Towards Precision Models of Collider Physics

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Towards Precision Models of Collider Physics
Harvard U, Mar 17 2009
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QuantumChromoDynamics

• Main Tool Matrix Elements calculated in
  fixed-order perturbative quantum field theory
• Example

High transverse-momentum interaction
Reality is more complicated
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Particle Production

• Starting point matrix element parton shower
• hard parton-parton scattering
• (normally 2?2 in MC)
• bremsstrahlung associated with it
• ? 2?n in (improved) LL approximation

ISR
FSR

FSR

• But hadrons are not elementary
• QCD diverges at low pT
• ? multiple perturbative parton-parton collisions

QF
QF gtgt ?QCD
e.g. 4?4, 3? 3, 3?2

• No factorization theorem
• Herwig, Pythia, Sherpa MPI models

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Particle Production
Stuff at QF ?QCD
QF gtgt ?QCD MEISR/FSR perturbative MPI

• 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?

ISR
FSR

FSR
QF
Need-to-know issues for IR sensitive quantities
(e.g., Nch)
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Factorization, Infrared Safety, and Unitarity

• Do we really need to calculate all of this?

• These Things
• Are Your Friends
• IR Safety guarantees non-perturbative (NP)
  corrections suppressed by powers of NP scale
• Factorization allows you to sum inclusively
  over junk you dont know how to calculate
• Unitarity allows you to estimate things you
  dont know from things you know (e.g., loop
  singularities - tree ones P(fragmentation)
  1, )

Hadron Decays
Non-perturbative hadronisation, color
reconnections, beam remnants, strings,
non-perturbative fragmentation functions,
charged/neutral ratio, baryons, strangeness...
Soft Jets and Jet Structure Bremsstrahlung,
underlying event (multiple perturbative parton
interactions more?), semi-hard brems jets, jet
broadening,
Exclusive
Width
My Resonance Mass
Hard Jet Tail High-pT jets at large angles
Inclusive
s

• Un-Physical Scales
• QF , QR Factorization(s) Renormalization(s)
• QE Evolution(s)

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Three Ways To High Precision
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The Way of the Chicken

• Who needs QCD? Ill 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 didnt solve
  QCD

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The Way of the Fox

• Ill 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

FASTJET
Cacciari, Salam, Soyez JHEP 0804(2008)063
Cone ? anti-kT IR safe cone
Plehn, Rainwater, PS PLB645(2007)217
Plehn, Tait 0810.2919 hep-ph
Alwall, de Visscher, Maltoni JHEP 0902(2009)017
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Now Hadronize This
Simulation from D. B. Leinweber, hep-lat/0004025
gluon action density 2.4 x 2.4 x 3.6 fm
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The 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. Matching
3. Hadronisation
4. The Underlying Event

1. Soft/Collinear Logarithms
2. Finite Terms, K-factors
3. Power Corrections (more if not IR safe)
4. ?

roughly
( many other ingredients resonance decays, beam
remnants, Bose-Einstein, )
Asking for complete events is a tall order
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Solving QCD Part 1 Bremsstrahlung
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(Bremsstrahlung Example SUSY _at_ LHC)

• Naively, brems suppressed by as 0.1
• Truncate at fixed order LO, NLO,
• However, if ME gtgt 1 ? cant 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

Plehn, Rainwater, PS PLB645(2007)217
Plehn, Tait 0810.2919 hep-ph
Alwall, de Visscher, Maltoni JHEP 0902(2009)017
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Beyond Fixed Order 1
DLA
a sab saisib

• dsX
• dsX1 dsX g2 2 sab /(sa1s1b) dsa1ds1b
• dsX2 dsX1 g2 2 sab/(sa2s2b) dsa2ds2b
• dsX3 dsX2 g2 2 sab/(sa3s3b) dsa3ds3b

dsX
dsX1
dsX2
This is an approximation of inifinite-order
tree-level cross sections
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Beyond Fixed Order 2
DLA
a sab saisib

• dsX
• dsX1 dsX g2 2 sab /(sa1s1b) dsa1ds1b
• dsX2 dsX1 g2 2 sab/(sa2s2b) dsa2ds2b
• dsX3 dsX2 g2 2 sab/(sa3s3b) dsa3ds3b
• Unitarisation stot int(dsX)
• ? sXexcl sX - sX1 - sX2 -

dsX
dsX1
dsX2
Given a jet definition, an event has either 0,
1, 2, or jets

• 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 sX1(Q) sXincl sXexcl(Q)
• Later, some 3-jets migrate further, etc ? sXn(Q)
  sXincl ?sXmltnexcl(Q)
• This evolution takes place between two scales,
  Qin s and Qend Qhad
• sXtot Sum (sX0,1,2,3,excl ) int(dsX)

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LL Shower Monte Carlos

• Arbitrary Process X

O Observable p momenta wX MX2 or
KMX2 S Evolution operator
Leading Order
Pure Shower (all orders)

• Evolution Operator, S
• Evolves phase space point X ?
• As a function of time t1/Q
• Observable is evaluated on final configuration
• S unitary (as long as you never throw away or
  reweight an event)
• ? normalization of total (inclusive) s unchanged
  (sLO, sNLO, sNNLO, sexp, )
• Only shapes are predicted (i.e., also s 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

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S (for Shower)

• Evolution Operator, S (as a function of time
  t1/Q)
• Defined in terms of ?(t1,t2) (Sudakov)
• The integrated probability the system does not
  change state between t1 and t2
• NB Will not focus on where ? comes from here,
  just on how it expands
• Generating function for parton shower Markov
  Chain

A splitting function
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Controlling 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, dFn1/dFn )
• The renormalization scheme (vertex-by-vertex
  argument of as)
• 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)
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Matching ?

• A (Complete Idiots) Solution Combine
• XME showering
• X 1 jetME showering
• Doesnt work
• X shower is inclusive
• X1 shower is also inclusive

Run generator for X ( shower) Run generator for
X1 ( shower) Run generator for (
shower) Combine everything into one sample
What you get
What you want
Overlapping bins
One sample
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The Matching Game

• XME shower already contains sing X n
  jetME
• So we really just missed the non-LL bits, not the
  entire ME!
• Adding full X n jetME 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
  jetME Showerwn-1,2,3,..
• I call these matching approaches additive
• Herwig, CKKW, MLM, ARIADNE MC_at_NLO
• Solution 2 work out the ratio between PS and ME
• ? multiply shower kernels by that ratio (lt 1 if
  shower is an overestimate)
• Correction factor on nth emission Pn X n
  jetME / ShowerXn-1 jetME
• 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
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(NLO with Addition)
Multiplication at this order ? a, ß 0 (POWHEG
)

• First Order Shower expansion

PS
Unitarity of shower ? 3-parton real 2-parton
virtual

• 3-parton real correction (A3 M32/M22
  finite terms a, ß)

Finite terms cancel in 3-parton O

• 2-parton virtual correction (same example)

Finite terms cancel in 2-parton O (normalization)
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VINCIA
VIRTUAL NUMERICAL COLLIDER WITH INTERLEAVED
ANTENNAE
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

• 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
r
b
Giele, Kosower, PS PRD78(2008)014026 Les
Houches NLM 2007
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VINCIA in Action
VIRTUAL NUMERICAL COLLIDER WITH INTERLEAVED
ANTENNAE

• 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

Parton-level
Hadron-level
Giele, Kosower, PS PRD78(2008)014026 Les
Houches NLM 2007
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VINCIA in Action
VIRTUAL NUMERICAL COLLIDER WITH INTERLEAVED
ANTENNAE

• 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

Parton-level
Hadron-level
Giele, Kosower, PS PRD78(2008)014026 Les
Houches NLM 2007
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VINCIA in Action
VIRTUAL NUMERICAL COLLIDER WITH INTERLEAVED
ANTENNAE

• Can vary
• evolution variable, kinematics maps, radiation
  functions, renormalization choice, matching
  strategy (here just varying splitting functions)
• After 2nd order matching
• Non-pert part can be precisely constrained.
• (will need 2nd order logs as well for full
  variation)

Parton-level
Hadron-level
Giele, Kosower, PS PRD78(2008)014026 Les
Houches NLM 2007
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Solving QCD Part 2 Underlying Event
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Naming Conventions
See also Tevatron-for-LHC Report of the QCD
Working Group, hep-ph/0610012
Some freedom in how much particle production is
ascribed to each hard vs soft models

• Many nomenclatures being used.
• Not without ambiguity. I use

Qcut

ISR
FSR

FSR

Qcut
Multiple Parton Interactions (MPI)
Beam Remnants
Primary Interaction ( trigger)
Underlying Event (UE)
Note each is colored ? Not possible to separate
clearly at hadron level
Inelastic, non-diffractive
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(Why Perturbative MPI?)

• Analogue Resummation of multiple bremsstrahlung
  emissions
• Divergent s for one emission (X jet,
  fixed-order)
• Finite s for divergent number of jets (X jets,
  infinite-order)
• N(jets) rendered finite by finite perturbative
  resolution parton shower cutoff

Bahr, Butterworth, Seymour arXiv0806.2949 hep-p
h

• (Resummation of) Multiple Perturbative
  Interactions
• Divergent s for one interaction (fixed-order)
• Finite s for divergent number of interactions
  (infinite-order)
• N(jets) rendered finite by finite perturbative
  resolution

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The Interleaved Idea
New Pythia model
Fixed order matrix elements
Parton Showers (matched to further Matrix
Elements)

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

multiparton PDFs derived from sum rules
perturbative intertwining?
Beam remnants Fermi motion / primordial kT
Sjöstrand PS JHEP03(2004)053, EPJC39(2005)129
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Underlying Event and Color

• Min-bias data at Tevatron showed a surprise

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

• 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 II Pythia 6.2 Min-bias ltpTgt(Nch)
Tune A
Diffractive?
old default
Non-perturbative ltpTgt component in string
fragmentation (LEP value)
Central Large UE
Peripheral Small UE
Successful models string interactions (area law)
Solving QCD Part 3 Hadronization
PS D. Wicke EPJC52(2007)133 J. Rathsman
PLB452(1999)364
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Perugia 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 ct 10mm)
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Perugia 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 ct 10mm)
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Perugia Models
? Aspen Predictions
? lt 2.5 pT gt 0.5 GeV LHC 10 TeV
(min-bias) ltNtracksgt 12.5 1.5 LHC 14 TeV
(min-bias) ltNtracksgt 13.5 1.5
1.8 lt ? lt 4.9 pT gt 0.5 GeV LHC 10 TeV
(min-bias) ltNtracksgt 6.0 1.0 LHC 14 TeV
(min-bias) ltNtracksgt 6.5 1.0
(stable particle definition ct 10mm)
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Conclusions

• QCD Phenomenology is in a state of impressive
  activity
• Increasing move from educated guesses to
  precision science
• Better matrix element calculatorsintegrators (
  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

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Classic Example Number of tracks
UA5 _at_ 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)
• It is not possible to tune anything better than
  the underlying physics model allows
• Failure of a physically motivated model usually
  points to more physics (interesting)
• Failure of a fit not as interesting

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The 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
36
The 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