Modern Physics Letters A

Short illustrated description of the Professor A.V. Efremov story in life and science on the occasion of his 75th birthday.

A retrospective historical overview of the phenomenon of spontaneous symmetry breaking (SSB) in quantum theory, the issue that has been implemented in particle physics in the form of the Higgs mechanism. The main items are:

– The Bogoliubov's microscopical theory of superfluidity (1946);

– The BCS-Bogoliubov theory of superconductivity (1957);

– Superconductivity as a superfluidity of Cooper pairs (Bogoliubov - 1958);

– Transfer of the SSB into the QFT models (early 60s);

– The Higgs model triumph in the electro-weak theory (early 80s).

The role of the Higgs mechanism and its status in the current Standard Model is also touched upon.

Note from Publisher: This article contains the abstract only.

We discuss some problems concerning the application of perturbative QCD to high energy processes. In particular for hard processes, we analyze higher order and higher twist corrections. It is argued that these effects are of great importance for understanding the behaviour of pion electromagnetic form factor at moderately large momentum transfers. For soft processes, we show that summing the contributions of the lowest twist operators leads to a Regge-like amplitude.

Some features of old results in the total summation of all logarithmic contributions of all diagrams in Yukawa theory are presented. We discuss some lessons from this picture for the description of Pomeron, odderon, etc. in QCD.

The personal view on some recent aspects of average spin and orbital momenta of partons in nucleon is discussed and compared with the previous understanding. The special attention is payed to the strangeness polarization mediated by gluon anomaly and treatment of the strange quarks in a heavy ones in a multiscale nucleon. The crucial role in the orbital structure of nucleon is played by relocalization (Belinfante) invariance and Equivalence Principle (EP). The new manifestation of EP for spin 1 particles is suggested and discussed.

We analyze small-x deeply virtual Compton scattering data using flexible generalized parton distribution models to pin down both the skewness and t dependence. We compare our outcome at t = 0 with the full Shuvaev transformation. We point out that this integral transform is a model which is equivalent to a conformal generalized parton distribution and a minimalist "dual" parameterization. Some mathematical subtleties of conformal representations are recalled.

We discuss the QCD sum-rule approach for the spacelike electromagnetic pion form factor in the O(α_s) approximation. We show that the nonlocality of the condensates is a key point to include nonperturbative contributions to the pion form factor. We compare our results with the Local-Duality predictions and show that the continuum threshold s₀(Q²) parameter is highly underestimated in the Local-Duality approach at Q² ≳ 2 GeV². Using our fit for this parameter, and applying the fractional analytic perturbation theory, we estimate with an accuracy of the order of 1% the contribution to the pion's form factor.

We use light-cone QCD sum rules to calculate the pion-photon transition form factor, taking into account radiative corrections up to the next-to-next-to-leading order of perturbation theory. We compare the obtained predictions with all available experimental data from the CELLO, CLEO, and the BaBar Collaborations. We point out that the BaBar data are incompatible with the convolution scheme of QCD, on which our predictions are based, and can possibly be explained only with a violation of the factorization theorem. We pull together recent theoretical results and comment on their significance.

I will review a recent progress in computing scattering amplitudes in strongly coupled gauge theories — a fascinating subject which has been recently boosted by the formulation of the gauge/string duality in maximally supersymmetric Yang–Mills theory. In addition to the conventional symmetry of the underlying Lagrangian, the scattering amplitudes in this theory exhibit a new, dual superconformal symmetry. This symmetry is powerful enough to completely determine the scattering amplitudes for arbitrary coupling in a suitably defined limit.

The parton content of the nucleon is explored within a meson-cloud model developed to derive light-cone wave functions for the physical nucleon. The model is here applied to study electromagnetic form factors, distribution amplitudes and nucleon-to-meson transition distribution amplitudes.

In this talk various spin effects in hard exclusive electroproduction of mesons are briefly reviewed. The data are discussed in the light of recent theoretical calculations within the frame work of the handbag approach. This talk has been presented at the Conference in Honor of Prof. Anatoly Efremov's 75th Birthday held at Trento, July, 2009.

The quark spin densities related to generalized parton distributions in impact-parameter space and to transverse-momentum dependent parton distributions are reviewed within a light-cone quark model, with focus on the role of the different spin-spin and spin-orbit correlations of quarks. Results for azimuthal spin asymmetries in semi-inclusive deep inelastic scattering due to T-even transverse-momentum dependent parton distributions are also discussed.

The ultraviolet and rapidity divergences of transverse-momentum dependent parton distribution functions with lightlike and transverse gauge links is studied, also incorporating a soft eikonal factor. We find that in the light-cone gauge with q^--independent pole prescriptions extra divergences appear which amount, at one-loop, to a cusp-like anomalous-dimension. We show that such contributions are absent when the Mandelstam-Leibbrandt prescription is used. In the first case, the soft factor cancels the anomalous dimension defect, while in the second case its ultraviolet-divergent part reduces to unity.

The standard theoretical description of Polarized DIS is based on the use of the DGLAP evolution equations. This approach controls the Q² -evolution of the DIS structure functions but cannot describe the x -evolution and therefore should not be used at small x. We complement this approach, accounting for the x-evolution of the spin structure function g₁ in the leading logarithmic approximation.

We consider pion electroproduction close to threshold for Q² in the region 1–10 GeV² on a nucleon target. The momentum transfer dependence of the S-wave multipoles at threshold, E₀₊ and L₀₊, is calculated in the chiral limit using light-cone sum rules. Predictions for the cross sections in the threshold region, both for π⁰p and π⁺n channels, are given that include P-wave contributions that, as we argue, are model independent to a large extent. The results are compared with the SLAC E136 data on the structure function F₂(W,Q²) in the threshold region.

I review a new technique for calculation of higher twist evolution equations in Quantum Chromodynamics.

A complete list of the so-called Lorentz invariance relations between parton distribution functions is given and some of their consequences are discussed, such as the Burkhardt-Cottingham sum rule. The violation of these relations is considered in a model independent way. It is shown that several Lorentz invariance relations are not violated in a generalized Wandzura–Wilczek approximation, indicating that numerically their violation may be small.

In the factorized picture of semi-inclusive deep inelastic scattering the naive time reversal-odd parton distributions exist by virtue of the gauge link which is intrinsic to their definition. The link structure describes initial/final-state interactions of the active parton due to soft gluon exchanges with the target remnant. Though these interactions are non-perturbative, calculations of final-state interaction have been performed in a perturbative one-gluon approximation. We include higher-order contributions by applying non-perturbative eikonal methods to calculate the Boer-Mulders function of the pion. Using this framework we explore under what conditions the Boer Mulders function can be described in terms of factorization of final state interactions and a spatial distortion.

The present knowledge about nontrivial relations between generalized parton distributions for a spin-1/2 hadron on the one hand and transverse momentum dependent distributions on the other is reviewed. While various relations can be found in the framework of simple spectator models, so far no model-independent nontrivial relations have been established. In fact, by relating the two types of parton distributions to the fully unintegrated, off-diagonal quark-quark correlator for a spin-1/2 hadron, we argue that none of the nontrivial relations can be promoted to a model-independent status.

We examine the large-x QCD evolution of the twist-three gluonic-pole strength defining an effective T-odd Sivers function, where evolution of the T-even transverse-spin DIS structure function g₂ is multiplicative. The result corresponds to a colour-factor modified spin-averaged twist-two evolution.

Transverse momentum dependent parton distribution functions are a key ingredient in the description of spin and azimuthal asymmetries in deep-inelastic scattering processes. Recent results from non-perturbative calculations in effective approaches are reviewed, with focus on relations among different parton distribution functions in QCD and models.

Single transverse-spin asymmetry in high energy hadronic reaction has been greatly investigated from both experiment and theory sides in the last few years. In this talk, I will summarize some recent theoretical developments, which, in my opinion, help to unvail the mysterious of the single spin asymmetry.

The study of transverse spin and transverse momentum effects is part of the scientific program of COMPASS, a fixed target experiment at the CERN SPS. For these studies, a 160 GeV/c momentum muon beam is scattered on a transversely polarized nucleon target, and the scattered muon and the forward going hadrons produced in DIS processes are reconstructed and identified in a magnetic spectrometer. The measurements have been performed on a deuteron target in 2002, 2003 and 2004, and on a proton target in 2007. The main results obtained measuring single spin asymmetries are reviewed, with particular emphasis on the most recent proton measurements. After two years of spectroscopy measurements with hadron beams, in 2008 and 2009, the Collaboration will resume measurements with the muon beam and a transversely polarized target in 2010.

We present predictions for the Z-boson p_t-spectrum at Tevatron within the framework of unintegrated distributions evolved according to evolution equations recently proposed by us. We discuss the dependence of the results on the choice of non-perturbative parameters, the coupling constant and the impact of soft gluon resummation.

The study of Drell–Yan (DY) processes involving the collision of an (un)polarised hadron beam on an (un)polarised proton target can result in a fundamental improvement of our knowledge on the transverse momentum dependent (TMDs) parton distribution functions (PDFs) of hadrons. The production mechanism of J/ψ and J/ψ - DY duality can also be addressed. One of the forthcoming polarised DY experiments (COMPASS (SPS, CERN)) is discussed in this context. The most important features of this project are briefly reviewed, as well as its sensitivity to the various transverse momentum dependent spin asymmetries.

Measurements of double-spin asymmetries for single-inclusive heavy flavor production and for heavy quark correlations are expected to provide valuable information about the spin structure of the nucleon, in particular, the elusive gluon polarization. We discuss progress towards a versatile parton-level Monte-Carlo code for the production and decay of heavy quarks in longitudinally polarized hadron-hadron and photon-hadron collisions at next-to-leading order accuracy of QCD. Phenomenological studies are presented for BNL-RHIC and COMPASS.

After a brief introduction to Deep Inelastic Scattering in the Bjorken limit and in the Regge Limit we discuss the operator product expansion in terms of non local string operator and in terms of Wilson lines. We will show how the high-energy behavior of amplitudes in gauge theories can be reformulated in terms of the evolution of Wilson-line operators. In the leading order this evolution is governed by the non-linear Balitsky-Kovchegov (BK) equation. In order to see if this equation is relevant for existing or future deep inelastic scattering (DIS) accelerators (like Electron Ion Collider (EIC) or Large Hadron electron Collider (LHeC)) one needs to know the next-to-leading order (NLO) corrections. In addition, the NLO corrections define the scale of the running-coupling constant in the BK equation and therefore determine the magnitude of the leading-order cross sections. In Quantum Chromodynamics (QCD), the next-to-leading order BK equation has both conformal and non-conformal parts. The NLO kernel for the composite operators resolves in a sum of the conformal part and the running-coupling part. The QCD and kernel of the BK equation is presented.