The Large Hadron ColliderMachine, Experiments, PhysicsBasics of proton-proton physics

Johannes HallerThomas Schörner-Sadenius

Hamburg UniversitySummer Term 2009

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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:

OVERVIEW OF pp REACTIONS (1)

UHH SS09: LHC

p p

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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).

INTRODUCTION TO THE QPM AND TO QCD

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Famous scattering experiments 1969 at SLAC (Breidenbach et al.): eNeX, deep-inelastic scattering (DIS):

“structure functions” F1,2 indeed 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:

INTRODUCTION TO THE QPM AND TO QCD

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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).

QPM: LIMITATIONS, AND QCD

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Partons interact inside proton:– qqg, gqq, ggg– … 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:

QCD: IMPLICATIONS FOR F1,2?

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THE PROTON – A COMPLEX OBJECT

Structure changes with resolution power Q2!

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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!

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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!

HERA: STRUCTURE FUNCTIONS

“Scaling” seenhere initially!

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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!

HERA: STRUCTURE FUNCTIONS

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x AND Q2 AT HERA AND THE LHC

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,Q0

2) 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.)

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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:

OVERVIEW OF pp REACTIONS (1 repeated)

UHH SS09: LHC

p p

JH/TSS 12

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:

OVERVIEW OF pp REACTIONS (2)

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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!

PRINCIPLE OF FACTORISATION, σij

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– 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:

Top production

SUSY particleproduction

Drell-Yan fermionpair production

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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 …

THE HARD SCATTERING CROSS-SECTION σij

Higgs production

W+t production

Leptoquarkproduction

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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, …)

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!

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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 vialeptonic decay modes). cross-sections known

to about 4%.

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 eeee scattering. Experimentally challenging (acceptance!). Typical uncertainties 1%.

– HERA: Bremsstrahlungs process epepγ.

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IMPORTANCE OF LUMI MEASUREMENT

Many important precision measurements are dominated by the lumi uncertainty, for examplein the Higgs and SUSY sectors:

Relative precision on the measurement of HBR 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)

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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:

CROSS-SECTIONS, PARTON LUMINOSITIES (1)

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.. 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

CROSS-SECTIONS, PARTON LUMINOSITIES (2)

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… 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:

TWO-JET PRODUCTION (1)

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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:

TWO-JET PRODUCTION (2)

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OVERVIEW

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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):

MINIMUM BIAS, PILE-UP, UNDERLYING EVENTS, AND MULTI-PARTON INTERACTIONSMost 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).

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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 ;-) ..

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!):

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SIMULATION

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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

reconstruction

UHH SS09: LHC