An interesting alternative to supersymmetry (SUSY) for extending physics beyond the Standard Model is a model with universal extra dimensions (UED), in which the SUSY superpartners are replaced by Kaluza-Klein excitations of the Standard Model particles. If new particles are discovered at the LHC, even if their mass spectrum favours SUSY or UED, it will be vital to distinguish between their spin assignments in the two models as far as possible. We extend the method proposed by Barr [1] to the UED case and investigate the angular and charge asymmetries of decay distributions for sample mass spectra of both SUSY and UED types. For hierarchical ('SUSY-type') mass spectra there is a good chance of distinguishing the spin structures of the two models. However, a mass spectrum of the quasi-degenerate type expected in UED would make it difficult to observe spin correlations.

We study the structure of soft gluon corrections to multi-leg scattering amplitudes in a non-Abelian gauge theory by analysing the corresponding product of semi-infinite Wilson lines. We prove that diagrams exponentiate such that the colour factors in the exponent are fully connected. This completes the generalisation of the non-Abelian exponentiation theorem, previously proven in the case of a Wilson loop, to the case of multiple Wilson lines in arbitrary representations of the colour group. Our proof is based on the replica trick in conjunction with a new formalism where multiple emissions from a Wilson line are described by effective vertices, each having a connected colour factor. The exponent consists of connected graphs made out of these vertices. We show that this readily provides a general colour basis for webs. We further discuss the kinematic combinations that accompany each connected colour factor, and explicitly catalogue all three-loop examples, as necessary for a direct computation of the soft anomalous dimension at this order.

We discuss the universal behaviour of scattering cross sections in the limit of infinite rapidity separation between all produced particles, and illustrate the behaviour explicitly for the production of n jets, W + n jets, Z + n jets for n = 2, 3, 4, and for H + 2, 3 jets. We give a set of rules for constructing scattering cross sections, which are exact in the given limit, and order-by-order reproduce well the full fixed order results when applied to LHC phenomenology. The approximation includes both real and virtual corrections, and is sufficiently simple to allow for the regulated all-order perturbative sum to be explicitly constructed. We test the expected accuracy by comparing results order-by-order with full fixed-order perturbation theory for the processes mentioned above.

If new particles are discovered at the LHC, it will be important to determine their spins in as model-independent a way as possible. We consider the case, commonly encountered in models of physics beyond the Standard Model, of a new scalar or fermion D decaying sequentially into other new particles C, B, A via the decay chain D → Cq, C → Bl near , B → Al far , l near and l far being opposite-sign same-flavour charged leptons and A being invisible. We compute the observable 2-and 3-particle invariant mass distributions for all possible spin assignments of the new particles, and discuss their distinguishability using a quantitative measure known as the Kullback-Leibler distance.

We consider the recently developed diagrammatic approach to soft-gluon exponentiation in multiparton scattering amplitudes, where the exponent is written as a sum of webs -closed sets of diagrams whose colour and kinematic parts are entangled via mixing matrices. A complementary approach to exponentiation is based on the multiplicative renormalizability of intersecting Wilson lines, and their subsequent finite anomalous dimension. Relating this framework to that of webs, we derive renormalization constraints expressing all multiple poles of any given web in terms of lower-order webs. We examine these constraints explicitly up to four loops, and find that they are realised through the action of the web mixing matrices in conjunction with the fact that multiple pole terms in each diagram reduce to sums of products of lower-loop integrals. Relevant singularities of multi-eikonal amplitudes up to three loops are calculated in dimensional regularization using an exponential infrared regulator. Finally, we formulate a new conjecture for web mixing matrices, involving a weighted sum over column entries. Our results form an important step in understanding non-Abelian exponentiation in multiparton amplitudes, and pave the way for higher-loop computations of the soft anomalous dimension.