arXiv subjects
Publications and source records attributed to Renata Jora.
We study a simple two Higgs doublet model which reflects, in a phenomenological way, the idea of compositeness for the Higgs sector. It is relatively predictive. In one scenario, it allows for a "hidden" usual Higgs particle in the 100 GeV region and a possible dark matter candidate.
We propose an electroweak model based on the identification of the Higgs with the dilaton. We show that it is possible in this context to have a massless Higgs boson at tree and one loop levels without contradicting the main experimental and theoretical constraints.
A generalized linear sigma model for low energy QCD is employed to study the quark structure of eight low lying scalar isomultiplets as well as eight low lying pseudoscalar isomultiplets. The model, building on earlier work, assumes the possible mixing of quark anti-quark states with others made of two quarks and two antiquarks. No {\it a priori} assumption is made about the quark contents of the states, which emerge as predictions. An amusing and contrasting pattern for the quark structure is found; the lighter conventional pseudoscalars are, as expected, primarily of two quark type whereas the lighter scalars have very large four quark admixtures. The new feature of the present paper compared to earlier ones in this series involves the somewhat subtle and complicated effects of SU(3) flavor breaking. They do not alter the general pattern of two quark vs. four quark mixing obtained in the SU(3)symmetric case but, of course, give a more detailed picture.
A generalized linear sigma model is employed to study the quark structure of low lying scalar as well as pseudoscalar states. The model allows the possible mixing of quark anti-quark states with others made of two quarks and two antiquarks but no a priori assumption is made about the quark contents of the predicted physical states. Effects of SU(3) symmetry breaking are included. The lighter conventional pseudoscalars turn out to be primarily of two quark type whereas the lighter scalars have very large four quark admixtures.
It is well known that the instanton approach to QCD generates an effective term which looks like a three flavor determinant of quark bilinears. This has the right behavior to explain the unusual mass and mixing of the $η(958)$ meson, as is often simply illustrated with the aid of a linear SU(3) sigma model. It is less well known that the instanton analysis generates another term which has the same transformation property but does not have a simple interpretation in terms of this usual linear sigma model. Here we point out that this term has an interpretation in a generalized linear sigma model containing two chiral nonets. The second chiral nonet is taken to correspond to mesons having two quarks and two antiquarks in their makeup. The generalized model seems to be useful for learning about the spectrum of low lying scalar mesons which have been emerging in the last few years. The physics of the new term is shown to be related to the properties of an "excited" $η'$ state present in the generalized model and for which there are some experimental candidates.
A brief discussion of the recent interest in light scalar mesons motivates the study of a generalized linear sigma model. In an SU(3) flavor invariant version of the model there is a prediction that the the lighter scalars have sizeable "four quark" content. It is further predicted that one of the singlet scalars should be exceptionally light. Due to the presence of scalar mesons, the model gives "controlled" corrections to the current algebra formula for threshold pion pion scattering. These corections act in the direction to improve agreement with current experiments.
An earlier calculation in a generalized linear sigma model showed that the well-known current algebra formula for low energy pion pion scattering held even though the massless Nambu Goldstone pion contained a small admixture of a two-quark two-antiquark field. Here we turn on the pion mass and note that the current algebra formula no longer holds exactly. We discuss this small deviation and also study the effects of an SU(3) symmetric quark mass type term on the masses and mixings of the eight SU(3) multiplets in the model. We calculate the s wave scattering lengths, including the beyond current algebra theorem corrections due to the scalar mesons, and observe that the model can fit the data well. In the process, we uncover the way in which linear sigma models give controlled corrections (due to the presence of scalar mesons) to the current algebra scattering formula. Such a feature is commonly thought to exist only in the non-linear sigma model approach.
We present a detailed study of a linear sigma model containing one chiral nonet transforming under U(1)$_A$ as a quark-antiquark composite and another chiral nonet transforming as a diquark-anti diquark composite (or, equivalently from a symmetry point of view, as a two meson molecule). The model provides an intuitive explanation of a current puzzle in low energy QCD: Recent work has suggested the existence of a lighter than 1 GeV nonet of scalar mesons which behave like four quark composites. On the other hand, the validity of a spontaneously broken chiral symmetric description would suggest that these states be chiral partners of the light pseudoscalar mesons, which are two quark composites. The model solves the problem by starting with the two chiral nonets mentioned and allowing them to mix with each other. The input of physical masses in the SU(3) invariant limit for two scalar octets and an "excited" pion octet results in a mixing pattern wherein the light scalars have a large four quark content while the light pseudoscalars have a large two quark content. One light isosinglet scalar is exceptionally light. In addition, the pion pion scattering is also studied and the current algebra theorem is verified for massless pions which contain some four quark admixture.
We propose a systematic procedure to study a generalized linear sigma model which can give a physical picture of possible mixing between $q{\bar q}$ and $qq{\bar q}{\bar q}$ low lying spin zero states. In the limit of zero quark masses, we derive the model independent results for the properties of the Nambu Goldstone pseudoscalar particles. For getting information on the scalars it is necessary to make a specific choice of terms. We impose two plausible physical criteria - the modeling of the axial anomaly and the suppression of effective vertices representing too many fermion lines - for limiting the large number of terms which are allowed on general grounds. We calculate the tree-level spectrum based on the leading terms in our approach and find that it prominently exhibits a very low mass isosinglet scalar state. Finally we point out that the low energy result for scattering of pions continues to hold in the general version of the model.
The form of the leptonic mixing matrix emerging from experiment has, in the last few years, generated a lot of interest in the so-called tribimaximal type. This form may be naturally associated with the possibility of a discrete permutation symmetry ($S_3$) among the three generations. However, trying to implement this attractive symmetry has resulted in some problems and it seems to have fallen out of favor. We suggest an approach in which the $S_3$ holds to first approximation, somewhat in the manner of the old SU(3) flavor symmetry of the three flavor quark model. It is shown that in the case of the neutrino sector, a presently large experimentally allowed region can be fairly well described in this first approximation. We briefly discuss the nature of the perturbations which are the analogs of the Gell-Mann Okubo perturbations but confine our attention for the most part to the $S_3$ invariant model. We postulate that the $S_3$ invariant mass spectrum consists of non zero masses for the $(τ,b,t)$ and zero masses for the other charged fermions but approximately degenerate masses for the three neutrinos. The mixing matrices are assumed to be trivial for the charged fermions but of tribimaximal type for the neutrinos in the first approximation. It is shown that this can be implemented by allowing complex entries for the mass matrix and spontaneous breakdown of the $S_3$ invariance of the Lagrangian.
Within a linear sigma model framework, possible mixing between two chiral nonets (a two quark nonet, and a four quark nonet) below 2 GeV is studied. Incorporating the U(1)$_A$ behavior of the underlying QCD, and working in the isospin invariant limit, the mass spectra of the I=0, $I=1/2$ and I=1 pseudoscalars, and the $I=1/2$ scalars are studied, and estimates of their quark content are presented. It is found, as expected, that the ordinary and the excited pseudoscalars generally have much less two and four quark admixtures compared to the respective scalars. As by-products, several quantities such as the four quark vacuum condensate, and the decay constant of excited states are predicted.
Motivated by the possibility that nonets of scalar mesons might be described as mixtures of "two quark" and "four quark" components, we further study a toy model in which corresponding chiral nonets (containing also the pseudoscalar partners) interact with each other. Although the "two quark" and "four quark" chiral fields transform identically under SU(3)$_L \times$ SU(3)$_R$ transformations they transform differently under the U(1)$_A$ transformation which essentially counts total (quark + antiquark) content of the mesons. To implement this we formulate an effective Lagrangian which mocks up the U(1)$_A$ behavior of the underlying QCD. We derive generating equations which yield Ward identity type relations based only on the assumed symmetry structure. This is applied to the mass spectrum of the low lying pseudoscalars and scalars. as well as their "excitations". Assuming isotopic spin invariance, it is possible to disentangle the amount of"two quark" vs."four quark" content in the pseudoscalar $π, K ,η$ type states and in the scalar $κ$ type states. It is found that a small "four quark" content in the lightest pseudoscalars is consistent with a large "four quark" content in the lightest of the scalar $κ$ mesons. The present toy model also allows one to easily estimate the strength of a "four quark" vacuum condensate. There seems to be a rich and interesting structure.