Extracting SUSY Parameters from the Higgs Boson Properties

We calculate the ratio of the two branching ratios, Br(h → bb) and Br(h → cc) + Br(h → gg), in the minimal supersymmetric standard model taking into account the SUSY-loop corrections to the Higgs sector and the hbb vertex. We show that the heavy Higgs mass can be extracted from the ratio, almost independently of other SUSY parameters, in the region of tanβ < ∼ 10. It was pointed out that the CP-odd Higgs mass mA can be determined by the measurements of the lightest Higgs decay branching ratios in the minimal supersymmetric standard model (MSSM) [1]. Since there is the region of moderate tan β where LHC may not be able to detect the CP-odd Higgs boson, mA > ∼ 200GeV [2], it is important to study such an option to indirectly constrain mA. Ref. [1] showed that we could extract mA from the double ratio, Rbr ≡ Br(h → cc) +Br(h → gg) Br(h → bb) , taking into account the SUSY-loop corrections to the Higgs sector. Since the dependence of the h → bb and h → cc branching ratios on the mixing angles α and β of the Higgs sector is given by Br(h → bb) ∝ sin 2 α cos β and Br(h → cc) ∝ cos 2 α sin β , the double ratio between Br(h → bb) and Br(h → cc) becomes Rc ≡ Br(h → cc)/Br(h → bb) ∝ 1/(tanα tan β), where the scalar-top-quark corrections to the Higgs sector are implicit in tanα and tan β. When the CP-odd Higgs boson is heavy, mA ≫ mh ∼ mZ , and the left-right mixing of the scalar top quarks is small, the double ratio Rc is approximately proportional to (m 2 h − m 2 A) 2/(m2Z + m 2 A) . 1) Talk given by S.Kiyoura at the Linear Collider Workshop 2000, October 24-28, 2000, Fermilab. 2) [email protected] 3) [email protected] From this expression, you can see that, once we measure the lightest Higgs mass mh, the double ratio Rc determines mA. Furthermore, Br(h → gg), dominantly induced by the top quark exchange, has the same dependence on the mixing angles α and β as the Br(h → cc), and therefore we can expect the double ratio Rbr determines the mass scale of the CP-odd Higgs boson. In the above discussion, we assume that Higgs-fermion Yukawa couplings are the same as those in the type-II two Higgs doublet model (THDM). Recently, the SUSY-loop corrections to the hbb coupling constant have been studied by many authors [3,4]. The one-loop-level coupling of a bottom quark to the neutral Higgs fields is given by L = fbbLbRH 0 d + ǫbfbbLbRH 0∗ u + h.c., (1) ǫb ≡ 2αS 3π μM3f(M 2 3 , m 2 b̃L , m b̃R ) + f 2 t 16π μAtf(μ , m2t̃L , m 2 t̃R ), (2) f(m21, m 2 2, m 2 3) ≡ 1 m23 [ x log x 1− x − y log y 1− y ] 1 x− y , x ≡ m21 m23 , y ≡ m22 m23 (3) where ǫb is induced by the gluinoand Higgsino-exchange diagrams. In Eq.(1) the second term proportional to ǫb is absent at the tree level in the MSSM (and also in the type-II THDM). The b-quark mass and the hbb coupling constant are then expressed as, mb = fbvd + fbǫbvu = fbv cos β × (1 + ǫb tan β), Lhbb = − mb sinα v cosβ × [ 1− ǫb/ tanα 1 + ǫb tan β ]