* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download The Quark & Bag Models
Old quantum theory wikipedia , lookup
Introduction to quantum mechanics wikipedia , lookup
Compact Muon Solenoid wikipedia , lookup
Symmetry in quantum mechanics wikipedia , lookup
History of quantum field theory wikipedia , lookup
Identical particles wikipedia , lookup
Atomic nucleus wikipedia , lookup
Light-front quantization applications wikipedia , lookup
Electron scattering wikipedia , lookup
ATLAS experiment wikipedia , lookup
Nuclear structure wikipedia , lookup
Minimal Supersymmetric Standard Model wikipedia , lookup
ALICE experiment wikipedia , lookup
Nuclear force wikipedia , lookup
Technicolor (physics) wikipedia , lookup
Mathematical formulation of the Standard Model wikipedia , lookup
Grand Unified Theory wikipedia , lookup
Standard Model wikipedia , lookup
Elementary particle wikipedia , lookup
The Quark & Bag Models Simona Stoica KVI, September 17, 2008 Outline • The Quark Model – – – – Original Quark Model Additions to the Original Quark Model How to form mesons and baryons Color • Quantum Chromodynamics (QCD) – Color Charge – Quark confinement • M.I.T. Bag Model – Assumptions – Predictions – Failures of the MIT Bag model • Heavy quark spectra 2 The Quark Model • By the early 60’s there was a large zoo of particle found in bubble chamber experiments 3 Sorting them out • We could classify them by various quantum numbers – Mass – Spin – Parity – C parity – Isospin – Strangeness 4 First steps It was realized that even these new particles fit certain patterns: pions: p+(140 MeV) p-(140 MeV) po(135 MeV) kaons: k+(496 MeV) k-(496 MeV) ko(498 MeV) If mass difference between proton neutrons, pions, and kaons is due to electromagnetism then how come: Mn > Mp and Mko > Mk+ but Mp+ > Mpo Lots of models concocted to try to explain why these particles exist: Model of Fermi and Yang (late 1940’s-early 50’s): pion is composed of nucleons and anti-nucleons (used SU(2) symmetry) p+ = pn, p- = np, po = pp - n n note this model was proposed before discovery of anti-proton ! 5 First steps With the discovery of new unstable particles (L, k) a new quantum number was invented: strangeness Gell-Mann, Nakano, Nishijima realized that electric charge (Q) of all particles could be related to isospin (3rd component), Baryon number (B) and Strangeness (S): Q = I3 +(S + B)/2= I3 +Y/2 hypercharge (Y) = (S+B) Interesting patterns started to emerge when I3 was plotted vs. Y Y I3 6 Original Quark Model 1964 The model was proposed independently by Gell-Mann and Zweig Three fundamental building blocks 1960’s (p,n,l) 1970’s (u,d,s) mesons are bound states of a of quark and anti-quark: Can make up "wave functions" by combing quarks: p+ = ud, p- = du, po = 1 (uu - d d), k + = ds, k o= ds 2 baryons are bound state of 3 quarks: proton = (uud), neutron = (udd), L= (uds) anti-baryons are bound states of 3 anti-quarks: p uu d n udd L uds p (du ) Λ= (uds) 7 Quarks These quark objects are: • point like • spin 1/2 fermions • parity = +1 (-1 for anti-quarks) • two quarks are in isospin doublet (u and d), s is an iso-singlet (=0) • Obey Q = I3 +1/2(S+B) = I3 +Y/2 • Group Structure is SU(3) • For every quark there is an anti-quark • The anti-quark has opposite charge, baryon number and strangeness • Quarks feel all interactions (have mass, electric charge, etc) 8 Early 1960’s Quarks Successes of 1960’s Quark Model: • Classify all known (in the early 1960’s) particles in terms of 3 building blocks • predict new particles (e.g. W-) • explain why certain particles don’t exist (e.g. baryons with spin 1) • explain mass splitting between meson and baryons • explain/predict magnetic moments of mesons and baryons • explain/predict scattering cross sections (e.g. spp/spp = 2/3) Failures of the 1960's model: • No evidence for free quarks (fixed up by QCD) • Pauli principle violated (D++= (uuu) wave function is totally symmetric) (fixed up by color) • What holds quarks together in a proton ? (gluons! ) • How many different types of quarks exist ? (6?) 9 Additions to the Original Quark Model – Charm • Another quark was needed to account for some discrepancies between predictions of the model and experimental results • Charm would be conserved in strong and electromagnetic interactions, but not in weak interactions • In 1974, a new meson, the J/Ψ was discovered that was shown to be a charm quark and charm antiquark pair 10 More Additions – Top and Bottom • Discovery led to the need for a more elaborate quark model • This need led to the proposal of two new quarks – t – top (or truth) – b – bottom (or beauty) • Added quantum numbers of topness and bottomness • Verification – b quark was found in a meson in 1977 – t quark was found in 1995 at Fermilab 11 Numbers of Particles • At the present, physicists believe the “building blocks” of matter are complete – Six quarks with their antiparticles – Six leptons with their antiparticles 12 Number of particles The additive quark quantum numbers are given below: Quantum # u d s c b t electric charge 2/3 -1/3 -1/3 2/3 -1/3 2/3 I3 1/2 -1/2 0 0 0 0 Strangeness 0 0 -1 0 0 0 Charm 0 0 0 1 0 0 bottom 0 0 0 0 -1 0 top 0 0 0 0 0 1 Baryon number 1/3 1/3 1/3 1/3 1/3 1/3 Lepton number 0 0 0 0 0 0 13 How to form mesons? 3 3 1 8 14 Baryons? 3 3 3 1 8 8 10 15 Color • Baryon decuplet (10) states consist of lowest mass J=3/2 states, assume that the quarks are in the spatially symmetric ground state (=0) • To make J=3/2, the quark spins must be ‘parallel’ (ex) D++ = u u u • The D++ wave function is symmetric 16 Color • Pauli exclusion principle? – two or more identical fermions may not exist in the same quantum state – what about the u quarks in D++ ? It must be antisymmetric under Pauli principle! • More questions on the quark model 17 Color • Another internal degree of freedom was needed “COLOR” • Postulates – quarks exist in three colors: – hadrons built from quarks have net zero color (otherwise, color would be a measurable property) • We overcome the spin-statistics problem by dropping the concept of identical quarks; now distinguished by color D++ = uR uG uB 18 Color & strong interactions • We have assigned a “hidden” color quantum # to quarks. – “hidden” because detectable particles are all “colorless” • It solves the embarrassment of fermion statistics problem for otherwise successful quark model. • Most importantly, color is the charge of strong interactions 19 Quantum Chromodynamics (QCD) • QCD gave a new theory of how quarks interact with each other by means of color charge • The strong force between quarks is often called the color force • The strong force between quarks is carried by gluons – Gluons are massless particles – There are 8 gluons, all with color charge • When a quark emits or absorbs a gluon, its color changes 20 More About Color Charge • Like colors repel and unlike colors attract – Different colors attract, but not as strongly as a color and its opposite colors of quark and antiquark • The color force between color-neutral hadrons (like a proton and a neutron) is negligible at large separations – The strong color force between the constituent quarks does not exactly cancel at small separations – This residual strong force is the nuclear force that binds the protons and neutrons to form nuclei 21 Quantum Chromodynamics (QCD) • Asymptotic freedom – Quarks move quasi-free inside the nucleon – Perturbation theoretical tools can be applied in this regime • Quark confinement – No single free quark has been observed in experiments – Color force increases with increasing distance • Chiral symmetry 22 Quark confinement • Spatial confinement – Quarks cannot leave a certain region in space • String confinement – The attractive( color singlet) quark-antiquark • Color confinement • The quark propagator has no poles 23 M.I.T. Bag Model • Developed in 1974 at Massachusetts Institute of Technology • It models spatial confinement only • Quarks are forced by a fixed external pressure to move only inside a given spatial region • Quarks occupy single particle orbitals • The shape of the bag is spherical, if all the quarks are in ground state 24 M.I.T Bag Model • Inside the bag, quarks are allowed to move quasi-free. • An appropriate boundary condition at the bag surface guarantees that no quark can leave the bag • This implies that there are no quarks outside the bag 25 M.I.T. Bag Model • The boundary condition generates discrete energy eigenvalues. R - radius of the Bag xn n x =2.04 R 1 xn Ekin ( R ) N q R 4 3 E pot ( R ) pR B 3 Nq = # of quarks inside the bag B – bag constant that reflects the bag pressure 26 M.I.T. Bag Model • Minimizing E(R), one gets the equilibrium radius of the system 14 N q xn Rn 4pB 4 3 3 14 En 4pBN q xn 3 Fixing the only parameter of the model B, by fitting the mass of the nucleon to 938MeV we have first order predictions 27 One gluon exchange • Model so far excluded all interactions between the quarks • There should be some effective interaction that is not contained in B( how do we know that?) sM q EX R αs – the strong coupling constant Mq depends on the quantum no. of the coupled quarks 28 The Casimir Term • The zero point energy of the vacuum ECas Z R • The Casimir term improves the predictions of the MIT bag model. • However, theory suggests the term to be negative • Best fits provide a slightly positive value 29 Predictions The masses of N, Δ, Ω, ω were used to fit the parameters. 30 Quark confinement q q 31 Color confinement • The non-perturbative vacuum can be described by a color dielectric function k(r) that vanishes for r→∞. • The total energy Wc of the color electric field Ec of a color charge Qc is 3 dr 2 Wc ~ Ec Dc d r ~ Qc 2 r (r ) 0 • Integral diverges, unless Qc=0 32 Failures of the Bag Model • Chiral symmetry is explicitly broken on the bag surface( static boundary condition) • Chiral extensions of the MIT-Bag model have been suggested: Cloudy bag model • Introduces a pion field that couples to the quarks at the surface. 33 Heavy quarks. Positronium Results • Positronium is an e+e- state that forms an “atom” • Two important decay modes – Two photon (singlet) • J=0 by Bose Symmetry • C=1 since C(photon)=-1 – Three photon • J=1 • C=-1 34 Postrionium Energy Levels • Can be done with non-relativistic Schrodinger equation & Coulomb Potential En 2 c2 2n 2 – Principal quantum number n=1,2,3… mM / m M m / 2 – Reduced mass • So result for positronium is En mc 2 4n 2 2 35 Relativistic Corrections • Spin-orbit couplings – Fine structure V ~ LS • Spin-spin couplings V ~ 1 2 ~ S1 S2 • These interactions split levels into – Hyperfine structure – Triplet (3S1) (orthopositronium) – Singlet (1S0) (parapositronium) DE fine ~ mc 4 n 3 2 36 Positronium Levels 23P2 23P1 S=1 23P0 L=1 n=2 S=0 L=0 S=1 S=0 n=1 L=0 21P1 23S1 21S0 S=1 13S1 S=0 11S0 37 Comparison with Charmonium 38 Why should these be similar? • Coulomb Potential has been shown before: mediated by massless photons Vem r • QCD has been found numerically to have a similar form VQCD 4 s kr 3r 39 Conclusions • The quark model – – – – classifies all known particles in terms of 6 building blocks Explains mass splitting between meson and baryons Explain/predict magnetic moments of mesons and baryons Explain/predict scattering cross sections • The MIT Bag Model – predicts fairly accurate masses of the particles – Explains color confinement – Helps predict heavy quark spectrum Simple models can give us a very good picture! 40 Bibliography • Y. IWAMURA and Y. NOGAMI, IL NUOVO CIMENTO VOL. 89 A, N. 3(1985) • Peter HASENFRATZ and Julius KUTI, PHYSICS REPORTS (Section C of Physics Letters) 40, No. 2 (1978) 75-179. • T. Barnes, arXiv:hep-ph/0406327v1 • Carleton E. DeTar, John 12. Donoghue, Ann. Rev. Nucl. Part. Sci. (1983) • E. Eichten et al. , Phys. Rev. D, 203 (1980) • E. Eichten et al. , Phys. Rev. Lett, 369 (1975) • Stephan Hartmann, Models and Stories in Hadron Physics 41