Kernfysica: quarks, nucleonen en kernen HL-2 May 2006 Outline lecture (HL-2) Quarkonium Charmonium spectrum quark-antiquark potential chromomagnetic interaction strong / em. decay widths Mesons in the quark model multiplets meson masses neutral Kaon decay CP violation Literature: PR 13-14; BJ 10.3,10.5,10.7 HL-2 May 2006 Kernfysica: quarks, nucleonen en kernen Kernfysica: quarks, nukleonen en kernen

Kernfysica: quarks, nucleonen en kernen HL-2 May 2006 hadron resonances J/ production h + - e- e+ Intermediate hadron state (decaying into leptons, hadrons) interpreted as bound state (JP=1-)  J/ resonance: e== 4.8 keV, h = 59 keV (lepton universality)  = 69 keV e c c bound states :  transitions between excited states HL-2 May 2006 Kernfysica: quarks, nucleonen en kernen Kernfysica: quarks, nukleonen en kernen

Crystal Ball (structure like Plastic Ball, now at KVI) HL-2 May 2006 Crystal Ball (structure like Plastic Ball, now at KVI) hollow sphere from ca. 900 NaI crystals around interaction point HL-2 May 2006 Kernfysica: quarks, nucleonen en kernen Kernfysica: quarks, nukleonen en kernen

charmonium  decay spectrum HL-2 May 2006 charmonium  decay spectrum Level scheme reminds of positronium states n 2S+1 Lj states characterized by parity P = (-1)L+1 charge conjugation parity C = (-1)L+S strong electric dipole L=1, S=0 transitions HL-2 May 2006 Kernfysica: quarks, nucleonen en kernen Kernfysica: quarks, nukleonen en kernen

charmonium level scheme HL-2 May 2006 charmonium level scheme only JPC = 1– directly accessible in e+ e- production C states reached by magnetic dipole L=0, S=1 spin-flip transitions (weaker than electric transitions) D mesons: narrow states below threshold: hindered by energy limit and suppressed (“OZI rule”) HL-2 May 2006 Kernfysica: quarks, nucleonen en kernen Kernfysica: quarks, nukleonen en kernen

low-energy hadron resonances HL-2 May 2006 low-energy hadron resonances +  - e- e+ 0 K- K + e- e+ 0 K0 e- e+ 0 =150 MeV =4.4 MeV, why not 3 decay? (18%) requires 3g coupling, amplitude suppressed by OZI rule (Okubo, Zweig, Iizuka) stronger suppression for J/ HL-2 May 2006 Kernfysica: quarks, nucleonen en kernen Kernfysica: quarks, nukleonen en kernen

quark-antiquark potential HL-2 May 2006 quark-antiquark potential level sequence reminds of positronium system: Coulomb-like potential (g exchange force, short range color charge 4/3 ) with linear confinement (asymptotic freedom) hints for ln(r) dependence from bottonium levels HL-2 May 2006 Kernfysica: quarks, nucleonen en kernen Kernfysica: quarks, nukleonen en kernen

realistic qq potential from Lattice QCD HL-2 May 2006 realistic qq potential from Lattice QCD solving Schrödinger equation with QCD Lagrangian on a discrete space-time lattice hybrid potential from glue excitations: states predicted discovery possible at future GSI accelerator ground state potential r0=0.5 fm HL-2 May 2006 Kernfysica: quarks, nucleonen en kernen Kernfysica: quarks, nukleonen en kernen

Kernfysica: quarks, nucleonen en kernen Hot News! HL-2 May 2006 Kernfysica: quarks, nucleonen en kernen

access to charmonium states in annihilation HL-2 May 2006 access to charmonium states in annihilation many unknown states and transitions hyperfine S-state splitting 120 MeV HL-2 May 2006 Kernfysica: quarks, nucleonen en kernen Kernfysica: quarks, nukleonen en kernen

chromomagnetic interaction HL-2 May 2006 chromomagnetic interaction strong (hyperfine) splitting of S states, like in positronium: zero-range spin-spin interaction, point interaction of magnetic moments of e+ e- modified for color-magnetic qq force: (eff. interaction, constituent mass) color-magnetic energy splitting HL-2 May 2006 Kernfysica: quarks, nucleonen en kernen Kernfysica: quarks, nukleonen en kernen

charmonium and bottonium levels HL-2 May 2006 charmonium and bottonium levels smaller hyperfine splitting in system due to larger b-quark mass HL-2 May 2006 Kernfysica: quarks, nucleonen en kernen Kernfysica: quarks, nukleonen en kernen

bottonium level scheme HL-2 May 2006 bottonium level scheme similar level structure (mc 1.3 GeV, mb 4.3 GeV) : flavour independent qq potential, surprising: very similar mass difference of lowest states:  : m(2S-1S) = 563 MeV  : m(2S-1S) = 589 MeV  (9460) = resonance “upsilon” =53 keV sensitive to long-range part of qq potential  r,  ln(r) HL-2 May 2006 Kernfysica: quarks, nucleonen en kernen Kernfysica: quarks, nukleonen en kernen

quarkonium em / strong decay width HL-2 May 2006 quarkonium em / strong decay width positronium decay width: 2 decay width: (including higher order radiative corrections rad. ) 2g decay width: ratio of decay widths: consistent with S from level spectrum HL-2 May 2006 Kernfysica: quarks, nucleonen en kernen Kernfysica: quarks, nukleonen en kernen

Kernfysica: quarks, nucleonen en kernen HL-2 May 2006 Outline lecture (HL-2) Quarkonium Charmonium spectrum quark-antiquark potential chromomagnetic interaction strong / em. decay widths Mesons in the quark model multiplets masses neutral Kaon decay CP violation HL-2 May 2006 Kernfysica: quarks, nucleonen en kernen Kernfysica: quarks, nukleonen en kernen

mesons in the quark model HL-2 May 2006 similar light quark masses: treated on same footing: ø è Ä s and ÷ ö ç æ - ¾ ® = × > ± u d axis about rotation isospin C i R G q parity 2 1 | ) ( : for eigenvalue good no triplet of product 3 t p conjugate triplet I- I+ in isospin (I3) and hypercharge (Y) Y=B+S HL-2 May 2006 Kernfysica: quarks, nucleonen en kernen Kernfysica: quarks, nukleonen en kernen

products of SU(3) representations HL-2 May 2006 products of SU(3) representations add conjugate representation to each point of fundamental triplet Y=B+S meson nonet reduced to singlet {1} and octet {8} states 1 u d s 1/3 1/2 I3 HL-2 May 2006 Kernfysica: quarks, nucleonen en kernen Kernfysica: quarks, nukleonen en kernen

meson multiplets (lowest L=0 states) HL-2 May 2006 meson multiplets (lowest L=0 states) pseudoscalar (JP = 0- ) octet + singlet vector (JP = 1- ) octet + singlet HL-2 May 2006 Kernfysica: quarks, nucleonen en kernen Kernfysica: quarks, nukleonen en kernen

mixing of multiplet states HL-2 May 2006 mixing of multiplet states SU(3) symmetry broken by s-quark mass larger than u, d mass mixing of I=0 multiplet states  of same JP physical states  from experimental meson masses: for pseudoscalar (0-), vector (1-) and tensor (2+) mesons ideal mixing (35o) octet state pure explanation of branching fractions: s s HL-2 May 2006 Kernfysica: quarks, nucleonen en kernen Kernfysica: quarks, nukleonen en kernen

color-magnetic energy splitting HL-2 May 2006 color-magnetic energy splitting remember: charmonium S-state splitting 120 MeV J = 1 mass gap 600 MeV/c2 J = 0 HL-2 May 2006 Kernfysica: quarks, nucleonen en kernen Kernfysica: quarks, nukleonen en kernen

Kernfysica: quarks, nucleonen en kernen HL-2 May 2006 meson masses calculated from constituent quark masses and color-magnetic mass splitting: free parameters: constituent q masses: HL-2 May 2006 Kernfysica: quarks, nucleonen en kernen Kernfysica: quarks, nukleonen en kernen

decay channels of lightest mesons HL-2 May 2006 strong decay not possible for lightest meson strong decay I-spin forbidden strong decay mixing HL-2 May 2006 Kernfysica: quarks, nucleonen en kernen Kernfysica: quarks, nukleonen en kernen

Kernfysica: quarks, nucleonen en kernen HL-2 May 2006 CP eigenstates Parity violating decay fast slow (phase-space restricted) K ® 2 p and 3 p S- but not CP eigenstates construct CP eigenstates (physical states) as linear combination of S-eigenstates HL-2 May 2006 Kernfysica: quarks, nucleonen en kernen Kernfysica: quarks, nukleonen en kernen

K0 mixing and regeneration HL-2 May 2006 K0 mixing and regeneration 450 GeV p HL-2 May 2006 Kernfysica: quarks, nucleonen en kernen Kernfysica: quarks, nukleonen en kernen

Kernfysica: quarks, nucleonen en kernen HL-2 May 2006 Summary lecture (HL-2) Quarkonium Charmonium spectrum (partly explored)  quark-antiquark potential (Coulomb like) level splitting: chromomagnetic interaction  long range part (asymptotic freedom) strong / em. decay widths  coupling strength Mesons in the quark model multiplets masses  broken SU(3) symmetry: mixing neutral Kaon decay: CP eigenstates CP violation HL-2 May 2006 Kernfysica: quarks, nucleonen en kernen Kernfysica: quarks, nukleonen en kernen

Addition: Baryons in the quark model HL-2 May 2006 Addition: Baryons in the quark model production multiplets masses Literature: PR 15; BJ 9, 10.4 -10.6 HL-2 May 2006 Kernfysica: quarks, nucleonen en kernen Kernfysica: quarks, nukleonen en kernen

pion nucleon scattering HL-2 May 2006 (1232) P33 (1950) N(1680) N(1520) pion nucleon scattering Isospin coupling, invariant mass (4-mom. sum) and phase-shift analysis yield energy (mass), I, L, J resonance assignment: L2I,2J (mass) and width (lifetime) HL-2 May 2006 Kernfysica: quarks, nucleonen en kernen Kernfysica: quarks, nukleonen en kernen

Kernfysica: quarks, nucleonen en kernen HL-2 May 2006 phase-shift analysis quantum scattering in 3 dimensions (halfplane =0) HL-2 May 2006 Kernfysica: quarks, nucleonen en kernen Kernfysica: quarks, nukleonen en kernen

phase-shift analysis (2) HL-2 May 2006 phase-shift analysis (2) will contain interferences of partial waves l  particular angular distributions total cross section: HL-2 May 2006 Kernfysica: quarks, nucleonen en kernen Kernfysica: quarks, nukleonen en kernen

phase-shift analysis (3) HL-2 May 2006 phase-shift analysis (3) elastic scattering: max. cross section for: resonance condition! at resonance energy E = ER: purely imaginary!! HL-2 May 2006 Kernfysica: quarks, nucleonen en kernen Kernfysica: quarks, nukleonen en kernen

phase-shift analysis (4) HL-2 May 2006 phase-shift analysis (4) expand partial wave amplitude Tl around resonance energy: HL-2 May 2006 Kernfysica: quarks, nucleonen en kernen Kernfysica: quarks, nukleonen en kernen

phase-shift analysis (5) HL-2 May 2006 phase-shift analysis (5) generalization: Breit-Wigner resonance (non-relativistic): HL-2 May 2006 Kernfysica: quarks, nucleonen en kernen Kernfysica: quarks, nukleonen en kernen

Kernfysica: quarks, nucleonen en kernen HL-2 May 2006 quark-flow diagrams quark composition in intermediate (10-23 s) state HL-2 May 2006 Kernfysica: quarks, nucleonen en kernen Kernfysica: quarks, nukleonen en kernen

Kernfysica: quarks, nucleonen en kernen baryon multiplets HL-2 May 2006 color-neutral lowest energy (L=0) qqq states require symmetric small (.1%) e.m. splitting of Isospin multiplets; strong SU(3) breaking HL-2 May 2006 Kernfysica: quarks, nucleonen en kernen Kernfysica: quarks, nukleonen en kernen

Kernfysica: quarks, nucleonen en kernen HL-2 May 2006 baryon mass spectrum I()=0=I(s)=I(ud) (ud) antisymmetric (ud) antisymmetric spin(ud)=0 spin()=spin(s)=1/2 -  mass splitting 80 MeV/c2 due to spin-spin interaction uds usd HL-2 May 2006 Kernfysica: quarks, nucleonen en kernen Kernfysica: quarks, nukleonen en kernen

Kernfysica: quarks, nucleonen en kernen HL-2 May 2006 Summary addition: Baryons in the quark model multiplets and SU(3) breaking masses: spin-spin interaction HL-2 May 2006 Kernfysica: quarks, nucleonen en kernen Kernfysica: quarks, nukleonen en kernen