Min -Bias C ros s S ection s & C h a r a c t e r i s t i c s - PowerPoint PPT Presentation

Min -Bias C ros s S ection s & C h a r a c t e r i s t i c s a t 3 0 - 1 0 0 Te V Peter Skands (CERN TH) What does the average collision look like? How many of them are there? ( σ pileup ) How much energy in the Underlying Event? (UE) Image Credits: blepfo (deviantart.com)

Theory Models See e.g. Reviews by MCnet [arXiv:1101.2599] and KMR [arXiv:1102.2844] Regge Theory Parton Based A B d σ 2 → 2 / dp 2 ⊗ PDFs ⊥ p 4 ⊥ Optical Theorem + Eikonal multi-Pomeron exchanges + Unitarity & Saturation σ tot,inel ∝ log 2 (s) → Multi-parton interactions (MPI) + Parton Showers & Hadronization Cut Pomerons → Flux Tubes (strings) Regulate d σ at low p T0 ~ few GeV Uncut Pomerons → Elastic (& eikonalization) Screening/Saturation → energy-dependent p T0 Cuts unify treatment of all soft processes EL, SD, DD, … , ND Total cross sections from Regge Theory Perturbative contributions added above Q 0 (Donnachie-Landshoff + Parametrizations) + “Mixed” E.g., PYTHIA, E.g., PHOJET, EPOS, E.g., QGSJET, SIBYLL HERWIG, SHERPA SHERPA-KMR 2 Min-Bias Cross Sections & Characteristics P. Skands

A) Parton-Based Models Central Jets/EWK/top/ Extrapolation to soft scales delicate. Main applications: Higgs/New Physics Impressive successes with MPI-based models but still far from a solved problem Saturation Form of PDFs at small x and Q 2 High Q 2 d σ 2 → 2 / dp 2 ⊗ PDFs Form and E cm dependence of p T0 regulator ⊥ and p 4 Modeling of the diffractive component ⊥ finite x Proton transverse mass distribution Colour Reconnections, Collective Effects Poor Man’s Saturation 7 p T0 scale vs CM energy 6 Range for Pythia 6 p T0 [GeV] Perugia 2012 tunes 5 100 TeV 4 Gluon PDF 30 TeV 3 x*f(x) 7 TeV 2 Q 2 = 1 GeV 2 E CM [GeV] Warning: 0.9 TeV NLO PDFs < 0 1 5000 1 ¥ 10 4 5 ¥ 10 4 1 ¥ 10 5 100 500 1000 See also Connecting hard to soft: KMR, EPJ C71 (2011) 1617 + PYTHIA “Perugia Tunes”: PS, PRD82 (2010) 074018 3 Min-Bias Cross Sections & Characteristics P. Skands

Inelastic Cross Sections & Scaling (elastic is included on summary slide) Disclaimer: for this talk, I do not aim for a precision better than, say, 10% I will be basing extrapolations mainly on Pythia 6 with LHC tunes If you find that too crude, I am willing to bet a bottle of good champagne on the numbers Total Inelastic: Donnachie-Landshof ( ε ~0.08) d σ sd( AX ) ( s ) g 3I 1 P 16 π β 2 = M 2 exp( B sd( AX ) t ) F sd , P β B I P A I d t d M 2 σ INEL = σ TOT - σ EL g 2 d σ dd ( s ) 1 1 3I P = exp( B dd t ) F dd . 16 π β A I P β B I σ ND = σ INEL - σ SD - σ DD P d t d M 2 1 d M 2 M 2 M 2 2 1 2 ref P ≈ 0 . 318 mb 1 / 2 ; w be g 3I What Cross Section? σ INEL @ 100 TeV: Total Inelastic σ INEL @ 30 TeV: Just over 100 mb Fraction with one charged particle in | η |<1 Just under 100 mb Ambiguous Theory Definition Say ~ 105 mb Say ~ 90 mb Ambiguous Theory Definition Ambiguous Theory Definition Observed fraction corrected to total ALICE def : SD has MX<200 σ SD : a few mb larger than at 7 TeV σ DD ~ just over 10 mb The point with an event generator is that we can now ask: What do these events look like? 4 Min-Bias Cross Sections & Characteristics P. Skands

Minimum-Bias Properties LHC has produced a huge repository of min-bias constraints. See e.g., mcplots.cern.ch Only a few significant comparisons can be included here Question: Why is it crucial to use updated (LHC) models/tunes? Central Charged-Track Multiplicity Relative increase in the central charged-track multiplicity from 7000 GeV pp 0.9 to 2.36 and 7 TeV Soft QCD (mb,diff,fwd) η EPJ C68 (2010) 345 9 4.2M events dN/d Charged Particle η Distribution (N > 0, | η | < 1.0, all p ) ch T ALICE INEL>0 | | < 1 η 8 ALICE 0.9 TeV 2.36 TeV → Pythia 6 (350:P2011) ≥ Rivet 1.8.2, Pythia 6 (370:P2012) 0.9 TeV 7.0 TeV → Pythia 6 (320:P0) 7 Pythia 6 (327:P2010) PHOJET 6 PYTHIA Perugia-0 5 Pre-LHC (Tevatron) Tunes PYTHIA 4 ATLAS-CSC mcplots.cern.ch PYTHIA 3 ALICE_2010_S8625980 D6T Pythia 6.427 0 20 40 60 -1 -0.5 0 0.5 1 Increase (%) η Tevatron tunes were ~ 10-20% low on MB and UE … and scaled too slowly Discovery at LHC: things are larger and scale faster than we thought they did See also energy-scaling tuning study, Schulz & PS, EPJ C71 (2011) 1644 5 Min-Bias Cross Sections & Characteristics P. Skands

Minimum-Bias Properties The updated models (as represented here by the Perugia 2012 tunes): Agree with the LHC min-bias and UE data at each energy And, non-trivially, they exhibit a more consistent energy scaling between energies So we may have some hope that we can use these models to do extrapolations Central Charged-Track Multiplicity A VERY SENSITIVE E-SCALING PROBE: relative increase in 7000 GeV pp Soft QCD (mb,diff,fwd) the central charged-track multiplicity from 0.9 to 2.36 and 7 TeV η 9 4.2M events dN/d Charged Particle η Distribution (N > 0, | η | < 1.0, all p ) INEL>0 | η |<1 ch T 8 ALICE Pythia 6 (350:P2011) ≥ Rivet 1.8.2, Pythia 6 (370:P2012) PHOJET Pythia 6 (320:P0) 7 Pythia 6 (327:P2010) DW 6 Perugia 0 (2009) 5 Pre-LHC (Tevatron) Tunes Min/Max Perugia 2012 4 Range mcplots.cern.ch Pythia 8.165 3 ALICE_2010_S8625980 Pythia 6.427 0% 10% 20% 30% 40% 50% 60% 70% -1 -0.5 0 0.5 1 η Tevatron tunes were ~ 10-20% low on MB and UE Data from ALICE EPJ C68 (2010) 345 Caveat: still not fully understood why Tevatron tunes were low. May point to a more subtle energy scaling? See also energy-scaling tuning study, Schulz & PS, EPJ C71 (2011) 1644 6 Min-Bias Cross Sections & Characteristics P. Skands

Scaling of Multiplicities A From soft models based on Regge Theory, expect: D. d’Enterria et al. [arXiv:1101.5596], ∝ Im f P ( s , 0) s ∆ P dN ch ( s , η ) � � , ∼ � log 2 s s σ inel d η � pp ( s ) � η = 0 8 QGSJET too =0 η NSD | agressive? Would η SIBYLL 2.1 7 /d predict very high ch QGSJET 01 dN densities 6 QGSJET II EPOS 1.99 5 EPOS too low (but there is coming 4 a new version which 3 fits LHC better, CMS (p-p NSD) ALICE (p-p NSD) worth trying out) 2 CDF (p- p MB) UA1 (p- p NSD) 1 Will keep these models in mind UA5 (p- p NSD) but will base main extrapolations 0 3 2 4 on PYTHIA Perugia tunes 10 10 10 10 s (GeV) 7 Min-Bias Cross Sections & Characteristics P. Skands

Extrapolations: Central <N ch > Note: I use INEL>0 (rather than NSD, INEL, …) B Recap: this means events with at From parton-based models, expect ~ power law least one charged particle in | η |<1 Similar to QGSJET? (We allow a lower margin since power law may be too fast and we saw that Similar to the data scales slower than SYBILL? the current models) 100 TeV Extrapolations for INEL>0 30 TeV Central <N ch > density 13 TeV (Per unit ΔηΔφ in | η |<1) 7 TeV @13 TeV : 1.1 ± 0.1 2.36 TeV 0.9 TeV @30 TeV : 1.33 ± 0.14 @100 TeV : 1.8 ± 0.4 8 Min-Bias Cross Sections & Characteristics P. Skands

(Multiplicities with p T cuts) Indication from LHC is that current PYTHIA models exhibit a slightly too hard pT spectrum. Rates of very soft particles may be underpredicted. Very hard particles may be overpredicted 7000 GeV pp 7000 GeV pp Soft QCD (mb,diff,fwd) Soft QCD (mb,diff,fwd) ] 3M events T 4 3M events 10 -2 dp [(GeV/c) 2 Charged Particle p Spectrum (| | < 2.4) η 3 Charged Particle p Spectrum (N > 2, p > 0.1 GeV/c) η 10 10 T /d T ch T σ 2 10 d CMS ATLAS ≥ ≥ Rivet 1.8.2, Rivet 1.8.2, Pythia 6 (370:P2012) Pythia 6 (370:P2012) 10 10 T T p dp Pythia 6 (103:DW) Pythia 6 (103:DW) π CMS 1 Pythia 6 (343:Z2) 1/2 Pythia 6 (343:Z2) η 1 Pythia 8 Pythia 8 /d -1 10 pT spectrum ch ev -2 N 1/N 10 ATLAS -1 2 10 -3 ) d 10 (linear x axis) T -4 p pT spectrum 10 -2 π 10 (1/2 -5 10 -6 (logarithmic x axis) 10 -3 10 -7 10 mcplots.cern.ch mcplots.cern.ch -8 10 -4 10 -9 10 CMS_2010_S8656010 ATLAS_2010_S8918562 -10 10 Pythia 6.427, Pythia 8.165 Pythia 6.427, Pythia 8.165 -5 10 0 2 4 6 -1 10 1 10 p [GeV/c] p [GeV] T T Ratio to CMS Ratio to ATLAS 1.5 1.5 High Theory/Data Low 1 1 Tevatron Tune (DW) 0.5 0.5 0 2 4 6 -1 10 1 10 9 Min-Bias Cross Sections & Characteristics P. Skands

(Multiplicities with p T cuts: Extrapolations) Note: here using INEL Thus, when we cut on p T (rather than INEL>0) to only include hard particles, PYTHIA’s numbers may be slightly high Pythia 6.4.28 MSTP(5) = 380 (Perugia 2012g) Nch density per unit eta-phi We also saw that the total N ch density in the central Multiply numbers by 2 π for Perugia 2012 model dN ch /d η | η =0 scaled bit faster than the ALICE measurement indicated. OK, so I would naively assume these numbers are conservative (high) 10 Min-Bias Cross Sections & Characteristics P. Skands

(Additional η regions) Rapidity spectrum is flat (apart from high-y tails) Pythia 6.4.28 MSTP(5) = 380 (Perugia 2012g) Nch density per unit eta-phi → Pseudorapidity distribution has well- 1<| η |<2.5 (INEL) known ‘seagull’ shape → small (O(10%)) dependence on region (apart from high-y tails) Here including two Nch density per unit eta-phi additional regions that 2.5<| η |<3 (INEL) may be relevant: 1 < | η | < 2.5 2.5 < | η | 3.0 Very small differences Log 10 (ECM[GeV]) 11 Min-Bias Cross Sections & Characteristics P. Skands