Peter Skands Theoretical Physics, Fermilab Harvard U, Mar 17 2009 Towards Precision Towards Precision Models of Collider Models of Collider Physics Physics
Dec 19, 2015
Peter SkandsTheoretical Physics, FermilabPeter SkandsTheoretical Physics, Fermilab
Harvard U, Mar 17 2009
Towards Precision Models of Towards Precision Models of Collider PhysicsCollider Physics
Towards Precision Models of Collider Physics - 2Peter Skands
► Main Tool: Matrix Elements calculated in fixed-order perturbative quantum field theory
• Example:
QQuantumuantumCChromohromoDDynamicsynamics
Reality is more complicated
High transverse-momentum interaction
Towards Precision Models of Collider Physics - 3Peter Skands
► 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 collisionse.g. 44, 3 3, 32
QF >> ΛQCD
QF
QF
…22
ISR
ISR
FSR
FSR
22
ISR
ISR
FSR
FSR
►No factorization theorem
Herwig++, Pythia, Sherpa: MPI models
Particle ProductionParticle Production
Underlying Event has perturbative part!
Towards Precision Models of Collider Physics - 4Peter Skands
Particle ProductionParticle 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?
Towards Precision Models of Collider Physics - 5Peter Skands
Factorization, Infrared Safety, and UnitarityFactorization, Infrared Safety, and Unitarity
► Do we really need to calculate all of this?
Non-perturbativehadronisation, color reconnections, beam remnants, strings, non-perturbative fragmentation functions, charged/neutral ratio, baryons, strangeness...
Soft Jets and Jet StructureBremsstrahlung, underlying event (multiple perturbative parton interactions + more?), semi-hard brems jets, jet broadening, …
My Resonance Mass…
Hard Jet TailHigh-pT jets at large angles
& W
idth
sInclusive
Exclusive
Hadron Decays
+ Un-Physical Scales:+ Un-Physical Scales:
• QF , QR : Factorization(s) & Renormalization(s)
• QE : Evolution(s)
These ThingsThese ThingsAre Your FriendsAre Your Friends
•IR Safety: guarantees non-perturbative (NP) corrections suppressed by powers of NP scale
• Factorization: allows you to sum inclusively over junk you don’t know how to calculate
• Unitarity: allows you to estimate things you don’t know from things you know (e.g., loop singularities = - tree ones; P(fragmentation) = 1, …)
Peter SkandsTheoretical Physics, FermilabPeter SkandsTheoretical Physics, Fermilab
Three Ways To High PrecisionThree Ways To High Precision
Towards Precision Models of Collider Physics - 7Peter Skands
The Way of the ChickenThe Way of the Chicken
►Who needs QCD? I’ll 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 didn’t solve QCD
H1 MC
Summary of Hera-LHC Workshop: Parton DistributionsBall et al; Feltesse, Glazov, Radescu; 0901.2504 [hep-ph]
Towards Precision Models of Collider Physics - 8Peter Skands
The Way of the FoxThe Way of the Fox
►I’ll 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
Cacciari, Salam, Soyez: JHEP 0804(2008)063
Alwall, de Visscher, Maltoni: JHEP 0902(2009)017
Cone “anti-kT” ~ IR safe cone
FAST
JET
Plehn, Tait: 0810.2919 [hep-ph] Plehn, Rainwater, PS: PLB645(2007)217
Towards Precision Models of Collider Physics - 9Peter 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
decay
b from t decay
qbar from W
q from W
hadronization
?
q from W
Towards Precision Models of Collider Physics - 10Peter Skands
The Way of the OxThe 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. Matching3. Hadronisation4. The Underlying Event
1. Soft/Collinear Logarithms2. Finite Terms, “K”-factors3. Power Corrections (more if not IR safe)
4. ?
roughlyroughly
(+ many other ingredients: resonance decays, beam remnants, Bose-Einstein, …)
Asking for complete events is a tall order …
Towards Precision Models of Collider Physics - 11Peter Skands
““Solving QCD” Part 1: BremsstrahlungSolving QCD” Part 1: Bremsstrahlung
Towards Precision Models of Collider Physics - 12Peter Skands
► Naively, brems suppressed by αs ~ 0.1
• Truncate at fixed order = LO, NLO, …
• However, if ME >> 1 can’t 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
(Bremsstrahlung Example: SUSY @ LHC)(Bremsstrahlung Example: SUSY @ LHC)
FIXED ORDER pQCD
inclusive X + 1 “jet”
inclusive X + 2 “jets”
LHC - sps1a - m~600 GeV
(Computed with SUSY-MadGraph)
Cross section for 1 or more 50-GeV jets larger than total σ, obviously non-sensical
Alwall, de Visscher, Maltoni: JHEP 0902(2009)017
Plehn, Tait: 0810.2919 [hep-ph] Plehn, Rainwater, PS: PLB645(2007)217
Towards Precision Models of Collider Physics - 13Peter Skands
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
► dσX+3 ~ dσX+2 g2 2 sab/(sa3s3b) dsa3ds3b
dσX
α sab
saisibdσX+1 dσ
X+2
dσX+2
This is an approximation of inifinite-order tree-level cross sections
“DLA”
Towards Precision Models of Collider Physics - 14Peter Skands
Beyond Fixed Order 2Beyond Fixed Order 2► dσX = …
► dσX+1 ~ dσX g2 2 sab /(sa1s1b) dsa1ds1b
► dσX+2 ~ dσX+1 g2 2 sab/(sa2s2b) dsa2ds2b
► dσX+3 ~ dσX+2 g2 2 sab/(sa3s3b) dsa3ds3b
+ Unitarisation: σtot = int(dσX)
σX;excl = 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, Qin ~ s and Qend ~ Qhad
► σX;tot = Sum (σX+0,1,2,3,…;excl ) = int(dσX)
dσX
α sab
saisibdσX+1 dσ
X+2
dσX+2
Given a jet definition, an
event has either 0, 1, 2, or … jets
“DLA”
Towards Precision Models of Collider Physics - 15Peter 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
Towards Precision Models of Collider Physics - 16Peter 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
Towards Precision Models of Collider Physics - 17Peter Skands
Controlling the CalculationControlling 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”, dΦn+1/dΦn )
• The renormalization scheme (vertex-by-vertex argument of αs)
• 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)
Towards Precision Models of Collider Physics - 18Peter Skands
““Matching” ?Matching” ?► A (Complete Idiot’s) Solution – 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
Towards Precision Models of Collider Physics - 19Peter Skands
The Matching GameThe Matching Game► [X]ME + shower already contains sing{ [X + n jet]ME }
• So we really just missed the non-LL bits, not the entire ME!
• Adding full [X + n jet]ME 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 jet]ME – Shower{wn-1,2,3,..}
• I call these matching approaches “additive” Herwig, CKKW, MLM, ARIADNE + MC@NLO
► Solution 2: work out the ratio between PS and ME multiply shower kernels by that ratio (< 1 if shower is an overestimate)
• Correction factor on n’th emission Pn = [X + n jet]ME / Shower{[X+n-1 jet]ME}
• 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 …
Towards Precision Models of Collider Physics - 20Peter Skands
(NLO with Addition)(NLO 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 )
Towards Precision Models of Collider Physics - 21Peter 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:
• 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
b
r
VIRTUAL NUMERICAL COLLIDER WITH INTERLEAVED ANTENNAE
Giele, Kosower, PS: PRD78(2008)014026 + Les Houches ‘NLM’ 2007
Towards Precision Models of Collider Physics - 22Peter Skands
► 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
VINCIA in ActionVINCIA in Action
Giele, Kosower, PS : PRD78(2008)014026 + Les Houches ‘NLM’ 2007
VIRTUAL NUMERICAL COLLIDER WITH INTERLEAVED ANTENNAE
Par
ton-
leve
l
Hadron-level
Towards Precision Models of Collider Physics - 23Peter Skands
► 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
VINCIA in ActionVINCIA in Action
Giele, Kosower, PS : PRD78(2008)014026 + Les Houches ‘NLM’ 2007
VIRTUAL NUMERICAL COLLIDER WITH INTERLEAVED ANTENNAE
Par
ton-
leve
l
Hadron-level
Towards Precision Models of Collider Physics - 24Peter Skands
► 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)
VINCIA in ActionVINCIA in Action
Giele, Kosower, PS : PRD78(2008)014026 + Les Houches ‘NLM’ 2007
VIRTUAL NUMERICAL COLLIDER WITH INTERLEAVED ANTENNAE
Coming soon to a pythia-8 near you
Par
ton-
leve
l
Hadron-level
Towards Precision Models of Collider Physics - 25Peter Skands
““Solving QCD” Part 2: Underlying EventSolving QCD” Part 2: Underlying Event
Towards Precision Models of Collider Physics - 26Peter Skands
Naming ConventionsNaming Conventions► Many nomenclatures being used.
• Not without ambiguity. I use:
Qcut
Qcut
22
ISR
ISR
FSR
FSR
22
ISR
ISR
FSR
FSR
Primary Interaction
(~ trigger)Underlying Event (UE)
Beam Remnants
Note: each is colored Not possible to separate clearly at hadron level
Some freedom in how much particle production is ascribed to each:
“hard” vs “soft” models
…
…
…
See also Tevatron-for-LHC Report of the QCD Working Group, hep-ph/0610012
Inelastic, non-diffractive
Multiple Parton Interactions (MPI)
Towards Precision Models of Collider Physics - 27Peter Skands
(Why Perturbative MPI?)(Why Perturbative MPI?)► Analogue: Resummation of multiple bremsstrahlung emissions
• Divergent σ for one emission (X + jet, fixed-order)
Finite σ for divergent number of jets (X + jets, infinite-order) N(jets) rendered finite by finite perturbative resolution = parton shower cutoff
►(Resummation of) Multiple Perturbative Interactions
•Divergent σ for one interaction (fixed-order)
Finite σ for divergent number of interactions (infinite-order)
N(jets) rendered finite by finite perturbative resolution
= color-screening cutoff(Ecm-dependent, but large uncert)
Bahr, Butterworth, Seymour: arXiv:0806.2949 [hep-ph]
Towards Precision Models of Collider Physics - 28Peter Skands
Underlying Event(note: interactions correllated in colour:
hadronization not independent)
Sjöstrand & PS : JHEP03(2004)053, EPJC39(2005)129
multipartonPDFs derivedfrom sum rules
Beam remnantsFermi motion / primordial kT
Fixed ordermatrix elements
Parton Showers(matched to further Matrix Elements)
perturbative “intertwining”?
The Interleaved IdeaThe Interleaved Idea
“New” Pythia model
Towards Precision Models of Collider Physics - 29Peter Skands
Underlying Event and ColorUnderlying Event and Color► Min-bias data at Tevatron showed a surprise
• 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 IIPythia 6.2 Min-bias <pT>(Nch)
Tune
A
old default
CentralLarge UE
Peripheral Small UE
Non-perturbative <pT> component in string fragmentation (LEP value)
Not only more (charged particles), but each one is harder
Diff
ract
ive?
Successful models: string interactions (area law)PS & D. Wicke : EPJC52(2007)133 ; J. Rathsman : PLB452(1999)364
Solving QCD Part 3: Solving QCD Part 3: HadronizationHadronization
Towards Precision Models of Collider Physics - 30Peter Skands
Perugia ModelsPerugia 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: cτ ≥ 10mm)
Towards Precision Models of Collider Physics - 31Peter Skands
Perugia ModelsPerugia 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: cτ ≥ 10mm)
Towards Precision Models of Collider Physics - 32Peter Skands
Perugia ModelsPerugia Models
|η| < 2.5
pT > 0.5 GeV
LHC 10 TeV (min-bias)
<Ntracks> = 12.5 ± 1.5
LHC 14 TeV (min-bias)
<Ntracks> = 13.5 ± 1.5
1.8 < η < 4.9
pT > 0.5 GeV
LHC 10 TeV (min-bias)
<Ntracks> = 6.0 ± 1.0
LHC 14 TeV (min-bias)
<Ntracks> = 6.5 ± 1.0
Aspen Predictions:
(stable particle definition: cτ ≥ 10mm)
Towards Precision Models of Collider Physics - 33Peter Skands
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
Towards Precision Models of Collider Physics - 34Peter Skands
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 dependence
Moral (will return to the models later):
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 (interesting)
3) Failure of a fit not as interesting
Towards Precision Models of 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
Towards Precision Models of Collider Physics - 36Peter 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