Improved SUSY QCD corrections to Higgs boson decays into quarks and squarks

TL;DR

This work addresses the instability of SUSY QCD one-loop corrections to MSSM Higgs decays into third-generation quarks and squarks, especially at large $\tanβ$, by reparametrizing tree-level Higgs–quark and Higgs–squark couplings using running quark masses and running trilinear couplings, while keeping squark mixing angles on-shell. By absorbing gluon- and gluino-induced corrections into $m_q(Q)$ and $A_q(Q)$, and by a Higgs-basis reformulation for bottom couplings, the authors achieve substantially improved perturbative convergence and eliminate physically problematic negative widths in the dominant channels such as $A^0, H^0 \to b\bar b$ and $H^+ \to t\bar b$. The numerical analysis demonstrates reduced scale sensitivity and robust behavior across large $\tanβ$, with detailed treatment of the sbottom sector via an iterative procedure to obtain consistent running and on-shell parameters. The methodology provides a practical framework for reliable predictions of Higgs decays to quarks and squarks in the MSSM and is applicable to related radiative corrections in Higgs–squark processes.

Abstract

We improve the calculation of the supersymmetric $O(α_s)$ QCD corrections to the decays of Higgs bosons into quarks and squarks in the Minimal Supersymmetric Standard Model. In the on-shell renormalization scheme these corrections can be very large, which makes the perturbative expansion unreliable. This is especially serious for decays into bottom quarks and squarks for large $\tanβ$. Their corrected widths can even become negative. We show that this problem can be solved by a careful choice of the tree-level Higgs boson couplings to quarks and squarks, in terms of the QCD and SUSY QCD running quark masses, running trilinear couplings $A_q$, and on-shell left-right mixing angles of squarks. We also present numerical results for the corrected partial decay widths for the large $\tanβ$ case.

Figures (5)

• Figure 1: Running bottom mass as a function of $\tan\beta$. The on--shell value is $M_b = 5$ GeV. Furthermore, $m_b(m_h)_{\rm SM} \simeq 3.0$ GeV with $m_{h^0} = 93$ to $103$ GeV, and $m_b(m_A)_{\rm SM} = 2.6$ GeV. The other parameters are given in the text.
• Figure 2: Widths of Higgs particle decays into quarks as a function of $\tan\beta$. Case (i): dash--dot--dotted line corresponds to the on--shell tree--level, and dash--dotted to the on--shell one--loop result. Case (ii): dashed line corresponds to the improved tree--level, and full line to the improved one--loop result. Case (iii): dotted line corresponds to the tree--level result improved only by using $m_b(Q)_{\rm SM}$. For details, see the related text.
• Figure 3: Widths of Higgs particle decays into squarks as a function of $\tan\beta$. Case (i): dash--dot--dotted line corresponds to the on--shell tree--level, and dash--dotted to the on--shell one--loop result. Case (ii): dashed line corresponds to the improved tree--level, and full line to the improved one--loop result. For details, see the related text.
• Figure 4: Contour lines for the improved one--loop decay widths of Higgs particle decays into bottom quarks as a function of $A_b$ running and $\mu$. In (b) the light gray area shows the region where the on--shell one--loop result is negative. The other parameters are given in the text. The dark gray area is excluded by LEP and Tevatron data search.
• Figure 5: Contour lines for the improved one--loop decay widths of Higgs particles decay into bottom squarks as a function of $A_b$ running and $\mu$. The light gray areas show the region where the on--shell one--loop result is negative. The other parameters are given in the text. The dark gray area is excluded by LEP and Tevatron data search.