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Quarks, Hadrons, and the Strong Force Physics 245C Prof Quarks, Hadrons, and the Strong Force Physics 245C Prof. Conway 1 1950’s-1960’s: “Particle Zoo” Life was simple back when we just had two elementary particles! Discovery of the pion. How did they do it? Great project! Mesons were thought to explain how nuclei were held together - was this it? By the 1950’s cyclotrons opened our eyes to a plethora of particles...what the $&%$^ ?? 2 Rutherford’s Nucleus • Geiger and Marsden, in 1911, sat for days in a darkened room recording flashes... • many came out at a large angle • Ernest Rutherford realized the significance of this, and calculated the scattering cross section versus angle: scattering center must be smaller than rmin 3 (Deeply) Inelastic eN Scattering • do the Rutherford experiment with electrons and protons! • e-p scattering has inelastic part 4-vectors! elastic: q2 = 2Mν inelastic: q2 < 2Mν interaction is via intermediate virtual photon 4 (Deeply) Inelastic eN Scattering • results show resonance structure • ep → eX (X can be delta resonance, e.g.) ∆+ → p + π0 ∆+ → n + π+ m(∆+) = 1232 MeV/c2 ...or X could be a bunch of hadrons, etc. 5 (Deeply) Inelastic eN Scattering e- p e- hadrons mass of recoil system Phys. Rev. Lett. 23, 930–934 (1969) 6 (Deeply) Inelastic eN Scattering • we measure the in-elastic-ness of the process using the Bjorken scaling variable x Q2 Q2 x ≡ = ; Q2 = −q2 2Pq 2Mν 2 2 2 d σ dσ × F2(Q ,ν) F1(Q ,ν) 2 θ ! = + 2 tan dΩdE !dΩ"Mott # ν Mc 2$ structure functions 7 BJ’s “Parton” Model 2 • at large Q , when F1 and F2 were extracted from SLAC data, it was observed that they depend weakly on Q2 - mainly on ν • this implies that the electrons are being scattered from point charges...much smaller than the proton! • BJ called them “partons” • since it was found that 2xF1 = F2 , and this is expected for spin-1/2 particles, the partons have spin 1/2 8 BJ’s Parton Model • let’s think about this from the point of view of an infinite- momentum frame • each parton (whatever it is) carries some fraction of the total momentum in this limit x is now seen to be that fraction! but what are the partons? 9 Gell-Mann’s Quarks • “three quarks for Muster Mark!” - James Joyce, Finnegan’s Wake • Gell-Mann proposed that the properties of baryons could be accounted for if they were constituted of quarks • initially needed only three: u - up quark, charge +2/3 d - down quark charge -1/3 s - strange quark charge -1/3 10 Baryon Quark Structure baryons are particles made from three quarks: n p - 0 Σ Σ + Λ0 Σ Ξ- Ξ0 (antibaryons are made from three antiquarks) 11 Meson Quark Structure • mesons are particles made from a quark and and antiquark - ds us- ud- Text ud- - us- ds more explanation needed here 12 The Strong Force • quarks interact via the weak, force the electromagnetic force, and the strong force • the charge associated with the strong force is called color: red green blue • quarks have color; antiquarks have anticolor • the color force grows with separation • quarks can be thought of as the ends of color flux tubes or strings (not string th.!) • if the tube breaks, new quarks are produced 13 The Strong Force electric dipole field color dipole field This is how we pop a qq- pair out of the vacuum! 14 Mark I at SLAC • Mark I was installed at the SPEAR e+e- collider at SLAC in the early 1970’s • the machine was able to run at cm energies of up to about 3.5 GeV • the goal: study qq - production and nail down the existence of quarks They succeeded beyond their wildest dreams... 15 e+e- → qq- • we can pair produce quarks via the electromagnetic interaction, exactly in analogy to muon pair production: well above threshold: 2 − π ¯hQcα σ(e+e → qq¯)= 3 ! E " • what happens to color string in this case? • need to consider vector meson resonances also 16 Breit-Wigner Resonances • the “point-like” cross section (γ*) drops like 1/Ecm = 1/s • s-channel exchange of a vector meson is governed by the Breit-Wigner formula: ∝ Γ σ(E) 2 2 (E − E0) +Γ /4 width related to lifetime: ¯h τ = Γ 17 The November Revolution • in late 1974, the Mark I was plugging away, scanning in energy • at Brookhaven, an experiment was underway to look for muon pair production using a hadron beam on a target • they saw something totally unexpected: a large, narrow resonance at about 3.1 GeV/c2 • the SLAC folks found out...tuned to 3.1 GeV • SLAC called it the “ψ”, Sam Ting called it the “J” ... we now call it the J/ψ 18 The November Revolution • the ψ is a bound state of a new quark, called 2 charm (mc ~ 1.8 GeV/c ) • very narrow resonance: 91 keV • higher resonances ψ’, ψ’’,... Sam Ting Nobel 1976 19 Clearly it should be called ψ ! R • needle in haystack problem? • measure ratio of multihadron production to muon pair production: σ(e+e− → hadrons) R ≡ σ(e+e− → µ+µ−) • can’t use e+e- in denominator...why? 2 R = 3ΣQi 20 R • measurement of R shows clear steps as we cross the threshold for the next heavier quark 21 Charmed Hadron Structure 22 The b Quark • In 1977 the highest energy e+e- colliders were still < 10 GeV cm energy • Leon Lederman and his group were studying Drell-Yan production of muon pairs in proton-nucleon collisions at high Leon Lederman energy at FNAL (Nobel 1988) • having founded the “I missed the J/psi club”, Leon and Co. found something new and not entirely unexpected: another new quark, dubbed the b quark (beauty, or bottom) • this is the Υ (upsilon = “oops - Leon!”) 23 Drell-Yan and Structure • even before the quark model was fully established, Drell and Yan worked out the consequences of hard collisions of hadrons: x1 = mom. fraction of antiquark in p x2 = mom. fraction of quark in N quark momentum mµµ = x1x2Ecm fraction distributions xF = x1 − x2 2 2 d σ 4πα 2 2 = 2 ! ef [qf (x1)¯qf (x2)+...] dm dxF 9sm µµ µµ f 24 Quark Structure of Hadrons • Did we just say that there were antiquarks inside protons? • Strong force holding together hadrons carried by gluons • If we look deep inside a hadron, we can sometimes catch the gluons: 25 Quark Structure of Hadrons • if we look even deeper, we can see the gluons undergo quantum fluctuations to quark antiquark pairs • this happens in QED too but the strong force is, well, stronger 26 Fundamental Fermions, ca. 1979 • by the close of the seventies, a tantalizing picture had emerged: • clearly nature had more in store... 27 Colors and QCD • QCD = quantum chromodynamics • two ways to make “white” (color neutrality): • red-antired, blue-antiblue, green-antigreen • red-green-blue (rgb) • clearly this is the basis of mesons/baryons • gluons carry color and anticolor simultaneously 28 Gluons • How many gluons are there? Nine? • No...the color-neutral ones can’t be gluons... • color charge is governed by an SU(3) symmetry • SU(3) - special unitary group of 3x3 matrices with determinant • ana1ogous to Pauli matrices: SU(2) 29 Gluons • there are 32 - 1 = 8 gluons which transform under the SU(3) matrices • Griffiths lists the states in eq. 9.4, and the matrices (Gell-Mann’s version) in 9.9 • to learn/use QCD fully you will need to have studied group theory and Lie algebras in particular • http://www.answers.com/topic/color-charge has links to any desired depth... • what do you need to know? Gluons in Hadrons • inside a hadron you can imagine the gluons moving color charge around: • this is not completely accurate...but not a bad way to think about hadrons Gluon Structure Functions • the complete structure function of the proton has three components: This is how the structure GLUONS functions look at a particular Q2 - at higher VALENCEQUARKS values, the shapes change: PARTONDENSITY the valence distribution SEAQUARKS drops and the gluon and sea components are enhanced Feynman Rules - QCD • these vertices are allowed in QCD: • the first has a counterpart in QED...the gluon self-coupling ones are new 33 Typical QCD Processes • in hadron collisions we find processes of the form • these lead to hadron jets Jets and QCD • at lower energies, get ~few hadrons • at high energies, get tightly collimated “jets” • particle multiplicity scales logarithmically with jet energy • significant chance of gluon radiation from quark line: 35 Discovery of the Gluon • TASSO experiment at PETRA (Hamburg), in e +e- collisions at Ecm = 27 GeV : This and a handful of similar events with three jets established the existence of the gluon in 1979 S.L. Wu, G. Zobernig 36 Running Coupling • we have a coupling constant in QCD, αs define in analogy to α in QED • however, it turns out that both of these coupling constants “run” with Q2 ! • potential is “screened” by quantum fluctuations to fermion pairs in both cases Λ~150 MeV/c Running Coupling • at the scale of the Z mass (electroweak scale we have • thus the strong interaction is about 16 times stronger than the electromagnetic... • in the high Q2 limit, we can perform “perturbative QCD” calculations • QCD “asymptotically free” (Nobel 2004) Loops and Orders • loop diagrams are very important in QCD • even the simplest processes cannot be estimated at leading order only • a very technical specialty... full set of diagrams at all orders in alpha must be added, w/ interference ! Widths and Decays • lifetime of a particle related to its total width Γ • total width is the sum of all the partial widths for each possible decay • we write the branching ratio of a particle to a particular final state i as Widths and Decays • basically impossible to calculate partial widths for hadronic decays due to unknown “hadronization factor”: non-perturbative QCD • however, in ratios of branching ratios (ratios of partial widths) these factors can drop out in certain cases • still, must include all diagrams to all orders in principle...we are left with approximations • works better for heavy quark systems (b mesons and baryons) Strong Decays • particles undergoing decay governed by the strong interaction happen very quickly, O(10-22 sec) • we tend to think of these more as resonances than particles phi resonance width: 4 2.
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