The ρ\rho parameter at three loops and elliptic integrals

We describe the analytic calculation of the master integrals required to compute the two-mass three-loop corrections to the $\rho$ parameter. In particular, we present the calculation of the master integrals for which the corresponding differential equations do not factorize to first order. The homogeneous solutions to these differential equations are obtained in terms of hypergeometric functions at rational argument. These hypergeometric functions can further be mapped to complete elliptic integrals, and the inhomogeneous solutions are expressed in terms of a new class of integrals of combined iterative non-iterative nature.Comment: 14 pages Latex, 7 figures, to appear in the Proceedings of "Loops and Legs in Quantum Field Theory - LL 2018", 29 April - 4 May 2018, Po

Perturbative dynamics of matrix string for the membrane

Recently Sekino and Yoneya proposed a way to regularize the world volume theory of membranes wrapped around $S^1$ by matrices and showed that one obtains matrix string theory as a regularization of such a theory. We show that this correspondence between matrix string theory and wrapped membranes can be obtained by using the usual M(atrix) theory techniques. Using this correspondence, we construct the super-Poincare generators of matrix string theory at the leading order in the perturbation theory. It is shown that these generators satisfy 10 dimensional super-Poincar\'e algebra without any anomaly.Comment: 23 pages, 1 figur

The process gg -> WW as a background to the Higgs signal at the LHC

The production of W pairs from the one-loop gluon fusion process is studied. Formulas are presented for the helicity amplitudes keeping the top mass finite, but all other quark masses zero. The correlations among the leptons coming from the W bosons are kept. The contribution of this background to the Higgs boson search in the WW decay mode at the LHC is estimated by applying the cuts foreseen in experimental searches using the PYTHIA Monte Carlo program. Kinematic distributions for the final state leptons are compared to those of the Higgs boson signal and of the q qbar -> WW background. After applying final cuts, the gg background is found to be large, at the level of 35% of the q qbar background.The characteristics of the gg background are very similar to those of the signal. Therefore, an experimental normalization of this background component appears to be very difficult and the uncertainty must largely be determined by theory. As a result, the significance of a Higgs signal in the gg -> H -> WW mode at the LHC is reduced.Comment: 24 pages, 4 figure