Results of dN/dt Elastic Scattering Jorge Molina

ELASTIC TRIGGER GIVEN BY FPD LAYOUT D S Q 4 3 2 A 1 P p z (m) 59 57 33 23 0 23 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)

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

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 16 + 16 fibers = 63 possible SEGMENT values with 0.27 mm resolution Bottom view of the detector Segment Numbers 1 2 3 4 ...

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

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

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.

Note the diffractive contamination due to particles with RESULTS The sample analysed consisted of 31 runs taken at: P1D = 17.05 mm (8.98 ) and P2D = 13.80 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| 0.04. This effect obligated us to introduce new cuts to certify that we have only elastic events

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

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:

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

The table shows the efficiency of each cut: EFFICIENCY OF THE CUTS The table shows the efficiency of each cut: 100 1308734 - 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.

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

|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

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

# 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 - 1308734 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

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

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

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|

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

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 138-141 Runs 176-180 2376 evts 3709 evts

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

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

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:

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

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|

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 = -3.47  0.37 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.