Higgs and the electroweak precision observables in the MRSSM
HHiggs and the electroweak precision observables inthe MRSSM
Philip Diessner † , Wojciech Kotlarski ∗ †§ † Institut für Kern- und Teilchenphysik, TU Dresden, 01069 Dresden, Germany § Faculty of Physics, University of Warsaw, Pasteura 5, 02093 Warsaw, PolandE-mail: [email protected],[email protected]
We briefly review recent progress in the analysis of the Higgs sector of the Minimal R-symmetricSupersymmetric Standard Model. Importance of the interplay between W and Higgs bosonmasses in constraining the parameter space of the model is shown.
Proceedings of the Corfu Summer Institute 2014 "School and Workshops on Elementary Particle Physicsand Gravity",3-21 September 2014Corfu, Greece ∗ Speaker. c (cid:13) Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. http://pos.sissa.it/ a r X i v : . [ h e p - ph ] M a y iggs boson and EWPO in the MRSSM Wojciech Kotlarski
1. Introduction
In recent years non-minimal SUSY models have been gaining increasing attention. This is, onone hand, due to the discovery of a Higgs boson whose mass is close to the maximal one allowed inthe MSSM, and to no discovery of SUSY particles during Run I of the LHC on the other. Proposedextensions vary greatly, from ’simple’ ones, like NMSSM, to rich and complicated like E MSSMand beyond. One of those models is MRSSM, which is a minimal supersymmetrized StandardModel preserving R-symmetry. It was proposed in [1], in the context of solving the flavor problemof the MSSM. Since the discovery of a Higgs boson by the ATLAS and CMS experiments at theLHC it became of interest if this model can accommodate it. First answer to this question was givenin [2], followed by calculation of complete one-loop corrections to Higgs and W boson masses [3]and two-loop corrections in the effective potential approximation and gauge-less limit [4]. In thisnote we briefly review results presented in [3].
2. The MRSSM
Table 1 lists the particle content of the MRSSM, together with R-charge assignment for thesuperfields. With this assignment, R-symmetric superpotential reads W = µ d ˆ R d · ˆ H d + µ u ˆ R u · ˆ H u + Λ d ˆ R d · ˆ T ˆ H d + Λ u ˆ R u · ˆ T ˆ H u + λ d ˆ S ˆ R d · ˆ H d + λ u ˆ S ˆ R u · ˆ H u − Y d ˆ d ˆ q · ˆ H d − Y e ˆ e ˆ l · ˆ H d + Y u ˆ u ˆ q · ˆ H u , (2.1)where ˆ H u , d are the MSSM-like Higgs weak iso-doublets, and ˆ S , ˆ T , ˆ R u , d are the singlet, weak iso-triplet and ˆ R -Higgs weak iso-doublets, respectively. The usual MSSM µ -term is forbidden; insteadthe µ u , d -terms involving R-Higgs fields are allowed. The Λ , λ -terms are similar to the usual Yukawaterms, where the ˆ R -Higgs and ˆ S or ˆ T play the role of the quark/lepton doublets and singlets.Since Majorana masses for the gauginos are forbidden by the R-symmetry, appearance ofgauge single, SU ( ) L triplet and SU ( ) C octet superfields ˆ S , ˆ T and ˆ O is dictated by the need towrite their Dirac mass terms of the form V D (cid:51) M DB ˜ B ˜ S + M DW ˜ W a ˜ T a + M DO ˜ g a ˜ O a + h.c. , (2.2)where ˜ B , ˜ W and ˜ g are familiar MSSM Weyl fermions.In the scalar sector, after the electroweak symmetry breaking, (neutral) scalar components ofˆ H d , ˆ H u , ˆ S and ˆ T acquire vev, which we parametrize as H d = √ ( v d + φ d + i σ d ) , H u = √ ( v u + φ u + i σ u ) , T = √ ( v T + φ T + i σ T ) , S = √ ( v S + φ S + i σ S ) . (2.3)Since R-Higgs bosons carry R-charge 2 their vev would spontaneously break R-symmetry leadingto a massles R-axion. Therefore we do not consider it here.In the next section we will discus v T , which is strongly constrained by the measurement of theW boson mass.CP-even components { φ d , φ u , φ S , φ T } mix giving rise to 4 physical Higgs boson. Due to themixing, lightest Higgs mass is always lower than in the MSSM, requiring larger radiative correc-tions to reach the measured value. In sec. 4 we will show that this is indeed achievable in theMRSSM. 2 iggs boson and EWPO in the MRSSM Wojciech Kotlarski
Field Superfield Boson FermionGauge Vector ˆ g , ˆ W , ˆ B g , W , B g , ˜ W ˜ B +1Matter ˆ l , ˆ e +1 ˜ l , ˜ e ∗ R +1 l , e ∗ R q , ˆ d , ˆ u +1 ˜ q , ˜ d ∗ R , ˜ u ∗ R +1 q , d ∗ R , u ∗ R H -Higgs ˆ H d , u H d , u H d , u − R d , u +2 R d , u +2 ˜ R d , u +1Adjoint Chiral ˆ O , ˆ T , ˆ S O , T , S O , ˜ T , ˜ S − Table 1:
The R-charges of the superfields and the corresponding bosonic and fermionic components.
3. Precision EW observables
The vev v T of the SU ( ) L triplet field T in eq. 2.3 breaks the custodial symmetry already atthe tree level shifting the W boson mass by m W = g v + g v T , (3.1)where v ≡ v u + v d . Large | v T | is therefore excluded by measurement of m W = . ± .
015 GeV[5]. Small | v T | corresponds, through tadpole equations, to large values of triplet soft-mass parame-ter m T , leading to somewhat split spectrum with heaviest Higgs boson around few TeV for | v T | offew hundred MeV.To approach experimental accuracy of 15 MeV for m W one has to include at least one-loopcorrections which can be concise written in the DR scheme as (see ref. [6]) m W = m Z ˆ ρ (cid:34) + (cid:115) − π ˆ α √ G µ m Z ˆ ρ ( − ∆ ˆ r W ) (cid:35) , (3.2)where ˆ ρ contains only oblique while ∆ ˆ r W both oblique and non-oblique corrections (see ref. [6] and[3] for the thorough discussion of this formula). Equation 3.2, although very useful for numericalevaluation of the contributions as it properly resums leading two-loop SM corrections [6], does notgive direct insight into importance of different contributions due to implicit cancelations betweenˆ α , ˆ ρ and ˆ r W .Expanding eq. 3.2 and recasting it in terms of familiar S,T and U parameters [7–12] we get m W = m ref W + ˆ α m Z ˆ c W ( ˆ c W − ˆ s W ) (cid:18) − S + ˆ c W T + ˆ c W − ˆ s W s W U (cid:19) . (3.3)where m ref W is W boson mass as calculated in the SM. Figure 1 shows result of this decompositionfor one of the benchmark points of ref. [3]. We see that the full result (given by the black line) iswell approximated by the sum of tree and one-loop contributions to the T -parameter. Importanceof formula 3.3 comes from the fact that in many cases one can find relatively simple, conciseexpressions for the T -parameter. Also, T -parameter constraints not only m W , but also other EWprecision observables. For the benchmark points devised in [3], the total contributions to the T -parameter were always smaller than 0.1. 3 iggs boson and EWPO in the MRSSM Wojciech Kotlarski Λ u m W tan β =3 Complete MRSSM predictionSM + v T contribution + approximation for T from all sectorsSM + approximation for T from all sectorsSM + approximation for T from neut/char sectorSM + v T contribution Figure 1:
Comparison of the mass of the W boson depending on Λ u , calculated using full MRSSM con-tributions and different approximations for the T -parameter. Black stars marks the benchmark points of ref[3].
4. Higgs mass at one loop
As already pointed out, the lightest Higgs boson mass in the MRSSM suffers at the tree-level from reduction (compared to MSSM) due to mixing with singlet and triplet states. Thiscan be seen from an approximate formula, when using the MSSM mixing angle α to diagonalize { φ d , φ u } submatrix for large m A when α = β − π /
2, further assuming λ = λ u = − λ d , Λ = Λ u = Λ d , µ u = µ d = µ and v S ≈ v T ≈
0, which reads m H , approx = m Z cos β − v (cid:16) g M DB + √ λ µ (cid:17) ( M DB ) + m S + (cid:0) g M DW + Λ µ (cid:1) ( M DW ) + m T cos β . (4.1)Beyond the tree-level the Higgs mass receives large corrections which push its value towards themeasured one. This is achieved with stops of mass around 1 TeV and without L-R mixing inthe squark sector which is forbidden by the R-symmetry. Figure 2 compares impact of full one-loop corrections with ones calculated in the effective potential approximation for 3 superpotentialparameters: Λ u , Λ d and λ u . Large values of couplings Λ , λ , needed to lift the mass of the lightestHiggs, could in principle cause conflict with W boson mass measurement. This is exemplifiedin fig. 3 where the mentioned interplay between m h and m W predictions for one selected pair ofsuperpotential parameters is shown. We emphasize that the analysis of T -parameter contributionsdiscussed in the previous section was done only in order to understand (approximate) functionaldependence of m W on the parameters of the model. All numerical calculations were done using eq.3.2. As already pointed out it the abstract, it is clear from fig. 3 that W and Higgs boson massesgive non-trivial constrains on the parameter space of the model. Nevertheless it is easy to identifyregions in the parameter space which accommodate both measurements.
5. Conclusions
In this work we have reviewed recent progress in the analysis of the Minimal R-symmetricSupersymmetric Standard Model. We showed that the model can accommodate measured Higgs4 iggs boson and EWPO in the MRSSM
Wojciech Kotlarski
Figure 2:
Comparison of the lightest Higgs boson mass calculated using the effective potential approach(blue) and the full one-loop calculation (red), as well as the tree-level mass (magenta). Results are shown asfunctions of one of the couplings: Λ u (solid), Λ d (dots), λ u (dashes), for benchmark point 1 of ref. [3]. λ u µ u . . . . . Figure 3:
Interplay between Higgs and W boson masses for superpotential parameters λ u and µ u . Greenregion corresponds to m h = ± ± m W . boson mass while being in agreement with measured mass of the W boson. The ∼
125 GeV Higgsmass is obtained without stop mixing, which is forbidden by the R-symmetry, and with stops ofmasses below 1 TeV, which is an attractive feature, both theoretically and experimentally. Despitethat, there are still some open questions like issue of dark matter or confronting MRSSM with LHClimits from direct searches of SUSY particles. We hope that these question will be addressed, withpositive outcome, in the near feature.
In ref. [4] we substantially refined the calculation by including two-loop corrections to Higgsmass in effective potential approximation and gauge-less limit. Although important, those contri-butions don’t change conclusions of [3]. iggs boson and EWPO in the MRSSM Wojciech Kotlarski
Acknowledgments
Work supported in part by the German DFG Research Training Group 1504 and the DFG grantSTO 876/4-1, the Polish National Science Centre grants under OPUS-2012/05/B/ST2/03306 andthe European Commission through the contract PITN-GA-2012-316704 (HIGGSTOOLS).
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