abstract

A short personal account is given of the impact of HERA data and the influence of Jan Kwiecinski on low \(x\) physics.

abstract

About 10 years ago HERA has opened a new field of studies, namely that of low-\(x\) in QCD, initially via structure function measurements, and later with dedicated measurements of the hadronic final state. Theoretical guidance has turned out to be very important for these studies. The hunt for low-\(x\) effects in data has been a constant interplay between experiment and theory. This paper gives a personal account of a few examples which are directly related to the work of Jan Kwieciński and his collaborators.

abstract

This is a review of experimental and phenomenological investigations of the nucleon spin dependent structure function \(g_1\) at low values of \(x\) and \(Q^2\).

abstract

A semiclassical description of structure functions in DIS at small \(x\) is presented. It gives an intuitive picture of the transition from the Double Leading Log approximation at large \(Q^2\), to the powerlike dependence on \(x\) in the BFKL region at limited \(Q^2\). Formal derivations from perturbative QCD, e.g. in the BFKL or the CCFM formalisms, are technically complicated, and therefore such an intuitive picture may be valuable and possibly helpful in the work towards a better understanding of DIS, and of the strong interaction in general.

abstract

At present there is no correct theory of evolution of \(F_2(x,Q^2)\) at small \(x\). It is a mixture of hard and soft pomeron exchange and perturbative QCD very successfully describes the evolution of the hard-pomeron component. This allows the gluon density to be calculated. It is somewhat different from what is conventionally supposed, but it leads to a clean PQCD description of the data for the charm structure function. Perturbative QCD breaks down for the evolution of the soft-pomeron component of \(F_2(x,Q^2)\).

abstract

We propose a new method to test the (resummed) next-to-leading-order BFKL evolution kernels using the Mellin transformed \(j\)-moments of the proton structure function \(F_2.\)

abstract

For an accurate description of the polarized deep inelastic scattering at low \(x\) including the logarithmic corrections, \(\ln ^2(1/x)\), is required. These corrections resummed strongly influence the behavior of the spin structure functions and their moments. Results of the work of J. Kwieciński and myself on this problem are reviewed.

abstract

I describe the search for universal properties of strongly interacting matter. The Color Glass Condensate is presented as the universal form of matter from which controls the high energy limit of strong interactions. At high energies, this strongly interacting but weakly coupled matter allows first computations from first principles in QCD.

abstract

Below the saturation momentum the sea quark occupation number reaches a pure number, independent of any parameters in QCD, reminiscent of a Pauli Principle result. We argue, however, that the Pauli Principle plays no role in this result.

abstract

We calculate, for nonzero momentum transfer, the dipole formula for the high energy behaviour of elastic and quasielastic scattering of a virtual photon. We obtain an expression of the nonforward photon impact factor and of the nonforward photon wave function, and we give a physical interpretation.

abstract

A saturation model of high energy scattering is analysed, taking into account the impact parameter dependence. The unitarisation is assumed to occur independently at each transverse location. In the single scattering regime the amplitude has features characteristic for the hard Pomeron, and at very high energies the soft Pomeron trajectory is obtained. It is shown, how the string tension may be embodied into the saturation model, linking the Regge phenomenology, the hadron structure and the saturation model.

abstract

In this paper \(\gamma ^*\)–\(\gamma ^*\) scattering with large, but more or less equal virtualities of two photons is discussed using BFKL dynamics, emphasizing the large impact parameter behavior (\(b_t\)) of the dipole–dipole amplitude. It is shown that the non-perturbative contribution is essential to fulfill the unitarity constraints in the region of \(b_t \gt 1/2 m_\pi \), where \(m_\pi \) is pion mass. The saturation and the unitarization of the dipole–dipole amplitude is considered in the framework of the Glauber–Mueller approach. The main result is that we can satisfy the unitarity constraints introducing the non-perturbative corrections only in initial conditions (Born amplitude).

abstract

I give an account of the definitions of parton densities, both the conventional ones, integrated over parton transverse momentum, and unintegrated transverse-momentum-dependent densities. The aim is to get a precise and correct definition of a parton density as the target expectation value of a suitable quantum mechanical operator, so that a clear connection to non-perturbative QCD is provided. Starting from the intuitive ideas in the parton model that predate QCD, we will see how the simplest operator definitions suffer from divergences. Corrections to the definition are needed to eliminate the divergences. An improved definition of unintegrated parton densities is proposed.

abstract

I discuss a degree of freedom in formulating perturbation theory that is often neglected: the \(in\)- and \(out\)-states need not be empty. The inclusion of (free) particles in the asymptotic states modifies the on-shell prescription of the free propagator. This affects loop contributions — but the modified expansion is a priori as justified as the standard one with Feynman prescription. It is possible to dress the quark propagator to all orders with zero-momentum gluons from the perturbative ground state. The dressed quark has no pole and thus cannot appear as an external particle in the \(S\)-matrix. Chiral symmetry may be spontaneously broken, but Lorentz and gauge symmetry is exact. Adding loop corrections to this “dressed tree approximation” gives a formally exact PQCD expansion.

abstract

Central role played by certain non-Abelian monopoles (of Goddard–Nuyts–Olive–Weinberg type) in the infrared dynamics in many confining vacua of softly broken \({\cal N}=2\) supersymmetric gauge theories, has recently been clarified. We discuss here the main lessons to be learned from these studies for the confinement mechanism in QCD.

abstract

We study an importance of the longitudinally polarized virtual photons \(\gamma ^{\ast }_{\rm L}\) in the semi-inclusive \(ep\) processes in the \(ep\) center-of-mass and Breit frames, and for various distributions. We used the factorization formulae for the unpolarized inclusive and semi-inclusive \(ep\) processes which hold in an arbitrary reference frame. The numerical studies were performed for the \(ep\) HERA collider for a process with a large-\(p_{\rm T}\) (prompt) photons production, i.e. , the unpolarized Compton process \(e p \rightarrow e \gamma X\), in the Born approximation. In the \(ep\) center-of-mass frame we found that the differential cross section for the longitudinally polarized intermediate photon, \(d \sigma _{\rm L}\), and the term due to the interference between the longitudinal- and transverse-polarization states of the photon, \(d \tau _{\rm LT}\), are small, i.e. below \(10 \%\) of the cross section. Moreover, these two contributions almost cancel one another, leading to a stronger domination of the transversely polarized virtual photon, even for its large virtuality \(Q^2\). We found that in this frame the interference term gives non-vanishing contributions even for the cross sections integrated over the azimuthal angle, contrary to a naive expectation. Relevance of the contributions of the longitudinal photon in a jet production in DIS events at the HERA collider is commented. A relatively large (\(\sim 30 \%\)) effect due to the interference term \(d \tau _{\rm LT}\) was found for the considered process at the HERA collider in the azimuthal-angle distribution in the Breit frame. Here this contribution vanishes in the cross section integrated over \(\phi \).

abstract

Measurements of the proton structure function at large \(x\), low \(Q^2\) display a strong \(Q^2\) dependence which is usually interpreted as evidence for a significant higher twist contribution. Recent progress in understanding the resummation of large logs, \(\ln (1-x)\), up to next-to-next-to-leading log order and beyond suggest that the observed enhancement may possibly be due to such terms alone. We study the implications for different theoretical scenarios in the light of novel suggestions for extracting large \(x\) information from future measurements at HERA.

abstract

We review the description of high energy diffraction from both the \(s\) and \(t\) channel viewpoints, and demonstrate their consistency. We emphasize the role played by \(s\) channel unitarity and multi-Pomeron exchanges. We explain how these effects suppress hard diffractive processes. As examples, we describe the calculation of diffractive dijet production at the Tevatron and predict some of the rich diffractive phenomena accessible in proton–nuclear collisions at RHIC.

abstract

The inclusive distributions of gluons and pions are calculated with absolute normalization for high-energy nucleon–nucleon collisions. The results for several unintegrated gluon distributions from the literature are compared. The gluon distribution proposed recently by Kharzeev and Levin based on the idea of gluon saturation is tested against DIS data from HERA. We find huge differences in both rapidity and transverse momentum distributions of gluons and pions in nucleon–nucleon collisions for different models of unintegrated gluon distributions. The approximations used recently in the literature are discussed. The Kharzeev–Levin gluon distribution gives extremely good description of momentum distribution of charged hadrons at midrapidities. Contrary to a recent claim in the literature, we find that the gluonic mechanism discussed does not describe the inclusive spectra of charged particles in the fragmentation region, i.e. in the region of large \(|y|\) for any unintegrated gluon distribution from the literature.

abstract

We argue that study of the cross section of coherent photo(electro) production of vector mesons off nuclear targets provides an effective method to probe the leading twist hard QCD regimes of color transparency and perturbative color opacity as well as the onset of Black Body Limit (BBL) in the soft and hard QCD interactions. In the case of intermediate energies we use the Generalized Vector Dominance Model (GVDM) to take into account coherence effects for two distinctive limits — the soft interactions for production of \(\rho \) and \(\rho '\)-mesons and the color transparency regime for production of charmonium states. We demonstrate that GVDM describes very well \(\rho \)-meson coherent photoproduction at \(6 \leq E_{\gamma } \leq 10\) GeV and predict an oscillating energy dependence for the coherent charmonium production. In the limit of small \(x\) we find that hard QCD leads to onset of the perturbative color opacity even for production of very small onium states, like \({\mit \Upsilon }\). The advantages of the process of coherent dijet photoproduction and hard diffractive processes in general for probing the onset of BBL and measuring the light-cone wave function of the photon in a hard scattering regime where decomposition over twists becomes inapplicable are explained. We apply this analysis to the study of the photon induced coherent processes in ultra peripheral collisions of ions at LHC and demonstrate that the counting rates will be sufficient to study the physics of color opacity and color transparency at the energies beyond the reach of the electron–nucleon (nucleus) colliders.

abstract

We apply our solution of the nonlinear evolution equation to the case of \(J/\psi \) photo and DIS production on nucleons and nuclei targets. The uncertainty in the \(J/\psi \) wave function normalisation due to Fermi motion is treated as a free parameter. We obtain good reproduction of the HERA experimental data on a proton target. Calculations of \(J/\psi \) mesons coherent production on nuclei targets are presented and discussed. Our analysis supports the conclusions reached in our previous studies, stressing the importance of nonlinear evolution in the kinematical domain of high-density QCD.

abstract

We improve the accuracy of the extrapolation of the gluon distribution of the proton to very small \(x\), and show that the charm production cross section, needed to calculate the cosmic ray-induced ‘atmospheric’ flux of ultrahigh energy prompt \(\nu _\mu \) and \(\nu _\tau \) neutrinos, may be predicted within perturbative QCD to within about a factor of three. We follow the sequence of interactions and decays in order to calculate the neutrino fluxes as a function of energy up to \(10^9\) GeV. We also compute the prompt \(\nu _\tau \) flux from \(b\bar {b}\) production, hadronization and decay. New cosmic sources of neutrinos will be indicated if more prompt neutrinos are observed than predicted. If fewer neutrinos are observed than predicted, then constraints will be imposed on the nuclear composition of cosmic rays. The advantages of studying \(\nu _\tau \) neutrinos are emphasized. We provide a simple parametrization of the prediction for the inclusive cross section for \(c\) quark production in high energy proton–air collisions.

abstract

Predictions for the difference of proton–antiproton and proton–proton cross sections in the heavy quark production within LO DGLAP analysis together with the \(\ln ^2x\) terms resummation are presented. An important role of the double logarithmic \(\ln ^2x\) corrections in a case of the large rapidity gap between a quark and an antiquark is discussed.

abstract

In multiparticle production one has the sensation that problems are never solved. They come back again and again. Here I try to illustrate how it happens.

abstract

In the framework of a microscopic string model inclusive charged particle distribution and baryon and antibaryon production are described. The emphasis is put on high energies (RHIC) where shadowing corrections play a crucial role. Some recent developments on \(J/\psi \) suppression at CERN-SPS are also discussed. Possible consequences for the crucial issue of thermal equilibration of the produced system are considered.

abstract

Coincidence probabilities of multiparticle events, as measured in finite momentum intervals for Bose and Fermi ideal gas, are calculated and compared with the exact expressions given in statistical physics.

abstract

Relations between Wigner functions and the source functions used in models of Bose–Einstein correlations in multiple particle production are derived and discussed. These relations are model dependent. In particular it is important whether the particles are emitted simultaneously and if not, whether the production amplitudes corresponding to different moments of time can interfere with each other.

abstract

\(P\)-wave amplitudes for elastic \(K^+K^-\) photoproduction on hydrogen near the \(\phi (1020)\) resonance have been derived in an analytical form and a partial wave decomposition of the amplitudes has been performed. We discuss the high energy limit of the resulting amplitudes and compare two types of pomeron coupling to nucleons.

abstract

Using the PCAC relation, we derive a compact formula for the pion decay constant \(F_{\pi }\) in the nonlocal chiral quark model. For practical calculations this formula may be used both in the Minkowski and in the Euclidean space. For the pion momentum \(P_{\mu }\rightarrow 0\) it reduces to the well known expression derived earlier by other authors. Using a generalized dipole Ansatz for the momentum dependence of the constituent quark mass in the Minkowski space, we express \(F_{\pi }^{2}\) in terms of a single integral over the quark momentum fraction \(u\). We interpret the integrand as a pion distribution amplitude \(\phi (u)\). We discuss its properties and compare with the \(\pi \)DA’s obtained in other models.

abstract

I start with a brief summary of Higgs mechanism and supersymmetry. Then I discuss the theoretical constraints, current limits and search strategies for Higgs boson(s) at LHC — first in the SM and then in the MSSM. Finally, I discuss the analogous constraints and search strategies for the superparticles, concentrating on the minimal supergravity model. Recent advances in identifying the most promising channels for Higgs and SUSY searches are emphasized.

abstract

Supersymmetric extensions of the Standard Model provide new sources of CP-violation. Here the CP properties of neutralinos are described and possible experimental signatures of CP-violation in the neutralino production processes at \(e^+e^-\) linear colliders are discussed.