^{1}

^{2}

^{1}

^{2}

The differential cross-section of the top quark pair production via the quark-antiquark annihilation subprocess in hadron collision is calculated within the noncommutative standard model. A pure NC analytical expression for the forward-backward asymmetry at the tree level is obtained. Moreover, using recent Tevatron results from the full RUN2 data, a new lower bound on the noncommutative geometry parameter is deduced.

In 2012, the validity of the standard model of particle physics has been confirmed, following the announcement of both research groups Atlas [

In this work, we study the top-antitop quarks production in proton-antiproton collisions at the Tevatron energy within NCSM, obtain another correction to the forward-backward asymmetry which could give information about this new physics and derive a new lower limit of the noncommutativity parameter. The motivation is due to the huge quantity of available data from Tevatron and LHC and the fact that these data are among the most accurately available ones. In Section

The original idea of taking space-time coordinates to be noncommutative (NC) goes back to the pioneering work of Snyder [

Contrary to most other beyond standard models where new particles are introduced, there are no new massive degrees of freedom are included here, but the standard model interactions get modified due to the space-time noncommutativity. So new interactions that are forbidden in ordinary SM become allowed and therefore new phenomena appear.

In the noncommutative standard model (general properties of noncommutative field theories can be found in ref. [

The noncommutativity may be separated into two classes: (1) space-space noncommutivity with

It is very important to mention that if fields are assumed to be Lie algebra valued and allow for the closure of the Lie algebra valued noncommutative transformation gauge parameters, constraints that only U(N) structure groups are conceivable as well as the corresponding gauge transformations must be in the fundamental representation of this group. The matching of the noncommutative action to the ordinary one requires that the noncommutative fields are mapped to commutative ones by means of the Seiberg-Witten maps. The latter has the remarkable property that ordinary gauge transformations induce noncommutative ones. In this case, the low energy action is local in the sense that there is no UV/IR mixing. However, the basic assumption is that the noncommutative fields are not Lie algebra valued but are in the enveloping algebra and allows them to consider SU(N) groups. Despite the nice mathematical properties of noncommutative gauge theories, at high energies (where the theory is relevant), one can have the violation of Lorentz invariance. Contrary to theories beyond the standard model, no new particle degrees of freedom are introduced in NCSM but rather standard model (SM) interactions are modified as well as the presence of new interactions (forbidden in SM) and thus a new phenomenology will take place due to the noncommutativity of the space-time.

In SM or NCSM, the dominant diagrams involved in the physical elastic cross-section of top-antitop quarks production in hadronic collisions are those coming from quark-antiquark and gluon fusion subprocesses (see Figure

Tree level Feynman diagrams subprocesses for the Top quark pair production.

Here,

The scattering amplitude

After straightforward but tedious calculations, the spin and color-averaged and summed square amplitude is given by

After some simplifications, the noncommutative differential cross-section is shown to have the form:

In this section, we study numerically the effect of noncommutativity on the processes

Figure

The

The forward-backward asymmetry (denoted by

As we can see, this contribution is proportional to

The CDF and D0

one can derive a lower limit of the noncommutativity parameter. By taking into account the fact that the quark-antiquark subprocess contribution is about

there is no physical principle or mathematical formalism which can constrain the order of magnitude of the noncommutativity parameter nor the scale for which the NC model in consideration is relevant

The related energy scale could be as low as a few TeV, the same order of magnitude of energies employed in collider experiments (LHC, ILC, etc.), and it is a process dependent [

Forward-backward asymmetry for

Figure

The cross-section

In this work, we have investigated the effect of the Seiberg-Witten space-time noncommutativity on the top-antitop pair production at the Tevatron. In fact, we have considered the NC forward-backward asymmetry

No data were used to support this study.

The authors declare that they have no conflict of interest.

We are very grateful to MESRS et DGRSDT for the financial support

^{+}e

^{-}colliders

^{+}

^{−}⟶

^{+}

^{‑}scattering in the noncommutative standard model

^{+}

^{−}→

^{+}

^{−}scattering in the noncommutative standard model with hybrid gauge transformation