Precise QCD predictions on top quark pair production mediated by massive color-octet vector boson at hadron colliders

We present a theoretical framework for systematically calculating next-to-leading order (NLO) QCD effects to various experimental observables in models with massive COVB in a model independent way at hadron colliders. Specifically, we show the numerical results for the NLO QCD corrections to total cross sections, invariant mass distribution and AFB of top quark pairs production mediated by a massive COVB in both the fixed scale (top quark mass) scheme and the dynamical scale (top pair invariant mass) scheme. Our results show that the NLO QCD calculations in the dynamical scale scheme is more reasonable than the fixed scheme and the naive estimate of the NLO effects by simple rescaling of the LO results with the SM NLO Kfactor is not appropriate. In many extensions of the Standard Model (SM), massive Color-Octet Vector Boson (COVB) is necessarily engaged at the TeV scale, for example, in the top-color [1], warped (RS) or universal extra dimensions [2, 3], technicolor [4] and chiral color models [5]. In all these cases, the COVB could have large impacts on the interaction of top quarks, which are being copiously produced at the CERN Large Hadron Collider (LHC). With a large sample of t t̄ data, the CDF collaboration at the Tevatron has recently reported an observation of a large Forward–Backward asymmetry (AFB) in t t̄ production, Atot FB = 0.158 ± 0.075, compared with the SM prediction 0.058 ± 0.009 [6–8]. The disagreement is more profound in the region of large t t̄ invariant mass, where CDF reported AFB(mtt̄ > 450 GeV) = 0.475 ± 0.114, and the SM gives 0.088 ± 0.013 [9]. This leads to a more than 3.4σ deviation from the SM prediction [9]. Similarly, the DO/ collaboration [10] has also reported the total AFB to be a e-mail: [email protected] b e-mail: [email protected] Atot FB = 0.196 ± 0.065 using 5.4 fb−1 of data. Furthermore, DO/ has also measured the charge asymmetry of the leptons from top decay, AlFB = 0.152 ± 0.04. These results have generated extensive theoretical studies on this observable in various models beyond the SM. Among these, models with massive COVB are in particular attractive, cf., Ref. [11] and references therein. There have also been substantial efforts in searching for the signal of COVB at the Tevatron and LHC, which can shows up as a clear resonant peak in the t t̄ invariant mass distribution [12–15]. While current experimental limits depend on the detailed choices of couplings [16–18], they nevertheless indicate that COVB with mass below 1 TeV is severely constrained. It is well known that QCD effects play an important role in t t̄ production. The NLO QCD corrections to SM t t̄ production, which significantly enhance the t t̄ total cross sections, have been calculated for a long time [19–21]. In the SM, AFB is related to higher order QCD radiation effects, which first appear at O(α3 s ) [6]. Complete NLO corrections to this observable are not available currently, but calculation based on soft gluon resummation indicates that higher order QCD effects are small [22]. Recently electroweak corrections to AFB have also been calculated and are found to slightly increase the asymmetry [23]. In the case of massive COVB, its QCD gauge interaction is uniquely determined by its color content, resembling a SM gluon. Therefore, it is reasonable to expect that higher order QCD effects will also have significant impacts on processes mediated by massive COVB, at least at an energy scale comparable to the mass of COVB. This has motivated the model dependent calculation of COVB production by gluon fusion [24] and the model independent (using dimension-six operators) calculation of t t̄ production mediated by COVB [25]. However, a complete NLO analysis of the QCD effects to models with massive Page 2 of 6 Eur. Phys. J. C (2012) 72:2232 COVB in the resonant t t̄ region is still absent.1 In this letter, we present the model independent complete NLO QCD corrections to top quark pair production mediated by a general massive COVB, and show the detailed numerical analysis of top quark pair production, including invariant mass distribution and AFB at the NLO level. We also show that the NLO corrections significantly stabilize the renormalization and factorization scale dependence, as compared to the LO results. Below, we briefly outline our approach to systematically calculating the NLO QCD effects to processes of COVB production. We consider a model independent massive COVB originated from a broken SU(3) gauge group. The effective Lagrangian for color-octet vector Gμ in unitary gauge can be written as LG =− 2 TrGμνG μν +M2 G TrGμG, (1) where a = 1, . . . ,8 are the broken SU(3) “color” indices, and μ= 0, . . . ,3 are the Lorentz indices. Gμν ≡GμνT a = (∂μG a ν − ∂νGμ)T a is the field strength tensor, where T a is the conventional Gell-Mann matrix with the normalization Tr[T T b] = 2δ . The mass of the COVB is denoted by MG. The QCD color interaction between COVB and SM gluon Aμ can be easily implemented by changing the ordinary derivative into covariant derivative: ∂μG a ν →DμGν = ∂μGaν + g1f abcAbμGcν, (2) where g1 is the coupling constant of QCD. The Lagrangian in Eq. (1), after the replacement in Eq. (2), is already invariant under the conventional SU(3)c transformation. If desired, NLO QCD calculation can be done with the Feynman rule derived from the above Lagrangian, where unitary gauge is chosen for the broken SU(3) gauge symmetry. However, it is well known that loop calculation in unitary gauge is inconvenient because of the violent ultra-violet (UV) behavior of the propagator. Instead, we choose to carry out the calculation in conventional ’t Hooft–Feynman gauge for the broken gauge group. To this end, we separate the longitudinal component (the would-be Goldstone boson) of the COVB from Eq. (1), by modifying the mass term in Eq. (1) as follows, Gμ(x)→ G̃μ(x)=U(x) ( i