arXiv subjects

Victor L. Chernyak

Publications and source records attributed to Victor L. Chernyak.

At least 19 recordsLinked to original sources

arXiv2025

Mass spectra in ${\cal N}=1\, SU(N_c)$ SQCD with $N_F=N_c$ and problems with S-confinement

The low energy mass spectra of the direct $SU(N_c)$, $\,N_F=N_c$ $\,{\cal N}=1$ SQCD theory and its N.Seiberg's dual variant [1], are calculated in sections 2 and 3. It is shown that these two mass spectra are parametrically different, both for equal or unequal small quark masses $m_{Q,i}\neq 0$. In [17] the very special non-SUSY lattice $SU(N_c)$ QCD theory with $N_F=N_c$ scalar defective "quarks" was considered by E.Fradkin and S.H.Shenker. The conclusion of [17] was that the transition between the confinement and higgs regimes in this theory is the analytic crossover, not the non-analytic phase transition. And although the theory considered in [17] was very specific, the experience shows that up to now there is a widely spread opinion that this conclusion has general applicability. This model used in [17] is criticized in section 5 of this paper as incompatible with and qualitatively different from the standard non-SUSY $SU(N_c)$ $N_F=N_c$ QCD theory with standard scalar quarks $ϕ^i_β$ with all their $2N^2_F$ real degrees of freedom. It is emphasized that this model [17] is really the Stuckelberg $SU(N_c)$ YM-theory with no dynamical electric quarks and with massive all $N_c^2-1$ electric gluons with fixed by hands nonzero masses. There is no genuine confinement in this theory, it stays permanently in the completely higgsed phase only. And this is a reason for a crossover in this theory. While in the theory with standard scalar quarks there is the phase transition between the confinement and higgs phases. Besides, in section 5, the arguments presented in [2] by K.Intriligator and N.Seiberg for the standard direct $SU(N_c)$, $N_F=N_c$ $\,{\cal N}=1$ SQCD in support of the crossover from [17] are criticized as erroneous. Besides, in section 5 a qualitative mechanism of confinement in our ordinary (i.e. not SUSY) QCD is proposed.

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arXiv2024

Mass Spectra in ${\cal N}=1$ SQCD, in ${\cal N}=1$ SQCD-type theory and in softly broken ${\cal N}=2\rightarrow {\cal N}=1$ SQCD. And problems with the ${\cal N}=1$ Seiberg duality

Mass spectra are calculated for ${\cal N}=1$ SQCD and SQCD-type theories and for softly broken ${\cal N}=2$ SQCD in vacua with unbroken $Z_{(2N_c-N_F)\geq 2}$ symmetry. It is shown that the Seiberg ${\cal N}=1$ duality works, at best, for massless quarks within the conformal window only. Besides: a) the gauge invariant order parameter for scalar quarks is introduced which distinguishes confinement and higgs phases, b) the phase transition are described in ${\cal N}=1$ SQCD-type and broken ${\cal N}=2$ SQCD theories between confinement and higgs phases, c) the confinement mechanism is proposed for the ordinary YM and ${\cal N}=1$ SYM theories.

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arXiv2024

Phase transitions between confinement and higgs phases in ${\cal N}=1\,\, SU(N_c)$ SQCD with $1\leq N_F\leq N_c$ quark flavors

Considered is the standard 4-dimensional ${\cal N}=1\,\,SU(N_c)$ SQCD with $1\leq N_F\leq N_c$ quark flavors with masses $m_{Q,i}$. {\bf The gauge invariant order parameter $ρ$ is introduced in \cite{ch1} distinguishing confinement (with $ρ=0$) and higgs (with $ρ\neq 0$) phases}. Using a number of independent arguments for different variants of transition between the confinement and higgs regimes in these theories, it is shown that {\bf transitions between these regimes are not crossovers but the phase transitions}. In \cite{FS} the very special $SU(N_c)$ QCD theory with $N_F=N_c$ defective scalar "quarks" was considered by E.Fradkin and S.H.Shenker. The conclusion of \cite{FS} was that {\bf the transition between the confinement and higgs regimes is the analytic crossover}. And although the theory considered in \cite{FS} was very specific, the experience shows that up to now there is a widely spread opinion that this conclusion has general applicability. This model \cite{FS} is criticized in \cite{ch1},\cite{ch2} as incompatible with and very different from the standard non-SUSY $SU(N_c)\,\,N_F=N_c$ QCD theory with standard scalar quarks with all their physical degrees of freedom. It is emphasized that this model \cite{FS} is really {\bf the Stuckelberg $SU(N_c)$ YM-theory with no dynamical electric quarks and massive all $N_c^2-1$ electric gluons with fixed by hands nonzero masses}. There is no genuine confinement in this theory, it stays permanently in the completely higgsed (i.e. condensed) by hands phase only. And this is a reason for a crossover in this theory. While in the theory with standard scalar quarks there is the phase transition between the confinement (at $0 < |v|\ll Λ_{QCD}$) and higgs (at $|v|\ggΛ_{QCD}$) regimes.

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arXiv2023

Phase transitions between confinement and higgs phases in ${\cal N}=1\,\, SU(N_c)$ SQCD with $1\leq N_F\leq N_c-1$ quark flavors

Considered is 4-dimensional ${\cal N}=1$ supersymmetric $SU(N_c)$ QCD (SQCD) with $1\leq N_F\leq N_c-1$ equal mass quark flavors in the fundamental representation. The gauge invariant order parameter $ρ$ is introduced distinguishing confinement (with $ρ=0$) and higgs (with $ρ\neq 0$) phases. Using a number of independent arguments for different variants of transition between the confinement and higgs regimes, it is shown that transitions between these regimes are not crossovers but the phase transitions. Besides, it is argued that these phase transitions are of the first order. This is opposite to the conclusion of the paper of E. Fradkin and S.H. Shenker [10] that the transition between the confinement and higgs regimes is the crossover, not the phase transition. And although the theories considered in this paper and in [10] are different, an experience shows that there is a widely spread opinion that the conclusion of [10] is applicable to all QCD-like theories: both lattice and continuum, both not supersymmetric and supersymmetric. This opinion is in contradiction with the results of this paper.

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arXiv2023

Mass spectra in ${\cal N}=1$ SQCD with additional colorless fields and problems with Seiberg's duality

Considered is the direct ${\cal N}=1$ SQCD-like $Φ$-theory with $SU(N_c)$ colors and $3N_c/2< N_F<2N_c$ flavors of light quarks ${\overline Q},\,Q$. Besides, it includes $N^2_F$ additional colorless but flavored fields $Φ_{i}^{j}$ with the large mass parameter $μ_Φ\ggΛ_Q$, interacting with quarks through the Yukawa coupling. In parallel, is considered its Seiberg's dual variant, i.e. the $dΦ$-theory with $(N_F-N_c)$ dual colors, $N_F$ flavors of dual quarks ${\overline q},\,{q}$ and $N_F^2$ elementary mion fields $M^i_j\rightarrow ({\overline Q}_j Q^i)$. In considered here vacua, the quarks of both theories are in the conformal regimes at scales $μ<Λ_Q$. The mass spectra are calculated in sections 4 and 5. It is shown that they are different in the direct and dual theories, in disagreement with the Seiberg hypothesis about equivalence of two such theories. Besides it is shown in the direct theory that a qualitatively new phenomenon takes place: the seemingly heavy fields $Φ$ `return back' and there appear two additional generations of light $Φ$-particles with small masses $μ^{\rm pole}_{2,3}(Φ)\llΛ_Q$. In Conclusions also presented comparison of mass spectra of these two theories for such values of parameters when the direct theory is in the very strong coupling regime, while the dual one is in the weak coupling IR-free logarithmic regime. It is shown that mass spectra of these two theories are parametrically different in this case.

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arXiv2021

Mass spectra in ${\cal N}=1$ SQCD with additional colorless fields. Strong coupling regimes. II

This paper continues our studies in arXiV:1608.06452 [hep-th] of ${\cal N}=1$ gauge theories in the strongly coupled regimes. We also consider here the ${\cal N}=1$ SQCD-like theories with $SU(N_c)$ colors (and their Seiberg's dual), with $N_F$ flavors of light quarks and $N_F^2$ additional colorless flavored scalars $Φ^j_i$, but now with $N_F$ in the range $N_F>3N_c$. The mass spectra of these direct and dual theories in various vacua are calculated within the dynamical scenario introduced by the author in [8]. It assumes that quarks in such ${\cal N}=1$ SQCD-like theories without elementary colored adjoint scalars can be in two {\it standard} phases only. These are either the HQ (heavy quark) phase where they are confined or the Higgs phase. Recall that this scenario satisfies all those tests which were used as checks of the Seiberg hypothesis about the equivalence of the direct and dual theories. Calculated mass spectra of the direct $SU(N_c)$ theory are compared to those of its Seiberg's dual $SU(N_F-N_c)$ variant and appeared to be parametrically different.

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arXiv2020

Mass spectra in ${\cal N}=1$ SQCD with additional colorless fields. Strong coupling regimes

We consider the ${\cal N}=1$ $SU(N_c)$ SQCD-like (direct) theory (and its Seiberg's dual with $SU(N_F-N_c)$ dual colors), and with $N_F$ flavors of light quarks ${\overline Q}_j, Q^i$ with the mass term in the superpotential $m_Q{\rm Tr}({\overline Q} Q),\,\, m_Q\llΛ_Q$. Besides, there are $N_F^2$ additional colorless but flavored fields $Φ^j_i$ with the large mass parameter $μ_Φ\ggΛ_Q$. But now considered is the region $N_c+1<N_F<3N_c/2$ where the UV free direct $SU(N_c)$ theory is strongly coupled at scales $μ<Λ_Q$. The mass spectra of this direct theory in various vacua and at different values of $μ_Φ\ggΛ_Q$ are calculated within the dynamical scenario introduced by the author in [10]. This scenario assumes that quarks in such ${\cal N}=1$ SQCD-like theories can be in two standard phases only. These are either the HQ (heavy quark) phase where they are confined or the Higgs phase. It is shown that due to the strong power-like RG evolution, the seemingly heavy and dynamically irrelevant at scales $μ<Λ_Q$ fields $Φ^j_i$ can become light and relevant at lower energies, and there appear then two additional generation of light $Φ$-particles with masses $μ_{2,3}^{\rm pole}(Φ)\llΛ_Q$. The calculated mass spectra of this strongly coupled at $μ<Λ_Q\, SU(N_c)$ theory are compared to those of its weakly coupled at $μ<Λ_Q$ Seiberg's dual $SU(N_F-N_c)$ variant and appeared to be parametrically different. It is worth to recall that the dynamical scenario from [10] used in this article satisfies all those tests which were used as checks of the Seiberg hypothesis about the equivalence of the direct and dual theories. This parametrical difference shows, in particular, that all these tests, although necessary, may well be insufficient.

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arXiv2020

Softly broken ${\cal N}=2$ SQCD: mass spectra in vacua with unbroken $Z_{2N_c-N_F}$ symmetry

Considered are ${\cal N}=2\, SU(N_c)$ or $U(N_c)$ SQCD with $N_F<2N_c-1$ equal mass quark flavors. ${\cal N}=2$ supersymmetry is softly broken down to ${\cal N}=1$ by the mass term $μ_{\rm x}{\rm Tr}\,(X^2)$ of colored adjoint scalar partners of gluons, $μ_{\rm x}\llΛ_2$ ($Λ_2$ is the scale factor of the $SU(N_c)$ gauge coupling). There is a large number of different types of vacua in these theories with both unbroken and spontaneously broken global flavor symmetry, $U(N_F)\rightarrow U({\rm n}_1)\times U({\rm n}_2)$. We consider in this paper the large subset of these vacua with the unbroken non-trivial $Z_{2N_c-N_F\geq 2}$ discrete symmetry, at different hierarchies between the Lagrangian parameters $m\gtrlessΛ_2,\,\, μ_{\rm x}\gtrless m$. The forms of low energy Lagrangians, charges of light particles and mass spectra are described in the main text for all these vacua. The calculations of power corrections to the leading terms of the low energy quark and dyon condensates are presented in two important Appendices. The results agree with also presented in these Appendices independent calculations of these condensates using roots of the Seiberg-Witten spectral curve. This agreement confirms in a non-trivial way a self-consistency of the whole approach. Our results differ essentially from corresponding results in e.g. recent related papers arXiv:1304.0822, arXiv:1403.6086 and arXiv:1704.06201 of M.Shifman and A.Yung (and in a number of their previous numerous papers on this subject), and we explain in the text the reasons for these differences. (See also the extended critique of a number of results of these authors in section 8 of arXiv:1308.5863).

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arXiv2019

Mass Spectrum in SQCD and Problems with the Seiberg Duality. Another Scenario

N=1 SQCD with SU(N_c) colors and N_F flavors of light quarks is considered within the dynamical scenario which assumes that quarks can be in two different phases only. These are: a) either the HQ (heavy quark) phase where they are confined, b) or they are higgsed, at the appropriate values of parameters of the Lagrangian. The mass spectra of this (direct) theory and its Seiberg's dual are obtained and compared, for quarks of equal or unequal masses. It is shown that in all cases when there is the additional small parameter at hand (it is 0<(3N_c-N_F)/N_F << 1 for the direct theory, or its analog 0<(2N_F-3N_c)/N_F << 1 for the dual one), the mass spectra of the direct and dual theories are parametrically different. A number of other regimes are also considered.

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arXiv2019

Mass spectra in ${\cal N}=1\,\, SQCD$ with additional colorless but flavored fields

Considered is the ${\cal N}=1$ SQCD-like theory with $SU(N_c)$ colors and $0< N_F<2N_c$ flavors of equal mass $0< m_Q\llΛ_Q$ quarks. Besides, it includes $N^2_F$ additional colorless but flavored fields $Φ_{i}^{j}$, with the large mass parameter $μ_Φ\ggΛ_Q$. The mass spectra of this $Φ$-theory are first directly calculated at $0<N_F<N_c$ where the quarks are weakly coupled, in all different vacua with the unbroken or spontaneously broken flavor symmetry $U(N_F)\rightarrow U(n_1)\times U(n_2)$. Further, the mass spectra of this direct $Φ$-theory and its Seiberg's dual variant, the $dΦ$-theory, are calculated at $3N_c/2<N_F<2N_c$ and various values of $μ_Φ/Λ_Q\gg 1$ (in strong coupling regimes), using the dynamical scenario introduced by the author in his previous article \cite{ch3}. This scenario assumes that quarks can be in two different standard phases only: either this is the HQ (heavy quark) phase where they are confined, or they are higgsed. Within the used dynamical scenario, it is shown that mass spectra of the direct $Φ$ and dual $dΦ$ - theories are parametrically different. Besides it is shown in the direct $Φ$-theory that a qualitatively new phenomenon takes place: under appropriate conditions, the seemingly heavy and dynamically irrelevant fields $Φ$ 'return back' and there appear two additional generations of light $Φ$-particles with small masses $μ^{\rm pole}(Φ)\llΛ_Q$. Also considered is the $X$-theory which is the ${\cal N}=2$ SQCD with $SU(N_c)$ colors and $0< N_F<2N_c$ flavors of light quarks, broken down to ${\cal N}=1$ by the large mass parameter of the adjoint scalar superfield $X, \, μ_X\ggΛ_2$. The tight interrelations between these $X$ and $Φ$ theories are described, in particular, the conditions under which they are equivalent.

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arXiv2019

Mass spectra in N=1 SQCD with additional colorless but flavored fields.II

This paper continues our previous study of similar theories in \cite{ch5}. We also consider here the ${\cal N}=1$ SQCD-like theories with $SU(N_c)$ colors (and their Seiberg's dual with $SU(N_F-N_c)$ dual colors) and $N_F$ flavors of light quarks, and with $N_F^2$ additional colorless flavored fields $Φ^j_i$, but now with $N_F$ in the range $2N_c<N_F<3N_c$. The multiplicities of various vacua and quark and gluino condensates in these vacua are found. The mass spectra of the direct and Seiberg's dual theories in various vacua are calculated within the dynamical scenario which assumes that quarks in such ${\cal N}=1$ SQCD-like theories can be in two {\it standard} phases only. These are either the HQ (heavy quark) phase where they are confined or the Higgs phase. The word {\it standard} implies here also that, in such ${\cal N}=1$ theories without elementary colored adjoint scalars, no {\it additional} parametrically light solitons (e.g. magnetic monopoles or dyons) are formed at those scales where quarks decouple as heavy or are higgsed. Recall that this scenario satisfies all those tests which were used as checks of the Seiberg hypothesis about the equivalence of the direct and dual theories. The mass spectra of these direct and Seiberg's dual theories calculated within this framework were found to be different, in general. These parametrical differences of mass spectra of direct and dual theories show, in particular, that all those tests, which were used as checks of the Seiberg hypothesis about the equivalence of the direct and dual theories, although necessary, may well be insufficient. Besides, the mass spectrum of the dual theory with $SU(N_F-N_c)$ colors and $N_c+1<N_F<3N_c/2$ dual quark flavors was calculated. And finally, considered is the direct ${\cal N}=2$ SQCD with $SU(N_c)$ colors and $N_c+1<N_F<3N_c/2$ flavors of light quarks...

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arXiv2017

Mass spectra in softly broken ${\cal N}=2$ SQCD

Considered are ${\cal N}=2\, SU(N_c)$ or $U(N_c)$ SQCD with $N_F<2N_c-1$ quark flavors with the quark mass term $m{\rm Tr}\,({\bar Q} Q)$ in the superpotential. ${\cal N}=2$ supersymmetry is softly broken down to ${\cal N}=1$ by the mass term $μ_{\rm x}{\rm Tr}\,(X^2)$ of colored adjoint scalar partners of gluons, $μ_{\rm x}\llΛ_2$ ($Λ_2$ is the scale factor of the $SU(N_c)$ gauge coupling). There is a large number of different types of vacua in these theories with both unbroken and spontaneously broken flavor symmetry, $U(N_F)\rightarrow U({\rm n}_1)\times U({\rm n}_2)$. We consider in this paper the large subset of these vacua with the unbroken nontrivial $Z_{2N_c-N_F\geq 2}$ discrete symmetry, at different hierarchies between the Lagrangian parameters $m\gtrlessΛ_2,\,\, μ_{\rm x}\gtrless m$. The forms of low energy Lagrangians, quantum numbers of light particles and mass spectra are described in the main text for all these vacua. The calculations of power corrections to the leading terms of the low energy quark and dyon condensates are presented in two important Appendices. These calculations confirm additionally in a non-trivial way a self-consistency of the whole approach. Our results differ essentially from corresponding results in recent related papers arXiv:1304.0822, arXiv:1403.6086, and arXiv:1704.06201 of M.Shifman and A.Yung (and in a number of their numerous previous papers on this subject), and we explain in the text the reasons for these differences (see also the extended critique of a number of results of these authors in section 8 of arXiv:1308.5863).

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arXiv2014

Hard exclusive two photon processes in QCD

This is a short review of some hard two-photon processes: $\\ a) \,\,γγ\to {\overline P}_1 P_2,\,\, {\overline P}_1 P_2= \{π^+π^-, K^+ K^-, K_S K_S, π^oπ^o, π^oη\}\,, \\ b) \,\,γγ\to V_1 V_2,\,\, V_1 V_2=\{ρ^oρ^o, ϕϕ, ωϕ, ωω\},\\ c) \,\,γγ\to {\rm baryon-antibaryon},\\ d) \,\,γ^*γ\to P^o,\,\, P^o=\{π^o, η, η^\prime, η_c\}$. The available experimental data are presented. A number of theoretical approaches to calculation of these processes is described, both those based mainly on QCD and more phenomenological (the handbag model, the diquark model, etc). Some theoretical questions tightly connected with this subject are discussed, in particular: the applications of various types of QCD sum rules, the endpoint behavior of the leading twist meson wave functions, etc.

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arXiv2012

Mass spectra in N=1 SQCD with additional fields. II

This article continues 1205.0410 [hep-th]. Considered is the N=1 SQCD-like theory with SU(N_c) colors and 3N_c/2 >Lambda. The mass spectra of this Phi theory (and its dual variant, the dPhi theory) are calculated at different values of μ_Phi/Lambda >>1 within the dynamical scenario which implies that quarks can be in two different phases only: either this is the HQ (heavy quark) phase where they are confined, or they are higgsed at appropriate values of the lagrangian parameters. It is shown that at the left end of the conformal window, i.e. at 0<(2N_F-3N_c)/N_F << 1, the mass spectra of the direct and dual theories are parametrically different.

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arXiv2012

Hard two photon processes γγ--> M_2 M_1 in QCD

A short review of leading term QCD predictions vs those of the handbag model for large angle cross sections γγ--> P_2 P_1 (P is the pseudoscalar meson π^{\pm,o}, K^{\pm,o}, η), and for γγ--> V_2 V_1 (V is the neutral vector meson ρ^o, ω, ϕ), in comparison with Belle Collaboration measuments

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arXiv2012

Mass spectra in N=1 SQCD with additional fields. I

Considered is the N=1 SQCD-like theory with SU(N_c) colors and 0 >Lambda. The mass spectra of this Phi-theory (and its dual variant, the dPhi-theory) are calculated at different values of μ_{Phi}/Lambda >>1 within the dynamical scenario which implies the (quasi)spontaneous breaking of chiral symmetry. It is shown that, under appropriate conditions, the seemingly heavy and dynamically irrelevant fields Phi 'return back' and there appear two additional generations of light Phi-particles with small masses μ(Phi)< >Lambda_2. The tight interrelations between these X and Phi-theories are described, in particular, the conditions under which they are equivalent.

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arXiv2009

On Mass Spectrum in SQCD, and Problems with the Seiberg Duality. Equal quark masses

The dynamical scenario is considered for N=1 SQCD, with N_c colors and N_c \neq 0, while quarks alone don't condense, =<\bar Q>=0, so that the color is confined. Such condensation of quarks results in formation of dynamical constituent masses μ_C \gg m_Q of quarks and appearance of light "pions" (similarly to QCD). The mass spectrum of SQCD in this phase is described and comparison with the Seiberg dual description is performed. It is shown that the direct and dual theories are different (except, possibly, for the perturbative strictly superconformal regime).

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arXiv2009

On Mass Spectrum in SQCD. Unequal quark masses

N=1 SQCD with N_c colors and two types of light quarks: N_l flavors with smaller masses m_l and N_h=N_F-N_l flavors with larger masses m_h, N_c<N_F<3N_c, 0<m_l \leq m_h \ll Λ, is considered within the dynamical scenario in which quarks can form the coherent colorless diquark-condensate. There are several phase states at different values of parameters r=m_l/m_h, N_l, and N_F. Properties of these phases and the mass spectra therein are described.

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