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A Novel Method for Measuring Absolute Luminosity at the LHC

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

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A Novel Method for Measuring Absolute Luminosity at the LHC

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  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. Beamophobic Optical Theorem • Total cross section • Fwd scatter. amplitude • Optical theorem Define: • In terms of rates

  6. Beamophobic Using the Optical Theorem 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. p e+ e- p Beamophobic Using theoretically clean reactions • e+e- accelerators (LEP, B-factories, …): use Bhabha scattering • See e.g. Budnev, Ginzburg, Meledin & Serbo, NP B63 (1973) 519: ‘ The analysis of the process ppppe+e- 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. Beamophobic Using a calibrated reaction • 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. Philobeamic Try to Study the Beams and Measure Luminosity • 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. Rate vs offset, taken from Potter in Yellow report CERN 94-01 v1 • Now the trick: scan the offset while measuring the rate, over the whole non-zero range, then integrate the result: Philobeamic Van der Meer’s Trick 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. Philobeamic Length Calibration in Van der Meer’s Method • 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. Let’s come to today’s subject Philobeamic Van der Meer Method at the LHC ? 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. Philobeamic Vertex Reconstruction of Beam-Gas Interactions • 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 AB group (Accelerator and Beams dept.) Measured by the experiments

  15. Philobeamic Remarks and Requirements • 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 Alice CMS LHCb

  17. Muons ECAL HCAL Tracker Magnet Which is the Luckiest ? • All four LHC vertex detectors are comparable in precision (for what concerns today’s subject) • LHCb VELO has a better acceptance for beam-gas (fwd vs onion) • LHCb has no veryforward appendage, contrary to CMS and ATLAS • LHCb can’t measure momentum for beam2-gas events beam1 beam2  IP8 at LHC

  18. IP8 VD Gas Scenario Interactions IP3±2 • 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 LVDand 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. Beam2-gas Beam1-gas Beam1-beam2 VD RP Beam 2 Beam 1 RP Gas Expt 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 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| < zouter and |zintersect| < zinner outer inner z / mm

  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 10’000 beam2-gas inelastic interactions • 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 ? 6648

  23. have a dedicated run with large * such that x,y > pv,xy Primary Vertex Resolution • Nominal beam sizes at Point 8 : x  y  109 um (* = 24 m, N=1011) • 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 << bunch sizes

  24. See next slide example 10-7 mbar at 293 K still high vacuum ! One bunch ! • Beam-beam rate: 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: => Contamination < 0.1% • b1-b2: => Contamination < 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 < 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 • Determine angle from beam-gas interactions (with some accuracy) • Adjust angle and * accordingly: for * > 10 m the dependence on  is already very small * 25 m 10 m 2 m

  33. d1 d2 x ct2 x2 /2 d2 z 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. 2.5 ns Leading-Olive Next – to – Leading - Olive Next – to – Next – to – Leading - Olive 75 cm 75 cm LO collision t0 NLO t0 + 1.25 ns NNLO t0 + 2.5 ns IP 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 < 1% (5%) for nominal (pilot) bunch charges • In fact, expect that NNLO > NLO (like in other fields…) • But we think it’s 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 aren’t ghost any more…

  36. Longitudinal Density Monitor Taken from De Santis, LARP meeting, 17sep2003 Bunch (270 ps)

  37. Density Profile in Transverse Directions • Don’t need to know the gas density itself ! • Don’t 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 atom’s 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 • LHCb’s 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: beam–gas 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 can’t one just use the shape of the luminous region ? VELO • Take as a reasonable starting point: two Gaussian bunches, no crossing angle and perfectly head-on • 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… => very much like a Van der Meer scan

  43. Transverse Emittance

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