Huh...

[danalwyn]

So I notice that everyone's favorite wannabe rapist and misogynist, PRED, has returned as a subject of conversation on GAFF. I don't dare go through the links, since the machine I'm on is technically monitored by the FBI, but I'm sort of curious whether he's done anything new, or whether this is just people reacting to his presence for the first time. Am I evil for hoping that he'll notice that we're taunting him and show up in person to defend himself and his worldview? It would amuse me to no end to watch him get stomped.

I've learned that perturbative Quantum Field Theory doesn't work on Higgs boson/top interactions. That puts a hole in my skills. What am I supposed to use if I don't use perturbative QFT? Life is hard...

I'm also thinking of writing up something about the latest failures of the UN peacekeepers in the Ivory Coast. I don't expect that it will get a lot of attention, but it will poke fun at the French, so at least Avari will show up for it.

Back to some more background material...

Comments

[john-yik.livejournal.com]

I've learned that perturbative Quantum Field Theory doesn't work on Higgs boson/top interactions. That puts a hole in my skills. What am I supposed to use if I don't use perturbative QFT? Life is hard...

Hold on, Dan--why *doesn't* Quantum Field Theory work on Higgs reactions? It can't be an experimental result, certainly--is it predicted in theory somewhere? Come to think of it, what sort of interaction is the Higgs/top, anyway? Could you enlighten a sadly ignorant undergraduate?

[danalwyn.livejournal.com]

It's not that Quantum Field Theory doesn't work. It's that the perturbutive version, which is all that I know, doesn't work. The short answer is that the coupling constant is of order unity. If that answers your question, you can stop reading now.

I don't know how much you know, so I'll give you my best explanation-and probably the low-gear physics explanation. I learned Quantum Field Theory mostly via the perturbation theory approach. This means that if you want to calculate the cross-section, you propose a Lagrangian and write down a whole bunch of Feynman diagrams. The easiest one to do is two electrons scattering off of each other; in Field Theory we interpret this as being through the interchange of a virtual photon.



Note that the diagram has two verticies, one at the generation, and one at the absorption, of the virtual photon. In order to calculate the cross-section, we measure the chance of interacting through a complicated process, basically we break things into three different pieces, multiply their "probabilities" together, and integrate this over all particle states. The "probability" we use for a cross-section is the coupling term-basically how strong the particles interact with each other. For electrons you can basically use the electromagnetic field terms derived in Classical E&M. Doing this we can calculate the cross-section for this one interaction.

In any real interaction there are about a dozen different paths that you can take. The electron example has several, some including positrons:



Once you've summed up all the amplitudes of each diagram (basically of each possible way the particles can scatter), then you've successfully completed the first assignment in a QED class, calculating the scattering cross-section of the Coulumb interaction.

But now you can ask another question. Since there is only one electroweak force, what's to prevent the electrons from exchanging a Z0 boson instead of another virtual photon? After all, the electron does couple to the Z through the Weak force. Well, it does. But you'll find that the coupling constant is small enough that it takes precision machinery to locate it. Basically, when you've got two electrons scattering off of each other, the Z0 contribution is small enough that you can ignore it.

But that raises another problem. What about complicated bastards like this one:



Well, it gets worse. That object in the middle is a loop. This may not seem like a bad thing, but there's nothing in the physics that prevents there from being three or ten or an infinite amount of loops in that diagram. A pair of virtual quarks can turn into a pair of virtual quarks can turn into a pair of virtual quarks as long as you want. This is a headache. We hates it.

What saves us is that every time we add another loop, we add another vertex. And every time we add another vertex, our cross-section contribution from this diagram gains another factor of g (the coupling constant). So when we calculate the contribution of a Feynman diagram to the total cross-section (in the above, the total probability of e- qbar -> e+ q), the terms from diagrams or sequences with >1 loop become negligible.

Of course, this utterly fails in the case of top/Higgs, because there g is of order 1. So you quickly find that the diagrams with ten or more loops make more of a contribution than the diagrams that are immediate. If you sum them up, you quickly realize that the cross-section goes to infinity. It's just a case where perturbation theory doesn't work.

There's an entire field of non-perturbative QFT out there. QCD depends on it if I remember correctly. But I don't know it; so when people talk about top/Higgs interaction I get totally lost.


Continued below:

[danalwyn.livejournal.com]

To be honest, answering your second question will be hard. I have very little grasp on how the Higgs works, but I'll give it my best shot. In order for QED to work, they had to postulate the existence of a uniform field throughout space, the Higgs field. This is what gives three of what we see as the weak bosons mass, and leaves the photon massless. In reality the two massless vector bosons mix with each other and create a pair of mass Eigenstates, the massless photon and the massive Z0. This is done by separating terms in the Lagrangian in order to create good observable eigenstates, and takes several pages of algebra.

The Higgs field was designed to couple to particles simply dependent upon their mass. Although I don't know the original intent, the theory works for fermions as well as bosons: objects couple along the order of m_particle² / m_Higgs². This would normally not be impressive, but the Top is so damn massive that its mass is comparable to that of the Higgs. I don't think anybody knows why it is, but apparently it couples strongly enough that they could make temporary bound states.

No. I don't understand what that means for our detector either. But I hope I answered some of your questions.

[danalwyn.livejournal.com]

Just remembered. If you're really curious, you might want to ask around there. Supposedly there are thirty-nine people from your institution at CMS alone (I may have your institute wrong, but I don't think so). Some of them have to be around, and all of them can give you a better picture of expected top/Higgs interactions than I can.

Thank you, Dan.

[john-yik.livejournal.com]

That was informative. I suppose I will be asking around my institution, at least once I get back from the holidays. And in the meantime, I just happen to have a QFT textbook here with me.

Let's see how much of it I can cram into my brain before October...

Re: Thank you, Dan.

[danalwyn.livejournal.com]

Be careful about QFT. It can make your brain overheat. I've lost friends like that...

I'm not sure how much I've written is correct from a theoretical point of view. I don't know any theorists. We Experimentalists live a very sheltered existence.