One-to-one correspondence between dual diagrams of dual resonance model and QCD based color diagrams describing non vacuum exchanges in pi+ pi-, pi+- p, p anti p interactions is discussed. Both for dual and color diagrams there are state with quark-antiquark in t channel and state, in which only coherent quark string exists, in s channel. There are no such dual diagrams in pp interaction. Color diagram for pp interaction was found basing on principle of conformity. Secondary hadrons spectrum, obtained from this diagram, has nucleon in its central region. This effect may lead to increase of baryon chemical potential in nucleus-nucleus collisions in facilities NICA and FAIR.
Contribution of simplest loops for hadron-nucleus scattering cross-sections is studied in the Local Reggeon Field Theory with a supercritical pomeron. It is shown that inside the nucleus the supercritical pomeron transforms into a subcritical one, so that perturbative treatment becomes possible. The pomeron intercept becomes complex, which leads to oscillations in the cross-sections.
The CKMT model describing the nucleon structure function $F_2(x,Q^2)$ in the framework of conventional Regge theory with smooth soft-hard pomeron is modified. Smooth soft-hard non-vacuum reggeon dependence on incoming photon virtuality $Q^2$ is introduced. This dependence has the same functional form as the smooth soft-hard functional $Q^2$ dependence for pomeron in original CKMT model. In regeon of low $W^2$ better agreement with experimental data is observed.
By using the concept of duality between direct channel resonances and Regge exchanges we relate the small- and large-$x$ behavior of the structure functions. We show that even a single resonance exhibits Bjorken scaling at large $Q^2$.
We study hard diffractive scattering in hadron-hadron collisions including, on top of the standard Pomeron-initiated processes, contributions due to the exchange of Reggeons. Using a simple model to describe the parton content of the Reggeon, we compute di-jet production in single diffractive and central diffractive events. We show that Reggeon contributions can be sizable at the LHC, and even sometimes dominant, and we identify kinematic windows in which they could be experimentally studied. We argue that suitable measurements must be performed in order to properly constrain the model, and be…
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.
I will discuss how the non-vacuum, quark-antiquark Reggeon-exchange contribution to meson-meson elastic scattering, at high energy and low tranferred momentum, can be related to the path-integral of a certain Wilson-loop expectation value over the trajectories of the exchanged fermions. Making use of this representation, I will show how a linear Regge trajectory is obtained through gauge/gravity duality and the use of minimal surfaces.
The "triple-Regge" analysis of subleading Reggeon contributions to the diffractive structure function in DIS at HERA is presented. The recently published data allow to estimate the only free parameter of the analysis related to the ratio of the RRP and PPP couplings. The large value of this ratio is prefered which is in agreement with analyses of soft hadronic interactions. The role of the subleading Reggeons as well as pions for the fast forward neutron production in diffractive processes is estimated. The forward piN state production is also discussed.
The processes of exclusive photo- and electroproduction of vector mesons $ρ^0$(770), $ϕ$(1020) and $J/ψ$(3096) at collision energies $30 GeV<W<300 GeV$ and transferred momenta squared $0<-t<2 GeV^2$ are considered in the framework of a phenomenological Regge-eikonal scheme with nonlinear Regge trajectories in which their QCD asymptotic behavior is taken into account explicitly. By comparison of available experimental data from ZEUS and H1 Collaborations with the model predictions it is demonstrated that corresponding angular distributions and integrated cross-sections in the above-mentioned ki…
Hadron-nucleus amplitudes at high energies are studied in the "toy" Regge model in zero transverse dimension for finite nuclei, when the standard series of fan diagrams is converted into a finite sum and looses physical sense at quite low energies. Taking into account all the loop contributions by numerical methods we find a physically meaningful amplitudes at all energies. They practically coincide with the amplitudes for infinite nuclei. A surprizing result is that for finite nuclei and small enough triple pomeron coupling the infinite series of fan diagrams describes the amplitude quite wel…
The equivalence is found between high-energy QCD in the generalized leading logarithmic approximation and the one-dimensional Heisenberg magnet. According to Regge theory, the high energy asymptotics of hadronic scattering amplitudes are related to singularities of partial waves in the complex angular momentum plane. In QCD, the partial waves are determined by nontrivial two-dimensional dynamics of the transverse gluonic degrees of freedom. The "bare" gluons interact with each other to form a collective excitation, the Reggeon. The partial waves of the scattering amplitude satisfy the Bethe-Sa…
The inclusive production of light mesons in pp-scattering is considered in the framework of reggeon phenomenology with supercritical Pomeron. Available low-energy data can be explained with three reggeon particles taken into account. With the obtained results rapidity and pseudorapidity distributions for light-meson production at LHC energies are predicted.
Some results on the perturbative Regge asymptotics are reviewed. The concepts of the reggeon interaction approach and the double logarithmic approximation are outlined. Contribution to the Zeuthen Workshop on QCD and QED at higher order, Rheinsberg, April 1996.
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 r…
We study the fluctuation theory analysis of multiple soft interactions that are used to design SIBYLL 2.1 and related cosmic ray event generators. We examine fluctuation stabilities of Lund string fragmentation involving quark-antiquark and diquark-antidiquark pairs. Using the primordial transverse momentum hadron-hadron pairs, we find that the resulting Gaussian distribution yields an ill-defined ensemble under fluctuation of the model parameters of parent quark and diquarks. Further, we investigate the nature of multiple soft interactions through Pomeron-Reggeon fluctuations at various energ…
The standard additive quark model and the ensuing counting rules are modified to take into account the quark-gluonic content of the Pomeron and of the secondary Reggeons. The result is that a much improved description of $pp, πp, γp$ and $γγ$ cross-sections is achieved.
It is proposed, that ``the colorless objects'' which manifest themselves in large-rapidity-gap events are color-singlet gluon-clusters due to self-organized criticality (SOC), and that optical-geometrical concepts and methods are useful in examing the space-time properties of such objects. A simple analytical expression for the $t$-dependence of the inelastic single diffractive cross section $dσ/dt$ ($t$ is the four-momentum transfer squared) is derived. Comparison with the existing data and predictions for future experiments are presented. The main differences and similarities between the SOC…
High energy hadronic and nuclear interactions are described within Gribov's Reggeon scheme. An approach to re-summation of enhanced Pomeron graphs is proposed. The latter is applied to develop a new Monte Carlo model which treats non-linear interaction effects explicitely in individual hadronic collisions. On the other hand, we discuss a possible generalization of the scheme, which allows to account also for pQCD effects. In particular, this offers a possibility to fix model parameters on the basis of data on hadron-hadron cross sections, hadronic multi-particle production, and on total and di…
Experimental data on total and differential elastic cross sections for $p+p(\bar{p})$, $n+p(\bar{p})$, $K^\pm+p$, $K^\pm+n$, $π^\pm+p$ starting from energy 3.5 GeV in CMS are used to determine parameters of vacuum contribution and parameters of basic non vacuum reggeons: $f$, $ω$, $ρ$ and $A_2$. It is argued that non vacuum contributions to proton-proton and proton-neutron collisions correspond to spectrum in which baryon number is moved from the fragmentation region to central region in rapidity space. In this case it is possible that chemical potential is increased in central region of spect…
The influence of non-linear interaction effects on the characteristics of hadronic collisions and on the development of extensive air showers (EAS) is investigated. Hadronic interactions are treated phenomenologically in the framework of Gribov's Reggeon approach with non-linear corrections being described by enhanced (Pomeron-Pomeron interaction) diagrams. A re-summation algorithm for higher order enhanced graphs is proposed. The approach is applied to develop a new hadronic interaction model QGSJET-II, treating non-linear effects explicitely in individual hadronic and nuclear collisions. The…
The construction of a Monte Carlo generator for high energy hadronic and nuclear collisions is discussed in detail. Interactions are treated in the framework of the Reggeon Field Theory, taking into consideration enhanced Pomeron diagrams which are resummed to all orders in the triple-Pomeron coupling. Soft and "semihard" contributions to the underlying parton dynamics are accounted for within the "semihard Pomeron" approach. The structure of cut enhanced diagrams is analyzed; they are regrouped into a number of subclasses characterized by positively defined contributions which define partial …
Employing the Worldline casting of the Dosch-Simonov Stochastic Vacuum Model(SVM) for QCD, a simulated meson-meson scattering is studied in the Regge kinematical regime. The process is modelled in terms of the "helicoidal" Wilson contour first introduced by Janic and Peschanski in a related study based on an AdS/CFT-type approach. Using lattice supported estimations for the behavior of a two-point, field strength correlation function, as defined in the framework of the SVM, the reggeon slope and intercept are calculated in a semiclassical approximation. The resulting values are in good agreeme…
Multi-hadron production in inelastic neutrino-nucleon interactions is investigated within the framework of the quark-gluon string model. The contributions of the planar (one-Reggeon exchange) and cylindrical (one-Pomeron exchange) graphs to different observables is computed using a Monte Carlo program for the generation of hadrons produced from the decay of colorless quark-antiquark strings. The suggested approach results in a satisfactory description of the experimental data on $ν(\barν) N\toμ^-(μ^+) h X$ reactions obtained recently at CERN by the NOMAD Collaboration. The data extends over a …
It is demonstrated that the "soft pomeron" (together with a secondary reggeon) describing cross-sections of hadron-hadron collisions is fairly able to describe the energy dependence of cross-sections of exclusive (virtual) photoproduction of vector mesons $(ρ^0, ϕ, J/ψ)$ obtained at HERA. However these poles are insufficient for description of the total DIS cross-section.
We analyse the extraction of the bound-state form factor from vacuum-to-hadron correlator, which is the basic object for the calculation of hadron form factors in the method of light-cone sum rules in QCD. We study this correlator in quantum mechanics, calculate it exactly, and derive the corresponding OPE. We then apply the standard procedures of QCD sum rules to isolate the ground-state form factor from this correlator. We demonstrate that fixing the effective continuum threshold, one of the key ingredients of the sum-rule calculation of bound-state parameters, poses a serious problem for su…
We propose a new type of the measurement which is sensitive to the QCD vacuum color-magnetic fluctuations: A measure of the axial assymetry of the hadronic final states produced in the high energy $e^{+}e^{-}$ collisions is related to the chromomagnetic vacuum field strength.
Traditional idea of Pomeron/Reggeon description for hadron scattering is now being given theoretical foundation in gravity dual descriptions, where Pomeron corresponds to exchange of spin-$j \in 2\mathbb{Z}$ states in the graviton trajectory. Deeply virtual Compton scattering (DVCS) is essentially a 2 to 2 scattering process of a hadron and a photon, and hence one should be able to study non-perturbative aspects (GPD) of this process by the Pomeron/Reggeon process in gravity dual. We find, however, that even one of the most developed formulations of gravity dual Pomeron (Brower--Polchinski--St…
1. QCD Sum Rules: 20 Years After; 2. QCD Vacuum and Basics of the SVZ Method: 2.1 General ideas; 2.2. Getting started/Playing with toy models; 3. Vacuum Condensates; 4. Rho Meson in QCD; 5. Basic Theoretical Instrument -- Wilson's OPE; 6. Practical Version of OPE; 7. Low Energy Theorems; 8. Are All Hadrons Alike? 9. Ecological Niche; 10. New Developments: 10.1 Light-cone sum rules; 10.2 Heavy flavor sum rules; 11. Sum Rules and Lattices; 12. Vacuum Fluctuations are Subtle Creatures; 13. Instead of Conclusions.
In this paper we estimate the production of dimuons ($μ^+ μ^-$) in exclusive photon -- photon ($γγ$) and diffractive Pomeron - Pomeron $(I\!P I\!P)$, Pomeron - Reggeon $(I\!P I\!R)$ and Reggeon - Reggeon $(I\!R I\!R)$ interactions in $pp$ collisions at the LHC energy. The invariant mass, rapidity and tranverse momentum distributions are calculated using the Forward Physics Monte Carlo (FPMC), which allows to obtain realistic predictions for the dimuon production with two leading intact hadrons. In particular, predictions taking into account the CMS and LHCb acceptances are presented. Moreover,…
The anomalously large cos(2 phi) asymmetry measured in the Drell-Yan process is discussed. Possible origins of this large deviation from the Lam-Tung relation are considered with emphasis on the comparison of two particular proposals: one that suggests it arises from a QCD vacuum effect and one that suggests it is a hadronic effect. Experimental signatures distinguishing these effects are discussed.
The hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon is parametrized by using the quark-resonance model formulated in \cite{QR}. In this context a recent prediction obtained within the ENJL model \cite{RAF} can be affected by two additional contributions: the next to leading corrections in the inverse cutoff expansion and the gluonic corrections. Motivated by the necessity of reaching a highly accurate theoretical prediction of the hadronic contribution to the muon g-2, we study in detail both the effects.
A simple model of hadron which exhibits the quark confinement and the asymptotic freedom is described. The hadron is modelled as a sphere of radius equal to its Compton wavelength in which quarks occur surrounded by space with the uniformly distributed {\it negative} vacuum energy density characterized by $λ$. The acceleration stemming from this vacuum energy causes the quark confinement. However, in the center of hadron quarks behave as practically free particles. From the requirement that the Compton wavelength of a hadron should remain constant while the scale factor varies with time we est…
We consider the subleading contributions of the hadronic vacuum polarization, involving the $π^0γ^*γ^*$ transition form factor, to the muon anomalous magnetic moment $g-2$. Various models for the form factor, based on hadronic ansatzes and holographic principles, are considered: They are the Wess-Zumino-Witten, vector meson dominance, lowest meson dominance (one and two vector resonances) models, and AdS/QCD. The model parameters are determined by fitting the experimental data for the $e^+ e^- \rightarrow π^0 γ$ total cross section. We report numerical results of the corrections to the muon $g…
The hadronic vacuum polarization function $Π_h$ for two light flavors is computed on the entire domain of spacelike and timelike momenta using a framework of Dyson-Schwinger equations. The analytical continuation of the function $Π_h$ is based on the utilization of the Gauge Technique with the entry of QCD Green's functions determined from generalized quark spectral functions. For the first time, the light quark spectral functions are extracted from the solution of the gap equation for the quark propagator. The scale is set up by the phenomena of dynamical chiral symmetry breaking, which is a …
A simple model for the hadronic contribution to the photon vacuum polarization function $Π_{had}(q^2)$, for spacelike momenta, is presented. For small momenta, the two loop contribution from the pseudoscalar meson octet is computed from the chiral Lagrangian. The light quark contribution (which at low momentum gives the ${\cal O}(q^6)$ counterterm in the chiral Lagrangian) is calculated within a relativistic constituent quark model incorporating the momentum dependence of the quark mass. The perturbative gluons of QCD are included in a standard fashion. The total result is close to an estimate…
The definition of QCD vacuum is an important issue in the description of hadronic properties. Recent researches on the vacuum condensates have resulted in the suggestion of in-hadron condensates which can be taken as a paradigm shift concerning the viewpoints on the QCD vacuum. In this Letter, we will try to define the in-hadron regions and to classify the hadronic and multiquark states. Topological classifications are naturally introduced and by considering nonlocal measure we can estimate the variations of dimension 2 condensate $< A_μ^2 >$. The calculational techniques can be easily applied…
This report discusses some results on differential cross sections for high energy and small momentum transfer elastic hadron-hadron scattering in QCD, using a functional integral approach. In particulary a matrix cumulant expansion for the vacuum expectation values of lightlike Wegner-Wilson loops, which governs the hadronic amplitudes, is presented. The cumulants are evaluated using the model of the stochastic vacuum.
Precise data on e^+e^- to hadrons have recently become available and are used to compute the lowest-order hadronic vacuum polarisation contribution to the muon magnetic anomaly through dispersion relations. This is the case for the dominant pi+ pi- channel, but the most significant progress comes from the near completion of the BABAR program of measuring exclusive processes below 2 GeV with the initial-state radiation method which allows an efficient coverage of a large range of energies.. In this paper we briefly review the data treatment, the achieved improvements, and the result obtained fo…
Total and differential cross sections for high energy and small momentum transfer elastic hadron-hadron scattering are studied in QCD using a functional integral approach. The hadronic amplitudes are governed by vacuum expectation values of lightlike Wegner-Wilson loops, for which a matrix cumulant expansion is derived. The cumulants are evaluated within the framework of the Minkowskian version of the model of the stochastic vacuum. Using the second cumulant, we calculate elastic differential cross sections for hadron-hadron scattering. The agreement with experimental data is good.
The consequence of vacuum instability against particles creation is described using lattice gas model. It is shown that the tail of multiplicity distribution should decrees slower than any power of $\exp\{-n\}$, but faster than any power of $1/n$ if the vacuum is unstable against particles creation.
The experimental value of g-2 of the muon is larger by $4.2 σ$ than the Standard Model prediction based on the hadronic vacuum polarization contribution (HVP) determined from the measured R-ratio, $σ(e^+e^- \! \rightarrow \! \mathit{hadrons})/σ(e^+e^- \! \rightarrow \!μ^+ μ^-)$; the HVP calculated in lattice QCD also significantly exceeds the measured R-ratio value. We show here that these discrepancies can be explained by an undetected contribution to $e^+e^- \! \rightarrow \! \mathit{hadrons}$ as could arise from production of neutral, long-lived hadrons which have not previously been identi…
We discuss the production of soft photons in high energy hadron-hadron collisions. We present a model where quarks and antiquarks in the hadrons emit ``synchrotron light'' when being deflected by the chromomagnetic fields of the QCD vacuum, which we assume to have a nonperturbative structure. This gives a source of prompt soft photons with frequencies $ω<= 300 MeV$ in the c.m. system of the collision in addition to hadronic bremsstrahlung. In comparing the frequency spectrum and rate of ``synchrotron'' photons to experimental results we find some supporting evidence for their existence. We mak…
We briefly review the key aspect of the QCD instanton vacuum in relation to the quantum breaking of conformal symmetry and the trace anomaly. We use Ji$^\prime s$ invariant mass decomposition of the energy momentum tensor together with the trace anomaly, to discuss the mass budget of the nucleon and pion in the QCD instanton vacuum. A measure of the gluon condensate in the nucleon, is a measure of the compressibility of the QCD instanton vacuum as a dilute topological liquid.
We report on the computation of the light quark vacuum polarization with 2+1+1 flavors of H ISQ fermions at the physical point and its contribution to the muon anomalous magnetic moment. Three ensembles, generated by the MILC collaboration, are used to take the continuum limit. We compare our result with recent ones in the literature.
We compute the slope and curvature, at vanishing four-momentum transfer squared, of the leading order hadron vacuum polarization function, using lattice QCD. Calculations are performed with 2+1+1 flavors of staggered fermions directly at the physical values of the quark masses and in volumes of linear extent larger than 6fm. The continuum limit is carried out using six different lattice spacings. All connected and disconnected contributions are calculated, up to and including those of the charm.
We study the nonperturbative QCD vacuum with two light quarks at finite temperature in the framework of hadron resonance gas. Temperature dependence of the quark and gluon condensates in the confined phase are obtained. We demonstrate that the quark condensate and one half (chromo-electric component) of gluon condensate evaporate at the same temperature, which corresponds to the temperature of quark-hadron phase transition. Critical temperature is T_c~190 MeV when temperature shift of hadron masses is taken into account.
The estimations of the light quark mass differences, $m_d-m_u$, and the light quark condensate differences, $<\bar DD> - <\bar UU>$, are obtained in the framework of the \qm\ with QCD vacuum induced \q\ \ia . We consider long - wave condensate and short - wave \s\ contributions to the electromagnetic \hn\ mass \di s and show that the latter significantly improve the results on baryon octet. The results are: $m_d-m_u \approx 3.5\ MeV$ and $<\bar DD> - <\bar UU> \approx -(0\sim 3)\cdot10^{-3}<\bar UU>$.
We present a lattice calculation of the hadronic vacuum polarization and the lowest-order hadronic contribution to the muon anomalous magnetic moment, a_μ= (g-2)/2, using 2+1 flavors of improved staggered fermions. A precise fit to the low-q^2 region of the vacuum polarization is necessary to accurately extract the muon g-2. To obtain this fit, we use staggered chiral perturbation theory, including the vector particles as resonances, and compare these to polynomial fits to the lattice data. We discuss the fit results and associated systematic uncertainties, paying particular attention to the r…
We compute the vacuum polarisation on the lattice in quenched QCD using non-perturbatively improved Wilson fermions. Above Q^2 of about 2 GeV^2 the results are very close to the predictions of perturbative QCD. Below this scale we see signs of non-perturbative effects which we can describe by the use of dispersion relations. We use our results to estimate the light quark contribution to the muon's anomalous magnetic moment. We find the result 446(23) x 10^{-10}, where the error only includes statistical uncertainties. Finally we make some comments on the applicability of the Operator Product E…
We calculate the masses of the vector and axial-vector mesons as well as the nucleon and the delta resonance in the chiral symmetry restored vacuum. This is accomplished by separating the quark operators appearing in the QCD sum rules for these hadrons into the chiral symmetric and symmetry breaking parts depending on the contributions of the fermion zero modes. We then extract the vacuum expectation values of all the separated parts of the quark operators using the QCD sum rule relations for these hadrons with their vacuum masses and widths. By taking the chiral symmetry breaking parts to be …
In this paper, we discuss how windows in Euclidean time can be used to isolate the origin of potential conflicts between evaluations of the hadronic-vacuum-polarization (HVP) contribution to the anomalous magnetic moment of the muon in lattice QCD and from $e^+e^-\to\text{hadrons}$ cross-section data. We provide phenomenological comparison numbers evaluated from $e^+e^-\to\text{hadrons}$ data for the window quantities most commonly studied in lattice QCD, complete with the correlations among them. We discuss and evaluate modifications of window parameters that could be useful in dissecting the…
We compute the standard Euclidean window of the hadronic vacuum polarization using multiple independent blinded analyses. We improve the continuum and infinite-volume extrapolations of the dominant quark-connected light-quark isospin-symmetric contribution and address additional sub-leading systematic effects from sea-charm quarks and residual chiral-symmetry breaking from first principles. We find $a_μ^{\rm W} = 235.56(65)(50) \times 10^{-10}$, which is in $3.8σ$ tension with the recently published dispersive result of Colangelo et al., $a_μ^{\rm W} = 229.4(1.4) \times 10^{-10}$, and in agree…
We present a calculation of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment, $a_μ^{\mathrm hvp}$, in lattice QCD employing dynamical up and down quarks. We focus on controlling the infrared regime of the vacuum polarization function. To this end we employ several complementary approaches, including Padé fits, time moments and the time-momentum representation. We correct our results for finite-volume effects by combining the Gounaris-Sakurai parameterization of the timelike pion form factor with the Lüscher formalism. On a subset of our ensembles we have deri…
The value of the parton to hadron fragmentation function in QCD in vacuum (for example from proton-proton collisions at high energy colliders) is directly/indirectly used in the literature to study the jet quenching and the hadron production from quark-gluon plasma at RHIC and LHC. In this paper we show that this is not possible because, unlike the perturbative propagator in non-equilibrium QCD, the parton to hadron fragmentation function is a non-perturbative quantity in QCD and hence it is not possible to decompose the fragmentation function in non-equilibrium QCD into the vacuum part and th…
The anomalous magnetic moment of the muon $a_μ$ is one of the most accurate quantities in Particle Physics. The long-standing discrepancy of about $3.7$ standard deviations between the experimental value and the prediction of the Standard Model could represent an intriguing indication of New Physics. The experiments at Fermilab (E989) and at J-PARC (E34) aim at reducing significantly the experimental uncertainty, thus making the theoretical one due to hadronic corrections the main limitation of this stringent test of the Standard Model. In this contribution we present the results of a first-pr…
Recently it was claimed that QCD condensates were associated with the internal dynamics of the hadrons. We challenge this "in-hadron" picture of the QCD condensates and show that it conflicts well established concepts and experimental facts for the example of the quark condensate. We explicitly demonstrate the vacuum nature of the quark condensate by a model calculation.
