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Register a new userAspects of QCD Current Algebra on a Null Plane
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Consequences of QCD current algebra formulated on a light-like hyperplane are derived for the forward scattering of vector and axial-vector currents on an arbitrary hadronic target. It is shown that current algebra gives rise to a special class of sum rules that are direct consequences of the independent chiral symmetry that exists at every point on the two-dimensional transverse plane orthogonal to the lightlike direction. These sum rules are obtained by exploiting the closed, infinite-dimensional algebra satisfied by the transverse moments of null-plane axial-vector and vector charge distributions. In the special case of a nucleon target, this procedure leads to the Adler-Weisberger, Gerasimov-Drell-Hearn, Cabbibo-Radicatti and Fubini-Furlan-Rossetti sum rules. Matching to the dispersion-theoretic language which is usually invoked in deriving these sum rules, the moment sum rules are shown to be equivalent to algebraic constraints on forward S-matrix elements in the Regge limit.
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We have studied the null-plane hamiltonian structure of the free Yang-Mills fields and the scalar chromodynamics ($SQCD_{4}$). Following the Diracs procedure for constrained systems we have performed a detailed analysis of the constraint structure of both models and we give the generalized Dirac brackets for the physical variables. In the free Yang-Mills case, using the correspondence principle in the Diracs brackets we obtain the same commutators present in the literature.
We studied the scalar electrodynamics ($SQED_{4}$) and the spinor electrodynamics ($QED_{4}$) in the null-plane formalism. We followed the Diracs technique for constrained systems to perform a detailed analysis of the constraint structure in both theories. We imposed the appropriated boundary conditions on the fields to fix the hidden subset first class constraints which generate improper gauge transformations and obtain an unique inverse of the second class constraint matrix. Finally, choosing the null-plane gauge condition, we determined the generalized Dirac brackets of the independent dynamical variables which via the correspondence principle give the (anti)-commutators for posterior quantization.
A dynamical model is applied to the study of the pion valence light-front wave function, obtained from the actual solution of the Bethe-Salpeter equation in Minkowski space, resorting to the Nakanishi integral representation. The kernel is simplified to a ladder approximation containing constituent quarks, an effective massive gluon exchange, and the scale of the extended quark-gluon interaction vertex. These three input parameters carry the infrared scale {Lambda}QCD and are fine-tuned to reproduce the pion weak decay constant, within a range suggested by lattice calculations. Besides f{pi}, we present and discuss other interesting quantities on the null-plane, like: (i) the valence probability, (ii) the dynamical functions depending upon the longitudinal or the transverse components of the light-front (LF) momentum, represented by LF-momentum distributions and distribution amplitudes, and (iii) the probability densities both in the LF-momentum space and the 3D space given by the Cartesian product of the covariant Ioffe-time and transverse coordinates, in order to perform an analysis of the dynamical features in a complementary way. The proposed analysis of the Minkowskian dynamics inside the pion, though carried out at the initial stage, qualifies the Nakanishi integral representation as an appealing effective tool, with still unexplored potentialities to be exploited for addressing correlations between dynamics and observable properties.
On a null-plane (light-front), all effects of spontaneous chiral symmetry breaking are contained in the three Hamiltonians (dynamical Poincare generators), while the vacuum state is a chiral invariant. This property is used to give a general proof of Goldstones theorem on a null-plane. Focusing on null-plane QCD with N degenerate flavors of light quarks, the chiral-symmetry breaking Hamiltonians are obtained, and the role of vacuum condensates is clarified. In particular, the null-plane Gell-Mann-Oakes-Renner formula is derived, and a general prescription is given for mapping all chiral-symmetry breaking QCD condensates to chiral-symmetry conserving null-plane QCD condensates. The utility of the null-plane description lies in the operator algebra that mixes the null-plane Hamiltonians and the chiral symmetry charges. It is demonstrated that in a certain non-trivial limit, the null-plane operator algebra reduces to the symmetry group SU(2N) of the constituent quark model.
Multiparticle production processes provide valuable information about the mechanism of the conversion of the initial energy of projectiles into a number of secondaries by measuring their multiplicity distributions and their distributions in phase space. They therefore serve as a reference point for more involved measurements. Distributions in phase space are usually investigated using the statistical approach, very successful in general but failing in cases of small colliding systems, small multiplicities, and at the edges of the allowed phase space, in which cases the underlying dynamical effects competing with the statistical distributions take over. We discuss an alternative approach, which applies to the whole phase space without detailed knowledge of dynamics. It is based on a modification of the usual statistics by generalizing it to a superstatistical form. We stress particularly the scaling and self-similar properties of such an approach manifesting themselves as the phenomena of the log-periodic oscillations and oscillations of temperature caused by sound waves in hadronic matter. Concerning the multiplicity distributions we discuss in detail the phenomenon of the oscillatory behaviour of the modified combinants apparently observed in experimental data.
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