Introduction to Monte-Carlo Event Generators — 24th Vietnam School of Physics — Quy Nhon, Vietnam Outline: - Why MCEG? - Birds hit by balls - Modelling Collider Physics - The steps it needs..
Johannes Bellm, Lund University , 28.-30.5.2018 Short notice lectures!!
I jumped in ans accepted to give this lectures two weeks ago…
Therefore these lectures are written in a hurry!! The last lecture is not even ready..
Many of the pictures/slides are from other lectures from:
Stefan Gieseke, Stefan Höche, Frank Krauss, Jonas Lindert Leif Lönnblad, Mike Seymour, Andrzej Siodmok, Torbjörn Sjöstrand
So I have to thank those!!
Johannes Bellm, Lund University , 28.-30.5.2018 Tutorials
I tried to put some simplified examples together to allow you to get your hands on and see how the things I will explain actually work in practice.
Usually the installation and getting everything to work takes 20-40% of the tutorials. Let’s hope it will be better…
In the first parts we will use python notebooks to do some examples.
In the end I will make a live presentation of Herwig and how to use it.
Johannes Bellm, Lund University , 28.-30.5.2018 Further Reading:
Books: The Black Book of Quantum Chromodynamics (Campbell,Huston,Krauss, 2018) QCD and Colliders Physics (Ellis, Stirling, Webber, 1996) Basics of Perturbative QCD (Dokshitzer, Khoze, Mueller, Troyan, 1991)
Other: Buckley et al.: General-purpose event generators for LHC physics Höche: Introduction to parton-shower event generators Skands: Introduction to QCD
Johannes Bellm, Lund University , 28.-30.5.2018 What topic am I trying to cover?
symmetrymagazine.org
…common words in the titles of the 2012 top 40 papers.
Johannes Bellm, Lund University , 28.-30.5.2018 What topic am I trying to cover?
symmetrymagazine.org
Johannes Bellm, Lund University , 28.-30.5.2018 Event Simulation
Goal: Describe Collider events as realistic as possible.
picture: arXiv:1411.4085
Johannes Bellm, Lund University , 28.-30.5.2018 Birds Goal: Learn something about birds.
Properties: • average Size • preferred Food • typical Color • Relation between Species • max. Speed • Availability to flight • average Age • … • average Weight Measurement: • Design/Reuse methods to quantify the known properties. • E.g. use same apparatus was used to quantify the weight of stones. • Construct experiments to find new observations. • Travel around the world to find new species, relate them. Posible Outcomes: • Use observations to learn how to build planes. • Relate species and build a model of evolution.
Picture from: wikipedia.org/wiki/Bird
Johannes Bellm, Lund University , 28.-30.5.2018 Birds
We can observe birds with our eyes, touch them, put them in cages..
Good for bird watchers…
Picture from: wikipedia.org/wiki/Bird
Johannes Bellm, Lund University , 28.-30.5.2018 Birds
What if we could not see birds and birds would be extremely small objects?
— hard to touch — hard to catch — hard to observe
Picture from: wikipedia.org/wiki/Bird
Johannes Bellm, Lund University , 28.-30.5.2018 Birds
What if we could not see birds and birds would be extremely small objects?
Picture from: wikipedia.org/wiki/Bird
Johannes Bellm, Lund University , 28.-30.5.2018 Particle Physics (in the bird picture)
Data:
• Counting experiment: • Number of birds hit as a function of ball speed: Independent of ball direction afterwards —> Inclusive w.r.t. ball direction —> sum/integrate over all possibilities.
• Differential measurement: • Measure for example the change of direction of the bird as a function of the angle or transverse momentum w.r.t the bird-ball-axis.
Inclusive: Sum/integrate over degrees of freedom. Exclusive: Be sensitive to certain degrees of freedom. We will repeat this later…
Johannes Bellm, Lund University , 28.-30.5.2018 Particle Physics (in the bird picture)
Theory:
• cross section definition + Feynman rules (see Lecture by G. Heinrich) can predict • the rate of birds getting hit if you throw (enough) balls. • the probability of the ball-bird-fusion to create an elephant and decaying to modified ball-bird-system • the probability of exited ball states. • It might be needed to describe the bird as a composite object (wings,head,tails) and extract ( f(x) ) the probabilities to hit a wing with different probabilities as a tail. • Also a wing-hit might give a different functional form w.r.t. scattering angle.
Johannes Bellm, Lund University , 28.-30.5.2018 Particle Physics (in the bird picture) Theory vs. Data comparison:
• Measure the wing-extraction p(wing,speed) probability as function of bird-speed in shooting experiments. • Create a model of a bird and a ball and calculate probability distribution of ball directions modifications for different hits. • Model the wind/detector/feather loss or estimate effect from other data. • Sum over all possible hits folded with the extraction probabilities. • Compare theory distribution with a lot of bird-hit-data measuring the angular distribution. • Improve model: • Allow feathers to modify impact of ball • Include feathers sticking to ball • Include rotation of bird and ball. • Estimate uncertainties by variation of ball and bird size, different feather models….
Johannes Bellm, Lund University , 28.-30.5.2018 Particle Physics Goal: Learn something about basic forces and particles in nature
Properties: • Mass • Production & Decay • Forces & Charges • Species & Families • average Age (lifetime) • Excitations • Relations between • Resonances hadrons (Symmetries) • …
Model: • Understand the underlying symmetries/forces as QFT and build a model to describe the properties. —> SM (after years of development!)
Measurement: • Usually in collider experiments like LHC/LEP/Tevatron/fixed target… • Produce new particles by collision of particles.
Johannes Bellm, Lund University , 28.-30.5.2018 Event Simulation — Break down to topics
Monte Carlo
Hard Process
Shower
Underlying Event
Hadronization
Goal: Describe Collider events as realistic as possible.
Johannes Bellm, Lund University , 28.-30.5.2018 Event Simulation — Break down to topics
Lecture 1 Hard Process Overview Lecture 3
Lecture 5 Phenomenology MC methods Shower Events Lecture 2 Lecture 4 Observables Predictions Calibration Hadronization & Underlying Event
Lecture 6
Johannes Bellm, Lund University , 28.-30.5.2018 Buzzwords
— Hard Process — MC@NLO, POWHEG, — LO/NLO — MEPS@NLO, FxFx, UNLOPS,…. — Parton Shower — QED and QCD — DGLAP and Splitting Kernels — Spin-Correlations and Decays — Herwig, Pythia, Sherpa… — Uncertainties — Hadronization — Hard and Soft — Angular Ordering and Dipole — … — ME corrections, Matching and Merging
Johannes Bellm, Lund University , 28.-30.5.2018 MC Method ME PS Matching Merging MPI Hadronization Decays Stating the problem
Observables — Stating the problem
I Want to compute expectation values of observables
O = d n P ( n) O( n) h i n X Z n - Point in n-particle phase-space P ( n) - Probability to produce n O( n) - Value of observable at n
I Problem #1: Computing P ( n)
I Problem #2: Performing the integral
I At LO and NLO problem #2 is harder to solve This is where MC event generators come in
Johannes Bellm, Lund University , 28.-30.5.2018
Stefan H¨oche MC Event Generators 6 P. Skands Introduction to QCD
Secondly, and more technically, at NLO and beyond one also has to settle on a factorization scheme in which to do the calculations. For all practical purposes, students focusing on LHC physics are only likely to encounter one such scheme, the modified minimal subtraction (MS) one already mentioned in the discussion of the definition of the strong coupling in Section 1.4. At the level of these lectures, we shall therefore not elaborate further on this choice here. We note that factorization can also be applied multiple times, to break up a complicated calculation into simpler pieces that can be treated as approximately independent. This will be very useful when dealing with successive emissions in a parton shower, section 3.2, or when factoring off decays of long-lived particles from a hard production process, section 3.4. We round off the discussion of factorization by mentioning a few caveats the reader should be aware of. (See [52] for a more technical treatment.) Firstly, the proof only applies to the first term in an operator product expansion in “twist” = mass dimension - spin. Since operators with higher mass dimensions are suppressed by the hard scale to some power, this leading twist approximation becomes exact in the limit Q , !1 while at finite Q it neglects corrections of order [ln(Q2/⇤2)]m<2n Fixed Order (inHigher �) Twist : (n =2for DIS) . (43) Q2n In section 5, we shall discuss some corrections that go beyond this approximation, in the context of multiple parton-parton interactions. Secondly, the proof only really applies to inclusive cross sections in DIS [51] and in Drell- Yan [55]. For all other hadron-initiated processes, factorization is an ansatz. For a general hadron-hadron process, we write the assumed factorizable cross section as: 1 1 2 2 dˆ ij f ! d h1h2 = dxi dxj d f fi/h1 (xi,µF ) fj/h2 (xj,µF ) . (44) 0 0 dxi dxj d f Xi,j Z Z Xf Z
Note that, if dˆ is divergent (as, e.g., Rutherford scattering is) then the integral over d f must be regulated, e.g. by imposing some explicit minimal transverse-momentum cut and/or otherGenerator phase-space Idea of restrictions.event/cross section: 1. At highest scale Q: 2.2• Extract Parton quarks Densities or gluons with PDFs
• Calculate cross section (hard process,2 Feynman rules…). The parton density function, fi/h(x,µF ), represents the effective density of partons of type/flavor 14 Result: i, as a function of the momentum fraction xi, when a hadron of type h is probed at the fac- Fixed Order LO torization scale µF . The PDFs are non-perturbative functions which are not a priori calculable, pp -> f but a perturbative differential equation governing their evolution with µF can beLecture obtained 3 by requiring that physical scattering cross sections, such as the one for DIS in equation (42), be independent of µF to the calculated orders [56].Johannes The resultingBellm, Lundrenormalization University , 28.-30.5.2018 group equation (RGE) is called the DGLAP15 equation and can be used to “run” the PDFs from one pertur- bative resolution scale to another (its evolution kernels are the same as those used in parton showers, to which we return in section 3.2). This means that we only need to determine the form of the PDF as a function of x a single (arbitrary) scale, µ0. We can then get its form at any other scale µF by simple RGE evolution. 14Recall: the x fraction is defined in equation (41). 15DGLAP: Dokshitzer-Gribov-Lipatov-Altarelli-Parisi [56–58].
— 20 — Minimum Bias Multiple Interactions Underlying Events ˇ What happens at LHC? (13 TeV)
Total 100 mb Non-diffractive 56 mb Elastic 22 mb Diffractive 22 mb „barn“ Jets p⊥ > 150 GeV 220 nb W+Z 200 nb Top 600 pb Higgs 30 pb
Lecture 3
Johannes Bellm, Lund University , 28.-30.5.2018
Event Generators IV 3 Leif Lönnblad Lund University Minimum Bias Multiple Interactions Underlying Events ˇ What happens at LHC? (13 TeV)
Jets p⊥ > 2 GeV 900 mb ??? Jets p⊥ > 4 GeV 120 mb That Total 100 mb can’t Non-diffractive 56 mb be Elastic 22 mb Diffractive 22 mb true!! Jets p⊥ > 150 GeV 220 nb W+Z 200 nb Top 600 pb Higgs 30 pb BSM ∼ 0? fb Can this be true? Lecture 6
Johannes Bellm, Lund University , 28.-30.5.2018
Event Generators IV 3 Leif Lönnblad Lund University Fixed Order (Corrections in �)
100 LO NLO NLO (Born Approx.) (Loop / Virtual)50 (Real Emission)
0.2 0.4 0.6 0.8 1.0 q -50 �(q) ∞ d R dq = -100 dq 1 Z0
d R d V Higher order corrections: + dq = finite 0 dq dq — Inclusion of virtual and real emission diagrams Z ✓ ◆ — Divergencies arise • High Energy Loops (UV) -> Renormalisation of parameters • Small Resolution (infra red and collinear) -> cancel between V and R (and C (PDF renormalisation))
Johannes Bellm, Lund University , 28.-30.5.2018 QED bremsstrahlung – 1 Event Simulation Accelerated electric charges radiate photons , see e.g. J.D. Jackson, Classical Electrodynamics. A charge ze that changes its velocity vector from to 0 radiates a spectrum of photons that depends on its trajectory. In the long-wavelength limit it reduces to
2 2 2 2 d I z e 0 lim = ✏⇤ ! 0 d!d⌦ 4⇡2 1 n 1 n ! ✓ 0 ◆ where n is a vector on the unit sphere ⌦, ! is the energy of the radiated photon, and ✏ its polarization.
1 For fast particles radiation collinear with the and 0 directions is strongly enhanced. 2 dN/d! =(1/!)dI /d! 1/! so infinitely many infinitely soft / photons are emitted, but the net energy taken away is finite.
Torbj¨orn Sj¨ostrand PPP 3: Evolution equations and final-state showers slide 3/50 Johannes Bellm, Lund University , 28.-30.5.2018 EventQED Simulation bremsstrahlung — Break – 2 down to topics
An electrical charge, say an electron, e is surrounded by a field: For a rapidly moving charge e this field can be expressed in terms of an equivalent flux of photons:
2↵em d✓ d! dn ⇡ ⇡ ✓ ! e Equivalent Photon Approximation, or method of virtual quanta (e.g. Jackson) e (Bohr; Fermi; Weisz¨acker, Williams 1934) . ⇠ ✓: collinear divergence, saved by me > 0 in full expression. !: true divergence, n d!/! = , but E ! d!/! finite. / 1 / These are virtual photons:R continuously emitted andR reabsorbed.
Torbj¨orn Sj¨ostrand PPP 3: Evolution equations and final-state showers slide 4/50 Johannes Bellm, Lund University , 28.-30.5.2018 TitleQED bremsstrahlung – 3 When an electron is kicked into a new direction, the field does not have time fully to react:
e
Initial State Radiation (ISR): part of it continues in original direction of e ⇠ Final State Radiation (FSR): the field needs to be regenerated around outgoing e, and transients are emitted around outgoing e direction ⇠ Emission rate provided by equivalent photon flux in both cases. Approximate cuto↵s related to timescale of process: the more violent the hard collision, the more radiation!
Torbj¨orn Sj¨ostrand PPP 3: Evolution equations and final-state showers slide 5/50
Johannes Bellm, Lund University , 28.-30.5.2018 InitialThe State Parton-Shower and Final Approach State Radiation
2 n = (2 2) ISR FSR ! !
FSR = Final-State Radiation = timelike shower Q2 m2 > 0 decreasing i ⇠ ISR = Initial-State Radiation = spacelike showers Q2 m2 > 0 increasing i ⇠
Lecture 3 Torbj¨orn Sj¨ostrand PPP 3: Evolution equations and final-state showers slide 7/50 Johannes Bellm, Lund University , 28.-30.5.2018 Parton Shower 6.2 Shower dynamics d R d V With the kinematicsd defined, R we now consider the dynamics governing the parton branchings. + dq = finite Each parton but: branching is approximated large by the quasi-collinear limit [62], in which the transverse 0 dq dq 2 Z ✓ ◆ momentum squared, pdq⊥,andthemasssquaredoftheparticlesinvolvedaresmall(compared to p n)butp2 /m2 is not necessarily small. In this limit the probability of thebranchingij i+ j · ⊥ → 100 can be written as 2 αS d˜q e e ! d ij→ij = 2 dzPij→ij (z, q˜) , (6.13) 50 P 2π q˜
where Pije→ij (z, q˜)arethequasi-collinearsplittingfunctionsderivedin[62]. In terms of our light-
0.2 0.4 0.6 0.8 1.0 cone momentum fraction and (time-like) evolution variable the quasi-collinear splitting functions 2 are ↵S 1+z
-50 Pq qg(z)= CF !C 2⇡ 2m21 z P = F 1+z2 q , (6.14a) q→qg 1 z − zq˜2 -100 − " # Altarelli Parisiz Splitting1 z Kernel P = C + − + z (1 z) , (6.14b) g→gg A 1 z z − " − # 2m2 Describe splittingP = T in 1soft/collinear2z (1 z)+ q , (6.14c) g→qq¯ R − − z (1 z)˜q2 " − # approximation withC splitting 2functions.m2 P = A 1+z2 g˜ , (6.14d) Not yet probabilities.g˜→gg˜ 1 z − zq˜2 − " # 2C m P = F z q˜ , (6.14e) q˜→qg˜ 1 z − zq˜2 − " # for QCD and singular SUSYAP: inspirehep:119585 QCD branchings12.Thesesplittingfunctionsgiveacorrectphysical 6450 citations description of theJohannes dead-cone Bellm, region Lundp⊥ ! Universitym,wherethecollinearsingularlimitofthematrix , 28.-30.5.2018 element is screened by the mass m of the emitting parton. The soft limit of the splitting functions is also important. The splitting functions with soft singularities Pq→qg, Pq˜→qg˜ , Pg→gg,andPg˜→gg˜ ,inwhichtheemittedparticlej is a gluon, all behave as e 2 2Cij mi lim P e = 1 , (6.15) z→1 ij→ij 1 z − q˜2 − $ % 1 13 in the soft z 1limit,whereC e equals C for P and P , C for P ,andC for → ij F q→qg q˜→qg˜ 2 A g→gg A Pg˜→gg˜ .Inusingthesesplittingfunctionstosimulatetheemissionofagluonfromatime-like mother parton ij,associatedtoageneraln parton configuration with matrix element ,one Mn is effectively approximating the matrix element for the process with the additional gluon, , Mn+1 by ! 2 8παS 2 e n+1 = 2 2 Pij→ij n . (6.16) |M | q e m e |M | ij − ij 12 The Pg→gg splitting presented here is for final-state branching where the outgoing gluons are not identified and therefore it lacks a factor of two due to the identical particle symmetry factor. For initial-state branching one of the gluons is identified as being space-like and one as time-like and therefore an additional factor of 2 is required. 13Note that for g gg,thereisalsoasoftsingularityatz 0withthesamestrength,sothatthetotal → → emission strength for soft gluons from particles of all typesinagivenrepresentationisthesame: CF in the fundamental representation and CA in the adjoint.
37 Using the definitions of our shower variables, Eq. (6.4), and making the soft emission approxi- 2 2 2 mations q e q p, q m = m e in Eqs. (6.15, 6.16)wefind[23] ij ≈ i ≈ i ≈ i ij 2 8παS n p lim P e = 4παSC e . (6.17) z→1 q2 m2 ij→ij − ij n q − p q ije − ije ! · j · j " Recalling that we choose our Sudakov basis vector n to point in the direction of the colour partner of the gluon emitter (ij/i), Eq. (6.17)isthenjusttheusualsofteikonaldipolefunction describing soft gluon radiation by a colour dipole [63], at least for the majority of cases where the colour partner is massless or# nearly massless. In practice, the majority of processes we intend to simulate involve massless or light partons, or partons that are light enough that n reproduces the colour partner momentum to high accuracy14. For the case that the underlying process with matrix element n is comprised of a single colour dipole (as is the case for a number of important processes),M the parton shower approxi- mation to the matrix element n+1,Eq.(6.16), then becomes exact in the soft limit as well as, and independently of, the collinearM limit. This leads to a better description of soft wide angle radiation, at least for the first emission, which is of course the widest angle emission in the an- gular ordered parton shower. Should the underlying hard process consist of a quark anti-quark pair, this exponentiation of the full eikonal current, Eq. (6.17), hidden in the splitting functions, combined with a careful treatment of the running coupling (Sect. 6.7), will resum all leading and next-to-leading logarithmic corrections [32,64–66]. In the event that there is more than one colour dipole in the underlying process, the situation is more complicated due to the ambiguity in choosing the colour partner of the gluon, and the presence of non-planar colour topologies. In general, the emission probability for the radiation of gluons is infinite in the soft z 1 andParton collinearq ˜ Shower0limits.Physicallythesedivergenceswouldbecanceledbyvirtual corrections,→ → which we do not explicitly calculate but rather include through unitarity. We impose a physical d R d V d R cutoff on the gluon and+ light quarkdq virtualities= finite and call radiation above this limit resolvable. The cutoff ensures that dq the contribution dq from resolvable but: radiat ion is finite. large Equally the uncalculated Z0 ✓ ◆ dq 1.0 virtual corrections ensure that the contribution of the virtual and unresolvable emission belowSudakov peak 100 the cutoff is also finite. Imposing unitarity,
50 (resolved) + (unresolved) = 1, 0.5 (6.18) P P gives the probability of no branching in an infinitesimal increment of the evolution variable d˜q as
0.2 0.4 0.6 0.8 1.0
1 d ije →ij, (6.19) − P 0.5 1.0 1.5 2.0 -50 i,j Q $ where the sum runs over all possible branchings of the particle ij.Theprobabilitythataparton -100 does not branch betweend ( twoq) scales(Q, is given q)+ by the product(Q, µ of)=1 the probabilities-0.5 that it did not branch in any of the small increments d˜q between the two scales.# Hence, in the limit d˜q 0the which is the probabilityµ of evolvingP between the scaleq ˜ andq ˜ without resolvable emission.→Sudakov The suppression probabilityZ of no branching exponentiates, giving theh Sudakov form factor no-emission probability for a given type of radiation is
∆ (˜q, q˜h)= ∆ije→ij (˜q, q˜h)(6.20)-1.0 q˜h ′2 ′ d˜q αS (z,i,jq˜ ) ′ 2 e % e ∆ij→ij (˜q, q˜h)=exp ′2 dz Pij→ij (z, q˜ ) Θ p⊥ > 0 . (6.21) 14 − q˜ 2π + − Even when the colour! partner"q˜ has a" large mass, as in e e tt¯,thefactthateachshowerevolvesintothe% forward hemisphere, in the opposite direction to the colour partner,→ means that# the difference$ between Eq. (6.17) The allowedand the phase exact space dipole forfunction each is branching rather small in is practice. obtained by requiring- Working that the relative with transverse probabilities. momentum is real, or p2 > 0. For a general time-like branching ij i + j this gives ⊥ → 38 - Missing finite corrections. 2 2 2 2 2 2 z (1 z) q˜ (1 z) m zm + z (1 z) m e > 0, (6.22) − − − i − j − &- ijValid in IRC limit. from Eq. (6.6). In practice rather than using the physical masses for the ligJohannesht quarks Bellm, and gluon Lund we University impose a , 28.-30.5.2018 cutoff to ensure that the emission probability is finite. We useacutoff, Qg,forthegluonmass, and we take the masses of the other partons to be µ =max(m, Qg), i.e. Qg is the lowest mass allowed for any particle. There are two important special cases. 1. q qg,theradiationofagluonfromaquark,orindeedanymassiveparticle. In this case Eq.→ (6.22)simplifiesto z2(1 z)2q˜2 > (1 z)2 µ2 + zQ2, (6.23) − − g which gives a complicated boundary in the (˜q, z)plane.Howeveras
(1 z)2 µ2 + zQ2 > (1 z)2 µ2,z2Q2 (6.24) − g − g the phase space lies inside the region µ Q p = (1 z)2 (z2q˜2 µ2) zQ2. (6.26) ⊥ − − − g ' 2. g gg and g qq¯,orthebranchingofagluonintoanypairofparticleswiththesame mass.→ In this case→ the limits on z are 1 4µ z How to model? Divide and conquer Partonic cross section from FeynmanMini diagrams event generator Divide and conquer ds = dsharddP(partons hadrons) !I We generate pairs (~xi,wi). PartonicNote, that cross section from Feynman diagrams I Use immediately to book weighted histogram of arbitrary ds = ds dP(partons hadrons) harddP(partons !hadrons)=observable1 , (possibly with additional cuts!) Note, that ! Z I Keep event~xi with probability I s remainsd unchangedP(partons hadrons)=1 , ! Z wi I introduce realistic fluctuations into distributions. Pi = . I s remains unchanged wmax I introduce realistic fluctuations into distributions. Generate events with same frequency as in nature! Simulation steps governed by different scales separation into (Q 1GeV > L ) ! 0 ⇡ QCD dP(partons hadrons)= dP(resonance decays)[G > Q ] ! 0 dP(parton shower)[TeV Q ] ⇥ ! 0 dP(hadronisation)[Q ] ⇥ ⇠ 0 dP(hadronic decays)[O(MeV)] ⇥ Stefan Gieseke CTEQ School 2013 36/91 · Stefan Gieseke CTEQ School 2013 11/91 Stefan Gieseke· CTEQ School 2013 11/91 · Johannes Bellm, Lund University , 28.-30.5.2018 Radiation Factorization PDFs Jets Fluctuations Q2 - Example: PDFs - Proton has 3 valence quarks (uud) - But also gluons and sea quarks - This Dirac sea is pretty flat from the outside Radiation Factorization PDFs Jets - But tested with large scale/PDFs: small parametrisations and results 1/x times the structure changes Example below: CT14NNLO, at Q =2GeVandQ =100GeV dramatically. CT14 NNLO CT14 NNLO 0.8 0.8 g!x,Q"#5 g!x,Q"#5 u u 0.6 0.6 d at Q = 2 GeV at Q = 100 GeV " 0.4 " 0.4 d x,Q x,Q ! ! xf xf d!bar ! ! 0.2 s bar u bar 0.2 d!bar u!bar s!bar 0. 0. 0.001 0.003 0.01 0.03 0.1 0.3 1 0.001 0.003 0.01 0.03 0.1 0.3 1 x x Johannes Bellm, Lund University , 28.-30.5.2018 F. Krauss IPPP QCD at Colliders F. Krauss IPPP QCD at Colliders Hadronisation - Colors not visible Physical input (to strong to separate/Confinement)Self coupling of gluons Physical input Linear static potential V(r) kr. “attractive field lines” ⇡ - Colors are pulled back similar$ to rubber band / string Self coupling of gluons Linear static potential V(r) kr. “attractive field lines” ⇡ - Pair creation / string break!$ Lund string model Supported by lattice QCD, hadron spectroscopy. Ajacent breaks form hadrons. Supported by lattice QCD, Stefan Gieseke CTEQ School 2013 hadron spectroscopy. 65/98 · Stefan Gieseke CTEQ School 2013 65/98 · Lecture 6 Johannes Bellm, Lund University , 28.-30.5.2018 Works in both directions (symmetry). Lund symmetric fragmentation function 2 2 1 a b(mh + p ) f (z,p ) (1 z) exp ? ? ⇠ z z ! 2 a,b,mh main adjustable parameters. Note: diquarks baryons. ! Stefan Gieseke CTEQ School 2013 70/98 · Modelled as Colorlines In PS usually color is treated in large color limit SU(3)×SU(2)×U(1). Generators keep track of colors and build colorless objects. Johannes Bellm, Lund University , 28.-30.5.2018 Cluster (Herwig) or Lund Strings (Pythia) Several models in different generators (cluster and strings). Cluster models in Herwig and Sherpa. Lund Strings in Pythia and Vincia. Lecture 6 Johannes Bellm, Lund University , 28.-30.5.2018 Multi Parton Interactions One needs to care about the rest of the proton parsons and colors. Various MPI models implemented. Needed for interpretation of cross section. Lecture 6 Johannes Bellm, Lund University , 28.-30.5.2018 Resummation Introductory example (courtesy of Gavin Salam) Why resummation is needed 10 OPAL 91 GeV T B d / s d 1 s / 1 0.1 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Total Broadening (BT) Resummation () WebberFest 22/ 09/ 2010 3 / 20 Johannes Bellm, Lund University , 28.-30.5.2018 Resummation Introductory example (courtesy of Gavin Salam) Why resummation is needed 10 OPAL 91 GeV LO T B d / s d 1 s / 1 d 2 (α s ln B) dB 0.1 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Total Broadening (BT) Resummation () WebberFest 22/ 09/ 2010 3 / 20 Johannes Bellm, Lund University , 28.-30.5.2018 Resummation Introductory example (courtesy of Gavin Salam) Why resummation is needed 10 OPAL 91 GeV LO NLO T B d / s d 1 s / 1 d 2 2 4 (α s ln B+ α ln B) dB s 0.1 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Total Broadening (BT) Resummation () WebberFest 22/ 09/ 2010 3 / 20 Johannes Bellm, Lund University , 28.-30.5.2018 Resummation Introductory example (courtesy of Gavin Salam) Why resummation is needed 10 OPAL 91 GeV LO NLO NLL + NLO T B d / s d 1 s / 1 d 2 2 4 (α s ln B+ α ln B+ ··· ) dB s 0.1 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Total Broadening (BT) Resummation () WebberFest 22/ 09/ 2010 3 / 20 Johannes Bellm, Lund University , 28.-30.5.2018 ResummationIntroductory example (courtesy of Gavin Salam) Why resummation is needed • Resummation probes 10 OPAL 91 GeV NLO + NLL high-order structure of + hadronisation perturbation theory: leads to non- T B d perturbative structure / s d 1 s / 1 d 2 2 4 (α s ln B+ α ln B+ ··· ) dB s 0.1 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Total Broadening (BT) Resummation () Johannes Bellm, LundWebbe rUniversityFest 22/ 09/ 201 0, 28.-30.5.20183 / 20 General Purpose Event Generators Go to: http://mcplots.cern.ch Find large set of measured observables and the corresponding predictions from generators. Johannes Bellm, Lund University , 28.-30.5.2018 General Purpose Event Generators Z-boson transverse momentum Number of jets in W-boson (recoil against emission) production (in this plot: merging only in Sherpa) Johannes Bellm, Lund University , 28.-30.5.2018 + 7.1. Parton Production in e e Annihilation 89 Matching and Merging 10 8 10 8 [pb] q¯q(0,1,2) [pb] q¯q(0,1,2) 34 V 34 y 10 7 q¯q (0) y 10 7 q¯q(0,-,-) V /d q¯qC (1) -1 /d q¯q(-,1,-) s V ⇥ s d q¯q (1) d q¯q(-,-,2) 10 6 q¯qV (2) -1 10 6 C ⇥ q¯q(2) 10 5 10 5 10 4 10 4 10 3 10 3 1.4 1.4 1.2 1.2 1 1 Ratio Ratio 0.8 0.8 0.6 0.6 4 3 2 1 4 3 2 1 10 10 10 10 10 10 10 10 y34 y34 Figure 7.2.: Di↵erential cross section as a function of y34, which separates three jet events Lecture 5 from four jet events in a Durham jet algorithm. The cross section is splitJohannes up into Bellm, the Lund di↵ Universityerent , 28.-30.5.2018 contributions leading to the combined q¯q(0, 1, 2) merged sample. The blue contributions in the left picture are compensated by the red, clustered subtraction terms. The red lines are multiplied by a factor minus one. In the right picture the blue contributions are the sum of the red and blue lines in the left plot, e.g. q¯q(0, , )=q¯qV (0) + q¯qV (1). C 10 4 0 [pb] 23,..,67 q¯q( ) y 3 10 q¯q(0,1) ,excl. i /d s s q¯q(0,1,2) 2 d 2 = ij N 10 q¯q(0,1,2,3) i s  1/ 10 1 10 4 1 q¯q(0) q¯q(0,1) 1 10 q¯q(0,1,2) q¯q(0,1,2,3) 2 10 1.4 1.2 1.05 45 y 1 1.0 Ratio vs. 0.8 0.95 0.6 0.9 4 3 2 1 10 10 10 10 0 5 10 15 20 y23,..,67 incl. N-partons Figure 7.3.: Left: Di↵erential jet rates as a function of the various Durham ya,a+1 parameter, where a particular event changes the multiplicity from an a-jet to an a+1-jet configuration within the Durham jet algorithm. The di↵erential cross sections have been normalized to their individual integrated cross section and the ratio is with respect to y45 of q¯q(0). Right: The cross section as a function of inclusive N-parton states. three to four jet events. The di↵erent distributions are plotted leading to q¯q(0, 1, 2). Here, we split the distribution according to Eqs. (4.35) and (4.36). On the left hand side of Fig. 7.2, the dashed lines correspond to configurations entering the vetoed shower with no additional emission. These are (before the vetoed showering) the pure e+e qq¯ events (blue dashed), ! which are compensated by the clustered events with one additional emission (red dashed) Collider Tools Hard Processes and Higher Orders Good Description At the LHC: ATLAS Z+jets 6 10 +− 3 ATLAS Preliminary Z/γ*(→ l l ) + jets 10 +− ) [pb] ATLAS Preliminary Z/γ*(→ l l ) + ≥ 1 jet 5 −1 Data 10 13 TeV, 3.16 fb −1 jets 2 13 TeV, 3.16 fb Data anti-k jets, R = 0.4 BLACKHAT + SHERPA 10 Z + ≥ 1 jet N NNLO 4 t jetti [pb/GeV] anti-k jets, R = 0.4 *+N 10 jet jet SHERPA 2.2 t BLACKHAT + SHERPA jet T γ p > 30 GeV, ⎜ y ⎜ < 2.5 jet jet T 10 p > 30 GeV, ⎜ y ⎜ < 2.5 HERPA 3 ALPGEN + PY6 T S 2.2 (Z/ 10 /dp ALPGEN + PY6 σ MG5_aMC + PY8 CKKWL σ d 2 1 MG5_aMC + PY8 CKKWL 10 MG5_aMC + PY8 FxFx MG5_aMC + PY8 FxFx -1 10 10 1 10-2 10-1 10-3 -2 10 10-4 1.5 1.5 100 200 300 400 500 600 700 1 1 Pred./Data 0.5 Pred./Data 0.5 1.5 ≥0 ≥1 ≥2 ≥3 ≥4 ≥5 ≥6 ≥7 1.5 100 200 300 400 500 600 700 1 1 Pred./Data Pred./Data 0.5 0.5 1.5 ≥0 ≥1 ≥2 ≥3 ≥4 ≥5 ≥6 ≥7 1.5 100 200 300 400 500 600 700 1 1 Pred./Data Pred./Data 0.5 0.5 ≥0 ≥1 ≥2 ≥3 ≥4 ≥5 ≥6 ≥7 100 200 300 400 500 600 700 N pjet (leading jet) [GeV] jets T ATLAS-CONF-2016-046 Johannes Bellm, Lund University , 28.-30.5.2018 Peter Richardson Collider Tools MCnet projects Pythia+Vincia Herwig Sherpa MadGraph “Plugin” – Ariadne+HEJ CEDAR – Rivet+Professor +Contur+hepforge+… Thank you! Johannes Bellm, Lund University , 28.-30.5.2018