Advances in High Energy Physics

Volume 2015, Article ID 760729, 12 pages

http://dx.doi.org/10.1155/2015/760729

## Two-Loop Correction to the Higgs Boson Mass in the MRSSM

^{1}Institut für Kern- und Teilchenphysik, TU Dresden, 01069 Dresden, Germany^{2}Faculty of Physics, University of Warsaw, Pasteura 5, 02093 Warsaw, Poland

Received 24 April 2015; Accepted 23 June 2015

Academic Editor: Mark D. Goodsell

Copyright © 2015 Philip Diessner et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP^{3}.

#### Abstract

We present the impact of two-loop corrections on the mass of the lightest Higgs boson in the minimal *R*-symmetric supersymmetric standard model (MRSSM). These shift the Higgs boson mass up by typically 5 GeV or more. The dominant corrections arise from strong interactions, and from the gluon and its superpartners, the sgluon and Dirac gluino, and these corrections further increase with large Dirac gluino mass. The two-loop contributions governed purely by Yukawa couplings and the MRSSM , parameters are smaller. We also update our earlier analysis which showed that the MRSSM can accommodate the measured Higgs and *W* boson masses. Including the two-loop corrections increases the parameter space where the theory prediction agrees with the measurement.

#### 1. Introduction

The recent discovery at the LHC of a particle consistent with the long sought Higgs boson seemingly completes the Standard Model (SM). The mass of the particle is measured with an astonishingly high accuracy of GeV [1]. The precise determination of this mass is of paramount importance not only within the context of the Standard Model, but also for finding the path beyond it. In fact, a number of experimental observations suggest that the SM cannot be the ultimate theory and many theoretical scenarios for the beyond SM (BSM) physics have been proposed in past decades. In some models of BSM, in particular in supersymmetric extensions of the SM, the Higgs boson mass can be predicted. However, the current experimental accuracy is far better than theoretical predictions for Higgs boson mass in any given model of BSM physics. From the point of view of theory, the best accuracy has been achieved in the minimal supersymmetric extension of the SM (MSSM), in which the discovery of the Higgs boson and the determination of its mass have given a new impetus to the theoretical efforts. The most recent improvements comprise the inclusion of leading three-loop corrections [2, 3], resummation of leading logarithms beyond the two-loop level [4, 5], inclusion of the external momenta of two-loop self-energies [6, 7], and the evaluation of the -contributions in the complex MSSM [8, 9]. The MSSM two-loop corrections controlled by Yukawa couplings and have been known for quite some time for the real MSSM (see the above references for an overview of the literature).

The absence of any direct signal of supersymmetric particle production at the LHC and the observed Higgs boson mass of ~125 GeV being rather close to the upper value of 135 GeV achievable in the MSSM are a strong motivation to consider nonminimal SUSY scenarios. In fact, nonminimal SUSY models can lift the Higgs boson mass (at the tree-level by new - or -term contributions or at the loop level from additional new states), which makes these models more natural by reducing fine-tuning. They can also weaken SUSY limits either by predicting compressed spectra or by reducing the expected missing transverse energy or by reducing production cross sections. The comparison of the measured Higgs boson mass with the theoretically predicted values in any given model is therefore highly desirable. Although the theoretical calculations for the SM-like Higgs boson mass in such models are less advanced, progress is being made in the development of highly automated tools which greatly facilitate the computations in nonminimal SUSY models: SARAH [10–12] automatically generates spectrum generators similar to SPheno [13, 14]; FlexibleSUSY [15] automatically generates spectrum generators similar to Softsusy [16].

In a recent paper [17] we considered the MRSSM, a highly motivated supersymmetric model with continuous -symmetry [18, 19] distinct from the MSSM. Since -symmetry forbids soft Majorana gaugino masses as well as the higgsino mass term, additional superfields are needed. The MRSSM has been constructed in [20] as a minimal viable model of this type. It contains adjoint chiral superfields with -charge 0 for each gauge sector and two additional Higgs weak iso-doublet superfields with -charge 2. It has been also argued that -symmetry generically forbids large contributions to CP- and flavor-violating observables due to the absence of chirality-changing Dirac gluino couplings [20, 21], relaxing flavor constraints on the sfermion sector, although recently it has been shown that the dramatic chirality-flip suppression of [20] can only work in a limited number of scenarios, and in general a certain correlation between flavor structure of fermion masses and superpartner spectrum is required [22]. Also, Dirac gluinos suppress the production cross section for squarks, making squarks below the TeV scale generically compatible with LHC data. Furthermore, models with -symmetry and/or Dirac gauginos contain promising dark matter candidates [23–25], and the collider physics of the extra, non-MSSM-like states has been studied [26–34].

In [17] the complete next-to-leading order computation and discussion of the lightest Higgs boson and boson masses have been performed. We showed that the model can accommodate measured values of these observables for interesting regions of parameter space with stop masses of order 1 TeV (a similar analysis has been done in [35], where also a welcome reduction of the level of fine-tuning was found). The outcome of the paper was not obvious since in the MRSSM (i) the lightest Higgs boson tree-level mass is typically reduced compared to the MSSM due to mixing with additional scalars, (ii) the stop mixing is absent, and (iii) -symmetry necessarily introduces an scalar triplet, which can increase already at the tree-level. Nevertheless, we identified benchmark points BMP1, BMP2, and BMP3 illustrating different viable parameter regions for , respectively, and also verified that they are not excluded by further experimental constraints from Higgs observables, collider, and low-energy physics.

These promising results motivate a more precise computation of the Higgs boson mass in the MRSSM and a more precise parameter analysis. Technically, this is facilitated by the Mathematica package SARAH, recently updated by providing SPheno routines, which calculate two-loop corrections to the CP-even Higgs scalars masses in the effective potential approximation and the gaugeless limit [36]. This is the level of precision of the established MSSM predictions except for the refinements mentioned above. It is also the level of precision at which the proof [37] applies that the employed regularization by dimensional reduction preserves supersymmetry. First applications of the improved SARAH version to the calculations of the Higgs boson masses in the -parity violating MSSM [38] and next-to-minimal SSM [39] have been published.

Since a judicious choice of the model parameters was needed to meet experimental constraints and an estimate of unknown two-loop contributions was presented, it is of immediate interest to verify our findings at higher precision with the new SARAH version. The aim of the current paper is to calculate two-loop corrections for the Higgs boson mass in the same MRSSM setup as in [17] and present an update of the results obtained there.

The paper is organized as follows. After a short recapitulation of the MRSSM setup in Section 2, we explain in Section 3 our calculation framework and discuss the dependence of two-loop corrections on parameters that entered already at the one-loop level. The dependence on parameters that enter only at the two-loop level is investigated in Section 4. In Section 5 we provide an update to the analysis presented in [17] using the two-loop corrected masses of Higgses, before concluding in Section 6.

#### 2. The MRSSM

The MRSSM has been constructed in [20] as a minimal supersymmetric model with unbroken continuous -symmetry. The superpotential of the model reads as where are the MSSM-like Higgs weak iso-doublets and are the singlet, weak iso-triplet, and -Higgs weak iso-doublets, respectively. The usual MSSM -term is forbidden; instead -terms involving -Higgs fields are allowed. -terms are similar to the usual Yukawa terms, where -Higgs and or play the role of the quark/lepton doublets and singlets.

The usual soft mass terms of the MSSM scalar fields are allowed just like in the MSSM. In contrast, -terms and soft Majorana gaugino masses are forbidden by -symmetry. The fermionic components of the chiral adjoint, for each standard model gauge group , , , respectively, are paired with standard gauginos to build Dirac fermions and the corresponding mass terms. The Dirac gaugino masses generated by -type spurions produce additional terms with the auxiliary -fields in the Lagrangian, which after being eliminated through their equations of motion lead to the appearance of Dirac masses in the scalar sector as well. For our phenomenological studies of two-loop effects we take the soft-breaking scalar mass terms that have been considered in [17]where the holomorphic mass terms for adjoint scalars, which might lead to tachyonic states, have been neglected (see also [40, 41] for discussions that these terms can be subdominant within a broad definition of gauge mediation).

The electroweak symmetry breaking (EWSB) is triggered by nonzero vacuum expectation values of neutral EW scalars, which are parameterized as -Higgs bosons carry -charge 2 and therefore do not develop vacuum expectation values. We stress that in general the mixing of with and leads to a reduction of the lightest Higgs boson mass at the tree-level compared to the MSSM.

#### 3. Higgs Mass Dependence on Superpotential Parameters

We now present the MRSSM Higgs boson mass prediction at the two-loop level. We use the same renormalization scheme as in [17], where all SUSY parameters are defined in the scheme and , , , and are determined by minimizing the effective potential at the two-loop order. The discussion is divided into two parts. In the present section we begin with the one-loop contributions, which are dominated by terms of , where collectively denotes squares of the superpotential couplings and . We then discuss the two-loop contributions of , that is, ones which depend on parameters which already play a role at the one-loop level. In the subsequent section we then discuss those two-loop corrections which involve new parameters.

In the usual MSSM, the one-loop contributions to the Higgs boson mass are dominated by top/stop contributions. In the MRSSM, these contributions are also important, but they are simpler since stop mixing is forbidden by -symmetry (corresponding to the MSSM parameter ). This implies that the top/stop contributions cannot reach values as high as in the MSSM for a given stop mass scale. However, as mentioned above, the MRSSM superpotential contains new terms governed by and which have a Yukawa-like structure. References [17, 35] have given a useful analytical approximation for these contributions. In the limit , , , and large , we get This result shows a behavior proportional to , , and . This is similar to the top/stop contributions as ’s and appear in a similar fashion in superpotential.

We expect therefore that the two-loop result will depend on these model parameters (which already entered at the one-loop level) in a manner similar to the pure top quark/squarks two-loop contributions, that is, similar to the MSSM contributions without stop mixing.

In Figures 1 and 2 the dependence of the lightest Higgs boson mass calculated at tree-, one-, and two-loop levels for two benchmarks BMP1 and BMP3 on different model parameters is shown. All parameters except the ones shown on the horizontal axes are set to the values of the benchmark points defined in [17] (see Table 2). Indeed behavior of the two-loop corrections is very similar to the one of the corresponding one-loop corrections. The numerical impact of the two-loop -contributions is rather small, typically less than GeV, except for very large , where they can reach several GeV. Particularly, the strong dependence for large is already manifest for the tree-level mass; this is due to the mixing with the singlet state already present in the tree-level mass matrix.