Numerical Examples In Physics By Nn Ghosh Pdf Download [REPACK]

Continuous and two-point variations are ad hoc techniques commonly used in the particle physics community to have some handle over these difficult-to-estimate uncertainties. Generating multiple simulations from different fragmentation models allows us to probe two points in an under-explored theory space of fragmentation models. The difference between these two models provides only a rough estimate of how different nature may be to either of them. Varying unphysical scales would not change the observed physics if the full calculations could be performed. The sensitivity of our simulations to these scale variations therefore provides a rough estimate of the uncertainty associated with truncating the calculations at lower order. While the numerical value of uncertainties coming from statistically interpretable origins is well trusted, the kind of theoretical uncertainties discussed above only provide a rough estimate. This is in contrast to experimental nuisance parameters (that give rise to experimental uncertainties), including the jet energy scale. Such nuisance parameters are constrained using calibration datasets. The statistical uncertainty of the control region becomes a systematic uncertainty for the experimental nuisance parameters. This justifies treating the corresponding nuisance parameters as (approximate) Gaussian random variables. A detailed discussion of the origin and validity of theory uncertainties is outside the scope of this paper.

Mellin-Barnes (MB) integrals are well-known objects appearing in many branches of mathematics and physics, ranging from hypergeometric functions theory to quantum field theory, solid-state physics, asymptotic theory, etc. Although MB integrals have been studied for more than one century, until now there has been no systematic computational technique of the multiple series representations of N-fold MB integrals for N>2. Relying on a simple geometrical analysis based on conic hulls, we show here a solution to this important problem. Our method can be applied to resonant (i.e., logarithmic) and nonresonant cases and, depending on the form of the MB integrand, it gives rise to convergent series representations or diverging asymptotic ones. When convergent series are obtained, the method also allows, in general, the determination of a single "master series" for each series representation, which considerably simplifies convergence studies and/or numerical checks. We provide, along with this Letter, a Mathematica implementation of our technique with examples of applications. Among them, we present the first evaluation of the hexagon and double box conformal Feynman integrals with unit propagator powers.