What is the $t\bar{t}$ production supposed to bring up The $t\bar{t}$ production, I've read, that will somehow confirm the QCD and might bring up new physics. Why are we studying $t\bar{t}$ production from $p-p$ collisions at the LHC?
What are we trying to find? What is the new physics that might bring up? What do we anticipate from this production?
 A: Here is a review of the top quark physics at LHC. The abstract:

This review summarizes the highlights in the area of top quark physics obtained with the two general purpose detectors ATLAS and CMS during the first two years of operation of the Large Hadron Collider LHC. It covers the 2010 and 2011 data taking periods, where the LHC provided pp collisions at a center-of-mass energy of sqrt(s)=7 TeV. Measurements are presented of the total and differential top quark pair production cross section in many different channels, the top quark mass and various other properties of the top quark and its interactions, for instance the charge asymmetry. Measurements of single top quark production and various searches for new physics involving top quarks are also discussed. The already very precise experimental data are in good agreement with the standard model.

Top production  can be used for precision measurements 

Amongst all known elementary particles, the top quark is peculiar: weighing as much as a Tungsten atom, it completes the so-called 3rd generation of quarks and is the only quark whose properties can be directly measured. Owing to its mass, the top quark is unstable and, in CMS, decays much before it can interact with the proton remnants through the strong interaction and form hadrons (the bound states of quarks). It decays mostly to a W boson and a bottom (b) quark, and can therefore be identified from final states which involve the complete usage of the CMS detector; electrons, muons, jets, missing transverse energy — almost all particles or experimental signatures one can think of may be produced in top-quark events.

At the moment they are exploring the limits of the standard model, which they have not reached. Disagreements with standard model predictions would point to new physics. For an example of such a search this abstract:

A search for the standard model Higgs boson produced in association with a top-quark pair is presented using data samples corresponding to an integrated luminosity of 5.0 inverse femtobarns (5.1 inverse femtobarns) collected in pp collisions at the center-of-mass energy of 7 TeV (8 TeV). Events are considered where the top-quark pair decays to either one lepton+jets (t tbar to ell nu q q' b bbar) or dileptons (t tbar to ell(+) nu ell(-) nu b bbar), ell being an electron or a muon. The search is optimized for the decay mode H to b bbar. The largest background to the t tbar H signal is top-quark pair production with additional jets. Artificial neural networks are used to discriminate between signal and background events. Combining the results from the 7 TeV and 8 TeV samples, the observed (expected) limit on the cross section for Higgs boson production in association with top-quark pairs for a Higgs boson mass of 125 GeV is 5.8 (5.2) times the standard model expectation. 

Had they found  an inconsistency with the standard model in this specific higgs production in association with the top, it would be a sign  of new physics, except that within their errors the standard model is confirmed. If in future searches a disagreement appears, the field will be open or theories outside the standard model to come in and explain the data.
