1. Results of dN/dt Elastic
Scattering
Jorge Molina

2. ELASTIC TRIGGER GIVEN BY
FPD LAYOUT D S Q 4 3 2 A 1 P p
z (m) 59 33
ELASTIC EVENTS
Halo
Early Hits
Halo
In time Hits
A2U
A1U LM P - P - P P VC
P1D
P2D
ELASTIC TRIGGER GIVEN BY
P1D·P2D·A1U·A2U·(EAU + EPD + VT + LM)

3. FPD Detector Setup
6 layers per detector in 3 planes and a trigger scintillator
U and V at 45 degrees to X, 90 degrees to each other
U and V planes have 20 fibers, X planes have 16 fibers
Layers in a plane offset by ~2/3 fiber
Each channel filled with four fibers
2 detectors in a spectrometer
0.8 mm
3.2 mm
1 mm
17.39 mm U U’ X X’ V V’
Trigger

4. SEGMENT CONCEPT
PLANE
(U, V, X) : Two layers of parallel fibers offset by 1/3 fiber width
SEGMENT : Coincidence of fibers hits in the two layes of each PLANE
fibers
= 63 possible
SEGMENT values
with 0.27 mm
resolution
Bottom
view
of the
detector
Segment Numbers

5. HIT RESOLUTION IN Y The hit resolution is given by the difference
y_ux - y_vu, where:
y_ux is the y value constructed by the intersection of segments u and x, and
y_vu is the y value constructed by the intersection of segments u and v.
u segment y
v segment
Exaggerated: just to give the idea.
x segment

6. SPATIAL RESOLUTION P2D = 155 m P1D = 136 m
The value of the resolution was obtained dividing the standard deviation of the distribution y_ux - y_uv by 2. For both detectors we found:
P1D = 136 m
P2D = 155 m

7. ACCEPTANCE
The geometrical acceptances were calculated by an event generator at the operational pot positions
The program generates tracks at the IP and propagates them through the Tevatron lattice until they reach the pots P1D and P2D in their operational positions.
Dead channels are taking into account
Note that the probability of receive any particle with
|t| 1.7 GeV2 is negligible. We will restrict to the region |t| < 1.7 GeV2.

8. Note the diffractive contamination due to particles with
RESULTS
The sample analysed consisted of 31 runs taken at:
P1D = mm (8.98 ) and P2D = mm (8.70 )
The  distribution after the reconstruction of events found in all runs considered are:
Note the diffractive contamination due to particles with
|t| This effect obligated us to introduce new cuts to certify that we have only elastic events

9. STUDYING THE HIT CORRELATION
Comparing the distribution of x1-x2 and y1-y2 with the event simulation we find:
The y1-y2 distribution shows a huge contamination of high t particles that we have to clean up
The x1-x2 correlation shows a lot of events off the axis

10. BACKGROUND CUTS
To cut the diffractive particles we based on the MC distributions. We will analyse only the particles that hits the areas enclosed by the lines:

11. FINAL SAMPLE
The final events considered are the ones that survived all the 6 cuts:
Multiplicity 1: One or zero hits in each of 12 planes (6 x detector)
Multiplicity 2: One segment per plane
Segment cut: must exist 3 reconstructed segments per detector, ie: all 6 segments must be nonzero
Fiducial cut: The distance yux-yuv between intersections of segments should not exceed in  2 of the gaussian distribution
Background cuts: events too far from the MC simulations are not considered
Acceptance cut: only the events that reaches the region allowed by simulation were considered

12. The table shows the efficiency of each cut:
EFFICIENCY OF THE CUTS
The table shows the efficiency of each cut:
100 -
1.3
17724
Acceptance
1.4
18569
Noise
1.6
21287
Fiducial
2.0
26428
Segments
2.2
29285
Multiplicity 2
5.9
78095
Multiplicity 1
% of total
# of evts that survived the cuts
Cut
Note that most of the events registered were cleaned by the multiplicity cuts, this can indicate that spray of particles reached the detectors.

13. The events that survived all the six cuts have the  distribution:
FINAL RESULTS
The events that survived all the six cuts have the  distribution: 
Events are peaked at zero as expected with a resolution of  = 0.019

14. |t| DISTRIBUTION
The events that survived all the six cuts presents the |t| distribution:
Events without
any cut
There’s an extra peak around |t|~1.4 GeV2 that is not expected and that we will try to subtract

15. HALO BACKGROUND SUBTRACTION
The events that survived to all cuts still have a contamination due to halo and diffractive particles
The halo events were simulated by the BD. It takes into account beam gas scattering and were simulated with the four pots at operational positions.
The simulation gave the position and the angle at P1D
The process consisted in propagate the particles until P2D, then convert the positions into fibers to reconstruct as usual data

16. # of evts that survived the cuts
NORMALIZATION USED
The normalization concept used to scale the halo distribution is based in the background cuts
Same amount of halo
inside and outside
Cut
# of evts that survived the cuts
% of total -
100
Mult 1
78095
5.9
Mult 2
29285
2.2
Segments
26428
2.0
Fiducial
21287
1.6
Noise
18569
1.4
Acceptance
17724
1.3

17. After dividing by acceptance and scale at 13% we have:
It cannot reproduce the data at high values of |t|, where we suppose it’s mainly halo
There’s no peak at |t|~1.4 GeV2 that we can subtract in the bckg file

18. FITTING RANGE The |t| distribution found after subtracting the halo
Spectra is:
It was decided to fit between bins 4 ± 1 to bin 12 ± 1
and take the average

19. UNSMEARING
The dN/dt spectra obtained with the events that survived all cuts and that were subtracted must be corrected by the factor that takes into account the resolution of the detector: fres = f(t)ideal/f(t)measured
To obtain this factor a exponential function were used as ansatz, that was convolute with a linear function that describes the variation of the resolution in |t|

20. FIT RESULTS Bin range -bdata -bbckg -bsubt -bunsm -bnorm -bpeak 3:11
3.10
1.90
3.21
3.20
3.38
3.51
3:12
3.23
1.88
3.36
3.35
3.55
3.52
3:13
1.83
3.34
3.56
4:11
3.27
2.02
3.40
3.39
3.58
3.70
4:12
1.98
3.54
3.75
3.68
4:13
1.89
3.50
3.49
3.72
3.71
5:11
3.53
2.47
3.66
3.64
3.81
3.74
5:12
3.63
2.32
3.79
3.78
3.99
5:13
2.15
3.92
Average
2.04
3.45
3.47

21. Both set of runs presents flat distribution after |t|~1.3 GeV2
DIFFERENT RUNS
Is not an statistical effect because all the other runs that shows the peak have less events
Both set of runs presents flat distribution after |t|~1.3 GeV2
Runs
Runs
2376 evts
3709 evts

22. Systematic errors due to the vertical position of the detectors
The error in the vertical position y were determined changing the position of the pots in +0.5 mm in the calculation of the acceptance. The dN/dt spectra measured then were divided by this value of the acceptance, obtaining the error + .
The value obtained using the acceptance in –0.5 mm is the same
The error in the vertical position were calculated through
a = (|A+|+|A-|)/2
Then this value was added in squared with the statistical error to obtain the
systematic error in the vertical position:
y = (2est + 2a )1/2

23. Systematic errors due to the halo background subtraction
The errors due to the halo subtration were obtained through the subtraction of the slopes found before and after the subtraction: ssubt = bdata - bsubt
Systematic errors due to the diffractive contamination
The uncertainties introduced by the remanent diffractive events in the final sample were estimated to contribute in the amount that the halo background: ssubt = sdiff
Systematic errors due to the unsmearing process
The errors due to the halo subtration were obtained through the subtraction of the slopes found before and after the unsmearing: suns = buns - bsubt

24. Final error in the slope b
The final error in the slope b is calculated through:
Where each term contributes to the final error in:
Uncertainty
Contribution (%)
y
88.1
halo
5.8
diff
uns
0.3
Finally the slope found is:

25. COMPARISON WITH OTHER EXPERIMENTS
The points corrected by the unsmearing procedure were normalized by the points obtained by the E710 experiment (which agrees with CDF for dN/dt in the determination of the slope b at low |t|).
The results are
in excellent agreement with the model of M. Block showed in the figure
Still need to understand why
the error bars are so little  In progress

26. CONCLUSIONS
1) Proton antiproton elastic scattering was measured by the D0 Roman Pots.
2) Elastic data samples contain diffractive and halo backgrounds, most of which were removed by simple cuts.
3) The halo remaining after the cuts were subtracted using a MC simulation normalized according to the background cuts assumption
4) The four momentum transfer range considered in the analysis were limited to the region
0.87 < |t| < 1.34 GeV2
5) The final result for the slope were obtained taking the average of different fit ranges around the limit imposed by the acceptance uncertainty at low |t| and the abnormal behavior of the accelerator at high |t|

27. 6) The first measurement of the dN/dt slope in the region analysed, at c.m.s. energy of s = 1.96 TeV gave the result:
b =  GeV-2
7) The error in the measurement are mostly dominated by the uncertainty in the determination of the vertical position of the detectors
8) The result of the slope found is in good agreement with the phenomenological model of M. Bloch based in measurements made by experiments E710 and CDF at
s = 1.8 TeV.