high energy theory seminar, u of toronto, may 2007 hadron collisions inside and out peter skands...

High Energy Theory Seminar, U of Toronto, May 2007

Hadron Collisions Inside and Out

Peter Skands

Fermilab / Particle Physics Division / Theoretical Physics

Peter Skands Event Generator Status 2

OverviewOverview► Introduction

• The structure of high-energy collisions

• Event Generators

► Combining higher-order matrix elements with parton showers

• The problem of double counting matching

• The VINCIA code

► The Underlying Event

• Multiple Perturbative Interactions (multiple parton interactions)

• A study of string reconnections and the top mass at the Tevatron


Monte Carlo Generators

Large-dimensional phase spaces

Monte Carlo integration

Stratified sampling + stochastic error ~ N1/2 independent of dimension ‘events’

+ Markov Chain formulation of fragmentation:

1. Parton showers: iterative application of universal and pertubatively calculable kernels for n n+1 partons ( = resummation of soft/collinear Sudakov logarithms)

2. Hadronization: iteration of X X’ + hadron, at present according to phenomenological models based on known properties of nonperturbative QCD, lattice studies, and fits to data.


Classic Example: Number of tracksClassic Example: Number of tracksUA5 @ 540 GeV, single pp, charged multiplicity in minimum-bias

events

Simple physics models ~ Poisson

Can ‘tune’ to get average right, but

much too small fluctuations

inadequate physics model

More Physics:

Multiple interactions +

impact-parameter

dependenceMorale (will return to the models later):

1) It is not possible to ‘tune’ anything better than the underlying physics model allows

2) Failure of a physically motivated model usually points to more, interesting physics

The Canadian Research Council phrases it more poetically:

Sjöstrand & van Zijl PRD36(1987)2019


Non-perturbativehadronisation, colour reconnections, beam remnants, non-perturbative fragmentation functions, pion/proton ratio, kaon/pion ratio, Bose-Einstein correlations ...

Soft Jets + Jet StructureMultiple collinear/soft emissions (initial and final state brems radiation), Underlying Event (multiple perturbative 22 interactions + … ?), semi-hard separate brems jets

Resonance Masses …

Hard Jet TailHigh-pT wide-angle jets

& W

idths

+ “UNPHYSICAL” SCALES:+ “UNPHYSICAL” SCALES:

• QF , QR : Factorisation(s) & Renormalisation(s)

sInclusive

Exclusive

Hadron Decays

Collider Energy ScalesCollider Energy Scales


TThe he BBottom ottom LLine ine

The S matrix is expressible as a series in gi, gin/tm, gi

n/xm, gin/mm, gi

n/fπm

, …

To do precision physics:

Solve more of QCD

Combine approximations which work in different regions: matching

Control it

Good to have comprehensive understanding of uncertainties

Even better to have a way to systematically improve

Non-perturbative effects

don’t care whether we know how to calculate them

FO DGLAP

BFKL

HQET

χPT


to Landau Pole

QQuantumuantumCChromohromoDDynamicsynamics

Problem 1: QCD becomes non-perturbative at scales below ~ 1 GeV

Problem 2: bremsstrahlung corrections singular for soft and collinear configurations

► To connect Feynman diagrams with ‘real’ final states:

e+e- 3 jets


► Starting observation: forward singularity of bremsstrahlung is universal (synchrotron radiation) Leading contributions to all radiation processes (QED & QCD)

can be worked out to all orders once and for all exponentiated (Altarelli-Parisi) integration kernels

► Iterative (Markov chain) formulation = parton shower• Generates the leading “collinear” parts of QED and QCD corrections to any

process, to infinite order in the coupling

• The chain is ordered in an “evolution variable”: e.g. parton virtuality, jet-jet angle, transverse momentum, …

a series of successive factorizations the lower end of which can be matched to a hadronization description at some fixed low hadronization scale ~ 1 GeV

Bremsstrahlung: Parton ShowersBremsstrahlung: Parton Showers

dσn+1 = dσn dΠnn+1 Pnn+1

dσn+2 = dσn (dΠnn+1 Pnn+1)2 and so on … exp[]

Schematic: Forward (collinear) factorization of QCD amplitudes exponentiation


A ProblemA Problem

►The best of both worlds? We want:

• A description which accurately predicts hard additional jets

• + jet structure and the effects of multiple soft emissions

►How to do it?

• Compute emission rates by parton showering?• Misses relevant terms for hard jets, rates only correct for strongly

ordered emissions pT1 >> pT2 >> pT3 ...

• (common misconception that showers are soft, but that need not be the case. They can err on either side of the right answer.)

• Compute emission rates with matrix elements?• Misses relevant terms for soft/collinear emissions, rates only correct for

well-separated individual partons

• Quickly becomes intractable beyond one loop and a handfull of legs


Double CountingDouble Counting► Combine different multiplicites inclusive sample?

► In practice – Combine

1. [X]ME + showering

2. [X + 1 jet]ME + showering

3. …

► Double Counting:

• [X]ME + showering produces some X + jet configurations• The result is X + jet in the shower approximation

• If we now add the complete [X + jet]ME as well• the total rate of X+jet is now approximate + exact ~ double !!

• some configurations are generated twice.

• and the total inclusive cross section is also not well defined

► When going to X, X+j, X+2j, X+3j, etc, this problem gets worse

X inclusiveX inclusive

X+1 inclusiveX+1 inclusive

X+2 inclusiveX+2 inclusive ≠X exclusiveX exclusive

X+1 exclusiveX+1 exclusive

X+2 inclusiveX+2 inclusive


MatchingMatching► Matching of up to one hard additional jet

• PYTHIA-style (reweight shower: ME = w*PS)

• HERWIG-style (add separate events from ME: weight = ME-PS)

• MC@NLO-style (ME-PS subtraction similar to HERWIG, but NLO)

► Matching of generic (multijet) topologies (at tree level)

• ALPGEN-style (MLM)

• SHERPA-style (CKKW)

• ARIADNE-style (Lönnblad-CKKW)

• PATRIOT-style (Mrenna & Richardson)

► Brand new approaches (still in the oven)

• Refinements of MC@NLO (Nason)

• CKKW-style at NLO (Nagy, Soper)

• SCET approach (based on SCET – Bauer, Schwarz)

• VINCIA (based on QCD antennae – Giele, Kosower, PS)Evolution


Improved Perturbative Monte CarloImproved Perturbative Monte Carlo► Zero’th order approach to matching:

• Improve the parton showers themselves• E.g. improved soft limit of ordering variable in HERWIG++• Completely new pT-ordered hybrid parton-dipole showers in PYTHIA 6.4 / PYTHIA 8

► Step 1: A comprehensive look at the uncertainty• Vary the evolution variable (~ factorization scheme)

• Vary the antenna function• Vary the kinematics map (angle around axis perp to 23 plane in CM)

• Vary the renormalization scheme (argument of αs)

• Vary the infrared cutoff contour (hadronization cutoff)

► Step 2: Systematically improve on it• Understand how each variation could be cancelled when

• Matching to fixed order matrix elements• Higher logarithms are included

► Step 3: Write a generator• Make Step 1 explicit in a Markov Chain Parton Shower MC algorithm ‘with

error band’• Include Step 2 Matched Parton Shower algorithm, ‘with smaller error band’


VINCIAVINCIA

► VINCIA Dipole shower

• C++ code for gluon showers• Standalone since ~ half a year

• Plug-in to PYTHIA 8 (C++ PYTHIA) since ~ last week

• Most results presented here use the plug-in version

► So far:

• 2 different shower evolution variables:• pT-ordering (~ ARIADNE, PYTHIA 8)

• Virtuality-ordering (~ PYTHIA 6, SHERPA)

• For each: an infinite family of antenna functions • shower functions = leading singularities plus arbitrary polynomials (up to 2nd order in sij)

• Shower cutoff contour: independent of evolution variable IR factorization “universal” less wriggle room for non-pert physics?

• Phase space mappings: 3 choices implemented • ARIADNE angle, Emitter + Recoiler, or “DK1” (+ ultimately smooth interpolation?)

Dipoles – a dual description of QCD

1

3

2

VIRTUAL NUMERICAL COLLIDER WITH INTERLEAVED ANTENNAE

Giele, Kosower, PS : in progress


Checks: Checks: Analytic vs Numerical vs SplinesAnalytic vs Numerical vs Splines

► Calculational methods1. Analytic integration over

resolved region (as defined by evolution variable) – obtained by hand, used for speed and cross checks

2. Numeric: antenna function integrated directly (by nested adaptive gaussian quadrature) can put in any function you like

3. In both cases, the generator constructs a set of natural cubic splines of the given Sudakov (divided into 3 regions linearly in QR – coarse, fine, ultrafine)

► Test example• Precision target: 10-6

• ggggg Sudakov factor (with nominal αs = unity)

ggggg: Δ(s,Q2)

• Analytic• Splined

pT-ordered Sudakov factor= no-branching probability,

generating function for shower

• Numeric / Analytic

• Spline (3x1000 points) / Analytic

Ratios Spline off by a few per mille at scales corresponding to less than a per mille of all dipoles global precision ok ~ 10-6

VINCIA 0.010(Pythia8 plug-in version)

(a few experiments with single & double logarithmic splines not huge success. So far linear ones ok for desired speed & precision)


Expanding the ShowerExpanding the Shower► Start from Sudakov factor

= No-branching probability: (n or more n and only n)

► Decompose inclusive cross section

► Simple example (sufficient for matching through NLO):

NB: simplified notation!

Differentials are over entire respective phase spaces

Sums run over all possible branchings of all antennae


Matching at NLO: tree partMatching at NLO: tree part► NLO real radiation term from parton shower

► Add extra tree-level X + jet (at this point arbitrary)

► Correction term is given by matching to fixed order:

variations (or dead regions) in |a|2 canceled by matching at this order

• (If |a| too hard, correction can become negative constraint on |a|)

► Subtraction can be automated from ordinary tree-level ME’s

+ no dependence on unphysical cut or preclustering scheme (cf. CKKW)

- not a complete order: normalization changes (by integral of correction), but still LO

NB: simplified notation!

Differentials are over entire respective phase spaces

Sums run over all possible branchings of all antennae

Twiddles = finite (subtracted) ME corrections

Untwiddled = divergent (unsubtracted) MEs


Matching at NLO: loop partMatching at NLO: loop part► NLO virtual correction term from parton shower

► Add extra finite correction (at this point arbitrary)

► Have to be slightly more careful with matching condition (include unresolved real radiation) but otherwise same as before:

► Probably more difficult to fully automate, but |a|2 not shower-specific• Currently using Gehrmann-Glover (global) antenna functions • Will include also Kosower’s (sector) antenna functions• Any other subtraction function used in NLO is just a finite part away use the polynomial terms

Tree-level matching just corresponds to using zero

• (This time, too small |a| correction negative)


Matching at NNLO: tree partMatching at NNLO: tree part► Adding more tree-level MEs is straightforward

► Example: second emission term from NLO matched parton shower

► X+2 jet tree-level ME correction term and matching equation

Matching equation looks identical to 2 slides ago

If all indices had been shown: sub-leading colour structures not derivable by nested 23 branchings do not get subtracted


VINCIA Example: H VINCIA Example: H gg gg ggg ggg

VINCIA 0.008

Unmatched

“soft” |A|2

VINCIA 0.008

Unmatched

“hard” |A|2

VINCIA 0.008

Matched

“soft” |A|2

VINCIA 0.008

Matched

“hard” |A|2

y12

y23

y23

y23

y23

y12

► First Branching ~ first order in perturbation theory

► Unmatched shower varied from “soft” to “hard” : soft shower has “radiation hole”. Filled in by matching.

radiation hole in high-pT region

Outlook:

Immediate Future:

Paper about gluon shower

Include quarks Z decays

Matching

Then:

Initial State Radiation

Hadron collider applications

The Underlying Event

Towards a complete picture of hadron collisions


► Domain of fixed order and parton shower calculations: hard partonic scattering, and bremsstrahlung associated with it.

► But hadrons are not elementary

► + QCD diverges at low pT

► multiple perturbative parton-parton collisions should occur

► Normally omitted in explicit perturbative expansions

► + Remnants from the incoming beams

► + additional (non-perturbative / collective) phenomena?• Bose-Einstein Correlations• Non-perturbative gluon exchanges / colour reconnections ?• String-string interactions / collective multi-string effects ?• Interactions with “background” vacuum / with remnants / with active

medium?

e.g. 44, 3 3, 32

Additional Sources of Particle ProductionAdditional Sources of Particle Production


Basic PhysicsBasic Physics► Sjöstrand and van Zijl (1987):

• First serious model for the underlying event

• Based on resummation of perturbative QCD 22 scatterings at successively smaller scales multiple parton-parton interactions

• Dependence on impact parameter crucial to explain Nch distributions.

• Peripheral collisions little matter overlap few interactions

• Central collisions many interactions (+ jet pedestal effect)

wider than Poissonian!

• Colour correlations also essential• Determine between which partons

hadronizing strings form (each string log(mstring) hadrons)

• Important ambiguity: what determines how strings form between the different interactions?

Sjöstrand & van Zijl PRD36(1987)2019


The ‘New’ ModelThe ‘New’ Model► Sjöstrand and PS (2005):

• ‘Interleaved’ evolution of event structure, all ordered in pT

Sjöstrand & PS : NPB659(2003)243; JHEP03(2004)053; EPJC39(2005)129

multipartonPDFs derivedfrom sum rules

Beam remnantsBaryon JunctionsFermi motion / Primordial kT

Fixed ordermatrix elements

pT-orderedparton shower(matched to MEfor W/Z/H/G + jet)

perturbative “intertwining”?(incomplete)

Pythia 6.4: available via PYTUNE (6.408+)

Pythia 8: default


Underlying Event and ColourUnderlying Event and Colour► Not much was known about the colour correlations, so some “theoretically

sensible” default values were chosen

• Rick Field (CDF) noted that the default model produced too soft charged-particle spectra.

• The same is seen at RHIC:

• For ‘Tune A’ etc, Rick noted that <pT> increased when he increased the colour correlation parameters

• But needed ~ 100% correlation. So far not explained

• Virtually all ‘tunes’ now used by the Tevatron and LHC experiments employ these more ‘extreme’ correlations

• Tune A is now also the default in PYTHIA

M. Heinz, nucl-ex/0606020; nucl-ex/0607033


Existing models only for WW a newtoy model for all final states: colour annealing

► Searched for at LEP • Major source of W mass uncertainty• Most aggressive scenarios excluded• But effect still largely uncertain Preconnect ~ 10%

► Prompted by CDF data and Rick Field’s studies to reconsider. What do we know?

• Non-trivial initial QCD vacuum

• A lot more colour flowing around, not least in the UE

• String-string interactions? String coalescence?

• Collective hadronization effects?

• More prominent in hadron-hadron collisions?

• What is <pT>(Nch) telling us?

• What (else) is RHIC, Tevatron telling us?

• Implications for Top mass? Implications for LHC?

Normal

W W

Reconnected

W W

OPAL, Phys.Lett.B453(1999)153 & OPAL, hep-ex0508062

Sjöstrand, Khoze, Phys.Rev.Lett.72(1994)28 & Z. Phys.C62(1994)281 + more …

Colour Reconnection

(example)

Soft Vacuum Fields?String interactions?

Size of effect < 1 GeV?

Color ReconnectionsColor Reconnections

Sandhoff + PS, in Les Houches ’05 SMH Proceedings, hep-ph/0604120

Baryons

Strangeness

Neutral/Charged


Colour AnnealingColour Annealing

Sandhoff + PS, in Les Houches ’05 SMH Proceedings, hep-ph/0604120

► Toy model of (non-perturbative) color reconnections, applicable to any final state

• at hadronisation time, each string piece has a probability to interact with the vacuum / other strings:

Preconnect = 1 – (1-χ)n

• χ = strength parameter: fundamental reconnection probability (free parameter)

• n = # of multiple interactions in current event ( ~ counts # of possible interactions)

► For the interacting string pieces:

• New string topology determined by annealing-like minimization of ‘Lambda measure’

• Similar to area law for fundamental strings: Lambda ~ potential energy ~ string length ~ log(m) ~ N

► good enough for order-of-magnitude

D. B. Leinweber, hep-lat/0004025


A First StudyA First Study► Using Tevatron min-bias as constraint

• Those were the distributions that started it all

• High-multiplicity tail should be somewhat similar to top less extrapolation required

• Why not use LEP? Again, since the extrapolation might not be valid.• No UE in ee, no beam remnants, less strings, no ‘bags’ in initial state.

• The comparison would still be interesting and should be included in a future study

► As a baseline, all models were tuned to describe Nch and <pT>(Nch)

No CR

Field’s Tunes &

new models

► Improved Description of Min-Bias

► Effect Still largely uncertain

► Worthwhile to look at top etc

Tevatron Run II min-bias

PYTHIA 6.408 PYTHIA 6.408

D. Wicke (DØ) + PS, hep-ph/0703081

(Available via PYTUNE)


Preliminary ConclusionsPreliminary Conclusions► Delta(mtop) ~ 1 GeV from parton shower

► Delta(mtop) ~ 0.5 GeV from infrared effects

• Pole mass does have infrared sensitivity. Can we figure out some different observable which is more stable?

• Infrared physics ~ universal? use complimentary samples to constrain it. Already used a few min-bias distributions, but more could be included

• Note: early days. May be under- or overestimated. Models are crude, mostly useful for reconnaissance

D. Wicke (DØ) + PS, hep-ph/0703081


ConclusionConclusion► Still far from a complete description of hadron collisions

• We are really looking at just the first few terms in large expansions.

• Non-perturbative physics not well understood


Words of WarningWords of Warning► Still far from a complete description of hadron collisions

• We are really looking at just the first few terms in large expansions.

• Non-perturbative physics not well understood

J. D. Bjorkenfrom a talk given at the 75th anniversary celebration of the Max-Planck Institute of Physics, Munich, Germany, December 10th, 1992. As quoted in: Beam Line, Winter 1992, Vol. 22, No. 4

[…] The Monte Carlo simulation has become the major means of visualization of not only detector performance but also of physics phenomena. So far so good. But it often happens that the physics simulations provided by the Monte Carlo generators carry the authority of data itself. They look like data and feel like data, and if one is not careful they are accepted as if they were data.

[…] They do allow one to look at, indeed visualize, the problems in new ways. But I also fear a kind of “terminal illness”, perhaps traceable to the influence of television at an early age. There the way one learns is simply to passively stare into a screen and wait for the truth to be delivered. A number of physicists nowadays seem to do just this.

high energy theory seminar, u of toronto, may 2007 hadron collisions inside and out peter skands...

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