peter skands theoretical physics, fermilab harvard u, mar 17 2009 towards precision models of...

Peter SkandsTheoretical Physics, FermilabPeter SkandsTheoretical Physics, Fermilab

Harvard U, Mar 17 2009

Towards Precision Models of Towards Precision Models of Collider PhysicsCollider Physics

Towards Precision Models of Collider Physics - 2Peter Skands

► Main Tool: Matrix Elements calculated in fixed-order perturbative quantum field theory

• Example:

QQuantumuantumCChromohromoDDynamicsynamics

Reality is more complicated

High transverse-momentum interaction


► Starting point: matrix element + parton shower

• hard parton-parton scattering (normally 22 in MC)

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

►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

Particle ProductionParticle Production

Underlying Event has perturbative part!


Particle ProductionParticle Production

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?


Factorization, Infrared Safety, and UnitarityFactorization, Infrared Safety, and Unitarity

► Do we really need to calculate all of this?

Non-perturbativehadronisation, color reconnections, beam remnants, strings, non-perturbative fragmentation functions, charged/neutral ratio, baryons, strangeness...

Soft Jets and Jet StructureBremsstrahlung, underlying event (multiple perturbative parton interactions + more?), semi-hard brems jets, jet broadening, …

My Resonance Mass…

Hard Jet TailHigh-pT jets at large angles

& W

idth

sInclusive

Exclusive

Hadron Decays

+ Un-Physical Scales:+ Un-Physical Scales:

• QF , QR : Factorization(s) & Renormalization(s)

• QE : Evolution(s)

These ThingsThese ThingsAre Your FriendsAre Your Friends

•IR Safety: guarantees non-perturbative (NP) corrections suppressed by powers of NP scale

• Factorization: allows you to sum inclusively over junk you don’t know how to calculate

• Unitarity: allows you to estimate things you don’t know from things you know (e.g., loop singularities = - tree ones; P(fragmentation) = 1, …)

Peter SkandsTheoretical Physics, FermilabPeter SkandsTheoretical Physics, Fermilab

Three Ways To High PrecisionThree Ways To High Precision


The Way of the ChickenThe Way of the Chicken

►Who needs QCD? I’ll use leptons

• Sum inclusively over all QCD Leptons almost IR safe by definition

WIMP-type DM, Z’, EWSB may get some leptons

• Beams = hadrons for next decade (RHIC / Tevatron / LHC)

At least need well-understood PDFs

High precision = higher orders enter QCD

• Isolation indirect sensitivity to dirt

• Fakes indirect sensitivity to dirt

• Not everything gives leptons Need to be a lucky chicken …

►The unlucky chicken

• Put all its eggs in one basket and didn’t solve QCD

H1 MC

Summary of Hera-LHC Workshop: Parton DistributionsBall et al; Feltesse, Glazov, Radescu; 0901.2504 [hep-ph]


The Way of the FoxThe Way of the Fox

►I’ll use semi-inclusive observables

• Sum inclusively over the worst parts of QCD Still need to be friends with IR safety jet algs

FASTJET

• Beams = hadrons for next decade (RHIC / Tevatron / LHC)

Still need well-understood PDFs

High precision = more higher orders more QCD

• Large hierarchies (s, m1, m2, pTjet1, pTjet2, …) Careful ! Huge jet rate enhancements : perturbative series “blows up”

cannot truncate at any fixed order For 600 GeV particles, a 100 GeV jet can be “soft”

Use infinite-order approximations = parton showers Only “LL” not highly precise + only good when everything

is hierarchical Need to combine with explicit matrix elements matching

(more later) Still, non-factorizable + non-pert corrections set an

ultimate limit

Cacciari, Salam, Soyez: JHEP 0804(2008)063

Alwall, de Visscher, Maltoni: JHEP 0902(2009)017

Cone “anti-kT” ~ IR safe cone

FAST

JET

Plehn, Tait: 0810.2919 [hep-ph] Plehn, Rainwater, PS: PLB645(2007)217


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

decay

b from t decay

qbar from W

q from W

hadronization

?

q from W


The Way of the OxThe Way of the Ox

► Calculate Everything: solve QCD requires compromise

• Improve Born-level perturbation theory, by including the ‘most significant’ corrections complete events any observable you want

1. Parton Showers 2. Matching3. Hadronisation4. The Underlying Event

1. Soft/Collinear Logarithms2. Finite Terms, “K”-factors3. Power Corrections (more if not IR safe)

4. ?

roughlyroughly

(+ many other ingredients: resonance decays, beam remnants, Bose-Einstein, …)

Asking for complete events is a tall order …


““Solving QCD” Part 1: BremsstrahlungSolving QCD” Part 1: Bremsstrahlung


► Naively, brems suppressed by αs ~ 0.1

• Truncate at fixed order = LO, NLO, …

• However, if ME >> 1 can’t truncate!

► Example: SUSY pair production at 14 TeV, with MSUSY ~ 600 GeV

• Conclusion: 100 GeV can be “soft” at the LHC Matrix Element (fixed order) expansion breaks completely down at 50 GeV With decay jets of order 50 GeV, this is important to understand and control

(Bremsstrahlung Example: SUSY @ LHC)(Bremsstrahlung Example: SUSY @ LHC)

FIXED ORDER pQCD

inclusive X + 1 “jet”

inclusive X + 2 “jets”

LHC - sps1a - m~600 GeV

(Computed with SUSY-MadGraph)

Cross section for 1 or more 50-GeV jets larger than total σ, obviously non-sensical

Alwall, de Visscher, Maltoni: JHEP 0902(2009)017

Plehn, Tait: 0810.2919 [hep-ph] Plehn, Rainwater, PS: PLB645(2007)217


Beyond Fixed Order 1Beyond Fixed Order 1► dσX = …

► dσX+1 ~ dσX g2 2 sab /(sa1s1b) dsa1ds1b

► dσX+2 ~ dσX+1 g2 2 sab/(sa2s2b) dsa2ds2b


dσX

α sab

saisibdσX+1 dσ

X+2

dσX+2

This is an approximation of inifinite-order tree-level cross sections

“DLA”


Beyond Fixed Order 2Beyond Fixed Order 2► dσX = …

► dσX+1 ~ dσX g2 2 sab /(sa1s1b) dsa1ds1b



+ Unitarisation: σtot = int(dσX)

σX;excl = σX - σX+1 - σX+2 - …

► Interpretation: the structure evolves! (example: X = 2-jets)• Take a jet algorithm, with resolution measure “Q”, apply it to your events

• At a very crude resolution, you find that everything is 2-jets

• At finer resolutions some 2-jets migrate 3-jets = σX+1(Q) = σX;incl– σX;excl(Q)

• Later, some 3-jets migrate further, etc σX+n(Q) = σX;incl– ∑σX+m<n;excl(Q)

• This evolution takes place between two scales, Qin ~ s and Qend ~ Qhad

► σX;tot = Sum (σX+0,1,2,3,…;excl ) = int(dσX)

dσX

α sab

saisibdσX+1 dσ

X+2

dσX+2

Given a jet definition, an

event has either 0, 1, 2, or … jets

“DLA”


LL Shower Monte CarlosLL Shower Monte Carlos

► Evolution Operator, S

• “Evolves” phase space point: X … As a function of “time” t=1/Q

Observable is evaluated on final configuration

• S unitary (as long as you never throw away or reweight an event) normalization of total (inclusive) σ unchanged (σLO, σNLO, σNNLO, σexp, …)

Only shapes are predicted (i.e., also σ after shape-dependent cuts)

• Can expand S to any fixed order (for given observable) Can check agreement with ME Can do something about it if agreement less than perfect: reweight or add/subtract

► Arbitrary Process: X

Pure Shower (all orders)

O: Observable

{p} : momenta

wX = |MX|2 or K|MX|2

S : Evolution operator

Leading Order


““S” S” (for Shower)(for Shower)

► Evolution Operator, S (as a function of “time” t=1/Q)

• Defined in terms of Δ(t1,t2) (Sudakov)

The integrated probability the system does not change state between t1 and t2

NB: Will not focus on where Δ comes from here, just on how it expands

• = Generating function for parton shower Markov Chain

“X + nothing” “X+something”

A: splitting function


Controlling the CalculationControlling the Calculation► In the previous slide, you saw many dependencies on things not

traditionally found in matrix-element calculations:

► The final answer will depend on:

• The choice of shower evolution “time”

• The splitting functions (finite terms not fixed)

• The phase space map (“recoils”, dΦn+1/dΦn )

• The renormalization scheme (vertex-by-vertex argument of αs)

• The infrared cutoff contour (hadronization cutoff)

• + Matching prescription and “matching scales”

Variations

Comprehensive uncertainty estimates (showers with uncertainty bands)

Matching to MEs (& NnLL?)

Reduced Dependence (systematic reduction of uncertainty)


““Matching” ?Matching” ?► A (Complete Idiot’s) Solution – Combine

1. [X]ME + showering

2. [X + 1 jet]ME + showering

3. …

► Doesn’t work

• [X] + shower is inclusive

• [X+1] + shower is also inclusive

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

Run generator for X (+ shower)

Run generator for X+1 (+ shower)

Run generator for … (+ shower)

Combine everything into one sample

What you get

What you want

Overlapping “bins” One sample


The Matching GameThe Matching Game► [X]ME + shower already contains sing{ [X + n jet]ME }

• So we really just missed the non-LL bits, not the entire ME!

• Adding full [X + n jet]ME is overkill LL singular terms are double-counted

► Solution 1: work out the difference and correct by that amount add “shower-subtracted” matrix elements

• Correction events with weights : wn = [X + n jet]ME – Shower{wn-1,2,3,..}

• I call these matching approaches “additive” Herwig, CKKW, MLM, ARIADNE + MC@NLO

► Solution 2: work out the ratio between PS and ME multiply shower kernels by that ratio (< 1 if shower is an overestimate)

• Correction factor on n’th emission Pn = [X + n jet]ME / Shower{[X+n-1 jet]ME}

• I call these matching approaches “multiplicative” Pythia, POWHEG, VINCIA

Seymour, CPC90(1995)95+ many more recent …

Sjöstrand, Bengtsson : NPB289(1987)810; PLB185(1987)435+ one or two more recent …


(NLO with Addition)(NLO with Addition)► First Order Shower expansion

Unitarity of shower 3-parton real = ÷ 2-parton “virtual”

► 3-parton real correction (A3 = |M3|2/|M2|2 + finite terms; α, β)

► 2-parton virtual correction (same example)

PS

Finite terms cancel in 3-parton O

Finite terms cancel in 2-parton O (normalization)

Multiplication at this order α, β = 0 (POWHEG )


Gustafson, PLB175(1986)453; Lönnblad (ARIADNE), CPC71(1992)15.Azimov, Dokshitzer, Khoze, Troyan, PLB165B(1985)147 Kosower PRD57(1998)5410; Campbell,Cullen,Glover EPJC9(1999)245

VINCIAVINCIA

► Based on Dipole-Antennae Shower off color-connected pairs of partons

Plug-in to PYTHIA 8 (C++)

► So far:

• Choice of evolution time: pT-ordering

Dipole-mass-ordering

Thrust-ordering

• Splitting functions QCD + arbitrary finite terms (Taylor series)

• Phase space map Antenna-like or Parton-shower-like

• Renormalization scheme ( μR = {evolution scale, pT, s, 2-loop, …} )

• Infrared cutoff contour (hadronization cutoff) Same options as for evolution time, but independent of time universal choice

Dipoles (=Antennae, not CS) – a dual description of QCD

a

b

r

VIRTUAL NUMERICAL COLLIDER WITH INTERLEAVED ANTENNAE

Giele, Kosower, PS: PRD78(2008)014026 + Les Houches ‘NLM’ 2007


► Can vary • evolution variable, kinematics maps,

radiation functions, renormalization choice, matching strategy (here just varying splitting functions)

► At Pure LL, • can definitely see a non-perturbative

correction, but hard to precisely constrain it

VINCIA in ActionVINCIA in Action

Giele, Kosower, PS : PRD78(2008)014026 + Les Houches ‘NLM’ 2007


Par

ton-

leve

l

Hadron-level




► At Pure LL, • can definitely see a non-perturbative

correction, but hard to precisely constrain it




Par

ton-

leve

l

Hadron-level




► After 2nd order matching Non-pert part can be precisely

constrained.(will need 2nd order logs as well for full variation)




Coming soon to a pythia-8 near you

Par

ton-

leve

l

Hadron-level


““Solving QCD” Part 2: Underlying EventSolving QCD” Part 2: Underlying Event


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 (UE)

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

…

…

…

See also Tevatron-for-LHC Report of the QCD Working Group, hep-ph/0610012

Inelastic, non-diffractive

Multiple Parton Interactions (MPI)


(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

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

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


Underlying Event(note: interactions correllated in colour:

hadronization not independent)

Sjöstrand & PS : JHEP03(2004)053, EPJC39(2005)129

multipartonPDFs derivedfrom sum rules

Beam remnantsFermi motion / primordial kT

Fixed ordermatrix elements

Parton Showers(matched to further Matrix Elements)

perturbative “intertwining”?

The Interleaved IdeaThe Interleaved Idea

“New” Pythia model


Underlying Event and ColorUnderlying Event and Color► Min-bias data at Tevatron 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 different MPI partons 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

Solving QCD Part 3: Solving QCD Part 3: HadronizationHadronization


Perugia ModelsPerugia Models► 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)

(stable particle definition: cτ ≥ 10mm)


Perugia ModelsPerugia Models► 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)



Perugia ModelsPerugia Models

|η| < 2.5

pT > 0.5 GeV

LHC 10 TeV (min-bias)

<Ntracks> = 12.5 ± 1.5


<Ntracks> = 13.5 ± 1.5

1.8 < η < 4.9

pT > 0.5 GeV


<Ntracks> = 6.0 ± 1.0


<Ntracks> = 6.5 ± 1.0

Aspen Predictions:



ConclusionsConclusions► QCD Phenomenology is in a state of impressive activity

• Increasing move from educated guesses to precision science

• Better matrix element calculators+integrators (+ more user-friendly)

• Improved parton showers and improved matching to matrix elements

• Improved models for underlying events / minimum bias

• Upgrades of hadronization and decays

• Clearly motivated by dominance of LHC in the next decade(s) of HEP

► Early LHC Physics: theory

• At 14 TeV, everything is interesting

• Even if not a dinner Chez Maxim, rediscovering the Standard Model is much more than bread and butter

• Real possibilities for real surprises

• It is both essential, and I hope possible, to ensure timely discussions on “non-classified” data, such as min-bias, dijets, Drell-Yan, etc allow rapid improvements in QCD modeling (beyond simple retunes) after startup


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 dependence

Moral (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 physics (interesting)

3) Failure of a fit not as interesting


The Underlying Event and ColorThe Underlying 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 reconnections too

peter skands theoretical physics, fermilab harvard u, mar 17 2009 towards precision models of...

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