A Novel Method for Measuring Absolute Luminosity at the LHC

1
A Novel Method for Measuring Absolute Luminosity
at the LHC

• Introdumotivation
• What is luminosity ?
• Why we need to know the absolute luminosity
• Reminder of the methods on the market, like
• Optical Theorem
• Reference reaction
• Van der Meer scan
• The proposed method
• Principle
• Application to LHC (LHCb ?)
• Systematics, limitations
• Summary and outlook

2
What is Luminosity ?
Luminosity Reaction Rate / Cross Section
L R / ?

• Luminosity for a colliding bunch pair (beam 1 and
  2, single pass)
• L N1 N2 OverlapIntegral
• In simple case of 2 Gaussian bunches (no crossing
  angle, identical bunch profiles, no offsets)
• L N1 N2 / 4? ?x ?y

Depends on the two bunch profiles, crossing
angle, bunch offsets in x, y, t
Total bunch populations get from beam current
measurements
3
Why we need to know the absolute luminosity

• Most studies of systematics can be done with
  knowledge of the relative luminosity
• Reconstruction and trigger efficiencies, wrong
  tag rates, spillover, etc. , which can (and
  probably will in some cases) depend on luminosity
• Stability of detector components
• Stability of colliding beam conditions
• etc.

• Absolute luminosity brings
• Physics cross sections (absolute)
• Test models of heavy flavour production (tt, bb,
  cc)
• Control SM backgrounds, needed to pull out
  interesting physics (Higgs, New)
• Constrain Parton Distribution Functions from EW
  processes
• Test calculations of total pp cross section,
  comparison to cosmic rays
• Etc.
• Measure of accelerator performance

Taken from Busato in Hadron Collider Physics 2005
4
Methods used to get Absolute Cross-sections

• Beamophobic L is measured indirectly
• Using Optical Theorem
• Using a calculated theoretically clean
  cross-section
• Using a reference (previously measured)
  cross-section

• Philobeamic try to measure L directly
  from beam properties
• Van der Meer method
• Wire method
• Synchrotron light

5
Optical Theorem
Beamophobic

• Total cross section

• Fwd scatter. amplitude

• Optical theorem

Define

• In terms of rates

6
Using the Optical Theorem
Beamophobic
Measure elastic scattering in bins of 4-momentum
transfer, to as small as possible scattering
angle (then, extrapolate to 0)

• Total cross section

Measure total (i.e. elastic and inelastic)
scattering rates
Estimate/measure ? parameter (small at LHC ? ?
0.1 0.2)
See e.g. Bozzo et al (UA4), PL B147 (1984) 392,
Amos et al (E710), PRL 68 (1992) 2433, Abe et al
(CDF), PRD 50 (1994) 5550, Avila et al (E811), PL
B445 (1999) 419.

• This method also gives the luminosity

7
Optical Theorem Method at the LHC
Beamophobic
See TOTEM/CMS, and fwd ATLAS

• Attempt to measure elastic scattering at a few
  µrad scattering angle !
• Requires as small as possible angular spread in
  the beam,
• ??2 ? / ? ? run at large ?
• Parallel-to-point focusing, i.e. scattering
  angle related to displacement at the detector
  plane, independent of beam offsets
• Special optics, no crossing angle, i.e. increased
  bunch spacing

RP Roman Pots
m
8
Using theoretically clean reactions
Beamophobic

• ee- accelerators (LEP, B-factories, ) use
  Bhabha scattering

• See e.g. Budnev, Ginzburg, Meledin Serbo, NP
  B63 (1973) 519
• The analysis of the process pp?ppee- at high
  energies is carried out. It is shown that pure
  QED only is sufficient for the calculation of the
  main contribution to the cross section of this
  process with high accuracy.
• and Courau, PL B151 (1985) 469 (pp?pp l l-).

• See e.g. Dittmar, Pauss Zürcher, PRD 56 (1997)
  7284
• Measure the x distributions of sea and valence
  quarks and the corresponding luminosities to
  within 1 using the l pseudorapidity
  distributions from the decay of weak bosons.

Stolen from K. Ellis, HCP2005

• Extremely fwd pp elastic scattering cross-section

More precise formlua in e.g. Buttimore et al, PRD
35 (1987) 407
very small t
9
Using a calibrated reaction
Beamophobic

• Reaction with previously measured cross-section
  is available in the detector acceptance ? use
  it as a normalisation !
• L R ref / ?ref ? ? R / L ?ref R / R
  ref
• Many, many examples
• electron scattering use previously measured
  electron-nucleus elastic scattering cross-section
  for normalising cross-sections of inelastic
  channels (both measured simultaneously)
• Tevatron use ?inelastic previously measured by
  OptTheorem method

• At LHC there is no calibrated reaction at 14
  TeV, or

• not yet !
• Once someone has determined a given cross-section
  at the LHC, then others will use it.

10
Try to Study the Beams and Measure Luminosity
Philobeamic

• Reminder of general formula for two
  counter-rotating bunches
• All particles in bunch move with velocity
  in the lab frame
• position and time dependent density functions
  normalized to 1
• the bunch populations
• revolution frequency
• Velocity term taken out of integral if negligible
  angular spread

See e.g. in Napoly, Particle Acc., 40 (1993) 181.
(bunch) currents
crossing angle
beam overlap integral
11
Van der Meers Trick
Philobeamic
See S. Van der Meer, ISR-PO/68-31, June 18th, 1968
x
?

• Coasting beams with crossing angle ? and beam
  currents

z
y

• Luminosity (rate) insensitive to offsets in x and
  z, but sensitive to offsets in y

yo
x
12
Length Calibration in Van der Meers Method
Philobeamic

• In practice, is varied by some control
  parameter

• Need to calibrate/know the function
  over the whole scanned region of the control
  parameter
• In the simplest case, one has a linear relation
  (like at ISR)
• just need to measure the proportionality
  constant
• At ISR determined the absolute offset distance
  by cross-calibration with a precision beam scraper

See Bryant, Potter, CERN-ISR-BOM/82-15 (1982)
13
Van der Meer Method at the LHC ?
Philobeamic

• Yes, why not but we know it will be
  substantially more challenging than at the ISR.
• Bunched beams
• Need a 2D scan
• Bunch charges obtained from (fast) AC and (slow)
  DC current monitors
• Strong beam-beam effects
• Strength of long-range and number of head-on
  collisions varies bunch by bunch
• Each bunch pair may have its own overlap integral
  (own bunch offsets,
  shapes, etc.), while scan is done at once for
  whole beam
• Do the bunches change when they are offset ?
• Calibration of absolute offset distance how ?
• S. vd Meer A reasonable amount of background
  due to beam-gas interactions does not affect the
  measurement
• Well, yes, it does (in a positive way) use
  vertex detection of beam-gas events to determine
  beam offsets, bunch shapes and crossing angles
  per bunch ! Should greatly
  help the Van der Meer method at LHC.

Note tried at RHIC, see Drees, Xu, Fox in 2003
Part. Acc. Conf.
Head-on
See W. Herr, Proc. of CAS 2003 and many LHC
project notes
Long-range
Try it at large ? and large bunch spacing
14
Vertex Reconstruction of Beam-Gas Interactions
Philobeamic

• Again formula for two counter-rotating bunches
• Set and crossing
  angle
• Proposed method
• Inject a tiny bit of gas (if needed at all!) into
  the vertex detector region
• Reconstruct bunch-gas interaction vertices
• ? get beam angles, profiles relative positions
• ? overlap integral
• Simultaneously reconstruct bunch-bunch
  interaction vertices
• ? calibrate reference cross-section

Measured by the experiments
Measured by AB group (Accelerator and Beams dept.)
15
Remarks and Requirements
Philobeamic

• Remarks
• Vertex reconstruction of beam-gas events is
  sufficient to determine the overlap integral and
  (with use of bunch charges) the luminosity
• Simultaneous reconstruction of bunch-bunch
  interactions is needed for later, i.e. for
  continuous determination of the absolute
  luminosity
• The reference reaction does not need to be
  anything calculable by theory. Choose fiducial
  cuts such that rate is large and the detector
  response is as stable and reliable as possible
  (minimize systematic and statistical
  uncertainties)
• Requirements
• constant gas density in x and y (or well known
  profile)
• primary vertex resolution substantially smaller
  than bunch transverse dimensions
• Ability to distinguish beam1-gas, beam2-gas and
  beam1-beam2 events
• LHC where can it be done ?

16
Four Fantastic Vertex Detectors at LHC
CMS
Alice
LHCb
17
Which is the Luckiest ?
beam2
beam1
?
IP8 at LHC

• All four LHC vertex detectors are comparable in
  precision (for what concerns todays subject)
• LHCb VELO has a better acceptance for beam-gas
  (fwd vs onion)
• LHCb has no very forward appendage, contrary to
  CMS and ATLAS
• LHCb cant measure momentum for beam2-gas events

18
Scenario
Interactions
IP32
Beam2-gas Beam1-gas Beam1-beam2
VD
RP
Beam 2
Beam 1
RP
Gas
Expt

• Run Roman Pots and gas at Vtx Detector LRP ?
  LVD , get ?ref for 14TeV
• If not acceptable for RP, then do it in two
  steps
• measure LRP and a reference reaction at Expt,
• then measure LVD and same ref reaction
• In any case, ?ref can be compared/transferred
  from an IP to an other, provided one agrees on
  some fiducial cuts for the selected reference
  reaction.

Compare ?ref,RP ? ?ref,VD
19
Generated Pythia Events

• To get a feeling, generated single-interaction
  events with PYTHIA
• Beam-gas (s1/2 115 GeV, fixed p target,
  flat over -1.2 1.2 m)
• Beam-beam (s1/2 14 TeV, luminous ?z 53 mm)

beam1-beam2
Beam2-gas
Beam1-gas
Number of charged particles
Transverse momentum of charged particles
Pseudo-rapidity of charged particles
20
Simulated Pseudo Atlas/CMS Vtx Detector Acceptance
r / mm
outer inner
z / mm

• Pseudo ATLAS/CMS (pessimistic approach, very,
  very coarse)
• Two concentric cylinders around pixels outer
  and inner
• zouter 600 mm, router 100 mm
• zinner 270 mm, rinner 45 mm
• Particle seen if intersects two cylinders within
  range zintersect lt zouter and
  zintersect lt zinner

21
Simulated simple LHCb VELO geometry

• Simplified geometry
• Phi-R merged in one disc, no left-right
  staggering
• 42 mm outer radius with 8 mm inner beam clearance
• track is reconstructed if at least 4 R-Phi planes
  traversed

p
Si microstrip Phi-measuring R-measuring
p
22
Charged Particle Tracks for Pseudo Atlas/CMS and
VELO
10000 beam2-gas inelastic interactions
6648

• Primary vertex resolution depends on number of
  tracks per vertex
• Clearly, visibility of beam-gas vertices is much
  better for LHCb
• What is the real coverage of CMS, ATLAS, ALICE
  vtx detectors ?

23
Primary Vertex Resolution

• Nominal beam sizes at Point 8
• ?x ? ?y ? 109 um (? 24 m, N1011)
• Primary vertex resolution for LHCb events
• ?pv,x ? ?pv,y ? 10 um
• ?pv,z ? 50 um
• Beam-gas will give less tracks per vertex
• pT distributions quite similar
• PV resolution could be some factor 3-4 worse for
  beam-gas events than for LHCb events
• To reduce systematics associated with folding of
  PV resolution and bunch sizes, it would be
  advantageous to have PV resolution ltlt bunch sizes

24
Rate Estimates (just a numerical example)
Density and length of target gas

• Bunch-gas rate

inelastic
Detector acceptance
25
Acceptance versus Primary Vertex Position zpv

• Simple LHCb VELO example
• F inelastic event fraction with at least 6
  reconstructable tracks
• Reconstructable 4 or more VELO stations
  traversed

Beam1-beam2
F
Beam1-gas
Beam2-gas
26
Distinguishing beam-beam, beam1-gas beam2-gas

• From here on, consider only interactions that
  give at least 6 VELO reconstructable tracks
• Most obvious cut to distinguish b1-b2, b1-gas,
  b2-gas events for a given bunch pair cut on zpv

• Example zpv selection
• b1-gas
• b2-gas
• gt Contamination lt 0.1
• b1-b2
• gt Contamination lt 3.5
• But what if the tails are not gaussian ?
• Next slides, look for other cuts
• Number of tracks/vertex
• Highest pT in event
• Average pseudorapidity
• There are surely more cuts to be used

Beam2-gas
Beam1-gas
Beam1-beam2
Zpv / mm
27
Ntracks distributions

• Ntracks number of reconstructed tracks per
  interaction
• beam2-gas
• --- beam1-gas
• ___ beam1-beam2

28
Distributions of Highest PT from Vertex

• b2-gas
• --- b1-gas
• ___ b1-b2
• LHCb pT only available downstream only useful
  for distinguishing beam1-gas and beam1-beam2

29
Eta-average distributions

• ?avge average pseudo-rapidity of reconstructed
  tracks from vtx
• b2-gas
• --- b1-gas
• ___ b1-b2

30
Note on these Distributions and Possible
Contaminations

• Any contamination of a sample by another sample
  (e.g. beam1-beam2 events leaking into beam2-gas
  event sample) can be precisely measured,
  quantified and corrected for (if needed at all)
  without using any MC simulation.
• Simply use
• beam1 only crossings to get pure beam1-gas
  samples
• beam2 only crossings to get pure beam2-gas
  samples
• no gas runs to get pure beam1-beam2 sample

31
Possible Sources of Systematics

• The proposed absolute luminosity measurement will
  be dominated by systematics, not statistics
• Bunch charges accuracy lt 1 (!?)
• Beam overlap
• Crossing angle effects
• Varying beta-function as function of z
• Transverse (in)homogeneity of gas density
• ???

32
Crossing Angle Phi

• To determine the bunch overlap integral from the
  indvidual bunch profiles, one needs to know the
  crossing angle

? 25 m 10 m 2 m

• Determine angle from beam-gas interactions (with
  some accuracy)
• Adjust angle and ? accordingly for ? gt 10 m
  the dependence on ? is already very small

33
Longitudinal and Transverse Offsets

• In general, a crossing angle will mix transverse
  offsets and longitudinal offsets.
• Simple familiar case of Gaussian bunches
• Longitudinal offsets are not accessible with
  beam-gas vertex reconstruction (transverse
  offsets are)
• ? simpler and better to run at zero crossing
  angle

• It starts depending on the longitudinal dimension
  !
• profile
• phase offsets

34
Varying Beta Function Along z  Hourglass
Effect 

• We need to place cuts on z for selecting beam-gas
  or beam-beam
• need to correct for varying beam size along z
• to keep correction small, run at large ?
• Note we can also determine ?(z) from beam-gas
  data
• Can be used to check machine parameters /
  assumptions

35
Ghost bunches

• SPS RF 200 MHz, i.e. a bucket every 5 ns
• LHC RF 400 MHz , i.e. a bucket every 2.5 ns
• Beams could exhibit undesired satellite bunches
• Expect to be mostly in neighbour buckets

• They contribute to the total DC current
• Are they measurable by the fast AC current
  monitors ?
• Bunch charge normalisation problem
• A challenge for AB group !!
• LHC Design Report, vol 1, sec. 13.2.1 Fast Beam
  Transformers precision lt 1 (5) for nominal
  (pilot) bunch charges

• In fact, expect that NNLO gt NLO (like in other
  fields)
• But we think its all under control ! (like in
  other fields)

• Experiments can observe nearby satellites
• Extra luminous bumps at IP /- n x 37.5 cm ?
• If observed, at least they arent ghost any more

36
Longitudinal Density Monitor
Taken from De Santis, LARP meeting, 17sep2003
Bunch (270 ps)
37
Density Profile in Transverse Directions

• Dont need to know the gas density itself !
• Dont care about z-dependence of density profile
  !
• However, essential assumption gas density is
  homogeneous in x and y
• Are there effects that can spoil this assumption ?

• Ex probability that an atom gets ionized and
  kicked off by a bunch when the atoms trajectory
  crosses the beam region is of order
• where tbb is the time between 2 subsequent
  bunches.
• Using
• and the ultimate LHC conditions
• one would get something close to 3 probability.
• But use large ? , larger tbb and smaller N for
  the proposed luminosity measurement.
• Hence, expect no hole-burning in transverse
  gas density for the suggested running conditions.

v
4?
beam
38
Practical Implementation Aspects (LHCb)

• Most warm LHC elements are coated with
  Non-Evaporable Getter materials,
• NEG pumps gases like N2, O2, CO2, H2,
• Hence, the proposal to use a noble gas
• Like Xe
• Ne could probably do the job as well one simply
  obtains a bit less cross-section

• LHCbs VD (VELO) already has a complex vacuum
  system
• Includes sophisticated venting procedures with
  ultrapure neon while keeping pressure difference
  between beam and Si detector vacuum below 5 mbar
• Could easily accomodate a dedicated gas injection
  option for luminosity measurement

• For 10-7 mbar Xe ? inject
• Time constant ?

39
LHC Beam Lifetime with Gas
density

• Beam life time due to residual gas ?-1
• For the numerical example given earlier, and
  assuming the gas density extends over few
  meters, one gets ? ? 3 years compared to the
  expected 100 hours for nominal LHC.
• If needed and if properly done, the gas density
  could be increased by orders of magnitude.

40
Summary and Outlook

• Vertex detectors open a new way to determine the
  beam overlap integral
• Combined with a measurement of the bunch charges,
  this would allow a direct measurement of the
  absolute luminosity ? absolute cross-sections
  !!
• Method requires only a simple (properly designed)
  gas-injection system
• Measure for a given bunch pair both beam-gas and
  beam-beam collisions
• the former to get the bunch profiles, the latter
  to normalize the chosen reference reaction
  (e.g. the visible cross-section
  with some fiducial cuts)
• Accuracy limited by systematics
• how much ? Hard to say now, but I have good hopes
  !!
• need accurate bunch charge measurements !!
• choose proper running conditions
• Relatively large ? (perhaps 30 m), depending
  f.i. on primvtx resolution
• Increased space between bunches and zero crossing
  angle
• Clearly, all beam parameters are controllable
  (?, offsets, crossing angle, bunch spacing,
  bunch charge, etc.) and could (should!) be varied
  to study systematics
• Dedicated LHC running time how long ?
• Depends on how much systematic studies one wants
  to carry out
• Guestimate 1 or 2 days

41
Summary Outlook (continued)

• Advantage over conventional methods do not touch
  the beams during the measurement !
  (unlike vdMeer or wire scanners)
• Note beamgas vertexing can be used as a helper
  tool for Van der Meer scan method (provide beam
  crossing angle, absolute scale of offset, )
• Optical Theorem method is quite challenging
  (measure scattered protons at few µrad scatter
  angle!!) ? cross-check luminosity result !
• Note that OT method requires also large ? and
  increased bunch spacing
• To be studied can it cope with simultaneous
  beam-gas collisions ?
• The proposed method is documented in Preprint on
  CDS CERN-PH-EP/2005-023
• (and NIM A to come very soon)
• Tevatron CDF (and D0 ?) could probably also use
  this method.
• Resolve the total cross section discrepancy at
  1.9 TeV.
• Remember that the inelastic cross-section is
  used for luminosity determination most (all?) of
  their published cross sections
• maybe they already have the required data on
  tape ?

Veni...
VD ...
Lumi !
42
Why cant one just use the shape of the luminous
region ?

• Take as a reasonable starting point two Gaussian
  bunches, no crossing angle and perfectly head-on

VELO

• Assume also bunches are identically shaped
  ?x,1 ?x,2
• Then, compare with a shift in (which
  will reduce luminosity!)

Same shape (?x) and  x-d/2 is x with unknown
offset
Extra factor How do you know there is (or not
) a shift ? You have to scan beams across gt
very much like a Van der Meer scan
43
Transverse Emittance