QCD & Monte Carlo Event Generators

Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

Frank Krauss

Institute for Particle Physics Phenomenology Durham University

Maria Laach, September 2016

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

Content of lectures

Introduction: QCD Basics Simulating Perturbative QCD Parton Level Event Generation Parton Showers Precision Monte Carlo NLO Matching Multijet Merging Soft Stuﬀ

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

INTRODUCTION

EVENT GENERATORS

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

Strategy of event generator

principle: divide et impera

hard process:

ﬁxed order perturbation theory traditionally: Born-approximation bremsstrahlung: resummed perturbation theory

hadronisation: phenomenological models hadron decays: eﬀective theories, data ”underlying event”: phenomenological models

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

... and possible improvements possible strategies:

improving the phenomenological models:

“tuning” (ﬁtting parameters to data) replacing by better models, based on more physics (my hot candidate: “minimum bias” and “underlying event” simulation)

improving the perturbative description: inclusion of higher order exact matrix elements and correct connection to resummation in the parton shower: “NLO-Matching”& “Multijet-Merging” systematic improvement of the parton shower: next-to leading (or higher) logs & colours

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

Example: QCD precision in Higgs physics

after discovery: time for precision studies of the newly found boson precision determinartion of Yukawa couplings finding or constraining “Higgs portal” (e.g. to Dark Matter) maybe new particles in loops? Higgs signals suffers from different backgrounds, depending on production and decay channel considered in the analysis decomposing in bins of different jet multiplicities yields different signal composition (e.g. WBF vs. ggF) different backgrounds (e.g. t¯t in WW final states) to this end: must understand Standard Model in detail name of the game: uncertainties and their control

despite far-reaching claims: analytic resummation and ﬁxed-order calculations will not be suﬃcient same reasoning also true for new resonances/phenomena

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

QCD BASICS

SCALES & KINEMATICS

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

Factorization: an electromagnetic analogy

consider a charge Z moving at constant velocity v

v = 0 v ≅ c v ≅ c

at v = 0: radial E field only at v = c: B field emerges: E~ ⊥ B~ , B~ ⊥ ~v, E~ ⊥ ~v, energy flow ∼ Poynting vector ~S ∼ E~ × B~ , k ~v approximate classical fields by “equivalent quanta”: photons

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

spectrum of photons:

(in dependence on energy ω and transverse distance b⊥)

2 2 electron(Z=1) 2 Z α dω db⊥ α dω db⊥ dnγ = 2 2 π · ω · b⊥ −→ π · ω · b⊥

Fourier transform to transverse momenta k⊥:

2 α dω dk⊥ dnγ = 2 π · ω · k⊥

note: divergences for k⊥ 0 (collinear) and ω 0 (soft) → → therefore: Fock state for lepton = superposition (coherent):

e phys = e + eγ + eγγ + eγγγ + ... | i | i | i | i | i photon ﬂuctuations will “recombine”

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

lifetime of electron–photon ﬂuctuations: e(P) e(p) + γ(k) → estimate: use uncertainty relation and Lorentz time dilation 2 2 2 P = (p + k) = Mvirt the virtual mass of the incident electron life time = life time in rest frame · time dilation 1 E E E k ω τ ∼ · = ∼ ≈ ≈ 2 2 2 2 Mvirt Mvirt (p + k) 2Ek(1 − cos θ) k sin θ/2 k⊥ lifetime larger with smaller transverse momentum

(i.e. with larger transverse distance)

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

QED Initial and Final State Radiation

physical interpretation: equivalent quanta = quantum manifestation of accompanying ﬁelds in absence of interaction: recombination enforced by coherence but: hard interaction possibly “kicks out” quantum coherence broken −→ equivalent (virtual) quanta become real −→ emission pattern unravels −→

alternative idea: initial state radiation of photons oﬀ incident electron

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

consider ﬁnal state radiation in γ∗ ``¯ (electron velocities/momenta→ labelled as v and v 0/p and p0) classical electromagnetic spectrum from radiation function:

(this is from Jackson or any other reasonable book on ED)

2 2 0 2 d I e ∗ ~v ~v = ~ , dωdΩ 4π2 · 1 ~v ~n − 1 ~v 0 ~n − · − · with the polarisation vector and ~n(Ω) the direction of the radiation recast with four–momenta, equivalent photon spectrum:

3 µ 0µ 2 d k α ∗ p p dN = 3 µ 0 (2π) 2k0 π p k − p k · · 3 2 d k α 0 = 3 Wpp ;k (2π) 2k0 π

with the eikonal Wpp0;k

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

repeat exercise in QFT, Feynman diagrams:

p p

k k

p′ p′

0 p/ k/ µ µ p/ + k/ 0 ∗ + − = eu¯(p) Γ − γ γ Γ u(p ) (k) MX →e e γ (p0 k)2 − (p + k)2 µ µ 0µ− soft ∗ p p 0 e (k) u¯(p )Γu(p) = e + − Wpp0;k −→ µ p k − p0 k MX →e e γ · · · manifestation of Low’s theorem: soft radiation independent of spin ( classical) → (radiation decomposes into soft, classical part with logs – i.e. dominant – and hard collinear part)

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

DGLAP equations for QED

(Dokshitser–Gribov–Lipatov–Altarelli–Parisi Equations)

deﬁne probability to ﬁnd electron or photon in electron:

at LO in α(noemission): `(x, k2 ) = δ(1 x) ⊥ − 2 and γ(x, k⊥) = 0

(introduced x = energy fraction w.r.t. physical state) including emissions: probabilities change energy fraction ξ of lepton parton w.r.t. the physical lepton object reduced by some fraction z = x/ξ 2 reminder: diﬀerential of photon number w.r.t. k⊥:

2 α dk⊥ dω dnγ α dx dnγ = 2 ↔ 2 = π k⊥ ω d log k⊥ π x

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

evolution equations (trivialised)

1 2 2 Z d`(x, k⊥) α(k⊥) dξ x 2 2 2 = `` , α(k⊥) `(ξ, k⊥) d log k⊥ 2π ξ P ξ x 1 2 2 Z dγ(x, k⊥) α(k⊥) dξ x 2 2 2 = γ` , α(k⊥) `(ξ, k⊥) . d log k⊥ 2π ξ P ξ x

2 k⊥ plays the role of “resolution parameter” the ab(z) are the splitting functions, encoding quantum mechanics of theP “splitting cross section”, for example (at LO)

1 + z2 3 ``(z) = + δ(1 z) P 1 z 2 − − + if γ ``¯ splittings included, have to add entries/splitting functions into →evolution equations above

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

Running of αs and bound states

quantum eﬀect due to loops: couplings change with scale running driven by β–function

2 2 ∂αs(µR ) β(αs) = µR 2 ∂µR β β = 0 α2 + 1 α3 + ... 4π s (4π)2 s with 11 4 β0 = CA TR nf 3 − 3 34 2 20 β1 = C CATR nf 4 CF TR nf 3 A − 3 −

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

Casimir operators in the fundamental and adjoint representation:

2 Nc 1 CF = − and CA = Nc 2Nc

with Nc = 3 colours and TR = 1/2.

nf = the number of (quark) ﬂavours the Casimirs correspond to quark and gluon colour charges explicit expression for strong coupling

g 2(µ2 ) 1 ( 2 ) s R = αs µR µ2 ≡ 4π β0 R log 2 4π ΛQCD

withΛ QCD the Landau pole of QCD,Λ QCD 250MeV. ≈

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

Hadrons in initial state: DGLAP equations of QCD

similar to QED case: deﬁne probabilities (at LO) to ﬁnd a parton q – quark or gluon – in hadron h at energy fraction x and resolution parameter/scale Q: 2 parton distribution function (PDF) fq/h(x, Q ) scale-evolution of PDFs: DGLAP equations

2 ∂ fq/h(x, Q ) 2 2 ∂ log Q fg/h(x, Q ) 1 (Q2) Z z x x 2 αs d qq z qg z fq/h(z, Q ) = P x P x 2 , 2π z gq z gg z fg/h(z, Q ) x P P

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

QCD splitting functions:

2 (1) 1 + x 3 (1) (1) qq (x) = CF + δ(1 x) = Pqq (x) + γq δ(1 x) P (1 x)+ 2 − + − − (1) 2 2 (1) (x) = TR x + (1 x) = P (x) Pqg − qg 2 (1) 1 + (1 x) (1) (x) = CF − = P (x) Pgq x gq (1) x 1 x gg (x) = 2CA + − + x(1 x) P (1 x)+ x − − 11CA 4nf TR (1) (1) + − δ(1 x) = Pgg (x) + γg δ(1 x) . 6 − + − remark: IR regularisation by +–prescription & terms δ(1 x) from physical conditions on splitting functions ∼ − (ﬂavour conservation for q → qg and momentum conservation for g → gg, qq¯)

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

Hadron production: Scales

consider QCD ﬁnal state radiation pattern for q qg similar to ` `γ in QED: → → 2 2 2 q→qg αs(k⊥) dk⊥ dω ω dw = CF 2 1 + 1 2π k⊥ ω − E 2 2 2 2 2 ω=E(1−z) αs(k⊥) dk⊥ 1 + z αs(k⊥) dk⊥ (1) = CF dz = CF dz P (z) . 2π k2 1 z 2π k2 qg ⊥ − ⊥ divergent structures for: z 1 (soft divergence) infrared/soft logarithms k2→ 0 (collinear/mass divergence) ←→ collinear logarithms ⊥ → ←→ cut regularise with cut-oﬀ k⊥,min 1GeV > ΛQCD ∼

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

ﬁnd two perturbative regimes:

a regime of jet production, where k⊥ ∼ kk ∼ ω k⊥,min and emission probabilities scale like w ∼ αs(k⊥) 1; and a regime of jet evolution, where k⊥,min ≤ k⊥ kk ≤ ω and 2 2 > therefore emission probabilities scale like w ∼ αs(k⊥) log k⊥ ∼ 1. in jet production: standard ﬁxed–order perturbation theory in jet evolution regime, perturbative parameter not αs any more 2 but rather towers of exp αs log k⊥ log kk 2n induces counting of leading logarithms (LL), αsL , 2n−1 next-to leading logarithms (NLL), αsL , etc.

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

MONTE CARLO FOR

PARTON LEVEL

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

Simulating hard processes (signals & backgrounds)

+ Simple example: t bW b¯lνl : → → 2 2 1 8πα pt ·pν pb ·pl = 2 sin2 θ (p2 −M2 )2+Γ2 M2 |M| W W W W W

Phase space integration (5-dim):

2 2 2 1 1 R 2 d ΩW d Ω pW 2 Γ = 2m 128π3 dpW 4π 4π 1 2 t − mt |M| 5 random numbers = four-momenta = “events”. ⇒ ⇒ Apply smearing and/or arbitrary cuts. Simply histogram any quantity of interest - no new calculation for each observable

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

Calculating matrix elements eﬃciently

stating the problem(s): multi-particle ﬁnal states for signals & backgrounds. need to evaluate dσN :

Z " N 3 # ! Y d qi 4 X 2 3 δ p1 + p2 − qi |Mp1p2→N | . (2π) 2Ei cuts i=1 i problem 1: factorial growth of number of amplitudes. problem 2: complicated phase-space structure. solutions: numerical methods.

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

Including higher order corrections

obtained from adding diagrams with additional: loops (virtual corrections) or legs (real corrections)

eﬀect: reducing the dependence on µR & µF NLO allows for meaningful estimate of uncertainties additional diﬃculties when going NLO: ultraviolet divergences in virtual correction infrared divergences in real and virtual correction enforce UV regularisation & renormalisation IR regularisation & cancellation

(Kinoshita–Lee–Nauenberg–Theorem)

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

general structure of NLO calculation for N-body production

dσ = dΦB N (ΦB) + dΦB N (ΦB) + dΦR N (ΦR) B V R (S) = dΦB N + N + + dΦR ( N N ) B V IN R − S

phase space factorisation assumed here (ΦR = ΦB Φ1) ⊗ Z (S) dΦ1 N (ΦB Φ1) = (ΦB) S ⊗ IN process independent, universal subtraction kernels

N (ΦB Φ1) = N (ΦB) 1(ΦB Φ1) S ⊗ B ⊗S ⊗ (S) (S) (ΦB Φ1) = N (ΦB) (ΦB) , IN ⊗ B ⊗I 1 and invertible phase space mapping (e.g. Catani-Seymour)

ΦR ΦB Φ1 ←→ ⊗

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

Aside: choices ...

common lore: NLO calculations reduce scale uncertainties this is, in general, true. however: unphysical scale choices will yield unphysical results

more ways of botching it at higher orders

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

Availability of exact calculations (hadron colliders) ﬁxed order matrix elements (“parton level”) are exact to a given

perturbative order. (and often quite a pain!) important to understand limitations: only tree-level and one-loop level fully automated, beyond: prototyping

done 2 for some processes m loops first solutions 1 0

1 2 3 4 5 6 7 8 9 n FS particles

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

GOING MONTE CARLO

PARTON SHOWERS – THE BASICS

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

An analogy: Radioactive decays

consider radioactive decay of an unstable isotope with half-life τ.

(and ignore factors of ln 2.) “survival” probability after time t is given by

(t) = nodec(t) = exp[ t/τ] S P −

(note “unitarity relation”: Pdec(t) = 1 − Pnodec(t).) probability for an isotope to decay at time t:

d dec(t) d nodec(t) 1 P = P = exp( t/τ) dt − dt τ − now: connect half-life with width Γ = 1/τ. probability for the isotope to decay at any ﬁxed time t determined by Γ.

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

spice things up now: add time–dependence, Γ = Γ(t0) rewrite t Z Γt dt0Γ −→ 0 decay-probability at a given time t is given by

 t  Z d dec(t) 0 0 P = Γ(t) exp  dt Γ(t ) = Γ(t) nodec(t) dt − P 0

(unitarity strikes again: dPdec(t)/dt = −dPnodec(t)/dt.) interpretation of l.h.s.: ﬁrst term is for the actual decay to happen. second term is to ensure that no decay before t =⇒ conservation of probabilities. the exponential is - of course - called the Sudakov form factor.

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

diﬀerential cross section for gluon emission in e+e− jets → 2 2 dσee→3j CF αs x1 + x2 = σee→2j dx1dx2 π (1 x1)(1 x2) − − singular for x1,2 1. → rewrite with opening angle θqg and gluon energy fraction x3 = 2Eg /Ec.m.:

2 dσee→3j CF αs 2 1 + (1 x3) = σee→2j 2 − x3 d cos θqg dx3 π sin θqg x3 −

singular for x3 0(“soft”), sin θqg 0(“collinear”). → →

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

re-express collinear singularities

2d cos θqg d cos θqg d cos θqg 2 = + sin θ 1 cos θqg 1 + cos θqg qg − 2 2 d cos θqg d cos θqg¯ dθqg dθqg¯ = + 2 + 2 1 cos θqg 1 cos θqg¯ ≈ θ θ − − qg qg¯ independent evolution of two jets (q andq ¯)

2 X CF αs dθjg dσee→3j σee→2j P(z) , ≈ 2π θ2 j∈{q,q¯} jg

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

note: same form for any t θ2: ∝ transverse momentum k2 z2(1 z)2E 2θ2 ⊥ ≈ − invariant mass q2 z(1 z)E 2θ2 ≈ − 2 2 2 dθ dk⊥ dq 2 2 2 θ ≈ k⊥ ≈ q parametrisation-independent observation: (logarithmically) divergent expression for t 0. 2 → practical solution: cut-oﬀ Q0 . = divergence will manifest itself as log Q2. ⇒ 0 similar for P(z): divergence for z 0 cured by cut-oﬀ. →

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

what is a parton? collinear pair/soft parton recombine!

introduce resolution criterion k⊥ > Q0.

combine virtual contributions with unresolvable emissions: cancels infrared divergences = ﬁnite at (αs ) ⇒ O (Kinoshita-Lee-Nauenberg, Bloch-Nordsieck theorems) unitarity: probabilities add up to one (resolved) + (unresolved) = 1. P P

+ =1.

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

the Sudakov form factor, once more diﬀerential probability for emission between q2 and q2 + dq2:

zmax α dq2 Z d = s dzP(z) =: dq2 Γ(q2) P 2π q2 zmin from radioactive example: evolution equation for ∆

d∆(Q2, q2) d = ∆(Q2, q2) P = ∆(Q2, q2)Γ(q2) − dq2 dq2

 Q2  Z = ∆(Q2, q2) = exp  dk2Γ(k2) ⇒ −  q2

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

maximal logs if emissions ordered impacts on radiation pattern: in each emission t becomes smaller

2 2 2 2 0 2 q1 > q2 > q3 , q1 > q2

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

Quantum improvements

improvement: inclusion of various quantum eﬀects 2 trivial: eﬀect of summing up higher orders (loops) αs αs (k ) → ⊥

2 much faster parton proliferation, especially for small k⊥. 2 2 2 2 avoid Landau pole: k⊥ > Q0 ΛQCD = Q0 = physical parameter. ⇒

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

soft limit for single emission also universal problem: soft gluons come from all over (not collinear!) quantum interference? still independent evolution? answer: not quite independent. consider case in QED

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

+ − assume photon into e e at θee and photon oﬀ electron at θ photon momentum denoted as k energy imbalance at vertex: kγ k θ, hence ∆E k2 /k k θ2. ⊥ ∼ k ∼ ⊥ k ∼ k formation time for photon emission: ∆t 1/∆E k /k2 1/(k θ2). ∼ ∼ k ⊥ ∼ k ee-separation: ∆b θee ∆t ∼ must be larger than transverse wavelength of photon: 2 θee /(kkθ ) > 1/k⊥ = 1/(kkθ)

thus: θee > θ must be satisﬁed for photon to form angular ordering as manifestation of quantum coherence

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

pictorially:

= ⇒ gluons at large angle from combined colour charge!

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

experimental manifestation: ∆R of 2nd & 3rd jet in multi-jet events in pp-collisions

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

Parametric precision

analyse connection to QT resummation formalism consider standard Collins-Soper-Sterman formalism (CSS):

Z 2 dσAB→X d b⊥ ~ ~ ˜ 2 = dΦX ij (ΦX ) 2 exp(ib⊥ Q⊥)Wij (b;ΦX ) dydQ⊥ B · (2π) · | {z }| {z } guarantee 4-mom conservation higher orders with

collinear bits loops z }| {z }| { W˜ ij (b;ΦX )= Ci (b;ΦX , αs)Cj (b;ΦX , αs)Hij (αs)  2  QX Z dk2 Q2 exp  ⊥ A( (k2 )) log X + B( (k2 ))   2 αs ⊥ 2 αs ⊥  − k⊥ k⊥ 2 1/b⊥ | {z } Sudakov form factor, A, B expanded in powers of αs

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

Lm analyse structure of emissions above NLL resummed µ in PS logarithmic accuracy in log N (a la CSS) k⊥ possibly up to next-to leading log, if evolution parameter ∼ transverse momentum, if argument in αs is ∝ k⊥ of splitting, if Kij,k → terms A1,2 and B1 upon integration

(OK, if soft gluon correction is included, and if Kij,k → AP splitting kernels) αn

in CSS k⊥ typically is the transverse momentum of produced system, in parton shower of course related to the cumulative eﬀect of explicit multiple emissions

resummation scale µN µF given by (Born) kinematics – simple for cases like qq¯≈0 V , gg H,... tricky for more complicated→ cases →

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

Example: achievable precision of shower alone in DY

pT spectrum, Z ee (dressed) φη∗ spectrum, Z ee (dressed) 1 → → ] 10− b b ∗ η 1 b b b ﬁd. 1 b b b b b φ b b − b b σ 10 b b

MC b MC b d b b d b b b b b 0 yZ 1 b b 2 b < 0.8 b 1 y b

ﬁd. Z ≤| | ≤ b b GeV 10 − b b b σ b [ b | | b b b b b b b b b b b b

T b b b b herpa b b herpa ﬁd b b b b p b b 1 b b S S

σ b b b b d 1 2 ( 0.1) b b d 3 yZ b b b 10 b b b b − ≤|b |b ≤ × b b b b b 0.8 yZ 1.6 ( 0.1) b ﬁd 1 b b b b b b b σ b b b ≤| | ≤ × b b b b b b b b b b b 1 b b 4 b b b b b b b 10 b b 10 2 < 2.4 ( 0.01) b − b b − yZ b b b b b b b b b b b | | ≤ × b b b b b b b 1.6 < yZ ( 0.01) b b b b b b b | | × b 5 b b b b b b 10− b 2 b b 10− b b b b b ATLAS data b b b 6 b b b 10 ATLAS data b b − JHEP 09 (2014) 145 b b 3 b 1 10 Phys.Lett. B720 (2013) 32 b ME+PS ( -jet) − b

7 b ME+PS (1-jet) b 10 5 Qcut 20 GeV b − ≤ ≤ b 5 Qcut 20 GeV b b 4 ≤ ≤ 8 10− b 10− b b | | b → || 10 9 1−.2 1 2 1.2 3 2 1 0 y 1 y < 0.8 1.1 ≤| Z| ≤ 1.1 | Z| 1.0 b b b bbbbbbbbbbbbbbbbbbb b b b b 1.0 b b b bbbbbbbbbbbbbbbbbbbbbbbb b bbbbbb 0.9 0.9 MC/Data MC/Data 0.8 | | 0.8 → ≤|| 1.2 1 2 1.2 3 2 1 1 y 2 0.8 y 1.6 1.1 ≤| Z| ≤ 1.1 ≤| Z| ≤ 1.0 b b b bbbbbbbbbbbbbbbbbbb b b b b 1.0 b b b bbbbbbbbbbbbbbbbbbbbbbbb b bbbbbb 0.9 0.9 MC/Data MC/Data 0.8 | | 0.8 → ||≥ 1.2 1 2 1.2 3 2 1 2 < y 2.4 1.6 < y 1.1 | Z| ≤ 1.1 | Z| 1.0 b b b bbbbbbbbbbbbbbbbbbb b b b b 1.0 b b b bbbbbbbbbbbbbbbbbbbbbbbb b bbbbbb 0.9 0.9 MC/Data MC/Data 0.8 0.8 1 2 3 2 1 1 10 10 10− 10− 10− 1 pT,ll [GeV] φη∗

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

Higher logarithms in parton showering (?)

start including higher orders/log (A3 & B2) – see below

(for NNLO the “natural” accuracy is NNLL) example below: diﬀerent orders in DY

(a snapshot from ongoing work within SHERPA)

Differential 0 1 jet resolution Differential 0 1 jet resolution → → 3 10 PS 10 3 PS [pb] [pb] ) ) ire ire D D /GeV /GeV 2 2 01 10 12 10 d d ( (

10 Γ γ 10 Γ γ 1 ⊕ 1 1 ⊕ 1 Γ1 γ1 Γ2 Γ1 γ1 Γ2 ⊕ ⊕ 10 1 ⊕ ⊕ /d log 1 Γ1 γ1 Γ2 γ2 /d log Γ1 γ1 Γ2 γ2

σ 10 ⊕ ⊕ ⊕ σ ⊕ ⊕ ⊕

d Γ γ Γ γ Γ d Γ γ Γ γ Γ 1 ⊕ 1 ⊕ 2 ⊕ 2 ⊕ 3 1 ⊕ 1 ⊕ 2 ⊕ 2 ⊕ 3

+ + pp e e− @ 8TeV 1 pp e e− @ 8TeV 1 → →

1.2 1.2 1.1 1.1 1.0 1.0 Ratio Ratio 0.9 0.9 0.8 0.8 0.5 1 1.5 2 2.5 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 log10(d01/GeV) log10(d12/GeV)

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

FIRST IMPROVEMENTS:

ME CORRECTIONS

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

NLO calculations, in a nutshell remember structure of NLO calculation for N-body production

dσ = dΦB N (ΦB) + dΦB N (ΦB) + dΦR N (ΦR) B V R (S) = dΦB N + N + + dΦR ( N N ) B V IN R − S

phase space factorisation assumed here (ΦR = ΦB Φ1) ⊗ Z (S) dΦ1 N (ΦB Φ1) = (ΦB) S ⊗ IN process independent subtraction kernels

N (ΦB Φ1) = N (ΦB) 1(ΦB Φ1) S ⊗ B ⊗ S ⊗ (S) (S) (ΦB Φ1) = N (ΦB) (ΦB) IN ⊗ B ⊗ I1 (S) with universal 1(ΦB Φ1) and (ΦB) S ⊗ I1

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

Parton showers, compact notation

Sudakov form factor (no-decay probability)

t " Z Z # (K) dt αs dφ ∆ij,k (t, t0) = exp dz ij,k (t, z, φ) − t 2π 2π K| {z } t0 splitting kernel for (ij) → ij (spectator k)

evolution parameter t deﬁned by kinematics

generalised angle (HERWIG ++) or transverse momentum (PYTHIA,SHERPA) dt dφ will replace dz dΦ1 t 2π −→ 2 scale choice for strong coupling: αs(k⊥) resums classes of higher logarithms regularisation through cut-oﬀ t0

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

(K) “compound” splitting kernels n and Sudakov form factors∆ n for emission oﬀ n-particle ﬁnalK state:

t " Z # αs X (K) n(Φ1)= ij,k (Φij,k ) , ∆ (t, t0) = exp dΦ1 n(Φ1) K 2π K n − K all {ij,k} t0 consider first emission only off Born configuration

dσB = dΦN N (ΦN ) B µ2 ( Z N ) (K) 2 (K) 2 ∆ (µ , t0) + dΦ1 N (Φ1)∆ (µ , t(Φ1)) · N N K N N t0 | {z } integrates to unity −→ “unitarity” of parton shower

further emissions by recursion with Q2 = t of previous emission

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

Matrix element corrections

ME over PS

parton shower ignores interferences 2 1 1 x typically present in matrix elements 0.9 0.8 0.8 pictorially 0.7 2 0.6 0.6 + 0.5 ME : 0.4 0.4 0.3 2 2 0.2 0.2 + 0.1 0 0 PS : 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x1

form many processes N < N N R B × K typical processes: qq¯0 V , e−e+ qq¯, t bW → → → practical implementation: shower with usual algorithm, but reject ﬁrst/hardest emissions with probability = N /( N N ) P R B × K

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

analyse ﬁrst emission, given by

dσB = dΦN N (ΦN ) B µ2 ( Z N ) (R/B) 2 N (ΦN Φ1) (R/B) 2 ∆N (µN , t0) + dΦ1 R × ∆N (µN , t(Φ1)) · N (ΦN ) t0 B | {z } once more: integrates to unity −→ “unitarity” of parton shower

radiation given by N (correct at (αs)) Lm NLL R O (R/B) (but modiﬁed by logs of higher order in α from ∆ ) resummed s N in PS

emission phase space constrained by µN also known as “soft ME correction” hard ME correction ﬁlls missing phase space used for “power shower”: n µN Epp and apply ME correction α →

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

PRECISION MONTE CARLO

NLO MATCHING

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

NLO matching: Basic idea

parton shower resums logarithms fair description of collinear/soft emissions m jet evolution (where the logs are large) L NLL resummed matrix elements exact at given order in PS fair description of hard/large-angle emissions

jet production (where the logs are small) adjust (“match”) terms: cross section at NLO accuracy& correct hardest emission in PS to exactly reproduce ME at order αs (R-part of the NLO calculation) αn (this is relatively trivial) maintain (N)LL-accuracy of parton shower

(this is not so simple to see)

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

POWHEG

reminder: ij,k reproduces process-independent behaviour of K N / N in soft/collinear regions of phase space R B

N (ΦN+1) IR αs dΦ1 R dΦ1 ij,k (Φ1) N (ΦN ) −→ 2π K B deﬁne modiﬁed Sudakov form factor (as in ME correction)

 2  µN Z (Φ ) (R/B) 2  N N+1  ∆N (µN , t0) = exp dΦ1 R , − N (ΦN )  t0 B

assumes factorisation of phase space: ΦN+1 = ΦN Φ1 ⊗ typically will adjust scale of αs to parton shower scale

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

deﬁne local K-factors

start from Born conﬁguration ΦN with NLO weight:

(“local K-factor”)

(NLO) ¯ dσN = dΦN (ΦN ) ( B = dΦN N (ΦN ) + N (ΦN ) + N (ΦN ) B |V {zB ⊗ S} V˜N (ΦN ) Z ) + dΦ1 [ N (ΦN Φ1) N (ΦN ) dS(Φ1)] R ⊗ − B ⊗

by construction: exactly reproduce cross section at NLO accuracy

note: second term vanishes if N N dS R ≡ B ⊗ (relevant for MC@NLO)

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

analyse accuracy of radiation pattern (R/B) 2 generate emissions with ∆N (µN , t0):

(NLO) dσ = dΦN ¯(ΦN ) N B  µ2   Z N   (R/B) 2 N (ΦN Φ1) (R/B) 2 2  ∆N (µN , t0) + dΦ1 R ⊗ ∆N (µN , k⊥(Φ1)) ×  N (ΦN )   t0 B  | {z } integrating to yield 1 - “unitarity of parton shower”

radiation pattern like in ME correction 2 pitfall, again: choice of upper scale µN (this is vanilla POWHEG!) apart from logs: which conﬁgurations enhanced by local K-factor

( K-factor for inclusive production of X adequate for X + jet at large p⊥?)

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

large enhancement at high pT ,h can be traced back to large NLO correction fortunately, NNLO correction is also large agreement → ∼

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

improving POWHEG split real-emission ME as

2 2 ! h p⊥ = 2 2 + 2 2 R R p⊥ + h p⊥ + h | {z } | {z } R(S) R(F ) can “tune” h to mimick NNLO - or other (resummation) result

diﬀerential event rate up to ﬁrst emission

s " Z (S) # (R(S)) (R(S)/B) (R(S)/B) 2 dσ = dΦB ¯ ∆ (s, t0) + dΦ1 R ∆ (s, k ) B ⊥ t0 B (F ) +dΦR (ΦR ) R

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

MC@NLO

MC@NLO paradigm: divide N in soft (“S”) and hard (“H”) part: R (S) (H) N = + = N d 1 + N R RN RN B ⊗ S H P identify subtraction terms and shower kernels d 1 ij,k S ≡ {ij,k} K (modify K in 1st emission to account for colour)

µ2 " Z N # ˜ (K) 2 (K) 2 2 dσN = dΦN N (ΦN ) ∆N (µN , t0) + dΦ1 ij,k (Φ1) ∆N (µN , k⊥) |B {z } K B+V˜ t0

+dΦN+1 N H eﬀect: only resummed parts modiﬁed with local K-factor

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

phase space eﬀects: shower vs. ﬁxed order

Rapidity separation betw. Higgs and leading jet in pp h + X 0.1 →

[pb] 0.09 NLO α = 0.03 ) α = α = 0.08 1 0.01

st jet α = 0.3 α = 0.003 1 0.07 α = 0.1 α = 0.001 h, (

y 0.06 ∆ 0.05 /d σ

d 0.04 0.03 0.02

0.01 Sherpa 0

1.5 Ratio 1

0.5 -4 -3 -2 -1 0 1 2 3 4 ∆y(h, 1st jet)

problem: impact of subtraction terms on local K-factor (ﬁlling of phase space by parton shower) studied in case of gg H above → proper ﬁlling of available phase space by parton shower paramount

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

PRECISION MONTE CARLO

MULTIJET MERGING

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

Multijet merging: basic idea

parton shower resums logarithms fair description of collinear/soft emissions Lm exact ME NLL jet evolution (where the logs are large) LO 4jet 5 resummed in PS matrix elements exact at given order 5

fair description of hard/large-angle emissions 4 5 exact ME (where the logs are small) LO 5jet, but also jet production 4 5 NLO 4jet combine (“merge”) both: 4 5

result: “towers” of MEs with increasing 4 5 number of jets evolved with PS 4 5 multijet cross sections at Born accuracy αn maintain (N)LL accuracy of parton shower

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

102 p W

[ pb/GeV ] W + 0jet W separate regions of jet production and jet W + 1jet

/dp W + 2jet σ

d 10 evolution with jet measure Q W + 3jet J W + 4jet D0 Data (“truncated showering” if not identical with evolution parameter) 1 matrix elements populate hard regime 10-1 parton showers populate soft domain

10-2 SHERPA

0 20 40 60 80 100 120 140 160 180 200

p W / GeV

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

Why it works: jet rates with the parton shower consider jet production in e+e− hadrons → Durham jet deﬁnition: relative transverse momentum k⊥ > QJ

2 Ec.m. ﬁxed order: one factor αS and up to log per jet QJ use Sudakov form factor for resummation & replace approximate ﬁxed order by exact expression:

2 2 2 2(QJ ) = ∆q(E , Q ) R c.m. J

2 Ec.m. Z 2 " 2 2 2 dk⊥ αs(k⊥) 2 3(QJ ) =2∆ q(Ec.m., QJ ) 2 dz q(k⊥, z) R k⊥ 2π K 2 QJ # 2 2 2 2 2 2 ∆q(E , k )∆q(k , Q )∆g (k , Q ) × c.m. ⊥ ⊥ J ⊥ J

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

Multijet merging at LO

expression for ﬁrst emission

µ2 " Z N # (K) 2 (K) 2 dσ = dΦN N ∆ (µ , t0) + dΦ1 N ∆ (µ , tN+1)Θ(QJ QN+1) B N N K N N − t0 (K) 2 +dΦN+1 N+1 ∆ (µ , tN+1)Θ(QN+1 QJ ) B N N+1 − note: N + 1-contribution includes also N + 2, N + 3, . . .

(no Sudakov suppression below tn+1, see further slides for iterated expression)

potential occurence of diﬀerent shower start scales: µN,N+1,...

“unitarity violation” in square bracket: N N N+1 B K −→ B (cured with UMEPS formalism, L. Lonnblad & S. Prestel, JHEP 1302 (2013) 094 &

S. Platzer, arXiv:1211.5467 [hep-ph] & arXiv:1307.0774 [hep-ph])

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

Di-photons @ ATLAS: mγγ, p ,γγ, and ∆φγγ in showers ⊥

(arXiv:1211.1913 [hep-ex])

10 1 ATLAS ATLAS ATLAS

1 [pb/rad]

s = 7 TeV s = 7 TeV γγ [pb/GeV] [pb/GeV]

γγ γγ 2 •1 •1 •1 φ 10 s = 7 TeV

T, 10 Data 2011, ∫ Ldt = 4.9 fb Data 2011, ∫ Ldt = 4.9 fb ∆ •1 /d /dm •1 Data 2011, Ldt = 4.9 fb /dp PYTHIA MC11c × 1.2 (MRST2007) PYTHIA MC11c × 1.3 (MRST2007) σ ∫

σ 10 d σ d SHERPA MC11c × 1.2 (CTEQ6L1) d SHERPA MC11c × 1.3 (CTEQ6L1) PYTHIA MC11c × 1.2 (MRST2007) 10•2 SHERPA MC11c × 1.2 (CTEQ6L1) 10•2 10 10•3 10•3

10•4 10•4 1 10•5

3 3 3 2.5 2.5 2.5 2 2 2 1.5 1.5 1.5 1 1 1 data/SHERPA 0.5 data/SHERPA 0.5 data/SHERPA 0.5 0 0 0 3 3 3 2.5 2.5 2.5 2 2 2 1.5 1.5 1.5

data/PYTHIA 1 data/PYTHIA 1 data/PYTHIA 1 0.5 0.5 0.5 0 0 0 0 100 200 300 400 500 600 700 800 0 50 100 150 200 250 300 350 400 450 500 0 0.5 1 1.5 2 2.5 3 p [GeV] ∆φ [rad] m γγ [GeV] T, γγ γγ

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

Aside: Comparison with higher order calculations

10 1 ATLAS ATLAS ATLAS

1 [pb/rad]

s = 7 TeV s = 7 TeV γγ [pb/GeV] [pb/GeV]

γγ γγ 2 •1 •1 •1 φ 10 s = 7 TeV

T, 10 Data 2011, ∫ Ldt = 4.9 fb Data 2011, ∫ Ldt = 4.9 fb ∆ •1 /d /dm •1 Data 2011, Ldt = 4.9 fb /dp DIPHOX+GAMMA2MC (CT10) DIPHOX+GAMMA2MC (CT10) σ ∫

σ 10 d σ d 2γNNLO (MSTW2008) d 2γNNLO (MSTW2008) DIPHOX+GAMMA2MC (CT10) 10•2 2γNNLO (MSTW2008) 10•2 10 10•3 10•3

10•4 10•4 1 10•5

3 3 3 2.5 2.5 2.5 2 2 2 1.5 1.5 1.5 1 1 1 data/DIPHOX data/DIPHOX data/DIPHOX 0.5 0.5 0.5 0 0 0 3 3 3 2.5 2.5 2.5 NNLO NNLO NNLO γ 2 γ 2 γ 2 1.5 1.5 1.5

data/2 1 data/2 1 data/2 1 0.5 0.5 0.5 0 0 0 0 100 200 300 400 500 600 700 800 0 50 100 150 200 250 300 350 400 450 500 0 0.5 1 1.5 2 2.5 3 p [GeV] ∆φ [rad] m γγ [GeV] T, γγ γγ

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

Multijet-merging at NLO: MEPS@NLO

basic idea like at LO: towers of MEs with increasing jet multi (but this time at NLO) combine them into one sample, remove overlap/double-counting maintain NLO and (N)LL accuracy of ME and PS

this eﬀectively translates into a merging of MC@NLO simulations and can be further supplemented with LO simulations for even higher ﬁnal state multiplicities

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

First emission(s), once more

µ2 " Z N # (K) 2 (K) 2 dσ = dΦN ˜N ∆ (µ , t0) + dΦ1 N ∆ (µ , tN+1)Θ(QJ QN+1) B N N K N N − t0 (K) 2 +dΦN+1 N ∆ (µ , tN+1)Θ(QJ QN+1) H N N −

µ2 Z N ! N+1 +dΦN+1 ˜N+1 1 + B dΦ1 N Θ(QN+1 QJ ) B ˜N+1 K − B tN+1 t " ZN+1 # (K) (K) ∆ (tN+1, t0) + dΦ1 N+1∆ (tN+1, tN+2) · N+1 K N+1 t0 (K) 2 (K) +dΦN+2 N+1∆ (µ , tN+1)∆ (tN+1, tN+2)Θ(QN+1 QJ )+ ... H N N N+1 −

F. Krauss IPPP QCD & Monte Carlo Event Generators MC@NLO pp → h + jet for Qn+1 > Qcut restrict emission oﬀ pp → h + jet to Qn+2 < Qcut MC@NLO pp → h + 2jets for Qn+2 > Qcut iterate sum all contributions

eg. p⊥(h)>200 GeV has contributions fr. multiple topologies

Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision pH in MEPS@NLO ⊥ Transverse momentum of the Higgs boson ﬁrst emission by MC@NLO pp h + jets → Sherpa S-MC@NLO [pb/GeV] 1

⊥ 10− p /d σ d

2 10−

3 10−

4 10− 0 50 100 150 200 250 300 p (h) [GeV] ⊥

eg. p⊥(h)>200 GeV has contributions fr. multiple topologies

Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision pH in MEPS@NLO ⊥ Transverse momentum of the Higgs boson ﬁrst emission by MC@NLO , restrict to

pp h + jets Qn+1 < Qcut → pp h + 0j @ NLO [pb/GeV] 1 →

⊥ 10− p /d σ d

2 10−

3 10−

4 10− 0 50 100 150 200 250 300 p (h) [GeV] ⊥

F. Krauss IPPP QCD & Monte Carlo Event Generators restrict emission oﬀ pp → h + jet to Qn+2 < Qcut MC@NLO pp → h + 2jets for Qn+2 > Qcut iterate sum all contributions

eg. p⊥(h)>200 GeV has contributions fr. multiple topologies

Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision pH in MEPS@NLO ⊥ Transverse momentum of the Higgs boson ﬁrst emission by MC@NLO , restrict to

pp h + jets Qn+1 < Qcut → pp h + 0j @ NLO [pb/GeV] 1 → MC@NLO pp → h + jet

⊥ 10− pp h + 1j @ NLO p → for Qn+1 > Qcut /d σ d

2 10−

3 10−

4 10− 0 50 100 150 200 250 300 p (h) [GeV] ⊥

F. Krauss IPPP QCD & Monte Carlo Event Generators MC@NLO pp → h + 2jets for Qn+2 > Qcut iterate sum all contributions

eg. p⊥(h)>200 GeV has contributions fr. multiple topologies

Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision pH in MEPS@NLO ⊥ Transverse momentum of the Higgs boson ﬁrst emission by MC@NLO , restrict to

pp h + jets Qn+1 < Qcut → pp h + 0j @ NLO [pb/GeV] 1 → MC@NLO pp → h + jet

⊥ 10− pp h + 1j @ NLO p → for Qn+1 > Qcut /d σ

d restrict emission oﬀ pp → h + jet to 2 Q < Q 10− n+2 cut

3 10−

4 10− 0 50 100 150 200 250 300 p (h) [GeV] ⊥

F. Krauss IPPP QCD & Monte Carlo Event Generators iterate sum all contributions

eg. p⊥(h)>200 GeV has contributions fr. multiple topologies

Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision pH in MEPS@NLO ⊥ Transverse momentum of the Higgs boson ﬁrst emission by MC@NLO , restrict to

pp h + jets Qn+1 < Qcut → pp h + 0j @ NLO [pb/GeV] 1 → MC@NLO pp → h + jet

⊥ 10− pp h + 1j @ NLO p → pp h + 2j @ NLO for Qn+1 > Qcut /d → σ

d restrict emission oﬀ pp → h + jet to 2 Q < Q 10− n+2 cut MC@NLO pp → h + 2jets for Qn+2 > Qcut 3 10−

4 10− 0 50 100 150 200 250 300 p (h) [GeV] ⊥

F. Krauss IPPP QCD & Monte Carlo Event Generators sum all contributions

eg. p⊥(h)>200 GeV has contributions fr. multiple topologies

Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision pH in MEPS@NLO ⊥ Transverse momentum of the Higgs boson ﬁrst emission by MC@NLO , restrict to

pp h + jets Qn+1 < Qcut → pp h + 0j @ NLO [pb/GeV] 1 → MC@NLO pp → h + jet

⊥ 10− pp h + 1j @ NLO p → pp h + 2j @ NLO for Qn+1 > Qcut /d → σ

d restrict emission oﬀ pp → h + jet to 2 Q < Q 10− n+2 cut MC@NLO pp → h + 2jets for Qn+2 > Qcut 3 10− iterate

4 10− 0 50 100 150 200 250 300 p (h) [GeV] ⊥

F. Krauss IPPP QCD & Monte Carlo Event Generators sum all contributions

eg. p⊥(h)>200 GeV has contributions fr. multiple topologies

Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision pH in MEPS@NLO

⊥ Transverse momentum of the Higgs boson ﬁrst emission by MC@NLO , restrict to

pp h + jets Qn+1 < Qcut → pp h + 0j @ NLO [pb/GeV] 1 → MC@NLO pp → h + jet

⊥ 10− pp h + 1j @ NLO p → pp h + 2j @ NLO for Qn+1 > Qcut /d → σ pp h + 3j @ LO d → restrict emission oﬀ pp → h + jet to 2 Q < Q 10− n+2 cut MC@NLO pp → h + 2jets for Qn+2 > Qcut 3 10− iterate

4 10− 0 50 100 150 200 250 300 p (h) [GeV] ⊥

F. Krauss IPPP QCD & Monte Carlo Event Generators eg. p⊥(h)>200 GeV has contributions fr. multiple topologies

Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision pH in MEPS@NLO

⊥ Transverse momentum of the Higgs boson ﬁrst emission by MC@NLO , restrict to

pp h + jets Qn+1 < Qcut → pp h + 0j @ NLO [pb/GeV] 1 → MC@NLO pp → h + jet

⊥ 10− pp h + 1j @ NLO p → pp h + 2j @ NLO for Qn+1 > Qcut /d → σ pp h + 3j @ LO d → restrict emission oﬀ pp → h + jet to 2 Q < Q 10− n+2 cut MC@NLO pp → h + 2jets for Qn+2 > Qcut 3 10− iterate sum all contributions

4 10− 0 50 100 150 200 250 300 p (h) [GeV] ⊥

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision pH in MEPS@NLO

⊥ Transverse momentum of the Higgs boson ﬁrst emission by MC@NLO , restrict to

pp h + jets Qn+1 < Qcut → pp h + 0j @ NLO [pb/GeV] 1 → MC@NLO pp → h + jet

eg. p⊥(h)>200 GeV 4 has contributions fr. 10− 0 50 100 150 200 250 300 multiple topologies p (h) [GeV] ⊥

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

Example: MEPS@NLO for W +jets

(up to two jets @ NLO, from BLACKHAT, see arXiv: 1207.5031 [hep-ex])

Inclusive Jet Multiplicity

b ) [pb] b ) 0.3 ATLAS data 1 jets

− b jets MePs@Nlo jet b b N jet 4 MePs@Nlo µ/2...2µ 0.25 ≥ N b b

10 ( MEnloPS σ ≥ /

b )

+ MEnloPS µ/2...2µ 0.2 jets b b jet W Mc@Nlo ( N σ

≥ jet ( 0.15 p > 20 GeV 3 σ ⊥ 10 jet b p > 20 GeV b ⊥( 10) × ) jet 0.25 p > 30 GeV b 1 jets − ⊥ b b jet 2 b

10 N 0.2 b ≥ (

b σ / ) b 0.15 jets jet N 1 b ≥ jet 10 ( 0.1 p > 30 GeV σ ⊥ b

0 1 2 3 4 5 N jet 0 1 2 3 4 5 N jet

F. Krauss IPPP QCD & Monte Carlo Event Generators

b Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

First Jet p Second Jet p ⊥ ⊥ 3 2 10 10 b ATLAS data b ATLAS data MePs@Nlo 1 W 2 [pb/GeV] 10 + 2 jets ( 1) MePs@Nlo b ≥ × MePs@Nlo µ/2...2µ 10 ⊥ b [pb/GeV] p MEnloPS MePs@Nlo µ/2...2µ b ⊥ b W+ 1 jet ( 1) /d 1 MEnloPS µ/2...2µ σ p 1 b ≥ × b MEnloPS d Mc@Nlo 10 b b

/d 1 b 10− b σ b MEnloPS µ/2...2µ b b d b b 1 b Mc@Nlo 2 10− b b W+ 2 jets ( 0.1) W+ 3 jets ( 0.1) b b ≥ × b ≥ × b b 3 1 b 10− b 10− b b b b 1.8 2 b b 1.6 10− W+ 3 jets ( 0.01) 1.4 ≥ × b . b 1 2 b b b b b b b b b b 1 b 3 b b 0.8 10 b . − MC/data 0 6 b 0.4 b 0.2 4 10− 1.8 b b 1.6 1.4 1.2 1 b b b b b b b 1.8 0.8 . MC/data 0.6 1 6 0.4 1.4 0.2 1.2 1 b b b b b b b b b b 40 60 80 100 120 140 160 180 0.8 p [GeV] . ⊥ MC/data 0 6 Third Jet p 0.4 ⊥ 0.2 b b ATLAS data . 1 1 8 b MePs@Nlo

. [pb/GeV] 1 6 MePs@Nlo µ/2...2µ 1.4 ⊥ b p MEnloPS 1.2 1 b b b b b b b b b b /d 10− MEnloPS µ/2...2µ b 1 σ . d Mc@Nlo 0 8 W+ 3 jets . ≥ b MC/data 0 6 0.4 2 10− 0.2 b 1.8 1.6 3 1.4 10− 1.2 1.8 1 b b b b b b b b b b 1.6 1.4 0.8 1.2 b b b b b b

MC/data 0.6 1 0.4 0.8

MC/data 0.6 0.2 0.4 0.2 50 100 150 200 250 300 40 60 80 100 120 140 p [GeV] p [GeV] ⊥ ⊥

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

1.8 1.6 1.4 1.2 bbbbbbbbb b b b b 3 1 10 b ATLAS data 0.8 . MePs@Nlo MC/data 0 6 2 .

[pb/GeV] 0 4 10 .

T MePs@Nlo µ/2...2µ 0 2

H W+ 1 jet ( 1) 1 ≥ × MEnloPS 10 b /d 1.8 b MEnloPS µ/2...2µ σ b 1.6 d b 1 b Mc@Nlo 1.4 b 1.2 W+ 2 jets ( 0.1) b bbbbbbbb b b b b ≥ × b 1 1 b b . 10− b b 0 8 b b . b MC/data 0 6 b b . 2 b 0 4 10− b b 0.2 b b W+ 3 jets ( 0.01) b b ≥ b b × 3 b b 10 b 1.8 − b b 1.6 b b 1.4 10 4 b − b 1.2 1 bbbbbbbbb b b b 0.8

MC/data 0.6 100 200 300 400 500 600 700 . H 0 4 T [GeV] 0.2 100 200 300 400 500 600 700 HT [GeV] ∆R Distance of Leading Jets Azimuthal Distance of Leading Jets 100 b b [pb] [pb] ATLAS data 140 ATLAS data φ R b ∆

∆ MePs@Nlo MePs@Nlo b 80 120 /d /d MePs@Nlo µ/2...2µ MePs@Nlo µ/2...2µ σ σ d d MEnloPS 100 MEnloPS b b MEnloPS µ/2...2µ MEnloPS µ/2...2µ 60 b b b Mc@Nlo 80 Mc@Nlo

b b 40 b 60

b b

b b 40 b 20 b b b b b b b b b b b b b b b b b b 20 b b b b b b b b b 2 b b 2

1.5 1.5

1 bbbbbbbbbbbbbbbbbbbbbbbbbbbb 1 bbbbbbbbbbbbbbbb

MC/data 0.5 MC/data 0.5

0 0 1 2 3 4 5 6 7 8 0 0.5 1 1.5 2 2.5 3 ∆R(First Jet, Second Jet) ∆φ(First Jet, Second Jet)

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

SIMULATING SOFT QCD

HADRONISATION

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

QCD radiation, once more

remember QCD emission pattern

2 2 q→qg αs(k⊥) dk⊥ dω h ω i dw = CF 2 1 + 1 . 2π k⊥ ω − E spectrum cut-oﬀ at small transverse momenta and energies by onset of hadronization, at scales R 1 fm/ΛQCD ≈ two (extreme) classes of emissions: gluons and gluers determined by relation of formation and hadronization times

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

> gluers formed at times R, with momenta k k⊥ ω 1/R k ∼ ∼ ∼ assuming that hadrons follow partons,

Q Z 2 2 dk⊥ CF αs(k⊥) h ω i dω dN(hadrons) 2 1 + 1 ∼ k⊥ 2π − E ω k⊥>1/R C α (1/R2) dω F s log(Q2R2) ∼ π ω or - relating their energyn with that of the gluers -

dN(hadrons)/d log = const.,

a plateau in log of energy (or in rapidity)

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

impact of additional radiation new partons must separate before they can hadronize independently therefore, one more time

form kk t 2 ∼ k⊥ sep form t Rθ t (Rk⊥) ∼ ∼ had 2 form 2 t k R t (Rk⊥) . ∼ k ∼

for gluers Rk⊥ 1: all times the same ≈ naively; new & more hadrons following new partons but: colour coherence primary and secondary partons not separated enough in

< < 1/R ω 1/(Rθ) ∼ (hadron) ∼ and therefore no independent radiation

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

Hadronisation: General thoughts

conﬁnement the striking feature of low–scale sotrng interactions transition from partons to their bound states, the hadrons the Meissner eﬀect in QCD

QED:

QCD:

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

linear QCD potential in Quarkonia – like a string

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

combine some experimental facts into a naive parameterisation + − in e e hadrons: exponentially decreasing p⊥, ﬂat plateau in y for hadrons→

try “smearing”: ρ(p2 ) exp( p2 /σ2) ⊥ ∼ − ⊥

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

use parameterisation to “guesstimate” hadronisation eﬀects:

Z Y 2 2 E = dydp⊥ρ(p⊥)p⊥ cosh y = λ sinh Y 0 Z Y 2 2 P = dydp⊥ρ(p⊥)p⊥ sinh y = λ(cosh Y 1) E λ 0 − ≈ − Z 2 2 λ = dp ρ(p )p⊥ = p⊥ . ⊥ ⊥ h i

estimate λ 1/Rhad mhad, with mhad 0.1-1 GeV. ∼ ≈ eﬀect: jet acquire non-perturbative mass 2λE ( (10GeV) for jets with energy (100GeV∼ )). O O

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

similar parametrization underlying Feynman-Field model for independent fragmentation recursively fragment q q0+ had, where → transverse momentum from (ﬁtted) Gaussian; longitudinal momentum arbitrary (hence from measurements); ﬂavour from symmetry arguments + measurements. problems: frame dependent, “last quark”, infrared safety, no direct link to perturbation theory, ... .

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

The string model

a simple model of mesons: yoyo strings

light quarks (mq = 0) connected by string, form a meson 2 area law: mhad ∝ area of string motion L=0 mesons only have ’yo-yo’ modes:

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

turn this into hadronisation model e+e− qq¯ as test case → ignore gluon radiation: qq¯ move away from each other, act as point-like source of string intense chromomagnetic ﬁeld within string: more qq¯ pairs created by tunnelling and string break-up analogy with QED (Schwinger mechanism): d dxdt exp πm2/κ, κ = “string tension”. P ∼ − q

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

string model = well motivated model, constraints on fragmentation (Lorentz-invariance, left-right symmetry, ... ) how to deal with gluons? interpret them as kinks on the string = the string eﬀect ⇒

infrared-safe, advantage: smooth matching with PS.

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

The cluster model

underlying idea: preconfinement/LPHD typically, neighbouring colours will end in same hadron hadron flows follow parton flows −→ don’t produce any hadrons at places where you don’t have partons works well in large–Nc limit with planar graphs follow evolution of colour in parton showers

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

paradigm of cluster model: clusters as continuum of hadron resonances

trace colour through shower in Nc limit → ∞ force decay of gluons into qq¯ or dd¯ pairs, form colour singlets from neighbouring colours, usually close in phase space mass of singlets: peaked at low scales Q2 ≈ 0 decay heavy clusters into lighter ones or into hadrons (here, many improvements to ensure leading hadron spectrum hard enough, overall eﬀect: cluster model becomes more string-like) if light enough, clusters will decay into hadrons naively: spin information washed out, decay determined through phase space only heavy hadrons suppressed (baryon/strangeness suppression) →

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

self–similarity of parton shower will end with roughly the same local distribution of partons, with roughly the same invairant mass for colour singlets adjacent pairs colour connected, form colourless (white) clusters. clusters (“ excited hadrons) decay into≈ hadrons

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

Practicalities

practicalities of hadronisation models: parameters kinematics of string or cluster decay: 2-5 parameters must “pop” quark or diquark ﬂavours in string or cluster decay — cannot be completely democratic or driven by masses alone −→ suppression factors for strangeness, diquarks 2-10 parameters transition to hadrons, cannot be democratic over multiplets −→ adjustment factors for vectors/tensors etc. 2-6 parameters tuned to LEP data, overall agreement satisfying validity for hadron data not quite clear

(beam remnant fragmentation not in LEP.) there are some issues with inclusive strangeness/baryon production

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

SIMULATING SOFT QCD

UNDERLYING EVENT

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

Multiple parton scattering

hadrons = extended objects! no guarantee for one scattering only.

running of αS = preference for soft scattering. ⇒

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

ﬁrst experimental evidence for double–parton scattering: events with γ + 3 jets: cone jets, R = 0.7, ET > 5 GeV; |ηj | <1.3; “clean sample”: two softest jets with ET < 7 GeV; cross section for DPS

σγj σjj σDPS = σeﬀ

σeﬀ 14 4 mb. ≈ ±

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

0.12 ATLAS Wlν unfolded data, s=7 TeV 0.1 Fit distribution A+H+J particle-level template A PYTHIA particle-level template B 0.08 more measurements, also at 0.06 -1 Ldt=36 pb

Events / 0.03 ∫ LHC 0.04

ATLAS results from W + 2 0.02

0 jets 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ∆n jets

q ν W + AFS (4 jets - no errors given) q 22 UA2 (4 jets - lower limit) ν [mb]

eff CDF (4 jets) + 20 W q¯ σ ℓ¯ CDF (γ + 3 jets) 18 D0 (γ + 3 jets) ATLAS (W + 2 jets) ℓ¯ ⊗ 16 14 12 g q g 10 8 6 4 ATLAS 2 0 102 103 104 s [GeV]

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

Multiple Parton Interactions Outgoing Parton

PT(hard)

Proton AntiProton

Underlying Event Underlying Event

Outgoing Parton

but: how to deﬁne the underlying event?

1 everything apart from the hard interaction, but including IS showers, FS showers, remnant hadronisation. 2 remnant-remnant interactions, soft and/or hard. 3 lesson: hard to deﬁne

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

origin of MPS: parton–parton scattering cross section exceeds hadron–hadron total cross section

s/4 Z 2 2 dσ(p⊥) σhard(p⊥,min) = dp⊥ 2 > σpp,total dp⊥ 2 p⊥,min

for low p⊥,min remember

1 2 Z dσ(p⊥) 2 2 dσˆ2→2 2 = dx1dx2f (x1, q )f (x2, q ) 2 dp⊥ dp⊥ 0

σhard(p⊥,min)/σpp,total 1 h i ≥ depends strongly on cut-oﬀ p⊥,min (energy-dependent)!

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

Modelling the underlying event

take the old PYTHIA model as example: 2 start with hard interaction, at scale Qhard. 2 select a new scale p⊥ from

 2  Qhard 1 Z dσ(p2 ) exp − dp 02 ⊥   ⊥ 02  σnorm dp⊥ 2 p⊥

2 2 with constraint p⊥ > p⊥,min rescale proton momentum (“proton-parton = proton with reduced energy”). repeat until no more allowed 2 → 2 scatter

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

Modelling the underlying event

possible reﬁnements: may add impact-parameter dependence −→ more ﬂuctuations add parton showers to UE “regularisation” to dampen sharp dependence on p⊥,min: replace 1/ˆt in MEs by 1/(t + t0), also in αs. treat intrinsic k⊥ of partons (→ parameter) model proton remnants (→ parameter)

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

Practicalities

see some data comparison in Minimum Bias practicalities of underlying event models: parameters profile in impact parameter space 2-3 parameters IR cut-off at reference energy, its energy evolution, dampening paramter and normalisation cross section 4 parameters treating colour connections to rest of event 2-5 parameters tuned to LHC data, overall agreement satisfying energy extrapolation not exactly perfect, plus other process categories such as diffraction etc..

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

STATE OF THE ART

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

State of the art: ﬁxed order

NLO (QCD) “revolution” consolidated: lots of routinely used tools for large FS multis (4 and more) incorporation in MC tools done, need comparisons, critical appraisals and a learning curve in their phenomenological use to improve: description of loop–induced processes amazing success in NNLO (QCD) calculations: emergence of first round of 2 → 2 calculations next revolution imminent (with question marks) first MC tools for simple processes (gg → H, DY), more to be learnt by comparison etc. (see above) first N3LO calculation in gg H, more to come (?) → attention turning to NLO (EW) first benchmarks with new methods (V +3j) calculational setup tricky need maybe faster approximation for high-scales (EW Sudakovs)

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

Limitations: ﬁxed order

practical limitations/questions to be overcome: dealing with IR divergences at NNLO: slicing vs. subtracting

(I’m not sure we have THE solution yet) how far can we push NNLO? are NLO automated results stable enough for NNLO at higher multiplicity? users of codes: higher orders tricky → training needed

(MC = black box attitude problematic - a new brand of pheno/experimenters needed?) limitations of perturbative expansion: breakdown of factorisation at HO (Seymour et al.) n higher-twist: compare (αs/π) with ΛQCD/MZ limitations in analytic resummation: process- and observable-dependent ﬁrst attempts at automation (CAESAR and some others) – checks/cross-comparison necessary

showering needs to be improved (for NNLO the “natural” accuracy is NNLL)

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

State of the art: event generation

Systematic improvement of event generators by including higher orders has been at the core of QCD theory and developments in the past decade: multijet merging (“CKKW”, “MLM”) NLO matching (“MC@NLO”, “POWHEG”) MENLOPS NLO matching & merging MEPS@NLO (“SHERPA”, “UNLOPS”, “MINLO”, “FxFx”)

multijet merging an important tool for many relevant signals and backgrounds - pioneering phase at LO & NLO over complete automation of NLO calculations done must beneﬁt from it! −→ (it’s the precision and trustworthy & systematic uncertainty estimates!)

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

Vision

we have constructed lots of tools for precision physics at LHC but we did not cross-validate them careful enough (yet) but we did not compare their theoretical foundations (yet) we also need unglamorous improvements: systematically check advanced scale-setting schemes (MINLO) automatic (re-)weighting for PDFs & scales (ME: X, PS:-) scale compensation in PS is simple (implement and check) PDFs: to date based on FO vs. data — will we have to move to resummed/parton showered?

(reminder: LO∗ was not a big hit, though) ... and maybe we will have to go to the “dirty” corners: higher-twist, underlying event, hadronization, ...

(many of those driven by experiment)

F. Krauss IPPP QCD & Monte Carlo Event Generators Introduction Perturbative Monte Carlo Higher-Order Improvements Simulating Soft QCD Summary & Vision

F. Krauss IPPP QCD & Monte Carlo Event Generators