Hadron scattering in two-dimensional QCD: (I). Formalism and leading order calculations

Two-dimensional quantum chromodynamics in the 1/N_c expansion is explored as a model for hadronic interactions. In meson-meson scattering, order 1/N_c terms exhibit embryonic “Regge” behaviour, with the crossed channel factorization, signature and exchange degeneracy properties found in dual Regge models. “Regge” intercepts are additive in the quark quantum numbers exchanged, and have a lower limit for large quark masses. Residues also factorize in the direct channel. An analogue for fixed angle scattering is presented which has deviations from dimensional counting rules related to form factors and Regge intercepts.     

Direct photon production beyond leading order in QCD

The significance of the quark-quark scattering process (quark+quark→quark+quark+photon) for the production of large-q_T real photons is discussed in the framework of perturbative QCD. To extract the finite contribution of this process to the differential cross section dσ/dy d²q_T (hadron 1+hadron 2→photon+anything) we define the gluon distribution and the quark-to-photon fragmentation function beyond the leading approximation. The calculations are performed consistently in the dimensional regularization scheme. Our numerical estimates show the resulting finite qq→qqγ contribution to be a small (order α_s/2π) correction in comparison with the basic QCD subprocesses.     

Higher order QCD corrections to an exclusive two-photon process

We calculate the next-to-leading order QCD corrections in the $\text{MS}$ scheme to the coefficient functions in an operator product expansion of the amplitude T(q², p²) for the process $\text{γ}{}^1\text{(q) + γ}{}^1\text{(p) →}\text{helicity-zero}$, flavour non-singlet meson in which ?q² is large and ?p² ? 0. For an asymptotic wave function the complete O(α_s) correction for a pseudoscalar meson is about 16% for p² = 0 and α_s = 0.3; most of this correction can be removed by using a modified evolution equation for the wave function, leaving a correction of about 7%. For large p² the complete O(α_s) correction for a pseudoscalar meson is about 10%. We discuss how our results can be combined with similar calculations for the pion form factor F_π(Q²) to give a prediction: F_π(Q²) = Aα_s(Q²)T_π²(q², 0)(1 + Bα_s) that is independent of the as yet unknown two-loop anomalous dimension matrix.     

Higher-order QCD corrections to exclusive processes: The multiple scattering mechanism

The multiple-scattering diagram, calculated to lowest order in QCD, fits well topp elastic scattering data at larget. It is shown that higherorder QCD corrections seem to spoil this agreement: calculated as far as the insertion of two additional gluons, they give an exponential factor. This factor differs in detail from some previous conjectures. For colour-singlet bound states of quarks, the exponential factor is independent of whether or not the gluon mass is zero, unlike the case of simple quark-quark scatterin. Two régimes are considered:t ands of the same order, andt large but much less thans. Exponentiation seems to occur in both cases, but in a non-abelian theory more diagrams are important for the latter case.     

Hadron interactions in lattice QCD

Progress on the potential method, recently proposed to investigate hadron interactions in lattice QCD, is reviewed. The strategy to extract the potential in lattice QCD is explained in detail. The method is applied to extract NN potentials, hyperon potentials and the meson–baryon potentials. A theoretical investigation is made to understand the origin of the repulsive core using the operator product expansion. Some recent extensions of the method are also discussed.     

Hadron spectroscopy in lattice QCD

A Monte Carlo computation of meson and hadron spectroscopy within lattice QCD is made. We give a detailed discussion of the statistical and systematic errors of the results and analyze the present limitations of our approach. The results are in agreement with the observed spectrum. We also estimate the values of up, down and strange quark masses.     

Processes involving fragmentation functions beyond the leading order in QCD

We point out that the electron propagator, calculated from a truncated Johnson-Baker-Willey equation, suffers from the following defects: lack of renormalizability gauge dependence of the electron electromagnetic mass, as well as unacceptable analytic structure.     

Hadronic lepton-pair production beyond the leading order in perturbative QCD

Hadronic lepton-pair production in perturbative QCD is calculated to order $\text{g}{}^{\mathrm{<mtext>2</mtext>}}$ to be usable in combination with the existing calculation of the anomalous dimension of order $\text{g}{}^{\mathrm{<mtext>4</mtext>}}$. The structure function of the subprocess $\text{q}\text{+}\text{q}\text{→ γ +}$ anything in an arbitrary covariant gauge for gluons is found to have gauge-dependent contributions which are exactly cancelled by contributions from operator matrix elements to give the gauge-independent “coefficient function” for lepton-pair production in the minimal subtraction scheme. This provides a consistency check of the perturbative QCD recipe. A comparison is made with other existing calculations.     

Hadron wave functions in lattice QCD

Coulomb gauge quark-antiquark wave functions for the pion and the rho are calculated in the valence approximation on a lattice 8³ × 16. We use gauge group SU(2) at β of 2.431 corresponding to an inverse lattice spacing of 1100 ± 100 MeV. The wave functions fall off significantly over the size of the box, are rotationally invariant except at the box's boundary, and are nearly independent of the lagrangian quark mass.     

Lepton-hadron processes beyond leading order in quantum chromodynamics

We present a summary of QCD formulae describing the effects of scaling violation in leptonhadron processes, with the inclusion of recently derived higher order corrections. Deep inelastic leptoproduction, one-hadron inclusive distributions in leptoproduction and ine ⁺ e ^? annihilation and Drell-Yan processes are discussed in detail. Higher order corrections to parton densities, fragmentation functions and to lepton-parton cross-sections in the above processes are presented in a common factorization scheme, so that a comparative analysis of various processes as well as an independent analysis of each of them is possible. A discussion of the various scheme dependences at next-to-leading level is also included.     

Beyond leading order QCD perturbative corrections to the pion form factor

The order α_s²(Q²) corrections to the pion form factor, F_π(Q²), are calculated using perturbative quantum chromodynamics and dimensional regularization. In the $\text{MS}$ renormalization scheme these corrections are large. This means that reliable perturbative predictions cannot be made until momentum transfers, Q, of about 300–400 GeV are reached or unless one can sum the large perturbative terms to all orders. Attempts to reorganize the perturbation series so that the first term gives a better approximation of the complete sum indicate that at Q = 10 GeV the pion form factor may be about a factor of two larger than the leading order result.     

Recent results on QCD thermodynamics: lattice QCD versus Hadron Resonance Gas model

We present our most recent investigations on the QCD cross-over transition temperatures with 2+1 staggered flavours and one-link stout improvement [JHEP 1009:073, 2010]. We extend our previous two studies [Phys. Lett. B643 (2006) 46, JHEP 0906:088 (2009)] by choosing even finer lattices (Nt=16$N_t=16$) and we work again with physical quark masses. All these results are confronted with the predictions of the Hadron Resonance Gas model and Chiral Perturbation Theory for temperatures below the transition region. Our results can be reproduced by using the physical spectrum in these analytic calculations. A comparison with the results of the hotQCD collaboration is also discussed.     

Hadron masses in QCD with one quark flavour

One-flavour QCD – a gauge theory with SU(3) colour gauge group and a fermion in the fundamental representation – is studied by Monte Carlo simulations. The mass spectrum of the hadronic bound states is investigated in a volume with extensions of L≃4.4r₀ (≃ 2.2 fm) at two different lattice spacings: a≃0.37r₀ (≃ 0.19 fm) and a≃0.27r₀ (≃ 0.13 fm). The lattice action is a Symanzik tree-level improved Wilson action for the gauge field and an (unimproved) Wilson action for the fermion.     

Collinear limits of one-loop helicity amplitudes in QCD

We point out that for QCD subprocesses involving multiple quark pairs, it is useful to investigate the collinear limits of full helicity amplitudes. We study the recently calculated one-loop $0 \to \bar q\bar QQqg$ helicity amplitudes and confirm the results found by Bern, Dixon, Dunbar and Kosower for the loop splitting amplitudes.