NNLO non-resonant corrections to threshold top-pair production from e+ e- collisions: Endpoint-singular terms

We analyse the subleading non-resonant contributions to the e+ e- -> W+ W- b bbar cross section at energies near the top-antitop threshold. These correspond to next-to-next-to-leading-order (NNLO) corrections with respect to the leading-order resonant result. We show that these corrections produce 1/epsilon endpoint singularities which precisely cancel the finite-width divergences arising in the resonant production of the W+ W- b bbar final state from on-shell decays of the top and antitop quarks at the same order. We also provide analytic results for the (m_t/Lambda)^2, (m_t/Lambda) and (m_t/Lambda)^0 log(Lambda) terms that dominate the expansion in powers of (Lambda/m_t) of the complete set of NNLO non-resonant corrections, where Lambda is a cut imposed on the invariant masses of the b W pairs that is neither too tight nor too loose (m_t Gamma_t << Lambda^2 << m_t^2).Comment: 36 pages, 6 figures. v2: minor title change and a few trivial corrections (mostly language) in accordance with the version published in PR

Resonance saturation of the chiral couplings at NLO in 1/Nc

The precision obtainable in phenomenological applications of Chiral Perturbation Theory is currently limited by our lack of knowledge on the low-energy constants (LECs). The assumption that the most important contributions to the LECs come from the dynamics of the low-lying resonances, often referred to as the resonance saturation hypothesis, has stimulated the use of large-Nc resonance lagrangians in order to obtain explicit values for the LECs. We study the validity of the resonance saturation assumption at the next-to-leading order in the 1/Nc expansion within the framework of Resonance Chiral Theory (RChT). We find that, by imposing QCD short-distance constraints, the chiral couplings can be written in terms of the resonance masses and couplings and do not depend explicitly on the coefficients of the chiral operators in the Goldstone boson sector of RChT. As we argue, this is the counterpart formulation of the resonance saturation statement in the context of the resonance lagrangian. Going beyond leading order in the 1/Nc counting allow us to keep full control of the renormalization scale dependence of the LEC estimates.Comment: 9 pages, 3 eps figures. Added references, version published in Phys. Rev.

Effective field theories for heavy and light fermions.

In this thesis, various aspects of different effective field theory (EFT) approximations to the Standard Model of elementary particle physics have been elaborated. The EFTs treated range from non-relativistic approximations to quantum electrodynamics (QED) and quantum chromodynamics (QCD), which can be applied if the quanta under consideration moves at velocities small compared with the speed of light, to chiral perturbation theory as well as the effective theory which emerges in the limit of a large number of colour degrees of freedom in QCD. The latter two constitute expansions in the energy of the process under investigation, and are applicable if this energy is small compared to a typical hadronic scale like, for example, the mass of the -meson. The first type of EFTs, namely NRQED and NRQCD, has been applied in chapter 2 and 3 to study the production cross section of tau lepton pairs as well as quark-antiquark pairs in electron-positron annihilation close to the production threshold, where the system is non-relativistic. In chapter 2 previous computations on tau threshold production are extended to the next-to-next-to-leading order in the velocity expansion and the full analytic form of the two-photon box amplitude, which had not been known explicitly before, is given. As an aside, in chapter 3 we discuss contributions to the total cross section of production of a heavy quark-antiquark pair which arise from intermediate states composed of light QCD degrees of freedom like light mesons or gluonia. These novel contributions constitute an advancement in the field of QCD sum rules for heavy quarks, since they point to the crucial necessity to exactly specify what is actually measured when one speaks about heavy quark production out of e+e- collisions. The second part of the thesis, chapters 4 and 5, tackles with several issues of low-energy hadronic physics. The effective approximation of QCD, chiral perturbation theory, as initially pioneered by Gasser and Leutwyler is only applicable up to energies roughly equal to the -meson mass. However, in recent years it proofed possible to extend this energy range by explicitly including higher resonance states into the effective Lagrangian. This so-called resonance chiral effective theory has been extended in chapter 3 to include a minimal odd-intrinsic parity sector constructed in such a way that it is fully compatible with short-distance QCD constraints. This is an important result for incorporating resonance fields in a chiral framework, and corrects a claim to the contrary put forward recently by other authors. As a by-product, predictions for odd-intrinsic-parity radiative decays of vector mesons in very good agreement with experiment are obtained. In the last chapter of this thesis, we move to the more crowded 1-2 Gev region in electron-positron annihilation where many more resonances need to be included in the field theoretic description. We outline the general strategy to follow in order to obtain a QCD-based parameterization of the total hadronic cross section at these energies, mainly focusing in the technical part of the analysis. A closed formula for the QCD vector-vector current correlator is proposed including contributions from resonance chiral theory at 1-loop with the odd-intrinsic-parity sector introduced before and resummation techniques. Although the practical implementation of the results shall require further investigations, this study shows that the use of EFTs of QCD in the intermediate energy region, populated by resonances, provides a powerful tool to endow the basic information of the underlying theory into the hadron phenomenology in an essentially model-independent way. __________________________________________________________________________________________________ RESUMEN Bajo el título de Effective field theories for heavy and light fermions se han englobado diversos temas relacionados con la aplicación de las teorías efectivas derivadas de la Electrodinámica y la Cromodinámica Cuántica a la producción de leptones y quarks a partir de la aniquilación de un par electrón-positrón. En el primer bloque, que se ocupa de la creación de sabores pesados, se estudia el cálculo de la sección eficaz de producción de leptones tau en la región umbral, y se hace una revisión profunda de la técnica de las reglas de suma para quarks pesados. La producción electromagnética de hadrones formados por quark ligeros se aborda en la segunda parte de esta tesis. En primer lugar se presenta el procedimiento para inferir relaciones entre las constantes del Lagrangiano efectivo con resonancias y QCD para el sector de paridad-intrínseca negativa, y a continuación se deriva una expresión teórica para el correlador de dos corrientes vectoriales en la región de las resonancias, cuya parte imaginaria se relaciona con la sección eficaz hadrónica

Vanishing chiral couplings in the large-N_C resonance theory

The construction of a resonance theory involving hadrons requires implementing the information from higher scales into the couplings of the effective Lagrangian. We consider the large-Nc chiral resonance theory incorporating scalars and pseudoscalars, and we find that, by imposing LO short-distance constraints on form factors of QCD currents constructed within this theory, the chiral low-energy constants satisfy resonance saturation at NLO in the 1/Nc expansion.Comment: 5 pages, 2 figures. Version published in Physical Review D. Some equations to facilitate the discussion have been adde

Heavy Pair Production Currents with General Quantum Numbers in Dimensionally Regularized NRQCD

We discuss the form and construction of general color singlet heavy particle-antiparticle pair production currents for arbitrary quantum numbers, and issues related to evanescent spin operators and scheme-dependences in nonrelativistic QCD (NRQCD) in n=3-2epsilon dimensions. The anomalous dimensions of the leading interpolating currents for heavy quark and colored scalar pairs in arbitrary (2S+1)L_J angular-spin states are determined at next-to-leading order in the nonrelativistic power counting.Comment: 39 pages, 2 tables, 10 figures; typos corrected, published versio

Phase Space Matching and Finite Lifetime Effects for Top-Pair Production Close to Threshold

The top-pair $t\bar t$ production cross section close to threshold in $e^+e^-$ collisions is strongly affected by the small lifetime of the top quark. Since the cross section is defined through final states containing the top decay products, a consistent definition of the cross section depends on prescriptions how these final states are accounted for the cross section. Experimentally, these prescriptions are implemented for example through cuts on kinematic quantities such as the reconstructed top quark invariant masses. As long as these cuts do not reject final states that can arise from the decay of a top and an anti-top quark with a small off-shellness compatible with the nonrelativistic power-counting, they can be implemented through imaginary phase space matching conditions in NRQCD. The prescription-dependent cross section can then be determined from the optical theorem using the $e^+e^-$ forward scattering amplitude. We compute the phase space matching conditions associated to cuts on the top and anti-top invariant masses at next-to-next-to-leading logarithmic (NNLL) order and partially at next-to-next-to-next-to-leading logarithmic (N${}^3$LL) order in the nonrelativistic expansion and, together with finite lifetime and electroweak effects known from previous work, analyze their numerical impact on the $t\bar t$ cross section. We show that the phase space matching contributions are essential to make reliable NRQCD predictions, particularly for energies below the peak region, where the cross section is small. We find that irreducible background contributions associated to final states that do not come from top decays are strongly suppressed and can be neglected for the theoretical predictions.Comment: 62 pages, 21 figure

The soft-energy region in the radiative decay of bound states

The orthopositronium decay to three photons is studied in the phase-space region where one of the photons has an energy comparable to the relative three-momentum of the e+e- system (w ~ m alpha). The NRQED computation in this regime shows that the dominant contribution arises from distances ~ 1/(mw)^(1/2), which allows to treat the Coulomb interaction perturbatively. The small-photon energy expansion of the 1-loop decay spectrum from full QED yields the same result as the effective theory. By doing the threshold expansion of the 1-loop QED amplitude we confirm that the leading term arises from a loop-momentum region where q^0 ~ q^2/m ~ w. This corresponds to a new non-relativistic loop-momentum region, which has to be taken into account for the description of a non-relativistic particle-antiparticle system that decays through soft photon emission.Comment: 28 pages, 5 figures; typos corrected, one reference added, published versio

El Trabajo de Fin de Grado en la Facultad de Derecho: experiencias y vivencias

El trabajo desarrollado en la Red analiza y evalúa el desarrollo e implementación de la asignatura de Trabajo Fin de Grado en las titulaciones de la Facultad de Derecho. Éste ha sido el primer año de su implantación y la gestión y evaluación del mismo han generado algunas incidencias que han puesto de manifiesto la necesidad de mejorar su gestión y aplicación. Distintos factores han influido a la hora de realizar una valoración del desarrollo del TFG en la Facultad de Derecho. En este sentido la existencia de una aplicación informática UA Project que facilita la gestión del mismo se valora como positiva. Sin embargo la misma presenta algunos inconvenientes que requieren de su revisión en el sentido que se plantea en el trabajo. Plantear estratégicamente una mínima formación del alumnado en el desarrollo del TFG se nos presenta como ineludible para conseguir unos resultados satisfactorios. A tal fin este trabajo realiza algunas propuestas de mejora que abundan en la necesidad de prestigiar el TFG

Odd-intrinsic-parity processes within the Resonance Effective Theory of QCD

We analyse the most general odd-intrinsic-parity effective Lagrangian of QCD valid for processes involving one pseudoscalar with vector mesons described in terms of antisymmetric tensor fields. Substantial information on the odd-intrinsic-parity couplings is obtained by constructing the vector-vector-pseudoscalar Green's three-point function, at leading order in 1/Nc, and demanding that its short-distance behaviour matches the corresponding OPE result. The QCD constraints thus enforced allow us to predict the decay amplitude omega -> pion gamma, and the O(p^6) corrections to pion -> gamma gamma. Noteworthy consequences concerning the vector meson dominance assumption in the decay omega -> 3 pions are also extracted from the previous analysis.Comment: 20 pages, 4 figure