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Tom Trainor

This research delves into improved isolation of the p-p underlying event by examining minimum-bias trigger-associated hadron correlations. Various models like the Glauber model are utilized to predict and analyze the systematics of p-p collisions, along with exploring dijets, parton fragmentation, and angular correlations. The study addresses the kinematic limits of dijets, trigger-associated correlations, and the structure of hard components from various data sets. It compares predictions from perturbative QCD with empirical observations and offers insights into jet production limits. The research also covers the extraction of conditional hard components from trigger-associated pairs, allowing for a deeper understanding of parton fragmentation and jet production in high-energy collisions.

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Tom Trainor

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  1. Improved isolation of the p-p Underlying Event based on minimum-bias trigger-associated hadron correlations Tom Trainor ISMD 2013

  2. Agenda Measure nch dependence of p-p pt or yt SP spectra Define a “Glauber” model for p-p collisions Predict nch systematics for p-p angular correlations Develop a two-component TA model (TCM) Extract a TA hard component  jet fragments Make direct comparisons with pQCD and dijets Test underlying-event (UE) conjectures re dijets/MPI Identify kinematic limits of dijets in p-p collisions trigger-associated (TA) correlations

  3. Two-component 1D Spectrum Model e.g. 2009 data dnch/dh≈ QCD power law 18 1.7 hard component spectrum data Lévy S0/18 subtract TCM soft component soft component dijet fragment spectra described by pQCD p-p spectra for seven nch classes n nucl-ex/0606028 factorized 2006 PRD: limit nch 0 basis for all that follows

  4. p-p “Glauber” Model A-A Glauber model: dijets  Nbin Npart4/3 ≈ nch4/3 exponent 4/3: eikonal signature low-x gluon participant fluctuations NSD all part. pairs eikonal trend  Npart dijets  nh ns2  Npart2 nch = ns + nh nh nch2 Dh = 2 eikonal approximation invalid dijet number nj = 0.03(ns/2.5 )2 no impact parameter p-p collisions: quantum transitions, Npart ns low-x gluons

  5. p-p Angular Correlations vs nch nch bin data model 6 1 soft c2 = 1.08 c2 = 1.10 200 GeV p-p dijets residuals NJ quad AS 1D SS 2D per-particle correlation measure three main components: (1) jet-related same-side 2D peak (2) away-side 1D peak (dipole), (3) nonjet quadrupole

  6. Predictions from pQCD, p-p “Glauber” from A-A NJ quadrupole  ns3 becomes CMS SS “ridge” in p-p becomes “elliptic flow” in A-A pQCD 2.5 mb SS 2D peak – not a fit no eikonal AS dipole dijets  ns2 minimum-bias (MB) jets – minijets in Au-Au collisions: in p-p collisions: soft component  ns NJ quadrupole proton dissociation to participant partons prediction:

  7. Trigger-associated Correlations in each event the highest yt is the “trigger” nch-1 others are “associated” form all trigger-associated pairs except self pairs subtract calculated TCM soft component(s) obtain conditional hard component Hh(yta:ytt ) Hh can be compared with parton-fragment FFs determine kinematic limits of jet production determine azimuth dependence relative to trigger for events with nch hadrons in Dh no pt cuts – all jets, all hadron pairs accepted

  8. Trigger-associated (TA) Distributions F n = 3 n = 1 marginal projections constrain 2D TCM 2D F distribution yt,assoc 1D SP spectrum four nch classes project n = 7 n = 5 yt,trig 2006 PRD 1D trigger spectrum new

  9. TA Two-component Model – TCM event-type prob void prob 1D 1D SP spectrum TCM TCM trigger model sample-type prob nj – dijet number void probability: exercise in compound probabilities derive 2D two-component TA model based on 1D spectra 1307.1819 derived from 1D SP spectra includes factorized hard-component model H0´(yta:ytt) as place holder

  10. Trigger Spectra T – Four nch Classes n = 3 n = 1 no vertical adjustment calculated solid curve points are measured trigger spectra Note: n = 7 n = 5 only one adjustment – O(1) parameter k accounts for non-Poisson correlations trigger spectrum components k k = 1.3-1.6

  11. Compare 2D TA Data and TA TCM F data F TCM major features agree quantitatively

  12. Associated-per-Trigger Ratios A = F/T Adata / ATCM data soft components well modeled n = 3 n = 1 due to nch-1 constraint jet structure yt,assoc n = 5 n = 7 data hard components: new information on dijet structure soft component

  13. Hard Component of A = F/T per Dijet per hard event dependent on nch per-dijet approximately independent of nch! ≈ 1.15 dijets 1 GeV/c compare with unbiased jet structure n = 3 n = 4 hep-ph/0606249 measured FFs – 2006 FFs estimated trigger 6 GeV/c 0.15 GeV/c lowest measured jets CLEO ≈ 2 dijets measured FFs n = 5 n = 6 2 GeV 200 GeV 0.5 GeV/c parton energy subtract TCM soft components

  14. Hard Component of F = TA most jets actual minbias trigger-associated pairs Porter 2004 minbias ≈ 1 dijet 2 GeV/c n =4 n = 3 compare with yt×yt correlations and… pQCD factorization FFsspectrum ≈ 2 dijets estimated trigger n = 5 n = 6 parton spectrum

  15. A = F/T vs Azimuth Intervals 4 GeV/c away toward harder softer harder sum three low-nch bins: MPI < 15% 4 GeV/c trans jets in TR! part of triggered dijet n = 2-4 0.6 GeV/c UE MPI conjecture inconsistent with data 0.3 GeV/c

  16. Dijet Structure in the “Trans” Region MB jets vs nch n=1 n=6 MB jets provide a base for higher-energy dijets relative to MB jets: for higher jet energies hadrons added nearer the jet axis do not contribute to the TR jet structure 2D fit model AS SS TR = “trans” substantial overlap: same-side SS vs away-side AS

  17. Underlying-Event Trends and the TR 200 GeV p-p fraction hard events 20 2 nch/Dh MPI more dijets,  nch2 control parameters MPI NSD single dijet NSD 0 0 number of dijets in hard events yt,trig 0 1 real UE = soft component plus MPI described above NSD p-p CDF jet contribution to TR comes from MB jet structure common to all dijets trig. jet hard component in TR soft 1.8 TeV soft 1210.5217 TR multiplicity not MPI

  18. Charge-pair Type Dependence toward trans away like-sign pt (GeV/c) 1 2 unlike-sign

  19. Kinematic Space for Jets & Fragments Trigger hadrons extend down to 1 GeV/c Associated hadrons extend down to 0.4 GeV/c (AS) or 0.8 GeV/c (SS) TA results consistent with measured FFs from LEP, HERA and CDF and with a pQCD parton spectrum that predicts measured dijet production Conventional trigger-associated ptcuts accept a tiny fraction of the actual jet number and jet fragments, produce a deceptive picture of jets in HE collisions effective boundaries for jet formation

  20. Summary “Glauber” model for p-p collisions, no eikonal “Soft” component represents participant partons Predict trends for dijet, nonjet-quadrupole correlations MPI trend with nch, jet contributions to “trans” region Develop TCM for trigger-associated TA correlations 1D T spectrum, 2D F = TA two-component models Hard components of F, A by subtraction  MB jets Direct link to measured fragmentation functions and underlying pQCD parton spectrum TA results confirm trigger contribution to “trans” region

  21. Hard Component of A = F/T per Dijet per-dijet approximately independent of nch! ≈ 1.15 dijets 1 GeV/c compare with unbiased jet structure n = 3 n = 4 hep-ph/0606249 measured FFs – 2006 FFs estimated trigger 6 GeV/c 0.15 GeV/c lowest measured jets CLEO ≈ 2 dijets measured FFs n = 5 n = 6 2 GeV 200 GeV 0.5 GeV/c parton energy subtract TCM soft components

  22. Hard Component of A = F/T per Dijet per hard event dependent on nch compare with unbiased jet structure hep-ph/0606249 measured FFs – 2006 FFs estimated trigger lowest measured jets CLEO measured FFs 2 GeV 200 GeV parton energy subtract TCM soft components

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