Introduction to Event Generators L e c t u re 4 : Ph y sic s a t Ha dro n C o llide rs Peter Skands (Monash University) 11th MCnet School, Lund 2017
PHENO AT THE LHC ๏ What are we really colliding? • Hadrons are composite, with time- d dependent structure u u • Partons within clouds of further partons, constantly being emitted and absorbed Lattice simulation, D. Leinweber (Adelaide) Hadrons are composite, with time-dependent structure: ๏ (for hadron to remain intact, virtualities k 2 < M h2 High-virtuality fluctuations suppresed by powers of: u p d α s M 2 M h : mass of hadron g h k 2 : virtuality of fluctuation k 2 u illustration by T. Sjöstrand 2 Peter Skands Monash University
SUCH STUFF AS BEAMS ARE MADE OF ๏ Lifetime of typical fluctuation ~ r p /c (=time it takes light to cross a proton) • ~ 10 -23 s; Corresponds to a frequency of ~ 500 billion THz ๏ To the LHC, that’s slow! (reaches “shutter speeds” thousands of times faster) • E= h ν ➜ ν LHC = 13 TeV/ h = 3.14 million billion THz • ➜ Protons look “frozen” at moment of collision But they have a lot more than just two “u” quarks and a “d” inside ๏ ๏ Hard to calculate (non-perturbative), so use statistics to parametrise the structure: parton distribution functions (PDFs) • @LO: Every so often I will pick a gluon, every so often a quark (antiquark) • Measured at previous colliders (+ now at LHC) , as function of energy fraction • Hard scattering knows nothing of the target hadron apart from the fact that it contained the struck parton → factorisation [M. Seymour] 3 Peter Skands Monash University
HADRON COLLISIONS ๏ Simple question: what does the average LHC collision look like? • First question: how many are there? • • What is σ tot (pp) at LHC ? • (could we compute it in perturbation theory?) 4 Peter Skands Monash University
THE TOTAL CROSS SECTION σ tot ( s ) = σ el ( s ) + σ inel ( s ) ∝ s 0 . 08 or ln 2 ( s ) ? Donnachie-Landshoff Froissart-Martin Bound σ tot (13 TeV) ∼ 110 ± 6 mb PP CROSS SECTIONS PYTHIA: 100 mb AUGER TOTEM, PRL 111 (2013) 1, 012001 σ inel (13 TeV) ∼ 80 ± 3 . 5 mb TOTEM PYTHIA: 78 mb AUGER TOTEM ALICE (2 . 9%) σ tot (8 TeV) = 101 ± 2 . 9 mb ALICE 13 TeV PYTHIA PYTHIA: 93 mb ATL CMS total 8 TeV (2 . 3%) inelastic σ inel (8 TeV) = 74 . 7 ± 1 . 7 mb 7 TeV PYTHIA: 73 mb PYTHIA elastic (5 . 1%) TOTEM is too low PYTHIA σ el (8 TeV) = 27 . 1 ± 1 . 4 mb elastic PYTHIA: 20 mb (PYTHIA versions: 6.4.28 & 8.1.80) 5 Peter Skands Monash University
HADRON COLLISIONS ๏ Simple question: what does the average LHC collision look like? • First question: how many are there? What is σ tot (pp) at LHC ? • Around 100mb (of which about half is “inelastic, non-diffractive”) Hit Hit Example of “Minimum Bias Trigger” Minimal trigger requirement At least one hit in some simple and efficient hit counters (typically at large η ) (Double-sided trigger requirement suppresses “single diffraction”) 6 Peter Skands Monash University
(ASIDE: WHAT IS DIFFRACTION?) Single Diffraction Glueball-Proton Collider with variable E CM Gap MBTS CALO TRACKING CALO MBTS ALFA/ ALFA/ ZDC? ZDC? TOTEM TOTEM n 0 , γ , … n 0 , γ , … V H H E V I I ? ? T T T O Measure p’ p p Pom = x Pom P p p’ p Also: “Double Diffraction”: both protons explode; defined by gap inbetween “Central Diffraction”: two protons + a central (exclusive) system 7 Peter Skands Monash University
M C v s H a d ro n C o l l i s i o n s CORRELATION STRENGTH b models 0.7 w UA5 DATA 0.6 Do not be scared of the failure of physical models 0.5 0.4 (typically points to more interesting physics) 0.3 0.2 Distribution of some global some the number of 0. 1 (quantum) mechanism for Charged Tracks number tells generating the entire Correlation Strength much bigger FIG, k (forward-backward) event to fluctations in fluctuate up or multiplicity Sjöstrand & v. Zijl, Phys.Rev.D36(1987)2019 down ? (here: of charged tracks)
HARD INTERACTIONS IN HADRON COLLISIONS ๏ 1983 : the “Pedestal Effect” Phys. Lett. B 132 (1983) 214-222 • UA1: p at √ s = 540 GeV p ¯ • Studies of jets with E T up to 100 GeV “Outside the [jet], a constant E T plateau is observed, whose height is independent of the jet E T . Its value is substantially higher than the one observed for minimum bias events.” In hadron collisions, hard jets sit on “pedestals” of increased particle production extending far from the jet cores. 9 Peter Skands Monash University
DISSECTING THE PEDESTAL ๏ Today, we call the pedestal d n/ d y Illustrations by “the Underlying Event” T. Sjöstrand jet ✓ E + p z ◆ y = 1 pedestal height 2 ln E − p z underlying event y Rapidity (along beam axis) Looks like something we’ve seen before … ? (but pedestal too high to be just one string …) Rapidity (along string axis) 10 Peter Skands Monash University
FROM HARD TO SOFT ๏ Factorisation and IR safety ” e g d i • Main tools for jet calculations R “ S M C s e i t i c i • Corrections suppressed by powers of l p i t l u m k c a r T Λ QCD /Q Hard p T spectra ๏ Soft QCD / Minimum-Bias s e l c t i r a P d e fi i n t e d I HADRONIZATION Baryon Transport NO HARD SCALE C o r r e l a t i Typical Q scales ~ Λ QCD o n s Extremely sensitive to IR effects C e n t r a l v s F o r w a r d → Excellent LAB for studying IR effects Collective Effects? C o l o • ~ ∞ statistics for min-bias r C o r r e l a t i o n s Rapidity Gaps → Access tails, limits ๏ • Universality: Recycling PU ⬌ MB ⬌ UE 11 Peter Skands Monash University
IS THERE NO HARD SCALE? ๏ Compare total (inelastic) hadron-hadron cross section to calculated parton-parton (LO QCD 2 → 2) cross section 200 GeV pp 0.2 TeV 4 Integrated Cross Section (mb) 10 Integrated cross section [mb] (p p ) vs p σ ≥ 2 → 2 T Tmin Tmin (fit) TOTEM 3 σ 10 INEL =0.130 NNPDF2.3LO α s =0.135 CTEQ6L1 α s Leading-Order pQCD 2 10 total inelastic cross section Z d σ Dijet dp 2 ⊥ dp 2 10 p 2 ⊥ Hard jets ⊥ , min 1 are a LO QCD 2 → 2 (Rutherford) small tail V I N C I A R O O T -1 10 d σ 2 → 2 / dp 2 Pythia 8.183 ⊗ PDFs ⊥ -2 10 p 4 ⊥ 1.5 RATIO Expect average pp event Ratio to reveal “partonic” 1 structure at 1-2 GeV scale 0.5 0 0 5 10 15 20 p Tmin 12 Peter Skands Monash University
→ 8 TEV → 100 TEV ๏ → Trivial calculation indicates hard scales in min-bias 100 TeV 8 TeV pp 100 TeV pp 8 TeV 5 10 Integrated cross section [mb] 4 Integrated Cross Section (mb) 10 Integrated cross section [mb] (p p ) vs p σ ≥ (p p ) vs p σ ≥ 2 2 → T Tmin Tmin 2 → 2 T Tmin Tmin TOTEM σ (data) TOTEM σ INEL 4 10 INEL 3 α =0.130 NNPDF2.3LO 10 =0.130 NNPDF2.3LO s α s =0.135 CTEQ6L1 α =0.135 CTEQ6L1 s α s 3 10 2 total inelastic cross section 10 2 10 10 LO QCD 2 → 2 (Rutherford) V I N C I A R O O T 10 V I N C I A R O O T 1 Pythia 8.183 Pythia 8.183 1 -1 10 → 10 GeV scale! 1.5 1.5 Expect average pp event RATIO Ratio Ratio to reveal “partonic” 1 1 structure at 4-5 GeV scale! 0.5 0.5 0 0 0 5 10 15 20 0 5 10 15 20 p p Tmin Tmin 13 Peter Skands Monash University
SUMMARY FOR NOW: WE KNOW 3 THINGS 1) Hadrons are composite Hadrons are composite, with time-dependent structure: Factorisation: hard interaction picks out a single parton; what about the rest? u At some level, multiple-parton-interactions p d g must occur (only a question of how often) u d n/ d y 2) Events with a hard trigger are accompanied by an “underlying event” jet Looks too high to be just one string underlying event Multiple colour exchanges ? 3) Simple calculations indicate the presence of (semi)hard scales even when no hard trigger is imposed (“minimum bias”) 14 Peter Skands Monash University
PHYSICS OF THE PEDESTAL ๏ Factorisation: Subdivide Calculation ๏ Q F Q 2 Multiple Parton Interactions go beyond existing theorems → perturbative short-distance physics in Underlying Event → Need to generalize factorisation to MPI 15 Peter Skands Monash University
Multiple Parton Interactions = Allow several parton-parton interactions per hadron-hadron collision. Requires extended factorization ansatz. Earliest MC model (“old” PYTHIA 6 model) Sjöstrand, van Zijl PRD36 (1987) 2019 Bahr, Butterworth, Seymour: arXiv:0806.2949 [hep-ph] d σ 2 → 2 / dp 2 ⇠ dp 2 ⊥ ⊥ f Q F Q 2 Leading-Order pQCD × f o p 4 p 4 t ) n u ⊥ ⊥ o C Z d σ Dijet s i dp 2 r r e a w ⊥ p dp 2 h n i > 1 m o p 2 h ⊥ o S ⊥ , min c n r o o f t ( r a P Lesson from bremsstrahlung in pQCD: divergences → fixed-order breaks down Perturbation theory still ok, with resummation (unitarity) h n i < 1 → Resum dijets? Yes → MPI! σ 2 → 2 ( p ⊥ min ) = ⌥ n � ( p ⊥ min ) σ tot Parton-Parton Cross Section Hadron-Hadron Cross Section P . Skands 16
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