Towards Precision Quantum Chromodynamics

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Towards Precision Quantum Chromodynamics
HEP Seminar, Northwestern U, 10 April 2006
Real life is more complicated
Right now at the Tevatron
(Butch Cassidy and the Sundance Kid)
Peter Skands Theoretical Physics Dept
Fermi National Accelerator Laboratory
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Why Study Supernovae?

• They are the highest energy explosions in the
  universe
• They give us clues to other physics
• Type Ia large-distance standard candles
  distance/redshift relation
• Cosmological constant problem
• SN1987a
• ? neutrino physics,
• Cooling ? limits on light/weak particles
• much much more ...

PRICE Extremely Complicated Dynamics ? They are
now almost making them explode in simulations

• ? Much can be done even in complex environments.
• More if the complex dynamics can be understood
  and modeled

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Why Study Hadron Collisions?

• Tevatron (2 TeV, Fermilab, running)
• 4 8 fb-1 by LHC turn-on (1fb-1 on tape now)
• Large Z, W, and ttbar samples (including hard
  tails !)
• Huge QCD samples
• Always Potential discoveries...

pp at 200 GeV, 450GeV? ? help to measure energy
scaling!
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No Free Lunch

• Not all discovery channels produce dramatic
  signatures ? Need theoretical control of shapes,
  backgrounds, uncertainties, ...
• Scattering at LHC? rescaled scattering at
  Tevatron/RHIC.
• Aiming for percent level measurements, PDFs,
  luminosities, jets etc ? solid understanding of
  QCD in hadron collisions, both perturbative and
  non-perturbative, is crucial.

Lot of activity in recent years (NNLO, matching,
underlying event, error pdfs, ) ? towards
precision hadron collider physics but long way
still to go, lots of hard problems. Exciting!
thats why they pay us
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Overview

• Quantum Chromodynamics _at_ high energy
• Large pT Fixed order / shower matching with QCD
  antennae (the VINCIA code)
• Medium pT Interleaved hybrid parton/dipole
  showers and multiple parton-parton interactions
  (with PYTHIA)
• Small pT (if time) Underlying event and Colour
  Reconnections?

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Collider Energy Scales
Hadron Decays
Non-Perturbative hadronisation, colour
reconnections, beam remnants, NP fragmentation
functions, pion/proton, kaon/pion, ...
Soft Jets Jet Structure Multiple collinear/soft
emissions (initial and final state brems
radiation), Underlying Event (multiple
perturbative 2?2 interactions ?), semi-hard
separate brems jets
Exclusive
Widths
Resonance Masses
This has an S matrix expressible as a series in
gi, ln(Q1/Q2), ln(x), m-1, fp-1 , To do
precision physics Need to compute and/or
control all large terms.
Hard Jet Tail High-pT wide-angle jets
Inclusive
s

• UNPHYSICAL SCALES
• QF , QR Factorisation Renormalisation

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QuantumChromoDynamics

• Large coupling constant also means perturbative
  expansion tricky.

• To calculate higher perturbative orders, 2
  approaches
• Feynman Diagrams
• Complete matrix elements order by order ?
• Complexity rapidly increases unstable in
  soft/collinear region ?
• Resummation
• In certain limits, we are able to sum the entire
  perturbative series to infinite order ? e.g.
  parton showers
• Exact only in the relevant limits ?

• Known Gauge Group and Lagrangian
• Rich variety of dynamical phenomena, not least
  confinement.

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Whats what?
Example generic radiation diagram
e
Diverges for collinear and soft radiation!
a
c
f
X
d
b
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Do I need resummation?Example SUSY pair
production at LHCCross Sections for extra jets
in Fixed Order pQCD
T 600 GeV top quark
sps1a sparticle masses 600 GeV
LHC
FIXED ORDER pQCD
inclusive X 1 jet
inclusive X 2 jets
1) Extra 100 GeV jets are there 25-50 of the
time! 2) Extra 50 GeV jets ??? From this, we
only know a lot!
NB I am cheating a little here, should really
compare to (N)NLO, but known KNLO lt 2, so no
huge difference
Rainwater, Plehn PS hep-ph/0510144
hep-ph/0511306
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Parton Showers the basicsEssentially a simple
approximation ? infinite perturbative orders

• Today, basically 2 (dual) approaches
• Parton Showers (1?2, e.g. HERWIG, PYTHIA)
• and Dipole Showers (2?3, e.g. ARIADNE, VINCIA)

• Formally correct in collinear limit pT(i) ltlt
  pT(i-1), but (very) approximate for hard
  emissions (we return to this)
• Depends on various phenomenological params (color
  screening cutoff, renorm. scale choice, ...) ?
  compare to data ? best choice tune'

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To quantify ttbar and SUSY jets _at_ LHC
Solid Black Fixed Order (good
approximation at large pT) Dashed Conventional
showers (phase space cutoff at factorisation
scale) Solid green/blue Power showers (no
phase space cutoff, collinear approximation
applied over all of phase space)
Rainwater, Plehn PS hep-ph/0510144
hep-ph/0511306ALCPG0417
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Fixed Order Resummation
XAnything (e.g. ttbar) PSParton Shower
new approaches NagySoper (NLO-CKKW)
BauerSchwartz (SCET), GieleKosowerPS
(Antennae),
FEHiP NNLO (no PS) for pp? hh??? jets
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New Approaches Why Bother?
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Overview

• Quantum Chromodynamics _at_ high energy
• Large pT Fixed order / shower matching with QCD
  antennae (the VINCIA code)
• Medium pT Interleaved hybrid parton/dipole
  showers and multiple parton-parton interactions
  (with PYTHIA)
• Small pT (if time) Underlying event and Colour
  Reconnections?

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VINCIA Basic Sketch

• Perturbative expansion for some observable J,
  ds Sm0dsm dsm dPmM2d(J-J(k1,k2,,km))
• Assume
• We calculate some Matrix Elements ds0 , ds1 ,
  dsn (w or w/o loops)
• And we have some approximation dsn1 Tn? n1
  dsn ( parton shower)
• A best guess cross section for J is then
  ds ds0 ds1 dsn (1 Tn? n1 Tn?
  n1Tn1?n2 ) ? ds ds0 ds1
  dsn Sn Sn 1 Tn? n1 Sn1
• For this to make sense, the Tn? n1 have to at
  least contain the correct singularities (in order
  to correctly sum up all logarithmically enhanced
  terms), but they are otherwise arbitrary.
• Now reorder this series in a useful way

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Reordering Example H? gluons

• Assume we know H?gg and H?ggg. Then reorder
• ds dsgg dsggg Sggg Sggdsgg Sggg
  (dsggg Tgg?gggdsgg) Sggdsgg Sggg
  dcggg (generalises to n gluons)
• I.e shower off gg and subtracted ggg matrix
  element.
• Double counting avoided since singularities
  (shower) subtracted in dcggg .
• The shower kernels, Tgg, are precisely the
  singular subtraction terms used in HO
  perturbative calculations. As a basis we use
  Gehrman-Glover antennae

Use 1Sn-Tn?n1Sn1
Gehrmann-De Ridder, Gehrmann, Glover
PLB612(2005)49
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The VINCIA code
Illustration with quarks, sorry
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VIrtual Numerical Collider with Interfering
Antennae

• C code running gluon cascade
• Dipole (Antenna) shower with three different
  possible ordering variables
• RI(m12,m23) 4 s12s23/s p2TARIADNE
• RII(m12,m23) 2 min(s12,s23) m2PYTHIA
• RIII(m12,m23) 27 s12s23s31/s2 p2TPYTHIA

2
m12
PS
3
m23
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VINCIA First Branching

• Starting scale Q 20 GeV
• Stopping scale Qhad 1 GeV
• 1st order expansion in perturbation theory
• Axes yab m2ab / m2dipole

Type I pT2 More collinear
Type II m2 More soft
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VINCIA Matching kT jet rates

• Type I Sudakov ( pT evolution) with C00 -1,0,1

Matched 2-jet 3-jet ME PS matched Parton
Shower
2-jet only no matching standard Parton Shower
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What is the Difference?

• CKKW ( friends) in a nutshell
• Generate a n-jet Final State from n-jet
  (singular) ME
• Construct a fake PS history
• Apply Sudakov weights on each line in history ?
  from inclusive n-jet ME to exclusive n-jet (i.e.
  probability that n-jet remains n-jet above
  cutoff) ? gets rid of double counting when mixed
  with other MEs.
• Apply PS with no emissions above cutoff

• VINCIA in a nutshell
• Subtract PS singularities from n-jet ME (antenna
  subtraction)
• Generate a n-jet Final State from the subtracted
  (finite) ME.
• Apply PS with same antenna function ? Leading
  Logs resummed
• full NLO divergent part already there ? just
  include extra finite contribution in ds ds0(0)
  ds1(0) singds0(1) F(1)
• NNLO/NLL possible?
• Easy to vary shower assumption
• ? first parton shower with error band! (novelty
  in itself)

Gehrmann-De Ridder, Gehrmann, Glover
JHEP09(2005)056
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Conclusions VINCIA
writeup in progress

• Construction of VINCIA shower MC
• gluon shower MC
• based on LO, done! (type III still in progress)
• based on NLO, done! (but trivial so far)
• Theyre just fooling around with it (T. Becher)
• Including initial-state radiation
• Including quarks
• ? Hadron collider shower MC
• Higher orders NNLO, NLL ?

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Overview

• Quantum Chromodynamics _at_ high energy
• Large pT Fixed order / shower matching with QCD
  antennae (the VINCIA code)
• Medium pT Interleaved hybrid parton/dipole
  showers and multiple parton-parton interactions
  (with PYTHIA)
• Small pT (if time) Underlying event and Colour
  Reconnections?

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Pythia 6.3 pT-ordered showers
Note optional. Old ones still kept as default

• Completely rewritten parton showers (both ISR and
  FSR)

• Hybrid parton/dipole description
• Evolution in terms of partons
• Kinematics constructed inside dipoles assuming
  yet unbranched partons on shell
• Massive splitting functions for c, b, t,
  sparticles,
• Merged with 1st order matrix elements for h/?/Z/W
  production, and most EW, top, and MSSM decays

Sjöstrand PS Eur.Phys.J.C39(2005)129
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Additional Sources of Particle Production

• Discussed so far hard scattering, and
  bremsstrahlung associated with it.
• But hadrons are not elementary ? multiple
  parton-parton collisions are also possible.
• Remnants left from the incoming beams
• ? Underlying Event!

PS Im not talking about pile-up here
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A complete model should address

• How are the initiators and remnant partons
  correllated?
• in impact parameter?
• in flavour?
• in x (longitudinal momentum)?
• in kT (transverse momentum)?
• in colour (? string topologies!)
• What does the beam remnant look like?
• (How) are the showers correlated / intertwined?

If a model is simple, it is wrong!
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Interleaved evolution with Multiple Parton
Interactions
? PYTHIA 6.3

• Underlying Event
• (note interactions correllated in colour
  hadronization not independent)

Evolution Event Resolution
Sjöstrand PS Eur.Phys.J.C39(2005)129
JHEP03(2004)053
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(Multiple Parton InteractionsRemnant PDFs)
Used to select flavor and x for each
parton-parton interaction, and for the
interleaved evolution of the initial-state
shower. Dynamically evaluated.
Sjöstrand PS JHEP03(2004)053
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Multiple Parton InteractionsJunction
Hadronisation

• Several valence quarks kicked out ? string
  topology with explicit baryon number ? Junction
  hadronisation

Assume Y-shaped topology. Baryon number carried
by topology, rather than quarks
Montanet, Rossi, Veneziano Phys.Rep.63(1980)149
junction
Tstrings120 in Junction Rest Frame ? inverse
Junction Motion in LAB
Sjöstrand PS Nucl.Phys.B659(2003)243
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(Multiple InteractionsBaryon Number Flow)

• Test case (from high-pT) R-parity violating
  SUSY, neutralino decay ? 3 jets.
• (Compare with HERWIG BN flow not modeled)
• Junction Baryon follows string pull, slow in CM

Sjöstrand PS Nucl.Phys.B659(2003)243
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Multiple InteractionsA recent (almost true)
example

• Call from CDF at 2 a.m.
• Somethings up with W2jets!
• def electron, jets, and missing energy, all
  pTgt20 GeV
• For the SM, were using matched MADGRAPH
  PYTHIA Tune A (like you told us), but there is a
  discrepancy

Mock data

• In this case, they didnt ask us whether it was
  new physics (maybe next time), just fix the
  blessed Monte Carlo!
• OK so what would YOU do?

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Overview

• Quantum Chromodynamics _at_ high energy
• Large pT Fixed order / shower matching with QCD
  antennae (the VINCIA code)
• Medium pT Interleaved hybrid parton/dipole
  showers and multiple parton-parton interactions
  (with PYTHIA)
• Small pT (if time) Underlying event and Colour
  Reconnections?

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Underlying Event and Colour

• Fragmentation strongly depends on colour
  connections.
• Multiplicity in string fragmentation
  log(mstring)
• More strings ? more hadrons, but average pT stays
  same
• Flat ltpTgt(Nch) spectrum soft underlying event
• But if MPI interactions correlated in colour
• each scattering does not produce an independent
  string,
• average pT ? not flat.
• Central point multiplicity vs pT correllation
  probes colour correllations! (applicable in AA as
  well?)

Sjöstrand v Zijl Phys.Rev.D362019,1987 ?
Old Pythia model
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Colour Reconnections?
Sjöstrand, Khoze, Phys.Rev.Lett.72(1994)28 Z.
Phys.C62(1994)281 more

• Searched for at LEP (major source of W mass
  uncertainty) Most aggressive scenarios excluded,
  but effect still largely uncertain.
• Prompted by CDF data and Rick Fields Tune A to
  reconsider. What do we know?

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

• More prominent in hadron-hadron collisions? Top
  mass? QCD? AA?

A possible complete picture? MPI perturbative
2?2 interactions interleaved with perturbative
bremsstrahlung (parton showers) plus
non-perturbative interconnection effects? From
hadronic vacuum? More in AA? What is ltpTgt(Nch)
telling us? (string) hadronization
(Nielsen-Olesen vortex lines w/ linear Vkr)
still universal?
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Colour Annealing
Sandhoff PS, in Les Houches 05 SMH Proceedings

• Toy model at hadronisation time, all colour
  information from perturbative stage is lost
• String formation only determined by minimization
  of Lambda measure (string lengthlog(m)N)
• Problem closed gluon loops ? Version I and II.
• NB Present model ? local minimum, but
  more aggressive models still possible.

ttbar _at_ Tevatron area between W?qq jets.
hunting for string effects extremely challenging!
(Possible top mass shifts under investigation, w/
D. Wicke - D0)
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Conclusions Underlying Event

• Ever-present yet poorly understood part of QCD.
  How good are current physical models?
• Whats the relation between min-bias and
  underlying events? Are there color reconnections?
  Are they more prolific in hadron collisions? Are
  there other collective phenomena? Does this
  influence top mass etc?
• New generation of models address more detailed
  questions correllations, baryon flow, more?
• Energy Extrapolation largest uncertainty for LHC!
  RHIC pp collisions vital? ? energy scaling
• Increasing interest, both among theorists and
  experimenters.

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Coming Soon!
Recommended Reading Les Houches Guidebook to
Monte Carlo Generators for hadron collider
physics hep-ph/0403045 QCD () Event
Generators (DIS05 minireview) hep-ph/0507129
QCD radiation in the production of high s-hat
final states hep-ph/0511306 Colour Annealing
A Toy Model of Colour Reconnections in Les
Houches 05 SMH proceedings
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(To Quantify)

• Compare Fixed-Order Perturbation Theory
  (MadGraph), with 0, 1, and 2 explicit additional
  jets to
• 5 different shower approximations (Pythia)

• Wimpy Q2-ordered (PHASE SPACE LIMIT lt QF)
• Power Q2-ordered (PHASE SPACE LIMIT s)
• Tune A (Q2-ordered) (PHASE SPACE LIMIT QF)

• Wimpy pT-ordered (PHASE SPACE LIMIT QF)
• Power pT-ordered (PHASE SPACE LIMIT s)

NB Renormalisation scale in pT-ordred showers
also varied, between pT/2 and 3pT
Rainwater, Plehn PS hep-ph/0510144
hep-ph/0511306ALCPG0417
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New Parton Shower Why Bother?

• Each has pros and cons, e.g.
• In PYTHIA, ME merging is easy, and emissions are
  ordered in some measure of (Lorentz invariant)
  hardness, but angular ordering has to be imposed
  by hand, and kinematics are somewhat messy.
• HERWIG has inherent angular ordering, but also
  has the (in)famous dead zone problem, is not
  Lorentz invariant and has somewhat messy
  kinematics.
• ARIADNE has inherent angular ordering, simple
  kinematics, and is ordered in a (Lorentz
  Invariant) measure of hardness, but is primarily
  a tool for FSR, and g?qq is 'artificial' in
  dipole formalism.
• Finally, while these all describe LEP data well,
  none are perfect.

? Try combining the virtues of each of these
while avoiding the vices?
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(Intermezzo)

• This overestimation of the shower in the hard
  tail also occurs for all colour-singlet
  resonances (basis of ME merging in PYTHIA).
  Could it be universal?
• Radiation Matrix Elements A/t B/u C
• Shower kernels are nothing but the t?0 limit
  (but 1/u also generated).
• So the error made is the finite bit, C (and
  kinematics).
• ? it would be interesting if it were possible to
  investigate C in a process-independent way.
• (But wait, what about HERWIG?)
• Caveat power showers violate factorization! ?
  Interesting for phenomenology but not solid ground

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(ttbar jets _at_ Tevatron)
ds vs Jet pT

• Hard tails
• Power Showers (solid green blue) surprisingly
  good (naively expect collinear approximation to
  be worse!)
• Wimpy Showers (dashed) drop rapidly around top
  mass.

Soft peak logs large _at_ mtop/6 30 GeV ? fixed
order still good for 50 GeV jets (did not look
explicitly below 50 GeV yet)
Rainwater, Plehn PS hep-ph/0510144
hep-ph/0511306
Rainwater, Plehn PS hep-ph/0510144
hep-ph/0511306ALCPG0417
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More Supersymmetry uLuL
Other sea-dominated initial states exhibit same
behaviour as gg
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More SUSY uLuL
ME Divergence much milder than for gg !
Possible cause qq-initiated valence-dominated
initial state ? less radiation.
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Parton Showers the basics

• Today, basically 2 approaches to showers
• Parton Showers (e.g. HERWIG, PYTHIA)
• and Dipole Showers (e.g. ARIADNE).
• Essential Difference Ordering Variable

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Parton Showers the basics

• Today, basically 2 approaches to showers
• Parton Showers (e.g. HERWIG, PYTHIA)
• and Dipole Showers (e.g. ARIADNE).
• Another essential difference kinematics
  construction, i.e. how e.g. 2?2 kinematics are
  mapped to 2?3.