Nonstandard Higgs decays
in the E 6 inspired SUSY models
Roman Nevzorov (University of Adelaide & ITEP)
in collaboration with Sandip Pakvasa
Outline
Introduction
E6 inspired SUSY models with extra U(1)N symmetry Inert neutralinos
Exotic Higgs decays Conclusions
Based on:
R. Nevzorov, S. Pakvasa, Phys. Lett. B 728 (2014) 210 [arXiv:1308.1021 [hep-ph]].
R. Nevzorov, Phys. Rev. D 87 (2013) 015029 [arXiv:1205.5967 [hep-ph]].
S. F. King, S. Moretti and R. Nevzorov, Phys. Lett. B 650 (2007) 57;
S. F. King, S. Moretti and R. Nevzorov, Phys. Rev. D 73 (2006) 035009;
S. F. King, S. Moretti and R. Nevzorov, Phys. Lett. B 634 (2006) 278.
Introduction
Recent astrophysical and cosmological observations indicate that 22% − 25% of the energy density of the Universe exists in the form of dark matter.
The existence of dark matter is the strongest piece of evidence for physics beyond the SM.
Dark sector may affect the Higgs decay rates to SM
particles and give rise to new channels of Higgs decays.
In particular, there exist several extensions of the SM in which Higgs can decay into invisible final states.
SUSY models;
models with compact and large extra dimensions;
littlest Higgs model with T-parity...
It is interesting to study Higgs phenomenology and dark sector within well motivated extensions of the SM.
E 6 inspired SUSY models
At high energies E6 may be broken to
E6 → SU(3)C × SU(2)W × U(1)Y × U(1)N × Z2M , U(1)N = 1
4U(1)χ +
√15
4 U(1)ψ , Z2M = (−1)3(B−L) ,
where E6 → SO(10) × U(1)ψ, SO(10) → SU(5) × U(1)χ.
In the E6 inspired SUSY models with extra U(1)N
symmetry right–handed neutrinos do not participate in the gauge interactions.
Thus right–handed neutrinos can be superheavy,
shedding light on the origin of the mass hierarchy in the lepton sector.
In this case lepton asymmetry can be dynamically
generated via the decays of N1c and then gets converted into baryon asymmetry due to sphaleron interactions.
To ensure anomaly cancellation the particle content of the E6SSM is extended to include three complete 27i
representations of E6.
In addition the spectrum of the E6SSM is supplemented by SU(2) doublet and anti-doublet from extra 27′ and 27′ (L4 and L4) to preserve gauge coupling unification in the one–loop approximation.
Together with survivors the particle content of the E6SSM becomes
3 × 27i + L4 + L4 = 3
Qi, uci, dci, Li, eci
+ 3(Di, Di)+
+3(Hiu) + 3(Hid) + 3(Si) + 3(Nic) + L4 + L4 .
Di and Di can be either diquarks or leptoquarks.
Hid and Hiu are either Higgs or inert Higgs fields.
To suppress baryon number violating and flavour
changing processes one can postulate Z˜2H symmetry under which all superfields except Hd ≡ H3d, Hu ≡ H3u, S ≡ S3, L4 and L4 are odd.
The Z˜2H symmetry reduces the structure of Yukawa interactions to:
WE6SSM ≃ λS(HuHd) + λαβS(HαdHβu) + κijS(DiDj) + ˜fαβSα(HβdHu) +fαβSα(HdHβu) + gijD(QiL4)Dj + hEiαeci(HαdL4) + µLL4L4
+1
2MijNˆicNˆjc + hNαj( ˆHαuLˆ4) ˆNjc + hij( ˆHuLˆi) ˆNjc + WM SSM(µ = 0) .
where α, β = 1, 2 and i = 1, 2, 3 .
Hu, Hd and S play the role of Higgs superfields.
The U(1)N symmetry forbids bilinear term µHuHd in the superpotential but allows interaction λS(HuHd) .
At the physical vacuum hHdi = v1
√2, hHui = v2
√2, hSi = s
√2, where v2 = v12 + v22 = (246 GeV )2 and tan β = v2/v1.
The VEV of S breaks U(1)N inducing the masses of Z′ boson and exotic particles as well as providing solution of the µ–problem µef f = λs/√
2.
At the tree level CP is preserved in the Higgs sector of the E6SSM so that the Higgs spectrum contains
– one pseudoscalar m2A ,
– two charged states m2H± = m2A + O(MZ2) ,
– three scalars m2h3 = m2A + O(MZ2), m2h2 = MZ2′ + O(MZ2) .
The mass of the lightest Higgs particle in the E6SSM does not exceed 150 − 155 GeV.
Inert neutralinos
The interactions of inert Higgs superfields Hαd, Hαu and Sα are described by
WIH = λαβS(HαdHβu) + fαβSα(HdHβu) + ˜fαβSα(HβdHu) . The fermionic components of these superfields form inert neutralino and chargino states.
We require
all Inert charginos to be heavier than 100 GeV to satisfy LEP constraints;
s to be large enough to avoid lower experimental bound on the Z′ mass (s & 8TeV);
the validity of perturbation theory up to the GUT scale that constrains the allowed range of all Yukawa couplings
Our analysis indicates that
the lightest and second lightest Inert neutralinos (χ1 and χ2), which are predominantly Inert singlinos, are always light (mχ1, χ2 . 60 − 65GeV);
χ1 and χ2 may have rather small couplings to Z so that they could escape detection at LEP.
The Lagrangian that describes interactions of the Z-boson with χ1 and χ2 can be written as
LZχχ = g¯ 4Zµ
χαγµγ5χβ
RZαβ ,
Since the masses of χ1 and χ2 are determined by v their couplings to the SM-like Higgs boson are
ghχαχα ≈ mχα/v .
Z2M and Z˜2H symmetries ensure that χ1 and the lightest ordinary neutralino χ˜1 are absolutely stable.
When mχ1 ≪ MZ/2 the lightest Inert neutralino has rather small couplings and σ(χ1χ1 → anything) is too
small leading to the extremely large dark matter density.
The reasonable dark matter density can be obtained for mχ1 ∼ MZ/2 when the s-channel annihilation through the Z-boson is the dominant annihilation channel.
However the SM-like Higgs boson decays more than 95% of the time into either χ1 or χ2 in this case while the branching ratios into SM particles are suppressed.
The simplest phenomenologically viable scenarios imply that χ1 is substantially lighter than 1 eV.
Exotic Higgs decays
In this case χ1 forms hot dark matter in the Universe but gives only a very minor contribution to the dark matter density.
The lightest ordinary neutralino may account for all or some of the observed cold dark matter density.
Since χ1 is extremely light it does not affect Higgs phenomenology.
The presence of χ2 with the GeV scale mass gives rise to the substantial branching ratio of the nonstandard Higgs decays h1 → χ2χ2.
The lifetime of χ2, which decays into χ1 + ff¯ via virtual Z, tends to be rather long
τχ2 ∼ 1
|RZ12|2m5χ2 .
Thus χ2 decays outside the detectors resulting in the invisible branching ratio of the SM-like Higgs.
We require that χ2 decays before BBN, i.e. τχ2 < 1 sec.
This requirement basically rules out too light χ2. It is quite problematic to satisfy this restriction if mχ2 . 100 MeV.
The branching fraction of the nonstandard Higgs decays depends rather strongly on mχ2.
If χ2 is heavier than 2.5 GeV the branching ratio of the exotic Higgs decays can be as large as 20-30%.
When χ2 is lighter than 0.5 GeV this branching ratio can be as small as 10−3 − 10−4.
Benchmark point A (All mass parameters are given in GeV):
Parameters : tanβ = 1.5, s = 12000, λ = 0.6 mQ,U = MS = 4000, Xt = √
6MS, mh1 ≃ 125,
−λ22 = λ11 = 0.012, λ12 = λ21 = 0, f12 = 0.00001, f21 = −0.1, f11 = −f22 = ˜f11 = ˜f22 = 0.1, f˜12 = 0.000011, f˜21 = 0.1 .
Spectrum: mχ±
2 ≃ 101.8, mχ6 ≃ 105.2, mχ5 ≃ 104.9, mχ4 ≃ 104.1, mχ±
1 ≃ 101.8, mχ3 ≃ 101.8, mχ2 ≃ 2.67, mχ1 ≃ 6.5 · 10−11, Couplings : |RZχ1χ1| ≃ −0.0212, |RZχ1χ2| ≃ 0.0271, RZχ2χ2 ≃ 0.0103, Higgs Decay Br(h1 → χ2χ2) ≃ 21.9%,
rates: Br(h1 → b¯b) ≃ 46.4%, Γtot ≃ 0.0051.
Benchmark point B (All mass parameters are given in GeV):
Parameters : tanβ = 1.5, s = 12000, λ = 0.6 mQ,U = MS = 4000, Xt = √
6MS, mh1 ≃ 125,
−λ22 = λ11 = 0.06, λ12 = λ21 = 0, f12 = 0.00001, f21 = −0.1, f11 = −f22 = ˜f11 = ˜f22 = 0.1, f˜12 = 0.000011, f˜21 = 0.1 . Spectrum: mχ±
2 ≃ 509.1, mχ6 ≃ 509.8, mχ5 ≃ 509.7, mχ4 ≃ 509.6, mχ±
1 ≃ 509.1, mχ3 ≃ 509.1, mχ2 ≃ 0.55, mχ1 ≃ 1.4 · 10−11, Couplings : |RZχ1χ1| ≃ −0.00090, |RZχ1χ2| ≃ 0.00116, RZχ2χ2 ≃ 0.00045, Higgs Decay Br(h1 → χ2χ2) ≃ 1.23%,
rates: Br(h1 → b¯b) ≃ 58.7%, Γtot ≃ 0.004.
Conclusions
The E6 inspired SUSY models with extra U(1)N symmetry lead to the presence of two light inert
neutralinos χ1 and χ2 with masses below 60-65 GeV.
In this model χ1 and the lightest ordinary neutralino are absolutely stable and can contribute to the dark matter density.
The simplest phenomenologically viable scenarios imply that χ1 is considerably lighter than 1 eV forming hot dark matter in the Universe.
If χ2 has GeV scale mass it tends to be longlived particle with τχ2 < 1 sec.
Such next–to–lightest inert neutralino can give rise to the substantial invisible branching ratio of the SM–like Higgs boson that can be as large as 20%.
Backup slides
In the E6SSM two–loop corrections to αi(µ) are large and could spoil gauge coupling unification.
However it was argued that within the E6SSM gauge coupling unification can be achieved for any value of α3(MZ) which is in agreement with current data [S.F.King,
S.Moretti, RN, Phys.Lett.B 650 (2007) 57].
Two–loop RG flow of αi(µ) in the E6SSM and MSSM
-60 -50 -40 -30 -20 -10 0
0.02 0.04 0.06 0.08 0.1 0.12 0.14
-60 -50 -40 -30 -20 -10 0
0.02 0.04 0.06 0.08 0.1 0.12 0.14
2 log[µ/MX] 2 log[µ/MX]
In the field basis ( ˜H2d0, H˜2u0, S˜2, H˜1d0, H˜1u0, S˜1) the mass matrix of the inert neutralino sector takes a form
MIN =
A22 A21 A12 A11
,
Aαβ = − 1
√2
0 λαβs f˜βαv sinβ λβαs 0 fβαv cos β f˜αβv sin β fαβv cos β 0
.
In the basis ( ˜H2u+, H˜1u+, H˜2d−, H˜1d−) the mass matrix of the inert chargino states is given by
MIC =
0 CT
C 0
, Cαβ = 1
√2λαβ s .
In order to clarify the obtained results let us consider
λαβ = λα δαβ, fαβ = fα δαβ, f˜αβ = ˜fα δαβ .
In this case the masses of the Inert charginos are
mχ±α = λα
√2 s .
In the limit when λα s ≫ f˜α v, fα v one obtains
mχα ≈ f˜αfαv2 sin 2β
2mχ±α , f˜α ∼ fα < 0.6 − 0.65 , LZχχ = g¯
4Zµ
χαγµγ5χβ
RZαβ , RZαβ = RZαα δαβ , RZαα = v2
2m2
χ±α
fα2 cos2 β − f˜α2 sin2 β
.
