A Few Finite Trigonometric Sums

Finite trigonometric sums occur in various branches of physics, mathematics, and their applications. These sums may contain various powers of one or more trigonometric functions. Sums with one trigonometric function are known, however sums with products of trigonometric functions can get complicated and may not have a simple expressions in a number of cases. Some of these sums have interesting properties and can have amazingly simple value. However, only some of them are available in literature. We obtain a number of such sums using method of residues.Comment: 11 pages, added references, corrected typo

Gluon Fusion Contribution to VHjVHj Production at Hadron Colliders

We study the associated production of an electroweak vector boson and the Higgs boson with a jet via gluon-gluon fusion. At the leading order, these processes occur at one-loop level. The amplitudes of these one-loop processes are gauge invariant and finite. Therefore, their contributions towards the corresponding hadronic cross sections and kinematic distributions can be calculated separately. We present results for the Large Hadron Collider and its discussed upgrades. We find that the gluon-gluon one-loop process gives dominant contribution to the $\gamma H j$ production. We observe a destructive interference effect in the $gg\to Z H j$ amplitude. We also find that in the high transverse momentum and central rapidity region, the $ZHj$ production cross section via gluon-gluon fusion becomes comparable to the cross section contributions coming from quark-quark and quark-gluon channels.Comment: 12 pages, 6 figures, 2 tables. Version to appear in PL

Quantum mutual information and quantumness vectors for multi-qubit systems

We introduce a new information theoretic measure of quantum correlations for multiparticle systems. We use a form of multivariate mutual information -- the interaction information and generalize it to multiparticle quantum systems. There are a number of different possible generalizations. We consider two of them. One of them is related to the notion of quantum discord and the other to the concept of quantum dissension. This new measure, called dissension vector, is a set of numbers -- quantumness vector. This can be thought of as a fine-grained measure, as opposed to measures that quantify some average quantum properties of a system. These quantities quantify/characterize the correlations present in multiparticle states. We consider some multiqubit states and find that these quantities are responsive to different aspects of quantumness, and correlations present in a state. We find that different dissension vectors can track the correlations (both classical and quantum), or quantumness only. As physical applications, we find that these vectors might be useful in several information processing tasks. We consider the role of dissension vectors -- (a) in deciding the security of BB84 protocol against an eavesdropper and (b) in determining the possible role of correlations in the performance of Grover search algorithm. Especially, in the Grover search algorithm, we find that dissension vectors can detect the correlations and show the maximum correlations when one expects.Comment: 18 pages 8 figures. Updated. Comments are welcom

Effect of Anomalous Couplings on the Associated Production of a Single Top Quark and a Higgs Boson at the LHC

We consider the production of a single top quark in association with a Higgs boson at the LHC. In particular, we compute the cross sections for the processes $p p \to t h j$, $t h b$, $t h W$, $t h j j$, $t h j b$, $t h W j$, $t h W b$ in the presence of the anomalous $Wtb, WWh$ and $tth$ couplings. We find that the anomalous $Wtb$ and $tth$ couplings can enhance the cross sections significantly. We also analyze a few signatures and show that, if these couplings are indeed anomalous, then with enough data, one should be able to observe the production of the Higgs boson in association with single top quark.Comment: 15 pages, 4 figures, 5 tables. Typos fixed, reference added. Journal versio

Gluon fusion contribution to HBBHBB (B=H,γ,ZB = H,\gamma, Z) at the LHC

We have calculated one-loop amplitudes for the production of Higgs boson in association with two electroweak bosons ($H,\gamma,Z$) via gluon-gluon fusion. We present preliminary results for the total cross section at 8, 13 and 100 TeV center-of-mass energies at $pp$ colliders. We study the interference effect and, also comment on the effect of new physics in terms of anomalous couplings of the Higgs boson in these processes.Comment: Proceedings for QCD@Work 201