J. Rodríguez-Quintero

The Infrared Behaviour of the Pure Yang–Mills Green Functions

We review the infrared properties of the pure Yang–Mills correlators and discuss recent results concerning the two classes of low-momentum solutions for them reported in literature, i.e. decoupling and scaling solutions. We will mainly focus on the Landau gauge and pay special attention to the results inferred from the analysis of the Dyson–Schwinger equations of the theory and from “quenched” lattice QCD. The results obtained from properly interplaying both approaches are strongly emphasized.

On the IR behaviour of the Landau-gauge ghost propagator

We examine analytically the ghost propagator Dyson-Schwinger Equation (DSE) in the deep IR regime and prove that a finite ghost dressing function at vanishing momentum is an alternative solution (solution II) to the usually assumed divergent one (solution I). We furthermore find that the Slavnov-Taylor identities discriminate between these two classes of solutions and strongly support the solution II. The latter turns out to be also preferred by lattice simulations within numerical uncertainties.

Nonperturbative comparison of QCD effective charges

We study the nonperturbative behavior of two versions of the QCD effective charge, one obtained from the pinch technique gluon self-energy, and one from the ghost-gluon vertex. Despite their distinct theoretical origin, due to a fundamental identity relating various ingredients appearing in their respective definitions, the two effective charges are almost identical in the entire range of physical momenta, and coincide exactly in the deep infrared, where they freeze at a common finite value. Specifically, the dressing function of the ghost propagator is related to the two form factors in the Lorentz decomposition of a certain Greens function, appearing in a variety of field-theoretic contexts. The central identity, which is valid only in the Landau gauge, is derived from the Schwinger-Dyson equations governing the dynamics of the aforementioned quantities. The renormalization procedure that preserves the validity of the identity is carried out, and various relevant kinematic limits and physically motivated approximations are studied in detail. A crucial ingredient in this analysis is the infrared finiteness of the gluon propagator, which is inextricably connected with the aforementioned freezing of the effective charges. Some important issues related to the consistent definition of the effective charge in the presence of such a gluon propagator are resolved. We finally present a detailed numerical study of a special set of Schwinger-Dyson equations, whose solutions determine the nonperturbative dynamics of the quantities composing the two effective charges.

Non-perturbative power corrections to ghost and gluon propagators

We study the dominant non-perturbative power corrections to the ghost and gluon propagators in Landau gauge pure Yang-Mills theory using OPE and lattice simulations. The leading order Wilson coefficients are proven to be the same for both propagators. The ratio of the ghost and gluon propagators is thus free from this dominant power correction. Indeed, a purely perturbative fit of this ratio gives smaller value ( 270MeV) of Λ than the one obtained from the propagators separately( 320MeV). This argues in favour of significant non-perturbative ~ 1/q2 power corrections in the ghost and gluon propagators. We check the self-consistency of the method.

Search for tau flavour violation at the LHC

We explore the prospects for searches at the LHC for sparticle decays that violate τ lepton number, in the light of neutrino oscillation data and the seesaw model for neutrino masses and mixing. We analyse the theoretical and phenomenological conditions required for tau flavour violation to be observable in χ2 → χ+τ±μ decays, for cosmologically interesting values of the relic neutralino LSP density. We study the relevant supersymmetric parameter space in the context of the Constrained Minimal Supersymmetric Extension of the Standard Model (CMSSM) and in SU(5) extensions of the theory. We pay particular attention to the possible signals from hadronic tau decays, that we analyse using PYTHIA event simulation. We find that a signal for τ flavour-violating χ2 decays may be observable if the branching ratio exceeds about 10%. This may be compatible with the existing upper limit on τ → μγ decays if there is mixing between right-handed sleptons, as could be induced in non-minimal SU(5) GUTs.

Basic features of the pion valence-quark distribution function

The impulse-approximation expression used hitherto to define the pions valence-quark distribution function is flawed because it omits contributions from the gluons which bind quarks into the pion. A corrected leading-order expression produces the model-independent result that quarks dressed via the rainbow–ladder truncation, or any practical analogue, carry all the pions light-front momentum at a characteristic hadronic scale. Corrections to the leading contribution may be divided into two classes, responsible for shifting dressed-quark momentum into glue and sea-quarks. Working with available empirical information, we use an algebraic model to express the principal impact of both classes of corrections. This enables a realistic comparison with experiment that allows us to highlight the basic features of the pions measurable valence-quark distribution, qπ(x)qπ(x); namely, at a characteristic hadronic scale, qπ(x)∼(1−x)2qπ(x)∼(1−x)2 for x≳0.85x≳0.85; and the valence-quarks carry approximately two-thirds of the pions light-front momentum.

Instantons and the A (2) condensate

We argue that the

Is the QCD ghost dressing function finite at zero momentum

condensate found in the Landau gauge on lattices, when an Operator Product Expansion of Green functions is performed, might be explained by instantons. We use cooling to estimate the instanton contribution and extrapolate back the result to the thermalised configuration. The resulting