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Topics in Baryon Spectroscopy and Structure

Topics in Baryon Spectroscopy and Structure. Volker D. Burkert Jefferson Lab. Scottish Universities Summer School in Physics August 22–29, 2004, St. Andrews, UK. I. II. III. Overview. Introduction, Multiplets, SU(6)xO(3) Analysis Tools, Equipment

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Topics in Baryon Spectroscopy and Structure

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  1. Topics in Baryon Spectroscopy and Structure Volker D. Burkert Jefferson Lab Scottish Universities Summer School in Physics August 22–29, 2004, St. Andrews, UK

  2. I II III Overview • Introduction, Multiplets, SU(6)xO(3) • Analysis Tools, Equipment • Electromagnetic Excitation of the D(1232) • Structure of the Roper and other lower mass resonances. • “Missing” Resonances • Exotic Baryons (Pentaquarks)

  3. Gluon flux simulation of a 3-quark system. Why N*’s are importantNathan Isgur, N*2000 Conference • Nucleons represent the real world, they must be at the center of any discussion on • Nucleons represent the simplest system where • Nucleons are complex enough to “why the world is the way it is” “the non-abelian character of QCD is manifest” “reveal physics hidden from us in mesons” Gell-Mann & Zweig - Quark Model: 3 x 3 x 3 = 10 + 8 + 8 + 1 O. Greenberg - The D++ problem and “color”

  4. p+p X D(1232) p-p X Phys. Rev. 85, 936 (1952) An energy excitation spectrum indicates that the proton has a substructure. This was two years later confirmed in elastic ep scattering by Hofstadter.

  5. Total cross sections (PDG2004) p-p X pp(GeV/c)

  6. D++ u u u ys = yflavoryspin p+ p D++ is the largest pN cross section, but the D ++ state is not allowed in CQM w/o color. The D++(1232) leads to “color” D ++ O. Greenberg introduces a new quantum number to get asymmetric w.f. Y as = yflavoryspinycolor D++ uuu

  7. Baryon multiplets N 2 S, L 1 X I3 W ─ +1/2 1 -1 -1/2 Baryons qqq Y=B+S D ++ D- S X

  8. |Baryon> : a |qqq> + b |qqq(qq)| + g |qqqG> + .. Lectures by F. Close SU(2) Quark spin sq = ½ Baryon spin: J = L + si S parity: P = (-1)L {qqq }: 6 6 6 = 56707020 + + + + + + + + + + + + + + + 56 = 410 28 70 = 210 48 28 21 20 = 28 41 Baryon Resonances and SU(6)xO(3) 3 Flavors: {u,d,s} SU(3) {qqq}: 3 3 3 = 10 8 8 1 O(3) SU(6) multiplets decompose into flavor multiplets:

  9. “Missing” P13(1870) Capstick and Roberts D13(1520) S11(1535) D(1232) Roper P11(1440) SU(6)xO(3) Classification of Baryons

  10. States with same I, Jp quantum numbers and different total quark spins Sq = 1/2 or Sq = 3/2, mix with mixing angle qM. The pure quark states |N2, 1/2- > and |N4, 1/2- > in [70,1-] project onto physical states S11(1535) and S11(1650). Sq = 1/2 Sq = 3/2 |S11(1535)> = cosq1|N2,1/2-> - sinq1|N4, 1/2-> |S11(1650)> = sinq1 |N2,1/2-> +cosq1|N4, 1/2-> p Notation: L2I,2J Q1 = 31o (measured in hadronic decays). Similarly for |N2,3/2-> and |N4,3/2- > |D13(1520)> = cosq2|N2,3/2-> - sinq2|N4, 3/2-> |D13(1700)> = sinq2 |N2,3/2-> +cosq2|N4, 3/2-> Q2 = 6o The |N4,5/2- > quark state has no N2 partner, and cannot mix. |D15(1675) > = |N4,5/2- > Configuration Mixing in [70,1-]

  11. Analysis Tools

  12. p1, m1 P, M p2, m2 4-vectors M2 = (pp + pp)2 Rarely can resonances be observed just in mass distributions, e.g. if state is narrow, or if strongly excited. It also gives no information on quantum numbers other than isospin. Simple searches for resonances For a 2-body decay one can search for resonance structures in the invariant mass distribution. proton pion M

  13. Dalitz Plot for 3-body decay (e.g. pp+K0) p1, m1 p2, m2 P, M p3, m3 Resonance at: m12 = 1.8 GeV Resonance at: m23 = 2.0 GeV A narrow resonance at m12 = 2.0 GeV may appear like a broad enhancement in m23 (kinematical reflection). 3-body decay

  14. gp pK+K- Dalitz Plot: Eg = 1.6-3.5 GeV F(1020) L(1520) L(1690) L(1820)

  15. S f(k,q) = 1/k (2l+1)alPl(cosq) l al = (hle2idl – 1)/2i , 0 < hl < 1 , dl :phase shift of lth partial wave sl = 4p/k2(2l+1)|al|2 < 4p(2l+1)/k2 Argand Diagram Elastic scattering amplitude of spinless particle with momentum k in cms: For purely elastic scattering: hl = 1, (e.g. pN -> pN) ds/dW = |f(k,q )|2 Optical theorem: stot = 4p/k[Im f(k,0)] Cross section for lth partial wave is bounded:

  16. Im A 1 inelasticity sets in h/2 1/2 2d al Re A +1/2 -1/2 Argand Diagram al: partial wave amplitude evolving with energy. The amplitude leaves the unitary circle where inelasticity sets in. al = (hl e2idl – 1)/2i

  17. Gel/2 - mGel al= al= ER – E – iGtot/2 s – m2 – imGtot Breit-Wigner Form • B-W (non-relativistic) form for an elastic amplitude al with a • resonance at cm energy ER and elastic width Gel and total width • Gtot is • Relativistic form: • Many other B-W forms exist, • dependent of process dynamics.

  18. Electromagnetic Excitation of Baryon Resonances

  19. resolution of probe π low N LQCD P.O. Bowman, et al., hep-lat/0209129 q high e.m. probe Why electroexcitation of N*s ? Addresses the question:What are the relevant degrees of freedom at different distance scales? => Constituent quark model with fixed quark masses only justified at photon point and low q. Spatial resolution ~1/q

  20. Spring-8 JLAB Reach of Current Accelerators

  21. Large Acceptance Detectors for N* Physics. • CLAS: (photon and electron reactions) • Final states with mostly charged particles. • Operates with electron beams and with energy-tagged photon beams. • Coverage for photons limited to lab angles < 45o • Crystal Barrel-ELSA: (photon reactions) • CsI crystals with excellent photon detection, e.g. Npopo , Npoh • SAPHIR-ELSA (photon reactions, detector dismantled) • Charged particles in final state • GRAAL (photon reactions): • BGO crystals, with excellent photon detection, limited charged particle, polarized laser-backscattered tagged photon • Crystal Ball – MAMI (photon reactions) • neutral final states with excellent resolution, limited W range • BES (Beijing) – N* in e+e- collisions. Not included are setups for more specialized applications.

  22. CLAS JLab Site: The 6 GeV CW Electron Accelerator Emax ~ 6 GeV Imax ~ 200 mA Duty Factor ~ 100% sE/E ~ 2.5 10-5 Beam P ~ 80% Eg(tagged) ~ 0.8- 5.5 GeV

  23. CEBAFLarge Acceptance Spectrometer Torus magnet 6 superconducting coils Large angle calorimeters Lead/scintillator, 512 PMTs Liquid D2 (H2)target + g start counter; e minitorus Gas Cherenkov counters e/p separation, 216 PMTs Drift chambers argon/CO2 gas, 35,000 cells Electromagnetic calorimeters Lead/scintillator, 1296 PMTs Time-of-flight counters plastic scintillators, 684 PMTs

  24. Single Event gd → p K+K─X K+ K- p

  25. Missing Mass Distribution gp pX f

  26. Super Photonring-8GeVSPring-8 • Third-generation synchrotron radiation facility • Circumference: 1436 m • 8 GeV • 100 mA • 62 beamlines

  27. Laser Electron Photon facility at SPring-8 g in operation since 2000

  28. g LEPS detector TOF wall Dipole Magnet (0.7 T) Aerogel Cerenkov (n=1.03) Start counter Liquid Hydrogen Target (50mm thick) MWDC 3 Silicon Vertex Detector MWDC 2 MWDC 1 1m

  29. The GRAAL Experiment

  30. p0 h gg invariant mass The Crystal Barrel @ ELSA CsI detector

  31. Electromagnetic Excitation of N*’s e’ , K γv e N*,△ N’,△’, L N Primary Goals • Extract photocoupling amplitudes for known △,N* resonances • Partial wave and isospin decomposition of hadronic decay • Assume EM and strong interaction vertices factorize • Helicity amplitudes A3/2 A1/2 S1/2 and their Q2 dependence • Study quark wave function and symmetries • Quark models: relativity, gluons vs. mesons. • Identify missing resonances expected from SU(6)xO(3) • More selective hadronic decays: 2p, h, r, w, KL

  32. Inclusive Electron Scattering p(e,e’)X

  33. W-Dependence of Selected Channels at 4 GeV p(e,e’)X (trigger) p(e,e’p)p0 p(e,e’p+)n p(e,e’pp+)p- p(e,e’pp+)X

  34. ND(1232) Transition

  35. N-D(1232) Quadrupole Transition SU(6): E1+=S1+=0

  36. N(938) D(1232) C2 C2 Coulomb single quark transition. ND - Quadrupole transition in SQT D(1232) N(938) M1 Magnetic single quark Transition.

  37. Pion Electroproduction Structure Functions • Longitudinal sensitivity w/o Rosenbluth separation. • Measurement requires out-of-plane detection of hadronic decay. • Structure functions extracted from fits to f* distributions for each (Q2 ,W, cosθ*) point. • LT and TT interference sensitive to weak quadrupole and longitudinal multipoles.

  38. Im(S1+)Im(M1+) Large P33(1232) Small The Power of Interference I sLT ~ Re(L*T) = Re(L)Re(T) + Im(L)Im(T) • Unpolarized structure function • Amplify small resonance multipole by an interfering larger resonance multipole

  39. Truncated Multipole Expansion in D(1232) Region • s, p waves only, Jmax= 3/2 , M1+ dominance, i.e. retain only • terms containing M1+ • 6 unknown terms remain, which can be determined uniquely by measuring the azimuthal and polar angle dependence of the cross section.

  40. N* program – ND(1232) transition f

  41. Structure Functions - Invariant Mass W Preliminary

  42. Structure Functions - cos θ* |M1+|2(1-3/5cos2q) Preliminary -|M1+|2-2Re(M1+E1+*) A+6cosqRe(M1+S1+*)

  43. Resonant Multipoles Non-Resonant Multipoles Legendre Expansion of Structure Functions (M1+ dominance) Preliminary

  44. * Im(M1+) => GM Electroproduction of △(1232) Recent quark models still fall short at low Q2 Missing qq strength? Sea quarks?

  45. Sign? Q2 dependence? • Data could not determine sign or Q2 dependence Multipole Ratios REM, RSM before 1999

  46. Multipole Ratios REM, RSM in 2002 Sign? < 0 ! Q2 dependence Slope < 0 ! • No trend towards zero crossing and pQCD behavior is observed for Q2 up to 4 GeV2.

  47. LQCD (unquenched) Deviation from spherical symmetry of the D(1232) in LQCD (unquenched). LQCD (unquenched) REM, RSM in 2004 REM 0 -5 0 RSM Dynamical models attribute the deformation to contributions of the pion cloud at low Q2. -5 -10 5 10-1 1 Q2 (GeV2)

  48. e / e / Deformation of N,△ quark core? e e Shape of pion cloud? Answer will depend on wavelength of probe. With increasing resolution, we are mapping out the shape of the D vs. the distance scale. What does empirical E1+/M1+ ratio measure?

  49. D13(1520) S11(1535) Roper P11(1440) SU(6)xO(3) Classification of Baryons

  50. - What are the issues? P11(1440): Poorly understood in nrCQMs Alternative models: - Light front kinematics (relativity) - Hybrid baryon with gluonic excitation |q3G> - Quark core with large meson cloud |q3m> - Nucleon-sigma molecule |Nm> - Dynamically generated resonance S11(1535): Hard form factor Not a quark resonance, but KS dynamical system? Change of helicity structure with increasing Q2 from l=3/2 dominance to l=1/2 dominance, predicted in nrCQMs, pQCD. D13(1520): CQM:

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