Particle theory

Abstract:

In this paper, we study positive monad vector bundles on complete intersection Calabi-Yau manifolds in the context of E 8 × E 8 heterotic string compactifications. We show that the class of such bundles, subject to the heterotic anomaly condition, is finite and consists of about 7000 models. We explain how to compute the complete particle spectrum for these models. In particular, we prove the absence of vector-like family anti-family pairs in all cases. We also verify a set of highly non-trivial necessary conditions for the stability of the bundles. A full stability proof will appear in a companion paper. A scan over all models shows that even a few rudimentary physical constraints reduces the number of viable models drastically.

Abstract:

Interpreting the way that the SU(3) bare lattice coupling runs with the lattice spacing is complicated by the fact that there is a smooth cross-over region in which the strong coupling expansion transforms into a weak-coupling one. For N 5, however, there is a first order bulk transition that cleanly separates the strong and weak coupling regimes. We find that in this case the calculated string tension can be readily fitted throughout the weak coupling region by a standard 3-loop expression modified by lattice spacing corrections of the expected form. While our fits demand the presence of the latter, they do not constrain the perturbative coupling scheme enough to enable us to extract a usefully accurate value of a(β) in units of Λ MS. To resolve this ambiguity we turn to SU(3) where we use the Schrodinger Functional coupling scheme to extract a value of r 0Λ SF as a benchmark. We then find that the Parisi mean-field improved coupling scheme closely reproduces this result. We also develop a comparison between different schemes that does not rely on the calculation of any physical quantity and which can therefore be applied much further into weak coupling. Again the Parisi scheme is favoured over the others that we compare. Using the mean-field scheme we have fitted the values of the string tension a 2σ that have been calculated for 2 N 8, to obtain Λ MS/σ = 0.503(2)(40)+0.33(3)(3)/N 2 for N 3, where the first error is statistical and the second is our estimate of the systematic error from all sources.

Abstract:

We show that the geometric scaling of the total virtual photon-proton cross section data can be explained using standard linear Dokshitzer-Gribov-Altarelli-Parisi perturbative evolution with generic boundary conditions in a wide kinematic region. This allows us to single out the region where geometric scaling may provide evidence for parton saturation.