The global electroweak Standard Model fit after the Higgs discovery

We present an update of the global Standard Model (SM) fit to electroweak precision data under the assumption that the new particle discovered at the LHC is the SM Higgs boson. In this scenario all parameters entering the calculations of electroweak precision observalbes are known, allowing, for the first time, to over-constrain the SM at the electroweak scale and assert its validity. Within the SM the W boson mass and the effective weak mixing angle can be accurately predicted from the global fit. The results are compatible with, and exceed in precision, the direct measurements. An updated determination of the S, T and U parameters, which parametrize the oblique vacuum corrections, is given. The obtained values show good consistency with the SM expectation and no direct signs of new physics are seen. We conclude with an outlook to the global electroweak fit for a future e+e- collider.Comment: 10 pages, 7 figures. Update: added a reference. To be published in the proceedings of the Rencontres de Moriond, La Thuile, Valle d'Aosta, Italy, 2-16 March, 201

On the Cauchy--Rassias Inequality and Linear n-Inner Product Preserving Mappings

We prove the Cauchy-Rassias stability of linear n-inner product preserving mappings in $n$-inner product Banach spaces. We apply the Cauchy-Rassias inequality that plays an influencial role in the subject of functional equations. The inequality was introduced for the first time by Th.M.Rassias in his paper entitled: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math.Soc. 72(1978), 297-300.Comment: 13 pages, Added references, and title and abstract change

Interpolation between multi-dimensional histograms using a new non-linear moment morphing method

A prescription is presented for the interpolation between multi-dimensional distribution templates based on one or multiple model parameters. The technique uses a linear combination of templates, each created using fixed values of the model's parameters and transformed according to a specific procedure, to model a non-linear dependency on model parameters and the dependency between them. By construction the technique scales well with the number of input templates used, which is a useful feature in modern day particle physics, where a large number of templates is often required to model the impact of systematic uncertainties.Comment: 20 pages, 6 figures. Algorithm publicly available in RooFi