Quantum Chromodynamics
Caterina Doglioni - Lund University
Note on references: all the images from experiments are taken from the experiment websites unless otherwise noted + diagrams and tables taken from Cahn&Goldhaber / Halzen & Martin Introduction
About me
Master’s thesis in Rome (Italy) Summer Student at CERN (Switzerland) PhD in Oxford (UK) Post-doc in Geneva (Switzerland) Lecturer in Lund since April 2015
Member of the ATLAS Collaboration Dark Matter, jet and HASCO enthusiast
This week: found either here or work-lurking on a desk outside Always found at [email protected] Wikipedia/NASA What I do: http://www.hep.lu.se/staff/doglioni/ @catdoglund 2 Introduction
About Quantum ChromoDynamics
Large Hadron Collider: Quark and gluon (→ jet) factory Force describing interactions of quarks and gluons: QCD
Measure QCD processes:
Precision measurements of the Standard Model
Search for deviations from QCD: look for new particles decaying intoWikipedia/NASA quarks and gluons
3 Introduction
A warning: not all of QCD is in these lectures Goal: brief introduction to basic concepts of QCD in chunks of ~ 25’ each, 5’ Q&A / activity after each chunk, then 10’ break
More detailed references and slides can be found as links Wikipedia/NASA on the slides or at the end of the lectures 4 Introduction
Outline of the QCD lectures
•Lecture 1: Quarks gluons and strong interactions •1.1 From the hadron zoo to the quark model •1.2 Experimental proof of the quark model •1.3 Strong force: confinement and asymptotic freedom •Lecture 2 (Tuesday): Experimental aspects of QCD •How to see quarks and gluons: jets •Jet substructure •Measurements of QCD at the LHC Wikipedia/NASA•Looking for bumps above QCD 5 1.1 From the hadron zoo to the quark model Quark models and spectroscopy Evidence of quarks The strong force
The most elementary particles (so far)
(at least we hope)
today/tomorrow
Wikipedia/NASA
http://arxiv.org/abs/1311.1769 7 Quark models and spectroscopy Evidence of quarks The strong force
Particle situation as of the 1960s
Particle Adventure website
Wikipedia/NASA Is there an order in this apparent chaos? This is how the Standard Model was born! 8 Quark models and spectroscopy Evidence of quarks The strong force
A necessity: better microscopes
Cosmotron - BNL - 1952-1966 Bevatron - LBNL - 1954-1993 First accelerator beyond the GeV scale Billions of electron volts (6.5 GeV/beam)
https://www.bnl.gov/about/history/accelerators.php interactions.org
Experimental study of the spectroscopy of zoo of composite particles! 9 Quark models and spectroscopy Evidence of quarks The strong force
What is a symmetry?
Symmetry
Nature likes symmetry! (our eye does too)
Conservation law
Quantum number https://it.wikipedia.org/wiki/Emmy_Noether 10 Quark models and spectroscopy Evidence of quarks The strong force An approximate symmetry: isospin (1930s)
proton neutron
mass = 938.272 MeV mass = 939.565 MeV
Same properties, same reactions to strong force slightly different mass, different electric charge
1/2 Isospin multiplet: = I3= -1/2 ( ) ( ) 11 Quark models and spectroscopy Evidence of quarks The strong force
Gell-Mann Nishijima relationship
baryon number quark quantum numbers
12 Quark models and spectroscopy Evidence of quarks The strong force
What does it mean for p,n contents?
13 Quark models and spectroscopy Evidence of quarks The strong force
Thinking ahead: quarks
Note that in the 1960s quarks had not been discovered!
Antiquark: opposite quantum numbers
14 Quark models and spectroscopy Evidence of quarks The strong force
Let’s try to classify these mesons
0 + 0 0 + ⇡ ,⇡ ,⇡ ,K , K¯ ,K ,K
Antiquark: opposite quantum numbers 15 Quark models and spectroscopy Evidence of quarks The strong force
Some order: meson nonets spin-parity 0−: pseudoscalar meson nonet spin-parity 1−: vector meson nonet.
16 Quark models and spectroscopy Evidence of quarks The strong force
An analogy…
17 Quark models and spectroscopy Evidence of quarks The strong force
More order: baryons
spin-parity 1+: octet of light baryons spin-parity 3+: baryon decuplet
18 QuarkFeynman models diagrams and spectroscopyTracking detectorsEvidence Muon of detectorsquarks CalorimetersThe strong forceEvents
Magnets!
Wikipedia/NASA
19 Quark models and spectroscopy Evidence of quarks The strong force Baryon spectroscopy: a summary tableFor further explanation, see pp 1-4 of: http://www.curtismeyer.com/material/lecture.pdf Charge conjugation
HistoryWikipedia/NASA of Principal Quantum Number: see http://ptp.oxfordjournals.org/ content/32/5/861.full.pdf+html 20 Quark models and spectroscopy Evidence of quarks The strong force
Resonances in CMS and LHCb
Wikipedia/NASA
21 Quark models and spectroscopy Evidence of quarks The strong force
Resonances in CMS and LHCb
Wikipedia/NASA
22 Quark models and spectroscopy Evidence of quarks The strong force What about the Δ and Pauli’s principle?
Quarks: udd Parity: + Charge: 2 Spin: 3/2 -> spins are aligned Isospin: Q+Y/2 = 3/2
Completely symmetric wavefunction!
But: three fermions should not all have the same state, according to Pauli’s principle!
23 Quark models and spectroscopy Evidence of quarks The strong force
Everyone needs more color
Solution to the Δ puzzle: add another degree of freedom that can be anti-symmetric color is the charge of quantum chromodynamics
Hyperphysics
Confinement ‘rule’:
Baryons and mesons are colourless 24 Quark models and spectroscopy Evidence of quarks The strong force
Evidence of color
25 Quark models and spectroscopy Evidence of quarks The strong force
Octets and quarks
“Three quarks for muster Mark” (J. Joyce, Finnegans Wake) Gell-Mann / Zweig: • hadrons are built by three constituent quarks, u d and s • mesons are composed by quark/antiquark pairs
Wikipedia/NASA
26 Quark models and spectroscopy Evidence of quarks The strong force
The “eightfold way” comes true
http://www.quantumdiaries.org/2011/01/29/mysteries-of-mesons-part-1-the-eightfold-way/
27 Quark models and spectroscopy Evidence of quarks The strong force
Fast-forward: a pentaquark!
http://arxiv.org/pdf/1507.03414v1.pdf
28 Quark models and spectroscopy Evidence of quarks The strong force
Not a tetraquark?
https://indico.cern.ch/event/509820/
news.fnal.gov
29 Conclusions
Concepts for part 1.1
•Part 1.1: Quarks gluons and strong interactions •From the hadron zoo to the quark model • Protons and neutrons: isospin multiplet •Characterizing hadrons: the eightfold way, color • Classification by isospin / hypercharge • Where there’s structure there is substructure: baryons and mesons contain quarks • Color is theorised and experimentally verified
Wikipedia/NASA
30 1.1.A A quick quiz about quarks https://www.mentimeter.com/s/2e80ff5e957166b493780b5a9959e7c5/e87a95d56892 1.1.B Q&A / 10’ Break 1.2 The discovery of quarks and gluons Quark models and spectroscopy Evidence of quarks The strong force
The smallest constituents of matter (so far)
Wikipedia/NASA
35 Quark models and spectroscopy Evidence of quarks The strong force
Deep inelastic scattering
proton
Increase of probe energy
Wikipedia/NASA
36 Quark models and spectroscopy Evidence of quarks The strong force
Elastic scattering
Remember the Rutherford experiment
How would you modify this for electrons to quarks (elastic scattering)?
Wikipedia/NASA
37 Quark models and spectroscopy Evidence of quarks The strong force
Elastic scattering
Remember the Rutherford experiment
How would you modify this for electrons to quarks (elastic scattering)?
Wikipedia/NASA
38 Quark models and spectroscopy Evidence of quarks The strong force
Elastic scattering (for electron)
Looking at entire solid angle:
Wikipedia/NASA
39 Quark models and spectroscopy Evidence of quarks The strong force More elastic scattering & form factors Point charge
Diffuse charge
Form factor
Form factor Can measure the charge radius of the proton Hofstadter & McAllister, 1960 Wikipedia/NASA assume fixed charge distribution
40 Quark models and spectroscopy Evidence of quarks The strong force More elastic scattering & form factors Point charge
photon exchange Diffuse charge
Form factor
Adding magnetic moment as well: two form factors G1 and G2
Wikipedia/NASA
41 Quark models and spectroscopy Evidence of quarks The strong force
The proton is not point-like!
If the proton had been point-like, the form factors would have been=1
Wikipedia/NASA
42 Quark models and spectroscopy Evidence of quarks The strong force
Elastic vs inelastic scattering
Elastic Inelastic
Dominates at high energies
43 Quark models and spectroscopy Evidence of quarks The strong force
Inelastic scattering
Cross-section for inelastic scattering
W1 and W2 are form factors depending on: - the momentum transfer Q2=-q2 - the energy lost by the electron (lab)
Bjorken (1967): If the proton is made by point-like constituents, 2 then W2 does not fall with Q2 but scales with ω = 2Mν/Q
44 Quark models and spectroscopy Evidence of quarks The strong force
Inelastic scattering
Cross-section for inelastic scattering
W1 and W2 are form factors depending on: - the momentum transfer Q2=-q2 - the energy lost by the electron (lab)
Bjorken (1967): If the proton is made by point-like constituents, 2 then W2 does not fall with Q2 but scales with ω = 2Mν/Q
Feynman (1967): The proton is composed of point-like partons, each taking a fraction of the original proton momentum 45 Quark models and spectroscopy Evidence of quarks The strong force Inelastic scattering and structure functions
Wikipedia/NASA Bjorken x = Feynman’s ‘fraction’ Proton structure functions
Callan-Gross relations Scaling invariance at high Q^2 -> expect ~flat structure function with Q2
Scaling invariance -> scatter against point-like something -> evidence for quarks! (later: scaling violations match QCD predictions)
46 Quark models and spectroscopy Evidence of quarks EvidenceThe strong of quarks force
Hot dog!
Wikipedia/NASA
47 Quark models and spectroscopy Evidence of quarks The strong force Scaling violations: the gluon and the sea
A proton is more complicated than a bag of three billiard balls
DGLAP evolution: how to predict evolution of structure functions with Q^2 Wikipedia/NASA —> allows to derive xf(x) from measurements http://www.scholarpedia.org/article/QCD_evolution_equations_for_parton_densities 48 Quark models and spectroscopy Evidence of quarks The strong force
Bjorken scaling
Wikipedia/NASA
49 Quark models and spectroscopy Evidence of quarks The strong force
Parton distribution functions
Wikipedia/NASA http://hepdata.cedar.ac.uk/pdf/pdf3.html Parton Distribution Functions (non-perturbative) are fitted directly from data, using the scaling violations and the DGLAP equations describing structure function evolution with Q2 50 Quark models and spectroscopy Evidence of quarks The strong force The first sight of the charm quark (J/psi) Some interesting history: http://history.fnal.gov/jyoh_docs/e288_internal_notes.html
51 Quark models and spectroscopy Evidence of quarks The strong force The first sight of the charm quark (J/psi) Some interesting history: http://history.fnal.gov/jyoh_docs/e288_internal_notes.html
(1974) Cahn & Goldhaber
52 Quark models and spectroscopy Evidence of quarks The strong force
Hit & miss discoveries: the Upsilon
Some interesting history: http://history.fnal.gov/jyoh_docs/e288_internal_notes.html
Why did we brashly name the 6.0 particle Upsilon (though in the PRL paper, we soften this name to describe either the 6.0, if confirmed, or the entire high mass di-lepton region)? Here are some thoughts -- (1) Jeff Weiss researched the Greek alphabet, and found 4 possibilities --we didn't like iota. Upsilon sounded promising. Furthermore, Walter Innes (I think) pointed out that if the particle is not confirmed, we could call it OOpsLeon [Leon Lederman was one of the physicists involved]. Due to our heritage (our Spokesman is well known for bad puns), we could not resist. [+ physics reasons]
53 Quark models and spectroscopy Evidence of quarks The strong force
The (un)discovery of the top quark
http://www.thphys.uni-heidelberg.de/~plehn/includes/bad_honnef_12/ferbel.pdf
54 Quark models and spectroscopy Evidence of quarks The strong force
The discovery of more quarks (top)
Only in 1995!
55 Quark models and spectroscopy Evidence of quarks The strong force
Why is the top mass interesting?
2011
56 Quark models and spectroscopy Evidence of quarks The strong force
Why is the top mass interesting?
See more in Efe Yazgan’s lectures about the top quark 57 Conclusions
Concepts for part 1.2
•Part 1.2: Experimental verification of quarks •Elastic scattering • The proton is not point-like, but what’s its structure? •Deep inelastic scattering: ‘break’ protons using photons •Structure functions (approximately) do not scale with momentum transfer: sign that there are point-like constituents within proton •The proton is not just three quarks: sea and gluons
Wikipedia/NASA
58 1.2.A Another quick quiz about quarks https://www.mentimeter.com/s/8f2ecf382075a58d67670f6797a91c08/050abc58864c 1.2.B Q&A / 10’ Break 1.3 Strong force: asymptotic freedom, confinement Quark models and spectroscopy Evidence of quarks The strong force
QCD and other forces
Force Charge Mediator Range Coupling constant
EM Electric photon Long ⍺EM charge
Strong Color charge gluon ? ⍺S
Weak Weak weak bosons ? ⍺W isospin
Wikipedia/NASA
63 Quark models and spectroscopy Evidence of quarks The strong force
QCD and other forces
Force Charge Mediator Range Coupling constant
EM Electric photon Long ⍺EM charge
Strong Color charge gluon Long ⍺S
Weak Weak weak bosons Short ⍺W isospin
Wikipedia/NASA
64 Quark models and spectroscopy Evidence of quarks The strong force
Difference with EM force
Vertices must be Photon: neutral under electric charge color-neutral Gluon: not neutral under color charge
Consequence: gluons self-interact! Wikipedia/NASAFurther consequences: confinement and asymptotic freedom
See F. Tanedo’s post: http://www.quantumdiaries.org/author/flip-tanedo/page/5/ 65 Quark models and spectroscopy Evidence of quarks The strong force
QCD (color) force as a spring
Intuitively: Wikipedia/NASA energy needed to pull quarks apart > energy needed to create meson 66 Quark models and spectroscopy Evidence of quarks The strong force
Connection to mesons energy levels
..from fitting meson energy levels…
Wikipedia/NASA
67 Quark models and spectroscopy Evidence of quarks The strong force
The discovery of the gluon
Wikipedia/NASA
68 Quark models and spectroscopy Evidence of quarks The strong force
The quark gluon plasma
Wikipedia/NASA
69 Quark models and spectroscopy Evidence of quarks The strong force
Hadronization and fragmentation
Hyperphysics A. Sidoti
Consequence: Wikipedia/NASA The more energy, the more particles (hadronization & fragmentation) 70 Quark models and spectroscopy Evidence of quarks The strong force
Confinement Proton appears as a bag of quarks and gluons: valence and sea
Wikipedia/NASA
Desy website 71 Quark models and spectroscopy Evidence of quarks The strong force Confinement and asymptotic freedom Coupling constant (strength of interaction)
Wikipedia/NASALattice gauge theory approximation Energy of interaction 72 Quark models and spectroscopy Evidence of quarks The strong force Confinement and asymptotic freedom
Number of flavours
Coupling constant at a given (chosen) scale This makes the coupling run (but what is it?) Wikipedia/NASA
73 Quark models and spectroscopy Evidence of quarks The strong force
Feynman diagrams as power series
Further orders First order (quantum fluctuations)
Problem: the Feynman dk 1 Wikipedia/NASA rules lead to infinities V = in the calculation! ⇡ 2⇡ k 1 Z Optional 74 Quark models and spectroscopy Evidence of quarks The strong force
A problem w/theory? Cut it off
Renormalization Regularization
What if the quantities we measure What if our theory only are not the quantities in the Lagrangian? works up to a point… Introduce bare quantities for the observables that reabsorb the infinities ⇤ dk 1 V = + =0 ⇡ 2⇡ k 1 1 1 Z0 (…for a little while?) If a theory is renormalizable, this procedure leads to finite Alternative: dimensional regularization results…
Optional 75 Quark models and spectroscopy Evidence of quarks The strong force
Running coupling constant
…BUT it introduces a dependence of the coupling on 1) the coupling constant at some defined value (μ0) 2) the ratio between scale of the process (μ) and scale of the interaction (μ0)
The coupling runs! Optional 76 Quark models and spectroscopy Evidence of quarks The strong force
QCD vs QED
QCD Antiscreening QED Screening
2 ↵QED(µ ) R. Craig Group ↵ (µ2)= 0 QED ↵ (µ2) 1 QED 0 ln( µ ) 3⇡ µ0 Wikipedia/NASA ?
77 Quark models and spectroscopy Evidence of quarks The strong force
QCD vs QED
QCD Antiscreening (dominates) QED Screening
Leif Johnson 78 Quark models and spectroscopy Evidence of quarks The strong force
QCD vs QED
79 1.3.A A video by a Fermilab scientist
https://www.youtube.com/watch?v=df4LoJph76A Quark models and spectroscopy Evidence of quarks The strong force
It’s still a mess…
Factorization theorem: can split perturbative (high-energy) and non-perturbative (low-energy) parts of QCD cross-section
parton distribution functions - from earlier lecture
Wikipedia/NASA
81 Monte Carlo generators
Wikipedia/NASA
http://home.thep.lu.se/~torbjorn/talks/standrews09a.pdf 82 T. Sjostrand’s lectures at SUSSP 2009: http://home.thep.lu.se/~torbjorn/talks/standrews09a.pdf
The structure of an event
Warning: schematic only, everything simplified, nothing to scale, . . .
p p/p
Incoming beams: parton densities 83 T. Sjostrand’s lectures at SUSSP 2009: http://home.thep.lu.se/~torbjorn/talks/standrews09a.pdf
W+
u g d p p/p
Hard subprocess: described by matrix elements 84 T. Sjostrand’s lectures at SUSSP 2009: http://home.thep.lu.se/~torbjorn/talks/standrews09a.pdf
c s
W+
u g d p p/p
Resonance decays: correlated with hard subprocess 85 T. Sjostrand’s lectures at SUSSP 2009: http://home.thep.lu.se/~torbjorn/talks/standrews09a.pdf
c s
W+
u g d p p/p
Resonance decays: correlated with hard subprocess 86 T. Sjostrand’s lectures at SUSSP 2009: http://home.thep.lu.se/~torbjorn/talks/standrews09a.pdf
c s
W+
u g d p p/p
Initial-state radiation: spacelike parton showers 87 T. Sjostrand’s lectures at SUSSP 2009: http://home.thep.lu.se/~torbjorn/talks/standrews09a.pdf
c s
W+
u g d p p/p
Final-state radiation: timelike parton showers 88 T. Sjostrand’s lectures at SUSSP 2009: http://home.thep.lu.se/~torbjorn/talks/standrews09a.pdf
c s
W+
u g d p p/p
Multiple parton–parton interactions . . . 89 T. Sjostrand’s lectures at SUSSP 2009: http://home.thep.lu.se/~torbjorn/talks/standrews09a.pdf
c s
W+
u g d p p/p
...withitsinitial- and final-state radiation 90 T. Sjostrand’s lectures at SUSSP 2009: http://home.thep.lu.se/~torbjorn/talks/standrews09a.pdf
Beam remnants and other outgoing partons 91 T. Sjostrand’s lectures at SUSSP 2009: http://home.thep.lu.se/~torbjorn/talks/standrews09a.pdf
Everything is connected by colour confinement strings Recall! Not to scale: strings are of hadronic widths 92 T. Sjostrand’s lectures at SUSSP 2009: http://home.thep.lu.se/~torbjorn/talks/standrews09a.pdf
The strings fragment to produce primary hadrons 93 T. Sjostrand’s lectures at SUSSP 2009: http://home.thep.lu.se/~torbjorn/talks/standrews09a.pdf
Many hadrons are unstable and decay further 94 T. Sjostrand’s lectures at SUSSP 2009: http://home.thep.lu.se/~torbjorn/talks/standrews09a.pdf
These are the particles that hit the detector 95 Conclusions
Concepts for part 1.3
•Part 1.3: The strong force •Strong force as a spring: confinement •QCD vs QED •The gluon self-interacts, the photon does not •Antiscreening vs screening •Running of the coupling constant: asymptotic freedom •From partons to jets (in MC generators)
Wikipedia/NASA
96