Supersymmetric Models with extra singlets: a review
DJ Miller, University of Glasgow Plenary talk, Whepp-9, Bhubaneswar, India 3-14 January 2006
This talk will lean heavily on the review
Models with extra singlets written
for the CPNSH Report by J. Gunion, DJM, A. Pilaftsis
: This talk presents of a personal viewpoint of the supersymmetric models with extra singlets. It does not claim to be complete, and if your favourite model/paper is omitted, please accept my apologies.
3rd January 2006 1
What’s wrong with the MSSM?
-problem with an extra singlet Breaking the Peccei-Quinn symmetry The Domain Wall Problem and its solution
The NMSSM parameters and mass spectrum Two interesting NMSSM scenarios Neutralinos in the NMSSM
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What’s wrong with the MSSM?
Supersymmetry has many motivations, but here are the two that I find most convincing:
Only possible extension of the Poincar é symmetry of space-time
To me, this alone tells me that SUSY exists, but it is no argument for low energy SUSY.
The hierarchy problem
If you ever want to extend the SM by including new physics, we will need to explain why the Higgs boson is so light. Supersymmetry tells us why.
Note that the hierarchy problem is not a problem at all if you new physics.
don’t include 3rd January 2006 3
Less convincing (but still good) arguments: The unification of gauge couplings at the GUT scale SUSY has a good
candidate – the neutralino
This isn’t really an argument for SUSY – it is an argument for a
symmetry This could equally well be part of an alternative theory, e.g. extra dimensions 3rd January 2006 4
So the Minimal Supersymmetric Standard Model (MSSM) has a lot going for it.
Why would we want to extend it?
MSSM Superpotential: Yukawa terms term The superpotential has mass dimensions [mass] 3 , so the
in the superpotential must have dimensions of
What mass should we use?
The natural choices would be
(forbidden by some symmetry) or
(or M GUT ) 3rd January 2006 5
Notice that this mass-parameter is in the supersymmetry breaking (via soft terms).
about the electroweak scale
superpotential , so it is present before
Therefore, it should know nothing
If = 0 then there is no mixing between the two Higgs doublets. Any breaking of electroweak symmetry generated in the up-quark sector (by M H 2 < 0) could not be communicated to the down-quark sector ) the down-type quarks and leptons would remain massless.
If = M Planck then the Higgs bosons and their higgsino partners would gain Planck scale masses, in contradiction with upper bounds from triviality and precision electroweak data.
For phenomenologically acceptable supersymmetry, the of order the electroweak scale.
-parameter must be This contradiction is known as the
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-problem with an extra singlet
One way to link the
-parameter with the electroweak scale is to make it a
Introduce a new iso-singlet neutral colorless chiral superfield usual two Higgs doublet superfields. The scalar part of this is , coupling together the If S gains a vacuum expectation value we generate and
with We must also modify the
supersymmetry breaking terms
to reflect the new structure 3rd January 2006 7
The new scalar naturally picks up a VEV of order the SUSY breaking parameters, just as for the usual Higgs doublets.
Writing: the minimization equations for the VEVs become:
So is of the electroweak/SUSY scale, as desired.
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So our superpotential so far is Yukawa terms effective term But this too has a problem – it has an extra U(1) Peccei-Quinn symmetry [Peccei and Quinn, Phys.Rev.Lett.
(1977) 1440; Phys.Rev.D
(1977) 1791] Setting U(1) charges for the states as: the Lagrangian is invariant under the (global) transformation This extra U(1) is broken with electroweak symmetry breaking (by the effective -term)
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This Peccei-Quinn axion can be very useful, since it solves the
strong CP problem
The most general QCD Lagrangian contains the -term with Even if this is set to zero by hand in the Lagrangian, it is regenerated by instantons.
However, this term is CP violating, and would lead to a dipole moment . Experimental limits imply non-zero neutron electric
So why is this so small?
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The axion also contributes a -term through an axion-gluon triangle anomaly diagram axion decay constant axion field As a result the potential is a function of and the axion naturally relaxes to a value thereby cancelling the -term and solving the strong CP problem
Unfortunatetly a (nearly) massless axion (actually a psudoscalar Higgs boson) has not been found, so this is a bit of a wild goose chase …..or is it?
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Removing the Peccei-Quinn axion
While the Peccei-Quinn axion would be nice to have around, we do not see it, so we have another problem. There are (at least) three possible ways out, all of which introduce more problems.
Decouple the axion
We could just make very small, thereby decoupling the axion so that it would not have been seen in colliders.
Unfortunately there are rather severe astrophysical constraints on the cooling rate of stars in globular clusters, which constrain from .
There is (to my knowledge) no good reason why should be so small.
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Since the restriction on ) Note that this is not an
problem since it is eff which is naturally of the EW scale e.g.
Any mechanism which makes small also makes large.
So we have solved the strong CP problem and the introducing a new “ problem”.
-problem at the expense of Unfortunately (fortunately?) we have a further, if rather mild,
fine tuning problem
: It is difficult to keep the vacuum stable since the lightest scalar mass-squared tends to become negative. It is only positive for a restricted parameter range.
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In order to keep the lightest Higgs boson (from the extra singlet) mass real, we need to enforce [where M A and tan in the MSSM] are as defined 3rd January 2006 This is a mild fine-tuning, but also provides a
for this model at the LHC [DJM, R Nevzorov, hep-ph/0309143] 14
Finally, there may be a problem with Dark Matter in this model. The higgsino partner has a very small mass, typically .
Since this is the lightest supersymmetry particle (LSP) it is stable and contributes to dark matter.
Usually such light particles are disastrous because they are very hard to annihilate, and therefore give too much dark matter. However, this LSP is so decoupled that it may never have come into equilibrium in the first place…..
Eat the axion
Making the U(1) Peccei-Quinn symmetry a
introduces a new gauge boson which will eat the PQ-axion when the PQ symmetry breaks and become massive (a Z 0 ). Searches for a Z 0 provide rather model dependent results but generally indicate that it must be heavier than a few hundred GeV.
To cancel anomalies one needs new chiral quark and lepton states too, so I discuss these models further here.
won’t 3rd January 2006 15
Explicity break the PQ symmetry
In principle, one can add
into the superpotential of the form S n with n 2 Z but only for n =3 will there be a break the PQ symmetry, giving the dimensionless coefficient . Any such term will “axion” a mass so that it can escape experimental constraints.
The superpotential of the
N ext-to M inimal S upersymmetric S tandard M odel
3rd January 2006 Yukawa terms effective term PQ breaking term 16
We also need soft supersymmetry breaking terms in the Lagrangian: [Higgs sector SUSY breaking terms only] This model has the same particle content as the MSSM except one extra scalar Higgs boson one extra pseudoscalar Higgs boson one extra higgsino for a total of 3 scalar Higgs bosons 2 pseudoscalar Higgs bosons 5 neutralinos The charged Higgs bosons and charginos are the same as in the MSSM.
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The Domain Wall Problem
Unfortunately we have yet another problem.
The Lagrangian above has a (global) Z
) the model has
3 degenerate vacua
separated by potential barriers [This was an unavoidable consequence of having dimensionless couplings.] vacuum 1 vacuum 2 We expect causally disconnected regions to choose different vacua and when they meet a
form between the two phases.
will These domain walls are unobserved (they would be visible in the CMBR) so we need to remove them.
3rd January 2006 domain wall [Y.B.Zeldovich, I.Y.Kobzarev and L.B.Okun, Zh.Eksp.Teor.Fiz.
The degeneracy may be broken by the unification with gravity at the Planck scale.
Introducing new higher dimensional operators raises the vacuum energies unequally, resulting in a preferred vacuum.
However, the same operators give rise at the loop level to
of the form
where n is the loop order they appear.
[S.A.Abel, S.Sarkar and P.L.White, Nucl.Phys.B
(1995) 663; S.A.Abel, Nucl.Phys.B
(1996) 55.] If such operators do break the degeneracy, then they must be suppressed to a high enough loop order that they don’t cause a new hierarchy problem.
Use symmetries to suppress then to high loop order.
Example of a 6-loop tadpole contribution 3rd January 2006 [C.Panagiotakopoulos and K.Tamvakis, Phys.Lett.B
(1999) 224; [ C.Panagiotakopoulos and A.Pilaftsis, Phys.Rev.D
(2001) 055003.] 19
There are many different choices of symmetries to do this. Which you choose, changes the model.
The 2 most studied are:
Next-to-Minimal Supersymmetric Standard Model (NMSSM)
Choose symmetries to forbid divergent tadpoles to a high enough loop order to make them phenomenologically irrelevant but still large enough to break the degeneracy.
Minimal Non-minimal Supersymmetric Standard Model (MNSSM)
Choose symmetries to forbid also the S^3 term, but allow tadpoles which have a coefficient of the TeV scale.
3rd January 2006 radiatively induced tadpole 20
The NMSSM mass spectrum
[DJM, R. Nevzorov, P.M. Zerwas, Nucl.Phys.B681 (2004) 3] The NMSSM Higgs sector has the potential V = V F + V D + V soft + V
Replace soft masses with vacuum expectation values using minimization condistions: 3rd January 2006 21
Parameters: A A m H d m Hu m S A v d v u v s The MSSM limit is !
0, keeping / and fixed.
3rd January 2006 Top left entry of CP-odd mass matrix. Becomes MSSM M A in MSSM limit.
M Z , tan , eff Will also sometimes use 22
and are forced to be reasonably small due to
renormalisation group running
To stop them blowing up, we need to insist that 3rd January 2006 23
Lightest Higgs mass bound
In the MSSM In the NMSSM The extra contribution from the new scalar raises the lightest Higgs mass bound, but only by a little.
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The expressions for the Higgs masses are rather complicated and unilluminating, even at tree level, but we can make some approximations to see the general features.
Regard both M EW /M A and 1/tan as small and expand as a power series.
CP-odd Higgs masses 2 :
heavy pseudoscalar one pseudoscalar whose mass depends on how well the PQ symmetry is broken
CP-even Higgs masses 2 :
heavy scalar Notice the different signs for A 3rd January 2006 intermediate mass scalar one scalar whose mass depends on how well the PQ symmetry is broken 25
Computer codes for NMSSM phenomenology: NMHDECAY
by Ellwanger, Gunion & Hugonie
A (hopefully!) soon to be released code by Djouadi, Kalinowski, King, DJM, Moretti. 3rd January 2006 26
Two interesting scenarios
PQ symmetry only “slightly” broken
[DJM, S Moretti, hep-ph/0403137] Most of the M A range is excluded (at 95%) by LEP2 higgs-strahlung but there is still a substantial region left.
Notice the rather light Higgs boson!
In the allowed region, the couplings of the lightest Higgs to gauge bosons is switching off, which is why LEP would not have seen it.
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Branching ratios of lightest Higgs: This Higgs decays mostly hadronically, so it will be difficult to see at the LHC, due to huge SM backgrounds.
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LHC production rates are quite high, but many channels switch off.
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A 500GeV linear e + e collider would be able to narrow the gap, but not close it. 3rd January 2006 30
A very light pseudoscalar
[Ellwanger, Gunion & Hugonie JHEP 0507:041,2005] For these parameters, The lightest pseudoscalar is now so light that » pseudoscalar pairs: 100% of H 1 decays are into ) the lightest scalar could be significantly lighter than 114GeV and have been missed by LEP 3rd January 2006 31
F It is claimed that this model is less fine tuned too.
Taking and scanning over parameter space [From J. Gunion’s talk at SUSY05] 3rd January 2006 £ have M H1 > 114GeV
have M H1 < 114GeV Points with high H 1 !
A 1 A 1 branching ratio have smaller fine tuning If the pseudoscalar is heavy enough, it may be observable through decays to tau pairs: 32
Recently (2 weeks ago) a paper by Schuster & Toro, hep-ph/0511344 , pointed out that this point has fine tunings with respect to other observables, e.g. the pseudoscalar mass with respect to A However, it was not clear how different fine-tunings should be
to form one measure of how fine tuned a model is.
To my mind, all this shows is that we really
need a better measure of fine tuning.
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Neutralinos in the NMSSM
[Choi, DJM, Zerwas, Nucl.Phys. B711 (2005) 83 ] The extra higgsino means that we have an extra neutralino in the spectrum.
The neutralino mass matrix: Again, the expressions for the masses helpful but we can make aren’t very approximations in particular limits to help understand what is going on.
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Large gaugino mass
Two neutralinos at the gaugino masses Two neutralinos split around One neutralino with mass strongly dependent on This is primarily a “singlino” e.g.
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Large higgsino mass
This is very similar to the previous scenario.
Large singlino mass
Now with other masses as in the MSSM The extra neutralino decouples, making this difficult to distinguish from the MSSM.
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If the singlino mass is small (ie. small) as indicated by RGEs, then in the LHC the singlino will be mainly produced through decays of heavier neutralinos, charginos and sleptons.
Some possble decay channels are: (three body) 3rd January 2006 Which of these channels is open or dominant for the singlino is highly dependent on the scenario.
e.g. for Huge variations in partial widths with .
Only for tiny is the neutralino decoupled enough to have observable displaced vertices 3rd January 2006 38
Conclusions & Summary
The MSSM has a serious flaw
: it phenomenologically requires a parameter of order the electroweak scale with no justification.
to be This problem can be circumvented by
introducing a new scalar field
the vacuum expectation value of this new field to the -parameter.
and linking The resulting model contains a
broken U(1) Peccei-Quinn symmetry which must be
with extra interactions. Extra symmetries must be enforced to prevent quadratically divergent tadpoles. Which symmetries are imposed determine which model we have, with examples being the NMSSM and the MNSSM.
The NMSSM spectrum contains the particles of the MSSM with an
scalar, and extra Higgs pseudoscalar and an extra neutralino
The mass of these extra particles strongly depends on
symmetry is broken
how severely the PQ
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is where the extra Higgs boson is » 90GeV or so and has suppressed couplings to the gauge bosons. This would have prevented it being seen at LEP. Its decays are primarily hadronic, making its observation challenging at the LHC.
A second interesting scenario has a
very light pseudoscalar
. The lightest scalar then decays predominantly into a pseudoscalar pair and is difficult to observe.
This scenario requires less fine-tuning to obtain the correct Z-boson mass, but may have fine-tuning to obtain other observables.
The NMSSM is a very interesting model, and more studies should be done to investigate its phenomenology at future colliders. Experimental studies are particularly needed.
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CP studies and Non-Standard Higgs physics
Aiming to produce a “
hitchhiker’s guide to non-standard Higgs physics
Editor: Sabine Kraml Topics include: The CP-violating two Higgs doublet model The MSSM with CP phases
SUSY models with an extra singlet
MSSM with R-parity violation Extra gauge groups Little Higgs models Large EDims: ADD Randall-Sundrum: Radion Higgsless models Chiral symmetry breaking Technicolour, topcolour Deadline for contributions: 31 st March 2006 .
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