Twistor string & the integrability of N=4 Sym (contd.)

0:00 Higgs boson is the least massive of course, coupled with two parts of gluons. What I want to talk a little bit about here is the electroweak vector boson coupled with the quarks. How to do that. And this is worked with Jim Kossauer and Darren Ford and Pierre Pell in Australia. So, let's look at the case of mixed electroweak QCD. You're bound to have QCD present because you're dealing with strongly interacting particles. This is a very typical situation. As soon as you produce a quark, you're bound to have radiation, ionic radiation, because of the strong interaction of a quark in front of an anus. So the question is, can we calculate something like this using twistor ideas? And in fact, maybe we can calculate lots and lots of gluonic radiation and quarks and antiquarks all in one fell swoop using these twistor ideas. Is there some way to do that? Well, if you look at this picture here, it's been very nicely colored in red for the QCD part and blue for the electroweak part. The idea that you might have is you try to split it into two pieces, one for the QCD and one for the electroweak. Now electroweak, like the name says, is weakly interacting, so in general you're not going to have large numbers of W's. Here, it's very easy to have large numbers of gluons and quarks because it's strong enough. So, it's this side that we want large numbers of particles. That's the more important place to try to simplify. So, once you've made this little separation, you might say, well, let's apply these MHD rules and these twistor motivated ideas to this part. And this part will do by finding them.

2:30 But as soon as you start thinking about that, you realize it's a very delicate thing because this kind of engages on it. In here, there's a reference we mentioned. In the sense that there's an arbitrary parameter that's been put in here that has to cancel related to the gait invariance. On this side here, you might notice there's a vector boson that's kind of stuck in there with a little electroweak thing. Somehow the whole thing has to work out to be gait invariant. It's a little bit delicate how to do that, but the solution turns out to be quite simple. The solution is just introduce a new vertex, a new MEP vertex for vector boson terms. These currents can be coupled to any lecture week process. So if you go back here, this here can be called the current of a lecture week that you can then couple to some other lecture week process. And using these new vertices, these new MAP vertices, which now have a W boson sticking off the end, or a Z boson, or whatever your favorite electroweak or vector boson particle is, you essentially use them exactly the same way that the MAP vertices are used, and so now we have an off-shell That can be coupled with any arbitrary off-scale source, and in fact, as with the rest of CSW, there's no proof that this is correct, but there's very strong evidence, overwhelming evidence, set by numerical checks and arguments about the various factorization limits. The amplitudes that we generate. In fact, we've done numerical checks up to 10 legs. In fact, we've counted on the length, which is 10 light-seals, up to 10 legs, comparing against the first and second diagrams, and it's a complete agreement. So, the bottom line is that the mixed QCD electroweak amplitudes can, in fact, take advantage of these twisted motivated ideas, but the twistor part is... The summary is that people will be telling me a lot of talks on scattering amplitudes, mostly in N equals 4 super-yang mills, but still...

5:00 The idea that scattering amplitudes are really crucial in particle physics. All our calculations, all our future understanding of particle physics at the electrolyte symmetry gradient scale, at the next scale, beyond the standard model, it relies on scattering amplitudes. The experiments are all scattering experiments. If you want detailed comparisons of the standard model for the experiment, but search for the new physics, then you must have high order calculations, many particles, high loop orders, and these are difficult to calculate, and we're looking for a new set of tools for dealing with all these problems. A really amazing result is that gauge theory scattering amplitudes are much simpler than anyone imagined, and that's of course, people have studied these gauge theory amplitudes very well for the last 30 years, and it's really a surprise at how simple they actually are, if you look at it the right way. And we're going to hear these talks, the MHB vertices. Peter Sertic will explain in much more detail than I did about these MHB vertices and the connections with their space. We'll hear talks about how to turn the simplicity that you find at tree level to turn it at the loop level through the unitary method. And then I just showed you an example of initial application to these twistor-modulated methods in the lecture week video. But at the end, it's clear that as we get a deeper understanding of the mathematical structures that underlie the scattering processes, there will surely be much more progress.

7:30 If you put in a large number of these words, it should work. That's all I'll say. It should work. I don't know, actually. There's some technical issues, but it should work. Let me say it will work.