Minimum-Bias and Underlying-Event Physics

Transcription

1 2008 CTEQ MCnet Summer School on QCD Phenomenology and Monte Carlo Event Generators 8 16 August 2008 Debrecen, Hungary Minimum-Bias and Underlying-Event Physics Torbjörn Sjöstrand Department of Theoretical Physics, Lund University

2 What is minimum bias? all events, with no bias from restricted trigger conditions σ tot = σ elastic +σ single diffractive +σ double diffractive +...+σ non diffractive dn/dy y reality: σ min bias σ non diffractive +σ double diffractive 2/3 σ tot What is underlying event? dn/dy jet pedestal height underlying event y

3 What is multiple interactions? Cross section for 2 2 interactions is dominated by t-channel gluon exchange, so diverges like dˆσ/dp 2 1/p4 for p Integrated cross section above ptmin for pp at 14 TeV jet cross section total cross section 1000 integrate QCD 2 2 qq qq qq q q qq gg qg qg gg gg gg qq with CTEQ 5L PDF s sigma (mb) ptmin (GeV)

4 σ int (p min ) = dx 1 dx 2 dp 2 f 1(x 1, p 2 ) f 2(x 2, p 2 ) dˆσ p min dp 2 Half a solution to σ int (p min ) > σ tot : many interactions per event P n σ tot = σ int = σ n n=0 n=0 n σ n σ int > σ tot n > 1 n = n If interactions occur independently then Poissonian statistics P n = n n e n n! but energy momentum conservation large n suppressed

5 Other half of solution: perturbative QCD not valid at small p since q,g not asymptotic states (confinement!). Naively breakdown at p min h r p 0.2 GeV fm 0.7 fm 0.3 GeV Λ QCD... but better replace r p by (unknown) colour screening length d in hadron r r r r d resolved λ 1/p d screened

6 so modify dˆσ/dp 2 dˆσ dp 2 α2 s (p2 ) p 4 α2 s (p2 ) p 4 θ(p p min ) (simpler) or α2 s(p p2 ) (p p2 )2 (more physical) where p min or p 0 are free parameters, empirically of order 2 GeV Typically 2 3 interactions/event at the Tevatron, 4 5 at the LHC, but may be more in interesting high-p ones. 0 p 2

7 Basic generation of multiple interactions For now exclude diffractive (and elastic) topologies, i.e. only model nondiffractive events, with σ nd 0.6 σ tot Differential probability for interaction at p is dp = 1 dσ dp σ nd dp Average number of interactions naively n = 1 σ nd Ecm /2 0 dσ dp dp Require 1 interaction in an event or else pass through without anything happening P 1 = 1 P 0 = 1 exp( n ) (Alternatively: allow soft nonperturbative interactions even if no perturbative ones.)

8 Can pick n from Poissonian and then generate n independent interactions according to dσ/dp (so long as energy left), or better generate interactions in ordered sequence p 1 > p 2 > p 3 >... recall Sudakov trick used e.g. for parton showers: if probability for something to happen at time t is P(t) and happenings are uncorrelated in time (Poissonian statistics) then the probability for a first happening after 0 at t 1 is and for an i th at t i is P(t 1 ) = P(t 1 ) exp P(t i ) = P(t i ) exp ( ( t1 ti 0 P(t)dt t i 1 P(t)dt Apply to ordered sequence of decreasing p, starting from E cm /2 P(p = p i ) = 1 σ nd dσ dp exp [ ) ) p (i 1) 1 dσ p σ nd dp dp Use rescaled PDF s taking into account already used momentum = n int narrower than Poissonian ]

9 Impact parameter dependence So far assumed that all collisions have equivalent initial conditions, but hadrons are extended, e.g. empirical double Gaussian: ( ρ matter (r) = N 1 exp r2 r1 2 + N 2 exp r2 r2 2 where r 2 r 1 represents hot spots, and overlap of hadrons during collision is O(b) = or electromagnetic form factor: ) d 3 xdt ρ boosted 1,matter (x, t)ρboosted 2,matter (x, t) S p (b) = d 2 k 2π exp(ik b) (1 + k 2 /µ 2 ) 2 where µ = 0.71 GeV free parameter, which gives O(b) = µ2 96π (µb)3 K 3 (µb) ( )

10 1 0.1 Tune A double Gaussian old double Gaussian Gaussian ExpOfPow(d=1.35) exponential EM form factor p b p O(b) 0.01 n e b 1 all n 1 b Events are distributed in impact parameter b Average activity at b proportional to O(b) central collisions more active P n broader than Poissonian peripheral passages normally give no collisions at all finite σ tot Also crucial for pedestal effect (more later)

11 PYTHIA implementation (1) Simple scenario (1985): first model for event properties based on perturbative multiple interactions no longer used (no impact-parameter dependence) (2) Impact-parameter-dependence (1987): still in frequent use (Tune A, Tune DWT, ATLAS tune,... ) double Gaussian matter distribution, interactions ordered in decreasing p, PDF s rescaled for momentum conservation, but no showers for subsequent interactions and simplified flavours (3) Improved handling of PDFs and beam remnants (2004) Trace flavour content of remnant, including baryon number (junction) u Study colour (re)arrangement u among outgoing partons (ongoing!) Allow radiation for all interactions d

12 (4) Evolution interleaved with ISR (2004) Transverse-momentum-ordered showers dp dp = ( dpmi dp + dp ISR dp with ISR sum over all previous MI p ) exp ( p i 1 p ( dpmi dp + ) ) dp ISR dp dp (5) Rescattering (in progress) p max p 1 hard int. p 1 ISR p 2 mult. int. ISR is 3 3 instead of 4 4: p 3 mult. int. ISR p min interaction number

13 HERWIG implementation (1) Soft Underlying Event (1988), based on UA5 Monte Carlo y Distribute a ( negative binomial) number of clusters independently in rapidity and transverse momentum according to parametrization/extrapolation of data modify for overall energy/momentum/flavour conservation no minijets; correlations only by cluster decays (2) Jimmy (1995; HERWIG add-on; part of HERWIG++) only model of underlying event, not of minimum bias similar to PYTHIA (2) above; but details different matter profile by electromagnetic form factor (with tuned size) no p -ordering of emissions, no rescaling of PDF: abrupt stop when (if) run out of energy (3) Ivan (2002, code not public; in progress) also handles minimum bias soft and hard multiple interactions together fill whole p range

14 SHERPA implementation (1) Conventional approach (2005) Based on formalism of PYTHIA (2) but Full showers for all interactions, with CKKW matching (2) k -factorization-based approach (2007) unintegrated PDFs and off-shell matrix elements consistent with BFKL evolution (small x) combination with multiple interactions in progress

15 PhoJet (& relatives) implementation (1) Cut Pomeron (1982) Pomeron predates QCD; nowadays glueball tower Optical theorem relates σ total and σ elastic 2 Unified framework of nondiffractive and diffractive interactions Purely low-p : only primordial k fluctuations Usually simple Gaussian matter distribution (2) Extension to large p (1990) distinguish soft and hard Pomerons (cf. Ivan): soft = nonperturbative, low-p, as above hard = perturbative, high -p hard based on PYTHIA code, with lower cutoff in p

16 without multiple interactions

17 with multiple interactions

18 Direct observation of multiple interactions Four studies: AFS (1987), UA2 (1991), CDF (1993, 1997) Order 4 jets p 1 > p 2 > p 3 > p 4 and define ϕ as angle between p 1 p 2 and p 3 p 4 for AFS/CDF Double Parton Scattering 2 3 Double BremsStrahlung p 1 + p 2 0 p 3 + p 4 0 dσ/dϕ flat p 1 + p 2 0 p 3 + p 4 0 dσ/dϕ peaked at ϕ 0/π for AFS/CDF AFS 4-jet analysis (pp at 63 GeV): observe 6 times Poissonian prediction, with impact parameter expect 3.7 times Poissonian, but big errors low acceptance, also UA2

19 CDF 3-jet + prompt photon analysis Yellow region = double parton scattering (DPS) The rest = PYTHIA showers σ DPS = σ Aσ B σ eff for A B = σ eff = 14.5 ± mb Strong enhancement relative to naive expectations!

20 Same study also planned for LHC k T (R = 0.4), CDF selections Selection for DPS delicate balance: showers dominate at large p too large background multiple interactions dominate at small p, but there jet identification difficult. (nb / GeV/c) T dσ/dp ISR/FSR off MI off Pythia pp γ + 14 TeV p (jet 3) (GeV/c) T

21 Jet pedestal effect Events with hard scale (jet, W/Z,... ) have more underlying activity! Events with n interactions have n chances that one of them is hard, so trigger bias : hard scale central collision more interactions larger underlying activity. Centrality effect saturates at p hard 10 GeV. Studied in detail by Rick Field, comparing with CDF data: MAX/MIN Transverse Densities Jet #1 Direction Jet #1 Direction Toward-Side Jet TransMIN very sensitive to the beam-beam remnants! Toward Toward TransMAX TransMIN TransMAX TransMIN Away Jet #3 Away Away-Side Jet Define the MAX and MIN transverse regions on an event-by-event basis with MAX (MIN) having the largest (smallest) density.

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23 Tuned PYTHIA Transverse P T Distribution "Transverse" Charged Density "Transverse" Charged Particle Density: dn/d d CDF Preliminary data uncorrected theory corrected CTEQ5L PYTHIA (Set B) PARP(67)=1 PYTHIA (Set A) PARP(67)= PT(charged jet#1) (GeV/c) 1.8 TeV <1.0 PT>0.5 GeV P T (charged jet#1) > 30 GeV/c Charged Density dn/d d dpt (1/GeV/c) 1.0E E E E E E-05 "Transverse" Charged Particle Density PT(chgjet#1) > 5 GeV/c PT(chgjet#1) > 30 GeV/c CDF Data data uncorrected theory corrected PYTHIA Set A PARP(67)=4 PYTHIA Set B PARP(67)=1 PARP(67)=4.0 (old default) is favored over PARP(67)=1.0 (new default)! 1.8 TeV <1 PT>0.5 GeV/c 1.0E PT(charged) (GeV/c) Compares the average transverse charge particle density ( <1, P T >0.5 GeV) versus P T (charged jet#1) and the P T distribution of the transverse density, dn chg /d d dp T with the QCD Monte-Carlo predictions of two tuned versions of PYTHIA (P T (hard) > 0, CTEQ5L, Set B (PARP(67)=1) and Set A (PARP(67)=4)). MC Tools for the LHC CERN July 31, 2003 Rick Field - Florida/CDF Page 28

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25 Rick Field December 1, 2004 Leading Jet: MAX & MIN Transverse Densities PYTHIA Tune A HERWIG "Transverse" Charge Density "MAX/MIN Transverse" Charge Density: dn/d d CDF Preliminary data uncorrected theory + CDFSIM Leading Jet "MAX" ET(jet#1) (GeV) PYTHIA Tune A 1.96 TeV "AVE" "MIN" Charged Particles ( <1.0, PT>0.5 GeV/c) "Transverse" Charge Density "MAX/MIN Transverse" Charge Density: dn/d d CDF Preliminary data uncorrected theory + CDFSIM Leading Jet "MAX" ET(jet#1) (GeV) HERWIG 1.96 TeV "AVE" "MIN" Charged Particles ( <1.0, PT>0.5 GeV/c) "Transverse" PTsum Density (GeV/c) "MAX/MIN Transverse" PTsum Density: dpt/d d CDF Preliminary data uncorrected theory + CDFSIM Leading Jet "MAX" ET(jet#1) (GeV) PYTHIA Tune A 1.96 TeV "MIN" "AVE" Charged Particles ( <1.0, PT>0.5 GeV/c) "Transverse" PTsum Density (GeV/c) "MAX/MIN Transverse" PTsum Density: dpt/d d CDF Preliminary data uncorrected theory + CDFSIM Leading Jet "MAX" "MIN" ET(jet#1) (GeV) HERWIG 1.96 TeV "AVE" Charged Particles ( <1.0, PT>0.5 GeV/c) Charged particle density and PTsum density for leading jet events versus E T (jet#1) for PYTHIA Tune A and HERWIG.

26 Transverse 1 Region vs Transverse 2 Region "Transverse 2" Nchg "Transverse 1" vs "Transverse 2" CDF Run 2 Preliminary data uncorrected theory + CDFSIM 1.96 TeV Leading Jet 30 < ET(jet#1) < 70 GeV PY Tune A Charged Particles ( <1.0, PT>0.5 GeV/c) HW "Transverse 2" Nchg "Transverse 1" vs "Transverse 2" CDF Run 2 Preliminary data uncorrected theory + CDFSIM PY Tune A Back-to-Back 30 < ET(jet#1) < 70 GeV HW Charged Particles ( <1.0, PT>0.5 GeV/c) "Transverse 1" Nchg "Transverse 1" Nchg "Transverse 2" <PT> (GeV/c) "Transverse 1" vs "Transverse 2" CDF Run 2 Preliminary data uncorrected theory + CDFSIM 1.96 TeV PY Tune A Leading Jet 30 < ET(jet#1) < 70 GeV Charged Particles ( <1.0, PT>0.5 GeV/c) HW "Transverse 1" Nchg "Transverse 2" <PT> (GeV/c) "Transverse 1" vs "Transverse 2" CDF Run 2 Preliminary data uncorrected theory + CDFSIM HW Back-to-Back 30 < ET(jet#1) < 70 GeV Charged Particles ( <1.0, PT>0.5 GeV/c) "Transverse 1" Nchg PY Tune A KITP Collider Workshop Rick Field - Florida/CDF Page 75

27 Rick Field December 1, 2004 PYTHIA Tune A vs JIMMY: Transverse Region "Transverse" PTsum Density (GeV/c) "MAX/MIN Transverse" PTsum Density: dpt/d d CDF Preliminary data uncorrected theory + CDFSIM Leading Jet "MAX" ET(jet#1) (GeV) PYTHIA Tune A 1.96 TeV "MIN" "AVE" Charged Particles ( <1.0, PT>0.5 GeV/c) "Transverse" PTsum Density "Transverse" PTsum Density: dpt/d d RDF Preliminary generator level PYA = dashed JM = solid 1.96 TeV Max Transverse Min Transverse PT(jet#1) (GeV/c) Average Transverse Charged Particles ( <1.0, PT>0.5 GeV/c) (left) Run 2 data for charged scalar PTsum density ( <1, p T >0.5 GeV/c) in the MAX/MIN/AVE transverse region versus P T (jet#1) compared with PYTHIA Tune A (after CDFSIM). (right) Shows the generator level predictions of PYTHIA Tune A (dashed) and JIMMY (P T min=1.8 GeV/c) for charged scalar PTsum density ( <1, p T >0.5 GeV/c) in the MAX/MIN/AVE transverse region versus P T (jet#1). The tuned JIMMY now agrees with PYTHIA for P T (jet#1) < 100 GeV but produces much more activity than PYTHIA Tune A (and the data?) in the transverse region for P T (jet#1) > 100 GeV!

28 Back-to-Back charge density Back-to to-back Associated Charged Particle Densities Jet #1 Direction Toward CDF Preliminary data uncorrected Charged Particle Density: dn/d d < ET(jet#1) < 70 GeV 34 Back-to-Back Transverse Transverse Jet# Away Back-to-Back associated density Jet #2 Direction "Transverse" Region PTmaxT "Transverse" Region PTmaxT Direction Jet#1 Region Jet#2 Region Polar Plot Charged Particles ( <1.0, PT>0.5 GeV/c) Associated Density 142 PTmaxT > 2 GeV/c (not included) Shows the dependence of the associated charged particle density, dnchg/d d, p T > 0.5 GeV/c, < 1, PTmaxT > 2.0 GeV/c (not including PTmaxT) relative to PTmaxT (rotated to 180 o ) and the charged particle density, dnchg/d d, p T > 0.5 GeV/c, < 1, relative to jet#1 (rotated to 270 o ) for back-to-back events with 30 < E T (jet#1) < 70 GeV. KITP Collider Workshop Rick Field - Florida/CDF Page 58

29 PTmaxT > 2 GeV/c Associated Particle Density CDF Preliminary data uncorrected theory + CDFSIM Associated Charge Density PYTHIA Tune A vs HERWIG Associated Particle Density: dn/d d PTmaxT > 2.0 GeV/c PY Tune A Charged Particles ( <1.0, PT>0.5 GeV/c) PTmaxT not included PTmaxT (degrees) Back-to-Back 30 < ET(jet#1) < 70 GeV "Jet#1" Region Data - Theory: Associated Particle Density dn/d d CDF Preliminary data uncorrected theory + CDFSIM But HERWIG (without multiple parton interactions) produces too few particles in the Back-to-Back direction opposite 30 < ET(jet#1) of PTmaxT! < 70 GeV PYTHIA Tune A Associated Particle Density CDF Preliminary data uncorrected theory + CDFSIM Associated Particle Density: dn/d d PTmaxT > 2.0 GeV/c HERWIG Charged Particles ( <1.0, PT>0.5 GeV/c) PTmaxT not included PTmaxT (degrees) Back-to-Back 30 < ET(jet#1) < 70 GeV "Jet#1" Region Data - Theory: Associated Particle Density dn/d d CDF Preliminary data uncorrected theory + CDFSIM For PTmaxT > 2.0 GeV both PYTHIA and HERWIG produce slightly too many associated particles in the direction of PTmaxT! HERWIG Back-to-Back 30 < ET(jet#1) < 70 GeV Data - Theory 0.0 Data - Theory Charged Particles ( <1.0, PT>0.5 GeV/c) PTmaxT > 2.0 GeV/c (not included) PTmaxT "Jet#1" Region Charged Particles ( <1.0, PT>0.5 GeV/c) PTmaxT > 2.0 GeV/c (not included) PTmaxT "Jet#1" Region (degrees) (degrees) KITP Collider Workshop Rick Field - Florida/CDF Page 71

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35 Multiple interactions also preferred by HERA photoproduction data: underlying activity in (anti)correlations in photoproduction vs. DIS energy flow around jet <E T >/( η φ) [GeV/rad] Ω(η*) [10-3 ] x γ jets η*

36 Colour correlations p (n ch ) is very sensitive to colour flow p p long strings to remnants much n ch /interaction p (n ch ) flat p p short strings (more central) less n ch /interaction p (n ch ) rising

37 Transverse <p< T > versus Transverse Nchg Leading Jet Back-to-Back Jet #1 Direction Toward Transverse Transverse Away Jet #1 Direction Toward Transverse Transverse Average PT (GeV/c) "Transverse" Average PT versus Nchg CDF Run 2 Preliminary data uncorrected theory + CDFSIM Min-Bias Leading Jet 30 < ET(jet#1) < 70 GeV Back-to-Back 30 < ET(jet#1) < 70 GeV PYTHIA Tune A 1.96 TeV Charged Particles ( <1.0, PT>0.5 GeV/c) Away Number of Charged Particles Jet #2 Direction Min-Bias Look at the <p T > of particles in the transverse region (p T > 0.5 GeV/c, < 1) versus the number of particles in the transverse region: <p T > vs Nchg. Shows <p T > versus Nchg in the transverse region (p T > 0.5 GeV/c, < 1) for Leading Jet and Back-to-Back events with 30 < E T (jet#1) < 70 GeV compared with min-bias collisions. KITP Collider Workshop Rick Field - Florida/CDF Page 35

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40 Extrapolation to LHC Energy dependence of p min and p 0 : Current PYTHIA 8 default, tied to CTEQ 5L, is p 0 (s) = 2.15 GeV ( s (1.8 TeV) 2 Larger collision energy probe parton ( gluon) density at smaller x smaller colour screening length d larger p min or p 0 Post-HERA PDF fits steeper at small x stronger energy dependence ) 0.08

41 LHC predictions: pp collisions at s = 14 TeV dn chg /d at = PYTHIA tuned PYTHIA default PHOJET1.12 pp - interactions Transverse < N chg > PYTHIA tuned PHOJET1.12 CDF data Central Region (min-bias dn chg /d ~ 7) dn chg /d ~ 30 LHC UA5 and CDF data 4 LHC 6 4 dn chg /d ~ 15 x x s (GeV) PYTHIA models favour ln 2 (s); PHOJET suggests a ln(s) dependence. Tevatron P t (leading jet in GeV) A. M. Moraes Minimum-bias and the Underlying Event at the LHC 5 th November 2004

42 LHC predictions: JIMMY4.1 Tunings A and B vs. PYTHIA6.214 ATLAS Tuning (DC2) Transverse < N chg > JIMMY4.1 - Tuning A JIMMY4.1 - Tuning B PYTHIA ATLAS Tuning CDF data LHC 10 x 5 5 x 3 x 4 A. M. Moraes P t (leading jet in GeV) Minimum-bias and the Underlying Event at the LHC Tevatron 5 th November 2004

43 UE tunings: Pythia vs. Jimmy LHC PTJIM=4.9 = 2.8 x (14 / 1.8) 0.27 x2.7 x3 energy dependent PTJIM generates UE predictions similar to the ones generated by PYTHIA6.2 ATLAS. Tevatron

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45 Multiple Interactions Outlook Issues requiring further thought and study: Multi-parton PDF s f a1 a 2 a 3 (x 1, Q 2 1, x 2, Q 2 2, x 3, Q 2 3,...) Close-packing in initial state, especially small x Impact-parameter picture and (x, b) correlations e.g. large-x partons more central!, valence quarks more central? Details of colour-screening mechanism Rescattering: one parton scattering several times Intertwining: one parton splits in two that scatter separately Colour sharing: two FS IS dipoles become one FS FS one Colour reconnection: required for p (n charged ) Collective effects (e.g. QGP, cf. Hadronization above) Relation to diffraction: eikonalization, multi-gap topologies,... Action items: Vigorous experimental program at LHC Study energy dependence: RHIC (pp) Tevatron LHC Develop new frameworks and refine existing ones Much work ahead!

46 - Perugia, Italy, October Perugia, Italy, October, 2008 Home Programme Registration Registered Partecipants Organizing Committee Accomodation Guidelines & Travelling Contacts Bullettin & Poster Instructions for Authors News & Announce 22/03/08 - Firts Bulletin available Courtesy of David Roberts for "ElementalParticles" Welcome to the first International Workshop on Multiple Partonic Interactions at the LHC "1st MPI@LHC". The objective of this first workshop on Multiple Partonic Interactions (MPI) at the LHC is to raise the profile of MPI studies, summarizing the legacy from the older phenomenology at hadronic colliders and favouring further specific contacts between the theory and experimental communities. The MPI are experiencing a growing popularity and are currently widely invoked to account for observations that would not be explained otherwise: the activity of the Underlying Event, the cross sections for multiple heavy flavour production, the survival probability of large rapidity gaps in hard diffraction, etc. At the same time, the implementation of the MPI effects in the Monte Carlo models is quickly proceeding through an increasing level of sophistication and complexity that in perspective achieves deep general implications for the LHC physics. The ultimate ambition of this workshop is to promote the MPI as unification concept between seemingly heterogeneous research lines and to profit of the complete experimental picture in order to constrain their implementation in the models, evaluating the spin offs on the LHC physics program..