Electroweak Symmetry Breaking in the E6SSM
arXiv:0708.3248v1 [hep-ph] 23 Aug 2007
Peter Athron1,3 , SF King2 , DJ Miller1 , S Moretti2 and R Nevzorov1
Department of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, UK School of Physics and Astronomy, University of Southampton, Southampton, SO17 1BJ
E-mail: 3 firstname.lastname@example.org Abstract. The Exceptional Supersymmetric Standard Model (E6 SSM) is an E6 inspired model with an extra gauged U(1) symmetry, which solves the ?-problem in a similar way to the NMSSM but without the accompanying problems of singlet tadpoles or domain walls. It predicts new exotic particles at the TeV scale. We investigate the Renormalisation Group Evolution of the model and test electroweak symmetry breaking for a selection of interesting scenarios with non-universal Higgs masses at the GUT scale. We present a detailed particle spectrum that could be observed at the LHC.
1. Introduction The E6 SSM[1, 2] is an E6 inspired model with an extra gauged U(1) symmetry. It provides a low energy alternative to the Minimal (MSSM) and Next to Minimal (NMSSM) Supersymmetric Models. The gauge √ group is SU(3)× SU(2)×U(1)Y ×U(1)N , where U(1)N is de?ned by U(1)N = 1/4U(1)χ + 15/4U(1)ψ , with U(1)χ and U(1)ψ in turn, de?ned by the breaking, E6 →SO(10)×U(1)ψ and SO(10)→SU(5)×U(1)χ . The matter content is based on three generations of complete 27plet representations of E6 in which anomalies are automatically cancelled. Each 27plet, (27)i , is ?lled with one generation of ordinary matter; singlet ?elds, Si ; up and down type Higgs like ?eld, H2,i and H1,i and exotic ? ? coloured matter, Di , Di . In addition the model contains two extra SU(2) doublets, H ′ and H ′ , which are required for gauge coupling uni?cation. ? The superpotential is WE6 SSM ≈ λi SH1,i H2,i + κi SDi Di + ht Hu Qtc + hb Hd Qbc + hτ Hd Lτ c , 0 0 where Hu = H2,3 and Hd = H1,3 and S = S3 develop vevs, Hu = vu , Hd = vd and S = s. vu and vd give mass to ordinary matter via the Higgs mechanism, while s both gives mass to the exotic coloured ?elds, κi S → κi s = mDi and generates an e?ective ?-term, ?ef f = λ3 s. Another striking advantage of this model is that the upper bound on the mass of the lightest Higgs is 155 GeV, signi?cantly larger than in either the MSSM or the NMSSM. 2. EWSB in the E6 SSM Our current work is to test if, following the imposition of some simple high scale assumptions, electroweak symmetry breaking (EWSB) may be radiatively driven in the E6 SSM as happens in the MSSM and NMSSM. This is an important test for the model and allows us to predict mass spectra which could be seen at the LHC from a small number of GUT scale parameters. Solutions with universal scalar masses at the GUT scale, in addition to universal gaugino masses and universal trilinears, are di?cult to ?nd. Relaxing the high scale assumptions to allow non-universal Higgs masses (NUHM) avoids this di?culty. This gives us the NUHM
E6 SSM GUT scale constraints: universal gauginos (M1/2 ), universal trilinears (A), GUT scale Higgs masses (mGU T , mGU T and mGU T ) and a common scalar mass (m0 ) for all other E6 SSM Hd S Hu scalars. The NUHM E6 SSM is an interesting scenario in it’s own right, but can also be used as a starting point in the search for solutions with stronger universality assumptions. Here we present results of the ?rst study into EWSB in this NUHM E6 SSM model. As a test case we chose the new E6 SSM Yukawas to be λ3 = 0.6, λ1,2 = 0.46 and κ1,2,3 = 0.162 at the GUT 2 2 scale. We also chose tan β = vu /vd = 10 and s = 3 TeV and ?xed v 2 = vu + vd = (174 GeV)2 . 1 (RGE) solutions for soft masses at the Next we obtained Renormalisation Group Equation electroweak (EW) scale, allowing us to write all low energy soft masses of the E6 SSM in terms of the NUHM E6 SSM GUT scale parameters,
2 m2 = αi M1/2 + βi A2 + γi AM1/2 + δi m2 + ?i mGU T 2 + ρi mGU T 2 + ζi mGU T 2 , i S Hu 0 Hd
Aj = aj M1,2 + bj A
Mk = ck M1/2 ,
where mi are the scalar masses, Aj the trilinears and Mk the gauginos masses and each mass has it’s own set of dimensionless coe?cients relating it to the GUT scale parameters. EWSB breaking constraints ?x the three Higgs masses (mHu , mHd and mS ) at the EW scale in terms of the Yukawas, gauge couplings, vevs and Aλ3 . The RGE solution for Aλ3 can be substituted into this. Since all vevs and susy-preserving parameters were either set to their observed values or already chosen, the Higgs masses can then be written as functions of A and M1/2 . For example m2 = pM1/2 + qA + l + 1loop, where p,q and l are dimensionful coe?cients ?xed by the vevs S and susy-preserving parameters. So for each of the Higgs masses we have two constraints which may be equated leaving three low energy constraints and six GUT scale parameters. For all choices of M1/2 , A and m0 we can then determine what values of m2 d , m2 u and m2 are required to satisfy the constraints. H H S The values obtained for these parameters are shown in Fig.1(a-c) with the large white regions ruled out by GUT scale tachyons when (mGU T )2 < 0, (mGU T )2 < 0 or (mGU T )2 < 0 respectively. S Hu Hd From (a) all parameter space accessible at future colliders with M1/2 > 0 is excluded, but M1/2 < 0 is valid in our scheme2 . (b),(c) exclude some additional points with M1/2 > 0. Fig.1(d) shows the combined exclusion region from (a-c) and also a large region of parameter space ruled out by EW scale tachyons and a small slice ruled out by experiment. While EWSB provides strong constraints on the NUHM E6 SSM, there is a large volume of parameter space which may be physically realised and could be discovered at the LHC. A sample spectrum which might be observed is shown in Fig.2. The presence of the exotic coloured ? particles (D1,2 and D) and the new Z ′ boson at low energies provide interesting experimental signatures for the model. The gluino is lighter than most of the squarks, which is unusual and phenomenologically interesting as it a?ects cascade decays. This is a result of the renormalisation group (RG) running of the soft masses in the E6 SSM and is typical of points we have looked at in the NUHM E6 SSM. The smaller the hierarchy amongst the GUT scale soft parameters, the stronger this e?ect. If solutions with fully universal scalar masses at the GUT scale can be found then the gluino will be lighter than all squarks and sleptons. 3. Conclusions For our benchmark choice of E6 SSM Yukawas and vevs there were no solutions with all universal scalar masses at the GUT scale. We allowed non universal Higgs masses, and obtained a dramatic
Two loop beta functions were used for the susy preserving E6 SSM parameters, but the soft susy-breaking parameters were only evolved with one loop RGEs. 2 Often conventions are chosen such that M1/2 > 0. We haven’t done this here but one can perform the transformation, A → ?A, M1/2 → ?M1/2 , s → ?s, to obtain solutions with M1/2 > 0 but with di?erent signs for some Yukawas and vevs.
Figure 1. EWSB exclusion plots in the m0 , M1/2 plane, with A = ?300 GeV. (a): mGU T Hd values consistent with the EWSB and NUHM E6 SSM boundary conditions. The white region is ruled out since (mGU T )2 < 0. (b): As (a) but for mGU T . (c): As (a) but for mGU T. (d): Full S Hu Hd exclusion plot. The blue (black) region shows the allowed region of the parameter space, the purple (dark grey) region is ruled out by searches for the charginos and gluinos, while the pink (light grey) and white regions are ruled out by EW and GUT scale tachyons respectively.
~ D2 Z′ ~ ~2 t2 u ~ u1 ~ t1 ~ e1 ~ d1,2 ~ e2 χ± 2 ~ g
0 χ5 0 χ6 χ0 3,4
D ~ D1
χ± 1 χ0 1
Figure 2. A sample NUHM E6 SSM spectrum that could be seen at the LHC. The parameters for this point are m0 = 600 GeV, M1,2 = ?500 GeV, A = ?300 GeV, mGU T = 2.39 TeV, S mGU T = 2.25 TeV & mGU T = 922 GeV Hd Hu
improvement. We discovered many spectra that could be seen at the LHC. The RG ?ow implies that the gluino is often lighter than the squarks. To improve this study we want to include two loop RGEs for gaugino masses, which preliminary results suggest are much more signi?cant than may naively be anticipated, and look for solutions with stronger universality assumptions. References
 S. F. King, S. Moretti and R. Nevzorov, Phys. Rev. D 73 (2006) 035009 [arXiv:hep-ph/0510419].  S. F. King, S. Moretti and R. Nevzorov, Phys. Lett. B 634 (2006) 278 [arXiv:hep-ph/0511256].