Pile-up Background

  Pile-up, the background due to the superposition of a low mass diffractive event with a hard scattering event, is a more serious concern since this combination can fake a hard diffractive signal. Using the two-arm (p and ) single diffractive (SD) cross section of mb, we see that there will be an appreciable pile-up background for the quadrupole spectrometers (the fake background for the dipole spectrometer is relatively less important due to the acceptance being weighted towards higher where the fake background is negligible). For example, from the third column of Table 6 at 4E31 luminosity 21% of all events (1-P(n=0)) will have at least one extra single diffractive event. Fortunately, this background is dominated by very low mass diffraction which could not produce jets and can easily be rejected at Level 1 by a cut such as , which will reduce the effective cross section to about 2 mb [21]. Applying this cut reduces the overlap of diffractive events with dijet events to a few percent (5% at 4E31). The aforementioned single interaction requirement will reduce this background by about a factor of 10 based on Run I experience. Note that virtually all single diffractive events with ( GeV/) will give enough hits in the Level Ø counters for this requirement to be effective. With these simple cuts the fake background is reduced to about 0.5% of dijet events, which is on the order of the expected 0.3-1% hard diffractive dijet signal [11]. As shown in Sec. 5.4, the Level 1 rates implied by this level of background are acceptable after the proton acceptance is taken into account. At Level 3 this background can be reduced to near zero as discussed below.

The hard double pomeron background, due to the pile-up of two opposite side single diffractive events with a dijet event, is also manageable. A tighter cut requiring that would likely be used for double pomeron events. Since only about is available for jet production (for this gives an GeV/), there will be no contribution to jet cross sections from lower values, but a large contribution to the pile-up background. The column in Table 6 labelled P() shows the probability of having two or more single diffractive events for a diffractive cross section of 1 mb is 0.00027. This gives a background more than an order of magnitude greater than the expected signal for hard double pomeron exchange, which is likely to be a few millionths of the dijet cross section [11]. Although this absolute rate is already small and additional cuts are not strictly necessary, we would still apply a single interaction requirement to reduce the contamination at Level 1 to the same order as the signal. The same arguments apply to background from two soft single diffractive events plus a dijet event or one hard single diffractive dijet event and one soft jet single diffractive event.

At Level 3 (or offline in the case of diffractive W bosons) there will be other tools available for identifying pile-up background which will be combined into a single interaction algorithm or tool:

• The new silicon tracking detector should be very efficient at finding multiple vertices (>99%) and can thus reject multiple interaction events for those interactions that have tracks with . The cuts suggested above will already ensure that the events will typically have several central tracks.
• The event interaction time from the trigger scintillators can be compared to the interaction time from Level Ø to determine whether the times are consistent with coming from the same interaction. With a single tube resolution of 240 ps, we expect a 170 ps time resolution for the two trigger counters. The Level Ø counters typically will have several counters hit and are expected to give a resolution of 100 ps. Convoluting these distributions with the time distribution of the event (about 1 nsec) and demanding a two sigma separation gives a rejection factor of three. This cut would be particularly useful for rejecting diffractive events where the diffractive system is produced at small angles for which the multiple vertex cut is ineffective.
• Conservation of longitudinal momentum can be imposed by requiring that the sum of the momentum of the trigger proton and the longitudinal energy in the DØ calorimeter on the trigger side is less than the initial 1 TeV beam momentum (within resolution). This is a very effective cut, particularly for low (for example with the proton alone contributes 990 GeV/c to the longitudinal momentum). Essentially, this makes use of the fact that a pile-up event will have a beam remnant and a diffractive event will have none to reject pile-up events. An equivalent cut for the UA8 collaboration was very successful and the FPD momentum resolution and DØ energy resolution are greatly superior.

A loose rapidity gap requirement could also be implemented. As an example consider the multiplicity distribution in Fig. 3. A cut of would provide a rejection factor of 100 on fake background events while preserving all rapidity gap events. We would be reluctant to adopt a rapidity gap cut online in the hard diffractive triggers except in the unlikely event that it proves absolutely necessary to control the rates, since there would potentially be some biases to the physics. For inclusive double pomeron exchange, rapidity gap requirements likely will be used due to higher backgrounds and less concern about biases.

Although lower luminosity is optimal for dedicated hard diffractive triggers, there is still an appreciable single interaction cross section at very high luminosity and there are many handles for rejecting pile-up background.