Copenhagen, Apr 28 2008 QCD Phenomenology at Hadron Colliders Peter Skands CERN TH / Fermilab

Copenhagen, Apr 28 2008

QCD Phenomenology at Hadron Colliders

Peter Skands

CERN TH / Fermilab

QCD Phenomenology at Hadron Colliders - 2Peter Skands

May 2008

OverviewOverview► Introduction

• Calculating Collider Observables

► The LHC from the Ultraviolet to the Infrared

• Bremsstrahlung• Hard jets

• Towards extremely high precision: a new proposal

• The structure of the Underlying Event• What “structure” ? What to do about it?

• Hadronization and All That • Stringy uncertainties

• QCD and Dark Matter: an example

Disclaimer: discussion of hadron collisions in full, gory detail not possible in 1 hour focus on central concepts and current uncertainties


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

• Example:

QQuantumuantumCChromohromoDDynamicsynamics

Reality is more complicated

High transverse-momentum interaction


Event GeneratorsEvent Generators

► Generator philosophy:

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

1. Parton Showers 2. Hadronisation3. The Underlying Event

1. Soft/Collinear Logarithms2. Power Corrections3. All of the above (+ more?)

roughlyroughly

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

Asking for fully exclusive events is asking for quite a lot …


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

Soft Jets and Jet StructureSoft/collinear radiation (brems), underlying event (multiple perturbative 22 interactions + … ?), semi-hard brems jets, …

Resonance Masses…

Hard Jet TailHigh-pT jets at large angles

& W

idths

sInclusive

Exclusive

Hadron Decays

Collider Energy ScalesCollider Energy Scales

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

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

• QE : Evolution(s)


TThehe BBottomottom LLineine

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

Establish comprehensive understanding of uncertainties

Improve and extend systematically

Non-perturbative effects

don’t care whether we know how to calculate them

FO DGLAP

BFKL

HQET

χPT


Problem 1: bremsstrahlung corrections are singular for soft/collinear configurations spoils fixed-order truncation

e+e- 3 jets

BremsstrahlungBremsstrahlung


► Supersymmetric particles: pair production

• + up to two explicit extra QCD bremsstrahlung jets• Each emission factor of the strong coupling naively factor 0.1 per jet

• For this example, we take MSUSY ~ 600 GeV

• Collider Energy = 14 TeV

• 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 @ LHCBremsstrahlung Example: SUSY @ LHC

FIXED ORDER pQCD

inclusive X + 1 “jet”

inclusive X + 2 “jets”

LHC - sps1a - m~600 GeV Plehn, Rainwater, Skands PLB645(2007)217

(Computed with SUSY-MadGraph)


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


► But it’s not a parton shower, not yet an “evolution”

• What’s the total cross section we would calculate from this?

• σX;tot = int(dσX) + int(dσX+1) + int(dσX+2) + ...

Probability not conserved, events “multiply” with nasty singularities! Just an approximation of a sum of trees.

But wait, what happened to the virtual corrections? KLN?

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;PS = 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, Q in and Qfin = QF;ME and Qhad

► σX;PS = int(dσX) - int(dσX+1) - int(dσX+2) + ...

= int(dσX) EXP[ - int(α 2 sab /(sa1s1b) dsa1 ds1b ) ]

dσX

α sab

saisibdσX+1 dσ

X+2

dσX+2

Given a jet definition, an

event has either 0, 1, 2, or … jets

“DLA”


Perturbative EvolutionPerturbative Evolution

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

• Defined in terms of Δ(t1,t2) – The integrated probability the system does not change state between t1 and t2 (Sudakov)

Pure Shower (all orders)

wX : |MX|2

S : Evolution operator

{p} : momenta

“X + nothing” “X+something”

A: splitting function

•S unitary total (inclusive) σ unchanged, •only shapes are predicted (i.e., also σ after shape-dependent cuts)


Constructing Parton ShowersConstructing Parton Showers► The final answer will depend on:

• The choice of evolution “time”

• The splitting functions (finite terms not fixed)

• The phase space map ( dΦn+1/dΦn )

• The renormalization scheme (argument of αs)

• The infrared cutoff contour (hadronization cutoff)

► They are all “unphysical”, in the same sense as QFactorizaton, etc.

• At strict “Leading Log”, any choice is equally good

• However, 20 years of parton showers have taught us: many NLL effects can be (approximately) absorbed by judicious choices

• Effectively, precision is much better than strict LL, but still not formally NLL

• E.g., (E,p) cons., “angular ordering”, using pT as scale in αs, with ΛMS ΛMC, …

Clever choices good for process-independent things, but what about the process-dependent bits? showers + matching to matrix elements


Some Holy GrailsSome Holy Grails► Matching to first order matrix elements + parton showers ~ done

• 1st order : (X+1)tree-level PYTHIA, HERWIG; + X1-loop : MC@NLO, POWHEG

• Multi-leg : (X+1,2,…)tree-level CKKW, MLM, … (but still no nontrivial loop information)

► Simultaneous 1-loop and multi-leg matching : not yet done

• 1st order : X1-Loop + (X+ 1,2,…)tree-level + (X + ∞)leading-log

• 2nd order : (X+1)1-Loop + (X + 1,2,…)tree-level + (X + ∞)leading-log

► Showers that systematically resum subleading singularities : not yet done

• Leading-Log Next-to-Leading-Log … ?

• Leading-Colour Next-to-Leading Colour ? Unpolarized Polarized ? (Herwig)

► Solving any of these would be highly desirable

• Solve all of them ?

• X2-Loop + (X+1,…?)1-loop + (X + 1,2,…)tree-level + (X + ∞)NLL + string-fragmentation

• + reliable uncertainty bands


Parton ShowersParton Showers► The final answer depends on:

• The choice of evolution “time”

• The splitting functions (finite/subleading terms not fixed)

• The phase space map ( dΦn+1/dΦn )

• The renormalization scheme (argument of αs)

• The infrared cutoff contour (hadronization cutoff)

► Step 1, Quantify uncertainty: vary all of these (within reasonable limits)

► Step 2, Systematically improve: Understand the importance of each and how it is canceled by

• Matching to fixed order matrix elements, at LO, NLO, NNLO, …

• Higher logarithms, subleading color, etc, are included

► Step 3, Write a generator: Make the above explicit (while still tractable) in a Markov Chain context matched parton shower MC algorithm


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:

• 3 different shower evolution variables:• pT-ordering (= ARIADNE ~ PYTHIA 8)

• Dipole-mass-ordering (~ but not = PYTHIA 6, SHERPA)

• Thrust-ordering (3-parton Thrust)

• For each: an infinite family of antenna functions • Laurent series in branching invariants with arbitrary finite terms

• Shower cutoff contour: independent of evolution variable IR factorization “universal”

• Several different choices for αs (evolution scale, pT, mother antenna mass, 2-loop, …)

• Phase space mappings: 2 different choices implemented • Antenna-like (ARIADNE angle) or Parton-shower-like: Emitter + longitudinal Recoiler

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

a

b

r

VIRTUAL NUMERICAL COLLIDER WITH INTERLEAVED ANTENNAE

Giele, Kosower, PS : hep-ph/0707.3652 + Les Houches 2007


Dipole-Antenna FunctionsDipole-Antenna Functions► Starting point: “GGG” antenna functions, e.g., ggggg:

► Generalize to arbitrary double Laurent series:

Can make shower systematically “softer” or “harder”

• Will see later how this variation is explicitly canceled by matching

quantification of uncertainty

quantification of improvement by matching

yar = sar / si

si = invariant mass of i’th dipole-antenna

Gehrmann-De Ridder, Gehrmann, Glover, JHEP 09 (2005) 056

Singular parts fixed, finite terms arbitrary

Frederix, Giele, Kosower, PS : Les Houches NLM, arxiv:0803.0494


Tree-level matching to X+1Tree-level matching to X+11. Expand parton shower to 1st order (real radiation term)

2. Matrix Element (Tree-level X+1 ; above thad)

Matching Term (= correction events to be added)

variations in finite terms (or dead regions) in Ai canceled (at this order)

• (If A too hard, correction can become negative negative weights)

Inverse phase space map ~ clustering

Giele, Kosower, PS : hep-ph/0707.3652


Matching by Reweighted ShowersMatching by Reweighted Showers

► Go back to original shower definition

► Possible to modify S to expand to the “correct” matrix elements ?

Pure Shower (all orders)

wX : |MX|2

S : Evolution operator

{p} : momenta

Sjöstrand, Bengtsson : Nucl.Phys.B289(1987)810; Phys.Lett.B185(1987)435

Norrbin, Sjöstrand : Nucl.Phys.B603(2001)2971st order: yes

Generate an over-estimating (trial) branching

Reweight it by vetoing it with the probability

But 2nd and beyond difficult due to lack of clean PS expansion

w>0 as long as |M|2 > 0


Towards an NNLO + NLL MCTowards an NNLO + NLL MC► Basic idea: extend reweigthing to 2nd order

• 23 tree-level antennae enough to reach NLO

• 23 one-loop + 24 tree-level antennae NNLO

► And exponentiate it

• Exponentiating 23 (dipole-antenna showers) (N)LL

• Complete NNLO captures the singularity structure up to (N)NLL

• So a shower incorporating all these pieces exactly should be able to• Reach NLL resummation, with a good approximation to NNLL;

• + exact matching up to NNLO should be possible

• Start small, do it for Z decay first (if you can’t do Z, you can’t do anything)


224 Matching 4 Matching by reweightingby reweighting

► Starting point:

• LL shower w/ large coupling and large finite terms to generate “trial” branchings (“sufficiently” large to over-estimate the full ME).

• Accept branching [i] with a probability

► Each point in Z4 phase space then receives a contribution

• Also need to take into account ordering cancellation of dependence

1st order matching term (à la Sjöstrand-Bengtsson) 2nd order matching term (with 1st order subtracted)

(If you think this looks deceptively easy, you are right)


Tree-level 2Tree-level 23 + 23 + 24 in Action4 in Action► The unknown finite terms are a major source of uncertainty

• DGLAP has some, GGG have others, ARIADNE has yet others, etc…

• They are arbitrary (and in general process-dependent)

αs(MZ)=0.137,

μR=pT,

pThad = 0.5 GeV

Varying finite terms only

with

First example of a parton shower including second-order corrections


LEP ComparisonsLEP Comparisons

Planning public release this summer, then on to hadrons


The Structure of the Underlying EventThe Structure of the Underlying Event


► 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 pairwise balancing minijets (‘lumpiness’) in the underlying event

► Normally omitted in explicit perturbative expansion

► + 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


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

dependenceMoral:

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


The ‘New’ ModelThe ‘New’ Model

Sjöstrand, Skands : JHEP03(2004)053, EPJC39(2005)129multipartonPDFs derivedfrom sum rules

Beam remnantsFermi motion / primordial kT

Fixed ordermatrix elements

parton shower(matched tofurther matrixelements)

perturbative “intertwining”?

► Parton Showers resum divergent emission cross sections

► Multiple interactions “resum” divergent interaction cross sections

A “complete” model for hadron collisions

Also note new Herwig++ model March 2008: Bahr, Gieseke, Seymour; arXiv:0803.3633


Hadronization and All ThatHadronization and All That

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

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


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

• What is their origin? Why are they needed?

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


► 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 (else) is RHIC, Tevatron telling us?

• Implications for precision measurements:Top mass? 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

Existing models only for WW a new toy model for all final states: colour annealingAttempts to minimize total area of strings in space-time

• Improves description of minimum-bias collisionsSkands, Wicke EPJC52(2007)133 ;

Preliminary finding Delta(mtop) ~ 0.5 GeVNow being studied by Tevatron top mass groups


WIMP

(QCD and Dark Matter: an example)(QCD and Dark Matter: an example)

► Imagine the galaxy is filled with dark matter zipping around at a few hundred km/s

• Look for elastic interactions with nuclei CDMS

• phonon detectors coupled to arrays of cryogenic (0.02 K) germanium and silicon crystals

► In MSSM, dominated by heavy Higgs exchange

Relation between CDMS Dark Matter search and Tevatron MSSM Higgs search

Need to know strange and gluon content of proton under elastic scattering: factor 2 uncertainty in our study

• Less important for discovery / exclusion, but would be significant for subsequent precision studies

Carena, Hooper, Skands PRL97 (2006) 051801

LEP excl

CD

MS

200

6 ex

clC

DM

S 2

007

proj

What does this have to do with colliders and QCD ?


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


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

an “inclusive” sample on which we could evaluate any observable, whether it is sensitive or not to extra hard jets, or to soft radiation


A ProblemA Problem

►How to do it?

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

emissions pT1 >> pT2 >> pT3 ...

• Unknown contributions from higher logarithmic orders, subleading colors, …

• Compute emission rates with matrix elements (ME)?• 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

• Unknown contributions from higher fixed orders


A (Stupid) SolutionA (Stupid) Solution► Combine different starting multiplicites

inclusive sample?

► In practice – 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


Double CountingDouble Counting

► 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• Is it the “LO” cross section?

• Is it the “LO” cross section plus the integral over [X + jet] ?

• What about “complete orders” and KLN ?

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

Documents

Copenhagen, Apr 28 2008 QCD Phenomenology at Hadron Colliders Peter Skands CERN TH / Fermilab