arXiv subjects

Joseph Schechter

Publications and source records attributed to Joseph Schechter.

At least 55 records · Page 3Linked to original sources

arXiv2006

An approach to permutation symmetry for the electroweak theory

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.

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arXiv2006

Generalized Sigma Model Description of the Light J=0 Mesons

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.

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arXiv2006

Chiral approach to phi radiative decays

The radiative decays of the phi meson are known to be a good source of information about the a0(980) and f0(980) scalar mesons. We discuss these decays starting from a non-linear model Lagrangian which maintains the (broken) chiral symmetry for the pseudoscalar (P), scalar (S) and vector (V) nonets involved. The characteristic feature is derivative coupling for the SPP interaction. In an initial approximation which models all the scalar nonet radiative processes together with the help of a point like vertex, it is noted that the derivative coupling prevents the a0 and f0 resonance peaks from getting washed out (by falling phase space). However, the shapes of the two final PP mass distributions do not agree well with the experimental ones. For improving the situation we verify that the inclusion of the charged K meson loop diagrams in the model does reproduce the experimental spectrum shapes in the resonance region. The derivative coupling introduces quadratic as well as logaritmic divergneces in this calculation. Using dimensional regularization we show that these divergences actually cancel out among the four diagrams, as expected from gauge invariance. We point out the features which are expected to be important for further work on this model and for learning more about the puzzling scalar mesons.

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arXiv2005

Toy model for two chiral nonets

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.

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arXiv2004

Leptonic CP violation in a two parameter model

We further study the "complementary" Ansatz, Tr$(M_ν)$=0, for a prediagonal light Majorana type neutrino mass matrix. Previously, this was studied for the CP conserving case and the case where the two Majorana type CP violating phases were present but the Dirac type CP violating phase was neglected. Here we employ a simple geometric algorithm which enables us to "solve" the Ansatz including all three CP violating phases. Specifically, given the known neutrino oscillation data and an assumed two parameter (the third neutrino mass $m_3$ and the Dirac CP phase $δ$) family of inputs we predict the neutrino masses and Majorana CP phases. Despite the two parameter ambiguity, interesting statements emerge. There is a characteristic pattern of interconnected masses and CP phases. For large $m_3$ the three neutrinos are approximately degenerate. The only possibility for a mass hierarchy is to have $m_3$ smaller than the other two. A hierarchy with $m_3$ largest is not allowed. Small CP violation is possible only near two special values of $m_3$. Also, the neutrinoless double beta decay parameter is approximately bounded as 0.020 eV $<|m_{ee}|<$ 0.185 eV. As a byproduct of looking at physical amplitudes we discuss an alternative parameterization of the lepton mixing matrix which results in simpler formulas. The physical meaning of this parameterization is explained.

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arXiv2004

Leptonic CP violation phases using an ansatz for the neutrino mass matrix and application to leptogenesis

We further study the previously proposed Ansatz, Tr(M)=0, for a prediagonal light Majorana type neutrino mass matrix. If CP violation is neglected this enables one to use the existing data on squared mass differences to estimate (up to a discrete ambiguity)the neutrino masses themselves. If it is assumed that only the conventional CP phase is present, the ansatz enables us to estimate this phase in addition to all three masses. If it is assumed that only the two Majorana CP phases are present, the Ansatz enables us to obtain a one parameter family of solutions for the masses and phases. This enables us to obtain a simple "global" view of lepton number violation effects. Furthermore, using an SO(10) motivation for the Ansatz suggests an amusing toy (clone) model in which the heavy neutrinos have the same mixing pattern and mass ratios as the light ones. In this case only their overall mass scale is not known (although it is constrained by the initial motivation). Using this toy model we make a rough estimate of the baryon to photon ratio induced by the leptogenesis mechanism. Solutions close to the CP conserving cases seem to be favored.

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arXiv2003

Radiative Decays involving a0(980) and f0(980) in the Vector Meson Dominance Model

We summarize some features of the vector meson dominance model which was recently proposed for studying radiative decays involving the scalar mesons. Using the experimental values of $Γ(a_0 \to γγ)$, $Γ(f_0 \to γγ)$ and $Γ(ϕ\to a_0 γ)$ as inputs, we show that the model predicts a large hierarchy between $Γ(a_0 \to ωγ)$ and $Γ(a_0 \to ργ)$ as well as between $Γ(f_0 \to ωγ)$ and $Γ(f_0 \to ργ)$.

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arXiv2003

Comparing the Higgs Sector of Electroweak Theory with the Scalar Sector of Low Energy QCD

We first review how the simple K-matrix unitarized linear SU(2) sigma model can explain the experimental data in the scalar pi pi scattering channel of QCD up to about 800 MeV. Since it is just a scaled version of the minimal electroweak Higgs sector, which is often treated with the same unitarization method, we interpret the result as support for this approach in the electroweak model with scaled values of tree level Higgs mass up to at least about 2 TeV. We further note that the relevant QCD effective Lagrangian which fits the data to still higher energies using the same method involves another scalar resonance. This suggests that the method should also be applicable to corresponding beyond minimal electroweak models. Nevertheless we note that even with one resonance, the minimal K matrix unitarized model behaves smoothly for large bare Higgs mass by effectively "integrating out" the Higgs while preserving unitarity. With added confidence in this simple approach we make a survey of the Higgs sector for the full range of bare Higgs mass. One amusing point which emerges is that the characteristic factor of the W-W fusion mechanism for Higgs production peaks at the bare mass of the Higgs boson, while the characteristic factor for the gluon fusion mechanism peaks near the generally lower physical mass.

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arXiv2002

Effects of light scalar mesons in $η\to 3π$ decay

We study the role of a possible nonet of light scalar mesons in the still interesting $η\to 3π$ decay process, with the primary motivation of learning more about the scalars themselves. The framework is a conventional non-linear chiral Lagrangian of pseudoscalars and vectors, extended to include the scalars. The parameters involving the scalars were previously obtained to fit the s-wave $ππ$ and $π$K scatterings in the region up to about 1 GeV as well as the strong decay $η' \to ηππ$. At first, one might expect a large enhancement from diagrams including a light $σ(560)$. However there is an amusing cancellation mechanism which prevents this from occurring. In the simplest model there is an enhancement of about 13 per cent in the \e3p decay rate due to the scalars. In a more complicated model which includes derivative type symmetry breakers, the cancellation is modified and the scalars contribute about 30 percent of the total decay rate (although the total is not significantly changed). The vectors do not contribute much. Our model produces a reasonable estimate for the related $a_0(980)-f_0(980)$ mixing strength, which has been a topic of current debate. Promising directions for future work along the present line are suggested.

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arXiv2002

Vector Meson Dominance Model for Radiative Decays Involving Light Scalar Mesons

We study a vector dominance model which predicts a fairly large number of currently interesting decay amplitudes of the types S -> γγ, V -> S γand S -> V γ, where S and V denote scalar and vector mesons, in terms of three parameters. As an application, the model makes it easy to study in detail a recent proposal to boost the ratio Gamma(phi -> f_0 gamma) / Gamma(phi -> a_0 gamma) by including the isospin violating a_0 - f_0 mixing. However we find that this effect is actually small in our model.

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arXiv2001

Introduction to effective Lagrangians for QCD

A brief introduction to the effective Lagrangian treatment of QCD (in the sense of using fields representing physical particles rather than quarks and gluons) will be given. The historical evolution of the subject will be discussed. Some background material related to a recent model for Gamma Ray Bursters will be given. Finally, some recent work on low energy strong interactions will be mentioned.

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arXiv2000

Exploring the structure of a possible light scalar nonet

We first review the work of the Syracuse group, which uses an effective chiral Lagrangian approach, on meson-meson scattering. An illustration providing evidence for the existence of a strange scalar resonance of mass around 900 MeV is given. An attempt to fit this $κ(900)$ together with a similarly obtained $σ(560)$ and the well known $a_0(980)$ and $f_0(980)$ into a nonet pattern suggests that the underlying structure is closer to a dual quark-dual antiquark than to a quark-antiquark. A possible mechanism to explain a next higher-in mass scalar meson nonet is also discussed. This involves mixing between $q{\bar q}$ and $qq{\bar q} {\bar q}$ states.

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arXiv1999

Light Scalar Mesons

We review how a certain effective chiral Lagrangian approach to pi pi scattering, pi K scattering and eta-prime decay to eta pi pi provides evidence for the existence of light scalars sigma(550) and kappa(900) as well as describing the f0(980) and the a0(980). An attempt to fit these into a nonet suggests that their structure is closer to a dual quark-dual antiquark than to a quark-antiquark. A possible mechanism to explain the next higher mass scalar nonet is also proposed.

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arXiv1999

Chiral Lagrangian treatment of pi eta scattering

We study pi eta scattering in a model which starts from the tree diagrams of a non-linear chiral Lagrangian including appropriate resonances. Previously, models of this type were applied to pi pi and pi K scattering and were seen to require the existence of light scalar sigma(560) and kappa(900) mesons and to be consistent with the f0(980). The present calculation extends this to include the a0(980), thereby completing a possible nonet of light scalars, all ``seen'' in the same manner. We note that, at the initial level, the pi eta channel is considerably cleaner than the pi pi and pi K channels for the study of light scalars. This is because the large competing effects of vector meson exchange and ``current-algebra'' contact terms are absent. The simplicity of this channel enables us to demonstrate the closeness of our exactly crossing symmetric amplitude to a related exactly unitary amplitude. The calculation is also extended to higher energies in order to let us discuss the role played by the a0(1450) resonance.

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arXiv1999

Mechanism for a next-to-lowest lying scalar meson nonet

Recent work suggests the existence of a non-conventional lowest-lying scalar nonet containing the a0(980). Then the a0(1450) and also the K0*(1430) are likely candidates to belong to a conventional p-wave $q \bar q$ nonet. However a comparison of their properties with those expected on this basis reveals a number of puzzling features. It is pointed out that these puzzles can be resolved in a natural and robust way by assuming a ``bare'' conventional p-wave scalar $q \bar q$ nonet to mix with a lighter four quark $qq \bar q \bar q$ scalar nonet to form new ``physical'' states. The essential mechanism is driven by the fact that the isospinor is lighter than the isovector in the unmixed $qq \bar q \bar q$ multiplet.

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arXiv1999

eta' to eta pi pi Decay as a Probe of a Possible Lowest-Lying Scalar Nonet

We study the eta' to eta pi pi decay within an effective chiral Lagrangian approach in which the lowest lying scalar meson candidates sigma(560) and kappa(900) together with the f0(980) and a0(980) are combined into a possible nonet. We show that there exists a unique choice of the free parameters of this model which, in addition to fitting the pi pi and pi K scattering amplitudes, well describes the experimental measurements for the partial decay width of eta' to eta pi pi and the energy dependence of this decay. As a by-product, we estimate the a0(980) width to be 70 MeV, in agreement with a new experimental analysis.

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arXiv1998

Putative Light Scalar Nonet

We investigate the "family" relationship of a possible scalar nonet composed of the a_0(980), the f_0(980) and the σand κtype states found in recent treatments of ππand πK scattering. We work in the effective Lagrangian framework, starting from terms which yield "ideal mixing" according to Okubo's original formulation. It is noted that there is another solution corresponding to dual ideal mixing which agrees with Jaffe's picture of scalars as qq\bar q \bar q states rather than as q\bar q states. At the Lagrangian level there is no difference in the formulation of the two cases (other than the numerical values of the coefficients). In order to agree with experiment, additional mass and coupling terms which break ideal mixing are included. The resulting model turns out to be closer to dual ideal mixing than to conventional ideal mixing; the scalar mixing angle is roughly -17 degrees in a convention where dual ideal mixing is 0 degrees.

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arXiv1997

Remark on the Potential Function of the Linear Sigma Model

It is shown that the potential functions for the ordinary linear sigma model can be divided into two topographically different types depending on whether the quantity $R\equiv(m_σ/m_π)^2$ is greater than or less than nine. Since the Wigner-Weyl mode (R=1) and the Nambu-Goldstone mode ($R=\infty$ belong to different regions, we speculate that this classification may provide a generalization to the broken symmetry situation, which could be convenient for roughly characterizing different possible applications of the model. It is noted that a more complicated potential does not so much change this picture as add different new regions.

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