Particle Physics 627: Particle Ordering Dr. Rupak Mahapatra Week 4 Chapter 3 Particle Classification: Fermion and Boson • Fermion – Spin ½ particle – Obeys Fermi Statistics – No two particles can exist in the same quantum state (Pauli’s exclusion principle) • Boson – Integral spin – Obeys Bose statistics Spin Statistics • Bosons are integral spin particles • Two particle wave function is identical under exchange of two particles. • Symmetric wave function : Ψ12 ↔Ψ21 • Fermions are spin ½ particles • Assymmetric wave function: Ψ12 ↔ ‐Ψ21 Elementary Particles and Forces +2/3 charge Neutral ‐1/3 charge Neutral Neutral Neutral ‐ve Charge +/‐ charge Fermions Bosons Particle Properties • Mass: All particles have mass (may be zero) – Mass is typically written in terms of energy mc2 – Unit eV: energy required to move an e‐ across 1V – Typically use MeV as the scale: electron rest mass is ½ MeV/c2 or simply often stated as ½ MeV – Recall momentum p is E/c, so p has unit MeV/c • Charge : All have charge (electric, weak, strong) • Lifetime: Probability that a particle created at t=0 is still alive after time P(t) = e‐t/τ – Half life t1/2 = 0. 693 τ Lepton Flavors (spin ½) • The leptons have lepton number conservation and come in 3 types (h(each type is conserved) – Electron type – Muon type – Tau type • Leptons may or may not carry electric charge – Neutral (()neutrinos) – Charged (electron, muon, tau) • No “color charge”, hence no strong interaction – More on Color in next lecture Lepton Flavors Conservation Laws • Charge and Lepton Number conserved Quark Flavors ((pspin ½) • Baryon Number is conserved • Unlike leptons, where each generation has a separate fully conserved lepton number, quarks come in only one baryon number • Thus quark can mix between generations, whereas leptons can’t Quark Flavors ((pspin ½) Masses: Huge Range Leptons Quarks Precise mass measurement of quarks difficult due to presence of gluons Flavor eigenstates ≠ Mass eigenstates • ⊗ means the “partner” of top row is NOT an eigen state of the TOTAL Hamiltonian • For neutrinos: solar and atmospheric neutrinos show neutrino oscillations dedue to mismatch of flavor and mass eigenstates Flavor eittigenstates Mass eigenstates Called the Maki‐Nakagawa‐Sakata matrix. Lots of interest in this mixing matrix Not an Identity Matrix Quark Mixing • CbibbCabibbo KbKobayas hi MkMaskawa (CKM) miiixing matrix 2 2 2 • Mdc ~5 MeV, Msc ~ 100 MeV, Mbc ~ 4.5 GeV CKM Matrix • Mostly diagonal. But some significant mixing across generations 2008 Physics Nobel Prize Cabibbo: Missed Nobel Prize? • Cabibbo introduced the the cabibbo angle in 1963 for 2 generations of quarks to explain down and strange quark decays to up quark • Or using Cabibbo angle 2 2 Vud and Vus didn’t add up to exactly 1, • Kobayashi and Maskawa but less than 1! generalized this to 3 generations Liftetime: Physics is in life time! • EitllExperimentally often know ittinstant of bir th t0t=0 • Repeatedly make particle at t=0, measure decay time and bin • Can measure exponential slope (independent of start time) • Lifetimes generally more interesting than masses Lepton Lifetimes • Electron: stable – charge can not go to lower energy (mass) state • Neutrinos: Mix among themselves • Muon lifetime : τμ ~ 2.2 μs – Used to determine the weak charge – Almost always decays to an electron and two neutrinos – cτ ~ 1 km! Muon is effectively stable inside detectors (size <=10m). Notice, it is longer than atmospheric thickness! ‐12 • τ Lepton lifetime: ττ ~ ps (10 sec) – Tests “Universality” of weak charge – cτ ~ 100 μm. In most experiments τ decays inside detectors. Huge effort starting mid‐80s to measure this Universality of weak interactions? More dldetails in later lectures • Do all leptons and quarks carry the same unit of weak ch?harge? τ ντ – Yes, for leptons and no for W − quarks e− ge ν e for quarks, the couplings to the weak gauge bosons depend on the quark flavors, due to “quark‐mixing” Î CKM mechanism Quark Lifetimes • U, d, s, c, b, t quarks always unstable • All can be unstable. The question is : • Is there lower mass (rest energy) state available? • Yes, in Hadrons • Hadrons (more later) – Baryons (3 quarks) – Mesons (quark‐antiquark) Force Career Lifetimes • γ, gluon and graviton: Mass ≡ 0 • W± : mass = 80.4 GeV • Z0: mass = 91.2 GeV • Dealing with these massive force careers is hard ‐1 • θw = cos (mw±/mZ0) is called the Weak Angle or Weinberg angle 0 • θw : Mixing angle between fields that make up γ, Z W and Z Bosons • τ W± and τZ0 very small life times • Energy –time Uncertainty principle tells us the uncertainty in energy must be high • This is the decay width, which is inversely proportional to the life time • ΔE * Δt ~ h • Large width implies lots of ways for these particles to decay • Decay width measured with fantastic accuracy and tells us presence or lack thereof new physics • Z0 width ΔE ~ 2.5 GeV, so cτ ~ 0.1 fm (10‐15m) – Not physically measurable! • Sim ilar ly, W± decay width: 2142.14 GVGeV Z0 width END OF LECTURE 02/09/2009 Charges and Feynman Diagrams • Feyman diagrams: Many levels (tree, loop) give most precise calculations ever • Allows computation of <f|H|i>, <Ψ|H|Ψ> ppyerturbatively Solid straight line = fermion e‐ γ Vertex Time Charge of OdOrder e or ‐√α amplitud e Coupling ‐e or ‐√α e‐ Arrow forward ⇒ Particle Conserved Quantities Many quantities that go in to the vertex must also come out: e‐ •Energy‐Momentum e •Electric Charge mm γ •SifiSpecific LtLepton NbNumber or Ti electron‐ness here •Others (Baryon number, e‐ Helicity, etc) Vector boson (s) couple to the lepton at the vertex Is the above process allowed, as is? If not, why not? e‐ → e‐ + γ Quiz 2 Amplitude for Interaction • If it did happen, the amplitude would be <f|H|i> proportional to –e (charge) Dimensionless –e/√hc = ‐√α Not Conserved ⇒ Not Allowed Antiparticles • Flip all additive quantum numbers Antiparticles Antiparticles e‐e+ annhiliation γ Can not happen, due to Energy‐ Momentum conservation me Ti e‐ e+ e‐e+ annhiliation Two vertices : Amplitude ∝ (√α)2 Rate or Cross‐section |<f|H|i>|2 ∝ α2 γ γ √α √α Time ‐ e e+ EM is Not the Only Force! Evidence of non‐EM Force γ γ e‐ √α e‐ γ √α √α Z√α e‐ e‐ Rutherford Scattering: Thomson Scattering: σ∝Z2α2 σ∝α2 Evidence of non‐EM Force π π e‐ √α √αs √α√αs pp Pion Proton Scattering (1951) Clearly, a new type of interaction was σ Experimental is 3 orders of at play, with very different coupling magnitude higher than the previous 2 strength or charge. This is evidence for EM calculation involving α ! strong force, with strength called αs. αs is of the order Unity! Much larger than α (1/137) Comparison between EM and Nuclear Electromagnetic Nuclear • Massless force carrier • Massive force carrier • Long range (infinite) • Short range (We know this force binds protons and • Interaction has 1/k2 term neutrons inside nucleus • Interaction has 1/(k2+m2) term (known as propagator, where m is the mass of the boson Range of Interaction and Mass • Uncertainty Principle: ΔE*Δt ≅ h • Range of interaction Δx = c*Δt ≅ (c*h/ ΔE) → 0 (for ΔE → 0), when m → 0 for EM interaction e‐ e+ M γ = 0 Propagation speed c + e‐ e Exchange particle (γ) Short Range of Force • Nuclear force between proton and neutron was known to be of short range, inside the nucleus • Yukawa proposed it is due to a massive scalar particle as the nuclear force carrier, thus limiting the range of the force • He estimated it to be around 200MeV in mass. Estimate led to a Huge Coincidence! Pion was discovered to be approximately of that mass and was thought for a while as the nuclear force carrier Lifetime • Lets use uncertainty principle to estimate the life time of Strong Interaction • Distance between proton and neutron, which are held by the strong force is ~ 1F (10‐15m) • The force carrier has to carry this message within the typical decay time or interaction time of say a baryon Δ++ • Ballpark time constant τ = 1F/c = 10‐23 secs • Strong interaction has a fast characteristic decay time of 10‐23 secs. • Characteristic decay time of EM: 10‐16 secs • Ratio of coupling strengths provides ratio of time 2 6 constants: τe/τs = (αe/ αs) ≅ 10 Problem with Strong Interaction • Baryons are bound states of three quarks, held together by the strong force • Examples of baryons: proton (uud), neutron (udd), etc. • A baryon Δ++ was dddiscovered in 1951 in the resonance from π+ and proton scattering • The particle matched the configuration uuu giving rise to charge of +2 and the spin J=1/2 was obtained by combining 3 idential J=1/2 up quarks in ground stttate • Here lies the problem: quark scheme forces us to combine 3 identical fermions (u) in their symmetric ground state in order to make up the known Δ++ Δ++ Violates Pauli’s Exclusion Principle? • To fix this problem, a new charge (quantum number) was introduced, namely “color” • Quarks come in 3 primary colors: red, green and blue • Utilizing the color, we solve the problem with Pauli’ s exclusion principle ++ • Δ = uRuGuB • Introduction of color also solved a few other problems such as non‐observance of uu with charge 4/3 Color is nice • ClColor provides a way to mathtch experitlimental dtdata on stable bound states of quark • It is fdfound tha t bdbound stttates only occur as Baryons (3 quarks) and Mesons (quark‐anti quark) • Why does not proton come in many differen t formats, since there are 3x3x3 options available? • RiRequire tha t all stbltable partic les be COLORLESS! – Equal mixture of R, G, B (or their anti‐colors): Baryons – ElEqual mitixture of color and complimen tary color (RRbar) : Mesons • 8 Types of gluons (color combinations), such as RRbar Quantum Colordynamics • Just like the photon (γ) is the carrier of Electromagnetic interaction and responsible for the Electromagnetic force • Gluon (massless like γ ) is the carrier of Strong Force • Gluon carries “Strong Charge”: Color • Theory is very much like Quantum Electrodynamics and is a renormalizable Gauge theory • For now, simply imagine QCD is exactly QED with a single gluon exchange between quarks at short dis.