Abstract: In calculations of the elementary scalar spectra of spontaneously broken gauge theories there are a number of subtleties which, though it is often unnecessary to deal with them in the order-of-magnitude type of calculations, have to be taken into account if fully consistent results are sought for. Within the “canonical” effective-potential approach these are, for instance: the need to handle infinite series of nested commutators of derivatives of field-dependent mass matrices, the need to cope with spurious IR divergences emerging in the consistent leading-order approximation and, in particular, the need to account for the fine interplay between the renormalization effects in the one-and two-point Green functions which, indeed, is essential for the proper stable vacuum identification and, thus, for the correct interpretation of the results. In this note we illustrate some of these issues in the realm of the minimal Abelian Higgs model and two of its simplest extensions including extra heavy scalars in the spectrum in attempt to exemplify the key aspects of the usual “hierarchy problem” lore in a very specific and simple setting. We emphasize that, regardless of the omnipresent polynomial cut-off dependence in the one-loop corrections to the scalar two-point function, the physical Higgs boson mass is always governed by the associated symmetry-breaking VEV and, as such, it is generally as UV-robust as all other VEV-driven masses in the theory.

Abstract: In order to study the Gamow-Teller (GT) transitions from the T-z = +2 nucleus Ca-44 to the T-z = +1 nucleus Sc-44, where T-z is the z component of isospin T, we performed the (p, n)-type (He-3, t) charge-exchange (CE) reaction at 140 MeV/nucleon and the scattering angles 0 degrees and 2.5 degrees. An energy resolution of 28 keV, that was realized by applying matching techniques to the magnetic spectrometer system, allowed the study of fragmented states. The GT transition strengths, B(GT), were derived up to the excitation energy (E-x) of 13.7 MeV assuming the proportionality between cross sections and B(GT) values. The total sum of B(GT) values in discrete states was 3.7, which was 31% of the sum-rule-limit value of 12. Shell model calculations using the GXPF1J interaction could reproduce the gross features of the experimental B(GT) distribution, but not the fragmentation of the strength. By introducing the concepts of isospin, properties of isospin analogous transitions and states were investigated. (i) Assuming isospin symmetry, the T-z = +2 -> +1 and T-z = -2 -> -1 mirror GT transitions should have the same properties, where the latter can be studied in the beta decay of Cr-44 to V-44. First, we confirmed that the beta-decay half-life T-1/2 of Cr-44 can be reproduced using the B(GT) distribution from the Ca-44(He-3, t) measurement. Then, the 0 degrees, (3He, t) spectrum was modified to deduce the “beta-decay spectrum” and it was compared with the delayed-proton spectrum from the Cr-44 beta decay. The two spectra were mostly in agreement for the GT excitations, but suppression of the proton decay was found for the T = 2 isobaric analog state (IAS). (ii) Starting from the T = 2 ground state of 44Ca, the (3He, t) can excite GT states (state populated by GT transitions) with T = 1, 2, and 3. On the other hand, the Ca-44(p, p') reaction can excite spin-M1 states (states populated by spin-M1 transitions) with T = 2 and 3 that are analogous to the T = 2 and 3 GT states, respectively. By comparing the spectra from these two reactions, a T value of 2 is suggested for several GT states in the E-x = 11.5-13.7 MeV region. (iii) It has been suggested that the T = 2, J(pi) = 0(+) double isobaric analog state (DIAS) at 9.338 MeV in the T-z = 0 nucleus Ti-44 forms an isospin-mixed doublet with a subsidiary 0(+) state at 9.298 MeV. Since no corresponding state was found in the T-z = +1 nucleus Sc-44, we suggest T = 0 for the subsidiary state.

Abstract: In the context of evolution equations and scattering amplitudes in the high energy limit of the N = 4 super Yang-Mills theory we investigate in some detail the BFKL gluon Green function at next-to-leading order. In particular, we study its collinear behavior in terms of an expansion in different angular components. We also perform a Monte Carlo simulation of the different final states contributing to such a Green function and construct the diffusion pattern into infrared and ultraviolet modes and multiplicity distributions, making emphasis in separating the gluon contributions from those of scalars and gluinos. We find that the combined role of the non-gluonic degrees of freedom is to improve the collinear behavior and reduce the diffusion into ultraviolet regions while not having any effect on the average multiplicities or diffusion into the infrared. In terms of growth with energy, the non-zero conformal spin components are mainly driven by the gluon terms in the BFKL kernel. For zero conformal spin (Pomeron) the effect of the scalar and gluino sectors is to dramatically push the Green function towards higher values.

Abstract: In the present paper we address the interaction of pairs of charmed mesons with hidden charm in a finite box. We use the interaction from a recent model based on heavy-quark spin symmetry that predicts molecules of hidden charm in the infinite volume. The energy levels in the box are generated within this model, and from them some synthetic data are generated. These data are then employed to study the inverse problem of getting the energies of the bound states and phase shifts for D (D) over bar or D*(D) over bar*. Different strategies are investigated using the lowest two levels for different values of the box size, and the errors produced are studied. Starting from the upper level, fits to the synthetic data are carried out to determine the scattering length and effective range plus the binding energy of the ground state. A similar strategy using the effective range formula is considered with a simultaneous fit to the two levels-one above and the other one below the threshold. This method turns out to be more efficient than the previous one. Finally, a method based on the fit to the data by means of a potential and a conveniently regularized loop function, turns out to be very efficient and allows us to produce accurate results in the infinite volume starting from levels of the box with errors far larger than the uncertainties obtained in the final results. A regularization method based on Gaussian wave functions turns out to be rather efficient in the analysis and as a byproduct a practical and fast method to calculate the Luscher function with high precision is presented.

Abstract: In this article we study in detail the prospects of determining the infrared finite QCD effective charge from a special kinematic limit of the vertex function corresponding to three background gluons. This particular Green's function satisfies a QED-like Ward identity, relating it to the gluon propagator, with no reference to the ghost sector. Consequently, its longitudinal form factors may be expressed entirely in terms of the corresponding gluon wave function, whose inverse is proportional to the effective charge. After reviewing certain important theoretical properties, we consider a typical lattice quantity involving this vertex, and derive its exact dependence on the various form factors, for arbitrary momenta. We then focus on the particular momentum configuration that eliminates any dependence on the (unknown) transverse form factors, projecting out only the desired quantity. A preliminary numerical analysis indicates that the effective charge is relatively insensitive to the numerical uncertainties that may afflict future simulations of the aforementioned lattice quantity. The numerical difficulties associated with a parallel determination of the dynamical gluon mass are briefly discussed.