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A. Vainshtein

Publications and source records attributed to A. Vainshtein.

At least 19 recordsLinked to original sources
arXiv2020

Operator Product Expansion and Calculation of the Two-Loop Gell-Mann-Low Function

This work was carried out in 1985. It was published in Russian in Yad. Fiz. 44, 498 (1986) [English translation Sov. J. Nucl. Phys. 44, 321 (1986)]. None of these publications are available on-line. Submitting this paper to ArXiv will make it accessible. *** A simple method is developed that makes it possible to determine the $k$-loop coefficient of the $β$-function if the operator product expansion for certain polarization operators in the $(k -1)$ loop is known. The calculation of the two-loop coefficient of the Gell-Mann-Low function becomes trivial -- it reduces to a few algebraic operations on already known expressions. As examples, spinor, scalar, and supersymmetric electrodynamics are considered. Although the respective results for $β^{(2)}$ are known in the literature, both the method of calculation and certain points pertaining to the construction of the operator product expansion are new.

hep-th↗
arXiv2020

New high-sensitivity searches for neutrons converting into antineutrons and/or sterile neutrons at the European Spallation Source

The violation of Baryon Number, $\mathcal{B}$, is an essential ingredient for the preferential creation of matter over antimatter needed to account for the observed baryon asymmetry in the universe. However, such a process has yet to be experimentally observed. The HIBEAM/NNBAR %experiment program is a proposed two-stage experiment at the European Spallation Source (ESS) to search for baryon number violation. The program will include high-sensitivity searches for processes that violate baryon number by one or two units: free neutron-antineutron oscillation ($n\rightarrow \bar{n}$) via mixing, neutron-antineutron oscillation via regeneration from a sterile neutron state ($n\rightarrow [n',\bar{n}'] \rightarrow \bar{n}$), and neutron disappearance ($n\rightarrow n'$); the effective $Δ\mathcal{B}=0$ process of neutron regeneration ($n\rightarrow [n',\bar{n}'] \rightarrow n$) is also possible. The program can be used to discover and characterise mixing in the neutron, antineutron, and sterile neutron sectors. The experiment addresses topical open questions such as the origins of baryogenesis, the nature of dark matter, and is sensitive to scales of new physics substantially in excess of those available at colliders. A goal of the program is to open a discovery window to neutron conversion probabilities (sensitivities) by up to three orders of magnitude compared with previous searches. The opportunity to make such a leap in sensitivity tests should not be squandered. The experiment pulls together a diverse international team of physicists from the particle (collider and low energy) and nuclear physics communities, while also including specialists in neutronics and magnetics.

physics.ins-det↗
arXiv2018

On instability of ground states in 2D CP(N-1) and O(N) models at large N

We consider properties of the inhomogeneous solution found recently for \mbox{$\mathbb{CP}^{\,N-1}$} model. The solution was interpreted as a soliton. We reevaluate its energy in three different ways and find that it is negative contrary to the previous claims. Hence, instead of the solitonic interpretation it calls for reconsideration of the issue of the true ground state. While complete resolution is still absent we show that the energy density of the periodic elliptic solution is lower than the energy density of the homogeneous ground state. We also discuss similar solutions for the ${\mathbb{O}}(N)$ model and for SUSY extensions.

hep-th↗
arXiv2013

Report of the Quark Flavor Physics Working Group

This report represents the response of the Intensity Frontier Quark Flavor Physics Working Group to the Snowmass charge. We summarize the current status of quark flavor physics and identify many exciting future opportunities for studying the properties of strange, charm, and bottom quarks. The ability of these studies to reveal the effects of new physics at high mass scales make them an essential ingredient in a well-balanced experimental particle physics program.

hep-ex↗
arXiv2013

Baryon Number Violation

This report, prepared for the Community Planning Study - Snowmass 2013 - summarizes the theoretical motivations and the experimental efforts to search for baryon number violation, focussing on nucleon decay and neutron-antineutron oscillations. Present and future nucleon decay search experiments using large underground detectors, as well as planned neutron-antineutron oscillation search experiments with free neutron beams are highlighted.

hep-ph↗
arXiv2012

More on the Tensor Response of the QCD Vacuum to an External Magnetic Field

In this Letter we discuss a few issues concerning the magnetic susceptibility of the quark condensate and the Son-Yamamoto (SY) anomaly matching equation. It is shown that the SY relation in the IR implies a nontrivial interplay between the kinetic and WZW terms in the chiral Lagrangian. It is also demonstrated that in a holographic framework an external magnetic field triggers mixing between scalar and tensor fields. Accounting for this, one may calculate the magnetic susceptibility of the quark condensate to all orders in the magnetic field.

hep-ph↗
arXiv2011

Higgs Decay into Two Photons through the W-boson Loop: No Decoupling in the m_W --> 0 Limit

We reanalyze the W-boson loop in the amplitude of the Higgs decay into two photons to show the absence of decoupling in the limit of massless W bosons, m_W --> 0. The Higgs coupling to longitudinal polarizations survive in this limit and generates a nonvanishing contribution in the $H\to γγ$ decay. This shows that the recent claim of decoupling by R. Gastmans, S.L. Wu, and T.T. Wu is incorrect, and the old calculations for the two photon decay well known in the literature are valid.

hep-ph↗
arXiv2008

Highly Excited Mesons, Linear Regge Trajectories and the Pattern of the Chiral Symmetry Realization

The chiral symmetry of QCD shows up in the linear Weyl--Wigner mode at short Euclidean distances or at high temperatures. On the other hand, low-lying hadronic states exhibit the nonlinear Nambu--Goldstone mode. An interesting question was raised as to whether the linear realization of the chiral symmetry is asymptotically restored for highly excited states. We address it in a number of ways. On the phenomenological side we argue that to the extent the meson Regge trajectories are observed to be linear and equidistant, the Weyl--Wigner mode is not realized. This picture is supported by quasiclassical arguments implying that the quark spin interactions in high excitations are weak, the trajectories are linear, and there is no chiral symmetry restoration. Then we use the string/gauge duality. In the top-down Sakai--Sugimoto construction the nonlinear realization of the chiral symmetry is built in. In the bottom-up AdS/QCD construction by Erlich et al., and Karch et al. the situation is more ambiguous. However, in this approach linearity and equidistance of the Regge trajectories can be naturally implemented, with the chiral symmetry in the Nambu--Goldstone mode. Asymptotic chiral symmetry restoration might be possible if a nonlinearity (convergence) of the Regge trajectories in an "intermediate window" of $n,J$, beyond the explored domain, takes place. This would signal the failure of the quasiclassical picture.

hep-ph↗
arXiv2006

Central Charge Anomalies in 2D Sigma Models with Twisted Mass

We discuss the central charge in supersymmetric ${\cal N}=2$ sigma models in two dimensions. The target space is a symmetric Kähler manifold, CP$(N-1)$ is an example. The U(1) isometries allow one to introduce twisted masses in the model. At the classical level the central charge contains Noether charges of the U(1) isometries and a topological charge which is an integral of a total derivative of the Killing potentials. At the quantum level the topological part of the central charge acquires anomalous terms. A bifermion term was found previously, using supersymmetry which relates it to the superconformal anomaly. We present a direct calculation of this term using a number of regularizations. We derive, for the first time, the bosonic part in the central charge anomaly. We construct the supermultiplet of all anomalies and present its superfield description. We also discuss a related issue of BPS solitons in the CP(1) model and present an explicit form for the curve of marginal stability.

hep-th↗
arXiv2005

Comments on Diquarks, Strong Binding and a Large Hidden QCD Scale

We present arguments regarding diquarks possible role in low-energy hadron phenomenology that escaped theorists' attention so far. Good diquarks, i.e. the $0^{+}$ states of two quarks, are argued to have a two-component structure with one of the components peaking at distances several times shorter than a typical hadron size (a short-range core). This can play a role in solving two old puzzles of the 't Hooft 1/N expansion: strong quark mass dependence of the vacuum energy density and strong violations of the Okubo-Zweig-Iizuka (OZI) rule in the quark-antiquark $0^\pm$ channels. In both cases empiric data defy 't Hooft's 1/N suppression. If good diquarks play a role at an intermediate energy scale they ruin 't Hoofts planarity because of their mixed-flavor composition. This new scale associated with the good diquarks may be related to a numerically large scale discovered in [V. Novikov, M. Shifman, A. Vainshtein and V. Zakharov, Nucl. Phys. B 191, 301 (1981)] in a number of phenomena mostly related to vacuum quantum numbers and $0^\pm$ glueball channels. If SU(3)$_{\rm color}$ of bona fide QCD is replaced by SU(2)$_{\rm color}$, diquarks become well-defined gauge invariant objects. Moreover, there is an exact symmetry relating them to pions. In this limit predictions regarding good diquarks are iron-clad. If passage from SU(2)$_{\rm color}$ to SU(3)$_{\rm color}$ does not lead to dramatic disturbances, these predictions remain qualitatively valid in bona fide QCD.

hep-ph↗
arXiv2004

Enhanced Worldvolume Supersymmetry and Intersecting Domain Walls in N=1 SQCD

We study the worldvolume dynamics of BPS domain walls in N=1 SQCD with N_f=N flavors, and exhibit an enhancement of supersymmetry for the reduced moduli space associated with broken flavor symmetries. We provide an explicit construction of the worldvolume superalgebra which corresponds to an N=2 Kahler sigma model in 2+1D deformed by a potential, given by the norm squared of a U(1) Killing vector, resulting from the flavor symmetries broken by unequal quark masses. This framework leads to a worldvolume description of novel two-wall junction configurations, which are 1/4-BPS objects, but nonetheless preserve two supercharges when viewed as kinks on the wall worldvolume.

hep-th↗
arXiv2004

Rational functions and real Schubert calculus

We single out some problems of Schubert calculus of subspaces of codimension 2 that have the property that all their solutions are real provided that the data are real. Our arguments explore the connection between subspaces of codimension 2 and rational functions of one variable.

math.AG↗
arXiv2003

Cluster algebras and Poisson geometry

We introduce a Poisson variety compatible with a cluster algebra structure and a compatible toric action on this variety. We study Poisson and topological properties of the union of generic orbits of this toric action. In particular, we compute the number of connected components of the union of generic toric orbits for cluster algebras over real numbers. As a corollary we compute the number of connected components of refined open Bruhat cells in Grassmanians G(k,n) over real numbers.

math.QA↗
arXiv2002

Counting real rational functions with all real critical values

We study the number of real rational degree n functions (considered up to linear fractional transformations of the independent variable) with a given set of 2n-2 distinct real critical values. We present a combinatorial reformulation of this number and pose several related questions.

math.AG↗
arXiv2002

Counting Domain Walls in N=1 Super Yang-Mills Theory

We study the multiplicity of BPS domain walls in N=1 super Yang-Mills theory, by passing to a weakly coupled Higgs phase through the addition of fundamental matter. The number of domain walls connecting two specified vacuum states is then determined via the Witten index of the induced worldvolume theory, which is invariant under the deformation to the Higgs phase. The worldvolume theory is a sigma model with a Grassmanian target space which arises as the coset associated with the global symmetries broken by the wall solution. Imposing a suitable infrared regulator, the result is found to agree with recent work of Acharya and Vafa in which the walls were realized as wrapped D4-branes in IIA string theory.

hep-th↗