theory models of hadron collisions

Peter SkandsTheoretical Physics, FermilabPeter SkandsTheoretical Physics, Fermilab

Theory Models of Hadron CollisionsTheory Models of Hadron Collisions

Joint UE/MB Meeting, CERN, Aug 14 2009

Underlying Event in Herwig and Pythia - 2Peter Skands

► Starting point: Matrix Elements + Parton Showers

• Hard parton-parton scattering Normally 22 at LO or NLO

• + bremsstrahlung associated with it 2n in (improved) LL approximation

2n at LO up to matched order

►But hadrons are not elementary

►+ QCD diverges at low pT

multiple perturbative parton-parton collisionse.g. 44, 3 3, 32 QF >> ΛQCD

QF

QF

…22

ISR

ISR

FSR

FSR

22

ISR

ISR

FSR

FSR

►No factorization theorem

Herwig++, Pythia, Sherpa: MPI models

MC Models: Perturbative PartMC Models: Perturbative Part

Underlying Event has perturbative part!


MC Models: Non-Perturbative PartMC Models: Non-Perturbative Part

Need-to-know issues for IRsensitive quantities (e.g., Nch)

+

Stuff at

QF ~ ΛQCD

QF >> ΛQCD

ME+ISR/FSR

+ perturbative MPI

QF

QF

…22

ISR

ISR

FSR

FSR

22

ISR

ISR

FSR

FSR

► Hadronization► Remnants from the incoming beams► Additional (non-perturbative /

collective) phenomena?• Bose-Einstein Correlations

• Non-perturbative gluon exchanges / color reconnections ?

• String-string interactions / collective multi-string effects ?

• “Plasma” effects?

• Interactions with “background” vacuum, remnants, or active medium?


Naming ConventionsNaming Conventions► Many nomenclatures being used.

• Not without ambiguity. I use:

Qcut

Qcut

22

ISR

ISR

FSR

FSR

22

ISR

ISR

FSR

FSR

Primary Interaction

(~ trigger)Underlying Event

Beam Remnants

Note: each is colored Not possible to separate clearly at hadron level

Some freedom in how much particle production is ascribed to each:

“hard” vs “soft” models

…

…

…

Inelastic, non-diffractive

Multiple Parton Interactions


► Models only as good as

• Their underlying physics assumptions (if a model is simple, it is wrong)

• Their parameter constraints (even the most fancy is useless without constraints)

► E.g., even a great Tevatron tune

• May be totally off at RHIC/LHC energies if energy scaling not well modeled & constrained

Even if “retunable”, which model would you trust more? One that also described RHIC, Tevatron? Or one that didn’t?

Starting at 7 TeV will help map out energy dependence improve models

• May be off for quantities that were inclusively summed over E.g., which model would you trust more?

One that describes total Nch, pT spectra, etc, or one that also described those distributions separately for pions, Kaons, Lambdas, B mesons etc?

One that describes those spectra in the ATLAS/CMS acceptance region, or one that also describes them in the region measured by LHCb?

E.g., validate on pT and Nch density at η=2.0 (or in 1.8<η<2.5? Or smaller?)

““Tuning”Tuning”Measurements Constraints


► Some examples of tuning an imperfect model

• Example 1: Proton lumpiness MPI Model A (e.g, the ‘old’ Pythia model) no showers off the MPI.

To help generate large fluctuations, need a very lumpy proton

large difference between peripheral and central collisions.

MPI Model B (e.g., the ‘new’ Pythia one) does have showers off the MPI. More/less active showers more intrinsic fluctuations Generally need a less lumpy proton.

• Example 2: ISR model ISR Model A: DY αS(0.2pT

2) (the ‘W’ in DW et al)

ISR Model B (dipole recoils): fine with αS(pT2)

ISR Model C: Modify behaviour close to IR cutoff less prim. kT

• Different cocktails indeed – But nonetheless hard to tell apart


Crucial to have many mutually complementary constraints

Proton mass distribution used to

compensate for lack of MPI showers?

Arg of αS used to compensate for ‘bad’ recoil model?

Non-perturbative ‘primordial kT’ used to compensate for ‘bad’ shower in IR?


► Some examples of tuning a good model

• Example A: Rick Field’s Tunes Tuning only used Underlying-Event data.

(‘W’ ones include Drell-Yan as well)

Robust model Tunes also in excellent agreement with min-bias

• Example B: Tune S0 and the Perugia Tunes The converse: Tunes only used Min-Bias data.

Robust models Tunes also in excellent agreement with Underlying-Event

• Note, however, that A and B on this and the previous slides are identical


Robust models have larger ranges of validity predictivity


MC ModelsMC ModelsPerturbative PartPerturbative Part


Why Perturbative MPI?Why Perturbative MPI?► Analogue: Resummation of multiple bremsstrahlung emissions

• Divergent σ for one emission (X + jet, fixed-order)

Finite σ for divergent number of jets (X + jets, infinite-order) N(jets) rendered finite by finite perturbative resolution = parton shower cutoff

►(Resummation of) Multiple Perturbative Interactions

•Divergent σ for one interaction (fixed-order)

Finite σ for divergent number of interactions (infinite-order)

N(jets) rendered finite by finite perturbative resolution

Saturation? Current models need MPI IR cutoff > PS IR cutoff

= color-screening cutoff(Ecm-dependent, but large uncert)

Bahr, Butterworth, Seymour: arXiv:0806.2949 [hep-ph]


► The interaction cross section

• … is an inclusive number.

► … so an event with n interactions …

• … counts n times in σ2j but only once in σtot

How many?How many?

With constant αs, neglecting x integrals

• Poisson only exact if the individual interactions are completely independent, so will be modified in real life

Herwig++/Jimmy starts directly from Poisson n, but includes vetos if (E,p) violated. Pythia uses a transverse-momentum ordered Sudakov formalism, interleaved with the shower evolution ~ resummation. (E,p) explicitly conserved at each step.


How many?How many?► Different Cocktails Probability distribution of NMPI

Not necessary to believe in these

particular numbers.

But good to know this is what is

obtained with out-of-the-box MC

models

<Nint>old ~ 6.0<Nint>new ~ 3.5

Note: This is min-bias; <Nint> larger

for UE.

PS, Perugia Proceedings, in preparationButtar et al., Les Houches SMH Proceedings (2007) arXiv:0803.0678 [hep-ph]

More plots collected at http://home.fnal.gov/~skands/leshouches-plots/

Important Difference:

Old model had no showers off MPI


Different Cocktails?Different Cocktails?► Observed charged particle multiplicity Moral: vastly

different cocktails can give similar answers

Buttar et al., Les Houches SMH Proceedings (2007) arXiv:0803.0678 [hep-ph] More plots collected at http://home.fnal.gov/~skands/leshouches-plots/

(stable particle definition: cτ ≥ 10mm)


Impact ParameterImpact Parameter► Impact parameter: central vs. peripheral collisions

All models currently assume f(x,b) = f(x) g(b) Obviously not the final word. Is this connected to E-scaling?

► Large fluctuations g(b) needs to be “lumpy”Large difference between

peripheral and central

μep = 0.7 GeV2 μ = 1.5 GeV2

Core size a2/a1 = 0.5Contains fraction β = 0.4

Herwig++/Jimmy: EM form factor, but width rescaled to smaller radius

Pythia: default: tune A double gaussian: “hard core” (valence lumps?)

“No” UE in peripheral collisions (low

multiplicity)

“Saturated” UE in central collisions (high multiplicity)

“Jet pedestal” effect


Multi-parton pdfsMulti-parton pdfsSnapshot of proton: re-use 1-parton inclusive f(x)

Subsequently impose (E,p) cons by vetoing events that violate it.

1-parton inclusive f(x) = pdf for “trigger” scattering

Multi-parton pdfs explicitly constructed, respecting flavour and momentum sum rules

quarks

gluons

Herwig

Pythia


Interleaved EvolutionInterleaved Evolution

Sjöstrand, PS; JHEP03(2004)053, EPJC39(2005)129

multipartonPDFs derivedfrom sum rules

Beam remnantsFermi motion / primordial kT

Fixed orderMatrix elements

parton shower(matched tofurther matrixelements)

perturbative “intertwining”?

Pythia

“New” Pythia model

Underlying Event(interactions correllated in colour: hadronization not independent)


MC ModelsMC ModelsNon-Perturbative PartNon-Perturbative Part


Now Hadronize ThisNow Hadronize This

Simulation fromD. B. Leinweber, hep-lat/0004025

gluon action density: 2.4 x 2.4 x 3.6 fm

Anti-Triplet

Triplet

pbar beam remnant

p beam remnantbbar

from

tbar

deca

y

b from

t d

ecay

qbar fro

m W

q from W

hadroniza

tion

?

q from W


Standard AssumptionsStandard Assumptions

►Jet universality

• Jets fragment in the same way in pp as they did at LEP

• Not unreasonable, but must be tested in situ

• Cannot be expected to hold to infinite precision Look for when breakdown occurs

Need tracers … (e.g., pT spectra for identified particles)

• Assumed by all models / tunes

►Remnant Fragmentation

• Gives “Soft Component” vs “Hard” MPI component

• What is the balance between the two? Need tracers … (e.g., remnant clearly identified by having a net baryon

number Lambdabar / Lambda < 1 traces remnant breakup)


Underlying Event and ColorUnderlying Event and Color► The colour flow determines the hadronizing string topology

• Each MPI, even when soft, is a color spark

• Final distributions crucially depend on color space

Note: this just color connections, then there may be color re-connections too

Need tracers …


Underlying Event and ColorUnderlying Event and Color► The colour flow determines the hadronizing string topology

• Each MPI, even when soft, is a color spark

• Final distributions crucially depend on color space

Need tracers …

Note: this just color connections, then there may be color re-connections too


Underlying Event and Color 2Underlying Event and Color 2► Min-bias data at Tevatron and RHIC showed a surprise

• Charged particle pT spectra were highly correlated with event multiplicity: not expected

• For his ‘Tune A’, Rick Field noted that a high correlation in color space between the interactions could account for the behavior

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

• Virtually all ‘tunes’ now employ these more ‘extreme’ correlations

But existing models too crude to access detailed physics

What is their origin? Why are they needed?

Tevatron Run IIPythia 6.2 Min-bias <pT>(Nch)

Tune

A

old default

CentralLarge UE

Peripheral Small UE

Non-perturbative <pT> component in string fragmentation (LEP value)

Not only more (charged particles), but each one is harder

Diff

ract

ive?

Successful models: string interactions (area law)PS & D. Wicke : EPJC52(2007)133 ;

J. Rathsman : PLB452(1999)364

SO: the hadron-level pT spectra depend non-trivially on UE model.

The parton-level ones do not.

frag. corr. depends on UE (but levels off const for hard triggers?)


Theory UncertaintiesTheory Uncertainties► Large uncertainties need more than just ‘central’ tunes

• Similar to PDFs Need MCs with uncertainty bands

► Perugia Tunes• Begin to address this issue small set of systematically different tunes

320 Perugia 0 : Central CTEQ5L Tune Also includes 2009 LEP fragmentation tunes by Professor Group (Bowler, etc.)

321 Perugia HARD : harder ISR/FSR, less non-pert. αS(0.5pT)CMW, PARP(67)=4, PARP(71)=4, larger ΛFSR, higher MPI cutoff, prim kT = 1.0

GeV 322 Perugia SOFT : softer ISR/FSR, more non-pert.

αS(sqrt(2)pT)MSbar, PARP(67)=0.5, PARP(71)=1, smaller ΛFSR, lower MPI cutoff 323 Perugia 3 : different ISR/MI balance different energy scaling 324 Perugia NOCR : best tune without color reconnections 325 Perugia LO* : LO* has more glue, so harder MPI

Higher MPI cutoff, αS(sqrt(2)pT)CMW

326 Perugia 6 : CTEQ6L1 has different glue different scaling

• Obviously not the last word Using a few main model parameters as substitutes for eigenvectors

• Note: one could imagine some well-motivated further variations E.g., a tune weighting B fragmentation higher, to be used for B physics?


Perugia Tunes: Min-BiasPerugia Tunes: Min-Bias► Huge model building and tuning efforts by many groups (Herwig, Professor, Pythia, Sherpa, … )

• Summarized at a recent workshop on MPI in Perugia (Oct 2008)

• For Pythia (PYTUNE), 6.4.20 now out “Perugia” and “Professor” tunes

• Scaling to LHC much better constrained, HARD/SOFT, + CTEQ6, LO* TeV-1960, TeV-1800, TeV-630, (UA5-900, UA5-546, UA5-200)



Drell-YanDrell-Yan► Both the CDF and D0 analyses have been included

• NB: Very tricky point: photon bremsstrahlung! Need to make sure corrections are done (and documented) in an “MC-friendly” way


Extrapolations to 10 TeV Extrapolations to 10 TeV (yes, I know…)(yes, I know…)


► Useful to get a first-order idea of uncertainties

• Encourage tuning groups to do systematic MIN/MAX variations along these lines (not necessarily exactly as done here)

As with all kinds of uncertainties, can be misleading. Important to get effort started.

Compare with PDF uncertainties: still on a learning curve. Good thing they started trying to develop a systematic approach already some years ago.


Pythia 8 – Tune 1Pythia 8 – Tune 1► First complete tune of Pythia 8

• Tune to LEP data by professor group, then by hand to Tevatron + UA5 data, roughly same procedure as for Perugia tunes

In fact, only minor readjustments were needed

For the parameters (for Pythia 8.125), just ask Torbjörn or me.

Will be included with next Pythia-8 release

theory models of hadron collisions

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