Maria Laura Piscopo — Page 2

arXiv2020

Renormalisation scale setting for D-mixing

A naive application of the heavy quark expansion (HQE) yields theory estimates for the decay rate of neutral $D$ mesons that are four orders of magnitude below the experimental determination. It is well known that this huge suppression results from severe GIM cancellations. We find that this mismatch can be solved by individually choosing the renormalisation scale of the different internal quark contributions. For $b$ and $c$ hadron lifetimes, as well as for the decay rate difference of neutral $B$ mesons the effect of our scale setting procedure lies within the previously quoted theory uncertainties, while we get enlarged theory uncertainties for the semi-leptonic CP asymmetries in the $B$ system.

hep-ph↗

arXiv2019

Solving differential equations with neural networks: Applications to the calculation of cosmological phase transitions

Starting from the observation that artificial neural networks are uniquely suited to solving optimisation problems, and most physics problems can be cast as an optimisation task, we introduce a novel way of finding a numerical solution to wide classes of differential equations. We find our approach to be very flexible and stable without relying on trial solutions, and applicable to ordinary, partial and coupled differential equations. We apply our method to the calculation of tunnelling profiles for cosmological phase transitions, which is a problem of relevance for baryogenesis and stochastic gravitational wave spectra. Comparing our solutions with publicly available codes which use numerical methods optimised for the calculation of tunnelling profiles, we find our approach to provide at least as accurate results as these dedicated differential equation solvers, and for some parameter choices even more accurate and reliable solutions. In particular, we compare the neural network approach with two publicly available profile solvers, \texttt{CosmoTransitions} and \texttt{BubbleProfiler}, and give explicit examples where the neural network approach finds the correct solution while dedicated solvers do not. We point out that this approach of using artificial neural networks to solve equations is viable for any problem that can be cast into the form $\mathcal{F}(\vec{x})=0$, and is thus applicable to various other problems in perturbative and non-perturbative quantum field theory.

hep-ph↗