The Large Hadron Collider Machine, Experiments, Physics Basics of proton-proton physics

1. The Large Hadron ColliderMachine, Experiments, PhysicsBasics of proton-proton physics Johannes HallerThomas Schörner-Sadenius Hamburg UniversitySummer Term 2009

2. OVERVIEW OF pp REACTIONS (1) • To be understood: • The complex protons.  proton structure  HERA physics and deep inelastic scattering • The reaction between (constituents of) the protons. (hard) QCD, using perturbation theory and Feynman rules  models for things that cannot be treated using pQCD. • The transformation to signals in the detector. detector simulations, detector understanding (not treated in detail) pp reactions:… from a simple (but potentially coloured!) initial state: … to a very complicated final state on “hadron level” and in the detector: p p UHH SS09: LHC

3. INTRODUCTION TO THE QPM AND TO QCD e± e± ν=E-E’ Q2: resolution λ=1/Q q p x Description: ... Assuming inelastic scattering between two spin-1/2 particles with target recoil: What can we say about the functions W1,2 (soon called F1,2) assuming the QPM? 1) If there are exactly 3 partons in the proton, then proton structure cannot depend on how closely we look (resolution), but only on the fractions of proton momentum xi, i=1,2,3, they carry: 2) F1,2 depend on electric charge distributions inside the proton given by the parton distribution functions (PDFs) q(x) as functions of x. qi(x): probability to find parton i with momentum fraction x inside the proton. • Situation 30-40 years ago: • – “Particle zoo” of hadrons with large variety of masses, spins, charges  “quarks” (u,d,s Gell- Mann, Zweig) as ordering scheme.– inelastic ep scattering revealed structures that might be explained by point-like constituents (Hofstadter)  “partons” (Feynman, Bjorken). • Quark-parton model (QPM) build on insight that all phenomena described by elementary particles with spin ½ and fractional charges (1/3, 2/3). UHH SS09: LHC

4. INTRODUCTION TO THE QPM AND TO QCD • Famous scattering experiments 1969 at SLAC (Breidenbach et al.): eNeX, deep-inelastic scattering (DIS): • “structure functions” F1,2indeed don’t depend on Q2 (resolution power, here given in terms of scattering angle θ), but only on momentum fraction they carry (x). • “confirmation” of QPM! Further evidence from EMC in muon-nucleon scattering (picture on the right) • Also nice confirmation of Callan-Gross relation: EMC UHH SS09: LHC

5. QPM: LIMITATIONS, AND QCD Try gauge theory for strong interactions: Quantum chromodynamics (QCD) – Quarks are held together by the exchange of QCD bosons = gluons. – The relevant charge is color. Gluons are themselves color-charged (non-abelian theory!). – Quarks only exist in color-neutral hadrons (“confinement”); only at very small distances / high energies relevant coupling becomes small enough to probe quarks (“asymptotic freedom”, NP 2004). – QCD potential: … well established experimentally (3-jets PETRA). UHH SS09: LHC

6. QCD: IMPLICATIONS FOR F1,2? x0 x1=x0-x2 x2 • Partons interact inside proton: • – qqg, gqq, ggg • – … and vice versa These processes change x distribution! • The x structure of the proton depends on resolution power: If I look closer I might see more radiation processes, more qq pairs from gluon splittings etc. Small resolution (low Q2): See only largest structures (3 valence quarks) with high momentum fractions x. High resolution (high Q2): See smaller and smaller structures with lower x values  populate PDFs at small x values! 3-jet events at e+e- collider PETRA: UHH SS09: LHC

7. THE PROTON – A COMPLEX OBJECT Structure changes with resolution power Q2! Q2 Small Q2, large wavelength, proton as such Larger Q2, smaller wavelength, resolve 3 partons Large Q2, small wavelength, see fluctuations Huge Q2, tiny wavelength, full proton beauty! UHH SS09: LHC

8. HERA: STRUCTURE FUNCTIONS Increasing Q2low x populates, high x depopulates! Low x: With increasing Q2, more and more radiated gluons and quark pairs from g qq are seen!High x: With increasing Q2, less and less un-radiated partons are left here! “Scaling” seenhere initially! UHH SS09: LHC

9. HERA: STRUCTURE FUNCTIONS Connection between structure function F2 and PDFs  extraction of PDFs from F2 data! – Remember definition of F2: – Consider “DGLAP” evolution of structure function with Q2:  Sufficient information to extract PDFs from behaviour of F2 with x and Q2! UHH SS09: LHC

10. x AND Q2 AT HERA AND THE LHC y:Inelasticity Q2:Momentum transfer [Resolution ~1/Q] x:momentum fraction LHC covers different (and much wider) range in x and Q2 as compared to HERA (and the Tevatron): – Options for determining the PDFs in an extended region? Probably very difficult! – Necessity to use HERA PDFs for LHC predictions. DGALP formalism: 1. Determine F2(x,Q02) at low start scale Q02. 2. Evolve F2 to higher Q2 using DGLAP equation: BUT: – Is DGLAP reliable over such a wide evolution? – Are other effects relevant for the LHC regime? – Do new dynamics (e.g. from lower x values not covered by HERA) play a role for the PDFs at LHC?  Need effort to control/test/improve PDFs at the LHC! Specific processes needed for that! (like W or Z production at large rapidities, later.) HERA DGALP UHH SS09: LHC

11. OVERVIEW OF pp REACTIONS (1 repeated) • To be understood: • The complex protons.  proton structure  HERA physics and deep inelastic scattering • The reaction between (constituents of) the protons. (hard) QCD, using perturbation theory and Feynman rules  models for things that cannot be treated using pQCD. • The transformation to signals in the detector. detector simulations, detector understanding (not treated in detail) pp reactions:… from a simple (but potentially coloured!) initial state: … to a very complicated final state on “hadron level” and in the detector: p p UHH SS09: LHC

12. OVERVIEW OF pp REACTIONS (2) Description/understanding of the different stages: The rate of proton-proton interactions is connected to the (proton-proton) cross-section σpp via the luminosity: Luminosity L is machine parameter; related to the bunch-crossing frequency f, the number of particles per bunch, and the cross-sections of the bunches: The proton-proton cross-section σpp is connected to the parton-parton cross-section σij (for partons i,j) via the parton distribution functions fi/p (probability to find parton of type i in proton p): The parton-parton cross-sections σij can (in principle) be calculated using perturbative methods. Need to disentangle multi-proton (overlay) and multi-parton collisions experimentally. pp reactions:… the global picture: 2835×2835 bunchesin the LHC ring. 109 protons / bunch ≤30 pp collisions per bunch crossing N parton-partoncollisions / pp collision Complex final-statesin every parton-partoncollision. UHH SS09: LHC

13. PRINCIPLE OF FACTORISATION, σij – We have already discussed the PDFs fi. – Now discuss the hard scattering matrix element σij. Most important insight: This is the process-dependent part! Examples: Remember the formula for the pp cross-section: – The “hard scattering matrix element” σij (or parton-parton cross-section) can be calculated perturbatively starting from (simple) Feynman diagrams. It contains processes at large (energy/momentum/mass) scales / small distances. – The PDFs fi must be determined experimentally from data (HERA!). They resum soft / long-range contributions to the cross-section. “Factorisation”: It is possible to disentangle effects that play at very different scales! Top production SUSY particleproduction Drell-Yan fermionpair production UHH SS09: LHC

14. THE HARD SCATTERING CROSS-SECTION σij For all processes: if you want to calculate a cross section then – use (universal) PDFs fi/p. – calculate, using Feynman rules, the hard cross- sections. -- put things together (“convlolute”), assuming factorisation to be valid. Missing in this picture:– Initial and final state radiation. – Hadronisation and decay.– Higher orders.– Parton showers. – Loads of subtleties … Higgs production W+t production Leptoquarkproduction UHH SS09: LHC

15. THE LHC CROSS-SECTIONS Putting all ingredients together and calculating: Note that cross-sections for known SM processes is huge – and small for Higgs, SUSY  necessity for trigger, later! Many interesting (specific, easy-to-identify) processes are very complicated even at lowest order: – SUSY cascade decays: There are tools that calculate the LO cross-section given any PDF and any given σij. And a few full-size event generators (HERWIG, PYTHIA, …) UHH SS09: LHC

16. LUMINOSITY DETERMINATION (AT LHC) Remember: – For each process i we measure the rate (or number) of events. – But we are truly interested in the pp cross-section σpp (for process i)  we need luminosity L. Simplest approach: – Define ‘test’ process with very precisely calculable cross-section. Then use above equation to get L. – LEP: Small-angle Bhabha eeee scattering. Experimentally challenging (acceptance!). Typical uncertainties 1%. – HERA: Bremsstrahlungs process epepγ. • For pp collisions: • – Precise lumi determination (5%) important, for example, for Higgs mass determination. • – No clear ‘candle’ to normalise to; various ideas on the market. • 1. method: Optical theorem: • 2. Photon-photon production of lepton pairs (leptons measured cleanly in experiments!). • 3. W and Z production • (clean signatures via • leptonic decay modes). •  cross-sections knownto about 4%. UHH SS09: LHC

17. IMPORTANCE OF LUMI MEASUREMENT Relative precision on the measurement of HBR for various channels, as function of mH, at Ldt = 300 fb–1. The dominant uncertainty is from Luminosity: 10% (open symbols), 5% (solid symbols). (ATLAS-TDR-15, May 1999) Many important precision measurements are dominated by the lumi uncertainty, for examplein the Higgs and SUSY sectors: UHH SS09: LHC

18. CROSS-SECTIONS, PARTON LUMINOSITIES (1) Now study parton luminosity for various processes and CMS energies. For example gg:  Much higher parton lumis at LHC than at Tevatron. High s-hat reached! • At hadron colliders, not the full CMS energy is ready for collision – only a fraction τ: • Might be useful to specify how many collisions are available at which s-hat • parton luminosities! • Then rewrite cross-section: UHH SS09: LHC

19. CROSS-SECTIONS, PARTON LUMINOSITIES (2) .. with the “partonic cross-section” (at LHC): LHC / Tevatron: – factor 40 for gg H @ MH= 120 GeV – factor 10000 for gg XX @ MX= 0.5 TeV UHH SS09: LHC

20. TWO-JET PRODUCTION (1) … with the following matrix elements and their values at 90 deg CMS scattering angle: The most intuitive process in pp collisions: two jet production: pp jet+jet. Can proceed from the following diagrams in LO: UHH SS09: LHC

21. TWO-JET PRODUCTION (2) Note the composition of the sample as a function of the jet transverse energy (relative to the beam axis):  qq interactions reach larger ET values than do gg interactions, mainly because of the different PDF distributions – quarks reach higher x values! One can measure and calculate the two-jet cross-section (for a given pseudorapidity): Factorised QCD can well describe these complicated measurements: UHH SS09: LHC

22. OVERVIEW UHH SS09: LHC

23. MINIMUM BIAS, PILE-UP, UNDERLYING EVENTS, AND MULTI-PARTON INTERACTIONS Most of the pp reactions: – “minimum bias” (MB) events: In most cases the protons will more or less “fly through” and undergo only very peripheral or soft interactions: elastic or single/double diffractive. … in these cases no high-pT exchange takes place – no particles are scattered under large angles, all reaction products go more or less in the proton flight direction (“diffractive” and “elastic” events). Only the hard, non-diffractive events can be calculated in perturbative QCD: – Soft events do not have a hard scale  αS is too large for perturbative calculations! Nevertheless MB events important – there are so many, and they may help to understand the detector! More complications: – Pile-up: More than one pp interaction in one bunch crossing (disentangle using vertex information?) – Multi-parton interactions: More than one pair of partons may scatter! – Underlying event: Everything except the hardest scattering (later): UHH SS09: LHC

24. THEORETICAL PREDICTIONS We distinguish: – Leading-order MC programs with parton-shower formalism. – Fixed-order calculations without parton showers (typically at NLO for QCD, NNLO for weak processes …) – “MC@NLO”-type programs that combine the best of all worlds – namely higher orders and details of the final state via parton-shower algorithms! Distinguish the “hard scattering matrix element” and the “parton shower” (and note the difficulty in combining them!): Hard matrix element:– correct treatment of large-angle, hard phenomena.– correct normalisation of cross sections via inclusion of real and virtual corrections. – Corrections lead to events with negative weights  inherent problems for combination with parton showers? Parton showers: – Summation of all (?) soft and collinear effects in the final state  correct description of soft behaviour. – Summation of “leading logarithms”.– Radiation in initial and final state and their interference can change kinematics of an event  cancellation of real and virtual divergencies not guaranteed anymore!  combination with NLO difficult!!!! Only lately: – Concepts for combination of next-to-leading order calculations and parton showers (key words MC@NLO, CKKW, …). – Far too deep to be discussed here today ;-) .. UHH SS09: LHC

25. SIMULATION Calculation of differential cross sections (according to known distributions)Result: 4 vectors! Parton showers: radiation of q,g.matrix elementsor LLA algos. Hadronisation (model!) decay Detector simulation detector simulation reconstruction UHH SS09: LHC