Phenomenological Aspects of Noncommutative Standard Model

Abstract

The Standard Model(SM) of Particle Physics has so far been extremely successful, with a recent major triumph in discovering and constraining the properties of the last missing bit of the SM, the Higgs boson. newlineApart from some discrete and isolated hints, it is broadly evasive, lacking any clinching evidence yet supporting the physics beyond the standard model (BSM) experiment at Large Hadron Collider (LHC) at the TeV energy scale, exploration of which is one of the primary motives for post-Higgs LHC. On the other side, it is widely admitted that the Standard Model is valid only up to a scale of newlineseveral hundred GeV i.e it is at most a very good description for low energy effective theory which, in fact, falls short to explain several outstanding issues both in terms of theoretical construction and elegance as well as experimental observations. The idea of field theories on the noncommutative (NC) spacetime is rather primeval, yet fascinate by introducing a fundamental length scale in the model consistent with the symmetry. These ideas are further revived after realization of their possible connection with quantum gravity, where noncommutativity is perceived as an outcome of certain string theory embedded into a background magnetic field. newlineJust like the quantization in phase space, the spacetime coordinate in the noncommutative spacetime gets replaced by an operator xand#956; which satisfy the commutation relation [ xand#956;, xand#957;] = iand#920;and#956;and#957; = i newlinecand#956;and#957; newlineand#923;2 . newlinewhere and#920;and#956;and#957; is an antisymmetric matrix tensor, which has the dimension of area reflecting the extent to which the spacetime is fuzzy i.e. noncommutative. cand#956;and#957; is the anti-symmetric constant c-number matrix which gives a preferred directionality and also a non-vanishing contribution results in deviating from exact Lorentz invariance is broken at all scale and#923;, the scale of spacetime noncommutativity. The construction of the noncommutative standard model relies on two important blocks: Moyal-Weyl(MW)-product of field functions on ordinary spacetime and the Seiberg-Witten(SW) maps.In th