We discuss the theoretical bases that underpin the automation of the computations of tree-level and next-to-leading order cross sections, of their matching to parton shower simulations, and of the merging of matched samples that differ by light-parton multiplicities. We present a computer program, MadGraph5 aMC@NLO, capable of handling all these computations — parton-level fixed order, shower-matched, merged — in a unified framework whose defining features are flexibility, high level of parallelisation, and human intervention limited to input physics quantities. We demonstrate the potential of the program by presenting selected phenomenological applications relevant to the LHC and to a 1-TeV e + e − collider. While next-to-leading order results are restricted to QCD corrections to SM processes in the first public version, we show that from the user viewpoint no changes have to be expected in the case of corrections due to any given renormalisable Lagrangian, and that the implementation of these are well under way.

/pdf/the-automated-computation-of-tree-level-and-next-to-leading-4etm0g6w46.pdf

The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations

Tables of integrals

Critical phenomena and renormalization-group theory

Non-perturbative renormalization flow in quantum field theory and statistical physics

Recently the series for two renormalization group functions (corresponding to the anomalous dimensions of the fields and ) of the three-dimensional field theory have been extended to next order (seven loops) by Murray and Nickel. We examine the influence of these additional terms on the estimates of critical exponents of the N-vector model, using some new ideas in the context of the Borel summation techniques. The estimates have slightly changed, but remain within the errors of the previous evaluation. Exponents such as (related to the field anomalous dimension), which were poorly determined in the previous evaluation of Le Guillou-Zinn-Justin, have seen their apparent errors significantly decrease. More importantly, perhaps, summation errors are better determined. The change in exponents affects the recently determined ratios of amplitudes and we report the corresponding new values. Finally, because an error has been discovered in the last order of the published expansions (order ), we have also re-analysed the determination of exponents from the -expansion. The conclusion is that the general agreement between -expansion and three-dimensional series has improved with respect to Le Guillou-Zinn-Justin.

https://iopscience.iop.org/article/10.1088/0305-4470/31/40/006/pdf

Critical exponents of the N-vector model

The equation of state of the universality class of the 3D Ising model is determined numerically in the critical domain from quantum field theory and renormalization group techniques. The starting point is the five loop perturbative expansion of the effective potential (or free energy) in the framework of renormalized $\phi^4_3$ field theory. The 3D perturbative expansion is summed, using a Borel transformation and a mapping based on large order behaviour results. It is known that the equation of state has parametric representations which incorporate in a simple way its scaling and regularity properties. We show that such a representation can be used to accurately determine it from the knowledge of the few first coefficients of the expansion for small magnetization. Revised values of amplitude ratios are deduced. Finally we compare the 3D values with the results obtained by the same method from the $\epsilon=4-d$ expansion.

3D Ising Model:The Scaling Equation of State

3D Ising model: the scaling equation of state

Short distance behavior of string theories is investigated by the use of the discretized path-integral formulation. In particular, the minimum physical length and the generalized uncertainty relation are re-derived from a set of Ward–Takahashi identities. Several issues related to the form of the generalized uncertainty relation and to its implications are discussed. A consistent qualitative picture of short distance behavior of string theory seems to emerge from such a study.

Riccardo Guida

Papers

Critical exponents of the N-vector model

3D Ising Model:The Scaling Equation of State

3D Ising model: the scaling equation of state

On the short distance behavior of string theories

Gauge invariance