Peter Skands Theoretical Physics, Fermilab Towards Precision Models of Collider Physics High Energy Physics Seminar, December 2008, Pittsburgh

Peter Skands Precision Collider Physics - 2 Dec 2008Overview ►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

Peter Skands Precision Collider Physics - 3 ►Main Tool: Matrix Elements calculated in fixed-order perturbative quantum field theory Example: Q uantum C hromo D ynamics Reality is more complicated High transverse- momentum interaction

Peter Skands Precision Collider Physics - 4 Non-perturbative hadronisation, colour reconnections, beam remnants, non-perturbative fragmentation functions, pion/proton ratio, kaon/pion ratio,... Soft Jets and Jet Structure Soft/collinear radiation (brems), underlying event (multiple perturbative 2  2 interactions + … ?), semi-hard brems jets, … Resonance Masses… Hard Jet Tail High-p T jets at large angles & Widths s Inclusive Exclusive Hadron Decays Collider Energy Scales + Un-Physical Scales: Q F, Q R : Factorization(s) & Renormalization(s) Q E : Evolution(s)

Peter Skands Precision Collider Physics - 5 Fixed Order (all orders) “Experimental” distribution of observable O in production of X : k : legsℓ : loops {p} : momenta Monte 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

Peter Skands Precision Collider Physics - 6 Event Generators ►Generator philosophy: Improve Born-level perturbation theory, by including the ‘most significant’ corrections  complete events 1.Parton Showers 2.Matching 3.Hadronisation 4.The Underlying Event 1.Soft/Collinear Logarithms 2.Finite Terms, “K”-factors 3.Power Corrections 4.All of the above (+ more?) roughly (+ many other ingredients: resonance decays, beam remnants, Bose-Einstein, …) Asking for fully exclusive events is asking for quite a lot …

Peter Skands Precision Collider Physics - 7 LL 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 ( σ LO, σ NLO, σ NNLO, σ exp, …)  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 w X = |M X | 2 or K|M X | 2 S : Evolution operator Leading Order

Peter Skands Precision Collider Physics - 8 “S” (for Shower) ►Evolution Operator, S (as a function of “time” t=1/Q ) Defined in terms of Δ(t 1,t 2 ) (Sudakov)  The integrated probability the system does not change state between t 1 and t 2  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

Peter Skands Precision Collider Physics - 9 Constructing 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”, dΦ n+1 /dΦ n ) The renormalization scheme (vertex-by-vertex argument of α s ) The infrared cutoff contour (hadronization cutoff) Variations  Comprehensive uncertainty estimates (showers with uncertainty bands) Matching  Reduced Dependence (systematic reduction of uncertainty)

Peter Skands Theoretical Physics, Fermilab Colliders in the Ultraviolet – VINCIA In collaboration with W. Giele, D. Kosower

Peter Skands Precision Collider Physics - 11Overview ►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?

Peter Skands Precision Collider Physics - 12 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 VINCIA ►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 α s (evolution scale, p T, mother antenna mass, 2-loop, …) Phase space mappings: 2 different choices implemented  Antenna-like (A RIADNE 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/ Les Houches 2007

Peter Skands Precision Collider Physics - 13 Example: 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 α s (M Z )=0.137, μ R =p T, p Thad = 0.5 GeV Varying finite terms only with

Peter Skands Precision Collider Physics - 14 Constructing 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”, dΦ n+1 /dΦ n ) The renormalization scheme (argument of α s ) The infrared cutoff contour (hadronization cutoff) ►They are all “unphysical”, in the same sense as Q Factorizaton, 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 p T as scale in α s, with Λ MS  Λ MC, …  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

Peter Skands Precision Collider Physics - 15 Matching 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, 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

Peter Skands Precision Collider Physics - 16 NLO with Addition ►First Order Shower expansion Unitarity of shower  3-parton real = ÷ 2-parton “virtual” ►3-parton real correction ( A 3 = |M 3 | 2 /|M 2 | 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 )

Peter Skands Precision Collider Physics - 17 ►Herwig In dead zone: A i = 0  add events corresponding to unsubtracted |M X+1 | Outside dead zone: reweighted à la Pythia  A i = |M X+1 |   no additive correction necessary ►CKKW and L-CKKW At this order identical to Herwig, with “dead zone” for k T > k Tcut introduced by hand In dead zone: identical to Herwig Outside dead zone: A Herwig > |M X+1 |  w X+1 negative  negative weights ►Pythia A i = |M X+1 | over all of phase space  no additive correction necessary ►Powheg At this order identical to Pythia   no negative weights HERWIG TYPE PYTHIA TYPE Matching to X+1: Tree-level

Peter Skands Precision Collider Physics - 18 Matching 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 ?

Peter Skands Precision Collider Physics - 19 Second Order ►Second Order Shower expansion for 4 partons (assuming first already matched) min # of paths AR p T + AR recoil max # of paths DZ ►Problem 1: dependence on evolution variable Shower is ordered  t 4 integration only up to t 3  2, 1, or 0 allowed “paths” 0 = Dead Zone : not good for reweighting Q E = p T (i,j,k) = m ij m jk /m ijk Q E = p T GGG AVG Vincia AVG Vincia MAX Vincia MIN Q E = p T Everyone’s usual nightmare of a parton shower

Peter Skands Precision Collider Physics - 20 Second Order with 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

Peter Skands Precision Collider Physics - 21 Leftover 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 resummation  But 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.

Peter Skands Precision Collider Physics  4 Matching by 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 2 nd order matching term (with 1 st 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

Peter Skands Precision Collider Physics - 23 General 2 nd Order (& 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 2  4 branching (if NLL) Addition/Subtraction: S = 1, K ≠ 1 Multiplication/Reweighting: S ≠ 1 K = 1 Hybrid: S = logs K = the rest

Peter Skands Precision Collider Physics - 24 The Z  3 1-loop term ►Second order matching term for 3 partons ►Additive (S=1)  Ordinary NLO subtraction + shower leftovers Shower off w 2 (V) “Coherence” term: difference between 2- and 3-parton (power-suppressed) evolution above Q E3. Explicit Q E -dependence cancellation. δ α : Difference between alpha used in shower (μ = p T ) and alpha used for matching  Explicit scale choice cancellation Integral over w 4 (R) in IR region still contains NLL divergences  regulate Logs not resummed, so remaining (NLL) logs in w 3 (R) also need to be regulated ►Multiplicative : S = (1+…)  Modified NLO subtraction + shower leftovers A*S contains all logs from tree-level  w 4 (R) finite. Any remaining logs in w 3 (V) cancel against NNLO  NLL resummation if put back in S

Peter Skands Precision Collider Physics - 25 VINCIA in Action: Jet Rates α s (M Z )=0.137, μ R =p T, p Thad = 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

Peter Skands Precision Collider Physics - 26 ►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 Action Giele, Kosower, PS : PRD78(2008) Les Houches ‘NLM’ 2007

Peter Skands Precision Collider Physics - 27 ►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 Action Giele, Kosower, PS : PRD78(2008) Les Houches ‘NLM’ 2007

Peter Skands Precision Collider Physics - 28 ►Can vary evolution variable, kinematics maps, radiation functions, renormalization choice, matching strategy (here just showing radiation functions) ►After 2 nd order matching  Non-pert part can be precisely constrained. (will need 2 nd order logs as well for full variation) VINCIA in Action Giele, Kosower, PS : PRD78(2008) Les Houches ‘NLM’ 2007

Peter Skands Precision Collider Physics - 29 The next big steps ►Z  3 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 Z  3 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, …)

Peter Skands Theoretical Physics, Fermilab Colliders in the Infrared – PYTHIA In collaboration with T. Sjostrand, S. Mrenna

Peter Skands Precision Collider Physics - 31 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 ► But hadrons are not elementary ► + QCD diverges at low p T  multiple perturbative parton-parton collisions ► Normally omitted in ME/PS expansions ( ~ higher twists / powers / low-x) But still perturbative, divergent e.g. 4  4, 3  3, 3  2 Note: Can take Q F >> Λ QCD QFQF QFQF … 2222 IS R FS R 2222 IS R FS R

Peter Skands Precision Collider Physics - 32 Additional Sources of Particle Production Need-to-know issues for IR sensitive quantities (e.g., N ch ) + Stuff at Q F ~ Λ QCD Q F >> Λ QCD ME+ISR/FSR + perturbative MPI QFQF QFQF … 2222 IS R FS R 2222 IS R FS R ►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?

Peter Skands Precision Collider Physics - 33 Now Hadronize This Simulation from D. B. Leinweber, hep-lat/ gluon action density: 2.4 x 2.4 x 3.6 fm Anti-Triplet Triplet pbar beam remnant p beam remnant bbar from tbar decay b from t decay qbar from W q from W hadronization ? q from W

Peter Skands Precision Collider Physics - 34 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

Peter Skands Precision Collider Physics - 35 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

Peter Skands Precision Collider Physics - 36 Future 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 Intensity Frontier The Astro Guys Precision Frontier The Tevatron and LHC data will be all the energy frontier data we’ll have for a long while Anno 2018