Supersymmetric Models with extra singlets: a review

1. Supersymmetric Models with extra singlets: a review This talk will lean heavily on the review Models with extra singlets written for theCPNSH Report by J. Gunion, DJM, A. Pilaftsis DJ Miller, University of Glasgow Plenary talk, Whepp-9, Bhubaneswar, India 3-14 January 2006 Disclaimer: 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.

2. PART I What’s wrong with the MSSM? Solving the -problem with an extra singlet Breaking the Peccei-Quinn symmetry The Domain Wall Problem and its solution PART II The NMSSM parameters and mass spectrum Two interesting NMSSM scenarios Neutralinos in the NMSSM

3. 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 Poincaré 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 don’t include new physics.

4. Less convincing (but still good) arguments: The unification of gauge couplings at the GUT scale SUSY has a good dark matter candidate – the neutralino This isn’t really an argument for SUSY – it is an argument for a Z2 symmetry This could equally well be part of an alternative theory, e.g. extra dimensions

5. So the Minimal Supersymmetric Standard Model (MSSM) has a lot going for it. Why would we want to extend it? MSSM Superpotential: -term Yukawa terms The superpotential has mass dimensions [mass]3, so the Higgs-higgsino mass parameter  in the superpotential must have dimensions of mass. What mass should we use? The natural choices would be 0 (forbidden by some symmetry) or MPlanck (or MGUT)

6. Notice that this mass-parameter is in the superpotential, so it is present before supersymmetry breaking (via soft terms). Therefore, it should know nothing about the electroweak scale. If  = 0 then there is no mixing between the two Higgs doublets. Any breaking of electroweak symmetry generated in the up-quark sector (by MH2 < 0) could not be communicated to the down-quark sector ) the down-type quarks and leptons would remain massless. If  = MPlanck 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 -parameter must be of order the electroweak scale. This contradiction is known as the -problem

7. Solving the -problem with an extra singlet One way to link the -parameter with the electroweak scale is to make it a vacuum expectation value. Introduce a new iso-singlet neutral colorless chiral superfield , coupling together the usual two Higgs doublet superfields. The scalar part of this is If S gains a vacuum expectation value we generate and effective -term with We must also modify the supersymmetry breaking terms to reflect the new structure

8. 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.

9. So our superpotential so far is effective -term Yukawa terms But this too has a problem – it has an extra U(1) Peccei-Quinn symmetry 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) [Peccei and Quinn, Phys.Rev.Lett.38 (1977) 1440; Phys.Rev.D 16 (1977) 1791] massless axion

10. 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 non-zero neutron electric dipole moment. Experimental limits imply So why is this so small?

11. 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?

12. 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  from the cooling rate of stars in globular clusters, which constrain . There is (to my knowledge) no good reason why  should be so small.

13. Since the restriction on ) Note that this is not an extra 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 -problem at the expense of introducing a new “-problem”. 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.

14. In order to keep the lightest Higgs boson (from the extra singlet) mass real, we need to enforce [where MA and tan are as defined in the MSSM] This is a mild fine-tuning, but also provides a prediction for this model at the LHC [DJM, R Nevzorov, hep-ph/0309143]

15. 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 gauge symmetry introduces a new gauge boson which will eat the PQ-axion when the PQ symmetry breaks and become massive (a Z0). Searches for a Z0 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 won’t discuss these models further here.

16. Explicity break the PQ symmetry In principle, one can add extra terms into the superpotential of the form Sn with n2Zbut only for n=3 will there be a dimensionless coefficient. Any such term will break the PQ symmetry, giving the “axion” a mass so that it can escape experimental constraints. The superpotential of the Next-to-Minimal Supersymmetric Standard Model (NMSSM) is effective -term Yukawa terms PQ breaking term

17. 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.

18. The Domain Wall Problem • Unfortunately we have yet another problem. • The Lagrangian above has a (global) Z3 symmetry • )the model has 3 degenerate vacua separated by potential barriers • [This was an unavoidable consequence of having dimensionless couplings.] We expect causally disconnected regions to choose different vacua and when they meet a domain wall will form between the two phases. These domain walls are unobserved (they would be visible in the CMBR) so we need to remove them. vacuum 2 vacuum 1 domain wall [Y.B.Zeldovich, I.Y.Kobzarev and L.B.Okun, Zh.Eksp.Teor.Fiz. 67 (1974) 3].

19. 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 quadratically divergent tadpole terms of the form where n is the loop order they appear. [S.A.Abel, S.Sarkar and P.L.White, Nucl.Phys.B 454 (1995) 663; S.A.Abel, Nucl.Phys.B 480 (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 [C.Panagiotakopoulos and K.Tamvakis, Phys.Lett.B 446 (1999) 224; [C.Panagiotakopoulos and A.Pilaftsis, Phys.Rev.D 63 (2001) 055003.]

20. 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. radiatively induced tadpole

21. The NMSSM mass spectrum [DJM, R. Nevzorov, P.M. Zerwas, Nucl.Phys.B681 (2004) 3] The NMSSM Higgs sector has the potential V = VF+ VD + Vsoft + V with Replace soft masses with vacuum expectation values using minimization condistions:

22.     A A A mHd vd mHu vu mS vs MZ, tan, eff Top left entry of CP-odd mass matrix. Becomes MSSM MA in MSSM limit. Parameters: Will also sometimes use The MSSM limit is ! 0, ! 0, keeping / and  fixed.

23. and are forced to be reasonably small due to renormalisation group running. To stop them blowing up, we need to insist that

24. 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.

25. Notice the different signs for A Approximate masses 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 MEW/MA and 1/tan as small and expand as a power series. CP-odd Higgs masses2: heavy pseudoscalar one pseudoscalar whose mass depends on how well the PQ symmetry is broken CP-even Higgs masses2: intermediate mass scalar heavy scalar one scalar whose mass depends on how well the PQ symmetry is broken

26. Computer codes for NMSSM phenomenology: NMHDECAY by Ellwanger, Gunion & Hugonie http://higgs.ucdavis.edu/nmhdecay/mnhdecay.html A (hopefully!) soon to be released code by Djouadi, Kalinowski, King, DJM, Moretti.

27. Two interesting scenarios PQ symmetry only “slightly” broken [DJM, S Moretti, hep-ph/0403137] Most of the MA 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.

28. 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.

29. LHC production rates are quite high, but many channels switch off.

30. A 500GeV linear e+e- collider would be able to narrow the gap, but not close it.

31. A very light pseudoscalar [Ellwanger, Gunion & Hugonie JHEP 0507:041,2005] For these parameters, The lightest pseudoscalar is now so light that » 100% of H1 decays are into pseudoscalar pairs: )the lightest scalar could be significantly lighter than 114GeV and have been missed by LEP

32. It is claimed that this model is less fine tuned too. Taking and scanning over parameter space £have MH1 > 114GeV + have MH1 < 114GeV F Points with high H1!A1A1 branching ratio have smaller fine tuning If the pseudoscalar is heavy enough, it may be observable through decays to tau pairs: [From J. Gunion’s talk at SUSY05]

33. 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 combined to form one measure of how fine tuned a model is. To my mind, all this shows is that we really need abetter measure of fine-tuning.

34. 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 aren’t very helpful but we can make approximations in particular limits to help understand what is going on.

35. 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.

36. Now with other masses as in the MSSM The extra neutralino decouples, making this difficult to distinguish from the MSSM. Large higgsino mass This is very similar to the previous scenario. Large singlino mass

37. 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. Neutralino production • Some possble decay channels are: • (three body) Which of these channels is open or dominant for the singlino is highly dependent on the scenario.

38. e.g. for • Huge variations in partial widths with . • Only for  tiny is the neutralino decoupled enough to have observable displaced vertices

39. Conclusions & Summary • The MSSM has a serious flaw: it phenomenologically requires a parameter  to be of order the electroweak scale with no justification. • This problem can be circumvented by introducing a new scalar field and linking the vacuum expectation value of this new field to the -parameter. • The resulting model contains a U(1) Peccei-Quinn symmetry which must be broken 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 extra Higgs scalar, and extra Higgs pseudoscalar and an extra neutralino. • The mass of these extra particles strongly depends on how severely the PQ symmetry is broken.

40. An interesting scenario 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.

41. 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: 31st March 2006.