PARTICLES AND FIELDS: Tenth Mexican School on Particles and Fields

Laudation in Honor of Augusto García
View Description Hide DescriptionA brief account of the achievements of Prof. Augusto García is presented.

Laudation in Honor of Arnulfo Zepeda
View Description Hide DescriptionA brief account of the achievements of Prof. Arnulfo Zepeda is presented.

Density Effects on the Pion Dispersion Relation at Finite Temperature
View Description Hide DescriptionWe study the behavior of the pion dispersion relation in a pion medium at finite density and temperature, introducing a chemical potential to describe the finite pion number density. Such description is particularly important during the hadronic phase of a relativistic heavy‐ion collision, between chemical and thermal freeze‐out, where the pion number changing processes, driven by the strong interaction, can be considered to be frozen. We make use of an effective Lagrangian that explicitly respects chiral symmetry through the enforcement of the chiral Ward identities. The pion dispersion relation is computed through the computation of the pion self‐energy in a non‐perturbative fashion by giving an approximate solution to the Schwinger‐Dyson equation for this self‐energy. The dispersion relation is described in terms of a density and temperature dependent mass and an index of refraction which is also temperature, density as well as momentum dependent. The index of refraction is larger than unity for all values of the momentum for finite μ and T. Given the strong coupling between ρ vectors and pions, we argue that the modification of the pion mass due to finite pion density effects has to be taken into account self‐consistently for the description of the in‐medium modifications of ρ’s.

Perturbative QCD at Next to Leading Order: a Case for Fracture Functions
View Description Hide DescriptionThis talk provides a survey of the more recent developments in semi‐inclusive deep inelastic scattering (DIS) processes in high energy collisions from the stand point of perturbative QCD. We discuss the factorization approach and the energy scale dependence of the relevant functions involved in the description of these processes. The central role played by the so called fracture functions to guarantee the correct cancellation of singularities is discussed in detail. We include recent results up to next to leading order with comments on the technical details involved in the calculation.

Quark‐Hadron Duality in Decays of Heavy Hadrons
View Description Hide DescriptionQuark‐hadron duality is often used to calculate rates of hadronic processes. For heavy mesons duality predicts small differences in lifetimes of the B ^{±}, B ^{0} and Λ_{ b }, in sharp disagreement with experimental results. We embark in a study of quark‐hadron duality in heavy meson decays. Using the ’t Hooft model as a laboratory, we discover violations to duality that scale as one inverse power of the heavy quark mass. In contrast, we find that the heavy quark mass smeared meson and quark widths differ by two inverse powers of the heavy quark mass. In 3 + 1 dimensions an analogous result holds, namely, the heavy meson hadronic decay widths satisfy quark‐hadron duality when smeared over the heavy quark mass to an accuracy of order 1/M ^{2}.

Spin and Resonant States in QCD
View Description Hide DescriptionI make the case that the nucleon excitations do not exist as isolated higher spin states but are fully absorbed by multiplets taking their origin from the rotational and vibrational excitations of an underlying quark‐diquark string. The Δ(1232) spectrum presents itself as the exact replica (up to Δ(1600)) of the nucleon spectrum with the K‐ clusters being shifted upward by about 200 MeV. QCD inspired arguments support legitimacy of the quark‐diquark string. The above K multiplets can be mapped (up to form‐factors) onto Lorentz group representation spaces of the type ψ_{μ1 ⋯μ K }, thus guaranteeing covariant description of resonant states. The quantum ψ_{μ1 ⋯μ K } states are of multiple spins at rest, and of undetermined spins elsewhere.

ππ Scattering: Theory is Ahead of Experiment
View Description Hide DescriptionI draw attention to a recent breakthrough in the field of low energy pion physics: the consequences of the hidden symmetry of the QCD Hamiltonian have successfully been incorporated in the general dispersive framework for the ππ scattering amplitude, which is due to Roy. The meagre experimental information about the imaginary parts at and above 0.8 GeV suffices to unambiguously and accurately pin down the scattering amplitude at lower energies. The recent Brookhaven data on the reaction K → ππev provide a significant test of the theory. They imply that the Gell‐Mann‐Oakes‐Renner relation is approximately valid — the bulk of the pion mass indeed originates in the quark condensate.

Strange Quark Matter and Colour Superconducting Phases of QCD
View Description Hide DescriptionWe discuss the evolution of the bubbles of quark matter which survive from the first‐order confinement phase transition till the increase of the internal pressure stops their contraction. We also show that at low temperature and high pressure a quark matter composition u d s is preferred to u d d. We finally describe the different colour superconducting phases which may be formed inside neutron stars, and the topological defects that can be generated, where the stable strangelets might be originated and perhaps already detected at high‐altitude observatories.

Scalar Mesons Effects in Radiative Decays of Vector Mesons
View Description Hide DescriptionWe review the results of our calculations for the energy spectrum and branching ratios of V ^{0} → P ^{0} P ^{0}′γ in the context of a U (3) × U (3) linear sigma model which includes ’t Hooft interaction. The corresponding amplitudes reduce to the O(p ^{4}) predictions of CHPT for these processes in the limit of heavy scalars (or equivalently in the low energy region). In this sense our approach extend to the resonance region the O(p ^{4}) predictions of CHPT in a chiral invariant way. The measured energy spectrum and branching ratios are well described in this formalism. In particular, the negative interference shown by the data around m _{ππ} = 500 MeV in φ → π^{0}π^{0}γ arises in a natural way in this framework.

Two‐loop QCD Corrections for 2 → 2 Parton Scattering Processes
View Description Hide DescriptionA summary is presented of the most recent matrix elements for massless 2 → 2 scattering processes calculated at two loops in QCD perturbation theory together with a brief review on the calculational methods and techniques used.

Parametrization of the Quark Mixing Matrix Involving its Eigenvalues
View Description Hide DescriptionA parametrization of the 3 × 3 Cabibbo‐Kobayashi‐Maskawa matrix, V, is presented in which the parameters are the eigenvalues and the components of its eigenvectors. In this parametrization, the small departure of the experimentally determined V from being moduli symmetric (i.e. V_{ij}  = V_{ji} ) is controlled by the small difference between two of the eigenvalues. In case, any two eigenvalues are equal, one obtains a moduli symmetric V depending on only three parameters. Our parametrization gives very good fits to the available data including CP‐violation. Our value of sin 2β ≈ 0.7 and other parameters associated with the ‘ unitarity triangle’ are in good agreement with data and other analyses.

Renormalization group evolution of the CKM matrix
View Description Hide DescriptionWe present here the most important ideas, equations and solutions for the running of all the quark Yukawa couplings and all the elements of the Cabibbo‐Kobayashi‐Maskawa matrix, in the approximation of one loop, and up to order λ^{4}, where λ ∼ 0.22 is the sine of the Cabibbo angle. Our purpose is to determine what the evolution of these parameters may indicate for the physics of the standard model (SM), the minimal supersymmetric standard model (MSSM) and for the Double Higgs Model (DHM).

Neutrino Masses and Mixings
View Description Hide DescriptionThese lectures discuss the possibilities for the origin of neutrino mass terms, as well as the evidence for masses and mixings from atmospheric and solar neutrino oscillations. The programme includes: 1.‐ Introduction, 2.‐ Dirac versus Majorana neutrinos, 3.‐ Effective Lagrangian approach, 4.‐ Absolute Neutrino Masses, 5.‐ Neutrino Oscillations, 6.‐ Atmospheric Neutrinos, 7.‐ Solar Neutrinos, 8.‐ Outlook.

Modeling Neutrino and Electron Scattering Cross Sections in the Few GeV Region with Effective LO PDFs
View Description Hide DescriptionWe use new scaling variables x_{w} and ξ_{ w }, and add low Q ^{2} modifications to GRV94 and GRV98 leading order parton distribution functions such that they can be used to model electron, muon and neutrino inelastic scattering cross sections (and also photoproduction) at both very low and high energies.

On the Neutrino Vector and Axial Vector Charge Radius
View Description Hide DescriptionA Majorana neutrino is characterized by just one flavor diagonal electromagnetic form factor: the anapole moment, that in the static limit corresponds to the axial vector charge radius . As is the case for the vector charge radius of a Dirac neutrino, proving that this quantity is a well defined physical quantity is non trivial. I will first describe briefly the origin of the long standing controversy about the physical or non physical nature of the neutrino charge radius. Then I will argue that, in contrast to Dirac neutrino electromagnetic form factors, for Majorana neutrinos cosmological and astrophysical arguments do not provide useful informations on . Therefore this quantity has to be studied by means of terrestrial experiment. Finally, I will discuss the constraints that can be derived on for the tau neutrino from a comprehensive analysis of the data on single photon production off Z‐resonance, and I will conclude with a few comments on ν_{μ} scattering data from the NuTeV, E734, CCFR and CHARM‐II collaborations and on the limits implied for for the muon neutrino.

CP and T Violation in Neutrino Oscillations
View Description Hide DescriptionIn this short lecture, I discuss some basic phenomenological aspects of CP and T violation in neutrino oscillation. Using CP/T trajectory diagrams in the bi‐probability space, I try to sketch out some essential features of the interplay between the effect of CP/T violating phase and that of the matter in neutrino oscillation.

Neutrino Oscillations in the Solar Noisy Matter and Magnetic Field
View Description Hide DescriptionSolar neutrino oscillations as a probe for the magnetic fields and matter density fluctuations in the solar interior as well as for the neutrino electromagnetic properties are discussed. The analysis of neutrino oscillations in the framework of the neutrino spin‐flavor conversion in the convective zone magnetic fields as a sub‐leading effect to the main LMA MSW oscillations could give the constraints to neutrino transition magnetic moment and magnetic field amplitude. We present the sensitivity of solar neutrino oscillations to the strength of the matter density perturbations given for the current experimental data and for future KamLAND result. The likely mechanism to generate the density noise based on the resonance between helioseismic and Alfvén waves is pointed.

Non‐perturbative Aspects of Schwinger‐Dyson Equations
View Description Hide DescriptionSchwinger‐Dyson equations (SDEs) provide a natural staring point to study non‐perturbative phenomena such as dynamical chiral symmetry breaking in gauge field theories. We briefly review this research in the context of quenched quantum electrodynamics (QED) and discuss the advances made in the gradual improvement of the assumptions employed to solve these equations. We argue that these attempts render the corresponding studies more and more reliable and suitable for their future use in the more realistic cases of unquenched QED, quantum chromodynamics (QCD) and models alternative to the standard model of particle physics.

Coupling constants from extended spin model
View Description Hide DescriptionA coupling constant definition is given using connections derived from an extended spin model. We consider a Dirac equation set on an extended spin space that contains fermion and boson solutions. The underlying Clifford algebra of the space, at given dimension, determines and classifies the Poincaré and scalar symmetries, and the resulting representations. The standard field equations can be equivalently written in terms of such degrees of freedom, and are similarly constrained. At 9+1 d, the SU (3) × SU (2)_{ L } × U (1) gauge groups emerge, as well as solution representations with quantum numbers of related gauge bosons, leptons, quarks, Higgs‐like particles and others as leptoquarks. For an appropriate configuration of the standard‐model vector particles in this space, one obtains an hypercharge coupling value close to the experimental one.

The Definition of Mass and Width of Relativistic Resonances
View Description Hide DescriptionFor relativistic resonances, the lineshape alone does not uniquely determine the resonance parameters, namely the mass (M) and width (Γ). A unique definition of the resonance parameters is given if one uses a broader theory of quasistable particles, i.e. which unifies resonances and decaying states. The theory of quasistable particles is developed in analogy to that of stable particles: Wigner’s Unitary Irreducible representations of the Poincare group characterize stable particles by mass (M) and spin (j), whereas quasistable particles will be characterized by mass squared s_{R} = (M_{R} − iΓ_{ R }/2) and spin (j). It follows that the resonance width Γ_{ R } is related to the lifetime of the state by Γ_{ R } = 1/τ. The Z‐boson is used as an example.