Inspired by the evidence of the odderon exchange recently observed by the D0 and TOTEM Collaborations, a QCD sum rule investigation is performed to study the odderon as a three-gluon bound state. There may exist six lowest-lying three-gluon odderons with the quantum numbers $J^{PC} = 1/2/3^{\pm-}$. We systematically construct their interpolating currents, and calculate their mass spectra. To verify their existence, we propose to search for the spin-3 odderons in their $VVV$ and $VVP$ decay channels directly at LHC, with $V$ and $P$ light vector and pseudoscalar mesons respectively.
We calculate the contribution arising from nonperturbative quark-gluon chromomagnetic interaction to the high energy total quark-quark cross section and to gluon distributions in nucleon. The estimation obtained within the instanton model of QCD vacuum leads to the conclusion that this type of interaction gives the dominating contribution to the Pomeron coupling with the light quarks and to gluon distribution in light hadrons at small virtualities of quarks and gluons. We argue that the Odderon, which is the $P=C=-1$ partner of Pomeron, is governed by the spin-flip component related to nonpert…
The study of the perturbative Odderon at high gluon densities in the color glass condensate requires to take into account states with more than three gluons. We formulate evolution equations for these states in which the number of gluons is not fixed during the evolution. We further determine the coupling of these Odderon states to the gamma to eta_c impact factor for arbitrary numbers of gluons. We find an exact solution of the evolution equation for the four-gluon Odderon state in terms of the three-gluon Odderon state. It is shown that a similar solution exists also for a different class of…
We discuss the odderon in the QCD and analyze the effects of running coupling introduced in a particular way to preserve the reggeization of the gluon within the leading logarithmic description. This idea is also applied to a family of BKP states with arbitrarily number of gluons in the planar limit. The numerical analysis shows that contrary to the pomeron case where the leading states become discretized, the odderon states still remain a continuous family starting at intercept one. The following rapidity dependence of the amplitude is studied. For the pomeron-odderon system the relation betw…
We describe the discovery of the colorless $C$-odd gluonic compound, the odderon, by the D0 and TOTEM Collaborations by comparing elastic differential cross sections measured in $pp$ and $p \bar{p}$ interactions at high energies.
We calculate the C=P=-1 contribution to high-energy scattering of hadrons in the framework of the model of the stochastic vacuum. In models, where the pomeron is generated by a two gluon exchange, this odderon contribution comes from a three gluon exchange and is much too large as compared to experimental data for pp- and $p\bar{p}$-scattering. In our model, where we have no quark-additivity, the hadron structure is very important. It is shown that a natural suppression of the odderon contribution is given by a diquark-structure of the nucleon.
We present and discuss a new bound state solution of the three gluon system in perturbative QCD. It carries the quantum numbers of the odderon, has intercept at one and couples to the impact factor $γ^* \to η_c$.
Theory and phenomenology of the eta_c photo- and electroproduction is developed from the point of view of probing the odderon singularity in QCD which corresponds to the three gluon exchange mechanism. This mechanism leads to the cross-sections which are independent of W^2 for the exchange of three non-interacting gluons or exhibit increase with increasing W^2 (or 1/x) for the odderon intercept above unity. The η_c electroproduction in the three gluon exchange mechanism is shown to be entirely controlled by the transversely polarised virtual photons. The magnitude of the eta_c photoproduction …
Recent results are summarized from the TOTEM experiment at CERN LHC, including measurements of the total, elastic and inelastic cross-sections, the nuclear slope parameter $B$, the differential cross-section of elastic scattering and the real to imaginary part ration $ρ$ at $\sqrt{s} = $ 2.76 and 13 TeV. The implications of these data for Odderon (odd-gluon colorless) exchange are discussed.
Starting from the leading Odderon solution of the three gluon system in perturbative QCD we introduce, as a first step towards the transition to the nonperturbative region, an infrared cutoff and use the running QCD coupling constant. In our numerical analysis we find that the fixed cut solution with intercept one persists, hinting at a physical Odderon with intercept one and a small t-slope.
The reactions gamma-gamma to eta_c eta_c and gamma gamma to eta_c + X are discussed within the three gluon exchange model. We give predictions for the differential cross-sections and discuss feasibility of measuring these processes at LEP2 and TESLA. The total cross-sections were estimated to be approximately equal to 40 fb and 120 fb for gamma-gamma to eta_c eta_c and gamma-gamma to eta_c + X respectively assuming exchange of elementary gluons that corresponds to the odderon with intercept equal to unity. These values can be enhanced by a factor equal to 1.9 and 2.1 for LEP2 and TESLA energie…
We study the perturbative Odderon in the quasidiffractive process gamma(*) gamma(*) to eta_c eta_c. At high energies this process is dominated by Odderon exchange and can be viewed as the theoretically cleanest test of the perturbative Odderon. We calculate the differential and total cross section, as well as the dependence on the energy and on the photon virtualities taking into account the effects of resummation of logarithms of the energy. The results are compared with those obtained with a simple exchange of three noninteracting gluons. We present the expected cross section for this proces…
The TOTEM 2.76, 7, 8, and 13 TeV pp elastic differential cross sections are extrapolated using a data-driven approach to obtain the 1.96 TeV pp elastic cross section. A difference with a 3.4$σ$ significance is observed between the extrapolated pp elastic cross section and the D0 p$\bar{\rm p}$ elastic cross section at 1.96 TeV in the region of the diffractive minimum and the second maximum of the pp cross section, providing evidence for colourless C-odd gluonic exchanges, also denoted as odderon. These results are combined with a TOTEM analysis of the same $t$-channel C-odd exchanges based on …
The eikonal spin-dependent Odderon and gluon Sivers function of a proton, and its small-$x$ evolution
University of Zagreb（萨格勒布大学）；Baruch College, CUNY（巴鲁克学院，纽约市立大学系统）；The Graduate School and University Center, The City University of New York（纽约市立大学研究生院与大学中心）；Stony Brook University（石溪大学）；Jagiellonian University（雅盖隆大学）
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…
Diffractive photoproduction of $η_c$ is an important process to study the effect of Odderon, whose existence is still not confirmed in experiment. A detailed interpretation of Odderon in QCD, i.e., in terms of gluons is also unclear.Taking charm quarks as heavy quarks, we can use NRQCD and take $η_c$ as a $c\bar c$ bound state. Hence, in the production of $η_c$a free $c\bar c$ pair is first produced and this pair is transformed into $η_c$ subsequently.In the forward region of the kinematics, the $c\bar c$ pair interacts with initial hadron through exchanges of soft gluons. This interaction can…
Single-spin asymmetry appears due to the interference of single and double gluon exchange between protons. A heavy fermion model is used to describe the jet production in the interaction of gluon with the proton implying the further averaging over its mass. As usually in one-spin correlations, the imaginary part of the double gluon exchange amplitude play the relevant role. The asymmetry in the inclusive set-up with the pion tagged in the fragmentation region of the polarized proton does not depend on the center of mass energy in the limits of its large values. The lowest order radiative corre…
We describe the discovery of the colorless $C$-odd gluonic compound, the odderon, by the D0 and TOTEM Collaborations by comparing elastic differential cross sections measured in $pp$ and $p \bar{p}$ interactions at high energies
We compute the gluon Sivers function $f_{1T}^{\perp g}(x,k_\perp)$ of the transversely polarized nucleon at small-$x$ by exploiting the known connection between the dipole gluon Sivers function and the Odderon. We numerically solve the evolution equation for the Odderon both in the linear and nonlinear regimes. While we find that the $x$ and $k_\perp$ dependences of the Sivers function do not factorize as a result of the quantum evolution, factorization breaking is not numerically significant, and is much milder than what one expects in the case of unpolarized TMDs. We also point out the possi…
One of the open questions of the strong interaction theory is the existence of the Odderon, which is an unambiguous prediction of Quantum Chromodynamics, but still not confirmed in the experiment. In this paper we propose the study of the diffractive $η_c$ photoproduction in coherent interactions as a new alternative to probe the Odderon in $pp$ and $PbPb$ collisions at CERN - LHC. As the Pomeron exchange cannot contribute to this process, its observation would indicate the existence of the Odderon. We predict total cross sections of order of $pb \, (μb)$ for $pp \, (PbPb)$ collisions and larg…
One of the open questions of the strong interaction theory is the existence of the Odderon, which is an unambiguous prediction of Quantum Chromodynamics, but still not confirmed experimentally. An alternative to probe the Odderon is the exclusive $η_c$ photoproduction in hadronic collisions. As the Pomeron exchange cannot contribute to this process, its observation would indicate the existence of the Odderon. In this paper we estimate the $η_c$ production in photon - induced interactions in hadronic collisions at the AFTER@LHC experiment. We demonstrate that the experimental analysis of this p…
We analyze the differences between the $pp$ and $p\bar{p}$ differentia l elastic cross section measurements by the D0 and TOTEM Collaborations at the Tevatron, Fermilab, and the LHC, CERN that lead to a significance larger than 3$σ$ of the existence of the colourless $C$-odd three-gluon state, the odderon.
The scattering of a baryon consisting of three massive quarks is investigated in the high energy limit of perturbative QCD. A model of a relativistic proton-like wave function, dependent on valence quark longitudinal and transverse momenta and on quark helicities, is proposed, and we derive the baryon impact factors for two, three and four t-channel gluons. We find that the baryonic impact factor can be written as a sum of three pieces: in the first one a subsystem consisting of two of the three quarks behaves very much like the quark-antiquark pair in gamma* scattering, whereas the third quar…
QCD predicts the existence of the perturbative Pomeron and of the Odderon. But both of them appear to be rather difficult to observe experimentally. We describe the experimental status of these two objects, discuss possible reasons for their elusive behavior, and point out promising search strategies.
We consider the first LHC data for pp collisions in the framework of Regge theory. The integral cross sections and inclusive densities of secondaries are determined by the Pomeron exchange, and we present the corresponding predictions for them. The first measurements of inclusive densities in midrapidity region are in agreement with these predictions. The possible contribution of Odderon (Reggeon with alpha(Odd)(0) ~ 1 and negative signature) exchange to the differences in the inclusive spectra of particle and antiparticle in the central region could be significant at LHC energies. The first d…
The three-gluon glueball states are studied with the generalization of a semirelativistic potential model giving good results for two-gluon glueballs. The Hamiltonian depends only on 3 parameters fixed on two-gluon glueball spectra: the strong coupling constant, the string tension, and a gluon size which removes singularities in the potential. The Casimir scaling determines the structure of the confinement. Our results are in good agreement with other approaches and lattice calculation for the odderon trajectory but differ strongly from lattice in the $J^{+-}$ sector. We propose a possible exp…
In this talk we report on recent calculation of high energy baryon scattering amplitudes in QCD. Elastic baryon impact factors for two, three and four gluons are presented and their energy evolution is described that incorporates unitarity corrections. We find that the baryon couples directly to the BFKL Pomeron, to the BKP odderon and to a new state, a three-gluon BKP Pomeron. The new state may decay into four gluons with a new 3 -> 4 transition vertex. This vertex defines the transition amplitude of the three-gluon BKP Pomeron state into two BFKL Pomerons.
Exclusive production of a $η_c$ pseudo-scalar meson in $γ^{(*)} + p \to η_c + p$ scattering at high energies involves a ${\cal C}$-odd exchange in the $t$-channel. We formulate the description of this process within the high-energy framework of eikonal dipole scattering. We obtain expressions for the light-cone wave function of the $η_c$ required in this framework as well as for the ${\cal C}$-odd amplitudes due to exchange of a single photon, of a photon plus two gluons, and of three gluons. We relate these amplitudes to correlators of the $+$ component of the quark current in the light-cone …
Minijet production in $\sqrt{s} = 5.5$ TeV Pb+Pb collisions at the LHC is expected to produce a gluon-dominated plasma with large initial temperatures and energy densities. We discuss the implications of the high initial temperatures on the screening mass and on the relative suppression of members of the $Υ$ family. We demonstrate that $p_T$-dependence of the $Υ'/Υ$ ratio is only expected if a quark-gluon plasma with significant energy density is present, and that the precise dependence of this ratio will strongly constrain the QGP models. We also propose that the $p_T$ spectra of the $Υ$ reso…
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 consider a two-component-liquid model, a la Landau, for the quark-gluon plasma. Qualitatively, the model fits well some crucial observations concerning the plasma properties. Dynamically, the model assumes the existence of an effective scalar field which is condensed. The existence of such a condensate is supported by lattice data. We indicate a possible crucial test of the model by lattice simulations.
The existence of glueballs within QCD is uncontroversial but their experimental verification is still in doubt. We discuss the new possibilities for a search of glueballs as the leading object in gluon jets at the LHC. We summarize previous results from LEP which demonstrate a significant excess rate of electrically neutral leading clusters in comparison with MC models.
Glauber gluons in Drell-Yan processes are soft gluons with the transverse momenta much larger than their momentum components along the directions of initial hadrons. Their existence has been a serious challenge in proving the factorization of Drell-Yan processes. The recently proposed soft collinear effect theory of QCD can provide a transparent way to show factorizations for a class of processes, but it does not address the effect of glauber gluons. In this letter we first confirm the existence of glauber gluons through an example. We then add glauber gluons into the effective theory and stud…
We propose to realize a mass gap in QCD by not imposing the transversality condition on the full gluon self-energy, while preserving the color gauge invariance condition for the full gluon propagator. This is justified by the nonlinear and nonperturbative dynamics of QCD. None of physical observables/processes in low-energy QCD will be directly affected by such a temporary violation of color gauge invariance/symmetry. No truncations/approximations and no special gauge are made for the regularized skeleton loop integrals, contributing to the full gluon self-energy, which enters the Schwinger-Dy…
Experimental evidence and theoretical arguments for the existence of self-organized criticality in systems of gluons and quarks are presented. It is observed that the existing data for high-transverse-momentum jet-production exhibit striking regularities; and it is shown that, together with first-principle considerations, such regularities can be used, not only to probe the possible compositness of quarks, but also to obtain {\em direct evidence} for, or against, the existence of critical temperature and/or critical chemical potential in quark-gluon systems when hadrons are squeezed together.
We review both lattice evidences and theoretical arguments supporting the existence of electric flux tubes in quark-gluon plasma, above the deconfinement transition temperature $T>T_c$. At the end of this comment, we also point out certain questions which still needs to be answered.
The two-component liquid model reproduces the basic properties of the quark-gluon plasma as observed in heavy-ion collisions. The key dynamic element of the model is the existence of a light scalar. We argue that existence of such a scalar is a generic feature of stringy models of quantum chromodynamics. The lattice data provide evidence for a condensed, three-dimensional scalar field as well. We outline a possible crucial check of the model on the lattice.
We report on some efforts recently made in order to gain a better understanding of some IR properties of the 3-point gluon Green's function by exploiting results from large-volume quenched lattice simulations. These lattice results have been obtained by using both tree-level Symanzik and the standard Wilson action, in the aim of assessing the possible impact of effects presumably resulting from a particular choice for the discretization of the action. The main resulting feature is the existence of a negative logaritmic divergence at zero-momentum, which pulls the 3-gluon form factors down at l…
We show that in pure gauge QCD (or any pure non-Abelian gauge theory) the condition for the existence of a global minimum of energy with a gluon (gauge boson) mass scale also implies the existence of a fixed point of the $β$ function. We argue that the frozen value of the coupling constant found in some solutions of the Schwinger-Dyson equations of QCD can be related to this fixed point. We also discuss how the inclusion of fermions modifies this property.
We show the existence of unstable color skyrmions in a class of nonabelian fluid models. Oscillating and expanding solutions are found in the time-dependent case.
The skeleton loop integrals which contribute into the gluon self-energy have been iterated (skeleton loops expansion) within the Schwinger-Dyson equation for the full gluon propagator. No any truncations/approximations as well as no special gauge choice have been made. It is explicitly shown that such obtained general iteration solution for the full gluon propagator can be exactly and uniquely decomposed as a sum of the two pricipally different terms. The first term is the Laurent expansion in integer powers of severe (i.e., more singular than $1/q^2$) infrared singularities accompanied by the…
Peripheral collisions of heavy ions can give rise to extremely intense magnetic fields. It has been suggested that these fields might invalidate the holographic description of the corresponding quark-gluon plasmas, assuming that these can be modelled by strongly coupled field theories. In the case of the plasmas produced in collisions at the RHIC facility (including in the beam energy scans), it is known how to deal with this problem: one has to take into account the large angular momenta generated in these plasmas, and the effects of the baryonic chemical potential. But this does not work for…
QCD theory allows the existence of states which cannot be built by the naive quark model; both theoretical arguments and experimental data confirm the hypothesis that gluons may have freedom degrees at the constituent level, and should be confined. In this work, we use a phenomenological potential motivated by QCD (with some relativistic corrections) to determine the masses and the wavefunctions of several hybrid mesons, within the context of a constituent q-qbar-g model. We compare our estimates of the masses with the predictions of other theoretical models and with the observed masses of can…
The Bulk Randall-Sundrum model, where all Standard Model particles except the Higgs are free to propagate in the bulk, predicts the existence of Kaluza-Klein (KK) modes of the gluon with a large branching into top-antitop pairs. We study the production of the lowest KK gluon mode at the Tevatron energy and use the data on the top cross-section from the Run II of Tevatron to put a bound on the mass of the KK gluon. The resulting bound of 800 GeV, while being much smaller than the constraints obtained on the KK gluon mass from flavour-changing neutral currents, is the first, direct collider boun…
