Mass Spectra in N = 1SQCD with Additional Colorless Fields and Problems with the Seiberg Duality

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Abstract

Considered is the direct N=1N=1 SQCD (i.e. supersymmetric QCD)-like ΦΦ-theory with SU(Nc)SU(Nc) colors and 3Nc/2<NF<2Nc3Nc/2<NF<2Nc flavors of light quarks Q¯¯¯¯bjQ¯jb, QiaQai, a,b=1...Nca,b=1...Nc, i,j=1...NFi,j=1...NF, with small mass parameter 0<mQ≪ΛQ0<mQ≪ΛQ in the superpotential. Besides, it includes N2FNF2 additional colorless but flavored fields ΦjiΦij, with the large mass parameter μΦ≫ΛQμΦ≫ΛQ, interacting with quarks through the Yukawa coupling in the superpotential. In parallel, is considered its Seiberg’s dual variant, i.e. the dΦdΦ-theory with N¯¯¯¯¯c=(NF−Nc)N¯c=(NF−Nc) dual colors and 3Nc/2<NF<2Nc3Nc/2<NF<2Nc flavors of dual quarks q¯¯jdq¯dj, qciqic, c,d=1...N¯¯¯¯¯cc,d=1...N¯c. The multiplicities of various vacua and values of the quark and gluino condensates in all vacua are found. It is shown that in considered vacua of both the direct and dual theories the quarks are in the conformal regimes at scales μ<ΛQμ<ΛQ. The dynamics of these regimes is sufficiently simple and well understood, so that no additional dynamical assumptions were needed to calculate the mass spectra in Sections 4 and 5. It is shown that mass spectra of the direct ΦΦ and dual dΦdΦ-theories are different, in disagreement with the Seiberg hypothesis about equivalence of two such theories. Besides it is shown in the direct ΦΦ-theory that a qualitatively new phenomenon takes place: the seemingly heavy and dynamically irrelevant fields ΦΦ ‘return back’ and there appear two additional generations of light ΦΦ-particles with small masses μpole2,3(Φ)≪ΛQμ2,3pole(Φ)≪ΛQ.

Original languageEnglish
Pages (from-to)997-1005
Number of pages9
JournalPhysics of Atomic Nuclei
Volume83
Issue number6
DOIs
Publication statusPublished - Nov 2020

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