A.Ereditato SS Elementarteilchenphysik Lesson on:Elementary particles (1) Exercise: relativistic kinematics and equations

A.Ereditato SS In this course we deal with elementary particles: what does it mean ? the electron came first (>100 years ago) and then…all the others circa 1960 >100 particles ! (really elementary ?) today: a handful elementary particles tomorrow ? In this course we deal with elementary particles: what does it mean ? the electron came first (>100 years ago) and then…all the others circa 1960 >100 particles ! (really elementary ?) today: a handful elementary particles tomorrow ? today 1900 Elementary ‘ particles ’

A.Ereditato SS ELEMENTARY = NO STRUCTURE = POINTLIKE Depends on the space resolution of the probe ! A A De Broglie:  = h/p Optical resolution:  r ~ /sin   r ~ /sin  h/p sin  h/q (q is the momentum transferred to the projectile) Example: q = 10 GeV implies a space resolution of m (HIGH ENERGY !) HIGH ENERGY is also needed to produce high mass (NEW) particles (E=mc 2 )

A.Ereditato SS International Unit System Energy :1 eV = 1.602· J Length :1 fm = m = 1 Fermi Speed of light :c = ms -1 Reduced Plank Constant :h = 1.055· J s natural units: Fine structure constant:

A.Ereditato SS Relativistic kinematics: 4-vectors Generic four-vector Examples: space-time: momentum-energy: The quantity a 2 is defined as: and is a Lorentz invariant quantity In the cases listed above: x 2 = x 2 - t 2 and p 2 = p 2 - E 2 In the second case p 2 - E 2 = - m 2 (that is the rest mass, the same in all systems)

A.Ereditato SS Energie [eV] Energie [Joule] Speed Electron [511keV] Speed Proton [938 MeV] 1 eV1.6 x J593 km/s c 14 km/s c 1 keV1.6 x J18730 km/s c 438 km/s c 1 MeV1.6 x J km/s 0.94 c km/s c 1 GeV1.6 x J km/s c km/s 0.88 c 1 TeV1.6 x J km/s c km/s c 7 TeV1.1 x J km/s c km/s c Energy and speed E 2 = p 2 + m 2

A.Ereditato SS Example: fixed target vs head-on collisions 2 colliding particles: and The CMS is defined as the reference frame where the total momentum is zero, and Fixed target collision: Head-on collision: For energy, and typical accelerator colliders, i.e. masses negligible w.r.t. momenta and equal energy colliding beams: Fixed targetHead-on

A.Ereditato SS The atom (around 1905) Before ~1905, nobody really knew: “ What does the inside of an atom look like ? ” Positive charge (uniformly distributed) Positive charge (uniformly distributed) corpuscles (electrons ) corpuscles (electrons ) The positive charge is spread out like a “plum-pudding” The positive charge is spread out like a “plum-pudding” Early “plum-pudding” model Thomson atom

A.Ereditato SS Ernest Rutherford  Electromagnetism predicted that the heavy  particles should be only slightly deflected by the “plum-pudding” atom…but, contrary to expectations, large scattering angles were detected:   Probability < ! The atom must have a solid core capable of applying large electric forces onto an incoming (charged) particle. The atom is not an ‘elementary particle’

A.Ereditato SS      Interpretation of the Rutherford experiment (discovery of the atomic nucleus) soon followed by the Bohr atom Interpretation of the Rutherford experiment (discovery of the atomic nucleus) soon followed by the Bohr atom ~10 -9 cm ~ cm Electrons Nucleus Volume Atom = 4/3  ) 3 ~ 4 x cm 3 Volume Nucleus = 4/3  ) 3 ~ 4 x cm 3 Fraction ~

A.Ereditato SS : Discovery of the antiparticle of the electron, the positron (Anderson). Confirmed the existence and prediction that anti-matter does exist (Dirac) : Discovery of the muon (Street and Stevenson). It’s very much like a “heavy electron” : Discovery of the pion (Powell). Hadron lighter that the proton. High energy cosmic-rays: discovery of new particles Anderson’s experiment: cloud chamber (discovery of the positron) Carl Anderson 1936 Nobel Prize positron track Direction of deflection inside a magnetic field: it is a positively charged particle

A.Ereditato SS More on antimatter (particles and antiparticles) Dirac postulated in 1931 (before the discovery of the positron) the concept of antiparticles: same mass but opposite electric charge and magnetic moment. Energy-momentum relation implies that negative energy solutions are in principle “allowed”: Interpreted as particles with -E and -p traveling backward in time, in turn equivalent to antiparticles traveling forward in time with positive energy (e.g. the positron). Dirac: vacuum is an infinite deep sea filled with negative energy states electrons. Positive energy electrons cannot fall in the sea (Pauli principle). If we supply an energy E>2 m e an electron can jump in the positive energy levels leaving a hole (i.e. a positron). The situation is different for bosons. Negative energy states ( E< - mc 2 ) Positive energy states ( E> mc 2 ) 2 mc 2 E=0

A.Ereditato SS e-e- e+e+   Ze e+e+ e-e-  Pair production:   e + + e - Electron-positron annihilation: e + + e -   +  Electron-positron annihilation: e + + e -   +  Need: E  > 2 m e “spectator” nucleus to conserve momentum Two back-to-back  each with 1/2 of the total available energy

A.Ereditato SS Evidence for antimatter in this early bubble chamber photo. The magnetic field in this chamber makes negative particles curl left and positive particles curl right. Many electron- positron pairs appear as if from nowhere, but are in fact from photons, which don't leave a track. Positrons (anti-electrons) behave just like the electrons but curl in the opposite way because they have the opposite charge. (One such electron-positron pair is highlighted.) Evidence for antimatter in this early bubble chamber photo. The magnetic field in this chamber makes negative particles curl left and positive particles curl right. Many electron- positron pairs appear as if from nowhere, but are in fact from photons, which don't leave a track. Positrons (anti-electrons) behave just like the electrons but curl in the opposite way because they have the opposite charge. (One such electron-positron pair is highlighted.)

A.Ereditato SS The muon and its role in the early times The discovery of the muon was published in "New Evidence for the Existence of a Particle Intermediate Between the Proton and Electron", Phys. Rev. 52, 1003 (1937). Before this point the fundamental particles were presumed to be electrons, protons and the (then) newly discovered neutron. The discovery brought attention to the prediction by Yukawa in 1935 that an intermediate mass "meson" might be responsible for the nuclear strong force. Yukawa had predicted a mass of about 100 MeV and the muon had a mass very close to that. Moreover, the mesons decayed emitting electrons, and Yukawa's nuclear quanta were expected to be responsible for  -radioactivity by disintegrating into electrons and undetectable neutrinos. From 1941 and through the difficult years of World War II, three young Italian physicists, Piccioni, Conversi, and Pancini, carried on a series of observations of mesons stopped in matter, which seemed at the beginning to support Yukawa’s predictions. At the end of 1946, they reported that the rates of absorption of mesons in light materials were in strong disagreement with the theory. The experiment was based on the magnetic separation of positive and negative muons. Negative muons decayed when at rest in Carbon, rather than being absorbed by the nucleus (as they should do being the quanta of the strong interaction).

A.Ereditato SS Discovery of the pion Cecil Powell and colleagues (Bristol University) used nuclear emulsions to see charged tracks in the upper atmosphere. In 1947, they announced the discovery of a particle called the  -meson or pion (  ) for short.  Pion (  ) comes to rest here, and then decays:     One neutrino is also produced but escapes undetected. e Muon (  ) comes to rest here, and then decays:   e  Two more neutrinos are also produced but escape undetected. Cecil Powell 1950 Nobel Prize

A.Ereditato SS Interaction of an antiproton in a bubble chamber: 8 pions are produced. One of them (positive) decays into a muon and a muon-neutrino

A.Ereditato SS Because one has no control over cosmic rays (energy, types of particles, location, etc), scientists focused their efforts on accelerating particles in the lab and smashing them together. Generically people refer to them as “particle accelerators”. (We’ll come back to the particle accelerators later…) Circa 1950, these particle accelerators began to uncover many new particles. Most of these particles are unstable and decay very quickly, and hence had not been seen in cosmic rays. Notice the discovery of the proton’s antiparticle, the antiproton, in 1955: more antimatter. Discovery of many more particles ( )

A.Ereditato SS CERN: European Laboratory for Particle Physics

A.Ereditato SS The Particle Zoo Too many to be elementary!

A.Ereditato SS An excerpt from Gell-Mann’s 1964 paper: “A search for stable quarks of charge –1/3 or +2/3 and/or stable di-quarks of charge –2/3 or +1/3 or +4/3 at the highest energy accelerators would help to reassure us of the non-existence of real quarks”. Murray Gell-Mann had just been reading Finnegan's Wake by James Joyce which contains the phrase "three quarks for Muster Mark" When the quark model was proposed, it was just considered to be a convenient description of all these particles.. A mathematical convenience to account for all these new particles… After all, fractionally charged particles… come on ! In 1964, Murray Gell-Mann and George Zweig (independently) came up with the idea that one could account for the entire “Zoo of Particles”, if there existed objects called QUARKS Murray Gell-Mann George Zweig

A.Ereditato SS Are protons/neutrons elementary ? In 1969 a Stanford-MIT Collaboration was performing scattering experiments e - + pe - + X The number of high angle scatters was far in excess of what one would expect based on assuming a uniformly distributed charge distribution inside the proton It’s as if the proton itself contained smaller constituents: QUARKS What they found was surprising as what Rutherford found more than 50 years earlier !

A.Ereditato SS These quarks are the same ones predicted by Gell-Mann & Zweig in x m (at most) Protons 2 “up” quarks 1 “down” quark Neutrons 1 “up” quark 2 “down” quarks Quarks, as leptons (see later), are fermions (Fermi-Dirac statistics) with spin 1/2 h, 3/2 h, Their electric charge is fractional: +2/3 or -1/3 Proton: 2/3 + 2/3 -1/3 = +1 Neutron: 2/3 - 1/3 -1/3 = 0 The force mediators (photon, gluon,..) are bosons (Bose-Einstein statistics) with integer spin The electric charge of the photon and of the gluon is 0 Quarks, as leptons (see later), are fermions (Fermi-Dirac statistics) with spin 1/2 h, 3/2 h, Their electric charge is fractional: +2/3 or -1/3 Proton: 2/3 + 2/3 -1/3 = +1 Neutron: 2/3 - 1/3 -1/3 = 0 The force mediators (photon, gluon,..) are bosons (Bose-Einstein statistics) with integer spin The electric charge of the photon and of the gluon is 0 Just like the atom, also the nucleon is basically empty space

A.Ereditato SS Atom  Nucleus  Nucleons  Quarks !!!

A.Ereditato SS MeV MeV MeV < MeV < 0.17 MeV < 15.5 MeV ~ 10 MeV~ 5 MeV ~ 150 MeV~ 1500 MeV ~ 4.5 MeV ~ 170’000 MeV Mass Quarks are held together by gluons (theory of strong force = Quantum Cromo Dynamics) Confinement: intensity of interaction increases with distance between quarks Quark flavor quantum number (S, C, B, T) is conserved in strong interactions, violated in weak interactions Quarks form all known hadrons. Some hadrons were discovered after having been postulated as specific quark combinations. Quark families

A.Ereditato SS Quark (antiquark) combinations form all hadrons (baryons and mesons) Baryons: (QQQ or QQQ) They are fermions Mesons: (QQ) They are bosons

A.Ereditato SS Mass 1777 MeV MeV MeV < MeV Mass < 0.17 MeV < 15.5 MeV ~ 10 MeV~ 5 MeV ~ 150 MeV~ 1500 MeV ~ 4.5 MeV ~ 170’000 MeV Leptons are point-like particles (elementary) Very special leptons: neutrinos Assign to leptons a quantum number L e, L , L  =1 for particles and -1 for antiparticles The lepton numbers are individually and, therefore, globally (L e +L  +L   conserved Examples:   e   e  +  e + +  has a branching ratio <10 -9 because of lepton number conservation  +   + +  L  = e + n  p + e -  Leptons

A.Ereditato SS Mass [GeV/c 2 ] Gold atom Silver atom Proton Example: t  b (~ [s]) b  c (~ [s]) c  s (~ [s]) s  u (~ [s]) Ordinary matter (our whole Universe) is essentially made of electrons, neutrinos, up quarks and down quarks. All other fermions were copious long ago, when the Universe was “very young”. Today they only exist in cosmic- rays and in our particle accelerators. These high-energy replica of stable particles are unstable and decay in the lighter partners:

A.Ereditato SS FamilyQuarksAntiquarks Q = +2/3Q = -1/3Q = -2/3Q = +1/3 1ud 2cs 3tb FamilyLeptonsAntileptons Q = -1Q = 0Q = +1Q = 0 1e-e- e e+e+ e 2     3     Elementary particles in one slide…

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A.Ereditato SS Milestones in particle physics

A.Ereditato SS Some considerations Atoms are > % empty space Protons and neutrons are % empty space The Universe is basically empty space So why matter appears to be so rigid ? The strong and electromagnetic give matter its solid structure Strong force: defines nuclear ‘size’ Electromagnetic force: defines atomic ‘size’ This gives an indication of the relative importance of forces over matter

A.Ereditato SS Matter Leptons Charged Neutrinos Forces Weak EM Strong Gravity Hadrons Baryons Mesons Quarks Anti-Quarks Quarks Anti-Quarks Particles and Interactions

A.Ereditato SS Interactions We will see later on in detail that the interactions between particles are mediated by the exchange of a boson field (e.g. the photon) q ~ p sin 

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A.Ereditato SS n p Strong p p EM Strong Relative strengths: Strong = 1 EM= Weak= Gravity= Leptons: electrically charged leptons feel all interactions except the strong. Neutrinos only feel weak (and gravitational interactions). Hadrons: Charged hadrons feel all interactions Leptons: electrically charged leptons feel all interactions except the strong. Neutrinos only feel weak (and gravitational interactions). Hadrons: Charged hadrons feel all interactions Interactions may compete

A.Ereditato SS Residual strong force: the protons are not electrically neutral but they stick together thanks to the attraction between quarks in the different nucleons repulsive attractive

A.Ereditato SS Definition of helicity (or handedness): = s p / | p | = ± 1/2 It measures the sign of the component of the spin of the particle (j z = ± 1/2) along the direction of motion (z axis) s is a pseudo-vector: does not change for spatial inversion Helicity of a particle

A.Ereditato SS Neutrinos are almost massless particles (Weyl equation) Massive particles (Dirac equation) Helicity is a Lorentz invariant quantity for massless particles (cannot reverse the helicity by any Lorentz transformation). Particles following the Dirac equation are an admixture of LH and RH helicity states. Interactions involving vector or axial-vector fields helicity is conserved in the relativistic limit (do not mix separate solutions LH and RH solutions) unlike for scalar interactions (mix LH and RH components). EM, weak and strong interactions (mediated by V and A boson particles) conserve helicity. Interactions and helicity of a particle