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 = dΦn P (Φn) O(Φn) h i n X Z Φn - Point in n-particle phase-space P (Φn) - Probability to produce Φn O(Φn) - Value of observable at Φn I Problem #1: Computing P (Φn) 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 dˆσij f ! dσh1h2 = dxi dxj dΦf fi/h1 (xi,µF ) fj/h2 (xj,µF ) . (44) 0 0 dxi dxj dΦf Xi,j Z Z Xf Z Note that, if dˆσ is divergent (as, e.g., Rutherford scattering is) then the integral over dΦf 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