MSSM corrections to the top–antitop quark forward–backward asymmetry at the Tevatron

Abstract

We study the effects of the complete supersymmetric QCD and electroweak one-loop corrections to the $t\bar{t}$ forward–backward asymmetry at the Fermilab Tevatron $p\bar{p}$ collider. We work in the complex Minimal Supersymmetric Standard Model (MSSM), only restricted by the condition of minimal flavor violation (MFV). We perform a comprehensive scan over the relevant parameter space of the complex MFV–MSSM and determine the maximal possible contributions of these MSSM loop corrections to the forward–backward asymmetry in the $t\bar{t}$ center-of-mass frame. We find that the SUSY loop-induced asymmetry at the Tevatron with $M_{t\bar{t}}>450~\mbox{GeV}$ can be at most +2 % for very light SUSY particles, i.e. for $m_{\tilde{t}_{1}} <100~\mbox{GeV}$ and $m_{\min} = \mathrm{Min}\{ m_{\tilde{g}},m_{\tilde{u}_{1,2}},m_{\tilde{d}_{1,2}}\}<100~\mbox{GeV}$, which reduces to 0.1 % for gluino and squark masses in the range 850 GeV–1000 GeV and a light top squark of $m_{\tilde{t}_{1}}=200~\mbox{GeV}$.

Appendix

1.1 A.1 Gluino–squark–quark couplings

The gluino–squark–quark couplings as defined in Eq. (7) are [39]

(A.1)

(A.2)

The index i and j have been omitted in the definition of $g_{n}^{\pm}$ of Eq. (A.1) to avoid large chains of indices in Sect. 2. The index i always refers to the squark index of flavor q={u,d,s,c,b} of the vertices Γ ₁ and Γ ₂ and the index j always refers to the stop quark index of Γ ₃ and Γ ₄. The complex phase of the gluino mass M ₃ is denoted by ϕ. The couplings are related by

$$\hat{g}_{2}^{\pm}=\hat{g}_{1}^{\mp*} ,\qquad\hat{g}_{3}^{\pm}=\hat{g}_{4}^{\mp*}. $$

The unitary squark mixing matrices are given as

(A.3)

For the squark mass and mixing matrices we use the conventions of Ref. [39].

1.2 A.2 Neutralino–squark–quark couplings

For the neutralino–squark–quark couplings, we again follow the notation of Ref. [39], where explicit expressions for these couplings can be found. For completeness, since the $u\bar{u}$-channel is the dominant $t\bar{t}$ production process, we provide here the neutralino–up-quark-squark coupling, which reads with the restriction m _u =0 GeV [39]

(A.4)

(A.5)

where we used the shorthand notations c _W =cosθ _W , s _W =sinθ _W and s _β =sinβ with $\tan\beta=\frac{v_{u}}{v_{d}}$ the ratio of the two Higgs field vacuum expectation values. Here the coupling parameters are related by

$$g_{2}^{\pm}=g_{1}^{\mp*},\qquad g_{3}^{\pm}=g_{4}^{\mp*}. $$

The neutralino mass matrices in the used convention have been taken from Ref. [63].

1.3 A.3 Analytic expressions for the one-loop functions D ^a

The partonic differential cross section $\frac{d\hat{\sigma}^{(a,b)}}{d\cos\theta}$ for the direct box diagrams of Fig. 1(a) and crossed box of Fig. 1(b) are given in Eq. (8) and Eq. (10), respectively, in terms of coupling parameters and loop functions D ^a. Neglecting the initial-state quark masses and using the mass assignments of Fig. 1, the functions $D^{a}(\hat{s},\cos\theta)$ are given with $\hat{t}=m_{t}^{2}-\frac{\hat{s}}{2} (1-\beta_{t}\cos\theta )$ as

(A.6)

where $D_{i,ij}=D_{i,ij} (0,m_{t}^{2},m_{t}^{2},0,\hat{t},\hat{s},m_{1}^{2},m_{2}^{2},m_{3}^{2},m_{4}^{2} )$ are written in the convention of Ref. [43]. From these expressions the contribution to Fig. 1(b) can be obtained by replacing $D^{a}(\hat{s},\cos\theta)\to D^{a}(\hat{s},-\cos\theta)$ and multiplying by a factor of (−1) for exchanging the final-state fermions.