# Vector Boson Fusion

I have been reading about the production mechanisms for the Higgs at the LHC. It is always mentioned that for Vector Boson Fusion, the initial quarks cause jets that are back to back and with a higher transverse momentum pT than jets in other processes. Is there a kinematic reason for why the jets have such a high pT? Is it because the initial quarks have high pT due to the large energies at the LHC?

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As mentione's by Davidz, I believe the jets actually have smaller pt as they are forward jets. –  JeffDror Feb 12 at 19:45

I would have thought that it's because (1) the initial state quarks are in the final state and (2) they each must have a very large momentum transfer in order to produce an on-shell Higgs. Small momentum transfer collisions won't put enough energy into the (virtual) VB's that fuse to make the Higgs. That large momentum transfer is going to produce large pT's.

There's a nice set of diagrams here . The only one with both quarks in the final state is the VBF one, so the large pT would distinguish those events.

(Pure speculation on my part on much of this. I haven't done phenomenology for 25 years.)

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I think I actually have an answer to this question even though I put a bounty on it.

The idea is that the amplitude is maximal when the $W$ bosons are produced on-shell (since the propagators are the largest in this limit). This allows us to treat the creation of the $W$'s separately from the rest of the diagram. The momenta of the particles in the lab frame is given by, \begin{align} & p _i = ( E ,0,0,E ) \\ & p _W = ( E _W , 0, p _W s _\theta ,p _W c _\theta ) \\ & p _f = p _i - p _W \end{align} where $p _i$, $p _f$, and $p _W$ denote the initial jet, final jet, and $W$ boson momenta respectively. The angle $\theta$ quantifies how far away the $W$ and final jet are from the beam line. The on-shell conditional for the final jet restricts the possible angles: $$0 = ( p _i - p _W ) ^2 = m _W ^2 - 2 E E _W + 2 p _W c _\theta$$ Simplifying gives, $$c _\theta = \frac{ E _W }{ p _W } - \frac{ m _W ^2 }{ 2 E p _W }$$ If the $W$ bosons are highly boosted (as one would expect at the LHC) then, $$c _\theta \approx \frac{ E _W }{ p _W }$$ This is just the velocity of the $W$ bosons and approaches $1$. Therefore, $\theta \approx 0$.

Therefore, we conclude that the $W$ bosons (and hence also the final jets) come out at small angles relative to the beam line. This creates the forward jets found in vector boson fusion.

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Don't quote me on this just yet (I want to check some sources), but my thought would be that it's because the VBF cross section is most dominant around the W and Z resonances which are at $80\text{ GeV}$ and $91\text{ GeV}$ respectively. That's a lot of energy tied up in those bosons, and in turn in the Higgs that they collide to produce. So when that Higgs decays, it's going to produce particularly high-momentum jets.

In other Higgs production processes, you wouldn't get the resonance around the large masses of the vector bosons because the virtual particles involved aren't so massive. The exception would be gluon fusion with a top quark loop, but that's also suppressed by the low gluon density at large Bjorken $x$.

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Oh, I'm sorry, my question is not very clearly worded. I am not asking about the jets that result from the decay of the Higgs. I mean the jets that result from the initial quarks, so the quarks that continue along after radiating a vector boson have very high pT, not necessarily the jets arising from the Higgs decay. –  Jess Aug 20 '12 at 18:11
Ah, I see. (Could you edit the question to reflect that?) I was actually under the impression that those jets come out in the forward direction, with $p_T$ not particularly large, but I could be wrong. –  David Z Aug 20 '12 at 19:23