Two-loop $$ \mathcal{O} $$((αt + αλ + ακ)2) corrections to the Higgs boson masses in the CP-violating NMSSM

Abstract

We present our computation of the $$ \mathcal{O} $$ O ((αt + αλ + ακ)2) two-loop corrections to the Higgs boson masses of the CP-violating Next-to-Minimal Supersymmetric Standard Model (NMSSM) using the Feynman-diagrammatic approach in the gaugeless limit at vanishing external momentum. We choose a mixed $$ \overline{\mathrm{DR}} $$ DR ¯ -on-shell (OS) renormalisation scheme for the Higgs sector and apply both $$ \overline{\mathrm{DR}} $$ DR ¯ and OS renormalisation in the top/stop sector. For the treatment of the infrared divergences we apply and compare three different regularisation methods: the introduction of a regulator mass, the application of a small momentum expansion, and the inclusion of the full momentum dependence. Our new corrections have been implemented in the Fortran code NMSSMCALC that computes the Higgs mass spectrum of the CP-conserving and CP-violating NMSSM as well as the Higgs boson decays including the state-of-the-art higher-order corrections. Our numerical analysis shows that the newly computed corrections increase with rising λ and κ, remaining overall below about 3% compared to our previously computed $$ \mathcal{O} $$ O (αt(αt + αs)) corrections, in the region compatible with perturbativity below the GUT scale. The renormalisation scheme and scale dependence is of typical two-loop order. The impact of the CP-violating phases in the new corrections is small. We furthermore show that the Goldstone Boson Catastrophe due to the infrared divergences can be treated in a numerically efficient way by introducing a regulator mass that approximates the momentum-dependent results best for squared mass values in the permille range of the squared renormalisation scale. Our results mark another step forward in the program of increasing the precision in the NMSSM Higgs boson observables.

Benchmarking Di-Higgs Production in Various Extended Higgs Sector Models

“…In the NMSSM, we use the program NMSSMCALC [166,167] and compute the Higgs mass corrections up to O((α t +α λ +α κ ) 2 +α t α s ) [168][169][170] with on-shell renormalisation in the top/stop sector. We demand the computed SM-like Higgs boson mass to lie in the range 122 GeV...128GeV which accounts for the present typically applied theoretical error of 3 GeV [79].…”

“…For further details of the Higgs mass computation and of the input parameters as well as their scan ranges, we refer to [170].…”

“…As stated above, in the NMSSM the Higgs boson masses are computed from the input parameters of the model and higher-order corrections are important to shift the SM-like Higgs mass to the observed 125 GeV. We have computed these masses using the new version of NMSSMCALC which includes the two-loop Higgs mass corrections at O((α λ +α κ +α t ) 2 +α t α s ) [170]. In Tab.…”

Dark Matter in the CP-violating NMSSM

“…The CPviolating phases of the SUSY-breaking Higgs-sfermion-sfermion couplings, A f , where f denotes a SM fermion, in the MSSM can be radiatively transmitted to the Higgs sector, but are tightly constrained by the measurements of fermion electric dipole moments (EDMs) [48,49]. In the NMSSM, if the Higgs self-couplings, λ and/or κ, appearing in the superpotential are complex, the scalar and pseudoscalar interaction eigenstates mix together to give five neutral CP-indefinite Higgs states; see [50,51,52,53,54,55] for recent studies of the NMSSM Higgs sector with CP violation and [56] for a review. We henceforth refer to this model as the cNMSSM.…”

“…We note that NMSSMTools provides a spectrum generator capable of handling CP violation[63] that contains a less accurate computation of the Higgs masses; whereas NMSSMCALC[80] provides an equivalent computation of the Higgs masses[55].…”