Dr. Peter Skands Theoretical Physics Dept, Fermilab A Quantum Journey.
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Transcript of Peter Skands Theoretical Physics, Fermilab Towards Precision Models of Collider Physics High Energy...
![Page 1: Peter Skands Theoretical Physics, Fermilab Towards Precision Models of Collider Physics High Energy Physics Seminar, December 2008, Pittsburgh.](https://reader035.fdocuments.us/reader035/viewer/2022081603/5697bf761a28abf838c80b4e/html5/thumbnails/1.jpg)
Peter SkandsTheoretical Physics, FermilabPeter SkandsTheoretical Physics, Fermilab
Towards Precision ModelsTowards Precision Modelsof Collider Physicsof Collider Physics
High Energy Physics Seminar, December 2008, Pittsburgh
![Page 2: Peter Skands Theoretical Physics, Fermilab Towards Precision Models of Collider Physics High Energy Physics Seminar, December 2008, Pittsburgh.](https://reader035.fdocuments.us/reader035/viewer/2022081603/5697bf761a28abf838c80b4e/html5/thumbnails/2.jpg)
Precision Collider Physics - 2Peter Skands
Dec 2008
OverviewOverview► Introduction
• Calculating Collider Observables
► Colliders from the Ultraviolet to the Infrared
• VINCIA Hard jets
Towards extremely high precision: a new proposal
• Infrared Collider Physics What “structure”? What to do about it?
Hadronization and All That
Stringy uncertainties
Disclaimer: discussion of hadron collisions in full, gory detail not possible in 1 hour focus on central concepts and current uncertainties
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Precision Collider Physics - 3Peter Skands
► Main Tool: Matrix Elements calculated in fixed-order perturbative quantum field theory
• Example:
QQuantumuantumCChromohromoDDynamicsynamics
Reality is more complicated
High transverse-momentum interaction
![Page 4: Peter Skands Theoretical Physics, Fermilab Towards Precision Models of Collider Physics High Energy Physics Seminar, December 2008, Pittsburgh.](https://reader035.fdocuments.us/reader035/viewer/2022081603/5697bf761a28abf838c80b4e/html5/thumbnails/4.jpg)
Precision Collider Physics - 4Peter Skands
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)
![Page 5: Peter Skands Theoretical Physics, Fermilab Towards Precision Models of Collider Physics High Energy Physics Seminar, December 2008, Pittsburgh.](https://reader035.fdocuments.us/reader035/viewer/2022081603/5697bf761a28abf838c80b4e/html5/thumbnails/5.jpg)
Precision Collider Physics - 5Peter Skands
Fixed Order (all orders)
“Experimental” distribution of observable O in production of X:
k : legs ℓ : loops {p} : momenta
Monte Carlo at Fixed OrderMonte Carlo at Fixed Order
High-dimensional problem (phase space)
d≥5 Monte Carlo integration
Principal virtues
1. Stochastic error O(N-1/2) independent of dimension
2. Full (perturbative) quantum treatment at each order
3. (KLN theorem: finite answer at each (complete) order)
Note 1: For k larger than a few, need to be quite clever in phase space sampling
Note 2: For ℓ > 0, need to be careful in arranging for real-virtual cancellations
“Monte Carlo”: N. Metropolis, first Monte Carlo calculation on ENIAC (1948), basic idea goes back to Enrico Fermi
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Precision Collider Physics - 6Peter Skands
Event GeneratorsEvent Generators
► Generator philosophy:
• Improve Born-level perturbation theory, by including the ‘most significant’ corrections complete events
1. Parton Showers 2. Matching3. Hadronisation4. The Underlying Event
1. Soft/Collinear Logarithms2. Finite Terms, “K”-factors3. Power Corrections4. 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 …
![Page 7: Peter Skands Theoretical Physics, Fermilab Towards Precision Models of Collider Physics High Energy Physics Seminar, December 2008, Pittsburgh.](https://reader035.fdocuments.us/reader035/viewer/2022081603/5697bf761a28abf838c80b4e/html5/thumbnails/7.jpg)
Precision Collider Physics - 7Peter Skands
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
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Precision Collider Physics - 8Peter Skands
““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
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Precision Collider Physics - 9Peter Skands
Constructing LL ShowersConstructing LL Showers► 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 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)
Variations
Comprehensive uncertainty estimates (showers with uncertainty bands)
Matching
Reduced Dependence (systematic reduction of uncertainty)
![Page 10: Peter Skands Theoretical Physics, Fermilab Towards Precision Models of Collider Physics High Energy Physics Seminar, December 2008, Pittsburgh.](https://reader035.fdocuments.us/reader035/viewer/2022081603/5697bf761a28abf838c80b4e/html5/thumbnails/10.jpg)
Peter SkandsTheoretical Physics, FermilabPeter SkandsTheoretical Physics, Fermilab
Colliders in the Ultraviolet – VINCIAColliders in the Ultraviolet – VINCIA
In collaboration with W. Giele, D. Kosower
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Precision Collider Physics - 11Peter Skands
OverviewOverview
►Matching Fundamentals, Current recipes
• Multiplicative ~ reweighted/vetoed showers
• Additive ~ sliced and/or subtracted matrix elements
►Matching à la Vincia
• Properties of dipole-antenna showers
• Additive Matching VINCIA: Additive matching through second order
Multi-leg 1-loop matching?
Multiplicative Matching VINCIA: Multiplicative matching through second order and beyond
positive-weight NLL showers? NNLO matching?
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Precision Collider Physics - 12Peter Skands
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
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Precision Collider Physics - 13Peter Skands
Example: Jet RatesExample: Jet Rates► Splitting functions only defined up to non-singular terms (finite terms)
• Finite terms generally process-dependent impossible to “tune”
• Uncertainty in hard region already at first order
• Cascade down to produce uncontrolled tower of subleading logs
αs(MZ)=0.137,
μR=pT,
pThad = 0.5 GeV
Varying finite terms only
with
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Precision Collider Physics - 14Peter Skands
Constructing LL ShowersConstructing LL Showers► The final answer will depend on:
• The choice of evolution “time”
• The splitting functions (finite terms not fixed)
• The phase space map (“recoils”, 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 LL, any choice is equally good
• Some NLL effects can be (approximately) absorbed by judicious choices E.g., (E,p) cons., coherence, using pT as scale in αs, with ΛMS ΛMC, …
Effectively, precision is better than strict LL, but still not formally NLL
Variations
Comprehensive uncertainty estimates (showers with
uncertainty bands)
Clever choices fine (for process-independent things), can we do better? … + matching
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Precision Collider Physics - 15Peter Skands
Matching in a nutshellMatching in a nutshell► There are two fundamental approaches
• Additive
• Multiplicative
► Most current approaches based on addition, in one form or another
• Herwig (Seymour, 1995), but also CKKW, MLM, MC@NLO, ...
• In these approaches, you add event samples with different multiplicities Need separate ME samples for each multiplicity. Relative weights a priori unknown.
• The job is to construct weights for them, and modify/veto the showers off them, to avoid double counting of both logs and finite terms
► But you can also do it by multiplication
• Pythia (Sjöstrand, 1987): modify only the shower
• All events start as Born + reweight at each step. Using the shower as a weighted phase space generator only works for showers with NO DEAD ZONES
• The job is to construct reweighting coefficients Complicated shower expansions only first order so far Generalized to include 1-loop first-order POWHEG
Seymour, Comput.Phys.Commun.90(1995)95
Sjöstrand, Bengtsson : Nucl.Phys.B289(1987)810; Phys.Lett.B185(1987)435
Norrbin, Sjöstrand : Nucl.Phys.B603(2001)297
Massive Quarks
All combinations of colors and Lorentz structures
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Precision Collider Physics - 16Peter Skands
NLO with AdditionNLO 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 )
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Precision Collider Physics - 17Peter Skands
► Herwig
• In dead zone: Ai = 0 add events corresponding to unsubtracted |MX+1|
• Outside dead zone: reweighted à la Pythia Ai = |MX+1| no additive correction necessary
► CKKW and L-CKKW
• At this order identical to Herwig, with “dead zone” for kT > kTcut introduced by hand
► MC@NLO
• In dead zone: identical to Herwig
• Outside dead zone: AHerwig > |MX+1| wX+1 negative negative weights
► Pythia
• Ai = |MX+1| over all of phase space no additive correction necessary
► Powheg
• At this order identical to Pythia no negative weights
HE
RW
IG T
YP
EP
YT
HIA
TY
PE
Matching to X+1: Tree-levelMatching to X+1: Tree-level
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Precision Collider Physics - 18Peter Skands
Matching in VinciaMatching in Vincia► We are pursuing three strategies in parallel
• Addition (aka subtraction) Simplest & guaranteed to fill all of phase space (unsubtracted ME in dead regions)
But has generic negative weights and hard to exponentiate corrections
• Multiplication (aka reweighting) Guaranteed positive weights & “automatically” exponentiates path to NLL
Complicated, so 1-loop matching difficult beyond first order.
Only fills phase space populated by shower: dead zones problematic
• Hybrid Combine: simple expansions, full phase space, positive weights, and
exponentiation?
► Goal
• Multi-leg “plug-and-play” NLO + “improved”-LL shower Monte Carlo
• Including uncertainty bands (exploring uncontrolled terms)
• Extension to NNLO + NLL ?
![Page 19: Peter Skands Theoretical Physics, Fermilab Towards Precision Models of Collider Physics High Energy Physics Seminar, December 2008, Pittsburgh.](https://reader035.fdocuments.us/reader035/viewer/2022081603/5697bf761a28abf838c80b4e/html5/thumbnails/19.jpg)
Precision Collider Physics - 19Peter Skands
Second OrderSecond Order► Second Order Shower expansion for 4 partons (assuming first already matched)
min # of paths
AR pT + AR recoil
max # of paths
DZ
►Problem 1: dependence on evolution variable
• Shower is ordered t4 integration only up to t3
• 2, 1, or 0 allowed “paths”
• 0 = Dead Zone : not good for reweighting QE = pT(i,j,k) = mijmjk/mijk
QE = pT
GGG
AVG
Vincia
AVG
Vincia
MAX
Vincia
MIN
QE = pT
Everyone’s usual
nightmare of a parton
shower
0
1
2
3
![Page 20: Peter Skands Theoretical Physics, Fermilab Towards Precision Models of Collider Physics High Energy Physics Seminar, December 2008, Pittsburgh.](https://reader035.fdocuments.us/reader035/viewer/2022081603/5697bf761a28abf838c80b4e/html5/thumbnails/20.jpg)
Precision Collider Physics - 20Peter Skands
Second Order Second Order with Unordered Showerswith Unordered Showers
► For reweighting: allow power-suppressed “unordered” branchings
Vincia Uord
MIN
Vincia Uord
MAX
• Removes dead zone + better approx than fully unordered (Good initial guess better reweighting efficiency)
► Problem 2: leftover Subleading Logs
• There are still unsubtractred subleading divergences in the ME
GGG Uord
AVG
Vincia Uord
AVG
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Precision Collider Physics - 21Peter Skands
Leftover Subleading LogsLeftover Subleading Logs► Subtraction in Dead Zone
• ME completely unsubtracted in Dead Zone leftovers
► But also true in general: the shower is still formally LL everywhere
• NLL leftovers are unavoidable
• Additional sources: Subleading color, Polarization
► Beat them or join them?
• Beat them: not resummed brute force regulate with Theta (or smooth) function ~ CKKW “matching scale”
• Join them: absorb leftovers systematically in shower resummationBut looks like we would need polarized NLL-NLC showers … !
Could take some time …
In the meantime … do it by exponentiated matching
Note: more legs more logs, so ultimately will still need regulator. But try to postpone to NNLL level.
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Precision Collider Physics - 22Peter Skands
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 4-parton phase space then receives a contribution
Sjöstrand-Bengtsson term
2nd order matching term (with 1st order subtracted out)
(If you think this looks deceptively easy, you are right)
Note: to maintain positivity for subleading colour, need to match across 4 events, 2 representing one color ordering, and 2 for the other ordering
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Precision Collider Physics - 23Peter Skands
General 2General 2ndnd Order Order (& NLL Matching)(& NLL Matching)
► Include unitary shower (S) and non-unitary “K-factor” (K) corrections
• K: event weight modification (special case: add/subtract events) Non-unitary changes normalization (“K” factors)
Non-unitary does not modify Sudakov not resummed
Finite corrections can go here ( + regulated logs)
Only needs to be evaluated once per event
• S: branching probability modification Unitary does not modify normalization
Unitary modifies Sudakov resummed
All logs should be here
Needs to be evaluated once for every nested 24 branching (if NLL)
• Addition/Subtraction: S = 1, K ≠ 1
• Multiplication/Reweighting: S ≠ 1 K = 1
• Hybrid: S = logs K = the rest
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Precision Collider Physics - 24Peter Skands
The ZThe Z3 1-loop term3 1-loop term► Second order matching term for 3 partons
► Additive (S=1) Ordinary NLO subtraction + shower leftovers
• Shower off w2(V)
• “Coherence” term: difference between 2- and 3-parton (power-suppressed) evolution above QE3. Explicit QE-dependence cancellation.
• δα: Difference between alpha used in shower (μ = pT) and alpha used for matching Explicit scale choice cancellation
• Integral over w4(R) in IR region still contains NLL divergences regulate
• Logs not resummed, so remaining (NLL) logs in w3(R)
also need to be regulated
► Multiplicative : S = (1+…) Modified NLO subtraction + shower leftovers
• A*S contains all logs from tree-level w4(R) finite.
• Any remaining logs in w3(V) cancel against NNLO NLL resummation if put back in S
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Precision Collider Physics - 25Peter Skands
VINCIA in Action: Jet RatesVINCIA in Action: Jet Rates
αs(MZ)=0.137,
μR=pT,
pThad = 0.5 GeV
Varying finite terms only
with
► Splitting functions only defined up to non-singular terms (finite terms)
• Finite terms generally process-dependent impossible to “tune”
• Uncertainty in hard region already at first order
• Cascade down to produce uncontrolled tower of subleading logs
![Page 26: Peter Skands Theoretical Physics, Fermilab Towards Precision Models of Collider Physics High Energy Physics Seminar, December 2008, Pittsburgh.](https://reader035.fdocuments.us/reader035/viewer/2022081603/5697bf761a28abf838c80b4e/html5/thumbnails/26.jpg)
Precision Collider Physics - 26Peter Skands
► Can vary • evolution variable, kinematics maps,
radiation functions, renormalization choice, matching strategy (here just showing radiation 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
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Precision Collider Physics - 27Peter Skands
► Can vary • evolution variable, kinematics maps,
radiation functions, renormalization choice, matching strategy (here just showing radiation 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
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Precision Collider Physics - 28Peter Skands
► Can vary • evolution variable, kinematics maps,
radiation functions, renormalization choice, matching strategy (here just showing radiation functions)
► After 2nd order matching Non-pert part can be precisely
constrained.(will need 2nd order logs as well for full variation)
VINCIA in ActionVINCIA in Action
Giele, Kosower, PS : PRD78(2008)014026 + Les Houches ‘NLM’ 2007
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Precision Collider Physics - 29Peter Skands
The next big stepsThe next big steps► Z3 at one loop
• Opens multi-parton matching at 1 loop
• Required piece for NNLO matching
• If matching can be exponentiated, opens NLL showers
► Work in progress
• Write up complete framework for additive matching NLO Z3 and NNLO matching within reach
• Finish complete framework multiplicative matching … Complete NLL showers slightly further down the road
► Turn to the initial state, massive particles, other NLL effects (polarization, subleading color, unstable particles, …)
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Peter SkandsTheoretical Physics, FermilabPeter SkandsTheoretical Physics, Fermilab
Colliders in the Infrared – PYTHIAColliders in the Infrared – PYTHIA
In collaboration with T. Sjostrand, S. Mrenna
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Precision Collider Physics - 31Peter Skands
Particle ProductionParticle Production
► 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 collisions
►Normally omitted in ME/PS expansions
( ~ higher twists / powers / low-x)
But still perturbative, divergente.g. 44, 3 3, 32
Note:
Can take
QF >> ΛQCD
QF
QF
…22
ISR
ISR
FSR
FSR
22
ISR
ISR
FSR
FSR
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Precision Collider Physics - 32Peter Skands
Additional Sources of Particle ProductionAdditional Sources of Particle 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?
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Precision Collider Physics - 33Peter Skands
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
deca
y
b from
t d
ecay
qbar fro
m W
q from W
hadroniza
tion
?
q from W
![Page 34: Peter Skands Theoretical Physics, Fermilab Towards Precision Models of Collider Physics High Energy Physics Seminar, December 2008, Pittsburgh.](https://reader035.fdocuments.us/reader035/viewer/2022081603/5697bf761a28abf838c80b4e/html5/thumbnails/34.jpg)
Precision Collider Physics - 34Peter Skands
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
![Page 35: Peter Skands Theoretical Physics, Fermilab Towards Precision Models of Collider Physics High Energy Physics Seminar, December 2008, Pittsburgh.](https://reader035.fdocuments.us/reader035/viewer/2022081603/5697bf761a28abf838c80b4e/html5/thumbnails/35.jpg)
Precision Collider Physics - 35Peter Skands
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
![Page 36: Peter Skands Theoretical Physics, Fermilab Towards Precision Models of Collider Physics High Energy Physics Seminar, December 2008, Pittsburgh.](https://reader035.fdocuments.us/reader035/viewer/2022081603/5697bf761a28abf838c80b4e/html5/thumbnails/36.jpg)
Precision Collider Physics - 36Peter Skands
Future DirectionsFuture Directions► Monte Carlo problem
• Uncertainty on fixed orders and logs obscures clear view on hadronization and the underlying event
► So we just need …
• An NNLO + NLO multileg + NLL Monte Carlo (incl small-x logs), with uncertainty bands, please
► Then …
• We could see hadronization and UE clearly solid constraints
Energy Frontier
Inte
nsity
Fro
ntierThe Astro G
uys
Precision Frontier
The Tevatron and LHC data will be all the energy frontier data we’ll have for a long while
Anno 2018