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

The low energy mass spectra of the direct standard $SU(N_c),\, N_F=N_c$ $\,{\cal N}=1$ SQCD theory and its N. Seiberg's dual variant [1], considered as {\it two independent theories}, are calculated in sections 2 and 3. It is shown that these two mass spectra are parametrically different, both for equal or unequal quark masses. Therefore, the proposal by N. Seiberg [1] of his $N_F=N_c$ dual theory of $N_F^2-1$ mesons $M^i_j$ and baryons $B, {\overline B}$ as the low energy form of the direct theory is erroneous (and similarly for the case $N_F=N_c+1$). In [17] the very special (not supersymmetric) lattice $SU(N_c)$ QCD theory with $N_F=N_c$ scalar non-standard "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: both to lattice and continuum theories, and both to not supersymmetric and supersymmetric ones. This model used in [17] is criticized in section 5 of this paper as incompatible with the standard $SU(N_c)$ $\,N_F=N_c$ QCD theory with scalar quarks with all their physical degrees of freedom. Besides, 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 theory in support of conclusions [17] about crossover are criticized as erroneous.Comment: 18 pages, no figure

Phase transitions between confinement and higgs phases in N=1 SU(Nc){\cal N}=1\,\, SU(N_c) SQCD with 1≤NF≤Nc−11\leq N_F\leq N_c-1 quark flavors

Considered is ${\cal N}=1$ supersymmetric $SU(N_c)$ QCD (SQCD) with $1\leq N_F\leq N_c-1$ equal mass quark flavors in the fundamental representation. 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. These are counterexamples to a widely spread opinion, originating from the paper of E. Fradkin and S.H. Shenker [10], about absence of the phase transition between the confinement and higgs phases.Comment: 10 pages, title and abstract changed, text expanded, argumentation strengthened, results unchange

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

Considered is the direct ${\cal N}=1$ SQCD-like $\Phi$-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 $\Phi_{i}^{j}$ with the large mass parameter $\mu_{\Phi}\gg\Lambda_Q$, interacting with quarks through the Yukawa coupling. In parallel, is considered its Seiberg's dual variant, i.e. the $d\Phi$-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 $\mu<\Lambda_Q$. 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 $\Phi$ `return back' and there appear two additional generations of light $\Phi$-particles with small masses $\mu^{\rm pole}_{2,3}(\Phi)\ll\Lambda_Q$. 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.Comment: 16 pages. Small improvements in the text, typos corrected, reference added. Talk given at Session of Nucl.Phys. section of RAS, Novosibirsk, Russia, 10-12 March 202

Selected topics in e^+e^- collisions

Content : 1) The leading twist pion wave function, 2) "Improved" QCD sum rules with non-local condensates, 3) Pion and kaon form factors and charmonium decays: theory vs experiment, 4) \gamma^{*}\gamma\pi^{o} - form factor, 5) The new non-local axial anomaly, 6) Cross sections \gamma\gamma --> \pi^+\pi^-, K^+K^-, K_S K_S .Comment: Talk given at the International Workshop "e^+e^- collisions from \phi to J/\psi", March 1, 2006, Novosibirsk, Russia; 20 pages, 7 figures; v2: sect.2 expanded to clarify the argumentation, a number of small improvements in the tex