We discuss strategies for comparisons of nonperturbative QCD predictions for parton distribution functions (PDFs) with high-energy experiments in the region of large partonic momentum fractions $x$. Analytic functional forms for PDFs cannot be uniquely determined solely based on discrete experimental measurements because of a mathematical property of mimicry of PDF parametrizations that we prove using a representation based on Bézier curves. Predictions of nonperturbative QCD approaches for the $x$ dependence of PDFs instead should be cast in a form that enables decisive comparisons against experimental measurements. Predictions for effective power laws of $(1-x)$ dependence of PDFs may play this role. Expectations for PDFs in a proton based on quark counting rules are compared against the effective power laws of $(1-x)$ dependence satisfied by CT18 next-to-next-to-leading order parton distributions. We comment on implications for studies of PDFs in a pion, in particular on the comparison of nonperturbative approaches with phenomenological PDFs.
Starting from the gauge-invariant quark-antiquark Green function the expression for the nonrelativistic meson scattering amplitude is obtained and the nonperturbative form of this amplitude is discussed.
Some nonperturbative aspects of spin studies at RHIC are discussed and the predictions for single- and two-spin asymmetries are given. Among them are those which emphasize the role of angular orbital momentum in the spin structure of the constituent quarks.
QCD-based analysis of nonfactorizable parts of weak nonleptonic amplitudes is reported. Nonperturbative effects due to soft gluon exchange play a key role leading to the emergence of a dynamical rule of discarding $1/N_c$ corrections.
We use soft collinear effective field theory (SCET) to study nonperturbative strong interaction effects in Z decays to hadronic final states that are enhanced in corners of phase space. These occur, for example, in the jet energy distribution for two jet events near E_J=M_Z/2, the thrust distribution near unity and the jet invariant mass distribution near zero. The extent to which such nonperturbative effects for different observables are related is discussed.
We calculate the nonperturbative $J/Ψ-N$ and $Ψ'-N$ cross sections with the model of the stochastic vacuum which has been succesfully applied in many high energy reactions. We also give a quantitative discussion of pre-resonance formation and medium effects.
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.
We study the nonperturbative functions in the Collins--Soper--Sterman resummation formalism by examing Drell--Yan data in both fixed target and collider experiments and then predict the transverse momentum distributions of the $W^\pm$ and $Z^0$ bosons at the Tevatron. Our results differ from that in the literature and agree better with published CDF data. Using statistical arguments, we find a $1\,$fb${}^{-1}$ luminosity at the Fermilab Tevatron should be able to provide useful constraints on the nonperturbative functions.
Based on the recently developed light-front similarity renormalization group approach and the light-front heavy quark effective theory, we derive analytically from first-principles QCD a heavy quark light-front Hamiltonian which contains explicitly a confinement interaction at long distances and a Coulomb-type interaction at short distances. With this light-front QCD Hamiltonian, we further demonstrate that the nonperturbative QCD dynamics of the strongly interacting heavy hadron bound states can be treated as a weak-coupling problem.
We consider low-x behavior of the spin structure functions g_1(x) and h_1(x) in the unitarized chiral quark model that combines the ideas on constituent quark structure of hadrons with a geometrical scattering picture and unitarity. A nondiffractive singular low-x dependence of g^p_1(x) and g_1^n(x) is obtained and a diffractive type smooth behavior of h_1(x) is predicted at small x.
We discuss the current picture of the standard model's scalar sector at strong coupling. We compare the pattern observed in the scalar sector in perturbation theory up to two-loop with the nonperturbative solution obtained by a next-to-leading order 1/N expansion. In particular, we analyze two resonant Higgs scattering processes, ff -> H -> f'f' and ff -> H -> ZZ, WW. We describe the ingredients of the nonperturbative calculation, such as the tachyonic regularization, the higher order 1/N intermediate renormalization, and the numerical methods for evaluating the graphs. We discuss briefly the …
Lectures discuss applications of semiclassical methods based on instantons to vacuum structure (chiral symmetry breaking), hadronic structure (various correlation functions), and high energy collisions of hadrons and heavy ions. We discuss phase diagram of hot/dense hadronic matter, and in the last lecture review current puzzles/lesons from the first RHIC run in summer of 2000.
For high energy processes ($M\gg Λ_{QCD}$) there are infrared safe hadronic shape variables that have a calculable perturbative expansion in $α_s(M^2)$. However, nonperturbative power suppressed corrections to these variables are not well understood. We use the behavior of large orders of the perturbation expansion to gain insight into the nonperturbative corrections. Our results suggest that certain shape variables have nonperturbative corrections suppressed by fractional powers of $Λ_{QCD}^2/M^2$.
Comparisons of experimental data with theoretical predictions for collider processes containing hadronic jets rely on shower Monte Carlo event generators to include corrections to perturbative calculations from hadronization, parton showering, multiple parton collisions. We examine current treatments of these corrections and propose alternative methods to take into account nonperturbative effects and parton showering in the context of next-to-leading-order (NLO) event generators. We point out sizeable parton-showering corrections to jet transverse energy spectra at high rapidity, and discuss k…
We discuss some experimental and theoretical results on single spin asymmetries (SSA) in high energy lepton-hadron and hadron-hadron reactions. In particular, recent results on meson SSA obtained by HERMES are considered in detail. We also discuss the SSA results obtained recently by COMPASS, as well as those from BRAHMS, PHENIX and STAR. Special attention is paid to a possible nonperturbative QCD mechanism that might be responsible for the observed meson SSA. This mechanism originates from the spin-flip quark-gluon chromomagnetic interaction induced by the complex topological structure of the…
High energy hadron-hadron collisions are discussed. It is argued that soft collisions should involve in an essential way nonperturbative QCD. A way is outlined how to calculate properties of high energy elastic hadron-hadron scattering using field theoretic methods. The functional integrals occuring there are evaluated using the ``stochastic vacuum model''. A satisfactory comparison between theory and experiment is achieved. Then the question of possible nonperturbative QCD effects in high energy hard hadron-hadron collisions is raised. It is shown that some spin effects in the Drell-Yan proce…
A test for the Gaussian and exponential Ansaetze for the nonperturbative parts of the coefficient functions, D^{nonpert.} and D_1^{nonpert.}, which parametrize the gauge-invariant bilocal correlator of the field strength tensors in the stochastic vacuum model of QCD, is proposed. It is based on the evaluation of the heavy-quark condensate within this model by making use of the world-line formalism and equating the obtained result to the one following directly from the QCD Lagrangian. This yields a certain relation between D^{nonpert.}(0) and D_1^{nonpert.}(0), which is further compared with an…
We present an analysis of the role of the running coupling constant at the intersection of perturbative and nonperturbative QCD in the context of the quark-hadron duality à la Bloom-Gilman. Our framework will be the unpolarized structure function of the proton in the resonance region. We suggest that the realization of duality is related to the inclusion of nonperturbative effects at the level of the coupling constant. The outcome of our analysis is a smooth transition from perturbative to nonperturbative QCD physics, embodied in the running of the coupling constant at intermediate scales.
Benefiting from the high statistics from $e^+e^-$ experiments at the $Z^0$ resonance, it is possible to impose strong two-jet cuts on the data without losing the statistical significance. In these events perturbative activity is suppressed and hadronization effects can be more prominent. I give two examples of observables that can be important tools for a more detailed study of the hadronization mechanism.
The motion of spectator quarks in decay of a beauty hadron is a nonperturbative effect which can usually be neglected. We find that the motion in some decay channels, which contribute total decay widths of beauty hadrons, can not be neglected.The contributions from these decay channels to decay widths are proportional to certain averages of the squared inverse of the momentum carried by a spectator quark. This fact results in that these contributions, suppressed by $1/m_b^3$ formally, are effectively suppressed by $1/m_b$. We find these contributions can be factorized into products of perturba…
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.
We discuss Strassler's hypothesis of matching nonperturbative effects in orbifold pairs of gauge theories which are perturbatively planar equivalent. One of the examples considered is the parent N=1 SU(N) supersymmetric Yang-Mills theory and its nonsupersymmetric orbifold daughter. We apply two strategies allowing us to study nonperturbative effects: (i) low-energy theorems; (ii) putting the theory on small-size T^4 or R^3 x S^1 the parent and daughter theories are weakly coupled and amenable to quasiclassical treatment. In all cases our consideration yields a mismatch between the parent and d…
In this thesis we explore a diverse array of issues that strike at the inherently nonperturbative structure of hadrons at momenta below the QCD confinement scale. In so doing, we mainly seek a better control over the partonic substructure of strongly-interacting matter, especially as this relates to the nonperturbative effects that both motivate and complicate experiments --- particularly DIS; among others, such considerations entail sub-leading corrections in $Q^2$, dynamical higher twist effects, and hadron mass corrections. We also present novel calculations of several examples of flavor sy…
Two-particle angular correlations have long been used as an observable for measuring the initial-state partonic transverse momentum $k_T$. Sensitivity to this small transverse momentum scale allows nonperturbative transverse momentum dependent effects to be probed in high $p_T$ dihadron and direct photon-hadron correlations. The observable $p_{out}$, the out-of-plane transverse momentum component from a near-side $π^0$ or direct photon, is sensitive to initial-state $k_T$ and final-state fragmentation transverse momentum $j_T$ and thus can probe nonperturbative transverse-momentum-dependent ef…
I describe the inception and development of nonperturbative OPE-based methods in hadronic physics, such as the SVZ sum rules, inverse heavy quark mass expansion (IHQME) and so on and related topics.
We discuss the possibility to suppress the nonperturbative effects if the very high multiplicity hadron final states are chosen. The theoretical uncertainties and possible experimental measurements are described.
Generalized parton distributions (GPDs) are studied at the hadronic (nonperturbative) scale within different assumptions based on a relativistic constituent quark model. In particular, by means of a meson-cloud model we investigate the role of nonperturbative antiquark degrees of freedom and the valence quark contribution. A QCD evolution of the obtained GPDs is used to add perturbative effects and to investigate the GPDs' sensitivity to the nonperturbative ingredients of the calculation at larger (experimental) scale.
The processes of D^{(*)}-mesons and Λ_c-baryons production in e^+e^--annihilation at 10.58 GeV and 91.18 GeV energies are concerned. At the 10.58 GeV energy the production of charmed particles via the B-mesons decays is also concerned. Scaling violation of the fragmentation functions is calculated at the NLL-accuracy. Nonperturbative fragmentation functions are retrieved from the experimental data of B-factories and are approximated by simple analytic expressions. It is proved, that the difference between nonperturbative fragmentation functions of mesons and baryons can be easily explained by …
We discuss the possibilities of testing of perturbative quantum chromodynamics through azimuthal asymmetries in polarized ep in the context of future collider and fixed target facilities, such as Electron Ion Collider and TESLA-N.
We discuss various ideas on the nonperturbative vacuum structure in QCD. The stochastic vacuum model of Dosch and Simonov is presented in some detail. We show how this model produces confinement. The model incorporates the idea of the QCD vacuum acting like a dual superconductor due to an effective chromomagnetic monopole condensate. We turn then to high energy, small momentum transfer hadron-hadron scattering. A field-theoretic formalism to treat these reactions is developed, where the basic quantities governing the scattering amplitudes are correlation functions of light-like Wegner-Wilson l…
The QCD phase transition at finite temperature is studied with the dual Ginzburg-Landau theory, which is the QCD effective theory based on the dual Higgs mechanism by QCD-monopole condensation. At high temperature, the confinement force is largely reduced by thermal effects, which leads to the swelling of hadrons. Simple formulae for the surface tension and the thickness of the phase boundary are derived from the shape of the effective potential at the critical temperature. We investigate also the process of the hadron-bubble formation in the early Universe.
We estimate the renormalon corrections to the inclusive decay rate of heavy hadrons. We assume the gluon mass term $λ^2 \gg `^2$ to imitate the short distance nonperturbative effects. It is found that the the inclusive decay rates are corrected by an amount of about 0.2 $Γ_0$ for $B$ meson and 0.21 $Γ_0$ for baryon. This is significant in view of the discrepancy of lifetimes of $B$ and $\lbb$.
We explore the deep inelastic structure functions of hadrons nonperturbatively in an inverse power expansion of the light-front energy of the probe in the framework of light-front QCD. We arrive at the general expressions for various structure functions as the Fourier transform of matrix elements of different components of bilocal vector and axial vector currents on the light-front in a straightforward manner. The complexities of the structure functions are mainly carried by the multi-parton wave functions of the hadrons, while, the bilocal currents have a dynamically dependent yet simple stru…
Recently there has been considerable interest in the subject of molecules, which are weakly bound states of hadron pairs. The question of the existence of molecules is closely related to the more general problem of the determination of low energy hadron-hadron scattering amplitudes, which is widely believed to require nonperturbative methods. In this contribution we report on quark model calculations using a simple perturbative scattering mechanism, one gluon exchange followed by constituent interchange. We refer to the associated diagrams as ``quark Born diagrams". For the cases chosen to iso…
A brief review of theoretical progress in hadron spectroscopy and nonperturbative QCD is presented. Attention is focussed on recent lattice gauge theory, the Dyson-Schwinger formalism, effective field theory, unquenching constituent models, and some beyond the Standard Model physics.
By expanding functions of parton fragmentation into a heavy hadron in the inverse of the heavy quark mass $m_Q$ we attempt to factorize them into perturbative- and nonperturbative parts. In our approach the nonperturbative parts can be defined as matrix elements in heavy quark effective theory, the shape of the functions is predicted by perturbative QCD. In this work we neglect effect at order of $m_Q^{-2}$ and calculate the perturbative parts at one-loop level for heavy quark- and gluon fragmentation. We compare our results from leading log approximation with experimental results from $e^+e^-…
We apply the phenomenological Reggeon Field Theory framework to investigate the relative importance of perturbative and nonperturbative multiparton correlations for the treatment of double parton scattering (DPS) in proton-proton collisions. We obtain a significant correction to the so-called effective cross section for DPS due to nonperturbative parton splitting. When combined with the corresponding perturbative contribution, this results in a rather weak energy and transverse momentum dependence of the effective cross section, in agreement with experimental observations at the Tevatron and t…
We present recent developments on the role of the running coupling constant at the intersection of perturbative and nonperturbative QCD. A number of experiments show a smooth transition from small to large scales given by the four-momentum transfer in the reactions. This is at variance with perturbative QCD where the running coupling constant becomes infinite when the scale equals $Λ_{\tiny QCD}$. Approaches using an effective coupling constant could help interpret the opposite trend of data as compared to standard perturbative QCD predictions. We give an overview of the role of the coupling c…
The QCD running coupling $α_s(Q^2)$ sets the strength of the interactions of quarks and gluons as a function of the momentum transfer $Q$. The $Q^2$ dependence of the coupling is required to describe hadronic interactions at both large and short distances. In this article we adopt the light-front holographic approach to strongly-coupled QCD, a formalism which incorporates confinement, predicts the spectroscopy of hadrons composed of light quarks, and describes the low-$Q^2$ analytic behavior of the strong coupling $α_s(Q^2)$. The high-$Q^2$ dependence of the coupling $α_s(Q^2)$ is specified by…
At small transverse momentum $q_T$, transverse-momentum dependent parton distribution functions (TMDPDFs) arise as genuinely nonperturbative objects that describe Drell-Yan like processes in hadron collisions as well as semi-inclusive deep-inelastic scattering. TMDPDFs naturally depend on the hadron momentum, and the associated evolution is determined by the Collins-Soper equation. For $q_T \sim Λ_\mathrm{QCD}$ the corresponding evolution kernel (or anomalous dimension) is nonperturbative and must be determined as an independent ingredient in order to relate TMDPDFs at different scales. We pro…
The nonperturbative approach to soft high-energy hadron-hadron scattering, based on the analytic continuation of Euclidean Wilson-loop correlation functions, makes possible the investigation of the problem of the asymptotic energy dependence of hadron-hadron total cross sections by means of lattice calculations. In this contribution we compare the lattice numerical results to analytic results obtained with various nonperturbative techniques. We also discuss the possibility to obtain indications of the rise of hadron-hadron total cross sections with energy directly from the lattice data.
We present an analysis of nonperturbative contributions to the transverse momentum distribution of $Z/γ^*$ bosons produced at hadron colliders. The new data on the angular distribution $ϕ^*_η$ of Drell-Yan pairs measured at the Tevatron is shown to be in excellent agreement with a perturbative QCD prediction based on the Collins-Soper-Sterman (CSS) resummation formalism at NNLL accuracy. Using these data, we determine the nonperturbative component of the CSS resummed cross section and estimate its dependence on arbitrary resummation scales and other factors. With the scale dependence included …
We discuss a nonperturbative mechanism for generation of the single-spin asymmetries in hadron interactions. It is based on the chiral quark model combined with unitarity and impact parameter picture and provides explanation for the experimental regularities observed under the measurements of the spin asymmetries.
We present a nonperturbative QCD calculation of diffractive vector meson production in virtual photon nucleon scattering at high energy. We use the nonperturbative model of the stochastic QCD vacuum which yields linear confinement and makes specific predictions for the dependence of high-energy scattering cross sections on the hadron size. Using light cone wave functions of the photon and vector mesons, we calculate electroproduction cross sections for $ρ$, $ω$, $ϕ$ and $J/ψ$. We emphasize the behavior of specific observables such as the ratio of longitudinal to transverse production cross sec…
Assuming so called global duality we argue that it is very likely that local duality needed to obtain results for the hadronic width of heavy meson decays within the $1/m_Q$ expansion holds. Hence, if the discrepancy between experiment and the theory concerning charm counting, the semileptonic branching fraction and the lifetimes of $b$ hadrons persist, it may be taken as a hint at some qualitatively new effect in (nonperturbative) QCD or even as a new physics.
The holographic mapping of gravity in AdS space to QCD, quantized at fixed light-front time, provides a precise relation between the bound-state amplitudes in the fifth dimension of AdS space and the boost-invariant light-front wavefunctions describing the internal structure of hadrons in physical space-time. In particular, the elastic and transition form factors of the pion and the nucleons are well described in this framework. The light-front AdS/QCD holographic approach thus gives a frame-independent first approximation of the color-confining dynamics, spectroscopy, and excitation spectra o…
We consider low-$x$ behavior of the spin structure functions $g_1(x)$ and $h_1(x)$ in the unitarized chiral quark model that combines the ideas on constituent quark structure of hadrons with a geometrical scattering picture and unitarity. A nondiffractive singular low-$x$ dependence of $g^p_1(x)$ and $g_1^n(x)$ is obtained and a diffractive type smooth behavior of $h_1(x)$ is predicted at small $x$.
Recent progress in modeling QCD for hadron physics through truncated Dyson-Schwinger equations is reviewed. Special emphasis is put upon comparison of dressed quark propagators and the dressed quark-gluon vertex with lattice-QCD results.
Quantum chromodynamics (QCD) predicts the existence of both nonperturbative intrinsic and perturbative extrinsic heavy quark contributions to the fundamental structure of hadrons. The existence of intrinsic charm at the 3-standard-deviation level in the proton has recently been established from structure function measurements by the NNPDF Collaboration. Here we revisit the physics of intrinsic heavy quarks using light-front holographic QCD (LFHQCD) - a novel comprehensive approach to hadron structure which provides detailed predictions for dynamical properties of the hadrons, such as form fact…
We show that the resummation of large perturbative corrections in QCD leads to ambiguities in high energy cross sections that are suppressed by powers of large momentum scales. These ambiguities are caused by infrared renormalons, which are a general feature of resummed hard-scattering functions in perturbative QCD, even though these functions are infrared safe order-by-order in perturbation theory. As in the case of the operator product expansion, the contributions of infrared renormalons to coefficient functions may be absorbed into the definition of higher-dimensional operators, which induc…
Fundamental aspects of nonperturbative QCD dynamics which are not obvious from its classical Lagrangian, such as the emergence of a mass scale and confinement, the existence of a zero mass bound state, the appearance of universal Regge trajectories and the breaking of chiral symmetry are incorporated from the onset in an effective theory based on superconformal quantum mechanics and its embedding in a higher dimensional gravitational theory. In addition, superconformal quantum mechanics gives remarkable connections between the light meson and nucleon spectra. This new approach to hadron physic…
We show that the form of the renormalization group invariant quark-gluon interaction predicted by a refined nonperturbative analysis of the QCD gauge sector is in quantitative agreement with the one required for describing a wide range of hadron observables using sophisticated truncation schemes of the Schwinger-Dyson equations relevant in the matter sector.
Nonperturbative QCD contributions to the inclusive semileptonic decay of the B meson consist of the dynamic and kinematic components. We calculate the decay width in an approach based on the light-cone expansion and the heavy quark effective theory, which is able to include both components of nonperturbative QCD contributions. The kinematic component results in the phase-space extension and is shown to be quantitatively crucial, which could increase the decay width significantly. We find that the semileptonic decay width is enhanced by long-distance strong interactions by +(9\pm 6)%. This anal…
We report on recent experimental and theoretical developments in our understanding of the QCD running coupling α_s in QCD's nonperturbative regime. They allow us to analytically compute the hadron mass spectrum, with Λ_s the only input necessary to this determination. The computed spectra agrees well with experimental data.
We summarize recent progress in understanding the effects of nonperturbative short-range interactions in QCD on the nucleon's partonic structure at a low scale: (a) Sea quarks have intrinsic transverse momenta up to the chiral symmetry-breaking scale rho^{-1} ~ 0.6 GeV, much larger than those of valence quarks. (b) Sea quarks in the nucleon light-cone wave function exist partly in correlated in pairs of transverse size rho with sigma and pi-like quantum numbers and a distinctive spin structure (L = 1 components). The effects are demonstrated in an effective model of the low-energy dynamics res…
Nonperturbative QCD approach is systematically derived starting from the QCD Lagrangian. Treating spin effects as a perturbation, one obtains the universal effective Hamiltonian describing mesons, hybrids and glueballs. Constituent mass of quark and gluon is calculated via string tension. The resulting spectrum of mesons, hybrids and glueballs obtained is in good overall agreement with lattice data and experiment.
We use local quark-hadron duality to estimate the purely nonperturbative soft contribution to the $γ^*p\to Δ$ form factors. Our results are in agreement with existing experimental data. We predict that the ratio $G_E^*(Q^2)/G_M^*(Q^2)$ is small for all accessible $Q^2$, in contrast to the pQCD expectations that $G_E^*(Q^2)\to -G_M^*(Q^2)$.
