[Paper Review] SUSY-QCD corrections to MSSM Higgs boson production via gluon fusion

Margarete Mühlleitner, Heidi Rzehak+1 more|arXiv (Cornell University)|Jan 19, 2010

Particle physics theoretical and experimental studies10 citations

TL;DR

This paper presents the first full next-to-leading-order (NLO) SUSY-QCD corrections to gluon fusion production of CP-even Higgs bosons (h, H) in the MSSM, including full mass dependence of top, bottom, and squark loops. It demonstrates that these corrections are sizeable and can be accurately approximated by the $Δ_b$ method when the bottom quark form factor is renormalized in the $ύb$ scheme, while also deriving a consistent effective Lagrangian for gluino decoupling in the heavy gluino limit, confirming adherence to the Appelquist-Carazzone theorem.

ABSTRACT

In the MSSM scalar h,H production is mediated by heavy quark and squark loops. The higher order QCD corrections have been obtained some time ago and turned out to be large. The full SUSY QCD corrections have been obained recently including the full mass dependence of the loop particles. We describe our calculation and present first numerical results. We also address the question of the proper treatment of the large gluino mass limit, i.e. the consistent decoupling of heavy gluino effects, and present the effective Lagrangian for decoupled gluinos.

Motivation & Objective

• To compute the complete NLO SUSY-QCD corrections to gluon fusion production of CP-even Higgs bosons (h, H) in the MSSM.
• To address the proper treatment of the large gluino mass limit and ensure consistency with the Appelquist-Carazzone decoupling theorem.
• To derive an effective Lagrangian for scalar Higgs couplings to gluons after gluino decoupling.
• To provide numerical results for the total cross section including full mass dependence of loop particles.
• To assess the validity of the $Δ_b$ approximation for SUSY-QCD corrections in the context of renormalization scheme dependence.

Proposed method

• The calculation employs a one-loop virtual correction and real emission processes (e.g., $gg \to gh/H$, $gq \to qh/H$) to compute the NLO SUSY-QCD corrections.
• The full mass dependence of top, bottom, and squark loops is included in the form factors $A_Q^{h/H}(\tau)$ and $A_{\tilde{Q}}^{h/H}(\tau)$, with the latter derived from triangle diagrams involving squarks.
• Renormalization is performed in the $\overline{\text{MS}}$ scheme for strong coupling and quark/squark masses, with collinear divergences absorbed into the parton distribution functions.
• The effective Lagrangian for gluino decoupling is derived via renormalization group evolution and momentum subtraction, yielding a modified relation between quark Yukawa and squark-Higgs couplings.
• The matching condition at the gluino mass scale includes a finite threshold correction and logarithmic terms from RGEs below $M_{\tilde{g}}$, ensuring consistency with decoupling theorems.
• Numerical results are obtained using the $\overline{\text{MS}}$-renormalized bottom quark form factor and compared to the $\Delta_b$ approximation.

Experimental results

Research questions

• RQ1 How do full NLO SUSY-QCD corrections affect the total cross section for $pp \to h/H$ via gluon fusion in the MSSM?
• RQ2 Can the $\Delta_b$ approximation accurately describe the genuine SUSY-QCD corrections when the bottom quark form factor is renormalized in the $\overline{\text{MS}}$ scheme?
• RQ3 What is the correct effective Lagrangian for Higgs-gluon couplings after consistent decoupling of heavy gluinos?
• RQ4 How do the radiative corrections modify the relation between quark Yukawa and squark-Higgs couplings in the heavy gluino limit?
• RQ5 Does the derived effective theory satisfy the Appelquist-Carazzone decoupling theorem in the large $M_{\tilde{g}}$ limit?

Key findings

• The full NLO SUSY-QCD corrections to $pp \to h/H$ via gluon fusion are sizeable and depend significantly on the masses of the top, bottom, and squark loops.
• The $\Delta_b$ approximation provides a good description of the genuine SUSY-QCD corrections when the bottom quark form factor is renormalized in the $\overline{\text{MS}}$ scheme.
• The effective Lagrangian for Higgs-gluon couplings after gluino decoupling includes a finite threshold correction and a logarithmic structure consistent with the Appelquist-Carazzone theorem.
• The coefficient $C_{\text{SQCD}} = \frac{37}{6}$ in the effective Lagrangian is well-defined in the large gluino mass limit, confirming consistent decoupling.
• Numerical results show that the corrections are most significant for light squarks and large $\tan\beta$, with the virtual and real corrections contributing substantially to the total cross section.
• The study confirms that the $\overline{\text{MS}}$-renormalized bottom quark form factor yields a reliable and accurate approximation to the full SUSY-QCD corrections.