Collinear Parton Research Articles

Collinearity approximations and kinematic shifts in partonic shower algorithms

We study kinematic effects due to the approximation of on-shell, collinear partons in shower Monte Carlo event generators. We observe that the collinearity approximation, combined with the requirements of energy-momentum conservation, gives rise to a kinematic shift, event by event, in longitudinal momentum distributions. We present numerical results in the case of jet and heavy flavor production processes measured at the LHC.

Evolution of cusped lightlike Wilson loops and geometry of the loop space

We discuss the possible relation between certain geometrical properties of the loop space and energy evolution of the cusped Wilson exponentials defined on the light-cone. Analysis of the area differential equations for this special class of the Wilson loops calls for careful treatment of the ultraviolet and rapidity divergences which make those loops non-multiplicatively-renormalizable. We propose to consider the renormalization properties of the light-cone cusped Wilson loops from the point of view of the universal quantum dynamical approach introduced by Schwinger. We conjecture and discuss the relevance of the Makeenko-Migdal loop equations supplied with the modified Schwinger principle to the energy evolution of some phenomenologically significant objects, such as transverse-momentum dependent distribution functions, collinear parton densities at large-$x$, etc.

Analyticity and sum rules for photon GPDs

The photon is explored as an object to test the applications of QCD to the perturbatively calculable collinear parton distributions. We investigate analytic properties of DVCS amplitudes and related sum rules of generalized parton distributions of the photon using as an input their earlier calculations in the leading order. The relation of these GPDs to the quintessential functions in the framework of the dual parametrization approach is also found.

Inclusive jet production at the tevatron collider in the Regge limit of quantum chromodynamics

We consider the inclusive hadroproduction of jets, prompt photons, and b-quark jets in the quasimulti-Regge kinematics approach based on the hypothesis of gluon and quark reggeization in t-channel exchanges at high energies. The data taken by CDF and D0 collaborations at the Fermilab Tevatron collider are well described in the region of \(x_T = 2p_T /\sqrt s \lesssim 0.1\) without the introduction of any free parameters. In numeric calculations we use the Kimber-Martin-Ryskin prescription for unintegrated gluon and quark distribution functions with Martin-Roberts-Stirling-Thorne collinear parton distribution functions taken as input.

LOOP SPACE AND EVOLUTION OF THE LIGHT-LIKE WILSON POLYGONS

We address a connection between the energy evolution of the polygonal light-like Wilson exponentials and the geometry of the loop space with the gauge invariant Wilson loops of a variety of shapes being the fundamental degrees of freedom. The renormalization properties and the differential area evolution of these Wilson polygons are studied by making use of the universal Schwinger quantum dynamical approach. We discuss the appropriateness of the dynamical differential equations in the loop space to the study of the energy evolution of the collinear and transverse-momentum dependent parton distribution functions.

Transverse momentum broadening and the jet quenching parameter, redux

We use soft collinear effective theory (SCET) to analyze the transverse momentum broadening, or diffusion in transverse momentum space, of an energetic parton propagating through quark-gluon plasma. Since we neglect the radiation of gluons from the energetic parton, we can only discuss momentum broadening, not parton energy loss. The interaction responsible for momentum broadening in the absence of radiation is that between the energetic (collinear) parton and the Glauber modes of the gluon fields in the medium. We derive the effective Lagrangian for this interaction, and we show that the probability for picking up transverse momentum ${k}_{\ensuremath{\perp}}$ is given by the Fourier transform of the expectation value of two transversely separated lightlike path-ordered Wilson lines. This yields a field-theoretical definition of the jet-quenching parameter $\stackrel{^}{q}$, and shows that this can be interpreted as a diffusion constant. We close by revisiting the calculation of $\stackrel{^}{q}$ for the strongly coupled plasma of $\mathcal{N}=4$ SYM theory, showing that previous calculations need some modifications that make them more straightforward and do not change the result.

Power corrections in e + e −→π + π −,K + K − and B→Kπ,ππ

CLEO-c measurements of the timelike form factors F π , F K at \(\sqrt{s}=3.671\) GeV provide a direct probe of power corrections (PC’s) at energies near m B . PC’s in F π,K and B→Kπ,ππ are separated into perturbative and soft parts. In F π,K the latter are ≥O(10) larger. A PC fit to the B→Kπ,ππ data also yields a ≥O(10) soft-to-perturbative hierarchy for the QCD penguin PC’s. Hence, both can be attributed to dominance of the soft-overlap between energetic (approximately) back-to-back collinear partons, and consistency of the B→Kπ,ππ fit with the Standard Model appears to be naturally realized. The CP asymmetries \(S_{K_{s} \pi^{0}}\), \(C_{K_{s} \pi^{0}}\) are well determined, providing a clean test for new physics.

Inclusivebandbb¯production with quasi-multi-Regge kinematics at the Tevatron

We consider $b$-jet hadroproduction in the quasi-multi-Regge-kinematics approach based on the hypothesis of gluon and quark Reggeization in $t$-channel exchanges at high energies. The preliminary data on inclusive $b$-jet and $b\overline{b}$-dijet production taken by the CDF Collaboration at the Fermilab Tevatron are well described without adjusting parameters. We find the main contribution to inclusive $b$-jet production to be the scattering of a Reggeized gluon and a Reggeized $b$ quark to a $b$ quark, which is described by the effective Reggeon-Reggeon-quark vertex. The main contribution to $b\overline{b}$-pair production arises from the scattering of two Reggeized gluons to a $b\overline{b}$ pair, which is described by the effective Reggeon-Reggeon-quark-quark vertex. Our analysis is based on the Kimber-Martin-Ryskin prescription for unintegrated gluon and quark distribution functions using as input the Martin-Roberts-Stirling-Thorne collinear parton distribution functions of the proton.

Diphoton production at the Tevatron in the quasi-multi-Regge-kinematic approach

We study the production of prompt diphotons in the central region of rapidity within the framework of the quasi-multi-Regge-kinematics approach applying the hypothesis of quark and gluon Reggeization. We describe accurately and without free parameters the experimental data which were obtained by the CDF Collaboration at the Tevatron Collider. It is shown that the main contribution to studied process is given by the direct fusion of two Reggeized gluons into a photon pair, which is described by the effective Reggeon-Reggeon to particle-particle vertex. The contribution from the annihilation of Reggeized quark-antiquark pair into a diphoton is also considered. At the stage of numerical calculations we use the Kimber-Martin-Ryskin prescription for unintegrated quark and gluon distribution functions, with the Martin-Roberts-Stirling-Thorne collinear parton densities for a proton as input.

Prompt photon photoproduction at HERA within the framework of the quark Reggeization hypothesis

We study the inclusive production of isolated prompt photons within the framework of the quasi-multi-Regge-kinematic approach, applying the quark Reggeization hypothesis. We describe accurately and without free parameters the transverse momentum and pseudorapidity spectra of prompt photons in the inclusive photoproduction at the HERA Collider. It is shown that the main mechanism of the inclusive prompt photon production in the $\ensuremath{\gamma}p$ collisions is the fusion of a Reggeized quark (antiquark) from the proton and a collinear antiquark (quark) from the photon into a photon, via the effective Reggeon-quark-gamma vertex. The fragmentation of the quark, which is produced via the gamma-Reggeon-quark and quark-Reggeon-quark vertices, into a photon is strongly suppressed by the isolation cone condition and it gives a significant contribution in the region of a large negative pseudorapidity only. At the stage of numerical calculations we use the Kimber-Martin-Ryskin prescription for unintegrated quark and gluon distribution functions, with the following collinear parton densities as input: Martin-Roberts-Stirling-Thorne for a proton and Gl\"uck-Reya-Vogt for a photon.

Transverse-momentum-dependent parton distribution function and jet transport in a nuclear medium

We show that the gauge-invariant transverse-momentum-dependent (TMD) quark distribution function can be expressed as a sum of all higher-twist collinear parton matrix elements in terms of a transport operator. From such a general expression, we derive the nuclear broadening of the transverse-momentum distribution. Under the maximal two-gluon correlation approximation, in which all higher-twist nuclear multiple parton correlations with the leading nuclear enhancement are given by products of twist-two nucleon parton distributions, we find the nuclear transverse-momentum distribution as a convolution of a Gaussian distribution and the nucleon TMD quark distribution. The width of the Gaussian, or the mean total transverse-momentum broadening squared, is given by the path integral of the quark transport parameter ${\stackrel{^}{q}}_{F}$ which can also be expressed in a gauge-invariant form and is given by the gluon distribution density in the nuclear medium. We further show that contributions from higher-twist nucleon gluon distributions can be resummed under the extended adjoint two-gluon correlation approximation and the nuclear transverse-momentum distribution can be expressed in terms of a transverse-scale-dependent quark transport parameter or gluon distribution density. We extend the study to hot medium and compare to dipole model approximation and $\mathcal{N}=4$ supersymmetric Yang-Mills (SYM) theory in the strong coupling limit. We find that multiple gluon correlations become important in the strongly coupled system such as $\mathcal{N}=4$ SYM plasma.

Heavy quarkonium production in the regge limit of quantum chromodynamics

Heavy quarkonium \((c\bar c,b\bar b)\) hadronic production at Tevatron (run I and run II) and LHC energies is considered in the framework of nonrelativistic quantum chromodynamics in the leading order with respect to α s and v using the quasi-multi-Regge kinematics approach. Fitting of p T spectra of different S and P wave heavy quarkonium states at Tevatron (run I and run II) energies is carried out. The obtained set of octet nonperturbative matrix elements is used for prediction of heavy quarkonium production at LHC energies. The results obtained in the framework of quasi-multi-Regge kinematics are compared with predictions of the collinear parton model.

Relative contributions of fusion and fragmentation mechanisms inJ/ψphotoproduction at high energy

We study J/psi photoproduction via the fusion and fragmentation mechanisms at the HERA Collider within the frameworks of the collinear parton model and the quasi-multi-Regge kinematics approach using the factorization formalism of non-relativistic QCD at leading order in the strong-coupling constant alpha_s and the relative velocity v of the bound quarks. It is shown that the fusion production mechanism dominates over the fragmentation production mechanism at the all relevant J/psi transverse momenta. The J/psi meson p_T-spectra in the fragmentation and fusion production at the asymptotically large p_T have equal slopes in the quasi-multi-Regge kinematics approach, oppocite the collinear parton model.

AssociatedΥ+b+b¯production at the Fermilab Tevatron and CERN LHC

In the framework of perturbative QCD and nonrelativistic bound state formalism, we calculate the production of {upsilon} mesons associated with open-beauty particles at the Tevatron and LHC conditions. We show that the contribution from the {upsilon}+b+b channel becomes comparable with that of {upsilon} sole production at the LHC at high enough transverse momenta, but is small at the Tevatron. We investigate the {upsilon} polarization effects and kinematic correlations between {upsilon} mesons and the accompanying open-beauty mesons. We show that the correlations are sensitive to the initial k{sub t} of the colliding partons, and so, can be considered as an additional test discriminating the collinear parton model and the k{sub t}-factorization approach.

Topics in associatedJ/ψ+c+c¯production at modern colliders

In the framework of perturbative QCD and nonrelativistic bound state formalism, we calculate the production of $J/\ensuremath{\psi}$ mesons associated with open-charm particles at HERA and Tevatron conditions. We show that the contribution from $J/\ensuremath{\psi}+c+\overline{c}$ channel becomes comparable with that of $J/\ensuremath{\psi}$ sole production at high $J/\ensuremath{\psi}$ transverse momenta (approximately, at ${p}_{\ensuremath{\psi},T}>10\text{ }\text{ }\mathrm{GeV}$). We investigate the $J/\ensuremath{\psi}$ polarization effects and kinematic correlations between $J/\ensuremath{\psi}$ mesons and the accompanying open-charmed mesons. We show that the correlations are sensitive to the initial ${k}_{t}$ of the colliding partons, and so, can be considered as an additional test discriminating the collinear parton model and the ${k}_{t}$-factorization approach.

Transverse momentum in semi-inclusive deep inelastic scattering

Within the framework of perturbative quantum chromodynamics we derive the evolution equations for transverse momentum dependent distributions and apply them to the case of semi-inclusive deep inelastic scattering. The evolution equations encode the perturbative component of transverse momentum generated by collinear parton branchings. The current fragmentation is described via transverse momentum dependent parton densities and fragmentation functions. Target fragmentation instead is described via fracture functions. We present, to leading logarithmic accuracy, the corresponding semi-inclusive deep inelastic scattering cross-section, which applies to the entire phase space of the detected hadron. Some phenomenological implications and further developments are briefly outlined.

APACIC++ 2.0. A PArton Cascade In C++

The new version of the parton shower module APACIC++ for the SHERPA event generator framework is presented. It incorporates some features, that are specific for the consistent merging with multi-particle matrix elements at tree-level. This publication also includes some example results and a short description of the upgraded class structure of APACIC++, version 2.0. Program summary Title of program: APACIC++, version 2.0 Catalogue identifier:ADNE_v2_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADNE_v2_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Catalogue identifier of previous version: ADNE Authors of previous version: R. Kuhn, F. Krauss, B. Iványi, G. Soff Journal reference of previous version: Comput. Phys. Commun. 134 (2001) 223 Licensing provisions: none Operating system under which the program has been tested: Linux, Unix, Darwin Programming language: C++ No. of lines in distributed program, including test data, etc.: 78 352 No. of bytes in distributed program, including test data, etc.: 2 561 276 External routines/libraries used: The makeinstall requires the autotools package Distribution format: tar gzip file Nature of the physical problem: Modern collider-based experiments in particle physics are characterized by increasing energies that are released and, thus, by a growing number of particles that are produced. The large numbers of involved particles renders it impossible to derive fully analytical predictions for a detailed description of the final state. In addition, the transformation of the partons of perturbative quantum field theory into the experimentally observable hadrons is until now not understood on a quantitative level. These obstacles prevent a direct comparison of analytical predictions with experimental data, and simulation tools need to be employed to bridge this gap. Method of solution: The event generator SHERPA with a new version of the parton shower module APACIC++ is able to simulate e + e − -annihilation experiments as well as hadron–hadron collision. The generated events are suitable for direct comparison with experiment. This is achieved by dividing the simulation into well-separated steps. First, the signal process is selected by employing multi-particle matrix elements at tree-level. Then the strong interacting particles experience additional radiation of soft or collinear partons described by means of the parton shower. Finally, the partons are translated into observable hadrons using phenomenological models. The module APACIC++ concentrates on the parton shower evolution of jets, both in the initial and in the final state of the signal process. Suitable interfaces to other modules of the event generator SHERPA are provided. Reasons for the new version: This new version is able to perform not only final state shower but also initial state shower evolutions. Thus the program gives now also a realistic description of proton–proton and proton–anti-proton collisions. It is particularly designed to simulate events at the Tevatron or the LHC. Summary of revisions: The package has been extended by a number of classes for the description of the initial state shower. In order to give optimal support for these new routines, all existing classes of the final state shower have been revised, but the basic structure and concept of the program has been maintained. In addition a new dicing strategy has been introduced in the time-like evolution routine, which substantially improved the performance of the final state shower. Additional comments: The package APACIC++ is used as the parton shower module of the general purpose event generator SHERPA. There it takes full advantage of its capabilities to merge multi-jet matrix element and parton shower evolution. Running time: The example programs take a matter of seconds to run.

Electroproduction of D*± mesons at high energies

A comparative analysis of the predictions of the collinear parton model and the kT-factorization approach is performed for the case of the D*-meson electroproduction at the HERA ep collider. It is shown that, owing to effectively taking into account, in noncollinear distributions, next-order corrections in the strong coupling constant αs, the kT-factorization approach increases, in contrast to the predictions of the collinear parton model, the absolute value of the cross sections for charmed-meson electroproduction by approximately a factor of 1.5 to 2. As a result, the agreement with experimental data is improved. This is not so only for the pseudorapidity spectrum, whose shape differs considerably from the experimental one and depends greatly on the choice of parametrization of the noncollinear gluon distribution within the proton.

Production of [formula omitted] mesons via fragmentation in the [formula omitted]-factorization approach

In the framework of the kT-factorization approach we have calculated in the fragmentation model the pT-spectra of Bc mesons at the energies of the Tevatron and the LHC Colliders and at the large pT domain. We compare the obtained results with the existing experimental data and with the predictions obtained in the collinear parton model.

Soft-collinear messengers: A new mode in soft-collinear effective theory

It is argued that soft-collinear effective theory for processes involving both soft and collinear partons, such as exclusive B-meson decays, should include a new mode in addition to soft and collinear fields. These "soft-collinear messengers" can interact with both soft and collinear particles without taking them far off-shell. They thus can communicate between the soft and collinear sectors of the theory. The relevance of the new mode is demonstrated with an explicit example, and the formalism incorporating the corresponding quark and gluon fields into the effective Lagrangian is developed.