1. Elastic Scattering at s=1.96 TeV Using the DØ Forward Proton Detector
Andrew Brandt University of Texas, Arlington
on behalf of DØ Collaboration
An FPD Quadrupole castle with
four detectors installed
Andrew Brandt UTA
DPF 2011 Brown University

2. Elastic Scattering
The particles after scattering are the same as the incident particles
=p/p=0 for elastic events;
The cross section can be written as:
This has the same form as light diffracting from a small absorbing disk, thus processes with one or more intact protons are referred to as diffraction
Characterized by a steeply falling |t| distribution and a dip where the slope becomes much flatter
Elastic “dip”
Structure from
Phys. Rev. Lett.
54, 2180 (1985).
t = -(pi-pf)2
Andrew Brandt UTA
DPF 2011 Brown University

3. Forward Proton Detector
There are 8 quadrupole spectrometers 4 each (Up, Down, In, Out) on the outgoing proton (P) and anti-proton (A) sides, with each spectrometer comprised of two detectors (1, 2)
Use Tevatron lattice and scintillating fiber hits to reconstruct  and |t| of scattered protons (anti-protons)
The acceptance for |t|>|tmin| where tmin is a function of pot position:
for standard operating conditions |t| > 0.8 GeV2
Andrew Brandt UTA
DPF 2011 Brown University

4. FPD Detectors
3 layers in detector: U and V at 45o degrees to X, 90o degrees to each other
Each layer has two planes (prime and unprimed) offset by ~2/3 fiber
Each channel contains four fibers
Two detectors in a spectrometer
Scintillator for timing (primariliy used for halo rejection)
17.39 mm V’ V
Trigger X’ X U’ U
17.39 mm
1 mm
0.8 mm
3.2 mm
Andrew Brandt UTA
DPF 2011 Brown University

5. Large β* Store
In 2005 DØ proposed a store with special optics to maximize the |t| acceptance of the FPD
In February 2006, the accelerator was run with the injection tune, β* =1.6m (about 5x larger than normal)
Only 1 proton and 1 anti-proton bunch were injected
Separators OFF (no worries about parasitic collisions with only one bunch)
Integrated Luminosity (30 ± 4 nb-1) was determined by comparing the number of jets from Run IIA measurements with the number in the Large β* store
A total of 20 million events were recorded with a special FPD trigger list
Andrew Brandt UTA
DPF 2011 Brown University

6. Track Finding Alignment Hit Finding Track Reconstruction.
Use over-constrained tracks that pass through horizontal and vertical detectors to do relative alignment of detectors and use hit distributions to align detectors with respect to the beam
A1U
A1I
A1O
A1D
Hit Finding
Require less than 5 hit fibers per layer (suppresses beam background)
Use intersection of fiber layers to determine a hit
Track Reconstruction.
For events with good hits in both detectors, use the aligned hit values and the Tevatron lattice transport equations to reconstruct the proton track
Andrew Brandt UTA
DPF 2011 Brown University

7. Elastic Spectrometer Combinations
Elastic events have tracks in diagonally opposite spectrometers
A1U
A2U
P2D
P1D LM
Proton
Anti-proton
Momentum dispersion in horizontal plane results in more halo (beam background) in the IN/OUT detectors, so concentrate on vertical plane AU-PD and AD-PU to maximize |t| acceptance while minimizing background
AU-PD combination has the best |t| acceptance
Andrew Brandt UTA
DPF 2011 Brown University

8. Detector Positions after Alignment
Andrew Brandt UTA
DPF 2011 Brown University

9. Hit Finding Combination of fibers in a plane determine a segment
Need two out of three possible segments to get a hit
U/V, U/X, X/V (or U/X/V)
reconstruct x and y position in detector
use alignment to go from detector to beam coordinates
Can also get an x directly from the x segment (can compare these x measurements to measure resolution) X U V
beam
Andrew Brandt UTA
DPF 2011 Brown University

10. Fiber Correlations within a Detector
Correlations between fibers in the primed and unprimed plane of each layer in
AU-PD elastic candidates
Fiber hit correlations are a useful debugging tool to demonstrate
that the detectors are operating as designed. The figure shows the fiber
correlation of primed and unprimed layers in the A1 and P1
detectors, respectively, for elastic trigger events with single hits in the three
different planes, U, V, and X. From the plots one can confirm the
correct cable mapping (given the expected correlation between primed
and unprimed layers) as well as determine dead or hot channels
(there were very few instances of either).
Andrew Brandt UTA
DPF 2011 Brown University

11. Layer Multiplicity for Elastic Candidates
This figure shows the fiber multiplicity distribution for a couple representative layers (out of the
six fiber layers) of the A1U detector for elastic candidate events selected with the
SDPRO and XTXT triggers, standard hit requirements
were applied with the exception of the number of struck
fibers <=4, this plot just shows that elastic events have low
fiber multiplicity and that the cut of number of struck fibers
throws away a very small fraction of events which are in any case later corrected by
the hit selection efficiency
Elastic events have low fiber multiplicity
Andrew Brandt UTA
DPF 2011 Brown University

12. Detector Resolutions xuv-xx=2 Andrew Brandt UTA
The figure shows distributions of the difference
between the x coordinate obtained from UV fiber intersections and
from the X fiber segment, for events with all 3 fiber planes ON in
the vertical quadrupole detectors. The detector resolution can be
estimated by dividing the width of this distribution by the square-root of 2,
since the difference depends on uncertainties from both the UV and
the X measurement fibers.
xuv-xx=2
Andrew Brandt UTA
DPF 2011 Brown University

13. Halo Rejection Proton Halo -78 -109
nsec
109
nsec
A1U
A2U
P2D
P1D LM
Proton Halo
-78
nsec
-109
The in-time bit is set if a pulse detected in the in-time window
(consistent with a proton originating from the IP)
The halo bit is set if a pulse is detected in early time window
(consistent with a halo proton)
We can reject a large fraction of halo events using the timing scintillators (depending on the pot locations)
Andrew Brandt UTA
DPF 2011 Brown University

14. Correlations Between Detectors
No Early Hits
fiducial
region
No Early Hits
In addition to providing a time measurement for particles that pass through the
detector at the expected time and setting an in-time bit, the TDC
system also set a halo bit for early time hits. Halo particles are
particles traveling far enough outside of the main beam core that
they can pass through the detectors and be mistaken for elastic or
diffractive protons. If these halo particles arrive at the proton
detectors at the time expected for an in-time proton, frequently
they have passed through the diagonally opposite antiproton
detectors at an earlier time (and vice versa).
The first column of the figure shows the
y coordinate correlations for the first detector of the proton
and anti-proton spectrometers for the two elastic combinations
AU-PD and AD-PU. Although the expected linear correlation for elastic events can be
observed, there is clearly some uncorrelated background.
A likely source of this background is halo contamination, which can
be reduced through the use of the FPD timing system.
The second column shows the y correlations for events
with one or more halo bits set in the elastic
configuration. Column 3 shows the elastic candidate events remaining
after removal of the halo events from Column 2. There is still some
residual background, partially due to inefficiency of the trigger
scintillator, but mostly due to the different acceptances of the
different spectrometers (if one spectrometer is not inserted as far
as its elastic partner, it will not only have lower acceptance for
elastic events, but it will also have less halo acceptance, reducing
the effectiveness of the halo veto). The red box shows the fiducial region kept for the elastic
analysis, which equalizes the acceptance for elastic tracks in both spectrometers.
residual halo due to
different acceptances of the two spectrometers
-> fiducial cuts
Elastic
Halo
Andrew Brandt UTA
DPF 2011 Brown University

15. Measuring Cross Section
Count elastic events
Divide by luminosity
Correct for acceptance and efficiency
Unsmearing correction for |t| resolution
Subtract residual halo background
Take weighted average of four measurements
(2 elastic configurations each with two pot positions)
Andrew Brandt UTA
DPF 2011 Brown University

16. Correcting Cross Section
Corrections:
f acceptance (geometrical loss due to finite size of opposite spectrometer)
Unsmearing correction due to beam divergence, |t| resolution (standard approach using ansatz function)
Efficiency: use triggers requiring A1-P1 or A2-P2 hits, offline demand 3rd hit, then measure efficiency of 4th detector
Use side bands to measure and subtract background
“observed”
“true”
“smearing”
“unsmearing” or “unfolding”
Andrew Brandt UTA
DPF 2011 Brown University

17. |t| Observe expected colinearity between proton and anti-proton
Resolution
ranges from 0.02 at low
|t| to at high |t|
Observe expected colinearity between proton and anti-proton
DPF 2011 Brown University
Andrew Brandt UTA

18. Measurement of Elastic Slope (b)
Systematic error dominated by trigger
efficiency correction (this is likely to be
significantly smaller in final result, which just missed the DPF deadline)
First measurement of b at s=1.96 TeV
Andrew Brandt UTA
DPF 2011 Brown University

19. d/d|t| Compared to E710+CDF
E710/CDF for s=1.8 TeV; expect logarithmic dependence with s
Andrew Brandt UTA
DPF 2011 Brown University

20. d/d|t| Compared to UA4
Comparison of D0 data to UA4 data. We observe the expected “shrinkage” effect with increasing center of mass energy, namely the slope is steeper and the dip moves to lower |t| values.
Slope steeper and slope change earlier for higher s (shrinkage)
Andrew Brandt UTA
DPF 2011 Brown University

21. Conclusions
We have measured d/d|t| for elastic scattering over the range: 0.2< |t| <1.2 GeV2 the first such measurement at s=1.96 TeV
For 0.2<|t|<0.6 GeV2 we have measured the elastic slope
b=16.5 ± 0.1 ± 0.8 GeV-2
We observe that the elastic slope is steeper and changes slope earlier than lower energy data such as UA4
Extra Points
Paper is in final review stages to be submitted to PRD in next few weeks
Arnab Pal (UTA Ph. D. student) just defended his thesis on
single diffractive cross section, analysis in early review stages
Andrew Brandt UTA
DPF 2011 Brown University