Approximating the radiatively corrected Higgs mass in the Minimal Supersymmetric Model
Howard E. Haber, Ralf Hempfling, Andre H. Hoang
TL;DR
The paper develops a compact analytic scheme to approximate the radiatively corrected MSSM Higgs masses by combining full one-loop corrections, all-orders RG-improvement of large logs, and dominant two-loop effects. The approach rewrites the RG-improved neutral CP-even Higgs mass matrix as ${ar{{ m M}}^2} = { m M}^2[m_t(_{ ilde t}), m_b(_{ ilde b}), X_t, X_b] - { m M}^2[m_t(_{ ilde t}), m_b(_{ ilde b}), 0, 0] + { m M}^2[m_t(_t), m_b(_b), 0, 0]$, with the leading logs absorbed by evaluating running masses at scales $ $ and $ $, e.g. $ = \, \mu_t = \sqrt{m_t M_{SUSY}}$. The authors show that this analytic construction reproduces the full RG-improved results for $m_{h^0}$ within about 2 GeV across a large portion of MSSM parameter space (for $M_{SUSY}$ up to ~2 TeV), and they extend the framework to include top/stop mixing through $X_t = A_t - \mu \cot\beta$, with threshold corrections handled via appropriate mass scales. The framework delivers a practical, accurate method for predicting MSSM Higgs masses and assessing LEP-2 discovery prospects, without requiring heavy numerical RG runs.
Abstract
To obtain the most accurate predictions for the Higgs masses in the minimal supersymmetric model (MSSM), one should compute the full set of one-loop radiative corrections, resum the large logarithms to all orders, and add the dominant two-loop effects. A complete computation following this procedure yields a complex set of formulae which must be analyzed numerically. We discuss a very simple approximation scheme which includes the most important terms from each of the three components mentioned above. We estimate that the Higgs masses computed using our scheme lie within 2 GeV of their theoretically predicted values over a very large fraction of MSSM parameter space.