peter skands theoretical physics, fermilab towards precision models of collider physics high energy...

Peter SkandsTheoretical Physics, FermilabPeter SkandsTheoretical Physics, Fermilab

Towards Precision ModelsTowards Precision Modelsof Collider Physicsof Collider Physics

High Energy Physics Seminar, December 2008, Pittsburgh

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


► Main Tool: Matrix Elements calculated in fixed-order perturbative quantum field theory

• Example:

QQuantumuantumCChromohromoDDynamicsynamics

Reality is more complicated

High transverse-momentum interaction


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)


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


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 …


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


““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


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)


Colliders in the Ultraviolet – VINCIAColliders in the Ultraviolet – VINCIA

In collaboration with W. Giele, D. Kosower


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?


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


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


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


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


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 )


► 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


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 ?


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


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


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.


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


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


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


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


► 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




► At Pure LL, • can definitely see a non-perturbative

correction, but hard to precisely constrain it






► After 2nd order matching Non-pert part can be precisely

constrained.(will need 2nd order logs as well for full variation)




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, …)


Colliders in the Infrared – PYTHIAColliders in the Infrared – PYTHIA

In collaboration with T. Sjostrand, S. Mrenna


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


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?


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


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


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

peter skands theoretical physics, fermilab towards precision models of collider physics high energy...

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