The influence of the medium dependent finite width of QGP bags on their equation of state is analyzed within an exactly solvable model. It is argued that the large width of the QGP bags not only explains the observed deficit in the number of hadronic resonances, but also clarifies the reason why the heavy QGP bags cannot be directly observed as metastable states in a hadronic phase. The model allows us to estimate the minimal value of the width of QGP bags from a variety of the lattice QCD data and get that the minimal resonance width at zero temperature is about 600 MeV, whereas the minimal resonance width at the Hagedorn temperature is about 2000 MeV. As shown these estimates are almost insensitive to the number of the elementary degrees of freedom. The recent lattice QCD data are analyzed and it is found that besides sigma T**4 term the lattice QCD pressure contains T-linear and T**4 ln T terms in the range of temperatures between 240 MeV and 420 MeV. The presence of the last term in the pressure bears almost no effect on the width estimates. Our analysis shows that at hight temperatures the average mass and width of the QGP bags behave in accordance with the upper bound of the Regge trajectory asymptotics (the linear asymptotics), whereas at low temperatures they obey the lower bound of the Regge trajectory asymptotics (the square root one). Since the model explicitly contains the Hagedorn mass spectrum, it allows us to remove an existing contradiction between the finite number of hadronic Regge families and the Hagedorn idea of the exponentially growing mass spectrum of hadronic bags.
In order to check the compatibility of the gluon Reggeization in QCD with the $s$-channel unitarity, the one-loop correction to the Reggeon-Reggeon-gluon vertex must be known at arbitrary space-time dimension $D$. We obtain this correction from the gluon production amplitude in the multi-Regge kinematics and present an explicit expression for it in terms of a few integrals over the transverse momenta of virtual particles. The one-gluon contribution to the non-forward BFKL kernel at arbitrary $D$ is also obtained.
Contributions from gluon interactions, which are non-leading in high-energy semi-hard processes, are studied and represented in terms of reggeon exchanges. Unlike the leading gluonic reggeon, related to the BFKL pomeron, the non-leading reggeons are sensitive to the spin and transverse momentum distributions of scattering partons. There are several gluonic reggeons with poles in the vicinity of angular momentum $j=0$ contributing to the perturbative Regge asymptotics of QCD. We extend the high-energy effective action including sub-leading terms which describe these reggeons and their interacti…
In spite of the fact that the Gribov's theorem about the region of applicability of the soft emission factorization cannot be referred literally to the case of massless charged particles, it can be used for the calculation of soft emission amplitudes in such a case also. We demonstrate this for the gluon production amplitude in the multi-Regge kinematics with small transverse momentum.
We study the next-to-leading gluon exchange in the high-energy scattering that contributes to the amplitude to order $s^0$ up to logarithmic corrections. Similar to the leading gluon exchange these contribution can be described in terms of reggeon exchanges. There are several gluonic reggeons at the next-to-leading level. Some of them transfer parity or gauge group representation different from the leading gluonic reggeon. Unlike the leading one they are sensitive to the helicity and transverse momenta of the scattering partons. We extend the high-energy effective action and derive from the ac…
The vertex is constructed for gluon production in interaction of two reggeons coupled to projectiles and two reggeons coupled to targets. The vertex can be used to build cross-sections for collisions of two pairs of nucleons in AA scattering. Transversality of the constructed vertex is demonstrated as well as its good behaviour at large longitudinal momenta necessary for applications. Poles at zero values of longitudinal momenta are discussed and it is found that they remain in the amplitudes unlike in the case of a single projectile.
One loop corrections to the coupling of the reggeized gluon to quarks are calculated in QCD. Combining this result with the known corrections to the gluon-gluon-reggeon vertex, we check the self-consistency of the representation of the amplitudes with gluon quantum numbers and negative signature in the $t$-channel in terms of Regge pole contribution.
The quark loop contribution to the reggeon-reggeon-gluon vertex is calculated in QCD, where the reggeon is the reggeized gluon. Compared with the vertex in the Born approximation, this contribution exhibits a new spin structure as well as the gluon loop one. A remarkable but not complete cancellation between gluon and quark contributions to this new spin structure takes place for the case of three massless quark flavours.
The method of calculation of effective vertices of interaction of the Reggeized gluon and quark with particles in QCD in the next-to-leading order is developed. The method is demonstrated in the case of already known vertices of both gluon-gluon and quark-quark transitions in the scattering of gluons and quarks on the Reggeized gluon. It is used for the calculation of the gluon-quark transition in the scattering on the Reggeized quark.
The appearance of the U(1) anomaly in the interactions of reggeized gluons is described. Also discussed is the crucial role the anomaly can play in providing the non-perturbative properties necessary for a transition from gluon and quark reggeon diagrams to hadron reggeons and a reggeon field theory description of the pomeron.
Using an exactly solvable statistical model we discuss the equation of state of large/heavy and short-living quark gluon plasma (QGP) bags. We argue that the large width of the QGP bags explains not only the observed deficit in the number of hadronic resonances, but also clarifies the reason why the heavy QGP bags cannot be directly observed even as metastable states in a hadronic phase. Also the Regge trajectories of large and heavy QGP bags are established both in a vacuum and in a strongly interacting medium. It is shown that at high temperatures the average mass and width of the QGP bags b…
The temperature and chemical potential dependent surface tension of bags is introduced into the gas of quark-gluon bags model. This resolves a long standing problem of a unified description of the first and second order phase transition with the cross-over. Such an approach is necessary to model the complicated properties of quark-gluon plasma and hadronic matter from the first principles of statistical mechanics. The suggested model has an exact analytical solution and allows one to rigorously study the vicinity of the critical endpoint of the deconfinement phase transition. The existence of …
Application of the effective action formalism is studied for processes in which the reggeons may split. It is shown that the gluon production on two centers is described by the contribution of the Reggeon-to-two-Reggeons-plus-Particle vertex supplemented by certain singular contributions from the double gluon exchange. The rules for longitudinal integrations are established from the comparison to perturbative QCD amplitude. Convenient expressions for application to the inclusive gluon production are derived.
The vertex for gluon emission during the splitting of a reggeized gluon into two is constructed in the framework of Lipatov effective action formalism. Its reduction to a pure transverse form for the diffractive amplitude gives the standard Bartels vertex plus an additional contribution corresponding to the emission from a pointlike splitting vertex. This additional contribution turns out to be given by a longitudinal integral divergent both in the ultraviolet and infrared. A certain specific recipe for this part, including the principal value prescription for the integration, allows to elimin…
We consider inclusive hadroproduction of jets, prompt photons, b-jets, and D-mesons in the quasi-multi-Regge-kinematics approach based on the hypothesis of gluon and quark Reggeization in t-channel exchanges at high energies. The data taken by the CDF and D0 Collaborations at the Fermilab Tevatron are well described without adjusting parameters. We find the main contribution to inclusive jet production to be the scattering of two Reggeized gluons, described by the effective Reggeon-Reggeon-gluon vertex, and to b-jet and D-meson production --- the scattering of a Reggeized gluon and a Reggeized…
Ward identities for reggeons are studied in the framework of effective action approach to the QCD in Regge kinematics. It is shown that they require introduction of new contributions not present in the reggeon diagrams initially. Application to vertices RR$\to$RP and RR$\to$RRP are considered and diagrams which have to be added to the QCD ones are found.
We study a smooth crossover transition in the gas of quark-gluon bags. The equation of state at high temperature is that of the quark-gluon plasma. However, the system consists of the bags with finite volumes which are defined by the model parameters of the mass-volume bag spectrum. Possible structures in this {\it cluster} quark-gluon plasma are classified.
Integral kernels describing the pair interaction of reggeized gluons and quarks are reconstructed in terms of conformal symmetric 4-point functions in the transverse plane of impact parameters.
I discuss radiative corrections to the BFKL equation for high energy cross sections in perturbative QCD. Due to the gluon Reggeization in the next-to-leading $\ln s$ approximation, the form of the BFKL equation remains unchanged and the corrections to the BFKL kernel are expressed in terms of the two-loop contribution to the gluon Regge trajectory, the one-loop correction to the Reggeon-Reggeon-gluon vertex and the contributions from two-gluon and quark-antiquark production in Reggeon-Reggeon collisions. I present the results of the calculation of the BFKL kernel in the next-to leading logarit…
General expressions for the impact factors up to terms vanishing at the space-time dimension $D\rightarrow 4$ are presented. Their infrared behaviour is analysed and calculation of exact in $D\rightarrow 4$ asymptotics at small momenta of Reggeized gluons is discussed.
We calculate the effective vertices for the quark-antiquark and the quark-antiquark-gluon production in the virtual photon - Reggeized gluon interaction. The last vertex is considered at the Born level; for the first one the one-loop corrections are obtained. These vertices have a number of applications; in particular, they are necessary for calculation of the virtual photon impact factor in the next-to-leading logarithmic approximation.
We calculate impact factors for Reggeon-gluon transition in supersymmetric Yang-Mills theory with four supercharges at large number of colours Nc. In the next-to-leading order impact factors are not uniquely defined and must accord with BFKL kernels and energy scales. We obtain the impact factor corresponding to the kernel and the energy evolution parameter, which is invariant under Moebius transformation in momentum space, and show that it is also Moebius invariant up to terms taken into account in the BDS ansatz.
Application of the effective action approach to amplitudes with loop integration is studied for collisions on two and three centers with possible gluon emission. A rule is formulated for the integration around pole singularities in the induced vertices which brings the results in agreement with the QCD. It is demonstrated that the amplitudes can be restored from the purely transverse picture by introducing the standard Feynman propagators for intermediate gluons and quarks.
We calculate spectra of secondary particles produced in process of single diffraction dissociation in the Model of Quark-Gluon Strings. For description of diffractive dissociation process we use the reggeon model where all legs of triple-reggeon diagrams are eikonalized. Numerical calculation shows that the model gives a good description of data on charged particles pseudorapidity distribution in $p\bar{p}$ single diffractive dissociation.
Starting from the multi-Regge effective action for high-energy scattering in QCD a $t$-channel approach can be developed which is similar to the approach by White based on general Regge arguments. The BFKL kernel of reggeized gluon interaction, contributions to the $2 \rightarrow 4 $ reggeized gluon vertex function and the one-loop correction to the BFKL kernel are considered. The conditions are discussed under which this approach can provide a simple estimante of the next-to-leading logarithmic corrections to the BFKL perturbative pomeron intercept.
We discuss exclusive central production of Higgs boson, quark-antiquark and digluon dijets. Some differential distributions are shown and disussed. Irreducible leading-order $b \bar b $ background to Higgs production is calculated. The signal-to-background ratio is shown and improvements are suggested by imposing cuts on $b$ ($\bar b$) transverse momenta and rapidities. We disuss also gluonic dijet production. Here we use rather reggeon-reggeon-gluon vertices. We discuss briefly also a new mechanism of emission of gluons from different $t$-channel gluons (reggeons). The latter contribution tur…
In the framework of the QCD effective action the vertices of gluon emission in interaction of reggeons are studied in the limit of small longitudinal momenta of the emitted gluon. It is found that the vertices drastically simplify in this limit so that the gluon becomes emitted from a single reggeon coupled to the projectile and target via multireggeon vertices. Contribution from this kinematical region is studied for double and 2x2 elementary collisions inside the composite projectile and target.
In the Regge kinematics the amplitude for gluon production off three scattering centers is found in the Lipatov effective action technique. The vertex for gluon emission with the reggeon splitting in three reggeons is calculated and its transversality is demonstrated. It is shown that in the sum of all contributions terms containing principal value singularities are cancelled and substituted by the standard Feynman poles. These results may be used for calculation of the inclusive cross-section for gluon production on two nucleons in the nucleus.
We study the properties of the colour-singlet compound states of reggeized gluons in multi-colour QCD. Applying the methods of integrable models, we calculate their spectrum and discuss the application of the obtained results to high-energy asymptotics of the scattering amplitudes in perturbative QCD.
The unitarity corrections to the propagator of reggeized gluons calculated in the framework of QCD RFT require a knowledge of the expressions for Reggeon propagator and vertices of interaction of three reggeized gluons (Reggeons) to one QCD loop precision, see \cite{Our6}. In this paper we calculate the vertex of interactions of $A_+ A_+ A_-$ Reggeon fields, i.e. vertex of transition of $A_-$ Reggeon field to $A_+ A_+$ fields, to this precision. We demonstrate, that all loop leading logarithmic order contributions to the vertex can be summed through the integro-differential equation similarly …
We continue the study of hadronic scattering amplitudes at high energy by systematically including nonlinear effects of finite partonic density in hadronic wave function as well as the effects of multiple rescatterings in the scattering process. In this paper we derive expressions for a single inclusive gluon production amplitude and multigluon inclusive production amplitudes when the rapidities of all observed gluons are not very different. We show that at leading order these observables exhibit a semiclassical structure. Beyond the semiclassical result, we find that the gluon emission has so…
Compatibility of gluon Reggeization with s-channel unitarity requires the vertices of the Reggeon interactions to satisfy a series of bootstrap conditions. In order to derive, in the next-to-leading order (NLO), conditions related to the gluon production amplitudes, we calculate the s-channel discontinuities of these amplitudes and compare them with those required by the Reggeization. It turns out that these conditions include the so called strong bootstrap conditions for the kernel and for the impact factors of scattering particles, which were proposed earlier without derivation, and recently…
We reinterpret the JIMWLK/KLWMIJ evolution equation as the QCD Reggeon field theory (RFT). The basic "quantum Reggeon field" in this theory is the unitary matrix $R$ which represents the single gluon scattering matrix. We discuss the peculiarities of the Hilbert space on which the RFT Hamiltonian acts. We develop a perturbative expansion in the RFT framework, and find several eigenstates of the zeroth order Hamiltonian. The zeroth order of this perturbation preserves the number of $s$ - channel gluons. The eigenstates have a natural interpretation in terms of the $t$ - channel exchanges. Study…
We calculate the quark part of the kernel of the generalized non-forward BFKL equation at non-zero momentum transfer $t$ in the next-to-leading logarithmic approximation. Along with the quark contribution to the gluon Regge trajectory, this part includes pieces coming from the quark-antiquark production and from the quark contribution to the radiative corrections in one-gluon production in the Reggeon-Reggeon collisions. The results obtained can be used for an arbitrary representation of the colour group in the $t-$channel. Using the results for the adjoint representation, we demonstrate expli…
We consider the flavour non-singlet Reggeon within the context of perturbative QCD. This consists of ladders built out of ``reggeized'' quarks. We propose a method for the numerical solution of the integro-differential equation for the amplitude describing the exchange of such a Reggeon. The solution is known to have a sharp rise at low values of Bjorken-x when applied to non-singlet quantities in deep-inelastic scattering. We show that when the running of the coupling is taken into account this sharp rise is further enhanced, although the Q^2 dependence is suppressed by the introduction of th…
Deep-inelastic diffractive scaling violations have provided fundamental insight into the QCD pomeron, suggesting a single gluon inner structure rather than that of a perturbative two-gluon bound state. This paper derives a high-energy, transverse momentum cut-off, confining solution of QCD. The pomeron, in first approximation, is a single reggeized gluon plus a ``wee parton'' component that compensates for the color and particle properties of the gluon. This solution corresponds to a supercritical phase of Reggeon Field Theory. Beginning with the multi-regge behavior of massive quark and gluon…
We study open charm production at high energies in the framework of the quasi-multi-Regge-kinematics approach applying the quark-Reggeization hypothesis implemented with Reggeon-Reggeon-particle and Reggeon-particle-particle effective vertices. Adopting the Kimber-Martin-Ryskin unintegrated quark and gluon distribution functions of the proton and photon, we thus nicely describe the proton structure function F_{2,c} measured at DESY HERA as well as the transverse-momentum distributions of D mesons created by photoproduction at HERA and by hadroproduction at the Fermilab 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 anti-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 anti-b-pair prod…
The critical indices α', β, γ' and δof the Quark Gluon Bags with Surface Tension Model with the tricritical endpoint are calculated as functions of the usual parameters of this model and two newly introduces parameters (indices). They are compared with the critical exponents of other models. It is shown that for the newly introduced indices χ= 0 and ξ^T < 1 there is a branch of solutions for which the critical exponents of the present model and the statistical multifragmentation model coincide, otherwise these models belong to different universality classes. It is shown that for realistic valu…
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 …
We study the spectrum of the reggeized gluon compound states in high-energy QCD. The energy of the states depends on the total set of quantum numbers whose values are constrained by the quantization conditions. To establish their explicit form we apply the methods of nonlinear WKB analysis to the Schrödinger equation for the $N$ reggeon state in the separated coordinates. We solve the quantization conditions for the N=3 reggeon states in the leading order of the WKB expansion and observe a good agreement of the obtained spectrum of quantum numbers with available exact solutions.
We study the properties of the colour-singlet compound states of reggeized gluons in multi-colour QCD using their relation with noncompact Heisenberg spin magnets. Applying the methods of integrable models, we calculate their spectrum and discuss the application of the obtained results to high-energy asymptotics of the scattering amplitudes in perturbative QCD.
We discuss here the novel view at the color confinement which, on the one hand, allows us to find out the surface tension coefficient of quark gluon bags and, under a plausible assumption, to determine the endpoint temperature of the QCD phase diagram, on the other hand. The present model considers the confining color tube as the cylindrical quark gluon bag with non-zero surface tension. A close inspection of the free energies of elongated cylindrical bag and the confining color tube that connects the static quark-antiquark pair allows us to find out the string tension in terms of the surface …
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 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 Regg…
We consider the QCD scattering amplitudes at high energies sqrt{s} and fixed momentum transfers sqrt{-t} in the leading logarithmic approximation at a non-zero temperature T in the t-channel. It is shown that the BFKL Hamiltonian has the property of holomorphic separability. The Pomeron wave function for arbitrary T is calculated using an integral of motion. In multi-colour QCD, the holomorphic Hamiltonian for n-reggeized gluons at temperature T is shown to coincide with the local Hamiltonian of an integrable Heisenberg model and can be obtained from the T=0 Hamiltonian by an unitary transform…
The chromo-dielectric soliton model (CDM) is Lorentz- and chirally-invariant. It has been demonstrated to exhibit dynamical chiral symmetry breaking and spatial confinement in the locally uniform approximation. We here study the full nonlocal quark self energy in a color-dielectric medium modeled by a two parameter Fermi function. Here color confinement is manifest. The self energy thus obtained is used to calculate quark wave functions in the medium which, in turn, are used to calculate the nucleon and pion masses in the one gluon exchange approximation. The nucleon mass is fixed to its empir…
Here we revisit the bag phenomenology of the deconfining phase transition to replenish it by introducing systematically the bag surface tension. Comparing the free energy of such bags and that one of the strings confining the static quark-antiquark pair, we express the string tension in terms of the bag surface tension and thermal pressure in order to estimate the bag characteristics using the lattice QCD data. Our analysis of the bag entropy density demonstrates that the surface tension coefficient is amazingly negative at the cross-over (continuous transition). This approach allows us to nat…
A detailed discussion of recent results obtained within the hadron resonance gas model with the multi-component hard core repulsion is presented. Among them there are the adiabatic chemical freeze-out criterion, the concept of separate chemical freeze-out of strange particles and the effects of enhancement and sharpening of wide resonances and quark gluon bags occurring in a thermal medium. These findings are discussed in order to strengthen the planned heavy-ion collision experimental programs at low collision energies. We argue, that due to found effects, at the center of mass collision ener…
Reggeized gluon interactions due to a single quark loop are studied in the full triple-regge limit and in closely related helicity-flip helicity-pole limits. Triangle diagram reggeon interactions are generated that include local axial-vector effective vertices. It is shown that the massless quark triangle anomaly is present as a chirality-violating infra-red divergence in the interactions generated by maximally non-planar Feynman diagrams. An asymptotic dispersion relation formalism is developed which provides a systematic counting of anomaly contributions. The asymptotic amplitude is written …
It is usually assumed -- following the parton model -- that the leading-twist structure functions measured in deep inelastic lepton-proton scattering are simply the probability distributions for finding quarks and gluons in the target nucleon. In fact, gluon exchange between the outgoing quarks and the target spectators effects the leading-twist structure functions in a profound way, leading to diffractive leptoproduction processes, shadowing and antishadowing of nuclear structure functions, and target spin asymmetries, physics not incorporated in the light-front wavefunctions of the target co…
We study the effects of the ground state entropy of colored quarks upon the bag pressure at low temperatures. The vacuum expectation values of the quark and gluon fields are used to express the interactions in QCD ground state in the limit of low temperatures and chemical potentials. Apparently, the inclusion of this entropy in the equation of state provides the hadron constituents with an additional heat which causes a decrease in the effective latent heat inside the hadronic bag and consequently decreases the non-perturbative bag pressure. We have considered two types of baryonic bags, $Δ$ a…
In ultra-relativistic heavy ion collisions at $\roots\approx200$ GeV, the azimuthal emission anisotropy of hadrons with low and intermediate transverse momentum ($p_T\lesssim 4$ GeV/c) displays an intriguing scaling. In particular, the baryon (meson) emission patterns are consistent with a scenario in which a bulk medium of flowing quarks coalesces into three-quark (two-quark) "bags." While a full understanding of this number of constituent quark (NCQ) scaling remains elusive, it is suggestive of a thermalized bulk system characterized by colored dynamical degrees of freedom-- a quark-gluon pl…
