Glueballs and the superfluid phase of Two-Color QCD

We present the first results on scalar glueballs in cold, dense matter using lattice simulations of two-color QCD. The simulations are carried out on a 6³×12 lattice and use a standard hybrid molecular dynamics algorithm for staggered fermions for two values of quark mass. The glueball correlators are evaluated via a multi-step smearing procedure. The amplitude of the glueball correlator peaks in correspondence with the zero temperature chiral transition, μ _c=m _π /2, and the propagators change in a significant way in the superfluid phase, while the Polyakov loop is nearly insensitive to the transition. Standard analysis suggest that lowest mass in the 0⁺⁺ gluonic channel decreases in the superfluid phase, but these observations need to be confirmed on larger and more elongated lattices. These results indicate that a non-zero density induces non-trivial modifications of the gluonic medium.     

Infrared gluon and ghost propagator exponents from lattice QCD

The compatibility of the pure power law infrared solution of QCD and lattice data for the gluon and ghost propagators in Landau gauge is discussed. For the gluon propagator, the lattice data are well described by a pure power law with an infrared exponent κ∼0.53, in the Dyson–Schwinger notation. κ is measured using a technique that suppresses finite volume effects. This value is consistent with a vanishing zero momentum gluon propagator, in agreement with the Gribov–Zwanziger confinement scenario. For the ghost propagator, the lattice data seem not to follow a pure power law, at least for the range of momenta accessed in our simulation.     

Lattice QCD thermodynamic results with improved staggered fermions

We present results on the QCD equation of state, obtained with two different improved dynamical staggered fermion actions and almost physical quark masses. Lattice cut-off effects are discussed in detail as results for three different lattice spacings are available now, i.e. results have been obtained on lattices with temporal extent of N _τ =4,6 and 8. Furthermore we discuss the Taylor expansion approach to non-zero baryon chemical potential and present the isentropic equation of state on lines of constant entropy per baryon number.     

Schwinger mechanism for gluon-pair production in the presence of arbitrary time-dependent chromo-electric field

We study the Schwinger mechanism for gluon-pair production in the presence of an arbitrary time-dependent chromo-electric background field E ^a (t) with arbitrary color index a=1,2,…,8 in SU(3) by directly evaluating the path integral. We obtain an exact expression for the probability of non-perturbative gluon-pair production per unit time per unit volume and per unit transverse momentum, , from arbitrary E ^a (t). We show that the tadpole (or single-gluon) effective action does not contribute to the non-perturbative gluon-pair production rate, . We find that the exact result for non-perturbative gluon-pair production is independent of all the time derivatives , where n=1,2,…,∞, and that it has the same functional dependence on the two Casimir invariants, [E ^a (t)E ^a (t)] and [d _abc E ^a (t)E ^b (t)E ^c (t)]², as the constant chromo-electric field E ^a result with the replacement: E ^a →E ^a (t). This result relies crucially on the validity of the shift conjecture, which has not yet been established. This result may be relevant to the study of the production of a non-perturbative quark–gluon plasma at RHIC and LHC.     

Body fixed frame,rigid gauge rotations and largeN random fields in QCD

The body fixed frame with respect to local gauge transformations is introduced. Rigid gauge rotations in QCD and their Schrödinger equation are studied for static and dynamic quarks. Possible choices of the rigid gauge field configuration corresponding to a nonvanishing static colormagnetic field in the body fixed frame are discussed. A gauge invariant variational equation is derived in this frame. For large numberN of colors the rigid gauge field configuration is regarded as random with maximally random probability distribution under constraints on macroiscopic-like quantities. For the uniform magnetic field the joint probability distribution of the field components is determined by maximizing the appropriate entropy under the area law constraint for the Wilson loop. In the quark sector the gauge invariance requires the rigid gauge field configuration to appear not only as a background but also as inducing an instantaneous quark-quark interaction. Both are random in the largeN limit.Communicated by F. Lenz     

On the temperature dependence of quarkonium correlators

I discuss the temperature dependence of quarkonium correlators calculated in lattice QCD. I show that the dominant source of the temperature dependence comes from the zero-mode contribution, while the temperature dependence associated with the melting of bound states is quite small. I study the zero-mode contribution quantitatively for various quark masses and show that it is well described by a quasi-particle model with temperature-dependent heavy quark mass. As a byproduct, an estimate of the medium dependence of the heavy-quark mass is obtained.     

Gauge-invariant sub-structures of tree-level double-emission exact QCD spin amplitudes

In this note we discuss possible separations of exact, massive, tree-level spin amplitudes into gauge-invariant parts. We concentrate our attention on processes involving two quarks entering a color-neutral current and, thanks to the QCD interactions, two extra external gluons. We will search for forms compatible with parton-shower languages, without applying approximations or restrictions on phase space regions. Special emphasis will be put on the isolation of parts necessary for the construction of evolution kernels for individual splittings and to some degree for the running coupling constant as well. Our aim is to better understand the environment necessary to optimally match hard matrix elements with parton-shower algorithms. To avoid complications and ambiguities related to regularization schemes, we ignore, at this point, virtual corrections. Our representation is quite universal: any color-neutral current can be used; in particular, our approach is not restricted to vector currents only. This work is partially supported by RTN European Programme, MRTN-CT-2006-035505 (HEPTOOLS, Tools and Precision Calculations for Physics Discoveries at Colliders).     

QCD sum rules with finite masses

The concept of QCD sum rules is extended to bound states composed of particles with finite mass such as scalar quarks or strange quarks. It turns out that mass corrections become important in this context. The number of relevant corrections is analyzed in a systematic discussion of the IR- and UV-divergencies, leading in general to a finite number of corrections. The results are demonstrated for a system of two massless quarks and two heavy scalar quarks.We wish to thank Dr. Lech Mankiewicz for very helpful discussions. This work was supported by DFG (G. Hess program).     

On the resolution of singularities of multiple Mellin–Barnes integrals

One of the two existing strategies of resolving singularities of multifold Mellin–Barnes integrals in the dimensional regularization parameter, or a parameter of the analytic regularization, is formulated in a modified form. The corresponding algorithm is implemented as a Mathematica code MBresolve.m     

Top-quark pair production near threshold at LHC

The next-to-leading order analysis for the cross section for hadroproduction of top-quark pairs close to threshold is presented. Within the framework of non-relativistic QCD a significant enhancement compared to fixed-order perturbation theory is observed which originates from the characteristic remnant of the 1S peak below production threshold of top-quark pairs. The analysis includes all color-singlet and color-octet configurations of top-quark pairs in S-wave states and, for the dominant configurations, it employs all-order soft-gluon resummation for the hard parton cross section. Numerical results for the Large Hadron Collider at TeV and TeV and also for the Tevatron are presented. The possibility of a top-quark mass measurement from the invariant-mass distribution of top-quark pairs is discussed.     

Sigma mesonic mode near the QCD critical point

Properties of the QCD critical point, an endpoint of the first order boundary line in the temperature T–baryochemical potential μ _B plane, are discussed with the Nambu–Jona-Lasinio model. It is demonstrated that the softening of the sigma mesonic mode is inherent to the crossover transition of the chiral symmetry while the spectral enhancement of the particle–hole mode near zero frequency is associated with the QCD critical point. Phenomenological implications in heavy-ion experiments are mentioned briefly.     

Quantitative comparison of filtering methods in lattice QCD

We systematically compare filtering methods used to extract topological excitations (like instantons, calorons, monopoles and vortices) from lattice gauge configurations, namely APE-smearing and spectral decompositions based on lattice Dirac and Laplace operators. Each of these techniques introduces ambiguities, which can invalidate the interpretation of the results. We show, however, that all these methods, when handled with care, reveal very similar topological structures. Hence, these common structures are free of ambiguities and faithfully represent infrared degrees of freedom in the QCD vacuum. As an application we discuss an interesting power law for the clusters of filtered topological charge.     

Compressibility of hadrons from operator sum rules

Monopole sum rules for ar ² transition operator are discussed for baryons and mesons. From these, the energy of the compression modes can be directly related to the hadronic compressibility. From the systematics of excited hadrons the compressibility of baryons is found to be in the order of 1.3 GeV, quite close to that of mesons in the light and strange quark sector. Experiments will be very important to study the compression modes in different hadron systems.The author is indepted to the Institute of Nuclear Theory (INT Seattle) for the invitation to the program N ^* Excitations and the Structure of the Nucleon where basic ideas of the paper have been discussed. In particular, discussion with O. Bohigas, B.K. Jennings, and J. Wambach is gratefully acknowledged.     

Medium-modified average multiplicity and multiplicity fluctuations in jets

The energy evolution of average multiplicities and multiplicity fluctuations in jets produced in heavy-ion collisions is investigated from a toy QCD-inspired model. In this model, we use modified splitting functions accounting for medium-enhanced radiation of gluons by a fast parton which propagates through the quark–gluon plasma. The leading contribution of the standard production of soft hadrons is enhanced by a factor while next-to-leading order (NLO) corrections are suppressed by , where the parameter N _s >1 accounts for the induced soft gluons in the medium. Our results for such global observables are cross-checked and compared with their limits in the vacuum.     

On Gribov’s supercriticality picture of quark confinement

Some years ago Gribov developed the so-called supercritical light-quark confinement scenario. Based on physical arguments he conjectured a drastic change in the analytical properties of the quark propagator when the back reaction of Goldstone bosons (pions) is considered. We investigate this scenario and provide numerical solutions for the quark propagator in the complex plane with and without the pion back reaction. We find no evidence for the scenario Gribov advocated. As an aside we present a novel method to solve the quark Dyson–Schwinger equation in the complex plane and discuss new characteristics of dynamical chiral symmetry breaking in our truncation scheme.     

Comment on the recent COMPASS data on the spin structure function <Emphasis Type="Italic">g</Emphasis><Subscript>1</Subscript>

We examine the recent COMPASS data on the spin structure function g ₁ singlet. We show that it is rather difficult to use the data in the present form in order to draw conclusions on the initial parton densities. However, our tentative estimate is that the data better agree with positive than with negative initial gluon densities.     

Novel sets of coupling expansion parameters for low-energy pQCD

In quantum theory, physical amplitudes are usually presented in the form of a Feynman perturbation series in powers of coupling constant α. However, it is known that these amplitudes are not regular functions at α = 0. For QCD, we propose new sets of expansion parameters w _k (α _s ) that reflect singularity at α _s = 0 and should be used instead of powers α _s ^k . Their explicit form is motivated by the so-called Analytic Perturbation Theory. These parameters reveal saturation in a strong coupling case at the level α _s ^eff (α _s 1) = w ₁(α _s 1) ∼ 0.5. They can be used for the quantitative analysis of divers low-energy amplitudes. We argue that this new picture with non-power sets of perturbation expansion parameters, as well as the saturation feature, is of a rather general nature. The text was submitted by the author in English. A preliminary version with the main results was published in [1].