The four-loop anomalous dimension of the Konishi operator in $$ \mathcal{N} $$ = 4 Supersymmetric Yang-Mills theory

We present the result of a full direct component calculation for the planar four-loop anomalous dimension of the Konishi operator in = 4 Supersymmetric Yang-Mills theory. Our result confirms the results obtained from superfield and superstring computations, which take into account finite size corrections to the all-loop asymptotic Bethe ansatz for the integrable models describing the spectrum of the anomalous dimensions of the gaugeinvariant operators and the spectrum of the string states in the framework of the gauge/string duality. The article is published in the original.     

Anomalous dimensions of the Wilson operators in $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills theory

We present results for the universal anomalous dimension γ _uni(j) of Wilson twist-2 operators in the = 4 supersymmetric Yang-Mills theory in the first four orders of perturbation theory. The text was submitted by the authors in English.     

Feynman-Kac and feynman formulas for evolution pseudodifferential equations in superspace

In the paper, evolution pseudodifferential equations in the space of superanalytic functions (X) of an infinite-dimensional argument with symbols in the space (Y) of Fourier supertransforms of distributions on the dual superspace are considered. For these equations, the “weak” Cauchy problem is posed and the existence theorem for the solutions of this problem is proved. The main result of the paper is the theorem concerning the representation of solutions of the “weak” Cauchy problem by the Feynman path integral in the phase superspace (the Feynman-Kac formula). The Feynman integral is understood in the sequential sense. Thus, the Feynman formula becomes an immediate consequence of the Feynman-Kac formula.     

CP-violation and unitarity triangle test of the Standard Model

Phenomenological issues of CP violation in the quark sector of the Standard Model are discussed. We consider quark mixing in the SM, standard, and Wolfenstein parametrization of the CKM mixing matrix and unitarity triangle. We discuss the phenomenology of CP violation in K _L ⁰ and B _d ⁰()-decays. The standard unitarity triangle fit of the existing data is discussed. In appendix A we compare the K ⁰ ⇆ , B _d,s ⁰ ⇆ , etc. oscillations with neutrino oscillations. In Appendix B we derive the evolution equation for the M − system in the Weisskopf-Wigner approximation. The text was submitted by the author in English.     

On the leptonic decay of a heavy quarkonium with a Higgs-boson emission

The leptonic () decay of a heavy quark-antiquark bound state T( Q) with a Higgs-boson H emission is investigated. Applying the low-energy theorem to meson-Higgs coupling allows one to estimate the probability of the decay T( Q) → H. Only the simple version of the Standard Model extension containing two-Higgs doublet is considered. The text was submitted by the author in English.     

Charmed meson rescattering in the reaction $$ \bar pd \uparrow \bar DDN $$

We examine the possibility to extract information about the DN and interactions from the reaction. We utilize the notion that the open-charm mesons are first produced in the annihilation of the antiproton on one nucleon in the deuteron and subsequently rescatter on the other (the spectator) nucleon. The latter process is then exploited for investigating the DN and interactions. We study different methods for isolating the contributions from the D ⁰ p and D ⁻ p rescattering terms.     

Inhomogeneous symbols, the Newton polygon, and maximal L p -regularity

We prove a maximal regularity result for operators corresponding to rotation invariant symbols (in space) which are inhomogeneous in space and time. Symbols of this type frequently arise in the treatment of half-space models for (free) boundary-value problems. The result is obtained by extending the Newton polygon approach to variables living in complex sectors and combining it with abstract results on the -calculus and -bounded operator families. As an application, we derive maximal regularity for the linearized Stefan problem with Gibbs-Thomson correction. Dedicated to the memory of Leonid Romanovich Volevich     

On the two-loop $$ \ma thcal{O} $$( αs2) correc tions to the pole mass of the t quark in the MSSM

The paper is devoted to the calculation of two-loop (α _s ²) MSSM corrections to the relation between the pole mass of the t quark and its running mass in the scheme. Firstly, the value of the second-order contribution from large-mass expansion in mt/M _SUSY is studied. Contrary to our expectations, this contribution turned out to be negligible. As a by-product of this calculation, the two-loop anomalous dimension of the running quark mass is obtained in the supersymmetric QCD. Secondly, the influence of the two-loop corrections to the t-quark mass on the predicted superpartner masses is investigated. The text was submitted by the authors in English.     

Superfield approach to symmetry invariance in quantum electrodynamics with complex scalar fields

We show that the Grassmannian independence of the super-Lagrangian density, expressed in terms of the superfields defined on a (4,2)-dimensional supermanifold, is a clear-cut proof for the Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST invariance of the corresponding four (3+1)-dimensional (4D) Lagrangian density that describes the interaction between the U(1) gauge field and the charged complex scalar fields. The above 4D field theoretical model is considered on a (4,2)-dimensional supermanifold parametrized by the ordinary four space-time variables x ^μ (with μ = 0, 1, 2, 3) and a pair of Grassmannian variables θ and (with θ ² = ² = 0, θ + θ = 0). Geometrically, the (anti-)BRST invariance is encoded in the translation of the super-Lagrangian density along the Grassmannian directions of the above supermanifold such that the outcome of this shift operation is zero.      

f0(980)-meson as a $$ \bar K $$ molecule in a phenomenological Lagrangian approach

We discuss a possible interpretation of the f ₀(980)-meson as a hadronic molecule —a bound state of K and mesons. Using a phenomenological Lagrangian approach we calculate the strong f ₀(980) → ππ and electromagnetic f ₀(980) → γγ decays. The compositeness condition provides a self-consistent method to determine the coupling constant between f ₀ and its constituents, K and . Form factors governing the decays of the f ₀(980) are calculated by evaluating the kaon loop integrals. The predicted f ₀(980) → ππ and f ₀(980) → γγ decay widths are in good agreement with available data and results of other theoretical approaches.     

Abelian 2-form gauge theory: superfield formalism

We derive the off-shell nilpotent Becchi–Rouet–Stora–Tyutin (BRST) and anti-BRST symmetry transformations for all the fields of a free Abelian 2-form gauge theory by exploiting the geometrical superfield approach to the BRST formalism. The above four (3+1)-dimensional (4D) theory is considered on a (4, 2)-dimensional supermanifold parameterized by the four even spacetime variables x ^μ (with μ=0,1,2,3) and a pair of odd Grassmannian variables θ and (with ). One of the salient features of our present investigation is that the above nilpotent (anti-) BRST symmetry transformations turn out to be absolutely anticommuting due to the presence of a Curci–Ferrari (CF) type of restriction. The latter condition emerges due to the application of our present superfield formalism. The actual CF condition, as is well known, is the hallmark of a 4D non-Abelian 1-form gauge theory. We demonstrate that our present 4D Abelian 2-form gauge theory imbibes some of the key signatures of the 4D non-Abelian 1-form gauge theory. We briefly comment on the generalization of our superfield approach to the case of Abelian 3-form gauge theory in four, (3+1), dimensions of spacetime.     

Status of the investigation of the spin structure of d, 3H, and 3He at VBLHE using polarized and unpolarized deuteron beam

The investigation of the spin structure of d, ³H, and ³He has been performed at the RIKEN acceleration research facility and VBLHE. Vector A _y and tensor A _yy , A _xx , A _xz analyzing powers for d → ³Hen and d → ³Hp are presented at 270 MeV. Themirror channels (³Hen and ³Hp) are comparedto each other in order to find possible manifestation of charge-symmetry breaking. The preliminary results on the polarization observables for d → ³Hp at 200MeV are also presented. The obtained data are compared with one-nucleon-exchange calculations.As a byproduct, d → pX and ¹²C → pX breakup reactions are investigated at 140, 200, and 270MeV. The experimental data on p elastic scattering were obtained at 270, 880, and 2000 MeV at the Nuclotron. The polarization of the deuteron beam was measured at 270 MeV at the internal target station. The preliminary data on the vector A _y and tensor A _yy , A _xx analyzing powers for the p elastic scattering at 880 MeV are presented. The calculations on A _y , A _yy , and A _xx analyzing powers for the p elastic scattering at 880 MeV were performed in the framework of the multiple-scattering model. The text was submitted by the authors in English.     

The small axial charge of the N(1535)-resonance

There is a natural cancellation between the contributions of the qqq and qqqq components to the axial charge of the N(1535)-resonance. While the probability of the former is larger than that of the latter, its coefficient in the axial charge expression is exceptionally small. The magnitude of two of the corresponding coefficients of the qqqq components is in contrast large and has the opposite sign. This result provides a phenomenological illustration of the recent unquenched lattice calculation result that the axial charge of the N(1535)-resonance is very small, if not vanishing (T.T. Takahashi, T. Kunihiro, arXiv: 0801.4707 [hep-lat]). The result sets an upper limit on the magnitude of the probability of qqqq components as well.     

Lepton decay channels of egret gluinos at the LHC

Prospects for observing a SUSY-like signal from two gluinos are investigated within a certain region of the mSUGRA parameter space, where the cross section of the two gluino production in pp collisions at the LHC ( = 14 TeV) via gluon-gluon fusion (gg → ) is estimated at a rather high level of 17.3 pb. In this so-called EGRET region, the lightest stable neutralinos can serve as cold dark matter particles and are natural explanations of the excess of diffuse galactic gamma rays observed by the EGRET space apparatus. The -event selection relies on a very clear signature when decay products of each gluino contain one b-anti-b pair, one or two lepton-antilepton pair(s) and a neutralino. Rather high transverse-missing energy, carried away by the two neutralinos, is an essential signature of the events and also allows the relevant Standard Model background to be reduced significantly. In particular, it was found that the clear signatures of the selected processes demonstrate good prospects discovering the EGRET gluinos at the LHC. Furthermore, these signatures allow one to distinguish different mSUGRA parameters m _1/2 inside the EGRET region. The text was submitted by the authors in English.     

Event-shape of dileptons plus missing energy at a linear collider as a supersymmetry/Arkani-Hamed-Dimopoulos-Dvali discriminant

An event-shape analysis of the dileptons in the process e ⁺ e ⁻ → ℓ⁺ℓ⁻ , studied in ILC or CLIC, can clearly discriminate between a supersymmetric or a large extra dimensional (ADD) production mechanism.      

On pair production of scalar top quarks in <Emphasis Type="Italic">e</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">e</Emphasis><Superscript>−</Superscript> collisions at ILC and a possibility of their mass reconstruction

We study pair production of scalar top quarks (stop, ) in e ⁺ e ⁻ collisions with the subsequent decay of the top squarks into b quarks and charginos . We simulate this process by using PYTHIA6.4 for the beam energy 2E _b = = 350, 400, 500, 800, 1000 GeV. A set of criteria for physical variables is proposed, which provides good separation of stop signal events from top quark pair production being the main background. These criteria allow us to reconstruct the mass of the top squark with an integrated luminosity of 1000 fb⁻¹ provided that the neutralino mass is known. The article is published in the original.     

An Index for 4 Dimensional Super Conformal Theories

We present a trace formula for an index over the spectrum of four dimensional superconformal field theories on S ³ × time. Our index receives contributions from states invariant under at least one supercharge and captures all information – that may be obtained purely from group theory – about protected short representations in 4 dimensional superconformal field theories. In the case of the theory our index is a function of four continuous variables. We compute it at weak coupling using gauge theory and at strong coupling by summing over the spectrum of free massless particles in AdS ₅ × S ⁵ and find perfect agreement at large N and small charges. Our index does not reproduce the entropy of supersymmetric black holes in AdS ₅, but this is not a contradiction, as it differs qualitatively from the partition function over supersymmetric states of the theory. We note that entropy for some small supersymmetric AdS ₅ black holes may be reproduced via a D-brane counting involving giant gravitons. For big black holes we find a qualitative (but not exact) agreement with the naive counting of BPS states in the free Yang Mills theory. In this paper we also evaluate and study the partition function over the chiral ring in the Yang Mills theory.     

Neutral-meson production in <Emphasis Type="Italic">pp</Emphasis> collisions at RHIC and QCD test of <Emphasis Type="Italic">z</Emphasis> scaling

New experimental data on inclusive cross section of neutral-vector-meson (ω ⁰, ϕ, K _S ⁰) production in proton-proton collisions at = 200 GeV obtained at RHIC are analyzed in the framework of z scaling. Properties of z-presentation are used to predict hadron yields over a wide range of transverse momentum p _T and collisions energy . The next-to-leading-order perturbative QCD calculations of inclusive cross sections of π ⁰ mesons produced in pp and collisions over a wide range of and p _T are compared with ISR, S pS, RHIC data and predictions of z scaling. The dependence of the spectra in p _T and z presentations for different parton distribution and fragmentation functions is studied. The sensitivity of the obtained results to the choice of the renormalization (μ _R ), initial-state factorization (μ _F ), and final-state factorization (fragmentation) (μ _H ) scales is verified. It is shown that self-similar features of particle production dictated by the z scaling give strong restriction on the asymptotic behavior of the inclusive spectra in high-p _T region. The text was submitted by the author in English.     

Supersymmetric Quantum Mechanics and Super-Lichnerowicz Algebras

We present supersymmetric, curved space, quantum mechanical models based on deformations of a parabolic subalgebra of osp(2p+2|Q). The dynamics are governed by a spinning particle action whose internal coordinates are Lorentz vectors labeled by the fundamental representation of osp(2p|Q). The states of the theory are tensors or spinor-tensors on the curved background while conserved charges correspond to the various differential geometry operators acting on these. The Hamiltonian generalizes Lichnerowicz’s wave/Laplace operator. It is central, and the models are supersymmetric whenever the background is a symmetric space, although there is an osp(2p|Q) superalgebra for any curved background. The lowest purely bosonic example (2p, Q) = (2, 0) corresponds to a deformed Jacobi group and describes Lichnerowicz’s original algebra of constant curvature, differential geometric operators acting on symmetric tensors. The case (2p, Q) = (0, 1) is simply the superparticle whose supercharge amounts to the Dirac operator acting on spinors. The (2p, Q) = (0, 2) model is the supersymmetric quantum mechanics corresponding to differential forms. (This latter pair of models are supersymmetric on any Riemannian background.) When Q is odd, the models apply to spinor-tensors. The (2p, Q) = (2, 1) model is distinguished by admitting a central Lichnerowicz-Dirac operator when the background is constant curvature. The new supersymmetric models are novel in that the Hamiltonian is not just a square of super charges, but rather a sum of commutators of supercharges and commutators of bosonic charges. These models and superalgebras are a very useful tool for any study involving high rank tensors and spinors on manifolds. Dedicated to the memory of Tom Branson