Quark Antiquark Research Articles

Measuring the flavor asymmetry in the sea quarks of the proton with the Drell–Yan process

The proton is a composite object made of fundamental, strongly interacting quarks. Many of the features of the proton can be described by a simple picture based on three “valence” quarks bound by the exchange of gluons. However, protons are much more complex objects with the vast majority of their mass dynamically generated by quantum chromodynamics (QCD). This mass manifests itself through a “sea” of gluons and quark–antiquark pairs. By measuring Drell–Yan scattering, the Fermilab E-906/Drell–Yan experiment will study the sea quark distribution in the proton and, in particular, the unusually large asymmetry between anti-up and anti-down quarks measured by earlier Drell–Yan experiments. This asymmetry cannot simply be generated through pair creation, but rather indicates an underlying, fundamental antiquark component in the proton. Using the same technique, the E-906/SeaQuest experiment will also investigate the differences between the antiquark distributions of the free proton and a proton bound in a nucleus. Nuclear binding is expected to modify the quark distributions and it has long been known that the overall quark distributions are different (the EMC effect). Surprisingly, present data suggest, however, that the antiquark distributions are not modified. To accomplish these goals, the experiment will use a 120 GeV proton beam extracted from the Fermilab Main Injector. While the experiment will be taking advantage of equipment from earlier Drell–Yan experiments, the changes in kinematics of the experiment require several, significant upgrades to the spectrometer. Japanese institutions, including Tokyo Institute of Technology, KEK, RIKEN, Kyoto University and Yamagata University, are making substantial contributions to this upgrade. The collaboration expects to begin data collection in Summer, 2010.

Supermodels for early LHC

We investigate which new physics signatures could be discovered in the first year of the LHC, beyond the expected sensitivity of the Tevatron data by the end of 2010. We construct “supermodels”, for which the LHC sensitivity even with only 10 pb−1 useful luminosity is greater than that of the Tevatron with 10 fb−1. The simplest supermodels involve s-channel resonances in the quark–antiquark and especially in the quark–quark channels. We concentrate on easily visible final states with small standard model backgrounds, and find that there are simple searches, besides those for Z′ states, which could discover new physics in early LHC data. Many of these are well-suited to test searches for “more conventional” models, often discussed for multi-fb−1 data sets.

Rotating mesons in the presence of higher derivative corrections from gauge–string duality

We consider a rotating quark–antiquark ( q q ¯ ) pair in N = 4 thermal plasma. By using the AdS/CFT correspondence, the properties of this system are investigated. In particular, we study variation of a rotating string radius at the boundary as a function of its tip and angular velocity. We also extend the results to higher derivative corrections, i.e. R 2 and R 4 which correspond to finite coupling corrections on the rotating quark–antiquark system in the hot plasma. In the R 4 case and for fixed angular velocity the string endpoints become more and more separated as λ − 1 decreases. To study R 2 corrections, rotating quark–antiquark system in Gauss–Bonnet background has been considered. We summarize the effects of these corrections in the conclusion section.

Sea quark contents of octet baryons

The flavor asymmetry of the nucleon sea, i.e., the excess of dd¯ quark–antiquark pairs over uu¯ ones in the proton, can be explained by several different models; therefore, it is a challenge to discriminate these models from each other. We examine in this Letter three models: the balance model, the meson cloud model, and the chiral quark model, and we show that these models give quite different predictions on the sea quark contents of other octet baryons. New experiments aimed at measuring the flavor contents of other octet baryons are needed for a more profound understanding of the non-perturbative properties of quantum chromodynamics (QCD).

Increase with energy of parton transverse momenta in the fragmentation region in DIS and related phenomena

The dipole and the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) approximations are combined with the ${k}_{t}$ factorization theorem to demonstrate the fundamental property of perturbative QCD: the smaller the size of the colorless quark-gluon configurations in the fragmentation region, the more rapid is the increase of its interaction with the target as a function of energy. First, we consider two closely related properties of the wave function of the projectile: (i) the transverse momenta of the quark(antiquark) within the $q\overline{q}$ pair, produced in the fragmentation region by the strongly virtual photon, increase with the decrease of $x$ for fixed ${Q}^{2}$, (ii) the relative contribution of perturbative QCD to the structure functions increases as compared to the soft QCD contribution at central impact parameters due to a rapid increase with energy of the cross section of interaction of small dipoles. Practical consequences of these effects are presented for the cases of the cross sections of deep inelastic scattering (DIS) and double virtual compton scattering (DVCS). We predict that the ratio of DVCS to DIS amplitudes should very slowly approach one from above at very large collision energies. Second, we study a closely related phenomenon of the increase of the transverse momenta with the energy of the characteristic transverse momenta of the gluon/quark configurations responsible for the transition to the black disk regime. We discuss the impact of this phenomenona on the slowing of the dependence on the initial energy of the coherence length. We demonstrate that a rapid projectile has the biconcave shape, which is different from the expectations of the pre-QCD parton model where a fast hadron has a pancake shape. We show that the increase of the transverse momenta leads to a new expression for the total cross section of a DIS at very large energies, relevant to LHeC and LHC. We discuss the impact of the discovered phenomena on the hard processes in $pp$ collisions, and on the dominance of different phases of chiral and conformal symmetries in the central and peripheral $pp$, $pA$, and $AA$ collisions.

On the quark component in prompt photon and electroweak gauge boson production at high energies

In the framework of the kT-factorization approach, we study the production of prompt photons and electroweak gauge bosons in high-energy proton–(anti)proton collisions at modern colliders. Our consideration is based on the amplitude for the production of a single photon or W±/Z0 boson associated with a quark pair in the fusion of two off-shell gluons. The quark component is taken into account separately using the quark–gluon scattering and quark–antiquark annihilation QCD subprocesses. Special attention is given to the contributions from the quarks involved in the earlier steps of the evolution cascade. Using the Kimber–Martin–Ryskin formalism, we simulate this component and demonstrate that it plays an important role at both the Tevatron and LHC energies. Our theoretical results are compared with recent experimental data taken by the D∅ and CDF Collaborations at the Tevatron.

Parton–hadron–string dynamics: An off-shell transport approach for relativistic energies

The dynamics of partons, hadrons and strings in relativistic nucleus–nucleus collisions is analyzed within the novel Parton–Hadron–String Dynamics (PHSD) transport approach, which is based on a Dynamical QuasiParticle Model (DQPM) for partons matched to reproduce recent lattice-QCD results – including the partonic equation of state – in thermodynamic equilibrium. Scalar- and vector-interaction densities are extracted from the DQPM as well as effective scalar- and vector-mean fields for the partons. The transition from partonic to hadronic degrees of freedom is described by covariant transition rates for the fusion of quark–antiquark pairs or three quarks (antiquarks), respectively, obeying flavor current-conservation, color neutrality as well as energy–momentum conservation. Since the dynamical quarks and antiquarks become very massive close to the phase transition, the formed resonant ‘pre-hadronic’ color-dipole states ( q q ¯ or qqq) are of high invariant mass, too, and sequentially decay to the groundstate meson and baryon octets increasing the total entropy. The PHSD approach is applied to nucleus–nucleus collisions from 20 to 160 A GeV in order to explore the space–time regions of ‘partonic matter’. We find that even central collisions at the top-SPS energy of 158 A GeV show a large fraction of non-partonic, i.e. hadronic or string-like matter, which can be viewed as a hadronic corona. This finding implies that neither hadronic nor only partonic ‘models’ can be employed to extract physical conclusions in comparing model results with data. On the other hand – studying in detail Pb + Pb reactions from 40 to 158 A GeV – we observe that the partonic phase has a very low impact on rapidity distributions of hadrons but a sizeable influence on the transverse mass distribution of final kaons due to the repulsive partonic mean fields. Furthermore, we find a significant effect on the production of multi-strange antibaryons due to a slightly enhanced s s ¯ pair production in the partonic phase from massive time-like gluon decay and a larger formation of antibaryons in the hadronization process.

A self-consistent thermodynamical quasiparticle description of QGP

We present a self-consistent quasiparticle model to investigate the thermal properties of quark–gluon plasma above the critical temperature. All effects of the interactions among the partons are contained in the thermal mass of partons, so the system may be treated as an ideal gas of the massive quarks and gluons. From the statistical mechanics, we can calculate the thermodynamical quantities without any inconsistency, and then obtain a good fit to the lattice QCD data. The results show that the main degree of freedom is from quark–antiquark pairs, even at the high temperature. Finally, the quark number fluctuation is also analyzed.

OFF-SHELL TWIST-FOUR PHOTON LIGHT-CONE WAVEFUNCTION FOR THE CHIRALITY-CONSERVING QUARK–ANTIQUARK VECTOR CURRENT IN THE LOW-ENERGY EFFECTIVE THEORY OF QCD

Within the framework of the low-energy effective theory arising from the instanton vacuum model of QCD, the twist-four virtual photon wavefunction, gγ3(u, P2), corresponding to the nonlocal quark–antiquark vector current is calculated at the low-energy scale. The coupling constant, fγ(P2), of the quark–antiquark vector current to the virtual photon state is also obtained. The behavior of the coupling as well as the obtained photon wave function especially at the end points is discussed.

On the shape of a rapid hadron in QCD

We visualize the fundamental property of pQCD: the smaller is the size of the colorless quark–gluon configuration, more rapid is the increase of its interaction with energy. Within the frame of the dipole model we use the kt factorization theorem to generalize the DGLAP approximation and/or leading ln(x0/x) approximation and evaluate the interaction of the quark dipole with a target. In the limit of fixed Q2 and x→0 we find the increase with energy of transverse momenta of quark (antiquark) within the qq¯ pair produced by the strongly virtual photon. The average pt2 is evaluated analytically within the double logarithmic approximation. We demonstrate that the invariant mass2 of the qq¯ pair increases with the energy as 0.7Q2(10−2/x)0.4αsNc/π, for transverse photons, and ∼0.7Q2exp0.36[(αsNc/π)log(10−2/x)]1/2 for longitudinal photons. We found similar pattern of the energy dependence of M2 in the LO DGLAP approximation generalized to account for the kt factorization. We discuss the impact of the found phenomenon on the dependence of the coherence length on the collision energy and demonstrate that in the regime of complete absorption effective shape of the sufficiently energetic hadron (nucleus) has the biconcave form instead of the pancake. We explain that the different representations of chiral symmetry for the central and peripheral collisions would be characteristic property of hadron (nucleus) nucleus collisions at large energies. Some implications of the found phenomena for pp collisions are discussed.

Heavy quark interactions and quarkonium binding**Based on joint work with O Kaczmarek and F Karsch.

We consider heavy quark interactions in quenched and unquenched lattice QCD. In a region just above the deconfinement point, non-Abelian gluon polarization leads to a strong increase in the binding. Comparing quark–antiquark and quark–quark interaction, the dependence of the binding on the separation distance r is found to be the same for the colorless singlet and the colored anti-triplet QQ state. In a potential model description of in-medium J/ψ behavior, this enhancement of the binding leads to a survival up to temperatures of 1.5 Tc or higher; it could also result in J/ψ flow.

Stability of asymmetric tetraquarks in the minimal-path linear potential

The linear potential binding a quark and an antiquark in mesons is generalized to baryons and multiquark configurations as the minimal length of flux tubes neutralizing the color, in units of the string tension. For tetraquark systems, i.e., two quarks and two antiquarks, this involves the two possible quark–antiquark pairings, and the Steiner tree linking the quarks to the antiquarks. A novel inequality for this potential demonstrates rigorously that within this model the tetraquark is stable in the limit of large quark-to-antiquark mass ratio.

Four-Quark Stability

The physics of charm has become one of the best laboratories exposing the limitations of the naive constituent quark model and also giving hints into a more mature description of meson spectroscopy, beyond the simple quark–antiquark configurations. In this talk we review some recent studies of multiquark components in the charm sector and discuss in particular exotic and non-exotic four-quark systems, both with pairwise and many-body forces.

Path integration in QCD with arbitrary space-dependent static color potential

We perform path integral for a quark (antiquark) in the presence of an arbitrary space-dependent static color potential A^a_0(x)(=-\int dx E^a(x)) with arbitrary color index a=1,2,...8 in SU(3) and obtain an exact non-perturbative expression for the generating functional. We show that such a path integration is possible even if one can not solve the Dirac equation in the presence of arbitrary space-dependent potential. It may be possible to further explore this path integral technique to study non-perturbative bound state formation.

QUARK MODEL WITH A REGULARIZED BREIT POTENTIAL

The Breit interaction contains terms that are singular in nature and cannot be used non-perturbatively for quark–antiquark bound state studies. We regularize the Breit interaction by subtraction such that the interaction is not singular at the origin but the intermediate and long-range parts of the interaction remain unchanged. With the regularized quark–antiquark potential and the confining potential, the solution of [Formula: see text] bound states are therefore stable possessing wave functions that can be used for future applications in other study of scattering and reaction problems.

Chiral partners and their electromagnetic radiation (Ingredients for a systematic in-medium calculation)

It is argued that the chiral partners of the lowest-lying hadrons are hadronic molecules and not three-quark or quark–antiquark states, respectively. As an example the case of a 1 as the chiral partner of the ρ is discussed. Deconfinement–or as a precursor large in-medium widths for hadronic states–is proposed as a natural way to accommodate for the fact that at chiral restoration the respective in-medium spectra of chiral partners must become degenerate. Ingredients for a systematic and self-consistent in-medium calculation are presented with special emphasis on vector-meson dominance which emerges from a recently proposed systematic counting scheme for the mesonic sector including pseudoscalar and vector mesons as active degrees of freedom.

Parton dynamics and hadronization from the sQGP

The hadronization of an expanding partonic fireball is studied within the Parton-Hadron-String Dynamics (PHSD) approach which is based on a dynamical quasiparticle model (DQPM) matched to reproduce lattice QCD results in thermodynamic equilibrium. Apart from strong parton interactions the expansion and development of collective flow is found to be driven by strong gradients in the parton mean-fields. An analysis of the elliptic flow v 2 demonstrates a linear correlation with the spatial eccentricity ϵ as in the case of ideal hydrodynamics. The hadronization occurs by quark–antiquark fusion or 3 quark/3 antiquark recombination which is described by covariant transition rates. Since the dynamical quarks become very massive, the formed resonant ‘pre-hadronic’ color-dipole states ( q q ̄ or q q q ) are of high invariant mass, too, and sequentially decay to the groundstate meson and baryon octets increasing the total entropy. This solves the entropy problem in hadronization in a natural way. Hadronic particle ratios turn out to be in line with those from a grand-canonical partition function at temperature T ≈ 170 MeV.

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.

Dileptons from a Chemically Equilibrating Quark–Gluon Plasma at Finite Baryon Density

We perform a complete calculation for the dilepton production from the processes qq̄→ll̄, Compton-like (qg→qll̄, q̄g→q̄ll̄), qq̄→gll̄, gluon fusion gḡ→cc̄, annihilation qq̄→cc̄ as well as multiple scattering of quarks in a chemically equilibrating quark–gluon plasma system at finite baryon density. It is found that quark–antiquark annihilation, Compton-like, gluon fusion and multiple scattering of quarks give important contribution. Moreover, the increase of the quark phase life-time with increasing initial quark chemical potential makes the dilepton yield as an increasing function of the initial quark chemical potential.

Erratum: Analytical solution oftt¯dilepton equations [Phys. Rev. D73, 054015 (2006)

The top quark antiquark production system in the dilepton decay channel is described by a set of equations which is nonlinear in the unknown neutrino momenta. Its most precise and least time consuming solution is of major importance for measurements of top quark properties like the top quark mass and $t\bar{t}$ spin correlations. The initial system of equations can be transformed into two polynomial equations with two unknowns by means of elementary algebraic operations. These two polynomials of multidegree two can be reduced to one univariate polynomial of degree four by means of resultants. The obtained quartic equation is solved analytically.