Another Milestone for the SM!

The standard model (SM) of particle physics has crossed another milestone as reported by LHCb collaboration at the recent hadron collider physics symposium held in Kyoto. They have done an incredible measurement of B meson decaying into muon anti-muon pairs. However, people started using this SM milestone as a bullet in SUSY's chest. BBC reported LHCb UK spokesperson saying, "SUSY might not be dead yet, but these results have certainly put her into hospital". And this statement was enough to spark off a debate in the blogosphere followed by couple of arXiv pre-prints. Well, its true that no sign of new physics in this measurement is disappointing, but it amazes me that SUSY has suffered the most whereas there are plenty of other beyond standard model frameworks in the market. I could see three different types of reactions : SUSY is dead or in hospital, SUSY is less natural than thought and SUSY is still alive or in good health. The first reaction is of course a bit harsh and extreme but probably was good for many others who have come up with pre-prints showing available parameter space (natural parameter space probably, I am confused though what to call natural nowadays) which exactly fit these observations. Even if we collect as much data as we want, they will probably never justify the first reaction and at the worst case will leave us with a situation which is a linear combination of the second two reactions.

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I am happy to be back in blogosphere after a gap of around one and a half months. There were too many things I was involved in related to the administrative branch of my home institute. Slow and inefficient Indian bureaucracy takes too much time to get things done, can't help it. Anyway, I am feeling quite blank regarding what to post. The easiest thing to post is about my latest paper which appeared in arxiv last week. The title of this post is the arxiv pre-print number of my article.

The paper titled as " Spontaneous Parity Breaking and Supersymmetry Breaking in Metastable Vacua with Consistent Cosmology" is all about study of some cosmological issues in a model where Left-Right symmetry can be broken spontaneously as well as Supersymmetry can be broken in a metastable vacua without any reference to hidden sectors (like in usual Supersymmetry breaking models) . Such a model was constructed recently by a Japanese group, we study it in details and point out some cosmological issues which needs to be addressed. The issue is related to the formation of domain walls (extended two dimensional topological objects) which are formed after the phase transition accompanying the discrete left right symmetry breaking. These domain walls have very high energy density compared to usual matter or radiation and if they start dominating the Universe, the standard cosmology will be in trouble in view of recent experimental data from WMAP (Wilkinson Mass Anisotropy Probe). We discussed some techniques to get rid of such unwanted walls in earlier works also and the basic idea is to incorporate gravitational effects which break the discrete symmetry explicitly leading to a pressure difference across the walls. Thus the true vacuum will expand and occupy the entire observable Universe. The model we are studying in this present paper is however different from earlier models in the sense that here both left right symmetry breaking and supersymmetry breaking mechanisms are specifically mentioned, that too without talking about hidden sectors. Such theories are based on Seiberg duality which relates a UV free supersymmetric gauge theory to an IR free magnetic theory thereby making computations easier in both the regimes. The magnetic theory , if assumed to describe the low energy world, also breaks Supersymmetry spontaneously. Supersymmetry preserving vacua also appear dynamically in the magnetic theory leading to metastable vacua. The work I have done, studied the constraints coming from such long lifetime of metastable vacua as well as domain wall disappearance in the left right symmetric model. The life time constraint gives a lower bound on the left right symmetry breaking scale whereas the domain wall disappearance puts an upper bound on that scale. Fortunately these bounds don't conflict each other and more excitingly the lower bound coming from long life time of metastable vacua requirement lies pretty close to the TeV scale. Anyway much more work needs to be done in these models and our work just tells a tiny part of it concerning mainly the domain wall disappearance!

SUSY..hope you are still there!

Couple of weeks back there were lots of hue and cry among young researchers who might have heard about SUSY but have not worked on it in great details. It's because of the ATLAS and CMS experiment at Large Hadron Collider (LHC), CERN (Geneva) publishing two independent results related to supersymmetry (SUSY) searches in the 7 TeV run of LHC. One of them looked for missing energy+ jet signatures whereas the other looked for lepton+jet signatures, but their conclusion was more or less similar. They ruled out significant amount of parameter space of Constrained Minimal Supersymmetric Standard Model (CMSSM). This is a rather constrained version of MSSM where the number of free parameters are just 5 compared to 124 or so parameters in the MSSM. So obviously the CMSSM has far more predictability and hence getting almost ruled out. Although its really heartbreaking to see such predictable models losing their fight, yet this does not really mean SUSY is not there. We still need more data and scan of other available models to rule out TeV scale SUSY. And even if LHC rule out TeV scale SUSY, it can not say anything about existence of SUSY at even higher energies. But many of the theoretical advantages of SUSY would be lost if we keep pushing SUSY towards higher and higher scales and will be as good as having no SUSY at all. Anyway, hope LHC will soon confirm its presence around the TeV corner. But nevertheless, the ATLAS/CMS result created lots of hype among both experts as well as others. One of our over-curious mate in the department got pumped up so much (may be after reading about it in some newspapers and not in the arxiv papers) that he asked one of our senior prof, what's the point of doing SUSY as LHC has already ruled it out? I don't know what was the professor's reaction at that moment, but I can imagine how shocking such a news (if true) to a person working in particle physics for a long time. Blame it on popular news sites or news papers which put the title of such news in such a way that young kids easily get misled. Anyway, hope many such news (positive I mean) about SUSY would be coming soon from the heart of LHC :)

Metastable Vacua!

Yesterday I gave a talk on Supersymmetry(SUSY) breaking in a metastable vacua in the department. It was kind of discussion session which I started by giving a summary on this topic, specially the famous paper hep-th/0602239 (ISS) which has currently 345 citations. Metastable vacua is basically the ground state of a theory which has finite lifetime. Generally we encounter ground state which is perfectly stable and has infinite lifetime. But there are some theories where there can be multiple vacua which corresponds to different ground state energies. Suppose one minimum corresponds to ground state energy e and another corresponds to E. Now the tunneling between these two vacua will be negligible if

Thus although the vacuum with ground state energy E is not the true vacuum, yet it can be very stable and can have a life time same as the age of the Universe.

In the theories of dynamical SUSY breaking, SUSY is broken at the tree level, and it is restored non-perturbatively at high energy. Thus there are two vacua, one corresponds to the one with SUSY breaking and the other SUSY preserving. Since SUSY preserving vacua has ground state energy zero, this means our Universe (where SUSY is broken) is in a metastable state now. Just imagine what will happen if the Universe suddenly decays to the true vacuum tomorrow ;-). We will meet our superpartner friends then. Anyway the ISS paper which I mentioned above talks about these issues. They start with a SUSY QCD(Quantum Chromodynamics) based on a general gauge group

with flavors of quarks. This theory is asymptotically free (which means the couplings become strong at low energy and quarks become almost free at high energy) like our usual QCD. This theory is strongly coupled at low energy which makes the low energy computations go out of control. But the good thing is that this theory is dual to theory with singlets and chiral fields which transform as fundamental/anti-fundamental representation under this new gauge group. This is known as Seiberg's electromagnetic duality . The good thing is that for smaller than this theory is IR free which means that it is weakly coupled at low energy and strongly coupled at high energy. Thus we can do all the low energy computations with full control unlike in the gauge theory. This dual theory is found to break SUSY at tree level and preserve SUSY non-perturbatively after integrating out the massive chiral fields. These two vacua are however widely separated in field space and hence there is no danger of one going into another. The SUSY breaking vacuum is close to the origin whereas the SUSY preserving one is far away in field space. Since the SUSY preserving vacuum has zero vacuum energy, the SUSY breaking vacuum is not the true vacuum since it has non-zero vacuum energy. This means that the SUSY breaking vacuum is a metastable one whose life time can be parametrically made as long as the age of the Universe. This duality works for

and it is easy to see that this does not hold in case of minimal supersymmetric standard model (MSSM) for which . But no matter how close this framework is to the reality, it is very impressive from a theorist's point of view and that's the reason I guess why people all over the world is taking this model so seriously. It would be worth studying in fact, how this theoretical framework can be used to arrive at the MSSM with TeV scale SUSY breaking.

Loss of perturbativity!

Electroweak Precision data still keeps room available to include one more chiral family into the standard model provided the quark and lepton masses are greater than some lower bound. The lower bound for the fourth generation quarks are around 200 GeV whereas for charged lepton it is around 100 GeV. The fourth generation neutrino should be more massive than

so as not to contribute to Z boson decay width which is experimentally measured very accurately and is in good agreement with three family Standard Model. Now in the standard model we have top quark yukawa coupling almost equal to 1 so as to account for its mass . Thus if we want to account for fourth generation quark masses, we have to take the corresponding yukawas large -->> Loss of perturbativity? In MSSM, the problem gets even more complicated. We have two Higgs doublet in this case, with vacuum expectation values and and their rations are denoted by . It turns out that with low value of ( close to unity) we can keep the yukawas perturbative at the electroweak scale and at the same time give rise to fourth generation quark and charged lepton masses above the experimental lower bound. However such a low value of will make the lightest Higgs boson mass at tree level very small and we have to check if loop corrections (including fourth generation) can make its mass greater than the LEP lower bound 114.5 GeV. Now suppose after taking loop corrections, we are getting Higgs mass greater than this limit as well as fourth generation masses are also above the lower bounds while keeping the yukawa perturbative. The problem is not yet solved, because when we evolve those yukawas under renormalization group, at every stage upto the grand unification scale (GUT) (assuming there is no new physics between MSSM and the GUT scale). But it turns out that (although I haven't checked it yet but there are works related to this in the literature)yukawas become non-perturbative near the TeV scale if there is not new physics between MSSM and GUT scales. People then incorporate new physics at the TeV scale which keeps the yukawas perturbative till the GUT scale. So far I have seen only one paper arXiv:0806.2064 where they have talked about adding some new vector like matter particles at the TeV scale. I personally find these vector like matter particles quite ad-hoc although they are serving this particular purpose here, I don't know how to incorporate them within the framework of some higher theories like Grand Unified Theories. But vector fields contribute differently to the beta function compared to chiral fields. Their contribution comes with opposite signs and may be that could be the reason why vector particles help the yukawas to slow down their running to keep them perturbative till the GUT scale. Anyway these are theoretical issues, but experimentally also fourth generation might have interesting signatures from colliders to dark matter search experiments as well. Will update about those issues next time :)

Light Higgs!

We all know that in minimal supersymmetric standard model (MSSM), we naturally arrive at a light Higgs whose mass is of the order of Z boson mass. Its only after taking loop corrections into account we can make it as heavy as the LEP limit which is around 114.5 GeV. The question of light Higgs bosons always puzzled me in Supersymmetric Left-Right(SUSYLR) models which forced me to work out the Higgs boson mass in MSSM at least. Only after the calculations I got the idea how things become so different when we add supersymmetry to the standard model. In standard model we have a Higgs potential involving the mass term and the quartic coupling term. However in MSSM we have only a bi-linear term in the superpotential which can give rise to the mass term in the scalar potential. But the quartic coupling term can come from only the D-terms. Hence the quartic coupling parameter in this case is a combination of the gauge coupling constants, not a free parameter like in the case of standard model. We have no choice in MSSM to fine tune these couplings to make the Higgs mass heavy. In richer theories like SUSYLR, things become more complicated.

Suppose we have triplet Higgs fields $ \triangle_L, \triangle_R $ in addition to the doublet Higgs fields which gives masses to the fermions. These triplets are added to break the SUSYLR gauge symmetry $ SU(2)_L \times SU(2)_R \times U(1)_{B-L} $ down to the MSSM gauge symmetry $ SU(2)_L \times U(1)_Y $. Here L, R denotes left handed and right handed respectively, B, L and Y denote baryon number, lepton number and weak hypercharges respectively. These triplet fields have B-L charge $\pm 2$ and hence we need to add two more such fields in SUSYLR model to cancel the anomalies. Now the common intuition will say that these triplet fields will acquire masses of the order of $ SU(2)_R $ symmetry breaking scales because these fields are introduced for this symmetry breaking. This intuition is sometimes called survival principle which I mentioned in one of my previous posts. Now if we actually calculate the mass spectra, we see that this principle is not always true. For example, consider these triplets. Gauge symmetry does not allow us to write the bi linear or trilinear terms of the same triplet field in the superpotential. We can however write bi linear mass terms involving one triplet and another of opposite B-L charge. Now when we write the scalar potential we only have the mass terms and no quartic terms. And unlike in MSSM where we could find some quartic terms coming from the D-terms, here we can't have it because that will break supersymmetry. We are breaking SUSYLR to MSSM which means that supersymmetry is not broken, but only the gauge symmetry is broken. Hence the D-term scalar potential will decouple at this stage. Thus we need to incorporate non-renormalizable quartic terms which will give rise to non-zero mass of these Higgs fields. The masses come out to be light naturally since these non-renormalizable terms are highly suppressed by the Planck scale or GUT sale. I think, if the $ SU(2)_R $ breaking scale is around the supersymmetry breaking scale, we can have quartic couplings. But in this case also existence of light Higgs will still be true. I was reading some papers by Mohapatra et al. where they describe the scenario in terms of some enhanced global symmetry in the superpotenal in the absence of some terms, then they break this approximate symmetry resulting in pseudo-goldstone bosons which are not exactly mass-less but have light masses. I am still not confident about those enhanced global symmetries and all, but the existence of light Higgs in such models is something unavoidable with minimal field content. Such light particles creates problems in gauge coupling unification since they keep contributing to the evolution till the electroweak scale which forces the couplings to reach Landau pole (non-perturbative) much before the GUT/Planck scale.

A purely supersymmetric origin of neutrino mass

Yesterday I came to know about a completely supersymmetric(SUSY) origin of tiny neutrino mass, that is, in the non-SUSY version of the model neutrino mass remains either zero or comparable to lepton/quark masses. This comes when neutrino mixes with the neutralinos in the Supersymmetric model. The neutralinos are the mass eigenstates of neutral gauginos as well as Higgsinos. Neutrinos can mix with the neutralinos only if the sneutrino field get a vacuum expectation value (vev). Diagonalizing the mixing mass matrix will give rise to a small neutrino mass by sutable adjustment of different scales. However since neutrino/sneutrino carry a lepton number whereas neutralinos do not, such mixing violate R-parity. This R-parity violation however should not lead to dangerous proton decay, but it will make the standard neutralinos decay into neutrinos. If neutralino is to be a dark matter candidate, the relic abundance will put a constraint on the R-parity violation. Thus this scenario will be tightly constrained by smallness of neutrino mass as well as dark matter relic abundance. I am trying to see if there is any other advantage of this approach, say from the point of view of recent positron excess measured by various dark matter indirect detection probes.

Finally got rid of sneutrino vev...:)

Finally I could get a vacuum in our model with no sneutrino(super-partner of the neutrino) vev(vacuum expectation value). That is quite relaxing for me since R-parity will be preserved now in the model. I have seen many models where people work with sneutrino vev also, but somehow I don't prefer that kind of scenario. The main problem in that case would be the stability of the dark matter candidates. In our model however one sparticle gets a vev. It is the superpartner of a sterile neutrino which we have added as a gauge singlet with zero B-L charge. I think even if it gets vev, R-parity won't be violated since it has zero B-L charge and R-parity is defined as $R_P =(-1)^{3(B-L)+2s}$, where s is the spin of the particle. I hope the remaining things will be pretty simple after getting the vacuum solution..........:)