Separation probabilities for products of permutations

We study the mixing properties of permutations obtained as a product of two uniformly random permutations of fixed cycle types. For instance, we give an exact formula for the probability that elements $1,2,...,k$ are in distinct cycles of the random permutation of $\{1,2,...,n\}$ obtained as product of two uniformly random $n$-cycles

No-signaling, perfect bipartite dichotomic correlations and local randomness

The no-signaling constraint on bi-partite correlations is reviewed. It is shown that in order to obtain non-trivial Bell-type inequalities that discern no-signaling correlations from more general ones, one must go beyond considering expectation values of products of observables only. A new set of nontrivial no-signaling inequalities is derived which have a remarkably close resemblance to the CHSH inequality, yet are fundamentally different. A set of inequalities by Roy and Singh and Avis et al., which is claimed to be useful for discerning no-signaling correlations, is shown to be trivially satisfied by any correlation whatsoever. Finally, using the set of newly derived no-signaling inequalities a result with potential cryptographic consequences is proven: if different parties use identical devices, then, once they have perfect correlations at spacelike separation between dichotomic observables, they know that because of no-signaling the local marginals cannot but be completely random.Comment: Published in 'Proceedings of the International Conference Advances in Quantum Theory', AIP Conference Proceedings, vol. 1327, 2011. pp. 36-5

Precision studies of the Higgs boson decay channel H -> ZZ -> 4l with MEKD

The importance of the H -> ZZ -> 4l "golden" channel was shown by its major role in the discovery, by the ATLAS and CMS collaborations, of a Higgs-like boson with mass near 125 GeV. We analyze the discrimination power of the matrix element method both for separating the signal from the irreducible ZZ background and for distinguishing various spin and parity hypotheses describing a signal in this channel. We show that the proper treatment of interference effects associated with permutations of identical leptons in the four electron and four muon final states plays an important role in achieving the best sensitivity in measuring the properties of the newly discovered boson. We provide a code, MEKD, that calculates kinematic discriminants based on the full leading order matrix elements and which will aid experimentalists and phenomenologists in their continuing studies of the H -> ZZ -> 4l channel.Comment: Major revision: added new sections discussing spin/ parity determination and the importance of using the full matrix element for the same flavor final state (involving both pairings of the leptons). Also added new functionality, including the most general couplings of a spin-0 or spin-2 boson to gluons and Zs, to the publicly-available code, MEKD, presented in this paper. 43 pages, 15 figure

First Measurements of Spin Correlation Using Semi-leptonic ttˉt\bar{t} Events at ATLAS

The top quark decays before it hadronizes. Before its spin state can be changed in a process of strong interaction, it is directly transferred to the top quark decay products. The top quark spin can be deduced by studying angular distributions of the decay products. The Standard Model predicts the top/anti-top quark ($t\bar{t}$) pairs to have correlated spins. The degree is sensitive to the spin and the production mechanisms of the top quark. Measuring the spin correlation allows to test the predictions. New physics effects can be reflected in deviations from the prediction. The measurement of the spin correlation of $t\bar{t}$ pairs, produced at the LHC with a center-of-mass energy of $\sqrt{s} = 7$ TeV and reconstructed with the ATLAS detector, is presented. The dataset corresponds to an integrated luminosity of 4.6 $\textrm{fb}^{-1}$. $t\bar{t}$ pairs are reconstructed in the $\ell$+jets channel using a kinematic likelihood fit offering the identification of light up- and down-type quarks from the $t \rightarrow bW \rightarrow bq\bar{q}'$ decay. The spin correlation is measured via the distribution of the azimuthal angle $\Delta \phi$ between two top quark spin analyzers in the laboratory frame. It is expressed as the degree of $t\bar{t}$ spin correlation predicted by the Standard Model, $f_{\textrm{SM}}$. The result of $f_{\textrm{SM}}= 1.12 \pm 0.11\,\text{(stat.)} \pm 0.22\,\text{(syst.)}$ is consistent with the Standard Model prediction of $f_{\textrm{SM}}= 1.0$.Comment: 4 pages, 3 figures, to appear in the proceedings of Top2014, Cannes, France (28th Sept - 3rd Oct 2014

Riffle shuffles with biased cuts

The well-known Gilbert-Shannon-Reeds model for riffle shuffles assumes that the cards are initially cut 'about in half' and then riffled together. We analyze a natural variant where the initial cut is biased. Extending results of Fulman (1998), we show a sharp cutoff in separation and L-infinity distances. This analysis is possible due to the close connection between shuffling and quasisymmetric functions along with some complex analysis of a generating function.Comment: 10 page