Par$cle Physics. Introducing FOR. Pablo del Amo Sánchez

Par$cle Physics FOR Introducing Par$cle Physics Pablo del Amo Sánchez 1

Aim of this lecture: Par$cles and Forces of the Standard Model The par$cle zoo Qualita$ve Feynman diagrams 0/07/017 Annecy Summer School Pablo DEL AMO SANCHEZ

The Standard Model: elementary par$cles and their interac$ons 0/07/017 Annecy Summer School Pablo DEL AMO SANCHEZ 3

Example of EM interac$on e - e collision, transferring momentum q by exchange of photon, quanta of EM field space q Feynman diagram for e -e collision $me 0/07/017 Annecy Summer School Pablo DEL AMO SANCHEZ 4

Example of EM interac$on e - e collision, transferring momentum q by exchange of photon, quanta of EM field Feynman diagrams are calcula$onal tools: will sketch computa$on of QM amplitude space Remember the probability current j k conserved by the Schrödinger equa$on j fi k =! # im ψ * f x ψ ψ k i f x ψ *& % k i ( $ '? i µ j q f Feynman diagram for e -e collision This one s similar except rela$vis$c (Dirac s equa$on!) jʹ µ $me 0/07/017 Annecy Summer School Pablo DEL AMO SANCHEZ 6

Example of EM interac$on e - e collision, transferring momentum q by exchange of photon, quanta of EM field Feynman diagrams are calcula$onal tools: will sketch computa$on of QM amplitude α = space e! c4πε 0 A ej µ 1 q e j " = e µ q jµ j " µ 1 q µ j jʹ µ e = e = q α α Feynman diagram for e -e collision $me 0/07/017 Annecy Summer School Pablo DEL AMO SANCHEZ 9

Photon propagator Can derive it from standard QM $me-indep. perturba$on theory: T fi = f V i + j n f V j j V i +... E i E j (See e.g. Halzen & Mar$n for a more detailed discussion) This is the term that concerns us: scaeering via an intermediate state (the photon) Two possibili$es (two different $me orderings): a X c a emits photon X, b absorbs it a X c b emits photon X, a absorbs it d d b b i j f i j f 0/07/017 Annecy Summer School Pablo DEL AMO SANCHEZ 10

Photon propagator Can derive it from standard QM $me-indep. perturba$on theory: f V j j V i T fi = j n E i E j Two different $me orderings: a X c a emits photon X, b absorbs it a X c b emits photon X, a absorbs it b i j f 1 1 = E i E j (E a + E b ) (E c + E X + E b ) = = 1 (E a E c ) E X d b i j f 1 E i E j = = d 1 (E a + E b ) (E a + E X + E d ) = 1 (E b E d ) E X = 1 (E a E c )+ E X Use energy conserva$on: E a +E b =E c +E d 0/07/017 Annecy Summer School Pablo DEL AMO SANCHEZ 11

Photon propagator Special rela$vity doesn t preserve simultaneity, have to sum over two $me orderings: T fi = = j i and we ve used f V j E i E j j V i 1 (E a E c ) E X + 1 (E a E c )+ E X 1 (E a E c ) E = 1 X (E a E c ) ( p! a p! c ) m = X 1 (p a p c ) m = 1 X q m X E X =! p X + m X = (! p a! p c )+ m X where q = p a p c is the transferred 4-momentum Photons are massless, m X = 0 and their propagator is 1/q 0/07/017 Annecy Summer School Pablo DEL AMO SANCHEZ 1

Example of EM interac$on e - e collision, transferring momentum q by exchange of photon, quanta of EM field Feynman diagrams are calcula$onal tools: will sketch computa$on of QM amplitude α = space e! c4πε 0 A ej µ 1 q e j " = e µ q jµ j " µ (See e.g. Halzen & Mar$n for a more detailed discussion) 1 q µ j jʹ µ e = e = 0/07/017 Annecy Summer School Pablo DEL AMO SANCHEZ 13 q α α Feynman diagram for e -e collision Cross sec$ons, decay rates propor$onal to A $me

Example of EM interac$on: maeer-an$maeer annihila$on An$par$cle: same proper$es (mass, spin) as par$cle, but all charges reversed (electric, weak force, strong force) positron = an$-electron = e + 0/07/017 Annecy Summer School Pablo DEL AMO SANCHEZ 14

Example of EM interac$on: maeer-an$maeer annihila$on An$par$cle: same proper$es (mass, spin) as par$cle, but all charges reversed (electric, weak force, strong force) Par$cle + an$par$cle = radia$on (E=mc!) positron = an$-electron = e + 0/07/017 Annecy Summer School Pablo DEL AMO SANCHEZ 15

Example of EM interac$on: maeer-an$maeer annihila$on An$par$cle: same proper$es (mass, spin) as par$cle, but all charges reversed (electric, weak force, strong force) Par$cle + an$par$cle = radia$on (E=mc!)! p e+ positron = an$-electron = e +! pe where m is rela$vis$c invariant mass of system: m e+e = (E e+ + E e ) ( p! e+ + p! e ) (p µ e+ + p e c = 1! µ ) 0/07/017 Annecy Summer School Pablo DEL AMO SANCHEZ 16

An$par$cles: the positron 193, Anderson: picture of cloud chamber in magne$c field Track crosses lead plate, looses energy, going upwards Posi$ve charge (curvature), mass < 0 m e A POSITIVE ELECTRON! Actually predicted by Dirac s equa$on (Oppenheimer 1930)! An$par$cle has same mass, spin, etc but opposite charge 0/07/017 Annecy Summer School Pablo DEL AMO SANCHEZ 18

Cosmic rays Par$cles from outer space constantly in collision with upper atmosphere Source of exo$c (unstable) par$cles from early $mes (pre WWII) Cloud chambers (or Wilson chambers): supersaturated vapor, passage of charged par$cles slightly ionizes medium, condensa$on occurs track Photographic emulsions also used 0/07/017 Annecy Summer School Pablo DEL AMO SANCHEZ 19

More cosmic rays: the muon 1936 Neddermeyer, Anderson: unit charge par$cle, spin 1/ heavier than electron, lighter than proton è penetra$ng tracks like electrons, does not induce nuclear reac$ons unstable but long-lived (10-6 s) Just like electron but heavy and unstable Who ordered that? (I.I. Rabi) 0/07/017 Annecy Summer School Pablo DEL AMO SANCHEZ 0

Example of EM interac$on: pair produc$on The inverse of maeer-an$maeer annihila$on: par$cle-an$par$cle pair produc$on For instance: μ + μ produc$on: α α q An$par$cules pictured as arrows opposite to flow of $me Emission of e = absorp$on of e + Possible only if invariant mass m e+e = q > (m μ ) Internal par$cles are called virtual par$cles. Note: m γ = q 0!!! 0/07/017 Annecy Summer School Pablo DEL AMO SANCHEZ 1

Quantum ElectroDynamics (QED) Many higher order diagrams possible for μ + μ produc$on: q α + + + α Feyman diagrams part of a perturba$on series in powers of coupling constant α q q α All this, and much more, described by Quantum ElectroDynamics (QED), a consistent Quantum Field Theory (Tomonaga (1946), Schwinger (1948) and Feynman (1948) based on Dirac 198) 0/07/017 Annecy Summer School Pablo DEL AMO SANCHEZ

The Standard Model: elementary par$cles and their interac$ons 0/07/017 Annecy Summer School Pablo DEL AMO SANCHEZ 3

Protons are composite Nucleons composed of 3 point-like par$cles: quarks =1 Angström =1 fm 0/07/017 Annecy Summer School Pablo DEL AMO SANCHEZ 4

Quarks and the Strong Force Strong force like EM but with three different types of charge instead of just one Let s call them red, green, blue, just for fun * Posi$ve charge is then red whereas nega$ve is an$-red (cyan, in this analogy). This kind of charge called color è theory called Quantum Chromodynamics (QCD) Call quark a par$cle with color charge. Leptons don t have color. EM Strong Force * Par$cles with color not responsible for colours of light! 0/07/017 Annecy Summer School Pablo DEL AMO SANCHEZ 5

Quantum ChromoDynamics (QCD) Charges repel(aeract) if same(different), e.g. red and red repel, red and an$-red aeract, red and blue aeract. Force carriers are called gluons Gluons must carry color charge è far-reaching consequences, very different from QED! Consequences: Very short range force Force gets stronger when quarks pulled apart Only see color-neutral free par$cles in Nature (quark confinement) 0/07/017 Annecy Summer School Pablo DEL AMO SANCHEZ 6

Quarks make up hadrons Can get color-neutrality (neither excess nor defect) with following combina$ons: color+an$-color red+green+blue since an$-red=cyan=green+blue So the quarks arrangements found in Nature are: quark+an$quark (meson) quark+quark +quark or 3 an$quarks (baryon) Hadrons 0/07/017 Annecy Summer School Pablo DEL AMO SANCHEZ 7

QCD Strong nuclear force Protons and neutrons bound in nucleus by residual force between quarks, same as atoms in molecules 0/07/017 Annecy Summer School Pablo DEL AMO SANCHEZ 8

How many different quarks? Experimentally find 6 quarks (flavours), 3 up-type and 3 down-type quarks All equal for QCD, except different masses Light Stable Heavy Unstable A few important mesons: pions, kaons (s quark), D (c quark), B(b quark) 0/07/017 Annecy Summer School Pablo DEL AMO SANCHEZ 9

Symmetries Classifica$on and descrip$on of hadrons thanks to symmetries (group theory) 0/07/017 Annecy Summer School Pablo DEL AMO SANCHEZ 30

Heavy flavours Heavy quarks unstable How? Up to now, always crea$ng/annihila$ng pairs of par$cle-an$par$cle of same type Weak force: induces decays of unstable elementary par;cles 0/07/017 Annecy Summer School Pablo DEL AMO SANCHEZ 31

The Standard Model: elementary par$cles and their interac$ons 0/07/017 Annecy Summer School Pablo DEL AMO SANCHEZ 3

Weak Force Neutron beta decay: n p + e + ν e Weak force responsible for decays of unstable elementary par$cles Mediated by Z 0 and W ± bosons Contrary to photons and gluons, Z 0 and W ± have non-zero masses Propagators propor$onal to 1/M Z, 1/M W è Weak Force very weak! 1/M W 0/07/017 Annecy Summer School Pablo DEL AMO SANCHEZ 33

Why are Z and W so heavy? Z and W are 100 and 85 $mes heavier than proton But photons and gluons massless! It s the Higgs boson s fault! 0/07/017 Annecy Summer School Pablo DEL AMO SANCHEZ 34

Weak Force Governs rate of energy produc$on in the sun (inverse beta decay a step in fusion process) 0/07/017 Annecy Summer School Pablo DEL AMO SANCHEZ 35

Weak Force: other examples Pion decay: important way of making neutrinos 0/07/017 Annecy Summer School Pablo DEL AMO SANCHEZ 36

Neutrinos? Nearly zero masses (but not quite!) No electric charge, no color charge, only interacts through Z et Ws So very hard to study Electron also light and without color è leptons Plenty of open ques$ons 0/07/017 Annecy Summer School Pablo DEL AMO SANCHEZ 37

Three families or genera$ons 3 $mes the u, d quark couple, except heavier and less stable Same story about leptons: muon is just an unstable, heavy electron Columns of table are called genera;ons Why more than one? Why three? 0/07/017 Annecy Summer School Pablo DEL AMO SANCHEZ 38

The Standard Model Are they all elementary? Are there any more? Why 3 genera$ons? Why this mass paeern? 0/07/017 Annecy Summer School Pablo DEL AMO SANCHEZ 39

Summary Much learnt; plenty of open ques$ons! Electromagne$sm, γ: all par$cles except ν s Strong force, gluon: only quarks Weak force, W ± et Z: all par$cles 0/07/017 Annecy Summer School Pablo DEL AMO SANCHEZ 40

Ques$ons? 0/07/017 Annecy Summer School Pablo DEL AMO SANCHEZ 41

Applica$ons Positron emission tomography (PET) 0/07/017 Annecy Summer School Pablo DEL AMO SANCHEZ 4

A VERY brief history of par$cles 1968-69 SLAC, Bjorken, Feynman 1911 Rutherford, Geiger, Marsden 0/07/017 Annecy Summer School Pablo DEL AMO SANCHEZ 43

The nucleus: Rutherford scaeering 1906, J.J. Thomson: plum pudding model of the atom Rutherford set to test it by firing α par$cles into a thin foil E kin α 1 q = 4πε 0 bullet R Q target target R target 10 14 m << 10 10 m R 1909, Geiger & Marsden: ~1/8000 alpha par$cles bounce off! 1911, Rutherford: nucleus small within atom, surrounded by e cloud 0/07/017 Annecy Summer School Pablo DEL AMO SANCHEZ 44 atom

The nucleus: Rutherford scaeering No$on of Cross Sec$on dσ/dω : par$cles crossing transverse area dσ are scaeered into a solid angle dω at an angle θ with the beam direc$on Can find out about force between target and bullet by looking at xsec$on, e.g. stronger forces bigger xsec$ons; range of force dependence on θ Ex, scaeering of spinless charged par$cles off a spinless charged target (Rutherford): dσ = dω Z1Z 4πε e 0E kin 1 ( θ / ) 0/07/017 Annecy Summer School Pablo DEL AMO SANCHEZ 45 sin 4

Back to history: protons are composite Post WWII: accelerator era 1968 SLAC: shoot e to proton target High energies: λ electron <<R proton pc=hc/λ electron >>1 GeV W As in Rutherford, large angle scaeering! Q = 4EEʹsin ( θ / ) 0/07/017 Annecy Summer School Pablo DEL AMO SANCHEZ 46

Orders of magnitude, units E I (H)=13,6 ev 1eV=1,6 x 10-19 J ~0,5 GeV =0,5 x 10 9 ev S p ( 40 Ca)=8,3 MeV =8,3 x 10 6 ev Masses in energy units (E=mc!) e.g. m(proton) = 938 MeV, m(electron) = 0,511 MeV 0/07/017 Annecy Summer School Pablo DEL AMO SANCHEZ 47

Applica$ons Radiothérapie 0/07/017 Annecy Summer School Pablo DEL AMO SANCHEZ 48

Applica$ons Le World Wide Web a été inventé au CERN! (1990) La grille de calcul 0/07/017 Annecy Summer School Pablo DEL AMO SANCHEZ 49