QCD, Structure Functions, Jets History of the Strong Interaction - - PowerPoint PPT Presentation

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QCD, Structure Functions, Jets History of the Strong Interaction - - PowerPoint PPT Presentation

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Particle Physics with Highest Energy Accelerators (Tevatron and LHC) QCD, Structure Functions, Jets History of the Strong Interaction QCD / QED Proton-structure: structure functions hadronisation factorisation

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Tevatron and LHC WS17/18 TUM S.Bethke, F. Simon V7: QCD. Structur Functions, Jets

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QCD, Structure Functions, Jets

  • History of the Strong Interaction
  • QCD / QED
  • Proton-structure: structure functions
  • hadronisation
  • factorisation
  • hadron jets
  • measurement of αs
  • search for new physics (BSM)

Particle Physics with Highest Energy Accelerators (Tevatron and LHC)

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History of Strong Interactions (1)

1947: discovery of π-mesons and long-living V-particles (K , Λ) in cosmic rays 1953: V-particles produced at accelerators new inner quantum number (“strangeness").

Baryon (p,n, Λ,...) Meson (π,K,...)

1932: discovery of neutrons p e n 1933: µ ≅ 2.5 σ ⇒ substructure of the protons e 2 mp

?

1964: static quark-model; new inner quantum number: colo r u

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αs Q2

History of Strong Interactions (2)

1964: static quark model ; new inner quantum number: Far be. 1969: dynamic parton model :

N } X q γ * e e

asymptotic freedom ; 1973: concept of Quantum Chromo Dynamics. 1975: 2-Jet structure in e e - annihilation: confirmation of quark-parton-model.

+ _ g

1979: discovery of gluons in 3-Jet-events

  • f e e -annihilations.

+ _ e e

+ –

Z ,γ

*

q q

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History of Strong Interactions (3)

1991: exp. signature of the gluon self coupling 1990-2000: confirmation of asymptotic freedom 2004: Nobel Prize (concept of A.F.) to

  • D. Gross, H.D. Politzer und F. Wilczek

10 20 30 40 20 40 60 80

  • DATA

Abelian QCD

L3

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History of Strong Interactions (4)

>2004: QCD as background in searches for New Physics (BSM) example: Higgs search

γ γ

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properties of QED and : QCD

QED QCD

fermions leptons (e, µ,τ) quarks (u, d, s, c, b, t ) exchange quantum gluons (g) force couples to electric charge 3 colo -charges photon (γ)

(carries no charge) (carry 2 color charges)

is possible

⇒

g g g

coupling "constant" αs

Q 2 α α

2

Q

s

Confinement Asymptotic freedom

free particles leptons (e, µ,τ) Hadronen

(color neutral bound states of q and q)

theory

perturbation theory up to O( )

α5

perturbation theory up toO( )

α4

s

precision achieved 10 .... 10 0.1% ... 20%

  • 6
  • 7

α 1 137 (Q =0) =

2

(Q = M ) ≈ 0.12

2 2 Z

r

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model, theory

experiment: measurement of scattered electrons result: too many electrons with large scattering
 angles (qualitatively similar to 
 experiments of Rutherford, 1911)

sandbag

explanation: the proton has „hard“ components: QUARKS

Truth

Quarks in the proton: model and experiment

(Ch. Kiesling)

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e e‘ γ,Z p

Quarks in the proton ?

1

x

θ,E

measurement of scattering angle and energy of electrons
 (2 given entities):

1

x

1/3 1

x

1/3

determine angle and momentum fraction x

  • f scattering partner of electron 


(2 unknowns)

θ‘

(Ch. Kiesling)

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Quarks and gluons in the proton !

u u d Gluon

  • nly half of momentum is carried by quarks ;


the rest is carried by „force carriers“, 
 the gluons for higher resolution, see more and more gluons! measurement of momentum fraction demonstrates
 complicated „Iinner life“ of the protons:

(Ch. Kiesling)

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QCD

energy dependence of coupling “constants”:

  • verified by high precision measurements

QCD αs(Mz) = 0.1185 ± 0.0006

Z pole fit 0.1 0.2 0.3

αs (Q)

1 10 100

Q [GeV]

Heavy Quarkonia (NLO) e+e– jets & shapes (res. NNLO) DIS jets (NLO)

  • Sept. 2013

Lattice QCD (NNLO)

(N3LO)

τ decays (N3LO) 1000 pp –> jets (NLO)

(–)

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theoretical description of hadronisation process

  • parametrisation of individual subprocesses :

– f(x,Q2) : parton density (q, g) im Proton [pdf]

(probability for a parton with fraction x of proton momentum)

– “hard” QCD cross section, e.g. for qq –> gg; qg –> q’g’ – parton shower: QCD radiation / splitting q–>qg, g–>gg, g–>qq – hadronisation: parametrisation of transition of q,g to hadrons (models!) – decays: parametrisation according to exp. data and spin-statistics

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factorisation (theorem!):

σij = fi(x1,Q2) f j(x2,Q2) ) σ

ij(Q2)

plus sequential application of “parton shower” and “hadronisation” .processes

structure functions:

F2(x,Q2) = eq

2 x f(x,Q2)

∑

QCD pertubation theory:

Leading order (LO) matrix elements e.g. for 2–>2 processes: (for precision measurements, at least next-to-leading

  • rder (NLO) or even NNLO calcuations required!)
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proton structure

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proton structure (HERA + LHC)

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proton structure

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kinematic regions accessible to experiments

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2-Jet final state in proton-antiproton collision (Tevatron; D0 detector)

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2-Jet final state in proton-antiproton collision (Tevatron; D0 detector)

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high-mass (9 TeV) di-jet event at LHC (13 TeV)

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Event with four reconstructed hadronic jets. The four jets have a calibrated pT > 50 GeV, and are found with the anti-kt algorithm with R=0.6. The highest pT jet has a calibrated jet pT of 144 GeV. Event collected on 10 April 2010.

4-jet event

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Jet momenta are calibrated according to the "EM+JES" scheme. Event collected on 8 October 2010. The highest jet multiplicity event collected by the end of October 2010, counting jets with pT greater than 60 GeV: this event has eight.

  • 1st jet (ordered by pT): pT = 290 GeV, η = -0.9, φ = 2.7
  • 2nd jet: pT = 220 GeV, η = 0.3, φ = -0.7
  • Missing ET = 21 GeV, φ = -1.9
  • Sum ET = 890 GeV

8-jet event

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Z  μμ event with 20 reconstructed vertices

(ellipses have 20 σ size for visibility reasons)

„pile-up“:

  • 10-40 collisions per

beam crossing

  • detectors and

electronics must cope with huge amounts of data

  • physics analyses

must cope with extremely high background rates

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WJS2010

!jet(ET

jet > 100 GeV)

!jet(ET

jet > "s/20)

!Higgs(MH=120 GeV)

200 GeV

LHC Tevatron

events / sec for L = 10

33 cm

  • 2s
  • 1

!b !tot

proton - (anti)proton cross sections

!W !Z !t

500 GeV

!!!!" !!!"nb# "s (TeV)

QCD- / Jet- production cross sections

total QCD cross section Jet cross section ETjet > 100 GeV Jet cross section ETjet > √s/20

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Es gibt keine "natürliche" Definition von Jets !

Zum Vergleich von Hadronen-Jets mit analytischen QCD -Rechnungen (Quark- und Gluonendynamik) muß man auflösbare Teilchenjets Theorie und Praxis definieren.

Physik der Hadronen-Jets

Dazu benötigt man:

  • Definition eines Auflösungskriteriums

(z.B. minimale invariante Paarmasse, minimale Winkel, minimale Energien ..)

  • Vorschrift, wie man nichtauflösbare Jets

rekombiniert. kT - Algorithmus und Jetdefinition: (meistbenutzt in e e -Vernichtung; seit LHC auch in Hadron-Kollisionen) allerdings:

überlappende Jets kollineare Divergenzen niederenergetische "Jets" Infrarot- Divergenzen

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kT - Algorithmus und Jetdefinition:

für jedes Objekt eines Ereignisses (Parton, Teilchen, Energie-Cluster) wird berechnet: kt,i : transversaler Impuls bezügl. Strahlachse ϕi : azimutaler Winkel y : Rapidität; = 1/2 ln [ (E+pz) / (E-pz) ] dij : Abstandsmass zwischen zwei Objekten i,j diB : Abstandsmass zwischen Objekt und Strahlachse eine Liste aller dij und diB wird erstellt. Falls der kleinste Eintrag dij ist, werden Objekte i und j kombiniert (Addition der 4er-Verktoren); falls diB der kleinste ist, wird Objekt i als „Jet“ definiert und aus der Liste entfernt. R : „Auflösungsparameter“, bei dem Objekte i und j noch getrennt werden können.

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anti-kT - Algorithmus und Jetdefinition:

(derzeit meist gebräuchlich am LHC, mit R ~ 0.4 … 0.7)

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Anmerkungen zum kT - Jetalgorithmus

  • die Jetdefinition über den Auflösungsparameter dij = 1/2 min(Ei2, Ej2) (1–cos θij)

ist eine Abwandlung der Formel für die invariante Paarmasse zweier masselose Teilchen: Mij2 = EiEj (1–cos θij) --- die historisch vor Einführung des kT Algorithmus verwendet wurde (unter dem Namen “JADE” Algorithmus).

  • die kT Jetdefinition ist infrarot und kollinear sicher, d.h. Berechnungen in QCD

Störungstheorie sind möglich und verfügbar. Die Benutzung von dij anstelle der mehr intuitiven Paarmasse hat Vorteile bei der theoretischen Berechnung; u.a. können durch einen mathematischen Trick führende Beiträge zu höheren Ordnungen aufsummiert werden, was bei der JADE Definition nicht möglich war.

  • der kT Algorithmus hat sich besonders in der Analyse von Jets in der

e+e– Vernichtung (zB bei LEP) als sehr erfolgreich erwiesen, sowohl in experimenteller wie in theoretischer Sicht.

  • am Hadron Collider muss bei Adaption des kT Algorithmus besondere Rücksicht

auf die durch die weiterfliegenden Proton-Reste verursachten “remnant jets” bzw. das “underlying event” in Vorwärts-/Rückwärts-Richtung genommen werden -- geschieht über die Definition von diB

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clustering performance of kT - type Jet algorithms

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Cone-Jet algorithm:

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Anmerkungen zum Cone - Jetalgorithmus

  • der Cone-Algorithmus ist historisch der am längsten und meist benutzte Jetalgorithmus

in der Analyse von Hadron Kollisionen (Tevatron).

  • seine Definition und Anwendung ist i.w. durch experimentelle Randbedingungen

(Zellgrösse hadronischer Kalorimeter) und technischer Details bestimmt; in der Vergangenheit hat daher auch jedes Experiment (zB CDF und D0 am Tevatron) leicht verschiedene Variationen des Cone-Algorithmus benutzt.

  • der Cone-Algorithmus ist weder infrarot noch kollinear sicher, kann daher nicht

für QCD Präzisionsstudien verwendet werden.

  • wegen der langen exp. Erfahrung mit dem Cone-Algorithmus wird dieser

auch weiterhin am Tevatron dominant (und zT auch am LHC) benutzt; hier besonders für technische Studien (z.B. Isolation von Leptonen, Ereignisklassifizierung, jet tagging etc).

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LHC Run-1 and Run-2

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} run-1 } run-2

LHC performance

LHC design

integrated Luminosity peak Luminosity

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dN / dET,Reco / 1/GeV ET,Reco / GeV

Jet-Wirkungsquerschnitt am LHC

  • Studie: Single-Jet-Spektrum nach einer Laufzeit von etwa 1 Jahr

(107s), bei niedriger Luminosität (L = 1032cm-2s-1): ∫ L dt = 1 fb-1

Messung bis 1 TeV sehr

früh möglich

Unsicherheiten: Jet-Energieskala

Energieauflösung

Triggereffizienzen

Luminosität

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Jet production cross section

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Jet multiplicities

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Measurement of event shapes at large momentum transfer

  • Eur. Phys. J. C (2012) 72: 2211
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Measurement of the ratio

  • f the inclusive 3-jet and 2-jet cross sections

and first determination

  • f the strong coupling constant αs in the TeV range
  • measurement of R32 = R3jet/R2-jet as function of 


Q = pT1,2 = (pT,1+pT,2)/2

  • most exp. uncertainties cancel in ratio
  • comparison to QCD predictions (NLO) as function of


coupling strength αs(Q)

  • use anti-kT algorithm with R=0.7
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R32 as function of pT1,2

arXiv:1304.7498

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R3/2

m3 pr.

  • incl. jets pr.

NLO ttbar NNLO New at LHC

summary of αs measurements

at hadron colliders (ep, pp, ppbar)

K.Rabbertz, ICFA Beijing 2014

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HERA Tevatron ATLAS CMS

summary of αs measurements

at hadron colliders (ep, pp, ppbar)

K.Rabbertz, ICFA Beijing 2014

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Jet pair masses and search for new heavy particles: excited quarks

production of excited quarks excluded in mass interval 0.3 < m < 3 TeV (Tevatron limit: 0.8 TeV)

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Summary

  • QCD (i.e. the strong interaction) largely dominates

interaction rates at Tevatron and at LHC (σtot )

  • apart from dedicated QCD studies like the

determination of αs , precise knowledge of QCD processes is indispensable for searches of new effects beyond SM at LHC (e.g. Higgs, SUSY, large extra dimensions).

  • QCD describes the dynamics of quarks and
  • gluons. Description of hadrons only possible

through hadronisation models

  • alternatively, define and analyse hadron jets;

theoretically, jets can be associated with quarks and gluons.

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Literature

  • Ellis, Stirling, Webber: “QCD and Collider Physics”, Cambridge Monographs,
  • A QCD primer, G. Altarelli, CERN School 2001,

https://cdsweb.cern.ch/record/619179/files/p65.pdf

  • Quantum Chromodynamics, M.H.Seymour, 2004 European School
  • f High-Energy Physics, hep-ph/0505192
  • Measurement of inclusive jet and dijet cross sections ...,

ATLAS Collaboration, arXiv:1009.5908v2, Eur.Phys.J. C71 (2011) 1512

next lectures:

11.12.2017: Top Quark Physics 18.12.2017: Standard Model Tests 08.01.2018: Physics Beyond Standard Model (BSM) 15.01.2018: Higgs Boson (I)

  • Measurement of the ratio of the inclusive 3-jet cross section to the inclusive

2-jet cross section …; CMS collab., arXiv:1304.7498, Eur.Phys.J. C73 (2013) 2604