Limitations on Dimensional Regularization in Renyi Entropy

Dimensional regularization is a common method used to regulate the UV divergence of field theoretic quantities. When it is used in the context of Renyi entropy, however, it is important to consider whether such a procedure eliminates the statistical interpretation thereof as a measure of entanglement of states living on a Hilbert space. We therefore examine the dimensionally regularized Renyi entropy of a 4d unitary CFT and show that it admits no underlying Hilbert space in the state-counting sense. This gives a concrete proof that dimensionally regularized Renyi entropy cannot always be obtained as a limit of the Renyi entropy of some finite-dimensional quantum system.Comment: 10 pages; v2: Minor corrections of typos; v3: Small modification of conclusion sectio

LHC Signatures of Two-Higgs-Doublets with Fourth Family

On-going Higgs searches in the light mass window are of vital importance for testing the Higgs mechanism and probing new physics beyond the standard model (SM). The latest ATLAS and CMS searches for the SM Higgs boson at the LHC (7TeV) found some intriguing excesses of events in the \gamma\gamma/VV^* channels (V=Z,W) around the mass-range of 124-126 GeV. We explore a possible explanation of the \gamma\gamma and VV^* signals from the light CP-odd Higgs A^0 or CP-even Higgs h^0 from the general two-Higgs-doublet model with fourth-family fermions. We demonstrate that by including invisible decays of the Higgs boson A^0 or h^0 to fourth-family neutrinos, the predicted \gamma\gamma and VV^* signals can explain the observed new signatures at the LHC, and will be further probed by the forthcoming LHC runs in 2012.Comment: 22pp, 10 Figs, JHEP published version, references adde

Statistical computation of Boltzmann entropy and estimation of the optimal probability density function from statistical sample

In this work, we investigate the statistical computation of the Boltzmann entropy of statistical samples. For this purpose, we use both histogram and kernel function to estimate the probability density function of statistical samples. We find that, due to coarse-graining, the entropy is a monotonic increasing function of the bin width for histogram or bandwidth for kernel estimation, which seems to be difficult to select an optimal bin width/bandwidth for computing the entropy. Fortunately, we notice that there exists a minimum of the first derivative of entropy for both histogram and kernel estimation, and this minimum point of the first derivative asymptotically points to the optimal bin width or bandwidth. We have verified these findings by large amounts of numerical experiments. Hence, we suggest that the minimum of the first derivative of entropy be used as a selector for the optimal bin width or bandwidth of density estimation. Moreover, the optimal bandwidth selected by the minimum of the first derivative of entropy is purely data-based, independent of the unknown underlying probability density distribution, which is obviously superior to the existing estimators. Our results are not restricted to one-dimensional, but can also be extended to multivariate cases. It should be emphasized, however, that we do not provide a robust mathematical proof of these findings, and we leave these issues with those who are interested in them.Comment: 8 pages, 6 figures, MNRAS, in the pres