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A. S. Sorin

Publications and source records attributed to A. S. Sorin.

At least 19 recordsLinked to original sources
arXiv2023

Observation of structures at $\sim 17$ and $\sim 38$ MeV/c$^{2}$ in the $γγ$ invariant mass spectra in pC, dC, and dCu collisions at $\textit{p}_{lab}$ of a few GeV/c per nucleon

The results of an analysis of the invariant mass spectra of photon pairs produced in dC, pC and dCu interactions at momenta of 2.75, 5.5 and 3.83 GeV/c per nucleon respectively, are presented. Signals in the form of enhanced structures at invariant masses of about 17 and 38 MeV/c2 are observed. The results of testing of the observed signals, including the results of the Monte Carlo simulation are presented. The test results support the conclusion that the observed signals are the consequence of detection of the particles with masses of about 17 and 38 MeV/c2 decaying into a pair of photons.

hep-ex↗
arXiv2022

Instantons: thick-wall approximation

We develop a new method for estimating the decay probability of the false vacuum via regularized instantons. Namely, we consider the case where the potential is either unbounded from below or the second minimum corresponding to the true vacuum has a depth exceeding the height of the potential barrier. In this case, the materialized bubbles dominating the vacuum decay naturally have a thick wall and the thin-wall approximation is not applicable. We prove that in such a case the main contribution to the action determining the decay probability comes from the part of the solution for which the potential term in the equation for instantons can be neglected compared to the friction term. We show that the developed approximation exactly reproduces the leading order results for the few known exactly solvable potentials. The proposed method is applied to generic scalar field potentials in an arbitrary number of dimensions.

hep-th↗
arXiv2019

On the invariants of the full symmetric Toda system

In this paper we continue our study of the geometric properties of full symmetric Toda systems from \cite{CSS14,CSS17,CSS19}. Namely we describe here a simple geometric construction of a commutative family of vector fields on compact groups, that include the Toda vector field, i.e. the field, which generates the full symmetric Toda system associated with the Cartan decomposition of a semisimple Lie algebra. Our construction makes use of the representations of the semisimple algebra and does not depend on the splitness of the Cartan pair. It is very close to the family of invariants and semiinvariants of the Toda system associted with $SL_n$, introduced in \cite{CS}.

nlin.SI↗
arXiv2018

Non-extensivity of the QCD pT spectra

We try to establish a connection between the hadronic distributions, in proton-proton collisions at very high transverse momentum $p_{\mathrm{T}}$, obtained via perturbative QCD and the Tsallis non extensive statistics. Our motivation is that while the former is expected to be valid at extremely high momentum, due to asymptotic freedom, the latter has been very successful in describing experimental spectra over a wide range of momentum. Matching the non extensive statistics with the asymptotic $p_{\mathrm{T}}$ behaviour expected from QCD leads to the value of $q=1.25$.

hep-ph↗
arXiv2017

Bruhat order in the Toda system on $\mathfrak{so}(2,4)$: an example of non-split real form

In our previous papers we described the structure of trajectories of the symmetric Toda system on normal real forms of various Lie algebras and showed that it was totally determined by the Hasse diagram of the Bruhat order on the corresponding Weil group. This note deals with the simplest non-split real Lie algebra, $\mathfrak{so}(2,4)$. It turns out, that the phase diagram in this case is also closely related with the Bruhat order of the relative Weyl group, but a bit more information is necessary to describe the dimensions of the trajectory spaces.

nlin.SI↗
arXiv2016

Integrable Cosmological Potentials

The problem of classification of the Einstein--Friedman cosmological Hamiltonians $H$ with a single scalar inflaton field $φ$ that possess an additional integral of motion polynomial in momenta on the shell of the Friedman constraint $H=0$ is considered. Necessary and sufficient conditions for the existence of first, second, and third degree integrals are derived. These conditions have the form of ODEs for the cosmological potential $V(φ)$. In the case of linear and quadratic integrals we find general solutions of the ODEs and construct the corresponding integrals explicitly. A new wide class of Hamiltonians that possess a cubic integral is derived. The corresponding potentials are represented in a parametric form in terms of the associated Legendre functions. Six families of special elementary solutions are described and sporadic superintegrable cases are discussed.

hep-th↗
arXiv2015

Phase portraits of the generalized full symmetric Toda systems on rank 2 groups

In this paper we continue investigations that we began in our previous works, where we proved, that the phase diagram of Toda system on special linear groups can be identified with the Bruhat order on symmetric group, when all the eigenvalues of Lax matrix are distinct, or with the Bruhat order on permutations of a multiset, if there are multiple eigenvalues. We show, that the coincidence of the phase portrait of Toda system and the Hasse diagram of Bruhat order holds in the case of arbitrary simple Lie groups of rank $2$: to this end we need only to check this property for the two remaining groups of second rank, $Sp(4,\mathbb R)$ and the real form of $G_2$.

nlin.SI↗
arXiv2015

Hyperinstantons, the Beltrami Equation, and Triholomorphic Maps

We consider the Beltrami equation for hydrodynamics and we show that its solutions can be viewed as instanton solutions of a more general system of equations. The latter are the equations of motion for an ${\cal N}=2$ sigma model on 4-dimensional worldvolume (which is taken locally HyperKähler) with a 4-dimensional HyperKähler target space. By means of the 4D twisting procedure originally introduced by Witten for gauge theories and later generalized to 4D sigma-models by Anselmi and Fré, we show that the equations of motion describe triholomophic maps between the worldvolume and the target space. Therefore, the classification of the solutions to the 3-dimensional Beltrami equation can be performed by counting the triholomorphic maps. The counting is easily obtained by using several discrete symmetries. Finally, the similarity with holomorphic maps for ${\cal N}=2$ sigma on Calabi-Yau space prompts us to reformulate the problem of the enumeration of triholomorphic maps in terms of a topological sigma model.

hep-th↗
arXiv2015

Femto-cyclones and hyperon polarization in Heavy-Ion Collisions

We study the structure of vorticity and hydrodynamic helicity fields in peripheral heavy-ion collisions using the kinetic Quark-Gluon String Model. The angular momentum conservation within this model holds with a good accuracy. We observe the formation of specific toroidal structures of vorticity field (vortex sheets). Their existence is mirrored in the polarization of hyperons of the percent order.

nucl-th↗
arXiv2014

The $c$-map, Tits Satake subalgebras and the search for $\mathcal{N}=2$ inflaton potentials

In this paper we address the general problem of including inflationary models exhibiting Starobinsky-like potentials into (symmetric) $\mathcal{N}=2$ supergravities. This is done by gauging suitable abelian isometries of the hypermultiplet sector and then truncating the resulting theory to a single scalar field. By using the characteristic properties of the global symmetry groups of the $\mathcal{N}=2$ supergravities we are able to make a general statement on the possible $α$-attractor models which can obtained upon truncation. We find that in symmetric $\mathcal{N}=2$ models group theoretical constraints restrict the allowed values of the parameter $α$ to be $α=1,\,\frac{2}{3},\, \frac{1}{3}$. This confirms and generalizes results recently obtained in the literature. Our analysis heavily relies on the mathematical structure of symmetric $\mathcal{N}=2$ supergravities, in particular on the so called $c$-map connection between Quaternionic Kähler manifolds starting from Special Kähler ones. A general statement on the possible consistent truncations of the gauged models, leading to Starobinsky-like potentials, requires the essential help of Tits Satake universality classes. The paper is mathematically self-contained and aims at presenting the involved mathematical structures to a public not only of physicists but also of mathematicians. To this end the main mathematical structures and the general gauging procedure of $\mathcal{N}=2$ supergravities is reviewed in some detail.

hep-th↗
arXiv2014

Investigation of hadron multiplicities and hadron yield ratios in heavy ion collisions

Here we thoroughly discuss some weak points of the thermal model which is traditionally used to describe the hadron multiplicities measured in the central nucleus-nucleus collisions. In particularly, the role of conservation laws, the values of hard-core radii along with the effects of the Lorentz contraction of hadron eigen volumes and the hadronic surface tension are systematically studied. It is shown that for the adequate description of hadron multiplicities the conservation laws should be modified, whereas for the description of hadron yield ratios the conservation laws are not necessary at all. Also here we analyzed the usual criteria for the chemical freeze-out and found that none of them is robust. A new chemical freeze-out criterion of constant entropy per hadron equals to 7.18 is suggested and a novel effect of adiabatic chemical hadron production is discussed. Additionally, we found that the data for the center of mass energies above 10 GeV lead to the temperature of the nil hadronic surface tension coefficient of about $T_0 = 147 \pm 7$ MeV. This is a very intriguing result since a very close estimate for such a temperature was obtained recently within entirely different approach. We argue that these two independently obtained results evidence that the (tri)critical temperature of the QCD phase diagram is between 140 and 154 MeV. In addition, here we suggest to consider the pion and kaon hard-core radii as new fitting parameters. Such an approach for the first time allows us to simultaneously describe the hadron multiplicities and the Strangeness Horn and get a very high quality fit of the available experimental data.

hep-ph↗
arXiv2013

Explicit Semi-invariants and Integrals of the Full Symmetric sl(n) Toda Lattice

We show how to construct semi-invariants and integrals of the full symmetric sl(n) Toda lattice for all n. Using the Toda equations for the Lax eigenvector matrix we prove the existence of semi-invariants which are homogeneous coordinates in the corresponding projective spaces. Then we use these semi-invariants to construct the integrals. The existence of additional integrals which constitute a full set of independent non-involutive integrals was known but the chopping and Kostant procedures have crucial computational complexities already for low-rank Lax matrices and are practically not applicable for higher ranks. Our new approach solves this problem and results in simple explicit formulae for the full set of independent semi-invariants and integrals expressed in terms of the Lax matrix and its eigenvectors, and of eigenvalue matrices for the full symmetric sl(n) Toda lattice.

nlin.SI↗
arXiv2013

Semi-invariants and Integrals of the Full Symmetric sl(n) Toda Lattice

We consider the full symmetric version of the Lax operator of the Toda lattice which is known as the full symmetric Toda lattice. The phase space of this system is the generic orbit of the coadjoint action of the Borel subgroup B^+(n) of SL(n,R). This system is integrable. We propose a new method of constructing semi-invariants and integrals of the full symmetric Toda lattice. Using only the Toda equations for the Lax eigenvector matrix we prove the existence of the semi-invariants which are Plucker coordinates in the corresponding projective spaces. Then we use these semi-invariants to construct the integrals. It is known that the full symmetric sl(n) Toda lattice has additional integrals which can be produced by Kostant procedure except for the integrals which can be derived by the chopping procedure. Altogether these integrals constitute a full set of the independent non-involutive integrals. Yet the unsolved complicated technical problem is their explicit derivation since Kostant procedure has crucial computational complexities even for low-rank Lax matrices and is practically unapplicable for higher ranks. Our new approach provides a resolution of this problem and results in simple explicit formulae for the full set of independent semi-invariants and integrals expressed both in terms of the Lax matrix and its eigenvector and eigenvalue matrices of the full symmetric sl(n) Toda lattice without using the chopping and Kostant procedures. We also describe the structure of the additional integrals of motion as functions on the flag space modulo the Toda flows and show how Plucker coordinates of different projective spaces define different families of the additional integrals. In this paper we present detailed proofs of the propositions of [24].

nlin.SI↗
arXiv2013

Inflation and Integrable one-field Cosmologies embedded in Rheonomic Supergravity

In this paper we show that the new approach to the embedding of the inflationary potentials into supergravity, presented in a quite recent paper [11] of Ferrara, Kallosh, Linde and Porrati can be formulated within the framework of standard matter coupled supergravity, without the use of the new minimal auxiliary set and of conformal compensators. The only condition is the existence of a translational Peccei Quinn isometry of the scalar Kahler manifold. We suggest that this embedding strategy based on a nilpotent gauging amounts to a profound Copernican Revolution. The properties of the inflaton potential are encoded in the geometry of some homogeneous one-dimensional Kahler manifolds that now should be regarded as the primary object, possibly providing a link with microscopic physics. We present a simple and elegant formula for the curvature of the Kahler manifold in terms of the potential. Most relevant consequence of the new strategy is that all the integrable potentials quite recently classified in a paper [7] that we have coauthored, are automatically embedded into supergravity and their associated Kahler manifolds demand urgent study. In particular one integrable potential that provides the best fit to PLANCK data seems to have inspiring geometrical properties deserving further study.

hep-th↗
arXiv2013

Axial Symmetric Kahler manifolds, the D-map of Inflaton Potentials and the Picard-Fuchs Equation

In this paper we provide a definition of the D-map, namely of the mathematical construction implicitly utilized by supergravity that associates an axial symmetric Kahler surface to every positive definite potential function V(phi). The properties of the D-map are discussed in general. Then the D-map is applied to the list of integrable cosmological potentials classified by us in a previous publication with A. Sagnotti. Several interesting geometrical and analytical properties of the manifolds in the image of this D-map are discovered and illustrated. As a by-product of our analysis we demonstrate the existence of (integrable) Starobinsky-like potentials that can be embedded into supergravity. Some of them follow from constant curvature Kahler manifolds. In the quest for a microscopic interpretation of inflaton dynamics we present the Ariadne's thread provided by a new mathematical concept that we introduce under the name of axial symmetric descendants of one dimensional special Kahler manifolds. By means of this token we define a clearcut algorithm that to each potential function V(phi) associates a unique 4th order Picard-Fuchs equation of restricted type. Such an equation encodes information on the chiral ring of a superconformal field theory to be sought for, unveiling in this way a microscopic interpretation of the inflaton potential. We conjecture that the physical mechanism at the basis of the transition from a special manifold to its axial symmetric descendant is probably the construction of an Open String descendant of a Closed String model.

hep-th↗
arXiv2013

Integrable Scalar Cosmologies II. Can they fit into Gauged Extended Supergavity or be encoded in N=1 superpotentials?

The question whether the integrable one-field cosmologies classified in a previous paper by Fre, Sagnotti and Sorin can be embedded as consistent one-field truncations into Extended Gauged Supergravity or in N=1 supergravity gauged by a superpotential without the use of D-terms is addressed in this paper. The answer is that such an embedding is very difficult and rare but not impossible. Indeed we were able to find two examples of integrable models embedded in Supergravity in this way. Both examples are fitted into N=1 Supergravity by means of a very specific and interesting choice of the superpotential W(z). The question whether there are examples of such an embedding in extended Gauged Supergravity remains open. In the present paper, relying on the embedding tensor formalism we classified all gaugings of the N=2 STU model, confirming, in the absence on hypermultiplets, the uniqueness of the stable de Sitter vacuum found several years ago by Fre, Trigiante and Van Proeyen and excluding the embedding of any integrable cosmological model. A detailed analysis of the space of exact solutions of the first Supergravity embedded integrable cosmological model revealed several new features worth an in depth consideration. When the scalar potential has an extremum at a negative value, the universe necessarily collapses into a Big Crunch notwithstanding its spatial flatness. The causal structure of these universes is quite different from that of the closed, positive curved, universe: indeed in this case the particle and event horizons do not coincide and develop complicated patterns. The cosmological consequences of this unexpected mechanism deserve careful consideration.

hep-th↗
arXiv2013

Integrable Scalar Cosmologies I. Foundations and links with String Theory

We build a number of integrable one--scalar spatially flat cosmologies, which play a natural role in inflationary scenarios, examine their behavior in several cases and draw from them some general lessons on this type of systems, whose potentials involve combinations of exponential functions, and on similar non--integrable ones. These include the need for the scalar to emerge from the initial singularity while climbing up sufficiently steep exponential potentials ("climbing phenomenon") and the inevitable collapse in a big Crunch whenever the scalar tries to settle at negative extrema of the potential. We also elaborate on the links between these types of potentials and "brane supersymmetry breaking", a mechanism that ties together string scale and scale of supersymmetry breaking in a class of orientifold models. We show that, under some assumptions that are spelled out in the text, the extended objects of these vacua can inject inflationary phases with discrete values of the spectral index that are determined by the number of unwrapped dimensions of the branes and by the inverse power with which the string coupling $g_s$ enters their world--volume actions. An NS fivebrane, which is interestingly unstable in this class of models, when wrapped on a small internal cycle would yield a spectral index that is amusingly close to the experimentally favored PLANCK value ns ~ 0.96.

hep-th↗