Collinear Factorization Approach Research Articles

Collinearly enhanced realizations of the Yennie-Frautschi-Suura (YFS) MC approach to precision resummation theory

We extend the Yennie-Frautschi-Suura (YFS) IR resummation theory to include all of the attendant collinear contributions which exponentiate. This improves the original YFS formulation in which only a part of these contributions was exponentiated. We show that the new resummed contributions agree with known results from the collinear factorization approach and we argue that they improve the attendant precision tag for a given level of exactness in the respective YFS hard radiation residuals.

Reformulation of the twist-3 gluon Sivers effect toward an application to heavy quarkonium production

In this paper, we propose a new calculation method for the twist-3 gluon Sivers effect within the collinear factorization approach. The method called pole calculation has been used to derive the cross section formula for the single transverse-spin asymmetry as a standard method. We point out that we encounter a problem when we try to apply the pole calculation to the single transverse-spin asymmetry in the heavy quarkonium production whose hadronization mechanism is described by nonrelativistic QCD framework. We show that the new calculation method solves this problem and successfully reproduces known results derived by the pole calculation. Our new method extends the applicability of the twist-3 calculation technique to heavy quarkonium productions that are ideal observables for the investigation of the gluon Sivers effect.

Progress and opportunities in backward angle (u-channel) physics

Backward angle (u-channel) scattering provides complementary information for studies of hadron spectroscopy and structure, but has been less comprehensively studied than the corresponding forward angle case. As a result, the physics of u-channel scattering poses a range of new experimental and theoretical opportunities and questions. We summarize recent progress in measuring and understanding high energy reactions with baryon charge exchange in the u-channel, as discussed in the first backward angle (u-channel) Physics Workshop. In particular, we discuss backward angle measurements and their theoretical description via both hadronic models and the collinear factorization approach, and discuss planned future measurements of u-channel physics. Finally, we propose outstanding questions and challenges for u-channel physics.

Production and polarization of direct J/ψ to O(αs3) in the improved color evaporation model in collinear factorization

We calculate the production and polarization of direct $J/\psi$ in the improved color evaporation model at $\mathcal{O}(\alpha_s^3)$ in the collinear factorization approach. We present the first calculation of polarization parameters $\lambda_\vartheta$, $\lambda_{\phi}$, and $\lambda_{\vartheta \phi}$ in the helicity and the Collins-Soper frames, as well as the frame-invariant polarization parameter $\tilde{\lambda}$ as a function of transverse momentum. We find agreement with both $J/\psi$ cross sections and the invariant polarization parameters at small and moderate $p_T$.

Intrinsic charm in the nucleon and charm production at large rapidities in collinear, hybrid and kT-factorization approaches

We discuss the role of intrinsic charm (IC) in the nucleon for forward production of c-quark (or overline{c} -antiquark) in proton-proton collisions for low and high energies. The calculations are performed in collinear-factorization approach with on-shell partons, kT-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 rapidity and transverse momentum of charm quark/antiquark are shown for a few different models of IC. Forward charm production is dominated by gc-fusion processes. The IC contribution dominates over the standard pQCD (extrinsic) gg-fusion mechanism of coverline{c} -pair production at large rapidities or Feynman-xF. We perform similar calculations within leading-order and next-to-leading order kT-factorization approach. The kT-factorization approach leads to much larger cross sections than the LO collinear approach. At high energies and large rapidities of c-quark or overline{c} -antiquark one tests gluon distributions at extremely small x. The IC contribution has important consequences for high-energy neutrino production in the Ice-Cube experiment and can be, to some extent, tested at the LHC by the SHIP and FASER experiments by studies of the ντ neutrino production.

How to include exclusive J/ψ production data in global PDF analyses

We compare the cross section for exclusive $J/\psi$ photoproduction calculated at NLO in the collinear factorization approach with HERA and LHCb data. Using the optimum scale formalism together with the subtraction of the low $k_t<Q_0$ contribution from the NLO coefficient function to avoid double counting we show that the existing global parton distribution functions (PDFs) are consistent with the data within their uncertainties. However, at low $x$ the uncertainties of the present global PDFs are large. On the other hand, the accuracy of the LHCb data are rather good. Therefore, these data provide the possibility to directly measure the gluon PDF over the very large interval of $x$, $10^{-6}<x<10^{-2}$, at a fixed low scale.

Pion valence quark distribution from matrix element calculated in lattice QCD

We present the first exploratory lattice QCD calculation of the pion valence quark distribution extracted from spatially separated current-current correlations in coordinate space. We show that an antisymmetric combination of vector and axial-vector currents provides direct information on the pion valence quark distribution. Using the collinear factorization approach, we calculate the perturbative tree-level kernel for this current combination and extract the pion valence distribution. The main goal of this article is to demonstrate the efficacy of this general lattice QCD approach in the reliable extraction of parton distributions. With controllable power corrections and a good understanding of the lattice systematics, this method has the potential to serve as a complementary to the many efforts to extract parton distributions in global analyses from experimentally measured cross sections. We perform our calculation on an ensemble of 2+1 flavor QCD using the isotropic-clover fermion action, with lattice dimensions $32^3\times 96$ at a lattice spacing \mbox{$a=0.127$ fm} and the quark mass equivalent to a pion mass $m_\pi \simeq 416$ MeV.

What can be learned from the transition form factor of gamma ^*gamma ^*rightarrow eta ': feasibility study

We present an analysis of the recent measurement of eta '-meson production by two virtual photons made by the BaBar collaboration. It is the first measurement of a transition form factor which is entirely within the kinematic regime of the collinear factorization approach, and it thus provides a clean test of the QCD factorization theorem for distribution amplitudes (DAs). We demonstrate that the data are in agreement with perturbative QCD. Also we show that it is sensitive to power corrections to the factorization theorem and to the decay constants. We discuss features of the meson production cross-section and point out the kinematic regions that are sensitive to interesting physics. We also provide an estimation of uncertainties on the extraction of DA parameters.

Next-to-leading order corrections to B→ρ transition in the kT factorization

In this paper, we investigate the factorization hypothesis step by step for the exclusive process $B \to \rho$ at next-to-leading order (NLO) with the collinear factorization approach, and then we extend our results to the $k_T$ factorization frame. We show that the soft divergence from the specific NLO diagrams will cancel each other at the quark level, while the remaining collinear divergence can be absorbed into the NLO wave functions. The full NLO amplitudes can be factorized into two parts: the NLO $B$ and $\rho$ meson wave functions containing the collinear divergence and the leading order (LO) finite hard kernels. We give the general form of the nonlocal hadron matrix for the NLO $B$ and $\rho$ meson wave functions and all results of factorization for different twists' combinations.

Production of W+W\u2212 pairs via \u03b3*\u03b3* \u2192 W+W\u2212 subprocess with photon transverse momenta

We discuss production of W+W− pairs in proton-proton collisions induced by two-photon fusion including, for a first time, transverse momenta of incoming photons. The unintegrated inelastic fluxes (related to proton dissociation) of photons are calculated based on modern parametrizations of deep inelastic structure functions in a broad range of their arguments (x and Q2). In our approach we can get separate contributions of different W helicities states. Several one- and two-dimensional differential distributions are shown and discussed. The present results are compared to the results of previous calculations within collinear factorization approach. Similar results are found except of some observables such as e.g. transverse momentum of the pair of W+ and W−. We find large contributions to the cross section from the region of large photon virtualities. We show decomposition of the total cross section as well as invariant mass distribution into the polarisation states of both W bosons. The role of the longitudinal FL structure function is quantified. Its inclusion leads to a 4–5% decrease of the cross section, almost independent of MWW.

Single-diffractive production of dijets within the kt -factorization approach

We discuss single-diffractive production of dijets. The cross section is calculated within the resolved pomeron picture, for the first time in the $k_t$-factorization approach, neglecting transverse momentum of the pomeron. We use Kimber-Martin-Ryskin unintegrated parton (gluon, quark, antiquark) distributions (UPDF) both in the proton as well as in the pomeron or subleading reggeon. The UPDFs are calculated based on conventional MMHT2014nlo PDFs in the proton and H1 collaboration diffractive PDFs used previously in the analysis of diffractive structure function and dijets at HERA. For comparison we present results of calculations performed within collinear-factorization approach. Our results remaind those obtained in the NLO approach. The calculation is (must be) supplemented by the so-called gap survival factor which may, in general, depend on kinematical variables. We try to describe the existing data from Tevatron and make detailed predictions for possible LHC measurements. Several differential distributions are calculated. The $\overline{E}_T$, $\overline{\eta}$ and $x_{\bar p}$ distributions are compared with the Tevatron data. A reasonable agreement is obtained for the first two distributions. The last one requires to introduce a gap survival factor which depends on kinematical variables. We discuss how the phenomenological dependence on one kinematical variable may influence dependence on other variables such as ${\overline E}_T$ and ${\overline \eta}$. Several distributions for the LHC are shown.

Gluon tomography from deeply virtual Compton scattering at small x

We present a full evaluation of the deeply virtual Compton scattering (DVCS) cross section in the dipole framework in the small-x region. The result features the $\cos \phi$ and $\cos 2\phi$ azimuthal angular correlations which have been missing in previous studies based on the dipole model. In particular, the $\cos 2\phi$ term is generated by the elliptic gluon Wigner distribution whose measurement at the planned electron-ion collider (EIC) provides an important information about the gluon tomography at small-x. We also show the consistency with the standard collinear factorization approach based on the quark and gluon generalized parton distributions (GPDs).

Perturbative QCD factorization ofργ⋆→ρ

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 $\rho \gamma^{\star} \to \rho$ 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 $\rho$ 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 the NLO meson wave functions. The full NLO amplitudes can therefore be factorized as the convolution of the NLO wave functions $ \Phi^{(1)}_{\rho}$ and the infrared-finite leading order (LO) hard kernels $G^0_{X,IJ,kl}$ in the $k_T$ factorization. We also write down the polarized NLO $\rho$ meson wave functions in the form of nonlocal hadron matrix elements with the gauge factor integral path deviating from the light cone. These NLO $\rho$ meson wave functions can be used to calculate the NLO hard corrections to some relevant exclusive processes, such as $B \to \rho$ transition.

Production of two charm quark–antiquark pairs in single-parton scattering within the [formula omitted]-factorization approach

We present first results for the 2→4 single-parton scattering gg→cc¯cc¯ subprocess for the first time fully within the kt-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 collinear approach. Inclusion of transverse momenta of gluons entering the hard process leads to a much stronger azimuthal decorrelation between cc and c¯c¯ than in the collinear-factorization approach. A comparison to predictions of double parton scattering (DPS) results and the LHCb data strongly suggests that the assumption of two fully independent DPS (gg→cc¯⊗gg→cc¯) may be too approximate.

Skewness dependence of generalized parton distributions, conformal OPE, and the AdS/CFT correspondence

The traditional idea of the Pomeron/Reggeon description for hadron scattering is now being given theoretical foundation in gravity dual descriptions, where Pomeron corresponds to an exchange of spin-$j\ensuremath{\in}2\mathbb{Z}$ states in the graviton trajectory. Deeply virtual Compton scattering (DVCS) is essentially a two-to-two scattering process of a hadron and a photon, and hence one should be able to study nonperturbative aspects (the generalized parton distribution [GPD]) of this process by the Pomeron/Reggeon process in gravity dual. We find, however, that even one of the most developed formulations of gravity dual, Pomeron [Brower-Polchinski-Strassler-Tan (BPST), 2006], is not able to capture skewness dependence of GPD properly. Therefore, we compute Reggeon wave functions on ${\mathrm{AdS}}_{5}$ so that the formalism of BPST can be generalized. These wave functions are used to determine the DVCS amplitude, bring it to the form of conformal operator product expansion/collinear factorization, and extract a holographic model of GPD, which naturally fits into the framework known as ``dual parametrization,'' or the ``(conformal) collinear factorization approach.''

Perturbative QCD factorization ofργ⋆→π

In this paper, we firstly verify that the factorization hypothesis is valid for the exclusive process $\ensuremath{\rho}{\ensuremath{\gamma}}^{\ensuremath{\star}}\ensuremath{\rightarrow}\ensuremath{\pi}$ 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 $\ensuremath{\pi}{\ensuremath{\gamma}}^{\ensuremath{\star}}\ensuremath{\rightarrow}\ensuremath{\pi}$ process where only the pseudoscalar $\ensuremath{\pi}$ meson is involved, and the remaining collinear divergences can be absorbed into the NLO hadron wave functions. The full amplitudes can be factorized as the convolution of the NLO wave functions and the infrared-finite hard kernels with these factorization approaches. We also write out the NLO meson distribution amplitudes in the form of nonlocal matrix elements.

Towards a fitting procedure to deeply virtual meson production – the next-to-leading order case

Based on the collinear factorization approach, we present a comprehensive perturbative next-to-leading (NLO) analysis of deeply virtual meson production (DVMP). Our representation in conformal Mellin space can serve as basis for a global fitting procedure to access generalized parton distributions from experimental measurements of DVMP and deeply virtual Compton scattering (DVCS). We introduce a rather general formalism for the evaluation of conformal moments that can be developed further beyond the considered order. We also confirm previous diagrammatical findings in the pure singlet quark channel. Finally, we use the analytic properties of the hard scattering amplitudes to estimate qualitatively the size of radiative corrections and illustrate these considerations with some numerical examples. The results suggest that global NLO GPD fits, including both DVMP and DVCS data, could be more stable than often feared.

A fresh look at exclusive electroproduction of light vector mesons

Relying on the collinear factorization approach, we demonstrate that H1 and ZEUS measurements of exclusive light vector meson and photon electroproduction cross sections can be simultaneously described for photon virtualities of $${\mathcal {Q}}\gtrsim 2\, \mathrm{GeV}$$ . Our findings reveal that quark exchanges are important in this small $$x_\mathrm{Bj}$$ region and that in leading order approximation the gluonic component is suppressed, e.g., the skewness ratio can be much smaller than one.

πNTDAs from charmonium production in association with a forward pion at P̅ANDA

Charmonium production in association with a forward or backward pion in nucleon-antinucleon annihilation is one of the most promising reaction to access nucleon-to-pion transition distribution amplitudes (TDAs) at PANDA. We briefly review the description of this reaction in terms of \pi N TDAs within the collinear factorization approach and present the first results of dedicated feasibility studies for the PANDA experimental setup.

Quark tensor charge and electric dipole moment within the Schwinger-Dyson formalism

We calculate the tensor charge of the quark in the QCD-like theory in the Landau gauge using the Schwinger--Dyson formalism. It is found that the dressed tensor charge of the quark is significantly suppressed against the bare quark contribution, and the result agrees qualitatively with the analyses in the collinear factorization approach and lattice QCD. We also analyze the quark confinement effect with the phenomenological strong coupling given by Richardson and find that this contribution is small. We show that the suppression of the quark tensor charge is due to the superposition of the spin flip of the quark arising from the successive emission of gluons that dress the tensor vertex. We also consider the relation between the quark and the nucleon electric dipole moments by combining with the simple constituent quark model.