Dipole Spectrometer Acceptance

 

The nominal values for dipole spectrometer pot locations are obtained by scaling the values from Table 1 and give an of 7.0 mm and 6.3 mm, for and , respectively. An anti-proton is considered to be accepted by the dipole spectrometer if it passes through the active area of both detectors while remaining within the limiting aperture of the beam pipe throughout its entire trajectory. The acceptance is determined as a function of the initial conditions of the anti-proton (, |t|, and ).

The geometric () acceptance of the dipole spectrometer is shown in bins of and |t| in Fig. 15. The size of the boxes are proportional to the geometric acceptance with the largest boxes representing 100% acceptance. The acceptance is especially good for 0<|t|<0.5 GeV and high (). At low |t| and the particle is not deflected enough to enter the pots, while at high |t| and the particle is deflected too much and scatters off the beam pipe.

  
Figure 15: The geometric acceptance in bins of and |t| for the dipole spectrometer with the detectors at the nominal displacements. The acceptance in each bin is proportional to the size of the box, with the largest box representing 100% acceptance.

We calculate the total acceptance (or cross section times acceptance, ) by integrating over the and |t| values accepted by the pots. We include the |t| dependence using the relation , where from Ref. [21]. This expression is valid for single diffractive and most likely double pomeron events, but for elastic events  [22]. The total acceptance is dominated by the |t| acceptance, since the cross section falls so steeply with |t|.

The solid line in Fig. 16 shows the total acceptance for diffractive events for pot positions. For comparison, the acceptance for pot positions of (dashed line) and (dotted line) are also shown. The acceptance increases rapidly with increasing for all pot displacements. Even for there is still acceptance at low . The acceptance for several and values is summarized in Table 2. Although we are only focussing on the acceptance for , the dipole spectrometer retains acceptance up to .

  
Table 2: Integrated total acceptance (in percent) for anti-protons using a Roman pot displacement in the horizontal plane versus and .

  
Figure 16: The total acceptance as a function of for the nominal pot displacements (solid line). The acceptance is integrated over |t| and and assumes a single diffractive |t| dependence as discussed in the text. For reference, the acceptance for (dashed line) and (dotted line) are also shown.

It was mentioned earlier that CDF had little acceptance for . This was due to several factors [39]:

• One loss of acceptance was due to 1.5 mm of dead area between the bottom of their pots and the active area of their detector. The dead area was due to the thickness of the bottom of the pot as well as the frame holding the fibers.
• The beams were separated by a few millimeters at the CDF pot locations, with the proton beam located between the beam and the pots, thus limiting the point of closest approach of the pots to the beam.
• Since the CDF pots were installed late in Run I, their procedure for installing the pots as close to the beam as possible was not optimized. Running a few millimeters closer to the beam than their nominal position increased both signal and background rates, but lack of time prevented a full study so a conservative (retracted) position was chosen.
• They did actually have a few percent acceptance for , but due to the limited running period, have little data for .

From our studies each extra millimeter corresponds to , thus the CDF detector location (about 13 mm from the beam), would give a and near full acceptance for , which is consistent with their results (the Run I and Run II lattices are not identical and the beam energy is different).

The situation for the DØ dipole spectrometer will be much improved. The design we are considering for our pots, discussed in Sec. 4.1 should result in a dead area on the order of 100 m, instead of a few millimeters. The separation of the beams is more advantageous at the DØ location, with the \ beam located 0.3 mm closer to the pots than the proton beam [40]. We will be preparing for a long run and will have adequate time to study the halo rates in order to minimize the pot displacement. The long running period will allow us to obtain large data samples even if the acceptance were significantly less than 1%. We consequently expect to have acceptance to near zero, as shown in Fig. 16.

To better understand the acceptance, it is instructive to study Fig. 17, which shows the horizontal and vertical displacements at the and pot locations for scattered 's with (top plots) and (bottom plots). The ellipses are contours of constant |t| ranging from 0.5 GeV for the inner-most ellipse to 2.0 GeV for the outer-most ellipse. The ellipses are displaced in the negative x direction due to the bending into the Tevatron ring of particles with less than the beam momentum. Comparing the ellipses for and shows that this deflection is larger for higher (lower momentum) as expected. The dashed bracket (superimposed on locations) represents a detector at the proposed displacement. It clearly intercepts a large portion of the ellipses, including the critical low |t| values. A detector with a displacement of 13 mm shown by the dotted bracket on the plots will clearly have much worse acceptance.

  
Figure 17: The x and y displacements at the (left plots) and (right plots) pot locations are shown as contours of constant |t|, ranging from 0.5-2.0 GeV (smaller |t| gives smaller displacement) for (top plots) and 0.05 (bottom plots). The dashed brackets show a pot displacement of 6.3 mm (10), while the dotted brackets show a pot displacement of 13 mm (CDF Run I position).