The Constrained E 6 SSM

The Constrained E6SSMDavid J Miller

The 2009 Europhysics Conference on High Energy Physics

17th July 2009

Based on:

P. Athron, S.F. King, DJM, S. Moretti, R. Nevzorov

arXiv:0901.1192

arXiv:0904.2169

The E6SSM

17th July 2009 2The 2009 Europhysics Conference on High Energy Physics

“Inspired” by the gauge group E6 , breaking to the SM via

where only one linear superposition of the extra U(1) symmetries survives to low energies:

So the E6SSM is really a gauge theory.

This combination is required in order to keep the right handed neutrinos sterile.

[S.F.King, S.Moretti & R. Nevzorov, Phys.Rev. D73 (2006) 035009 ; Phys.Lett. B634 (2006) 278-284]

Matter Content


All the SM matter fields are contained in one 27-plet of E6 per generation.

27

10, 1

5*, 2

5*, -3

5, -2

1, 0

+

+

+

+

U(1)N charge £ 40SU(5) reps.

1, 5+

singlets

right handed neutrino

3 generations of “Higgs”

exotic quarks

Placing each generation in a 27-plet forces us to have new particle states.:

Now have 3 generations of Higgs bosons. Only the third generation Higgs boson gains a VEV. The others are neutral and charged scalars - we call them “inert Higgs”.

Three generations of singlets, with

New coloured triplets of “exotic quarks” and with charge §1/3.

New gauge group structure, with unification:

Extra U(1) ! extra gauge boson, . After ewsb this will become massive (after eating the imaginary part of S3)

Additional SU(2) doublets and , relics of an additional 270 and 270 which survive down to low energies, and are required for gauge unification.

New exotic states


D i ¹D i

Si

[+ right handed neutrinos]

hS3i 6= 0

Z0

H 0 ¹H 0

Discrete Symmetries


Z2B or Z2

L Symmetries

To prevent proton decay, we need a baryon or lepton symmetryThis is analogous to R-parity in the MSSMNote that the exotic D is odd, while its partner D is even

Z2B D is a leptoquark Z2

L D is a diquark

Approximate Z2H Symmetry

To evade large Flavour Changing Neutral Currents, we need another Z2

Make the 3rd generation Higgs and singlet superfields even, all other fields odd.

Must only be approximate to allow exotic particles to decay.

For a Renormalisation Group analysis and mass spectra, Z2H violating

couplings can be neglected.

~

E6SSM Superpotential


To simplify the model a little:

Impose Z2B/L and (approximate) Z2

H symmetries,

Integrate out heavy right-handed Majorana neutrinos,

Assume a hierarchical structure of Yukawas, and keep only large ones.

Note: this is really an oversimplification – we have lots of very small Z2H violating

couplings such as which are unimportant for production, but may be important for decays.

Also need lots of new SUSY breaking parameters.

WE 6SSM ' ¸S(HdHu) +¸®S(H1;®H2;®) + · iS(D iD i )

+ht(HuQ)tc +hb(HdQ)bc +h¿ (HdL)¿c +¹ 0(H0H 0)

gi j kD i (QjQk)

The Constrained E6SSM


The E6SSM has 43 new parameters compared with the MSSM (14 are phases).

But if we apply constraints at the GUT scale, this is drastically reduced.

Set:

soft scalar masses

gaugino masses

Important parameters:

Renormalisation Group Running


We derived Renormalisation Group Equations, and modified SoftSuSY [Allanach, arXiv:hep-ph/0104145] to run down the GUT scale parameters to low energies.

Gauge and Yukawa couplings (2 loop),Soft breaking gaugino and trilinear masses (2 loop),Soft scalar masses (1 loop).

The evolution of Gauge and Yukawa couplings doesn’t depend on the soft SUSY breaking so they can be done separately and fed into the

Sensitive to thresholds.At one-loop , so need two loops.

Gauge and Yukawa

couplings

Soft SUSY breaking

parameters

¯3 ¼0

TM SSM

Gauge and Yukawa couplings


hSi; tan¯

g1; g2; g3

ht; hb; h¿

¸ i ; · i

experimental values

scenario inputs

first guess

MZ

TE 6SSM

MX

SM running

MSSM running

E6SSM running

g1 = g2 =g3 = g01¸ i ; · i scenario inputs

unification constraint

itera

te

t = ln£Q2=M 2

X

¤

®i (t)

Soft SUSY breaking parameters


m2i (Q) = ai (Q)M 2

1=2 +bi (Q)A20+ci (Q)A0M1=2 +di (Q)m2

0;

A i (Q) = ei (Q)A0+f i (Q)M1=2;

M i (Q) = pi (Q)A0+qi (Q)M1=2:

Generically, we can write

coefficients depend on gauge and Yukawa running

Set two of ________

to zero at MX

m20; M1=2; A0

run down to the low scale (full RGEs)

determine low scale coefficients

numerically

Fix using ewsb constraints

Calculate the mass spectrum

Apply experimental constraints

@V@s = @V

@v1= @V

@v2=0m2

0; M1=2; A0

including one-loop stop contributions

Phenomenological constraints


squarks and gluinos & 300 GeV

exotic quarks and squarks & 300 GeV [HERA]

MZ0 & 700 GeV

Insist on neutralino LSP (sort of)

Keep Yukawa couplings . 3

Inert Higgs and Higgsinos & 100 GeV

To ensure phenomenologically acceptable solutions, we require

Allowed regions in the m0 - M½ plane


(inert Higgs)

Set , and vary and tan ¯ = 10; s = 3;4;5T eV; ¸1;2 = 0:1 · = · 1;2;3¸3

Particle Spectra


Firstly, notice that for most allowed scenarios , so squarks tend to be heavier than the gluino

m~Â01¼M1

m~Â02¼m~Â§1

¼M2

m~g¼M3

m~Â03;4¼m~Â§2

¼¹ = ¸hSi

m~Â05;6¼MZ0

Neutralinos, charginos and gluino

mh3 ¼MZ0

mh1 ¼MZ + ¢mh2 ¼mH § ¼mA

Higgs bosons

exotic quarks ¼· ihSi¼m2

D i+· 2i hSi

2exotic squarks + mixing and auxiliary D-terms

inert Higgs ¼m2H i

+¸2i hSi2 + auxiliary D-terms

inert higgsino ¼¸ ihSi

Benchmark A


tan¯ = 3¸3(MX ) = ¡ 0:465

¸1;2(MX ) = 0:1· 3(MX ) = 0:3

· 1;2(MX ) = 0:3p2hSi = 3:3TeVM1=2 = 365GeVm0 = 640GeVA0 = 798GeV

gluino rather light

light Higgs and Bino

so Ds are degenerate and rather heavy· 1 = · 2 = · 3

Benchmark C


tan¯ = 10¸3(MX ) = ¡ 0:378

¸1;2(MX ) = 0:1· 3(MX ) = 0:42


so degeneracy of Ds is lifted.

lightest exotic quark is 300 GeV

· 1 = · 2 6= · 3

Benchmark E


tan¯ = 30¸3(MX ) = ¡ 0:38

¸1;2(MX ) = 0:1· 3(MX ) = 0:17


mixing causes a rather light (393 GeV) ~D

Heavy Exotics


tan¯ = 10¸3(MX ) = ¡ 2:0

¸1;2(MX ) = 2:6· 3(MX ) = 2:5

· 1;2(MX ) = 2:5p2hSi = 4:0TeVM1=2 = 389GeVm0 = 725GeVA0 = ¡ 1528GeV

it is possible to construct scenarios where all exotic particles are heavy

gluino is still lighter than the squarks

LHC signatures


If the exotic quarks are light, their discovery at the LHC should be rather straightforward.

Since the exotic quarks are colored, their production cross-sections are very large

¹ D =300GeV

~t

Db

~Â01

t

LHC signatures: Exotic quarks


pp! t¹tb¹b+EmissT +X

~¿D

t

~Â01

¿pp! b¹b+Emiss

T +X

~Â01

~b

Dº¿

b

Assuming Ds couple predominantly to the 3rd generation:

Diquarks decay to so would give an enhancement to

Leptoquarks decay to so give enhancements to

Notice that SM production of is suppressed by in comparison.

pp! t¹t¿+¿¡ +EmissT +X

t¹t¿+¿¡(®W=¼)2

LHC signatures: Exotic quarks and squarks


If the Z2H violating coupling, e.g. is very small, D quarks may

hadronize before they decay leading to spectacular signatures.gi j kD i (QjQk)

The exotic squarks are Z2B/L even, so don’t need to decay to the LSP.

They give an enhancement to, e.g.

Note that the Tevatron rules out the scalar diquarks lighter than about 630 GeV and scalar leptoquarks lighter than about 300 GeV.

Inert Higgs decays are similar to their MSSM counterparts

pp! t¹t¿¹¿ +X

~D

g

gg

~g

~g

~q

~q

~Â01

~Â01

¹qq

¹q q

Scenarios with heavy exotics


Even if all the exotic particles are heavy, the cE6SSM still makes striking predictions.

light gluino, much lighter than the squarks light neutralinos and light chargino

Gluino decays will provide an enhancement of

~Â01 ~Â0

2~Â§1

The 2009 Europhysics Conference on High Energy Physics 2217th July 2009

The E6SSM provides a credible example of a model which could arise from a GUT, where each generation forms a complete 27-plet of E6.

We have examined a constrained E6SSM, using RGEs to construct realistic, phenomenologically reasonable scenarios at LHC energies.

The model predicts a light gluino, much lighter than the squarks, light neutralinos, and , and a light chargino .

It also predicts new exotic quarks and squarks, “inert” Higgs bosons, and a Z0.

If the new exotic quarks are light, they will give striking signatures, such as a significant enhancement to which should be easily observable at the LHC.

Conclusions and Summary

~Â01

~Â02 ~Â§

1

pp! t¹tb¹b+EmissT +X

Benchmark B


tan¯ = 10¸3(MX ) = ¡ 0:37

¸1;2(MX ) = 0:1· 3(MX ) = 0:2


particularly light inert Higgs (154 GeV)

Benchmark D


tan¯ = 10¸3(MX ) = ¡ 0:395

¸1;2(MX ) = 0:1· 3(MX ) = 0:43


The Constrained E 6 SSM

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