Double-Parton Scattering is Not Rare

December 29, 2009 at 4:10 pm 2 comments

Despite lots of empirical evidence to the contrary, I tend to think of proton-proton interactions as the collision of single partons (quarks and/or gluons, one from each incoming proton) giving rise to all sorts of rich phenomena. A recent paper by Berger, Jackson and Shaughnessy reminded me that this way of thinking is too simplistic, and that the simultaneous scattering of two pairs of partons from the same two protons provides a non-negligible contribution, especially in certain corners of phase space – corners that may be quite relevant for finding physics beyond the standard model. Their paper is available on the physics archive: arXiv:0911.5348.

I grasp the essence of their paper as follows: imagine that you were looking at the production of b-quark pairs, as part of a search for the Higgs boson. You might look at the subset of events in which the hadron jets from the two b quarks are back-to-back, i.e., for which Δφ is nearly 180°. There will always be some extra activity in the event (even forgetting the contribution from other protons interacting) due to the initial-state radiation (ISR) of gluons. Naively, however, one would expect ISR to be small when Δφ is close to 180°. A standard event generator will simulate only those interactions coming from a single pair of partons, and will very rarely produce four jets – the two back-to-back b-quark jets and two other jets, which necessarily will be back-to-back, also. It would not be difficult to compare such a prediction to real data – in fact, this will surely be done as soon as the LHC delivers more data in a couple of months. According to the studies of Berger, Jackson and Shaughnessy, however, you would see a major discrepancy between the “standard” prediction and the real data…

These studies show that there would be a “surprise” contribution of jets which are themselves back-to-back, very much as if two events were overlayed. The important point is that these two “events” come from the same proton-proton interaction, and hence do not depend on the instantaneous luminosity, in contradistinction to the overlap of two proton collisions in the same beam crossing – which obviously depend on how many protons are in each bunch. Furthermore, collisions from different pairs of protons can be separated to some degree by reconstructing their different Z-coordinates (positions along the beam line), but this is not the case for double-parton scattering.

The thrust of the Berger, Jackson and Shaughnessy paper is a study showing that clear evidence for double-parton scattering can be obtained with a few pb-1 of data at 10 TeV. Here is one of the most telling distributions of their study:

S_phi distribution showing double-parton scattering

Sφ, which peaks toward one for double-parton scattering

Sφ = (1/√2) ⋅ √( (Δφbb)2 + (Δφjj)2)

The quantity Sφ peaks toward one for events in which the b-quark jets are back-to-back, and the other jet pair is also back-to-back. The bulk of the distribution indeed comes from single-parton scattering (“SPS”), in which two ISR gluons accompany the b-quark jets. For the SPS component, there is no special reason why the b-quark jets should be back-to-back, or the two ISR gluons should be back-to-back; the final state populates a four-body phase space which accommodates many other configurations. For the double-parton scattering (“DPS”) component, however, we have the overlay of two two-body final states, and each individual two-body final state is necessarily back-to-back. The DPS component may be small overall, but the plot shows a very tall spike at a corner of phase space. (The SPS component is represented by the red histogram, the DPS by the blue, and the sum of the two by black histogram.)

Double-parton scattering has been investigated empirically in the past, and many papers have been written about it in the context of high-energy hadron-hadron colliders. The paper by Berger, Jackson and Shaughnessy is particularly useful and I hope that the LHC experiments will follow-up once the necessary data have been recorded. At a minimum, an overall factor σeff must be measured in order to make progress. On the longer term, we should try to gain some knowledge of the double parton distribution functions (see arXiv:0911.5348 for details).

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