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TOTEM Prospects for Total Cross-Section and
Luminosity Measurements
M. Deile (CERN) for the TOTEM Collaboration 13.01.
2011
ultimate goal 1 (2011 3)
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Luminosity-Independent Method based on the
Optical Theorem

• measure the inelastic event rate Ninel (with
  forward tracking chambers)
• measure the elastic event rate Nel (detect
  surviving protons with Roman Pots)
• and extrapolate the cross-section dNel/dt to t
  0
• take r Re f(0) / Im f(0) f(0) forward
  elastic amplitude
• from theory, e.g. COMPETE extrapolation
• 
  
• later try to measure r at b 1 km elastic
  scattering in the Coulomb-nuclear interference
  region
• Requirements for this method
• Beam optics providing proton acceptance at low
  t in the Roman Pots
• Detector coverage at high h
• Trigger capability for all detector systems

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The TOTEM Detector Setup
installation in progress
operational in 2010
now installed
operational in 2010
3.1 ? h ? 4.7
5.3 ? h ? 6.5
T1
T2
T1 - arm during installation
p. 3
4
Acceptance for Inelastic Events

• Uncertainties in inelastic cross sections large
• non-diffractive min. bias (MB) 40 ?
  60 mb
• single diffraction (SD) 10 ? 15 mb
• double diffraction (DD) 4 ? 11 mb

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4
PHOJET ?s 7 TeV
3
2
T2
T2
T1
T1
1
h
Accepted event fractions
p. 4
5
Measurement of the Inelastic Rate Ninel
Trigger Losses at ?s 7 TeV, requiring 3 tracks
pointing to the IP
s T1/T2 trigger and selection loss
Minimum bias 50 mb 0.05 mb
Single diffractive 12.5 mb 4.83 mb
Double diffractive 7.5 mb 1.21 mb
Total 70 mb 6.1 mb
M

• Correction for trigger losses
• Extrapolation of the mass spectrum
• fit dN/dM2 1/Mn with n 2
• uncertainty depends on the purity of the
  diffractive
• event sample used for the extrapolation
• (e.g. errors from minimum bias events
  misidentified
• as diffractive events)
• Independent handle on low-mass diffraction
• At b 90 m the protons for all diffractive
  masses
• are visible (for t gt 10-2 GeV2).
• ? total uncertainty on Ninel 1.0 mb (1.4 ).

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Roman Pot System Leading Proton Detection
scattering angle q
Horizontal Pot
Vertical Pot BPM
p. 6
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Elastic Scattering
exponential region
Elastic Scattering Acceptance at ?s 7 TeV
7 TeV
RP220 detectors at 10 s from beam centre
b 3.5m
b 1540m
b 90m
t50 0.024 GeV2
(eN 3.75 mm)
squared 4-momentum transfer t ? - p2 q2
t50 0.0008 GeV2
(eN 1 mm)
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Preliminary t-distribution
? 84K elastic scattering candidate events TOTEM
special run ( 9 nb-1)
?s 7 TeV ? 3.5 m RPs _at_ 7 ? (V) and 16 ? (H)

• Raw distribution
• - No smearing corrections
• - No acceptance corrections
• - No background subtraction
• Syst. error sources under study
• alignment, beam position and
• divergence, background,
• optical functions, efficiency,

0.7 GeV2
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Elastic Scattering at low t
Exponential Slope B(t)
Cross-section
7 TeV
b 1540 m
b 90 m
fit interval
with detectors at 10 s b 1540 m t50
0.0008 GeV2 b 90 m t50 0.024 GeV2
best parameterisation B(t) B0 B1 t B2 t2
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Extrapolation to the Optical Point (t 0) at b
90 m
Study at 14 TeV, eN 3.75 mm rad
(extrapol. - model) / model in d?/dt t0
Statistical extrapolation uncertainty
14 TeV
14 TeV
? L dt 2 nb-1
upper bound 0.25 GeV2

• Common bias due to beam divergence (angular
  spread flattens dN/dt distribution) -2
  _at_14 TeV ? -3 _at_7 TeV, can be corrected.
• Spread between most of the models 1
  (Islam model needs different treatment, can be
  distinguished at larger t)
• Systematic error due to uncertainty of optical
  functions 1.5 , assuming dL/L 1
• Different parameterisations for extrapolation
  (e.g. const. B, linear continuation of B(t))
  negligible impact

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Acceptance versus Energy and Detector Approach

• Advantage of 7 or 8 TeV w.r.t. 14 TeV t50
  reduced ? shorter extrapolation
• reduced model dependence
• reduced statistical uncertainty

(eN 3.75 mm rad)
lower E
x 0.6
closer approach
x 0.4
(eN 1 mm rad)
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Desired Scenario for Runs at b 90 m
(subject to discussions with MPP and collimation
experts and to commissioning progress / surprises)
4 special runs (assuming E 4 TeV)
en mm rad RP distance(window) bunching L cm-2 s-1 m (inelastic pileup) t50 GeV2 statistics per 8 h statistical uncertainty of extrapol.
3 8 s 1b, 7 x 1010 p/b 6.9 x 1027 0.05 0.019 0.2 nb-1 1.5
3 6 s 1b, 7 x 1010 p/b 6.9 x 1027 0.05 0.011 0.2 nb-1 1
1 8 s 1b, 6 x 1010 p/b 1.5 x 1028 0.1 0.0070 0.4 nb-1 lt 1
1 6 s 1b, 6 x 1010 p/b 1.5 x 1028 0.1 0.0043 0.4 nb-1 lt 1
Dominated by systematics ? small RP distance much
more important than luminosity ! Crucial good
knowledge of the optical functions Aim
contribution from optical functions not larger
than angle resolution limit from beam
divergence dLy / Ly lt 1.1 or dby / by lt
1.1 dLx / Lx lt 0.2 or dbx / bx lt 0.2
(but our error estimates are based on 1
sufficient)
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Combined Uncertainty in ?tot

• At b 90 m, ?s 7 TeV
• Extrapolation of elastic cross-section to t 0
  2
• Total elastic rate (strongly correlated with
  extrapolation) 1
• Total inelastic rate
  
  1.4
• Error contribution from (1r2) using full
  COMPETE error band dr/r 33 (very
  pessimistic) 1.2
• ? Total uncertainty in stot including
  correlations in the error propagation 3
• Slightly worse in L ( total rate
  squared!) 4

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Outlook Extrapolation with the Ultimate Optics
(b 1540 m)
t50 0.0008 GeV2 for RP window at 10 s ? good
lever arm for choosing a suitable fitting
function for the extrapolation to t
0. Complication Coulomb-nuclear interference
must be included
14 TeV !!!
7 TeV
b 1540m
where
and b(t) is a function of fC(t) and fH(t).
For most models extrapolation within 0.2
. Islam model needs different treatment can be
distinguished in the visible t-range.
Difficulties - very-high-b optics at 7 or 8 TeV
still to be developed (b1540m exists only for
14 TeV). - additional magnet powering cables
needed.
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Outlook Measurement of r in the Coulomb-nuclear
Interference Region?
Aim get also the last ingredient to stot from
measurement rather than theory.
(eN 3.75 mm rad)
(eN 1 mm rad)

• might be possible at 8 TeV with RPs at 8 s
• incentive to develop very-high-b optics before
  reaching 14 TeV !E.g. try to use the same optics
  principle as for 90m and unsqueeze further.

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Summary
TOTEM is ready for a first stot and luminosity
measurement in 2011 with b 90m using the
Optical Theorem. Expected precision 3 in stot
, 4 in L Wish start soon with the development
of the b 90m optics to have enough time for
learning. Desired running conditions low beam
intensity, small RP distance to the beam Longer
term Measurement at the 1 level with
very-high-b optics (1 km) might give access to
the r parameter if the energy is still low (?s
8 TeV) needs optics development work.
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Backup
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Elastic Scattering ? ? f(0) / ? f(0)
COMPETE
PRL 89 201801 (2002)
Preferred fit predicts
E710/E811 r 0.135 0.044
asymptotic behaviour ? 1 / ln s for s ? ?
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Elastic Scattering from ISR to LHC
Coulomb - nuclear interference ? r
Pomeron exchange ? e B t
ds / dt mb / GeV2
B(s) Bo 2aP ln(s/so) ? 20 GeV-2 at LHC
diffractive structure
E710/811, CDF
pQCD ? 1/ t8
UA4, CDF
UA4
pp 14 TeV BSW model
Block model
0
1
2
-t GeV2
-t GeV2
546 GeV CDF 0.025 lt t lt 0.08 GeV2 B 15.28
0.58 GeV-2 (agreement with UA4(/2)) 1.8 TeV
CDF 0.04 lt t lt 0.29 GeV2 B 16.98 0.25
GeV-2 E710 0.034 lt t lt 0.65
GeV2 B 16.3 0.3 GeV-2
0.001 lt t lt 0.14 GeV2 B 16.99 0.25
GeV-2 , r 0.140 0.069 E811
0.002 lt t lt 0.035 GeV2 using ?B? from CDF,
E710 r 0.132 0.056 1.96 TeV D0 0.9 lt
t lt 1.35 GeV2
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Relative Luminosity Measurement

• For running conditions where measurement via
  Optical Theorem impossiblerelative measurement
  after a prior absolute calibration at b 90 m
  or 1540 m.
• Examples
• partial inelastic rates, e.g. (T2 left) x (T2
  right) robust against beam-gas background
• for running conditions with pileup count
  zero-events, e.g. failing (T2 left) x (T2 right)
• 
  e.g. P(n0) 15 _at_ L1033 cm-2s-1 ,
  2808 bunches Also usable for continuous
  luminosity monitoring (to be studied further).

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Measurements of stot
Conflicting Tevatron measurements at 1.8
TeV E710 stot 72.8 3.1 mb E811 stot
71.42 2.41 mb CDF stot 80.03 2.24
mb Disagreement E811CDF 2.6 s
Best combined fit by COMPETE But models vary
within (at least)
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TOTEM Detector Configuration
T1 3.1 lt h lt 4.7 T2 5.3 lt h lt 6.5
CMS
HF
T1
10.5 m
T2
14 m
(RP2)
RP1
RP3
147 m
(180 m)
220 m
Symmetric experiment all detectors on both sides!
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Level-1 Trigger Schemes
Always try to use 2-arm coincidence to suppress
background.
Elastic Trigger s ? 30 mb Single Diffractive
Trigger s ? 14 mb Double Diffractive
Trigger s ? 7 mb Central Diffractive
Trigger (Double Pomeron Exchange DPE) s ? 1
mb Non-diffractive Inelastic Trigger s ? 58
mb stot ? 110 mb
p
p
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Acceptance Losses and Selection Losses
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Detection of Leading Protons
Transport equations
TOTEM Proton Acceptance in (t, x) (contour
lines at A 10 ) RP220
(x, y) vertex position (?x, ?y) emission
angle x ?p/p
x resolved
Example Hit distribution _at_ TOTEM RP220
with b 90m
t -p2 ? 2
Optics properties at RP220
b 1540 m L 1028 2 x 1029 95 of all p seen all x
b 90 m L 1029 3 x 1030 65 of all p seen all x
b 0.5 2 m L 1030 1034 p with x gt 0.02 seen all t