sage
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Mass Problem IIa: Comments on flavor problem
2.a comments on flavor problem.
So far, we know of three generations of fermions. each generations has a family of quarks and a family of lepton. for example, the first generation is consistent of a) quark family: up and down quark; b) lepton family: electron and electron-neutrino.
The observed masses of the fermions are very different, between families, between fermions within the same family, and between fermions within the same quark or lepton sector. For example, electron mass is about
0.511 MeV, while top quark mass is 175 GeV. The goal of the flavor problem is to understand the reason behind these differences.
One first comment about the flavor problem is that it is in some sense 'technically natural'. Because of the reason I said when discussing the fermion mass, possible renormalizations of the fermion mass are always proportional to fermion mass. Or in other word, they are logarithmically divergent. A fermion with zero mass won't acquire mass through renormalization. For the same reason, renormalization won't make a large mass small, nor a small mass bigger. This fact is important because it means that any mechanism that solves the flavor problem would only have to mostly solve it at tree level. Because the renormalized mass is not very different from the tree level one.
Now there are many solutions to the flavor problem. Probably too many. For example, in the Standard Model, flavor problem reduces to the explanation of the Yukawa couplings. The electron Yukawa coupling is much smaller than the Yukawa coupling of the top quark. One possibilty is that there is some small order parameter in the flavor sector. Then, all Yukawa couplings are just different powers of such a small number. Electron Yukawa coupling comes presumably from a large power of some small number, and so on. The mechanism which guarantees this to happen is sometimes called flavor symmetries.
I would not talk here a lot about various flavor physics models. I would like to make one further comment about them. The ultimate judge for a physics theory is experiments, not whether it is beautiful or simple or not. Therefore, it is important that we have ways to test our theories. It is not enough that one theory reproduce something that we have already known. It must predict something to be tested. Various different theories with different predictions could be distinguished by experiment.
Unfortunately, many flavor physics models are not testable. The main reason for this is that the fermion mass, as I said before, is technically natural. It is not sensitive to some scale, such as renormalization scale. Therefore, we do not have a hint at all what is the scale of the fundamental physics which determines the flavor structure. It could be very high or quit low. The difference will just be a scale in the logarithmic correction, which is very insensitive. For this reason, it seems likely that the scale for flavor physics is far beyond any our experimental capability. This is a depressing possibility that we might never really learn the secret of flavor. Moreover, even if flavor physics is not so far away, we will never know ahead of time how hard we will have to try to get there. That why I said above that there are probably too many flavor models.
From this argument, it is easy to see that if something is not technically natural, or very sensitive to scales, the situation will be very different. We will precisely know how much we need to do to test them. We will see such an example in the scalar mass problem which we will disucss next.
Another more interesting direction to look is that whether there are new flavor structures beyond the Standard Model. This is not solving the problem. However, if there are new additional flavor structures, such as another family, it will be additional new data for the flavor physics, at least. This is why it is important to experimentally test the Standard Model flavor structure carefully, and look for deviations. Such experiments are mainly carried out by an experiment at SLAC, called Babar, and another experiment in Japan, called Belle. They study the flavor structure of the mixing between the third generation, mainly bottom quark, and other quarks. So far, no deviation of has been found. On the other hand, there are rooms for large improvement in precision in fiture experiments. Large Hadron Collider, LHC, scheduled to start at 2007, will produce a huge amount of bottom quarks. It will also do a lot of interesting b-physics.
| 发表时间：2006-05-23, 21:18:40 |
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萍踪浪迹
发表文章数: 1983
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Re: Mass Problem IIa: Comments on flavor problem
so good！
漫漫长夜不知晓 日落云寒苦终宵
痴心未悟拈花笑 梦魂飞度同心桥
| 发表时间：2006-05-24, 13:14:06 |
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