arXiv subjects

Amir H. Fariborz

Publications and source records attributed to Amir H. Fariborz.

At least 37 records · Page 2Linked to original sources

arXiv2016

Spontaneous symmetry breaking and Goldstone theorem for composite states revisited

We discuss the well-known phenomenon of spontaneous symmetry breaking for a linear sigma model for scalar and pseudoscalar mesons based on the meson composite structure and the normalization of the quantum states. To test our formulation and validate our approach we give another proof of the Goldstone theorem and derive the corresponding mass eigenstates of the theory. We briefly describe the possible wave function of a meson that leads to the adequate mass eigenstates.

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arXiv2016

Chiral Nonet Mixing in $πK$ Scattering

The underlying mixing of quark components of scalar mesons is probed in $πK$ scattering within a generalized linear sigma model that contains two scalar meson nonets and two pseudoscalar meson nonets (a quark-antiquark and a four-quark). In the leading order of this model, all free parameters have been previously fixed using the mass spectra and several low-energy parameters known from experiment and consistent predictions have been made. As other predictions of the model, in the present work the isospins $I$= 1/2, 3/2 and $J$=0 projection of $πK$ scattering amplitude (as well as phase shifts) are computed and compared with experiment. In the $I$=1/2 channel, it is shown that within the uncertainties of the model parameters a good agreement with experimental data up to an energy of about 1 GeV is obtained, whereas in the $I$=3/2 channel there is a better agreement with experiment which extends to about 1.4 GeV. The effect of final state interactions of $πK$ in the $I$=1/2 channel is approximated by the K-matrix method and the poles of the unitarized scattering amplitude are found. It is shown that the model predicts a light and broad kappa resonance with a mass and decay width of 670-770 MeV and 640-750 MeV consistent with other prior works. Moreover, the scattering lengths in the $I$=1/2, 3/2 are also computed and shown to qualitatively agree with experiment. The overall predictions presented here further support previous findings that the scalar mesons below and above 1 GeV have substantial underlying mixings and that those below 1 GeV have dominant four-quark substructures while those above 1 GeV are closer to conventional $P$-wave quark-antiquark states.

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arXiv2016

Proximity of $f_0(1500)$ and $f_0(1710)$ to the scalar glueball

Within a nonlinear chiral Lagrangian framework, the underlying mixings among quark-antiquark, four-quark and glue components of $f_0(1500)$ and $f_0(1710)$ are studied in a global picture that includes all isosinglet scalar mesons below 2 GeV. The quark components are introduced in the Lagrangian in terms of two separate nonets (a quark-antiquark nonet and a four-quark nonet) which can mix with each other and with a scalar glueball. The free parameters of the Lagrangian are studied by a simultaneous fit to more than 20 experimental data and constraints on the mass spectrum, decay widths, and decay ratios of the isosinglet scalars below 2 GeV. Moreover, constraints on the mass spectrum and decay widths of isodoublet and isovector scalars below 2 GeV as well as pion-pion scattering amplitude are also taken into account. The insights gained in this global picture, due to the complexities of the mixings as well as the experimental uncertainties, are mainly qualitative but are relatively robust, and reveal that the lowest scalar glueball hides between $f_0(1500)$ and $f_0(1710)$, resulting in a considerable mixing with various quark components of these two states. The overall current experimental and theoretical uncertainties do not allow to pin down the exact glue components of isosinglet states, nevertheless it is shown that the $f_0(1500)$ and $f_0(1710)$ have the highest glue component. While this global study does not allow precision predictions for each individual state, it provides useful "family" correlations among the isosinglet states that are found insightful in probing the substructure of all scalars, in general, and the isosinglets, in particular. The overall estimate of the scalar glueball mass is found to be $1.58 \pm 0.18$ GeV.

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arXiv2015

Note on the standard model as an effective theory

We present a criterion of consistency derived from the analogy between the partition function of a quantum field theory and that of a statistical system. Based on this we examine a new class of higher dimension operators that might act in the standard model.

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arXiv2015

A purely quark Lagrangian from QCD

We present a method for determining a purely quark Lagrangian by mocking up the QCD partition function for large gauge couplings $g$. The resulting effective theory displays all the symmetries of low energy QCD and can be potentially used to explore hadron properties.

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arXiv2015

How important is $iε$ in QFT?

We discuss the role of $iε$ in quantum field theories and suggest that it can be identified with the dimensional regularization parameter $iε=4-d$ thus clarifying and simplifying issues related to the infrared divergences without altering any of the present knowledge in QFT. We further present the relevance of this assumption for the optical theorem.

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arXiv2015

Connections between chiral Lagrangians and QCD sum-rules

It is shown how a chiral Lagrangian framework can be used to derive relationships connecting quark-level QCD correlation functions to mesonic-level two-point functions. Crucial ingredients of this connection are scale factor matrices relating each distinct quark-level substructure (e.g., quark-antiquark, four-quark) to its mesonic counterpart. The scale factors and mixing angles are combined into a projection matrix to obtain the physical (hadronic) projection of the QCD correlation function matrix. Such relationships provide a powerful bridge between chiral Lagrangians and QCD sum-rules that are particularly effective in studies of the substructure of light scalar mesons with multiple complicated resonance shapes and substantial underlying mixings. The validity of these connections is demonstrated for the example of the isotriplet $a_0(980)$-$a_0(1450)$ system, resulting in an unambiguous determination of the scale factors from the combined inputs of QCD sum-rules and chiral Lagrangians. These scale factors lead to a remarkable agreement between the quark condensates in QCD and the mesonic vacuum expectation values that induce spontaneous chiral symmetry breaking in chiral Lagrangians. This concrete example shows a clear sensitivity to the underlying $a_0$-system mixing angle, illustrating the value of this methodology in extensions to more complicated mesonic systems.

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arXiv2015

Probing the substructure of $f_0(1370)$

Within an effective nonlinear chiral Lagrangian framework the substructure of $f_0(1370)$ is studied. The investigation is conducted in the context of a global picture of scalar mesons in which the importance of the underlying connections among scalar mesons below and above 1 GeV is recognized and implemented. These connections are due to the mixings among various quark-antiquarks, four-quarks and glue components and play a central role in understanding the properties of scalar mesons. Iterative Monte Carlo simulations are first performed on the 14-dimensional parameter space of the model and sets of points in this parameter space (the global sets) that give an overall agreement with all experimental data on mass spectrum, various decay widths and decay ratios of all isosinglet scalar states below 2 GeV are determined. Then within each global set, subsets that give closest agreement for the properties of $f_0(1370)$ are studied. Unlike the properties of other isosinglet states that show a range of variation within each global set, it is found that there is a clear signal for $f_0(1370)$ to be predominantly a quark-antiquark state with a substantial $s {\bar s}$ component, together with small remnants of four-quark and glue components.

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arXiv2014

Why are there three generations of fermions in the standard model?

We show that by decomposing the gauge fields in fermion degrees of freedom and by saturating the remaining degrees of freedom as dynamical fields in the Lagrangian one might explain the proliferation of fermion states in the standard model Lagrangian. Thus the mere presence of the gauge symmetry $U(1)_Y \times SU(2)_L \times SU(3)_c$ is essential.

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arXiv2014

Tree level relations in a composite electroweak theory

We work out simple tree level relations in a top condensate model with dynamical electroweak symmetry breaking. We find that in this picture the mass of the composite Higgs boson at tree level is given by $m_H^2=\frac{m_t^2}{2}$ where $m_t$ is the mass of the top quark.

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arXiv2014

A semiclassical approach for the Higgs boson

Starting from the equations of motion of the fields involved in a theory with spontaneous symmetry breaking and by making simple assumptions regarding their behavior we derive simple tree level relations between the mass of the Higgs boson in the theory and the masses of the gauge bosons corresponding to the broken generators. We show that these mass relations have a clear meaning if both the scalars and the gauge bosons are composite states made of two fermions.

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arXiv2014

Probing scalar mesons in semi-leptonic decays of $D_s^+$, $D^+$ and $D^0$

With the primary motivation of probing the quark substructure of scalar mesons, a generalized linear sigma model for the lowest and the next-to-lowest scalar and pseudoscalar mesons is employed to investigate several semi-leptonic decays of $D$ mesons. The free parameters of the model (in its leading approximation) have been previously determined from fits to mass spectra and various low-energy parameters. With these fixed parameters, the model has already given encouraging predictions for different low-energy decays and scattering, as well as for semileptonic decay channels of $D_s^+$ that include a scalar meson in the final state. In the present work, we apply the same model (in its leading order with the same fixed parameters) to different semi-leptonic decay channels of $D_s^+$, $D^+$ and $D^0$ and thereby further test the model and its predictions for the quark substructure of scalar mesons. We find that these predictions are in reasonable agreement with experiment.

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arXiv2014

Chiral Nonet Mixing in $η' \rightarrow ηππ$ Decay

Underlying mixing of scalar mesons is studied in $η'\rightarrow ηππ$ decay within a generalized linear sigma model of low-energy QCD which contains two nonets of scalar mesons and two nonets of pseudoscalar mesons (a quark-antiquark nonet and a four quark nonet). The model has been previously employed in various investigations of the underlying mixings among scalar mesons below and above 1 GeV (as well as those of their pseudoscalar chiral partners) and has provided a coherent global picture for the physical properties and quark substructure of these states. It is found that the linear sigma model with only a single lowest-lying nonet is not accurate in predicting the decay width, but inclusion of the mixing of this nonet with the next-to-lowest lying nonet, together with the effect of final state interaction of pions, significantly improves this prediction and agrees with experiment up to about 1\%. It is also shown that while the prediction of the leading order of the generalized model for the Dalitz parameters is not close to the experiment, the model is able to give a reasonable prediction of the energy dependencies of the normalized decay amplitude squared and that this is expected to improve with further refinement of the complicated underlying mixings. Overall this investigation provides further support for the global picture of scalar mesons: those below 1 GeV are predominantly four-quark states and significantly mix with those above 1 GeV which are closer to the conventional p-wave quark-antiquark states.

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arXiv2014

A hierarchy of the quark masses in a top condensate model with multiple Higgses

We discuss the quark masses in a top condensate model where not only two quark but also four quark composite states may exist. We show that the presence of the top color group SU(3)_1\times SU(3)_2 with the correct non anomalous quark representations can justify even in the absence of additional technicolor interactions a hierarchy of the quark masses where the light quark masses have the same size, the charm and bottom masses are higher and similar and the top is the heaviest.

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arXiv2011

Probing Scalar Mesons Below and Above 1 GeV

Within the context of a generalized linear sigma model that includes two nonets of scalar mesons (a two-quark nonet and a four-quark nonet) and two nonets of pseudoscalar mesons (a two-quark nonet and a four-quark nonet) a collective description of scalar and pseudoscalar mesons below and above 1 GeV is studied. The quark contents of these states are probed; estimates on their quark components are extracted; and prediction for pi pi scattering amplitude is made. An overview of these studies is presented here.

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arXiv2011

Semi-leptonic $D_s^+$(1968) decays as a scalar meson probe

The unusual multiplet structures associated with the light spin zero mesons have recently attracted a good deal of theoretical attention. Here we discuss some aspects associated with the possibility of getting new experimental information on this topic from semi-leptonic decays of heavy charged mesons into an isosinglet scalar or pseudoscalar plus leptons.

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arXiv2011

Chiral Nonet Mixing in pi pi Scattering

Pion pion scattering is studied in a generalized linear sigma model which contains two scalar nonets (one of quark-antiquark type and the other of diquark-antidiquark type) and two corresponding pseudoscalar nonets. An interesting feature concerns the mixing of the four isosinglet scalar mesons which yield poles in the scattering amplitude. Some realism is introduced by enforcing exact unitarity via the K-matrix method. It is shown that a reasonable agreement with experimental data is obtained up to about 1 GeV. The poles in the unitarized scattering amplitude are studied in some detail. The lowest pole clearly represents the sigma meson (or f0(600)) with a mass and decay width around 500 MeV. The second pole invites comparison with the f0(980) which has a mass around 1 GeV and decay width around 100 MeV. The third and fourth poles, resemble some of the isosinglet state in the complicated 1-2 GeV region. Some comparison is made to the situation in the usual SU(3) linear sigma model with a single scalar nonet.

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arXiv2010

Are three flavors special?

It has become clearer recently that the regular pattern of three flavor nonets describing the low spin meson multiplets seems to require some modification for the case of the spin 0 scalar mesons. One picture which has had some success, treats the scalars in a chiral Lagrangian framework and considers them to populate two nonets. These are, in turn, taken to result from the mixing of two "bare" nonets, one of which is of quark- antiquark type and the other of two quark- two antiquark type. Here we show that such a mixing is, before chiral symmetry breaking terms are included, only possible for three flavors. In other cases, the two types of structure can not have the same chiral symmetry transformation property. Specifically, our criterion would lead one to believe that scalar and pseudoscalar states containing charm would not have "four quark" admixtures. This work is of potential interest for constructing chiral Lagrangians based on exact chiral symmetry which is then broken by well known specific terms. It may also be of interest in studying some kinds of technicolor theories.

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