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Yukawa Corrections to Top Quark Production at the LHC in Two- Higgs-Doublet Models

The O(alpha m_t^2/m_W^2) corrections to top quark pair production by gluon-gluon fusion at the LHC are calculated in two-Higgs-doublet models. We find that the correction to the cross-section can exceed about -10% for certain parameter values.


I. Introduction
Recently, the existance of the top quark is confirmed by the CDF and D0 Collaborations with the mass and production cross-section m t = 176±8(stat)±10(syst) GeV σ = 6.8 +3. 6 −2.4 pb, and m t = 199 +19 −20 (stat) ± 22(syst) GeV σ = 6.4 ± 2.2pb, respectively [1] . This is a remarkable success of the Standard Model (SM) since this measured mass is close to the central value predicted by the best fit of the SM to the LEP precision electroweak data. There are a number of new and interesting issues related to the top quark, such as the precision measurement of the mass, width and Yukawa couplings through its direct production and subsequent decay at both hadron and e + e − colliders. At the future multi-TeV proton colliders such as the CERN Large Hadron Collider (LHC), tt production will be enormously larger than the Tevatron rates, and the accuracy with which the top mass can be measured in proton colliders is around 2 GeV [2]. This makes the determination of production cross section at LHC more accurately than at Fermilab Tevatron. Processes related to the top quark (the heaviest fermion so far found) may be sensitive to possible new physics beyond the SM, especially the non-standard Higgs sector, due to the large Yukawa coupling.
The simplest extension of the SM Higgs sector is the two-Higgs-doublet models (2HDM) which can give an enhancement of the Yukawa couplings and may result in a considerable correction to the top quark production cross section. Yukawa correction to the top quark production in general 2HDM and in the minimal supersymmetric model(MSSM) at Fermilab Tevatron has been carried out in Ref. [3], where large corrections are found. Supersymmetric electroweak correction [5] and QCD correction [6] to top quark production at the Tevatron are also found to be large. At LHC the main production mechanism of top quark is the gluon-gluon fusion process gg → tt. The full electroweak corrections to this process as well as qq → tt in the Standard Model have been calculated in Ref. [4]. In this paper we investigate the Yukawa correction to the top quark production by the process gg → tt in a general 2HDM and in the minimal supersymmetric model at LHC. Our calculation of the corrections to the S-matrix elements will be given in Sec.II. In Sec III, we present our numerical results and discussions of the cross-sections in the SM , 2HDM and MSSM .

II. Calculation of the S-matrix Elements
The tree-level Feynman diagrams and the relevant Yukawa corrections to gg → tt are shown in Fig.1 (u-channel diagrams of Fig.1b and Fig.1d-Fig.1h are not explicitly shown) in which the dashed lines in Fig.1c and Fig.1e-Fig.1h represent H 0 , h, A, G 0 , H + and G + (G 0 and G + are, respectively, Goldstone bosons of Z and W + ), while those in Fig.1d represent only H 0 and h. The relavant Feynman rules can be found in Ref. [7].
At tree level, the S-matrix element is composed of three different production channels(s-,t-,u-channel) as follows: where Γ µ is given in the Appendix. Instead of calculating the square of the amplitudes explicitly, we calculate the amplitudes numerically by using the method of Ref. [8]. This method greatly simplifies our calculations.
The O(αm 2 t /m 2 W ) Yukawa corrections to gg → tt are shown in Fig.1c-Fig.1h, where Fig.1d alone is gauge invariant and the sum of Fig.1c,Fig.1e-Fig.1h is gauge invariant. In our calculation, we use dimensional regularization to regulate the ultaviolet divergences and adopt the on-mass-shell renormalization scheme.
We only give the explicit results of the s-and t-channel contributions to the total Yukawa correction. The u-channel results can be obtained by the following substitutions: The s-channel Higgs exchange of Fig.1d gives δM s2,t : The top quark self-energy δM self,t of Fig.1e is: δM v1,t and δM v2,t of the vertex corrections ( Fig.1f-Fig.1g) are: δM box,t of the box diagram ( Fig.1h) is: The following parameters are used in our calculation: The η and p T cuts are used in order to avoid the singularities in the calculation of form factors and increase the relative corrections.

III. Numerical Results and Discussions
In our calculation, we checked our program with gauge invariance and it is accurate to 10 −10 . For comparison, we first give the results of the SM in Fig.2. We see that the SM results are always negative and do not exceed −1.5%. The shape of the curve is like that of Ref. [4]. In Fig.3 and Fig.4 we present the results of the general 2HDM and the MSSM with a small β = 0.25 as in Ref. [3]. We give here the form factors for the matrix element appeared in the text. They are written in terms of the conventional one-, two-, three-and four-point scalar loop integrals defined in Ref. [10]. We set M Z and M W to zero in the numerical calculation as in Ref. [3].