arXiv subjects
Publications and source records attributed to F. del Aguila.
We describe in detail the constrained procedure of differential renormalization and develop the techniques required for one-loop calculations. As an illustration we renormalize Scalar QED and show that the two-, three- and four-point Ward identities are automatically satisfied.
We present a procedure of differential renormalization at the one loop level which avoids introducing unnecessary renormalization constants and automatically preserves abelian gauge invariance. The amplitudes are expressed in terms of a basis of singular functions. The local terms appearing in the renormalization of these functions are determined by requiring consistency with the propagator equation. Previous results in abelian theories, with and without supersymmetry, are discussed in this context.
Two applications of the method of differential renormalization to supersymmetric gauge theories are reviewed. The photon propagator in supersymmetric QED is renormalized at one loop and the first supergravity contributions to the anomalous magnetic moment of a charged lepton are obtained.
We review the method of differential renormalization, paying special attention to a new constrained version for symmetric theories.
The method of differential renormalization is extended to the calculation of the one-loop graviton and gravitino corrections to $(g-2)_l$ in unbroken supergravity. Rewriting the singular contributions of all the diagrams in terms of only one singular function, U(1) gauge invariance and supersymmetry are preserved. We compare this calculation with previous ones which made use of momentum space regularization (renormalization) methods.
We find a minimal set of constraints which are independent of the choice of weak quark basis and necessary and sufficient for CP conservation for four quark families, including also the case of degenerate quark masses. These invariant conditions are written in the mass eigenstate basis as a function of the fermion masses and charged current mixings. CP violation is then related to the areas of three unitarity quadrangles and the CP violating effects of the fourth family are discussed in the case of small mixings.
The invariant formulation of CP violation involves the generation of sets of invariant constraints for CP conservation, the manipulation of their expressions and the identification of complete and minimal subsets of such constraints. In this paper we present a collection of subroutines to deal with these three tasks in a fast, reliable and systematic way, with examples for the leptonic sector.
This is a short review of present and future limits on new neutral gauge bosons, in particular on hadrophilic or leptophobic $Z'$s recently proposed to interpret the observed fluctuations of $Γ_{c,b}$ at LEP. Light gauge bosons coupled to lepton number differences or to baryon number are also examples of the model dependence of these bounds. The mixing between the $U(1)$ factors plays an important role in the phenomenology of these extended electroweak models. Future improvements based on the analysis of precise electroweak data are emphasized.
We count the number of CP breaking phases in models with $SU(2)_L\times U(1)_Y$ and $SU(2)_L\times SU(2)_R\times U(1)_{B-L}$ electroweak gauge groups and extended matter contents with some fermion masses vanishing and/or degenerate. Quarks and leptons, including Majorana neutrinos, are treated in a similar way. CP violation is characterized in the mass-eigenstate and in the weak-eigenstate bases. Necessary and sufficient conditions for CP conservation, invariant under weak basis redefinitions are also studied in these models. CP violating factors entering in physical observables and only invariant under phase redefinitions are discussed.
We analize the structure of models with unbroken and spontaneously broken U(1)_a x U(1)_b gauge symmetry. We show that the quantum corrections to the 2N gauge charges, with N = #fermions + #scalars, can be absorbed in the redefinition of three independent gauge couplings (g_a,g_b and g_ab). We establish the (one-loop) conditions on the matter cotent for g_ab= = 0 (a value usually assumed in the literature) and we show that in the minimal extensions of the Standard Model with an extra U(1) symmetry the choice g_ab = 0 is not stable under radiative corrections induced by the standard Higgs fields. Moreover, g_ab = 0 to all orders seems to require an exact symmetry. The spontaneous breaking of the gauge symmetry induces further mixing between the two gauge bosons and introduces a fourth independent physical parameter. A consequence of our analysis is that the usual tree-level description with only three physical parameters (i.e., two gauge couplings and one gauge boson mixing angle) is not in general a justified zero order limit of the treatment including radiative corrections.
We study CP violation in the lepton sector in extended models with right-handed neutrinos, without and with left-right symmetry, and with arbitrary mass terms. We find the conditions which must be satisfied by the neutrino and charged lepton mass matrices for CP conservation. These constraints, which are independent of the choice of weak basis, are proven to be also sufficient in simple cases. This invariant formulation makes apparent the necessary requirements for CP violation, as well as the size of CP violating effects. As an example, we show that CP violation can be much larger in left-right symmetric models than in models with only additional right-handed neutrinos, {\it i.e.}, without right-handed currents.
The discovery of a new neutral gauge boson $Z'$ with a mass in the TeV region would allow for determination of gauge couplings of the $Z'$ to ordinary quarks and leptons in a model independent way. We show that these couplings in turn would allow us to determine the nature of the extended gauge structure. As a prime example we study the $E_6$ group. In this case two discrete constraints on experimentally determined couplings have to be satisfied. If so, the couplings would then uniquely determine the two parameters, $\tan β$ and $δ$, which fully specify the nature of the $Z'$ within $E_6$. If the $Z'$ is part of the $E_6$ gauge structure, then for $M_{Z'}=1$ TeV $\tan β$ and $δ$ could be determined to around $10\%$ at the future colliders. The NLC provides a unique determination of the two constraints as well as of $\tan β$ and $δ$, though with slightly larger error bars than at the LHC. On the other hand, since the LHC primarily determines three out of four normalized couplings, it provides weaker constraints for the underlying gauge structure.
We study a class of superstring models compactified in the 3-generation Calabi-Yau manifold of Tian and Yau. Our analysis includes the complete $E_6$-singlet sector, which has been recently evaluated using techniques of spectral and exact sequences. We use the discrete symmetries of the models to find flat directions of symmetry breaking that leave unbroken a low energy matter parity and make all leptoquarks heavy while preserving light Higgs fields. Then we classify the patterns of ordinary quark mass matrices and show that (without invoking effects due to nonrenormalizable terms) only one structure can accommodate the observed value of fermion masses and mixing angles, with preference for a heavy {\it top} quark ( $m_t\ge 170$ GeV for $V_{13}\le 0.013$ ). The model, which unifies perturbatively and predicts a realistic structure of quark mass matrices with texture zeroes, is one of the many possible string vacua. However, in contrast with what is often assumed in the search for realistic unified scenarios, it is highly nonminimal near the unification scale and the predicted mass matrices have no simple symmetry properties.
All couplings of a new heavy gauge boson to ordinary fermions can be determined in a model-independent way at a large $e^+e^-$ collider for large enough statistics. No such determination is possible at LEP 200, however, because its design integrated luminosity is too low for existing and forthcoming limits on $Z'$ interactions. At any rate, it should be possible to distinguish between models for $Z'$ masses $< 1\ TeV$, or to set limits of this order on $Z'$ masses for definite models. These are (preliminary) $1σ$ limits. We neglect systematic errors and assume an integrated luminosity of $0.5\ fb^{-1}$.
In these lectures we review the simplest gauge extensions of the standard model, and the present and future limits on new weak interactions.
We study the diagnostic power of future $e^+e^-$ colliders with ${\sqrt {s}} = 500$ GeV (the New Large Collider ($NLC$)) for a model independent determination of the $Z'$ gauge couplings to quarks and leptons. The interference of the $Z'$ propagator with the photon and the $Z$ propagator in the two-fermion final state probes are sensitive to the magnitude as well as relative signs of quark and lepton charges. For $Z'$ with $M_{Z'} \sim 1 $ TeV {\it all } the quark and lepton charges can be determined to around $10-20 \%$, provided heavy flavor tagging and longitudinal polarization of the electron beam is available. The errors are $2-10$ times larger without polarization, and very little information can be obtained about quark charges without heavy flavor tagging. We point out the complementarity of future hadron colliders. At the CERN Large Hadron Collider ($LHC$) primarily the magnitude of three out of four corresponding couplings can be measured; however, their error-bars are typically by a factor of $\sim 2$ smaller than those at the $NLC$.
We present recent developments in the diagnostic study of heavy gauge bosons at future colliders with the emphasis on the determination of gauge couplings of $Z'$ to quarks and leptons. Proposed diagnostic probes at future hadron colliders are discussed. The study of statistical uncertainties expected for the above probes at the LHC and $M_{Z'}\simeq 1$ TeV shows that three out of four normalized couplings can be determined, thus allowing for a distinction between models. The complementary nature of the probes at future $e^+e^-$ colliders is also discussed.
We review present Z' bounds, discuss future Z' constraints from TEVATRON, HERA and LEP, and give a brief review of the Z' diagnostics at future colliders.