) contribution to $c \bar c$ …
Extraction of the mass difference $Δm$ from $B^0\bar B^0$ oscillations involves tagging of bottom flavour at production and at decay. We show that the asymmetry between the unmixed and mixed events factorizes into two parts, one depending on the production-tag and the other on the decay-tag.
There a sizable and systematic discrepancy between experimental data on the $\bar{b}b$ production in $\bar{\mathrm p}$p, $γ$p and $γγ$ collisions and existing theoretical calculations within perturbative QCD. Before interpreting this discrepancy as a signal of new physics, it is important to understand quantitatively the ambiguities of conventional calculations. In this paper the uncertainty coming from renormalization and factorization scale dependence of finite order perturbation calculations of the total cross section of $\bar{b}b$ production in $\bar{\mathrm{p}}$p collisions is discussed i…
The NLO corrections to the DIS structure functions $F_2$ and $F_L$ (or equivalently the photon-target cross sections $σ^{γ^*}_{T}$ and $σ^{γ^*}_{L}$) at low $x_{Bj}$ are obtained, as a generalization of the dipole factorization formula. For the first time, the contributions of both the $q\bar{q}$ and the $q\bar{q}g$ Fock states in the photon are directly calculated, using earlier results for the $q\bar{q}$ light-front wave-functions at one loop inside a dressed virtual photon. Both the $q\bar{q}$ and the $q\bar{q}g$ contributions have UV divergences, which are shown to cancel each other, using…
We investigate the possibility of testing factorization hypothesis in non-leptonic exclusive decays of B-meson. In particular, we considered the non factorizable \bar{B^0} -> D^{(*)+} D_s^{(*)-} modes and \bar{B^0} -> D^{(*)+} (π^-, ρ^-) known as well-factorizable modes. By taking the ratios BR(\bar{B^0}-> D^{(*)+}D_s^{(*)-})/BR(\bar{B^0}-> D^{(*)+}(π^-,ρ^-)), we found that under the present theoretical and experimental uncertainties there's no evidence for the breakdown of factorization description to heavy-heavy decays of the B meson.
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…
In the framework of the k_T-factorization QCD approach we consider the production of b quark pairs in p\bar p collisions at the Fermilab Tevatron. We investigate the dependence of the b quark, B meson and decay muon differential cross sections on the different forms of unintegrated gluon distributions. The analysis also covers the azimuthal correlations between the b and \bar b quarks and their decay muons. Our theoretical results agree well with recent data taken by the D0 and CDF collaborations at Tevatron. Finally, we present our predictions for muon-muon and muon-jet cross sections at the …
The evaporation of primordial black holes with a mass in the $1\ {\rm gram}\lesssim M_{\rm PBH}\lesssim$1000 kg range can lead to the production of dark matter particles of almost any mass in the range $0.1\ {\rm MeV}\lesssim m_{\rm DM}\lesssim 10^{18}$ GeV with the right relic density at very early times, $τ\lesssim 10^{-10}$ s. We calculate, as a function of the primordial black holes mass and initial abundance, the combination of dark matter particle masses and number of effective dark degrees of freedom leading to the right abundance of dark matter today, whether or not evaporation stops a…
We investigate the factorization hypothesis of the four-quark condensate $\langle q \bar{q} q \bar{q} \rangle = \, A \, \langle q \bar{q} \rangle^2$ with the help of the Nambu Jona-Lasinio Model supplemented with eighth order interactions. For that purpose we use the bosonization method with multiple auxiliary variables. We find that in a simplified U(1) version of the model factorization holds, whereas in the full SU(3)-flavor version of the model factorization is broken by terms which are related to the 't Hooft interactions.
We discuss baryon production in the nucleon fragmentation region in deep inelastic scattering. The dependence of the nucleon spectra on Bjorken-$x$ is evaluated within the parton model and in QCD, and ways to look for the break-down of the DGLAP approximation via baryon production are suggested. We argue also that the leading neutron production in these small $x$ processes is rather insensitive to the pion parton densities of the nucleon.
We present first results for the $2 \to 4$ single-parton scattering $g g \to c \bar c c \bar c$ subprocess for the first time fully within the $k_t$-factorization approach. In this calculation we have used the Kimber-Martin-Ryskin unintegrated gluon distribution which effectively includes some class of higher-order gluon emissions, and an off-shell matrix element squared calculated using recently developed techniques. The results are compared with our earlier result obtained within the collinear-factorization approach. Only slightly larger cross sections are obtained than in the case of the co…
In the framework of QCD factorization, based on the first order of isospin violation, we study direct CP violation in the decay of $\bar{B}_{s}^{0} \to K^{0}ρ^{0}(ω)\to K^{0}π^{+}π^{-}$ including the effect of $ρ-ω$ mixing. We find that the CP violating asymmetry is large via $ρ-ω$ mixing mechanism when the invariant mass of the $π^{+}π^{-}$ pair is in the vicinity of the $ω$ resonance. For the decay of $\bar{B}_{s}^{0} \to K^{0}ρ^{0}(ω)\to K^{0}π^{+}π^{-}$, the maximum CP violating asymmetries can reach about 46%. We also discuss the possibility to observe the predicted CP violating asymmetri…
The two body charmless decays of $B_s$ meson to light vector mesons are analyzed within the framework of QCD factorization. This approach implies that the nonfactorizable corrections to different helicity amplitudes are not the same. The effective parameters $a_i^h$ for helicity $h=0,+,-$ states receive different nonfactorizable contributions and hence are helicity dependent, contrary to naive factorization approach where $a_i^h$ are universal and polarization independent. The branching ratios for $\bar{B}_s\to VV$ decays are calculated and we find that branching ratios of some channels are of…
The DELPHI Collaboration has recently reported the measurement of J/Psi production in photon-photon collisions at LEP II. These newly available data provide an additional proof of the importance of colored c bar{c} pairs for the production of charmonium because these data can only be explained by considering resolved photon processes. We show here that the inclusion of color octet contributions to the J/Psi production in the framework of the color evaporation model is able to reproduce this data. In particular, the transverse-momentum distribution of the J/Psi mesons is well described by this …
A factorization hypothesis is tested by examining a form factor of the $ωπ$ production in hadronic $B^0 \to D^{\ast \pm}ωπ^\mp$ decays. The form factor is compared to that from available $τ$-lepton as well as $e^+e^-$ data using the conserved vector current hypothesis. The difference of normalizations of form factor shapes from $B$ and $τ~(e^+e^-)$ data indicates the important role of the large $N_c$ limit in QCD. Moreover, the growth of the difference between the form factors with the $ωπ$ invariant mass is related to the perturbative QCD corrections of factorization. The current precision of…
The production and decay of the X(3872) are analyzed under the assumption that the X is a weakly-bound molecule of the charm mesons D^0 \bar D^{*0} and D^{*0} \bar D^0. The decays imply that the large D^0 \bar D^{*0} scattering length has an imaginary part. An effective field theory for particles with a large complex scattering length is used to derive factorization formulas for production rates and decay rates of X. If a partial width is calculated in a model with a particular value of the binding energy, the factorization formula can be used to extrapolate to other values of the binding ener…
Motivated by experimental results on $\bar B\to D^{(*)}K^-K^{0}$, we use a factorization approach to study these decays. Two mechanisms concerning kaon pair production arise: current-produced (from vacuum) and transition (from the $B$ meson). The kaon pair in the $\bar B {}^0\to D^{(*)+}K^-K^0$ decays can be produced only by the vector current (current-produced), whose matrix element can be extracted from $e^+e^-\to K\bar K$ processes via isospin relations. The decay rates obtained this way are in good agreement with experiment. The $B^-\to D^{(*)0}K^-K^0$ decays involve both current-produced …
The decay mode D^0 -> K^0 \bar{K^0} has no factorizable contribution. We calculate the nonfactorizable chiral loop contributions of order O(p^3)and then we use a heavy-light type chiral quark model to calculate nonfactorizable tree level terms, also of order O(p^3), proportional to the gluon condensate. Calculated chiral loops and the gluon condensate contributions are of the same order of magnitude as the experimental amplitude.
We study the fragmentation function of the gluon to color-octet $^3S_1$ heavy quark-antiquark pair using the soft gluon factorization (SGF) approach, which expresses the fragmentation function in a form of perturbative short-distance hard part convoluted with one-dimensional color-octet $^3S_1$ soft gluon distribution (SGD). The short distance hard part is calculated to next-to-leading order in $α_s$ and a renormalization group equation for the SGD is derived. By solving the renormalization group equation, threshold logarithms are resummed to all orders in perturbation theory. The comparison w…
Our goal is the study of color effects on the $J/ψ$ and $D$ mesons production, as well as the study of their elastic production. We use the Color Evaporation Model (CEM), where a single factor takes into account the probability that the $c\bar{c}$ produced in a color octet state turns into a physical (colorless) quarkonium or continues as a color octet, producing open charm. The main result of this work, besides investigating the range of applicability of the CEM, is to show that this model can be used to describe the elastic processes of $J/ψ$ and open charm photoproduction without the use of…
By differentiating the dressed quark propagator with respect to a variable background field, the linear response of the dressed quark propagator in the presence of the background field can be obtained. From this general method, using the vector background field as an illustration, we derive a general formula for the four-quark condensate $<{\tilde 0}|:{\bar q}(0)γ_μq(0){\bar q}(0)γ_μq(0):|{\tilde 0}>$. This formula contains the corresponding fully dressed vector vertex and it is shown that factorization for $<{\tilde 0}|:{\bar q}(0)γ_μq(0){\bar q}(0)γ_μq(0):| {\tilde 0}>$ holds only when the d…
I describe the NRQCD factorization approach to the inclusive production of heavy quarkonium, contrasting it with the color-singlet and color evaporation models. These approaches differ dramatically in their assumptions about the roles played by color and spin in the production process. They also differ dramatically in their predictions for the production of charmonium at large transverse momentum.
Using methods from soft-collinear and heavy-quark effective theory, a systematic factorization analysis is performed for the $\bar B\to X_sγ$ photon spectrum in the endpoint region $m_b-2E_γ={\cal O}(Λ_{\rm QCD})$. It is proposed that, to all orders in $1/m_b$, the spectrum obeys a novel factorization formula, which besides terms with the structure $H\,J\otimes S$ familiar from inclusive $\bar B\to X_u l\,\barν$ decay distributions contains "resolved photon" contributions of the form $H\,J\otimes S\otimes\bar J$ and $H\,J\otimes S\otimes\bar J\otimes\bar J$. Here $S$ and $\bar J$ are new soft …
Motivated by the first search for the rare charged-current $B$ decay to four leptons, $\ell \barν_\ell \ell^{(\prime)} \bar{\ell}^{(\prime)}$, we calculate the decay amplitude with factorization methods. We obtain the $B\to γ^*$ form factors, which depend on the invariant masses of the two lepton pairs, at leading power in an expansion in $Λ_{\rm QCD}/m_b$ to next-to-leading order in $α_s$, and at $\mathcal{O}(α_s^0)$ at next-to-leading power. Our calculations predict branching fractions of a few times $10^{-8}$ in the $\ell^{(\prime)} \bar{\ell}^{(\prime)}$ mass-squared bin up to $q^2=1~\text…
The breaking of conventional linear k_\perp-factorization for hard processes in a nuclear environment is by now well established. Here we report a detailed derivation of the nonlinear k_\perp-factorization relations for the production of quark-gluon dijets. This process is of direct relevance to dijets in the proton hemisphere of proton-nucleus collisions at energies of the Relativistic Heavy Ion Collider (RHIC). The major technical problem is a consistent description of the non-Abelian intranuclear evolution of multiparton systems of color dipoles. Following the technique developed in our ear…
We study inclusive processes involving two heavy quarkonia in nonrelativisitic QCD (NRQCD) and demonstrate that, in the presence of two P-wave Fock states, NRQCD factorization breaks down, leaving uncanceled infrared singularities. As phenomenologically important examples, we consider the decay $Υ\to χ_{cJ}+X$ via $b\bar{b}({}^3P_{J_b}^{[8]})\to c\bar{c}({}^3P_J^{[1]})+gg$ and the production process $e^+e^-\to J/ψ+χ_{cJ}+X$ via $e^{+}e^{-}\to c\bar{c}({}^3P_{J_1}^{[8]})+c\bar{c}({}^3P_J^{[1]})+g$. We infer that such singularities will appear for double quarkonium hadroproduction at next-to-lea…
The formalism for uniform description of Drell-Yan transverse-momentum spectrum is presented in a framework of High-Energy Factorization, which smoothly interpolates between Collins-Soper-Sterman formalism at $|{\bf q}_T|\ll Q$ and usual Collinear Parton Model at $|{\bf q}_T|\sim Q\ll \sqrt{S}$. The new formula for deriving Unintegrated Parton Distribution Functions(UPDFs) from collinear ones is introduced, which leads to excellent description of the shape of $Z$-boson $|{\bf q}_T|$-spectrum at high energies up to $|{\bf q}_T|/\sqrt{S}\simeq 0.02$. Description of normalized $|{\bf q}_T|$-distr…
A brief review of checking the factorization hypothesis for matrix element of $B^0 - \bar B^0$ mixing within operator product expansion and QCD sum rules is given. Both perturbative and power corrections are considered.
The $Z$-boson decay provides good opportunities for the research on $Ξ_{bQ'}$ baryon due to large quantity of $Z$ events that can be collected at the high-energy colliders. We performed a completed investigation of the indirect production of the $Ξ_{bc}$ and $Ξ_{bb}$ baryon via $Z$-boson decay $Z\to Ξ_{bQ'}+\bar b +\bar Q'$ with $Q'= (c, b)$ quark according to NRQCD factorizations approach. After considering the contribution of the diquark states $\langle bc\rangle [^3S_1]_{\bar 3/6}$, $\langle bc\rangle [^1S_0]_{\bar 3/6}$, $\langle bb\rangle [^1S_0]_{6}$ and $\langle bb\rangle [^3S_1]_{\bar …
The 1/N_c expansion for the baryon distribution amplitude is constructed in terms of a specially designed generating functional. At large N_c this functional shows exponential behavior. The exponential factor is universal for all low-lying baryons and baryon-meson scattering states. Simple factorization properties are established for the preexponential term. This factorization agrees with the large-N_c contracted SU(2N_f) spin-flavor symmetry. The consistency of the factorization with the soft-pion theorem for the baryon distribution amplitude is explicitly checked. A relation between the gene…
The asymptotic behaviour at large N of the MS-bar quark anomalous dimensions is derived to all orders assuming only MS-bar factorization and standard results for the exponentiation of soft logarithms in the quark initiated bare cross sections for deep inelastic scattering and Drell-Yan. The result is then used to write the MS-bar quark coefficient functions in a form in which all terms of $O(\ln^m N)$ are resummed.
We compare results of the $k_t$-factorization approach and the next-to-leading order collinear-factorization approach for photon-jet correlations in $pp$ and $p \bar p$ collisions at RHIC and Tevatron energies. We discuss correlations in the azimuthal angle as well as in the two-dimensional space of transverse momentum of photon and jet. Different unintegrated parton distributions (UPDF) are included in the $k_t$-factorization approach. The results depend on UPDFs used. The standard collinear approach gives cross section comparable to the $k_t$-factorization approach. For correlations of the p…
The form factors for semi-leptonic B decays, $\bar{B}\toπl\barν_l$, are calculated under collinear factorization approach. The end-point divergences are regularized by a $ξ$-regularization, where $ξ$ means the collinear fraction of the spectator anti-quark of the $\bar{B}$ meson. The form factors are calculated up-to $O(α_{s}/m_{B})$. The complete $O(1/m_{B})$ contributions from the $π$ meson are calculated explicitly by a collinear expansion method. A well-defined power expansion scheme is built such that the $O(1/m_{B})$ contributions are about 30% of the leading order contributions. A small…
A study of hadron pair production mechanism is motivated by the recent observed decays $\bar B^0\to D^{(*)+}K^-K^0$. One novel phenomenon is threshold enhancement of the kaon pair production. We show that these decays in the heavy quark mass limit can be factorized into a generalized form. The new non-perturbative quantity is the generalized distribution amplitude which describes how a quark-antiquark pair transmits into the hadron pair. A proof of factorization of $\bar B^0\to D^{(*)+}K^-K^0$ decays to all-orders is performed by using the soft-collinear effective theory. The phenomenological …
In this paper, we studied the $B_{(s)} \to (D_{(s)},\bar{D}_{(s)}) ρ\to (D_{(s)}, \bar{D}_{(s)})ππ$ decays by employing a framework for the quasi-two-body decays in the perturbative QCD (PQCD) factorization approach. We use the two-pion distribution amplitudes $Φ_{ππ}$, which contains both resonant and nonresonant contributions from the pion pair, to describe the final state interactions (FSIs) between the pions in the resonant region. We found that (a) for all considered decays, the PQCD predictions for their branching ratios based on the quasi-two-body and the two-body framework agree well w…
Using flavor SU(3) symmetry, we perform a model-independent analysis of charmless $\bar B_{u,d} (\bar B_s) \to PP, ~PV$ decays. All the relevant topological diagrams, including the presumably subleading diagrams, such as the QCD- and EW-penguin exchange diagrams and flavor-singlet weak annihilation ones, are introduced. Indeed, the QCD-penguin exchange diagram turns out to be important in understanding the data for penguin-dominated decay modes. In this work we make efforts to bridge the (model-independent but less quantitative) topological diagram or flavor SU(3) approach and the (quantitativ…
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 examine the validity of the generalized factorization method and calculate the angular correlations in the charmful three-body baryonic decays of $\bar B^0\to Λ\bar p D^{(*)+}$. With the timelike baryonic form factors newly extracted from the measured baryonic $B$ decays, we obtain ${\cal B}(\bar B^0\to Λ\bar p D^+,Λ\bar p D^{*+})=(1.85\pm 0.30,2.75\pm 0.24)\times 10^{-5}$ to agree with the recent data from the BELLE Collaboration, which demonstrates that the theoretical approach based on the factorization still works well. For the angular distribution asymmetries, we find ${\cal A}_θ(\bar …
We discuss the role of intrinsic charm (IC) in the nucleon for forward production of $c$-quark (or $\bar c$-antiquark) in proton-proton collisions for low and high energies. The calculations are performed in collinear-factorization approach with on-shell partons, $k_T$-factorization approach with off-shell partons as well as in a hybrid approach using collinear charm distributions and unintegrated (transverse momentum dependent) gluon distributions. For the collinear-factorization approach we use matrix elements for both massless and massive charm quarks/antiquarks. The distributions in rapidi…
$B\toχ_{c1}(1P,2P)K$ decays are studied in QCD factorization by treating charmonia as nonrelativistic bound states. No infrared divergences exist in the vertex corrections, while the logarithmic end-point singularities in the hard spectator corrections can be regularized by a momentum cutoff. With certain uncertainties we find that the $B\toχ_{c1}(2P)K$ decay rate can be comparable to $B\toχ_{c1}(1P)K$, and get $Br(B^0 \to χ_{c1}' K^0) =Br(B^+ \to χ_{c1}' K^+)\approx 2\times 10^{-4}$. This might imply a possible interpretation for the newly discovered X(3872) that this state has a dominant $J^…
