arXiv subjects

Yitzhak Frishman

Publications and source records attributed to Yitzhak Frishman.

13 recordsLinked to original sources

arXiv2018

On bound-states of the Gross Neveu model with massive fundamental fermions

In the search for QFT's that admit boundstates, we reinvestigate the two dimensional Gross-Neveu model, but with massive fermions. By computing the self-energy for the auxiliary boundstate field and the effective potential, we show that there are no bound states around the lowest minimum, but there is a meta-stable bound state around the other minimum, a local one. The latter decays by tunneling. We determine the dependence of its lifetime on the fermion mass and coupling constant.

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arXiv2014

Large N Chern-Simons with massive fundamental fermions - A model with no bound states

In a previous paper, we analyzed the theory of massive fermions in the fundamental representation coupled to a U(N) Chern-Simons gauge theory in three dimensions at level K. It was done in the large N, large K limits where Lambda=N/K was kept fixed. Among other results, we showed there that there are no high mass quark anti-quark bound states. Here we show that there are no bound states at all.

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arXiv2013

Breaking conformal invariance- Large N Chern-Simons theory coupled to massive fundamental fermions

We analyze the theory of massive fermions in the fundamental representation coupled to a U(N) Chern-Simons gauge theory at level K. It is done in the large N, large K limits where λ=N/K is kept fixed. Following arXiv:1110.4386 we obtain the solution of a Schwinger-Dyson equation for the two point function, the exact expression for the fermion propagator and the partition function at finite temperature. We prove that in the large K limit there exists an infinite set of classically conserved high spin currents also when a mass is introduced, breaking the conformal invariance. In analogy to the seminal work of 't Hooft on two dimensional QCD, we write down a Bethe-Salpeter equation for the wave function of a "quark anti-quark" bound state. We show that unlike the two dimensional QCD case, the three dimensional Chern-Simons theory does not admit a confining spectrum.

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arXiv2013

Tetraquarks, their Masses and Decays in QED_2

Recent observations by Belle and BESIII of charged quarkonium-like resonances give new stimulus for theoretical investigation of exotic hadrons in general and heavy tetraquarks in particular. We use QED_2, a confining theory, as a model for the masses and decays of tetraquarks. Here we discuss the states (Q Qbar q qbar) and (Q Q qbar qbar) (and its anti-particle), where Q and q are two fermion flavors with masses M and m, so that M > m. We then discuss decay modes of these states into (Q Qqbar), (q qbar), (Q qbar), (Qbar q). It turns out that (Q Qbar q qbar) is stable, while (Q Q qbar qbar) is not.

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arXiv2010

Non-Perturbative Field Theory - From two dimensional conformal field theory to QCD in four dimensions

This note is based on the summary of our book entitled "Non-perturbative field theoryfrom two dimensional conformal field theory to QCD in four dimensions", published recently by Cambridge University Press. It includes 436 pages. The book provides a detailed description of the tool box of non-perturbative techniques, presents applications of them to simplified systems, mainly of gauge dynamics in two dimensions, and examines the lessons one can learn from those systems about four dimensional QCD and hadron physics. In particular the book deals with conformal invariance, integrability, bosonization, large N, solitons in two dimensions and monopoles and instantons in four dimensions, confinement versus screening and finally the hadronic spectrum and scattering. We also attach the table of contents and the list of references of the book. We would be grateful for any comments or suggestions related to the material in the book. These may be incorporated in a possible future edition. They may be sent via the e-mails below.

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arXiv2005

Exotic Baryons in Two-Dimensional QCD

Two-dimensional QCD has often been used as a laboratory for studying the full four-dimensional theory, providing, for example, an explicit realization of baryons as solitons. We review aspects of conventional baryons in two-dimensional QCD, including the classical and quantum contributions to their masses. We then discuss the spectrum of exotic baryons in two-dimensional QCD, commenting on the solitonic radius inferred from the excitation spectrum as well as the two-dimensional version of the Goldberger-Treiman relation relating meson couplings to current matrix elements. Two-dimensional QCD provides strong overall support to the chiral-soliton picture for the structure of normal and exotic baryons in four dimensions.

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arXiv2003

Meson-Baryon Scattering in QCD_2 for any Coupling

Extending earlier work on strong-coupling meson-baryon scattering in QCD_2, we derive the effective meson-baryon action for any value of the coupling constant, in the large-N_c limit. Colour degrees of freedom play an important role, and we show that meson-baryon scattering can be formulated as a relativistic potential problem. We distinguish two cases that are non-trivial for unequal quark masses, and present the resulting equations for meson-baryon scattering amplitudes.

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arXiv2002

Scattering and Resonances in QCD_2

Extending previous works on the spectrum of QCD_2, we now investigate the 2D analogue of meson-baryon scattering. We use semi-classical methods, perturbing around classical soliton solutions. We start with the abelian case, corresponding to one flavor,and find that in this case the effective potential is reflectionless. We obtain an explicit expression for the forward phase shift. In the non-abelian case of several flavors, the method yields a potential which depends on the momentum of the incoming particle. In this case there is both transmission and reflection. In both cases no resonances appear. As a byproduct, we derive the general conditions for a 2D quantum field theoretical action to yield a reflectionless effective potential when one expands in small fluctuations about the classical solution.

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arXiv1997

QCD2-Screening, Confinement and Novel non-abelian Solutions

We analyze the question of screening versus confinement in bosonized massless QCD in two dimensions. We deduce the screening behavior of massless $SU(N_c)$ QCD with flavored fundamental fermions and fermions in the adjoint representation. This is done by computing the potential between external quarks as well as by bosonizing also the external sources and analyzing the states of the combined system. We write down novel "non-abelian Schwinger like" solutions of the equations of motion, compute their masses and argue that an exchange of massive modes of this type is associated with the screening mechanism.

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arXiv1996

The $ΔI = 1/2 $ Rule in the Light of Two-Dimensional QCD

We calculate in QCD$_2$ the ratios of baryonic matrix elements of $ΔI = 2$ and $ΔI = 0$ four-fermion operators, with a view to understanding better the mechanism of $ΔI = 1/2$ enhancement in QCD$_4$. We find relatively small suppressions of both the scalar-scalar and vector-vector $ΔI = 2$ four-fermion operators. We discuss the possible implications of these results, in view of a suggestion that gluon condensation may be an important contributing factor in the $ΔI = 1/2$ enhancement seen in QCD$_4$. At the technical level, our calculation of the vector-vector operator matrix element requires a treatment of the time dependence of the QCD$_2$ soliton which had not been developed in previous phenomenological calculations within this model.

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arXiv1995

On the Stability of Quark Solitons in QCD

We critically re-examine our earlier derivation of the effective low energy action for QCD in 4 dimensions with chiral fields transforming non-trivially under both color and flavor, using the method of anomaly integration. We find several changes with respect to our previous results, leading to much more compact expressions, and making it easier to compare with results of other approaches to the same problem. With the amended effective action, we find that there are no stable soliton solutions. In the context of the quark soliton program, we interpret this as an indication that the full low-energy effective action must include additional terms, reflecting possible modifications at short distances and/or the non-trivial structure of the gauge fields in the vacuum, such as $ \neq 0$. Such terms are absent in the formalism based on anomaly integration.

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arXiv1992

Quark solitons as constituents of hadrons

We exhibit static solutions of multi-flavour QCD in two dimensions that have the quantum numbers of baryons and mesons, constructed out of quark and anti-quark solitons. In isolation the latter solitons have infinite energy, corresponding to the presence of a string carrying the non-singlet colour flux off to spatial infinity. When $N_c$ solitons of this type are combined, a static, finite-energy, colour singlet solution is formed, corresponding to a baryon. Similarly, static meson solutions are formed out of a soliton and an anti-soliton of different flavours. The stability of the mesons against annihilation is ensured by flavour conservation. The static solutions exist only when the fundamental fields of the bosonized Lagrangian belong to $U(N_c{\times}N_f)$ rather than to $SU(N_c) \times U(N_f)$. Discussion of flavour symmetry breaking requires a careful treatment of the normal ordering ambiguity. Our results can be viewed as a derivation of the constituent quark model in QCD$_2$, allowing a detailed study of constituent mass generation and of the heavy quark symmetry.

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arXiv1991

Constituent Quarks as Solitons

We exhibit soliton solutions of QCD in two dimensions that have the quantum numbers of quarks. They exist only for quarks heavier than the dimensional gauge coupling, and have infinite energy, corresponding to the presence of a string carrying the non-singlet color flux off to spatial infinity. The quark solitons also disappear at finite temperature, as the temperature-dependent effective quark mass is reduced in the approach to the quark/hadron phase transition.

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