Minimal composite Higgs systems

Extending to technicolour models recent results on the chiral, large N_c limit of QCD, we argue that minimal composite Higgs systems must contain an η like Higgs particle, whose peculiar properties follow from current algebra and large N arguments only. By contrast, the usual scalar Higgs is a model-independent entity without clear experimental signature.     

The spinning superparticle

Doubly graded massless supersymmetric particle models with both world-line local and space-time global supersymmetry are considered. We describe the first quantization of the model with four-dimensional space-time and N=1 world-line SUSY. Using the Gupta-Bleuler method we obtain as the super wave-function a pair of D=4 chiral spinor superfields with the on-shell spectrum containing scalar and vector multiplets.     

The gauge-invariant N=2 supersymmetric σ-model with general scalar potential

We construct the supersymmetric σ-model, in six dimensions, for an arbitrary hyper-Kähler manifold, and its minimal coupling to super-Yang-Mills theory. Non-trivial reduction to five or four dimensions yields the corresponding five- or four-dimensional N = 2 supersymmetric model with general scalar potential. We discuss briefly the coupling to supergravity in six dimensions and we give the on-shell supergravity torsion constraints.     

Effective super-Higgs and Str M2 from four-dimensional strings

We introduce supersymmetry breaking terms into the superpotential of the supergravity theories recently derived as the point field limit of the four-dimensional N = 1 superstrings. The terms we discuss have the special feature of giving mass to the gravitino without inducing one-loop quadratic divergences in the effective theory. It is shown that this property of the effective theory is due to the special geometrical structure shared by the scalar Kähler manifolds of the four-dimensional superstring-induced models.     

Finiteness, 1/N expansion and supersymmetry breaking

The possibility of spontaneous supersymmetry breaking in the limit of large N, in models with an internal O(N) symmetry, is demonstrated by constructing an explicit example in two dimensions. The model is finite and this is shown to be important for the supersymmetry breaking. A general criterion for finiteness of scalar superfield theories in two dimensions is given. Finally, the generalization of our results to three dimensions, and their relevance to four-dimensional models, is discussed.     

Instanton interpolating current for σ-tetraquark

We perform a QCD sum rule analysis for the light scalar meson σ   (f₀(600)$f_0(600)$) with a tetraquark current related to the instanton picture for QCD vacuum. We demonstrate that instanton current, including equal weights of scalar and pseudoscalar diquark–antidiquarks, leads to a strong cancelation between the contributions of high dimension operators in the operator product expansion (OPE). Furthermore, in the case of this current direct instanton contributions do not spoil the sum rules. Our calculation, obtained from the OPE up to dimension 10 operators, gives the mass of σ-meson around 780 MeV.     

Self-consistent Gaussian model of nonperturbative QCD vacuum

We show that the minimal Gaussian model of nonlocal vacuum quark and quark-gluon condensates in QCD violates the transverse character of the correlator of two vector currents. We suggest the improved Gaussian model of the nonperturbative QCD vacuum, which respects QCD equations of motion and minimizes the revealed gauge-invariance breakdown. We obtain the refined values of pion distribution amplitude (DA) conformal moments 〈ξ^2N 〉_π (N = 1, ..., 5) using the improved QCD vacuum model, including the inverse moment 〈x ^?1〉_π, being inaccessible if one uses the standard QCD SR. We construct the allowed region for Gegenbauer coefficients a ₂ and a ₄ of the pion DA for two values of the QCD vacuum nonlocality parameter, λ _q ² = 0.4 and 0.5 GeV².     

Consistent massive anomalous dimensions

We re-evaluate the O(g²) momentum-subtracted anomalous dimensions of QCD with massive quarks. The QCD equations of motion are used to relate operator matrix elements with different tensor structures. This procedure yields explicitly gauge-invariant anomalous dimensions. Our results differ slightly from those in the literature. The forward Compton amplitude for scattering of massive quarks and a scalar current is examined. The large Q² behavior of this amplitude is shown to be simply related to the momentum-subtracted, mass-dependent anomalous dimension.     

Infinite-parameter symmetries and the Higgs effect in gravity-coupled sigma models in D+4 dimensions

We compute the mass spectra of small fluctuations of four-dimensional fields for Kaluza-Klein models in which the compactification from D+4 to 4 (flat) dimensions is induced by the scalar fields of a nonlinear sigma model defined on an S^N or CP^N manifold. The compactifications are stable for all values of N. The fact that the spectra contain no massless vector fields is traced to the absence of a local gauge invariance for the sigma-model action. We introduce a complete basis for the infinite-parameter symmetries that arise from the harmonic analysis of the higher-dimensional dynamical invariances. The spectrum of spin-one and spin-two fields is consistent with the Higgs effect associated with the breaking of the local symmetries corresponding to these generators. The commutation relations of the infinite parameter algebra for the case of CP¹ are also given. The algebra includes the spectrum-generating algebra SO(1,3) of Salam and Strathdee.     

Comments on mesonic correlators in the worldline formalism

We elaborate on how to incorporate mesonic correlators into the worldline formalism. We consider possible applications to QCD-like theories in various dimensions. We focus on large-Nc two-dimensional QCD (the ?t Hooft model) and relate it to a single harmonic oscillator. We also discuss the dependence of the Peskin S-parameter on the number of massless flavors and their representation and compare our expression to the corresponding expression obtained at weak coupling. Finally, we use the worldline formalism to discuss how the Veneziano limit of QCD is realized in holography in the limit of small Nf/Nc.     

The effective interactions of chiral families in four-dimensional superstrings

The low-energy effective interactions in four-dimensional superstrings with N = 2 and N = 1 space-time supersymmetry and massless twisted (family) sector are obtained. Our results rely on some general symmetry properties of superstring particle states and on tensor-calculus techniques for supergravity couplings. The novel feature is that the N = 2 quaternionic manifold and N = 1 Kähler space of the scalar superpartners of family multiplets are non-symmetric spaces whose structure can be obtained by “integrating out” the massive superstring modes.     

Graviton dominance in quantum Kaluza-Klein theory

We compute, at the one-loop level, the effective potential for pure gravity in a Kaluza-Klein background geometry which is the direct product of four-dimensional Minkowski spacetime M⁴ with the N-sphere S^N, N odd. The computation is performed in the physical Lorentz-signature spacetime, avoiding the difficulties of “euclideanization”. We find that the contribution of each gravitational degree of freedom to the O(?) part of the effective potential is significantly greater than that of a scalar or spinor in the same background geometry. No stable minima of the effective potential exist for 3 ≤ N ≤ 13. Geometries which may be interpreted as “unstable solutions” are found for all N from 3 through 13. These results, obtained in Lorentz-signature spacetimes, differ from those obtained by “euclideanization”; our “euclideanized” results agree with those obtained by Chodos and Myers using a different regularization scheme.     

Non-Abelian vortex in four dimensions as a critical superstring

We discuss recent progress in describing a certain non-Abelian vortex string as a critical superstring on a conifold and clarify some subtle points. This particular solitonic vortex is supported in four-dimensional supersymmetric QCD with the gauge group, N _f = 4 quark flavors and the Fayet–Iliopoulos term. Under certain conditions, the non-Abelian vortex can become infinitely thin and can be interpreted as a critical ten-dimensional superstring. In addition to four translational moduli, the non-Abelian vortex under consideration carries six orientational and size moduli. The vortex moduli dynamics are described by a twodimensional sigma model with the target space ?⁴ × Y ₆, where Y ₆ is a non-compact Calabi–Yau conifold. The closed string states that emerge in four dimensions (4D) are identified with hadrons of 4D bulk N= 2 QCD. It turns out that most of the states arising from the ten-dimensional graviton spectrum are non-dynamical in 4D. A single dynamical massless hypermultiplet associated with the deformation of the complex structure of the conifold is found. It is interpreted as a monopole–monopole baryon of the 4D theory (at strong coupling).     

QCD sum rules and radial excitations of light pseudoscalar and scalar mesons

The calculations of masses and decay constants of the radial excitations of light pseudoscalar and scalar mesons within the QCD sum rules method are briefly reviewed. The predictions are based on the 1/N _c -supported model spectra, which consist of an infinite number of infinitely narrow resonances, and on the assumption that the ground states of light scalar mesons may be considered as \(\bar qq\)-bound states. The results of the studies are compared with the existing experimental data and with the predictions of other theoretical approaches.     

The diagrammatic structure of deep inelastic scattering in asymptotically free theories

We investigate the structure of the leading diagrams in QCD. The diagrams of a simple scalar gluon model form the basis of a generalisation to the more complicated vector gluon theory. It is found that a certain set of a generalised ladder diagrams gives the standard QCD result for the non-singlet structure function in the limit x → 1. A simple brems-strahlung model is presented which forms a useful link between QCD field theory and more intuitive parton formulations. The value of a diagrammatic treatment is that it provides an accessible approach to the discussion of other processes such as the Drell-Yan mechanism for heavy muon pair production.     

On AdS/QCD correspondence and the partonic picture of deep inelastic scattering

We critically examine the question of scaling of the Deep Inelastic Scattering process in the medium Bjorken x region on a scalar boson in the framework of the AdS/QCD correspondence. To get the right polarization structure of the forward electroproduction amplitude, we show that one needs to add (at least) the scalar to scalar and scalar to vector hadronic amplitudes. This illustrates how the partonic picture may emerge from a simple scenario based on the AdS/QCD correspondence, provided one allows the conformal dimension of the hadronic field to equal 1 and use the concept of “hadron–parton duality”.     

Fermions and stability in quantum Kaluza-Klein theories

The effective action for spinor fields propagating in a time-dependent Kaluza-Klein background geometry is calculated explicitly to one-loop order in an adiabatic approximation. This result is used in a stability analysis of the Candelas-Weinberg model. It is found that the “internal” space (which we choose to be an odd-dimensional sphere S_N) is stable against small, uniform oscillations only if the ratio of the number of scalar fields to the number of spinor fields is greater than a certain minimum value.It is also shown that oscillations of the internal space produce conformal gravity waves in the four-dimensional space.     

NNLO QCD corrections to the resonant sneutrino/slepton production at hadron colliders

We present a complete next to next to leading order QCD corrections to the resonant production of sneutrino and charged slepton at the Tevatron and the Large Hadron Collider within the context of R-parity violating supersymmetric model. We have demonstrated the role of NNLO QCD corrections in reducing uncertainties resulting from renormalisation and factorisation scales and thereby making our predictions reliable. We have incorporated soft gluon effects at N³LO${\mathrm{N}}^3\mathrm{LO}$ level in order to study the stability of our results under perturbation. The results obtained in this article are also applicable to resonance production of any color-neutral scalar coupled to fermions through Yukawa interaction.     

Effects of threshold resummation

We investigate effects of threshold resummation of logarithmic corrections lnN in Mellin space quantitatively. Threshold resummation leads to enhancement of next-to-leading-order QCD predictions for jet production at large jet transverse energy, which is in the trend indicated by experimental data. We show that this enhancement is completely determined by the behavior of threshold resummation at small N, the region where hierarchy among different powers of lnN is lost and current next-to-leading-logarithm resummation is not reliable. Our analysis indicates that more accurate threshold resummation formalism should be developed in order to obtain convincing predictions.