Twistor Structure Loops N=4 Sym & Higgs + QCD

0:00 We're external minus hollicities, so I copied it three times through the three blobs, and I changed each one to this other vertex, which formerly was the same, again, except through the way that my method looked at it through the copy group. So the phi-dagger amplitudes are described by anti-MHD rules, which are related by a parity operation, which also exchanges the gluon helices. And what we want at the end is the H amplitudes, but since H is the sum of phi and phi-dagger, we just add the two amplitudes together. So this is the situation for the phi-MHD tower. These amplitudes were for the whole tape's amplitudes. So the all plus ones we were looking at were over here. So when we go from the tapes to phi, those get erased, and the next series gets erased. And the first non-vanishing step are the vertices I showed you before. And then these guys here are assembled by combining these vertices with the corresponding species of new vertices. Then there's a tower for the phi dagger, anti-self-rule related by parity, so it's just flipped across. And then for the Higgs, we'll just assemble the two. In these faces, you just get one tower contributing, in these you get overlap with both towers. And so we were able to write down the amplitudes with up to four negative gluon velocities and arbitrary numbers and positive ones interacting with It turns out if you just ignore the phi momentum, this gives you the four negative felicity preamplitude as a trivial special case in the CSW form. And for n equals phi of gluons, we evaluated these formulas and those were fewer gluons, negative gluons, and got agreement with previous results that used a more complicated, often expression. And Simon Badger, Nigel Glover, and Valia extended this to the case of external clarks. And we've also checked agreement for maximally grouply amplitudes which go off on one side of the tower. And I'm probably running a bit over, but let me just say you can do the

2:30 exact same thing, or amplitudes which are linear in another effective operator, the trace of GQ, which had previously been studied because it can model deviations from QCD that might happen at high energies. It could come from a top loop, but this coefficient is quite small, but it might come from some other kind of physics, like gluon composite or something. Anyway, it's a phenomenological model of this operator, and when you insert this amplitude in, you can similarly split it into self-dual and anti-self-dual terms. There hasn't been as much empirical work on this, but it seems clear that this is what the answer is going to be. The self-dual part has these MHD vertices, and the M is a little different, because here need three negative velocities, roughly speaking because we have three self-dual fields instead of just two. And instead of getting this ij to the fourth, these towers are democratically distributed among the three negative velocities. So the two towers in this case look a little different because you have this gap of three instead of with two. So in conclusion, n equals way to test methods for computing TCD amplitudes and forms one component of them. We assume that there's this intricate structure for these NMHV amplitudes. And the Higgs case is also quite useful and shows with NMHV a corresponding twisted structure, which trivially is inherited from the NMHV rules after we've separated out these two pieces. and there's a similar structure for the trade scheme to be stopped. So, thanks. I'm not sure the impact has the population of people have had on the country, but now it's been kind of bad for sure. Well, most of the impact, well, there are various examples.

5:00 The 5-Gluon amplitude enters into hadronic production of three jets, so you have gluon go on in and say three gluons going out. So there have been numerical programs written, two or three by now, and they are available to the experimentalists, and I think they've been, I don't know how much three-jet data analysis has actually been done. It's not done by some of that. Okay. Okay. I know that the 4JET at E plus E minus has received a fair amount of attention, and there, there's four or five different numerical programs, and it's certainly been studied by Aula, maybe Othal, at left, so they've been using those. So those are the, am I missing any uh any other good examples directly related to this i mean there there are obviously other i mean we've done some competitions using another multi-loop or or one move that's right i forgot uh steve showed a good example of that which was the campbell and the Glover computation of the WPlus Jets background, which is our interest to the telecoms, and it will be for the LHC too. Thank you.