arXiv subjects

Arkady Vainshtein

Publications and source records attributed to Arkady Vainshtein.

35 records · Page 2Linked to original sources

arXiv2006

Refinements in electroweak contributions to the muon anomalous magnetic moment

Effects of strong interactions on the two loop electroweak radiative corrections to the muon anomalous magnetic moment, $a_μ=(g_μ-2)/2$, are examined. Short-distance logs are shown to be unaffected. Computation of long-distance contributions is improved by use of an effective field theory approach that preserves the chiral properties of QCD and accounts for constraints from the operator product expansion. Small, previously neglected, two loop contributions, suppressed by a $1-4\sin^2θ_W$ factor, are computed and the complete three loop leading short-distance logs are reevaluated. These refinements lead to a reduction in uncertainties and a slight shift in the total electroweak contribution to $a_μ^{\rm EW} = 154(1)(2)\times 10^{-11}$ where the first error corresponds to hadronic uncertainties and the second is primarily due to the allowed Higgs mass range.

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arXiv2004

Background field calculations and nonrenormalization theorems in 4d supersymmetric gauge theories and their low-dimensional descendants

We analyze the structure of multiloop supergraphs contributing to the effective Lagrangians in 4d supersymmetric gauge theories and in the models obtained from them by dimensional reduction. When d=4, this gives the renormalization of the effective charge. For d < 4, the low-energy effective Lagrangian describes the metric on the moduli space of classical vacua. These two problems turn out to be closely related. In particular, we establish the relationship between the 4d nonrenormalization theorems (in minimal and extended supersymmetric theories) and their low--dimensional counterparts.

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arXiv2003

Hadronic light-by-light scattering contribution to the muon anomalous magnetic moment revisited

We discuss hadronic light-by-light scattering contribution to the muon anomalous magnetic moment a_μ^{\rm lbl}, paying particular attention to the consistent matching between the short- and the long-distance behavior of the light-by-light scattering amplitude. We argue that the short-distance QCD imposes strong constraints on this amplitude overlooked in previous analyses. We find that accounting for these constraints leads to approximately 50 per cent increase in the central value of a_μ^{\rm lbl}, compared to existing estimates. The hadronic light-by-light scattering contribution becomes a_μ^{\rm lbl}=136(25) \times 10^{-11}, thereby shifting the Standard Model prediction closer to the experimental value.

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arXiv2003

Triangle Anomaly and the Muon g-2

Hadronic electroweak corrections to the muon anomalous magnetic moment (g-2) are reviewed. Emphasis is on clarification of discrepancies among various published studies. A theorem on non-renormalization of the transversal part of a correlator of two vector currents and an axial current is reviewed and its consequences in the form of superconvergent sum rules are discussed.

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arXiv2002

Perturbative and nonperturbative renormalization of anomalous quark triangles

Anomalous quark triangles with one axial and two vector currents are studied in special kinematics when one of the vector currents carries a soft momentum. According to the Adler-Bardeen theorem the anomalous longitudinal part of the triangle is not renormalized in the chiral limit. We derive a new nonrenormalization theorem for the transversal part of the triangle. This nonrenormalization, in difference with the longitudinal part, holds on only perturbatively. At the nonperturbative level we use the operator product expansion and the pion dominance in the longitudinal part to determine the magnetic susceptibility of the quark condensate, $χ=-N_c/(4π^2 F_π^2)$.

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arXiv2001

Nonperturbative Continuity in Graviton Mass versus Perturbative Discontinuity

We address the question whether a graviton could have a small nonzero mass. The issue is subtle for two reasons: there is a discontinuity in the mass in the lowest tree-level approximation, and, moreover, the nonlinear four-dimensional theory of a massive graviton is not defined unambiguously. First, we reiterate the old argument that for the vanishing graviton mass the lowest tree-level approximation breaks down since the higher order corrections are singular in the graviton mass. However, there exist nonperturbative solutions which correspond to the summation of the singular terms and these solutions are continuous in the graviton mass. Furthermore, we study a completely nonlinear and generally covariant five-dimensional model which mimics the properties of the four-dimensional theory of massive gravity. We show that the exact solutions of the model are continuous in the mass, yet the perturbative expansion exhibits the discontinuity in the leading order and the singularities in higher orders as in the four-dimensional case. Based on exact cosmological solutions of the model we argue that the helicity-zero graviton state which is responsible for the perturbative discontinuity decouples from the matter in the limit of vanishing graviton mass in the full classical theory.

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arXiv2001

Monopole, gluino and charge condensates in gauge theories with broken N=2 supersymmetry

We consider chiral condensates in SU(2) gauge theory with broken N=2 supersymmetry and one fundamental flavor in the matter sector. Matter and gaugino condensates are determined by integrating out the adjoint field. The only nonperturbative input is the Affleck-Dine-Seiberg one-instanton superpotential. The results are consistent with those obtained by the `integrating in' procedure. We then calculate monopole, dyon, and charge condensates using the Seiberg-Witten approach. The key observation is that the monopole and charge condensates vanish at the Argyres-Douglas point where the monopole and charge vacua collide. We interpret this phenomenon as a deconfinement of electric and magnetic charges at the Argyres-Douglas point.

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arXiv2001

On Gribov's Ideas on Confinement

I comment on possible relations of Gribov's ideas on mechanism of confinement with some phenomena in QCD and in supersymmetric gauge theories.

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arXiv2001

Long Range Forces and Supersymmetric Bound States

We consider the long range forces between two BPS particles on the Coulomb branch of N=2 and N=4 supersymmetric gauge theories. The 1/r potential is unambiguously fixed, even at strong coupling, by the moduli dependence of central charges supported by the BPS states. The effective Coulombic coupling vanishes on marginal stability curves, while sign changes on crossing these curves explain the restructuring of the spectrum of composite BPS states. This restructuring proceeds via the delocalization of the composite state on approach to the curve of marginal stability. Therefore the spectrum of BPS states can be inferred by analyzing the submanifolds of the moduli space where the long range potential is attractive. This method also allows us to find certain non-BPS bound states and their stability domains. As examples, we consider the dissociation of the W boson and higher charge dyons at strong coupling in N=2 SU(2) SYM, quark-monopole bound states in N=2 SYM with one flavor, and composite dyons in N=2 SU(3) SYM.

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arXiv2000

Marginal Stability and the Metamorphosis of BPS States

We discuss the restructuring of the BPS spectrum which occurs on certain submanifolds of the moduli/parameter space -- the curves of the marginal stability (CMS) -- using quasiclassical methods. We argue that in general a `composite' BPS soliton swells in coordinate space as one approaches the CMS and that, as a bound state of two `primary' solitons, its dynamics in this region is determined by non-relativistic supersymmetric quantum mechanics. Near the CMS the bound state has a wave function which is highly spread out. Precisely on the CMS the bound state level reaches the continuum, the composite state delocalizes in coordinate space, and restructuring of the spectrum can occur. We present a detailed analysis of this behavior in a two-dimensional N=2 Wess-Zumino model with two chiral fields, and then discuss how it arises in the context of `composite' dyons near weak coupling CMS curves in N=2 supersymmetric gauge theories. We also consider cases where some states become massless on the CMS.

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arXiv1999

Instantons at Strong Coupling, Averaging over Vacua, and the Gluino Condensate

We consider instanton contributions to chiral correlators, such as <0| Tr λ^2 (x) Tr λ^2(x') |0>, in N=1 supersymmetric Yang-Mills theory with either light adjoint or fundamental matter. Within the former model, extraction of the gluino condensate from a connected 1-instanton diagram, evaluated at strong coupling, can be contrasted with expectations from the Seiberg-Witten solution perturbed to an N=1 vacuum. We observe a numerical discrepancy, coinciding with that observed previously in N=1 SQCD. Moreover, since knowledge of the vacuum structure is complete for softly broken N=2 Yang-Mills, this model serves as a counterexample to the hypothesis of Amati et al. that 1-instanton calculations at strong coupling can be interpreted as averaging over vacua. Within N=1 SQCD, we point out that the connected contribution to the relevant correlators actually vanishes in the weakly coupled Higgs phase, despite having a nonzero value through infra-red effects when calculated in the unbroken phase.

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arXiv1999

Instantons Versus Supersymmetry: Fifteen Years Later

An introduction to the instanton formalism in supersymmetric gauge theories is given. We explain how the instanton calculations, in conjunction with analyticity in chiral parameters and other general properties following from supersymmetry, allow one to establish exact results in the weak and strong coupling regimes. Some key applications are reviewed, the main emphasis is put on the mechanisms of the dynamical breaking of supersymmetry.

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arXiv1999

How Penguins Started to Fly

A mechanism explaining a strong enhancement of nonleptonic weak decays was suggested in 1975, later to be dubbed the penguin. This mechanism extends Wilson's ideas about the operator product expansion at short distances and reveals an intricate interplay of subtle features of the theory such as heavy quark masses in Glashow-Iliopoulos-Maini cancellation, light quarks shaping the chiral properties of QCD, etc. The penguins have subsequently evolved to play a role in a variety of fields in present-day particle phenomenology. I will describe the history of this idea and review its subsequent development. The recent measurement of direct CP violation in K decays gives a new confirmation of the penguin mechanism.

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arXiv1998

Heavy flavor decays and OPE in two-dimensional 't Hooft model

The 't Hooft model (two-dimensional QCD in the limit of large number of colors) is used as a testground for calculations of nonleptonic and semileptonic inclusive widths of heavy flavors based on the operator product expansion (OPE). The OPE-based predictions up to terms ${\cal O}(1/m_Q^4)$, inclusively, are confronted with the "phenomenological" results, obtained by summation of all open exclusive decay channels, one by one, a perfect match is found. The issue of duality violations is discussed, the amplitude of oscillating terms is estimated. The method is applied to the realistic case of hadronic $τ$ decays.

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arXiv1997

HQET and Semileptonic Form Factors

(Contribution to Proceedings of the Seventh International Symposium On Heavy Flavor Physics, July 7-11, 1997, Santa Barbara.) Theoretical approaches to form factors of semileptonic decays are discussed in application to $B \ra D + l+\bar ν_l$ decay.

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arXiv1995

Review of Selected Topics in HQET

A few topics on the expansion in heavy quark mass are discussed. The theoretical framework is the Wilson Operator Product Expansion rather than the Heavy Quark Effective Theory.

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arXiv1995

Matching Conditions and Duality in N=1 SUSY Gauge Theories in the Conformal Window

We discuss duality in $N=1$ SUSY gauge theories in Seiberg's conformal window, $(3N_c/2)<N_f<3N_c$. The 't Hooft consistency conditions -- the basic tool for establishing the infrared duality -- are considered taking into account higher order $α$ corrections. The conserved (anomaly free) $R$ current is built to all orders in $α$. Although this current contains all orders in $α$ the 't Hooft consistency conditions for this current are shown to be one-loop. This observation thus justifies Seiberg's matching procedure. We also briefly discuss the inequivalence of the ``electric" and ``magnetic" theories at short distances.

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