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Towards Precision Quantum Chromodynamics

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Overview Perturbative expansion for some observable J, ds = Sm=0dsm ; dsm= dPm|M|2d ... power showers violate factorization ... Hybrid parton/dipole ... – PowerPoint PPT presentation

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Title: Towards Precision Quantum Chromodynamics


1
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
2
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

3
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!
4
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
5
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?

6
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

7
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.

8
Whats what?
Example generic radiation diagram
e
Diverges for collinear and soft radiation!
a
c
f
X
d
b
9
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
10
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'

11
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
12
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
13
New Approaches Why Bother?
14
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?

15
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

16
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
17
The VINCIA code
Illustration with quarks, sorry
1
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
18
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
19
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
20
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
21
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 ?

22
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?

23
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
24
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
25
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!
26
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
27
(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
28
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
29
(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
30
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?

31
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?

32
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
33
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?
34
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)
35
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.

36
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
37
(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
38
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?
39
(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

40
(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
41
More Supersymmetry uLuL
Other sea-dominated initial states exhibit same
behaviour as gg
42
More SUSY uLuL
ME Divergence much milder than for gg !
Possible cause qq-initiated valence-dominated
initial state ? less radiation.
43
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

44
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.
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