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.

APS 2010

I am done with my second Annual Progress Seminar (APS) today. And traditionally, it was done without the presence of my PhD supervisor. Two examiners were there, may be the same will happen in my PhD defense as well ;) I mainly talked about the paper which I put in arXiv in June. (http://arxiv.org/abs/1006.2245). In the annual progress report also I just pasted the whole paper, nothing else. The seminar was cool, fortunately I was not attacked with too many questions but by some basic doubts which the examiners had. At the end I talked about some of the work which I have been doing recently. The paper I mentioned above is yet not published, the referee's comments have come, and I am done with almost all the suggested corrections and modifications. After I get green signal from my collaborators, I will probably resubmit it as soon as possible. Hope it gets published soon, I am dying to get one published paper so that I can apply for various conferences :)

Another Independence Day, 15th Aug'2010

So here comes another Independence day for us. Sitting inside my room also I can see the "virtual" celebrations through forwarded mails, social networking sites like facebook and all. Someone has put a tri-color in the profile pic or someone has uploaded a video which shows India's economy growth rate, number of Indians in NASA, India as largest democracy, India has x number of supercomputers, India has y number of CEO's in MNC's and so on. I get so much pissed off with such videos. I do not understand what these videos are meant for, and why these videos come at the time of Independence day or Republic day. I do not think people will forget the importance of the day if such unnecessary videos are not made. I am an Indian and I love my country and I do not need any reason to love my country. Even if my country has none of the "plus points" which these videos show, I will continue to love and respect my country. The worst thing about this videos are that they do not show everything. They show less than one percent of India just to win people's hearts and to gain popularity. They don't show the situations of millions of people under poverty line, common people who get killed by extremists, naxalites or security forces in various parts of the country. They don't show the civilian human rights violations in many parts of the so called "largest democracy". They don't show how much pride/shame India has earned hosting the Commonwealth Games which has been severely hit by large scale corruptions delaying all the preparations. There are many more things to be shown to the people about this country. If someone makes video showing India as a whole, he or she should include all such things. But they always put 10 bright things in the video and neglect thousands of dark sides of the country. India will change only when there will be enough awareness among the common people. The media, social networking sites should be used to increase the awareness, not to flatter the public to gain some cheap popularity. Happy Independence day to all, Jai Hind!

Things getting worse!

Things in the IITB campus getting worse and worse nowadays. We already had lots of problems running the common mess of Hostel 12 and Hostel 13. The caterer called Aditya Caterers was thrown out last year due to some stupid reasons. After that they hired another caterer which also gave up after six months. Its not an easy task to run a mess for around 1200 people. Now they have built up one brand new hostel and one new wing of Hostel 12. And to add to the woes of old H-13 and H-12 mates, they have included all these new people in the same mess which was already in trouble. Now there are 2000 people eating in the same mess. The food quality, hygiene, maintenance everything went down sharply. I can not understand why they could not start a new mess for the Hostel 14. I doubt how long this new caterer will be able to run this mess. One more disgusting thing which has happened is that IIT is charging 800 rupees per year from all students for the stupid facility of the transport system inside the campus no matter they use it or not. Many students have their own bi-cycles and many prefer to walk from hostels to the department. In such a case why a student will pay money for a facility which he or she is not going to use at all. I do not understand who decides these things, in a democratic country things should happen in a democratic way. But here only the big boss takes decisions and are imposed on thousand poor students forcefully.

Venice trip!

I managed to make a trip to Venice while coming back home from Trieste. My flight was on Saturday morning and I came from Trieste at 2 PM on Friday. Three of my friends also came with me. We reached Venice at around 5 PM. The weather was thankfully very shiny although it was raining like anything on Thursday. Venice was really different from other cities. The whole transport system in the city is based on boats. We did not take any boat ride although they are not very expensive compared to the famous Gondola. The city is pretty small like other Italian cities and we managed to walk around for sight seeing. We walked from the station to the piazza San Marco. That was the most famous place in the city I guess, there were lots of people there and some live concerts were also going on. It was a lovely atmosphere there. We stayed in the city till 10 pm and then took a bus to the airport. Venice airport is terribly small with hardly any shops inside. I could not find a shop to buy some food also, forget about my plans to buy chocolates and wine from there. We spent the whole night in the airport and then took flights at 7 am.

Italian Experiences!

During the ICTP summer school, we had a weekend in between and the plan was to make full use of it. Although there was a news of train strike during the weekend, fortunately it did not happen and we could stick to our earlier plans of visiting some places. Just after the lectures on Friday were over, we had dinner and then left to Trieste Central Railway station. By the time we reached, the ticket counter was closed and the only option left was the buy tickets from the machine. I got my ticket without any difficulty from the machine. But when my three other friends tried to buy their tickets together, somehow the machine did not deliver them and 130 euro got stuck inside. We went to the customer care and the guy (in little English and more Italian) told us that we have to fill up a form which he would sign and then show it to the ticket counter on weekdays (during work-hours). Losing 130 euro just before going out for a long trip was damn frustrating. But still we did not change our plans. My friends bought their tickets individually and we left for Rome.

As expected, the train was crowded and we could not have enough sleep in the train. The ticket inspectors kept coming one after another to check the same damn ticket and waking us up. I probably slept for 2 hours just before reaching Rome and that proved to be good enough for me. Just after getting down at the Rome station we bought a day ticket for the metro and went to locate our hotel. After asking couple of people on the streets, we finally found the hotel. The guy at the reception (to our surprise) was a Bangladeshi. He offered us free breakfast, although we could not check in at that time and he asked us to come at 2 PM. We then left for St. Peter's Basilica by metro. This place is damn crowded specially on weekends and fortunately we booked the entry tickets online and hence did not have to stand in those ques. We went to Vatican Museum, Vatican Church and finished everything there by noon. That was remarkable indeed. After that we went to see the Colosseum. There also we applied a trick (which was suggested by one Indian who is a ICTP regular associate). Instead of waiting in the long que in Colosseum to buy the ticket, we went to Roman Forum where there was hardly any que and bought the combined ticket to see both the forum and Colosseum. It took around 2-3 hours to see everything there. We felt tired indeed after that. We took rest in the hotel for sometime and came out in the evening to see some other places like Fontana di Trevi. We went to the Colosseum again to see the night view, it was really amazing. One very funny thing happened in the hotel with us by the way. We all four were(half naked) on our beds and gossiping, suddenly a lady came in and tried to teach us how to use the western toilet. Her English was pretty bad and one of us had to go with her to the toilet and understand what she wanted to say. We could not believe it, using the toilet was such a trivial thing. May be she thought we don't look western and might not be used to such toilets ;)
Next morning we went out for Pisa. It was a four hour journey by train, and was pretty enjoyable. The train was running just along the western coast of Italy and the beautiful beaches were often coming on the left side of our train. Pisa is a very small town with river Arno passing through it. Apart from the leaning tower there was nothing much to see there and hence we finished everything within 1-2 hours and then went to Florence. It took around 1 and a half hour to reach Florence. Florence was really amazing. The architecture, the various sculptures, the crowd, music and everything there were simply incomparable. The city has tiny streets with huge buildings on both sides, we found many street singers who were as good as professional ones. The river Arno added another charm to it. We had to come to another station at night to catch the train back to Trieste. We had lots of problems in finding out the station called Carpe di Mar (I guess). We got lost at many places as we did not have a map of the city. Finally a German lady helped us a lot. And we could manage to find the station. We had to wait there for couple of hours as our train was at 1:45 am. The train was again crowded and I could not sleep much which forced me to bunk the lectures on Monday (except the first one) :(