Photon structure function in supersymmetric QCD revisited

We investigate the virtual photon structure function in the supersymmetric QCD (SQCD), where we have squarks and gluinos in addition to the quarks and gluons. Taking into account the heavy particle mass effects to the leading order in QCD and SQCD we evaluate the photon structure function and numerically study its behavior for the QCD and SQCD cases.     

SUSY QCD Impact on Top-Pair Production Associated with a Z0-Boson at a Photon-Photon Collider

The top-pair production in association with a Z⁰-boson at a photon-photon collider is an important process in probing the coupling between top-quarks and vector boson and discovering the signature of possible new physics. We describe the impact of the complete supersymmetric QCD (SQCD) next-to-leading order (NLO)radiative corrections on this process at a polarized or unpolarized photon collider, and make a comparison between the effects of the SQCD and the standard model (SM) QCD. We investigate the dependence of the lowest-order (LO) and QCD NLO corrected cross sections in both the SM and minimal supersymmetric standard model (MSSM) on colliding energy s^1/2 in different polarized photon collision modes. The LO, SM NLO, and SQCD NLO corrected distributions of the invariantmass of t\bar{t}-pair and the transverse momenta of final Z⁰-boson are presented. Our numerical results show that the pure SQCD effects in γγ→t\bar{t}z⁰ process can be more significant in the + + polarized photon collision mode than in other collision modes, and the relative SQCD radiative correction in unpolarized photon collision mode varies from 32.09\% to -1.89\% when s^1/2 goes up from 500 GeV to 1.5 TeV.     

Consequences of the non-abelian anomaly in supersymmetric theories

In supersymmetric theories, the anomalous interactions involving the Goldstone supermultiplets are found not to be determined from symmetry considerations alone: they depend also on the dynamical details of the model. The origin of the unexpected results lies in the presence of the massless fermionic superpartners of the Goldstone bosons. For example, the decay π⁰ → γγ is found to be suppressed in supersymmetric QCD (SQCD). Low-energy effective actions with the correct symmetry properties are constructed, taking SQCD as an illustrative example. The axion decay a → γγ in a supersymmetric composite model might be suppressed with the same mechanism that works for π⁰ → γγ in SQCD.     

Supersymmetric enhancement factor for the 1-jet cross-section inp - \bar p reactions

We compare the 1-jet inclusive cross-section at highp _⊥ in proton-antiproton reaction atSPS collider predicted by standard QCD and by its simplest supersymmetric extension (SQCD). We first compute the total enhancement factorK between QCD and SQCD jets as a function ofp _⊥. Then we compute the observable enhancement factor which is smaller thanK since the transverse momentum of supersymmetric particles is not fully observable. We have analyzed two cases (i)p _⊥ is small compared to the masses of squarks and only light gluinos (2 GeV) are considered (ii)p _⊥ is large compared to the masses of squarks (17 GeV in our analysis) and both gluinos and squarks are taken into account. The observable enhancement factor between QCD and SQCD is found to be small (of order 1.3 to 1.5 forp _⊥=100 GeV). Missingp _⊥ events with one ordinary jet and one jet due to the production of a supersymmetric particle are found to be non negligible with respect to those with two supersymmetric jets. We also display some interesting supersymmetric relations among parton cross-sections.     

A three-loop check of the “a-maximization” in SQCD with adjoint(s)

The “a-maximization” was introduced by K. Intriligator and B. Wecht for finding anomalous dimensions of chiral superfields at the IR fixed points of the RG flow. Using known explicit calculations of anomalous dimensions in the perturbation theory of SQCD (with one or two additional adjoint fields), it is checked here at the three-loop level.     

Instanton effects in supersymmetric gauge theories

We investigate how in supersymmetric gauge theories non-perturbative effects are able to generate non-trivial vacuum properties otherwise forbidden by perturbative non-renormalization theorems. This conclusion can be reliably drawn since the constancy of certain Green functions — due to supersymmetry (SUSY) — allows one to connect vacuum-dominated large distances with short-distance behaviour which is reliably computed by instanton methods. In all the cases we discuss (without matter, with massive or massless matter in real representations and, finally, with matter in complex representations) instanton calculations imply the occurrence of a variety of condensates. For the pure SUSY gauge theory, a gluino condensate induces the spontaneous breaking of Z_2N. For massive super-quantum chromodynamics (SQCD) we find a peculiar mass dependence of matter condensates whose origin is traced to mass singularities of non-zero mode instanton contributions. These contributions force the massless limit of SQCD to differ from the strictly massless case, in which the spontaneous breaking of chiral symmetries is induced. Inconsistency with an anomaly equation forces either infinite matter condensates or spontaneous SUSY breaking in the massless cases. For non-constant Green functions, instantons are shown to provide new calculable short-distance singularities of an obvious non-perturbative nature.     

Solutions to the reflection equation and integrable systems for N = 2 SQCD with classical groups

Integrable systems underlying the Seiberg-Witten solutions for the N = 2 SQCD with gauge groups SO(n) and Sp(n) are proposed. They are described by the inhomogeneous XXX spin chain with specific boundary conditions given by reflection matrices. We attribute reflection matrices to orientifold planes in the brane construction and briefly discuss its possible deformations.     

Three-loop running of the strong coupling constant and the mass of the <Emphasis Type="Italic">b</Emphasis>-quark in the supersymmetric QCD

Supersymmetric extension of the QCD (SQCD) is considered and the scale dependence of some important parameters, i.e. strong coupling α _s and b-quark running mass m _b , is studied with the help of threeloop renormalization group equations. Five-flavour QCD is considered as a low-energy effective theory of SQCD and two-loop decoupling (threshold) effects are taken into account. Variations in running α _s and m _b at the GUT scale μ_GUT = 10¹⁶ GeV due to uncertainties in the initial experimental data and the ambiguities in the decoupling scale are analyzed for a particular point of the parameter space. Comparison with known results is given.     

On the mass spectrum of SQCD

We present a detailed study of the mass spectrum of SQCD in the vector, axial vector, Goldstone and flavour-singlet channels in the caseN _c =M _F by means of SVZ sum rules in their finite energy version. Our analysis constrains the relative strength of the two independent scalar condensates, φ⁺φ> and \(\left\langle {\tilde \phi \phi } \right\rangle \) .     

An Index for Confined Monopoles

We compute the index and associated spectral density for fluctuation operators which are defined via the Lagrangian of ${\mathcal{N} = 2}$ SQCD in the background of non-abelian confined multimonopoles. To this end we generalize the standard index calculations of Callias and Weinberg to the case of asymptotically nontrivial backgrounds. The resulting index is determined by topological charges. We conjecture that this index counts one quarter of the dimension of the moduli space of confined multimonopoles.     

Non-supersymmetric vacua and the D-flatness condition

Some N = 1 gauge theories, including SQED and N_F = 1 SQCD, have the property that, for arbitrary superpotentials, all stationary points of the potential V = F + D are D-flat. For others, stationary points of V are complex gauge transformations of D-flat configurations. As an implication, the technique to parametrize the moduli space of supersymmetric vacua in terms of a set of basic holomorphic G invariants can be extended to non-supersymmetric vacua. A similar situation is found in non-gauge theories with a compact global symmetry group.     

Metastable supersymmetry breaking without scales

We construct new examples of models of metastable D=4$D=4$N=1$N=1$ supersymmetry breaking in which all scales are generated dynamically. Our models rely on Seiberg duality and on the ISS mechanism of supersymmetry breaking in massive SQCD. Some of the electric quark superfields arise as composites of a strongly coupled gauge sector. This allows us to start with a simple cubic superpotential and an asymptotically free gauge group in the ultraviolet, and end up with an infrared effective theory which breaks supersymmetry dynamically in a metastable state.     

On Painlevé/gauge theory correspondence

We elucidate the relation between Painlevé equations and four-dimensional rank one \(\mathcal {N} = 2\) theories by identifying the connection associated with Painlevé isomonodromic problems with the oper limit of the flat connection of the Hitchin system associated with gauge theories and by studying the corresponding renormalization group flow. Based on this correspondence, we provide long-distance expansions at various canonical rays for all Painlevé \(\tau \)-functions in terms of magnetic and dyonic Nekrasov partition functions for \(\mathcal {N} = 2\) SQCD and Argyres–Douglas theories at self-dual Omega background \(\epsilon _1 + \epsilon _2 = 0\) or equivalently in terms of \(c=1\) irregular conformal blocks.     

Phases of supersymmetric gauge theories with flavors

We explore the phases of supersymmetric U(N) gauge theories with fundamental matter that arise as deformations of SQCD by the addition of a superpotential for the adjoint chiral multiplet. As the parameters in the superpotential are varied, the vacua of this theory sweep out various branches, which in some cases have multiple semiclassical limits. In such limits, we recover the vacua of various product gauge group theories, with flavors charged under some group factors. We describe in detail the structure of the vacua in both classical and quantum regimes, and develop general techniques such as an addition and a multiplication map which relate vacua of different gauge theories. We also consider possible indices characterizing different branches and potential relationships with matrix models.     

Flavored surface defects in 4d $$\mathcal{N}=1$$ N = 1 SCFTs

We discuss supersymmetric surface defects in compactifications of six-dimensional minimal conformal matter of types SU(3) and SO(8) to four dimensions. The relevant field theories in four dimensions are \(\mathcal{N}=1\) quiver gauge theories with SU(3) and SU(4) gauge groups, respectively. The defects are engineered by giving space-time-dependent vacuum expectation values to baryonic operators. We find evidence that in the case of SU(3) minimal conformal matter, the defects carry SU(2) flavor symmetry which is not a symmetry of the four-dimensional model. The simplest case of a model in this class is SU(3) SQCD with nine flavors, and thus the results suggest that this admits natural surface defects with SU(2) flavor symmetry. We analyze the defects using the superconformal index and derive analytic difference operators introducing the defects into the index computation. The duality properties of the four-dimensional theories imply that the index of the models is a kernel function for such difference operators. In turn, checking the kernel property constitutes an independent check of the dualities and the dictionary between six- dimensional compactifications and four-dimensional models.

     

Wino and zino production inp\bar p collisions: first order supersymmetric QCD corrections

We compute the first order supersymmetric QCD correction to wino \((\tilde W)\) and zino \((\tilde Z)\) production in \(p\bar p\) collisions via subprocesses involving two massless partons inside the nucleon or one massless parton and a massive SUSY parton (squark or gluino). The first order SQCD corrections to the rapidity dependence at CERN collider and Tevatron energies are found large (K～2). The rates are important (～10^?2 nb at \(\sqrt s = 630\) GeV and ～10^?1 nb at \(\sqrt s = 2\) TeV), as soon as the \((\tilde W)\) and \((\tilde Z)\) production by squarks is allowed. Transverse momentum distributions are also given and their shape is found very sensitive to the presence of SUSY partons inside the nucleon.     

Mass spectrum in SQCD and problems with the Seiberg duality. Another scenario

The N = 1 SQCD with SU(N _c ) colors and N _F flavors of light quarks is considered within the dynamical scenario that assumes that quarks can be in the two different phases only: the heavy-quark phase, where they are confined, and the phase of higgsed quarks, at the appropriate values of the Lagrangian parameters. The mass spectra of this (direct) theory and its Seiberg dual are obtained and compared for quarks of small equal or unequal masses. It is shown that in those regions of the parameter space where an additional small parameter exists (it is < [`(b)]₀ /N_F = (3N_c - N_F )/N_F << 1< \bar b_0 /N_F = (3N_c - N_F )/N_F \ll 1 at the right end of the conformal window, where the direct theory is weakly coupled in the vicinity of its IR fixed point, or its analog 0 < b ₀/N _F = (2N _F − 3N _c )/N _F ≪ 1 for the dual theory at the left end of the conformal window), the mass spectra of the direct and dual theories are parametrically different. A number of other regimes are also considered.     

On mass spectrum in SQCD. Unequal quark masses

The N = 1 SQCD with N _c colors and two types of light quarks, N _l flavors with the smaller mass m _l and N _h = N _F − N _l flavors with the larger mass m _h , N _c < N _F < 3N _c , 0 < m _l ≤ m _h ≪ Λ _Q , is considered within the dynamical scenario in which quarks can form a coherent colorless diquark condensate 〈$ \bar Q $ \bar Q Q〉. There are several phase states at different values of the parameters r = m _l /m _h . N _l , and N _F . Properties of these phases and their mass spectra are described.