On-shell methods in perturbative QCD

We review on-shell methods for computing multi-parton scattering amplitudes in perturbative QCD, utilizing their unitarity and factorization properties. We focus on aspects which are useful for the construction of one-loop amplitudes needed for phenomenological studies at the Large Hadron Collider.     

Renormalization group functions for the radiative symmetry breaking scheme

We obtain the renormalization group (RG) functions for the massless scalar field theory where symmetry breaking occurs radiatively. After obtaining the effective potential for the radiative symmetry breaking scheme by finite transformations for the classical field and coupling constant, we obtain the corresponding RG functions from that of the minimal subtraction (MS) scheme.     

Two-loop parameter relations between dimensional regularization and dimensional reduction applied to SUSY-QCD

The two-loop relations between the running gluino–quark–squark coupling, the gluino and the quark mass defined in dimensional regularization (DREG) and dimensional reduction (DRED) in the framework of SUSY-QCD are presented. Furthermore, we verify with the help of these relations that the three-loop β-functions derived in the minimal subtraction scheme combined with DREG or DRED transform into each other. This result confirms the equivalence of the two schemes at the three-loop order, if applied to SUSY-QCD.     

Orientifolds and slumps in G2 and Spin(7) metrics

We discuss some new metrics of special holonomy, and their roles in string theory and M-theory. First we consider Spin(7) metrics denoted by , which are complete on a complex line bundle over . The principal orbits are S⁷, described as a triaxially squashed S³ bundle over S⁴. The behaviour in the S³ directions is similar to that in the Atiyah–Hitchin metric, and we show how this leads to an M-theory interpretation with orientifold D6-branes wrapped over S⁴. We then consider new G₂ metrics which we denote by , which are complete on an bundle over T^1,1, with principal orbits that are S³×S³. We study the metrics using numerical methods, and we find that they have the remarkable property of admitting a U(1) Killing vector whose length is nowhere zero or infinite. This allows one to make an everywhere non-singular reduction of an M-theory solution to give a solution of the type IIA theory. The solution has two non-trivial S² cycles, and both carry magnetic charge with respect to the R–R vector field. We also discuss some four-dimensional hyper-Kähler metrics described recently by Cherkis and Kapustin, following earlier work by Kronheimer. We show that in certain cases these metrics, whose explicit form is known only asymptotically, can be related to metrics characterised by solutions of the su(∞) Toda equation, which can provide a way of studying their interior structure.     

On de Sitter vacua in type IIA orientifold compactifications

This Letter discusses the orientifold projection of the quantum corrections to type IIA strings compactified on rigid Calabi–Yau threefolds. It is shown that N=2$N=2$ membrane instanton effects give a holomorphic contribution to the superpotential, while the perturbative corrections enter into the Kähler potential. At the level of the scalar potential the corrections to the Kähler potential give rise to a positive energy contribution similar to adding anti-D3-branes in the KKLT scenario. This provides a natural mechanism to lift an AdS vacuum to a meta-stable dS vacuum.     

Anomaly structure of supergravity and anomaly cancellation

We display the full anomaly structure of supergravity, including new contributions to the conformal anomaly. Our result has the super-Weyl and Kähler U(1)$U(1)$, transformation properties that are required for implementation of the Green–Schwarz mechanism for anomaly cancellation.     

Field strength formulation,lattice Bianchi identities and perturbation theory for non-Abelian models

We develop an analytical approach for studying lattice gauge theories within the plaquette representation where the plaquette matrices play the role of the fundamental degrees of freedom. We start from the original Batrouni formulation and show how it can be modified in such a way that each non-Abelian Bianchi identity contains only two connectors instead of four. In addition, we include dynamical fermions in the plaquette formulation. Using this representation we construct the low-temperature perturbative expansion for U(1)$U(1)$ and SU(N)$\mathit{SU}(N)$ models and discuss its uniformity in the volume. The final aim of this study is to give a mathematical background for working with non-Abelian models in the plaquette formulation.     

Semi-inclusive deep inelastic scattering at small-x

We study the semi-inclusive hadron production in deep inelastic scattering at small-x. A transverse-momentum-dependent factorization is found consistent with the results calculated in the small-x approaches, such as the color-dipole framework and the color glass condensate, in the appropriate kinematic region at the lowest order. The transverse-momentum-dependent quark distribution can be studied in this process as a probe for the small-x saturation physics. Especially, the ratio of quark distributions as a function of transverse momentum at different x   demonstrates strong dependence on the saturation scale. The Q²$Q^2$ dependence of the same ratio is also studied by applying the Collins–Soper–Sterman resummation method.     

ERBL and DGLAP kernels for transversity distributions. Two-loop calculations in covariant gauge

The results of a two-loop calculation in the Feynman gauge of both the DGLAP and the ERBL evolution kernels for transversely polarized distributions are presented. The structure of these evolution kernels is discussed in detail. In addition, the effect of the two-loop evolution on the distribution amplitude of a twist-2 transversely polarized meson is explored.     

Brane gravitational interactions from 6D supergravity

We investigate the massive graviton contributions to 4D gravity in a 6D brane world scenario, whose bulk field content can include that of 6D chiral gauged supergravity. We consider a general class of solutions having 3-branes, 4D Poincaré symmetry and axisymmetry in the internal space. We show that these contributions, which we compute analytically, can be independent of the brane vacuum energy as a consequence of geometrical and topological properties of the above-mentioned codimension two brane world. These results support the idea that in such models the gravitational interactions may be decoupled from the brane vacuum energy.     

Two-loop threshold singularities,unstable particles and complex masses

The effect of threshold singularities induced by unstable particles on two-loop observables is investigated and it is shown how to cure them working in the complex-mass scheme. The impact on radiative corrections around thresholds is thoroughly analyzed and shown to be relevant for two selected LHC and ILC applications: Higgs production via gluon fusion and decay into two photons at two loops in the Standard Model. Concerning Higgs production, it is essential to understand possible sources of large corrections in addition to the well-known QCD effects. It is shown that NLO electroweak corrections can incongruently reach a 10% level around the WW vector-boson threshold without a complete implementation of the complex-mass scheme in the two-loop calculation.     

Pseudo-differential equations,and the Bethe ansatz for the classical Lie algebras

The correspondence between ordinary differential equations and Bethe ansatz equations for integrable lattice models in their continuum limits is generalised to vertex models related to classical simple Lie algebras. New families of pseudo-differential equations are proposed, and a link between specific generalised eigenvalue problems for these equations and the Bethe ansatz is deduced. The pseudo-differential operators resemble in form the Miura-transformed Lax operators studied in work on generalised KdV equations, classical W-algebras and, more recently, in the context of the geometric Langlands correspondence. Negative-dimension and boundary-condition dualities are also observed.     

NLO electroweak corrections to Higgs boson production at hadron colliders

Results for the complete NLO electroweak corrections to Standard Model Higgs production via gluon fusion are included in the total cross section for hadronic collisions. Artificially large threshold effects are avoided working in the complex-mass scheme. The numerical impact at LHC (Tevatron) energies is explored for Higgs mass values up to 500 GeV (200 GeV). Assuming a complete factorization of the electroweak corrections, one finds a +5% shift with respect to the NNLO QCD cross section for a Higgs mass of 120 GeV both at the LHC and the Tevatron. Adopting two different factorization schemes for the electroweak effects, an estimate of the corresponding total theoretical uncertainty is computed.     

On the formulation of D = 11 supergravity and the composite nature of its three-form gauge field

The underlying gauge group structure of the D = 11 Cremmer-Julia-Scherk supergravity becomes manifest when its three-form field A₃ is expressed through a set of one-form gauge fields, , , η_1α, and E^a, ψ^α. These are associated with the generators of the elements of a family of enlarged supersymmetry algebras parametrized by a real number s. We study in detail the composite structure of A₃ extending previous results by D’Auria and Fré, stress the equivalence of the above problem to the trivialization of a standard supersymmetry algebra E^(11|32) cohomology four-cocycle on the enlarged superalgebras, and discuss its possible dynamical consequences. To this aim we consider the properties of the first order supergravity action with a composite A₃ field and find the set of extra gauge symmetries that guarantee that the field theoretical degrees of freedom of the theory remain the same as with a fundamental A₃. The extra gauge symmetries are also present in the so-called rheonomic treatment of the first order D = 11 supergravity action when A₃ is composite. Our considerations on the composite structure of A₃ provide one more application of the idea that there exists an extended superspace coordinates/fields correspondence. They also suggest that there is a possible embedding of D = 11 supergravity into a theory defined on the enlarged superspace .     

Dimension six corrections to the vector sector of AdS/QCD model

We study the effects of dimension six terms on the predictions of the holographic model for the vector meson form factors and determine the corrections to the electric radius, the magnetic and the quadrupole moments of the ρ  -meson. We show that the only dimension six terms which contribute nontrivially to the vector meson form factors are X²F²$X^2{F}^2$ and F³$F^3$. It appears that the effect from the former term is equivalent to the metric deformation and can change only masses, decay constants and charge radii of vector mesons, leaving the magnetic and the quadrupole moments intact. The latter term gives different contributions to the three form factors of the vector meson and changes the values of the magnetic and the quadrupole moments. The results suggest that the addition of the higher dimension terms improves the holographic model.     

Gauge-invariant sub-structures of tree-level double-emission exact QCD spin amplitudes

In this note we discuss possible separations of exact, massive, tree-level spin amplitudes into gauge-invariant parts. We concentrate our attention on processes involving two quarks entering a color-neutral current and, thanks to the QCD interactions, two extra external gluons. We will search for forms compatible with parton-shower languages, without applying approximations or restrictions on phase space regions. Special emphasis will be put on the isolation of parts necessary for the construction of evolution kernels for individual splittings and to some degree for the running coupling constant as well. Our aim is to better understand the environment necessary to optimally match hard matrix elements with parton-shower algorithms. To avoid complications and ambiguities related to regularization schemes, we ignore, at this point, virtual corrections. Our representation is quite universal: any color-neutral current can be used; in particular, our approach is not restricted to vector currents only. This work is partially supported by RTN European Programme, MRTN-CT-2006-035505 (HEPTOOLS, Tools and Precision Calculations for Physics Discoveries at Colliders).     

(Non-)anomalous D-brane and O-plane couplings: the normal bundle

The direct string computation of anomalous D-brane and orientifold plane couplings is extended to include the curvature of the normal bundle. The normalization of these terms is fixed unambiguously. New, non-anomalous gravitational couplings are found.