Measuring a Known Unknown of             QCD     The Underlying Event  in Proton-Proton Collisions      at 900 GeV & 7 TeV...
Outline•   Introduction to the Underlying Event    -   The LHC, Parton Distributions, Color Rules, Event Topology•   Analy...
Introduction to the Underlying Event                      3
The Large Hadron Collider• Protons are produced by ionizing hydrogen.• Accelerated sequentially in LinAc2 (50 MeV) Booster...
Proton Contents                               up                                               charm                      ...
Color Charge Mnemonic                        • The “strong force” (which                         communicates an SU(3)    ...
Color Charge Mnemonic                               • Anti-quarks carry negative             anti-quark         charges, d...
Color Charge Mnemonic                                      • Colors are conserved!    radiated                            ...
Underlying Event                                             Outgoing                                         Transverse  ...
Particle Jets     1.       Radiated particles also radiate (or split) so              FSR results in a “shower” of quarks ...
Underlying Event•   Goal: Isolate the low-energy QCD contribution                             Toward                      ...
Underlying Event:Analysis Summary                    12
Tracks & Particles•   Transverse Momentum:                                                               Jet 1            ...
The ATLAS Inner Detector                                                       MBTS                                       ...
Number of Pixel hits per track                                                                                            ...
Tracks/0.2 mm                                                                                                             ...
1                                                                                                                         ...
Arbitrary units                            False Tracks                                                                   ...
Track                                                                              Systematic Uncertainty           Size  ...
Event Selection & Weighting•   Selected Events require:                                                                   ...
Migration Effects•    There are two migration effects, both due to the possibility that the     reconstruction will fail t...
Underlying Event: Analysis Details                    22
Track Correction•   Define P(T,pT) to be the distribution for track momentum pT, and track    number T, with P(T) the pT d...
Track Correction•   Making a measurement of y, which is the total track pT corrected for    the efficiency, is simply a ma...
Stat. Errors for Std. Dev.•   In general we are working with 2-dimensional distributions S(x,y)    defined by a counting a...
Stat. Errors for Std. Dev.•   After combining all of the weighted samples, the normalized moments    can be defined (combi...
Stat. Errors for Std. Dev.•   All of the profiles considered here can be considered to be derived by    a finite sample fr...
Migration Correction•   All corrections are derived from a sample of events generated using    the ATLAS MC09 tune of Pyth...
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Measurements of the Underlying Event
Upcoming SlideShare
Loading in …5
×

Measurements of the Underlying Event

945 views

Published on

First measurements of the charged Underlying Event at 900 GeV and 7 TeV using the ATLAS detector at CERN.

1 Comment
1 Like
Statistics
Notes
No Downloads
Views
Total views
945
On SlideShare
0
From Embeds
0
Number of Embeds
21
Actions
Shares
0
Downloads
15
Comments
1
Likes
1
Embeds 0
No embeds

No notes for slide

Measurements of the Underlying Event

  1. 1. Measuring a Known Unknown of QCD The Underlying Event in Proton-Proton Collisions at 900 GeV & 7 TeV Gabriel Hare University of California, Santa Cruz 30th June 2011 1
  2. 2. Outline• Introduction to the Underlying Event - The LHC, Parton Distributions, Color Rules, Event Topology• Analysis Summary: - ATLAS Inner Detector - Track Selection & Weights - Event Selection & Weights• Analysis Details• Underlying Event Measurements: - Particle Number - Transverse Momentum Density - Mean Particle Transverse Momentum★ Conclusions• Analysis Minutiae➡ References 2
  3. 3. Introduction to the Underlying Event 3
  4. 4. The Large Hadron Collider• Protons are produced by ionizing hydrogen.• Accelerated sequentially in LinAc2 (50 MeV) Booster (1.4 GeV) PS (26 GeV) SPS (450 GeV) LHC (7 TeV)• Protons are grouped in “bunches” in beams circulating in both directions that intersect at the center of ATLAS.• “Events” are bunch crossings in which there is at least one collision of protons.• “Pile-up” describes the situation in which there is more than one proton collision in an event.Map overlay from : http://upload.wikimedia.org/wikipedia/commons/0/06/Location_Large_Hadron_Collider.PNGAccelerator layout from : http://public.web.cern.ch/public/en/research/AccelComplex-en.html 4
  5. 5. Proton Contents up charm anti-charm updown down up proton up• “Parton” = any particle found in a proton. gluon• Mostly “Quarks” & “Gluons”. proton• Quarks radiate gluons.• Gluons split into a pairs of gluons or a quark & anti-quark.• At high energies a proton is gluon described by a “Parton Distribution” proton 5
  6. 6. Color Charge Mnemonic • The “strong force” (which communicates an SU(3) orientation) is quantized as gluons.quark quark • The charge carried by quarks that interacts with the strong force can be in one of 3 states of quark charges referred to (by analogy) as “Colors”. • Charges are represented by displacements in a plane. • “Confinement” of the strong force requires that only color- neutral particles can break free from protons. • Baryons are color neutral combinations of 3 quarks, quark such as a proton. 6
  7. 7. Color Charge Mnemonic • Anti-quarks carry negative anti-quark charges, described as the same color in the opposite direction. • “Confinement” of the strong force requires that only color- neutral particles can break free from protons. • Mesons are color neutral combinations of a quark and an anti-quark. Pions are the most common instance. • Hadrons are either color- neutral combinations of three quarks or three anti- quarks.anti-quark anti-quark 7
  8. 8. Color Charge Mnemonic • Colors are conserved! radiated • Gluons bind quarks & anti- quarks together by exchanginggreen + anti-red units color. gluon • There are 8 charge combinations for gluons: • 6 gluon charges describe displacements between quark or anti-quark color states. • 2 gluon non-colored states change the relative wave- front phase of quarks of different colors. radiated • The wave-front phase of quarks determines whether a pair of green + anti-red quarks can combine to a color gluon neutral hadron or one of the 2 non-colored gluon states. 8
  9. 9. Underlying Event Outgoing Transverse Toward Parton ISR Hard Scatter Incoming Incoming Parton Parton Incoming Incoming Proton Proton Outgoing FSR Parton Beam Remnants Beam Remnants Away Transverse In the context of event simulation the “UnderlyingIncoming Incoming Event” refers to everything that does not originate Proton Proton from the Hard Scatter outgoing partons. Model dependent contributions include: pp Collision Outgoing FSR • Multiple Parton Interactions (MPI): Parton - Associated with higher multiplicity events. - Angular distribution that is independent of the Hard Scatter. MPI Incomming Parton • Initial State Radiation (ISR): Incomming Parton - Angular distribution that is nearly independent of the Hard Scatter. Outgoing • Final State Radiation (FSR): ISR Parton - Yields jets of particles in the Toward and Away regions. 9
  10. 10. Particle Jets 1. Radiated particles also radiate (or split) so FSR results in a “shower” of quarks and gluons. • Particles produced in a shower are generally close together in angle. 2. Quarks and gluons are joined into color- neutral “strings”. • Energy is distributed along string. 3. Strings “fragment” into pieces with the masses of hadrons. • Pions are the most frequently produced hadron. 4. The string fragment hadrons form clusters of higher transverse momentum particles that are described as “jets”. • The are many possible definitions of jets... • This analysis avoids the problem of choosing a jet definition.Event Display from : http://www.atlas.ch/photos/atlas_photos/selected-photos/events/Atlantis-dijet-highpt-159224_3533152.png 10
  11. 11. Underlying Event• Goal: Isolate the low-energy QCD contribution Toward T1 to events (in a Minimum Bias sample) that is independent of the Hard Scatter energy.• Assume a Di-Jet structure for events. +ϕ - The ϕ intervals that are nearly transverse to the Di- Jets is assumed to be principally filled by the Transverse Transverse Underlying Event. - The energy of each of the jets is correlated to the hard scatter energy. Away ➡ At low energies it is sufficient to use the highest pT (leading) track T1, rather than the highest ET T2 (leading) jet.• Define ϕ with respect to the leading track. ➡ π/3 < |ϕ| < 2π/3 defines the “Transverse” region.• In the context of measurements, the content Toward of the Transverse region of events will be identified as the “Underlying Event”. Transverse Transverse - Correspondence between the measured Away Underlying Event and MPI or ISR is determined when generators are tuned. 11
  12. 12. Underlying Event:Analysis Summary 12
  13. 13. Tracks & Particles• Transverse Momentum: Jet 1 Transverse - Momentum Partons with equal and opposite momentum Jet 1 generally yield jets with equal and opposite Parton momentum. Center of Mass - Generally parton momenta are not balanced Rest Frame resulting in a “boosted” collision. Incoming Incoming Parton Parton ‣ Jet momenta along the incoming parton axis are not equal. Jet 2 Jet 2 Transverse ‣ Jet “Transverse Momentum” (pT) with respect to Momentum the incoming parton axis remains equal.• Particles: Jet 1 • Ionize detector material yielding currents in a Transverse Momentum cluster of responsive detector elements which are individually recorded as “hits”. Jet 1 Detector• Tracks: Rest Frame • Estimated trajectories of particles “reconstructed” Incoming Parton Incoming Parton from hits. ➡ Some particles might not be successfully Jet 2 Jet 2 reconstructed. Transverse Momentum 13
  14. 14. The ATLAS Inner Detector MBTS MBTS TRT• Tracker: |η| < 2.5 iRad • Trigger: 2.1 < |η| < 3.8 - Pixel Detectors: 3 barrel cylinders, 3 - Minimum Bias Trigger Scintillator (MBTS): disks in each end-cap. 16 cell disks in each end-cap. - Inner-most pixel layer is “B-Layer”. - Event Trigger: Hit in any cell of the MBTS. - Stereo-Strip Tracker (SCT): 4 barrel cylinders, 9 disks in each end-cap. • Reconstruction: - Transition Radiation Tracker (TRT): Axial - Space-points are defined by Pixel hits, and by hits on crossing strips in the SCT. straws in the barrel, radial straws in the end- caps. (Coverage for |η| < 2.1 only) - Tracks are seeded using space-points from Pixel and SCT, and are extrapolated to include hits - 2 Tesla Solenoid encloses the inner from Pixel, SCT, and TRT. detector. Central charged particles require ~500 MeV pT to pass through entire Tracker. 14
  15. 15. Number of Pixel hits per track 4.6Track Selection MC ND s=7 TeV 4.4 Data s=7 TeV 4.2 100 < p < 500 MeV T 4 ATLAS Preliminary 3.8 3.6 • Primary Vertex Tracks: 3.4 3.2 ➡ Used to fill profiles. 3 Average Number of Pixel Hits -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 ATLAS - “Inside-Out” or “Low-pT” reconstruction methods. 4.5 Preliminary s = 7 TeV track - pT ≥ 100 MeV, |η| < 2.5 iRad, 4 500 MeV ≤ pT Data 2010 - |d0Vtx| < 1.5 mm, |z0Vtx · Sin(θ)| < 1.5 mm. 3.5 Minimum Bias MC - The track is not required to have been used when 3 constructing the primary vertex. - 2.5 B-Layer hit if expected. -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 - ≥ 1 Pixel Hit, including B-Layer. Number of SCT hits per track 10 MC ND s=7 TeV - 9.5 SCT hit requirement depends on pT Data s=7 TeV 9 100 < p < 500 MeV ‣ T pT ≥ 100 MeV : ≥ 2 SCT Hits 8.5 ATLAS Preliminary ‣ pT ≥ 200 MeV : ≥ 4 SCT Hits 8 7.5 ‣ pT ≥ 300 MeV : ≥ 6 SCT Hits 7 - Fit requirement to suppress high pT fakes: 10.5 Average Number of SCT Hits -2.5 -2 -1.5 -1 -0.5 0 ATLAS 0.5 1 1.5 2 2.5 10 Preliminary s = 7 TeV track ‣ pT ≥ 10 GeV : Prob(χ2, NDofF) ≥ 0.01 9.5 9 500 MeV ≤ pT Data 2010 Minimum Bias MC 8.5 8Plots compare average hit counts in 7.5Measured & Simulated events. 7 6.5Orange plots from: https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/CONFNOTES/ATLAS-CONF-2010-024/ -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5Yellow plots from : https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/CONFNOTES/ATLAS-CONF-2010-046/ 15
  16. 16. Tracks/0.2 mm nch 2, | | < 2.5, 100 < p < 150 MeV TTrack Selection s = 900 GeV Data MC ND: 106 ATLAS Preliminary all primaries non-electrons electrons 105 • Preliminary Tracks: 104 ➡ Used to reconstruct primary vertices & identify pile-up vertices. -10 -8 -6 -4 -2 0 2 4 6 8 10 Vertex d0 [mm] - All reconstruction methods, (+ “Outside-In”, + “Very-Low-pT”) Tracks/0.2 mm nch 2, | | < 2.5, 200 < p < 250 MeV - T ≥ 1 Pixel Hit, ≥ 4 SCT Hits, ≥ 6 Pixel+SCT Hits, 107 s = 7 TeV Data MC ND: - ATLAS Preliminary all pT > 100 MeV, |η| < 2.5 iRad, 106 primaries non-electrons electrons - |d0BS| < 4 mm, |σd0BS| < 0.9 mm, |σz0BS| < 10 mm. 105 • Beam-Spot Tracks: ➡ Used to characterize the trigger and vertex reconstruction 104 efficiencies. -10 -8 -6 -4 -2 0 2 4 6 8 10 - Intended to be similar to Preliminary Tracks. Vertex d0 [mm] - Tracks/0.2 mm Dependency on the vertex reconstruction is avoided by nch 2, | | < 2.5, 400 < p < 450 MeV T 107 selecting with respect to the beam spot perigee. s = 7 TeV Data ATLAS Preliminary MC ND: - “Inside-Out”, “Low-pT” reconstruction methods. 106 all primaries - secondaries pT > 100 MeV, |η| < 2.5 iRad, 105 - |d0BS| < 1.8 mm, 104 - Same hit & fit requirements as Primary Vertex Tracks 103 -15 -10 -5 0 5 10 15Plots from : https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/CONFNOTES/ATLAS-CONF-2010-046/ Vertex z0 [mm] 16
  17. 17. 1 < Track fit prob. > generated particle p [GeV] ATLAS PreliminaryTrack pT Migration 140 Simulation (non-diffractive) T 120 -1 June 14, 2010 – 13 : 45 100 DRAFT 31 10 80 600 60 R [mm] 10-2 • Track reconstruction concludes with a χ2 fit to 500 40 20 all hits associated with a track. 400 0 10-3 20 40 60 80 100 120 140 160 180 200 • Top: there is a clear difference in the mean fit 300 reconstructed track p [GeV] T generated particle p [GeV] probabilities Prob(χ2, NDofF) for correct & Nsel ATLAS Preliminary 107 140 Simulation (non-diffractive) 106 incorrect pT. 200 T 120 105 • 100 100 Middle: pT migration from low pT tracks yields 80 104 103 the majority of the tracks above 40 -3000 GeV. -2000 0 -1000 60 0 1000 2000 3000 z [mm] 102 • Bottom: When a particle scatters Issue: Mis-measured high-pT tracks (II) off of 10 40 20 detector material (cryostat) the of badly measured tracks. The black boxes indicate the end vertex position of the matched generated par- 10 fit can yield a Figure 31: MC distribution of badly-reconstructed tracks in the detector zR-plane. See text for definition 1 Hadronic interaction can fake high40 T tracks 100 120 140 160 180 200 p 60 80 0 -1 very high track pT. 20 ticles, and the red (blue) boxes show the position of the SCT (Pixel) hits associated to the reconstructed tracks. - topology observed in MC±2.35, and η = ±2.55 . reconstructed track p [GeV] The gray dashed lines highlight η = / data T detector material in MC: O(1%) are decays in flight charged particle Alternative Requirements: reconstructed track • Require d0Vtx < 0.2 - preferred at high |#| interaction with material ✓ Used for systematics June 14, 2010 – 13 : 45 DRAFT 31 Figure 32: Illustration of a low momentum charged particle (blue line) that is reconstructed with high Simulation Simulation • momentum (red line). The black filled dots with the vertical lines represent the silicon measurements. Require TRT hits 600 R [mm] Entries 90 - 500 80 1 TRT covers |η| < 2.1 only < Track fit prob. > mc-truth-track p [GeV] Entries 103 70 140 400 0.9 • 60 0.8 T Wald-Wolfowitz (check for 120 300 50 0.7 100 102 40 SCT Hits 0.6 residual runs) 200 30 80 0.5 True End 20 - 0.4 Pixel Hits 100 60 10 Correlated to fit probability 10 40 0.3 0 0 -3000 -2000 -1000 0 1000 2000 0.2 3000 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 z [mm] ! 20 0.1 1 - current track reconstruction setup seems0.2 0.3to0.4 0.5 much discriminative Migration plots from : https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/CONFNOTES/ATLAS-CONF-2010-046/ 0 not have 0.6 0.7 0.8 0.9 1 Figure 31: MC distribution60 badly-reconstructed tracks in the detector 200 0 20 40 of 80 100 120 140 160 180 zR-plane. See text for definition 0.1 0 power in this region (long extrapolation distances between constraining hits) 2 prob(Track-fit ! ) Explanation from : http://indico.cern.ch/getFile.py/access?contribId=4&resId=0&materialId=slides&confId=102382 of badly measured tracks. The black boxes indicate the end vertex position of the matched generated par- reco-track p [GeV] T 5 ticles, and the red (blue) boxes show the position of the SCT (Pixel) hits associated to the reconstructed tracks. The gray dashed lines highlight η = ±2.35, and η = ±2.55 . Wednesday, August 4, 2010 17 detector material 2
  18. 18. Arbitrary units False Tracks 106 pT ≤ 500 MeV all 105 with common hit 1. Fake tracks are defined to be tracks that cannot 104 be matched to some true charged particle according March 15, 2010 – 11 : 25 to the following matching criteria. DRAFT 103 2 - Cone matched if pT > 500 MeV & ΔR < 0.05 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Minimal ∆R(track,particle) - Cone matched if pT ≤ 500 MeV & ΔR < 0.15 & one Fraction of Tracks Tracks common hit in the pixel detector. 10-1 10 -1 Primaries Figure 20: Minimal ∆R between a truth particle ATLAS Preliminary Strange decays and a reconstructed track. In red, Interactions Had. one common 2. Secondary tracks resulting from decays (or 10 -2 10-2 hit in the pixel detector is required. material interactions) that are identified instead as 10 -3 10-3 primary tracks. (Secondary fraction ~ 0.02.) 10-4 3. Out of Kinematic Range tracks whose matched -5 10-4 10 true particles are outside of the kinematic range,383 closest match is kept. The cone based method w 10-5 because either their pT is too low 0or 2 4 η is 8too384 -10 -8 -6 -4 -2 their 6 10 is nearby but did not generate the track. In thes -10 -8 -6 -4 -2 0 2 4 6 8 10 high. (OKR fraction ~0.2, but only at pT & η d0 [mm] 385 any hit in common and will have veryd0[mm] different Nevts/bin edges.) 386 matching in the following. InGenerated 2nd pile-up vertex Pile-up the previous analy 4 387 of 10 sources of used. The in the Monte matc Figure 1: Shape (left) and distribution (right) for the different < 0.05 wassecondariesObserved 2nd vertex Carlo ∆R effect of fake - A charged primary stable particlegreen ηtrue > shaded) long lived particles and in bluelike for minimum bias e In black the primaries, in with (light 2.5 can be multiplicity environment particles from hadronic 388 103 ATLAS Preliminary reconstructed if the are shown. interactions vertex is displaced towards -z, and track direction resolution dramatically degrades a 389 s= 7 TeV will pass the selection criteria if ηrec < 2.5. 2 10 4. Pile-up 48 yieldsfor the primaries (0 < barcode < 200000) and 390 secondaries Cone Plus 200000 and barcode = 01 ) additional vertices that can merge the 4.2 The (barcode > Hit Based Matching 10 with the49primary vertex are used reconstruction. in the data leaving the normalisation B for the secondaries These templates in the to fit the distribution 391 If a large cone is used, the fraction of fake match 50 freeMatching plot (top) from : ATL-COM-PHYS-2010-682 1Secondaries plot (middle) from : ATL-COM-INDET-2010-011 392 fake matching by 15 20 25 common hit40 5 10 requiring a 30 35 betweePile-Up plot (bottom) from : ATL-CONF-2010-046 393 required to be in the pixel detector. After requirin # tracks @ vertex f (d0 ) = A × ( f p (d0 ) + B/A × fs (d0 )) 18 394 shown in Fig. 20.
  19. 19. Track Systematic Uncertainty Size Region Track Selection ±1% flat in pT and Material ±2 15% decreases with pT , increases with | | Resolution ±5% 100 < pT < 150 MeV only, flat in ⇥2 prob. cut 10% flat, only for pT > 10 GeVWeighting 10-100% Only for pT > 10 GeV, Alignment and other high pT strong dependence, larger for the negative end-cap Table 1: The systematic uncertainties on the tracking e ciency. Stable uncertainties are quoted relative to 7 TeV : Efficiency of Charged Primary All Particle Reconstruction the track reconstruction e ciency. 2.5 1 η (iRad) 2 1 w trk (p T ,η ) = * (1- fFake ) * (1- fSec )2010(1-NDOKR ) ATLAS Preliminary s = 7 TeV s = 7 TeV 1.003 1.003 KS fitted mass ratio KS fitted mass ratio Data * / MC f (nominal) 1.5 ATLAS Preliminary ε trk Data 2010 / MC ND (nominal) 1.002 MC ND (+5%) / MC ND (nominal) 1.002 MC ND (+5%) / MC ND (nominal) 1 MC ND (+10%) / MC ND (nominal) MC ND (+10%) / MC ND (nominal) • The aggregation weight wtrk includes 1.001 0.5 1.001 corrections for the reconstruction Efficiency, 1 0 1 10-1 0 0 and for the fractions of Fakes, Secondaries, 0.999 -0.5 0.999 and tracks from Outside the Kinematic Range. 0.998 -1 0.998 -1.5 • Charged Primary Stable (CPS) Particles: -2.5 -2 -1.5 -1 -0.5 0 0.997 0.5 1 1.5 -2 2 + 2.5 η (π ) 0.997 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 - η (π ) -2.5 -1 10-2 ‣ Stable Particles: τ > 3*10-2 ns (a) 10 1 (b) 10 pT (GeV) ‣ Primary Particles: no Stable 8: Fitted K 0 mass ratios as a function of Figure predecessor 7 TeV : Track Reconstruction Efficiency : Absolute Systematic Uncertainty for data and various MC simulated material descriptions s 2.5 1 over to the nominal MC sample. The values are obtained from the positive (a) and negative (b) track. η (iRad) ‣ pT > 100 MeV & |η| < 2.5 iRad 0 The Ks candidates considered for these plots are required to have a reconstructed decay radius smaller 2 • than 25 mm, an 1.5 0 The reconstruction efficiency hasi.e. before the beam pipe. Furthermore, the two pion tracks of all Ks candidates are required to have at least four silicon hits. The vertical error bars show the statistical uncertainty only (data and uncertainty σtrk due principally to the horizontal and bands indicate the uncertainty due to the magnetic field strength. 10-1 MC), while material orange 1 0.5 interaction or decay uncertainties. 0 • This uncertainty’s effect is estimated in figure 8. From this-0.5in terms of radiation length and interaction length. The mass Detector has been increased by 10%, both versus is shown by study, one can see that the material description in the nominal 10 -2 making three versions of MC sample models the observed masses in the barrel (| | . 1.3) well; one can conclude that in the region the corrected -1 profiles, one corrected using εby , and two is a good estimate for the possible amount of extra material present in the probed trk this study, 10% -1.5 detector relative to the MC. -2 others using εtrk±σtrk. The track length method is also similar to that used in [2]; tracks are reconstructed using the Pixel -2.5 10 -3 -1 10 1 10 detector only and are matched to our good tracks that have the full track selection cuts (GeV) Table from: https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/CONFNOTES/ATLAS-CONF-2010-046/ pT applied. The fraction of Pixel only tracks with a successful match to a full track defines the SCT extension rate.19
  20. 20. Event Selection & Weighting• Selected Events require: MBTS_1 Trigger Efficiency 1 pT > 100 MeV, | | < 2.5, nBS - 2 Data Quality: Stable colliding bunches, solenoid ON, and 0.99 sel nominal inner detector performance. 0.98 ATLAS Preliminary - Trigger: At least one hit in the MBTS. → εtrig(nBS) 0.97 s = 7 TeV - Data 2010 Single Primary Vertex. → εvert(nBS, pTMin, Δz) 0.96 - The Primary Vertex is identified as the candidate with the 0.95 highest Σ(pT2) of its preliminary tracks. 2 4 6 8 10 12 14 16 18 20 n BS - sel No “Pile-Up”: At most one Primary Vertex Candidate with 4 1.02 Vertex reconstruction efficiency or more associated preliminary tracks. 1 - When there are only 2 beam-spot tracks εvert depends on 0.98 ATLAS Preliminary the lowest track pTMin and the Δz distance between the Data 2010 0.96 tracks. s = 7 TeV - 0.94 BS At least two selected tracks. → εevent p > 100 MeV, | | < 2.5, n T sel 2 - 0.92 Two selected tracks guarantees two beam-spot tracks. 0.9 - 2 3 4 5 6 7 8 9 Variation of the track reconstruction efficiency by σtrk also nBS sel varies εevent. Candidate Events: Selected Events/ 1 1 1 ∫L wev = * * Candidate Events ε trig (nBS ) ε vert (nBS ,p TMin ,Δz ) ε lead s= 900 GeV 9.12 μb-1 357511/449666 Luminosity at 900 GeV from Liquid Argon Forward Calorimeter: ATL-COM-LUM-2010-002 Luminosity at 7 TeV from LUCID: ATLAS-CONF-2010-046 s= 7 TeV 190 μb-1 10033043/12805094 Plots from: https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/CONFNOTES/ATLAS-CONF-2010-046/ 20
  21. 21. Migration Effects• There are two migration effects, both due to the possibility that the reconstruction will fail to identify the true highest pT Primary Stable Charged (PSC) particle.1. If the highest pT PSC particle is incorrectly reconstructed. Or, the highest pT PSC particle is missed, the second highest pT PSC particle may be identified as the leading track instead. - The effect is a reduction in the pT scale that characterizes the event. - In the rise preceding the plateau the migration yields densities that are too high.2. If the highest pT PSC particle is missed, the orientation of the reconstructed event will not be consistent with the orientation of the true event. - The effect in this case is that the Transverse region may receive contributions from the Toward & Away regions where there is jet-like activity. - This is most significant in the plateau region of the profile, and yields an increase in the track number & summed pT densities.• These effects are corrected by a final bin-by bin unfolding. - This unfolding assumes that migration in data and simulated events is similar. - An associated systematic uncertainty is estimated by comparing MC09 Pythia and PhoJet unfolding factors. 21
  22. 22. Underlying Event: Analysis Details 22
  23. 23. Track Correction• Define P(T,pT) to be the distribution for track momentum pT, and track number T, with P(T) the pT distribution normalized to T. • A sample for the n event drawn from this distribution yields T [n] tracks, where the t track has momentum p T [n,t ] .• Suppose that we are interested in the total pT of tracks y in (a region of) an event. Using the distribution P(T,pT) this is simply: N T M1 ( y ) = Meas ∫ p T * P(T,p T ) ≈ ∑ ∑ p T [n,t ] T,pT n t• Suppose that there is pT dependent track finding efficiency E p T and( ) a T dependent vertex finding efficiency V T . () • A sample E[ t ] or V [n] drawn from an efficiency is ∈{0,1}. • If no corrections are applied the measured distribution converges to E(T)*V(pT)*P(T,pT). ( ) () -1 -1  • Applying the weight E p T to each track, and V T to each event, the measured distribution converges to a function of the measured track number T and the measured momentum p T normalized to the  corrected number of tracks: P T,p T ( ) 23
  24. 24. Track Correction• Making a measurement of y, which is the total track pT corrected for the efficiency, is simply a matter of including the correction weights. ( ) ( ) N T M1 ( y ) = ∑ V T [n] ∑ E p T [n,t ] * p T [n,t ] -1 -1    n t• The event-to-event variation of M1(y) is used in the definition of the statistical error of a measurement of M1(y). In this case, simply square the result of the weighted sum over t, and weight by V  T -1. 2 ()  2 ( y ) ≈ V T [n] ⎛ E p [n,t ] ( ) ( ) ⎞ N T ∑ ∑ T * p T [n,t ]⎟ -1 -1 M ⎜ n ⎝ t ⎠• In the case of the event-mean track pT, the weighted sum of pT is divided by the weighted track count.• CONCLUSION: Weighting by 1/ε is correct!• In the case of the mean track pT versus track number, the track number migration is not corrected, so the corrected mean track pT refers to the (non-integer) average of the weighted track count, but the x axis bins will still refer to the integer count of measured tracks which receives contributions from higher true track number events. 24
  25. 25. Stat. Errors for Std. Dev.• In general we are working with 2-dimensional distributions S(x,y) defined by a counting a events from a finite sample. - x : the event scale. (e.g. lead track pT) - y : a region characterization. (e.g. scalar-summed track pT)• Define the additive 1-dimensional moment curves [MN(x)](y) by filling each bin weighted by zN. ∀ ⎡MN ( x ) ⎤ ( y ) = ∫ S ( x,y ) * yN ⎣ ⎦ y• S is the distribution of sampled events, including track and event correction weights (wev ≥ 1) and sample weights (ωev ≤ 1).• We need M1, M2, M3, M4.• For the statistical errors we also need X0 : a count of events without correction weights, and X1 a count of events with correction weights. - Simulated events can have X0 sample weights ωev < 1 when a region of phase space is over-produced. - The sample weight ensures a proportionate estimated uncertainty despite having a large sample. 25
  26. 26. Stat. Errors for Std. Dev.• After combining all of the weighted samples, the normalized moments can be defined (combining histogram bins if desired). mN ( y ) = MN ( y ) / X1 ( y )• To begin with, we are interested in the mean v1 value of a probability distribution P(y), and it’s standard deviation v2 with respect to event- to-event variations. v1 ( y ) = c1 ( y ) = m1 ( y ) v 2 ( y ) = c 2 ( y ) = m1 ( y ) - m2 ( y )• The statistical uncertainty for a measure of v1 is: ( ) ( ) U v1 ( y ) = U m1 ( y ) = c 2 ( y ) X 0 - 1 ( )• In order to define a statistical for v2 a new sampled value y2 can be defined whose mean value is c2: ( y2 ( x ) = y - m ( x ) ) 1 2• A sample of y2 is reduced by one, since m was used in the definition. ( ) ( ) c 2 ( y2 ) = m ( y ) - 4 * m ( y ) * m ( y ) - m ( y ) + 8 * m ( y ) m ( y ) - 4 * m ( y ) ( ) 4 3 1 2 2 2 1 2 1 4 ( ) U v 2 ( y ) = c 2 ( y2 ) X0 - 2 ( ) ( 2 * v ( y )) 2 26
  27. 27. Stat. Errors for Std. Dev.• All of the profiles considered here can be considered to be derived by a finite sample from a 2 dimensional probability density P(x,y).• In the absence of migration with respect to X-axis bins, and in the absence of event selection bias, individual track weights wtrk are sufficient to correct only the mean values of the Y-axis distributions. - For the mean transverse pT density the relevant distribution has the sum of the track pT (y1) in the transverse region as the Y-axis. - For the standard deviation the relevant distribution has the square of the sum of the track pT less the mean squared (y2) as the Y-axis.• In the entire event the individual CPS particle pT probability, and the number and pT densities as functions of eta are entirely corrected by track and event weights.• The CPS particle number probability must be corrected for migration.• The mean individual CPS particle pT as a function of the CPS particle number also must be corrected for migration, and in this case there is a correlation with the mean pT that must also be accounted for. 27
  28. 28. Migration Correction• All corrections are derived from a sample of events generated using the ATLAS MC09 tune of Pythia 6.4 and simulated in GEANT 4. • Similar detector conditions (disabled modules) to those of the runs during which the data would be collected. • A comparable misalignment is included in the simulation. • However, the simulated events have a wider distribution of the primary vertex z position so it is necessary to assign a sample weight ωev(z0Vtx) to the simulated events.• These simulated events were used to derive the reconstruction efficiency and false track fractions.• These events are also used to derive the final correction factors, expressed as bin multipliers, to account for migration effects.• The bin multiplier is simply defined to be the ratio of the values in the true profiles over the reconstructed & corrected values. v true ( x ) mmult ( x ) = corr v reco ( x )• An alternative set of correction factors derived using PhoJet was found to yield a difference of at most 2%. 28

×