Some Issues in Meson Spectroscopy Crystal Barrel and B-Factory Experiences

1. Some Issues in Meson Spectroscopy Crystal Barrel and B-Factory Experiences Stefan Spanier University of Tennessee, Knoxville

2. Introduction • Scalars in D and B Decays • Initial State Radiation • Study of Charmonia • The DSJ States

3. Spectroscopy qq Mesons L s1 s2 2 – + 0 – + 2 + + 2.5 Hybrids 2 + – 2 – + 2.0 1 – – Glueballs 1– + exotic nonets 1 + – 1 + + 1.5 0 + – 0 – + 0 + + 1.0 L = 0 1 2 3 4 S=1, L=0 + gluon 1- + 1.9 GeV 4.4 GeV in cc _ Lattice QCD 0++ 1.6 GeV

4. Access to gluon rich states in pp Annihilation For Hybrids, the angular momentum in the flux tube transfers to one of the daughter mesons (L=1) and (L=0) meson. L=0:,,,,… L=1: a,b,h,f,…  1b1,f1,,a1  not preferred. p1(1400) E852: a2(1320) dominates + P-wave resonance VES : resonances; also just phenomenolog. Bkg t-channel exchange (‘s’-pole) [PRL 91(2003)092002] E852: m~1260MeV  lower (m=1370MeV in diff.) VES : a2(1320) dominates; no p10 CBAR: I(p1(1400)) ~ I(a2(1320)); S=1 initial state CBAR: 2% content; 1S0 initial only; or S=1, FSI CBAR+OBELIX: rp resonance from S=0 initial state  Exotic waves? Resonances?

5. Kaon Identification with the BaBar DIRC

6. Scalars are special • As states are mixtures: ann + bss + cqqqq + dglue + • Decay obscures quark content need to study production and decay _ _ _ _  non-perturbative QCD (meson spectrum)  quantum numbers 3P0 (vacuum) Compare to 1+ 2+ too many / heavily shifted ! • Experiment: • broad states • often covered by tensors • featureless decay angle distributions

7. Formalism for X  3 body (Dalitz plot analysis) a R c l l b d  assuming dominance by 2-body interaction (isobar model) • scalar resonances strongly overlap / decay channels open in vicinity Dynamic amplitudenot just a simple Breit Wigner • Analytic • Unitary (2-body subsystem) • Lorentz-invariant • K-matrix formalism widely used: production / decay c 2-body scattering R R = (1-iKr)-1 r =2-body PS l d L Spectator ? T = R K F = R P P-vector = Q T Q-vector • Watson theorem: same phase motion in T and F in elastic range • Adler zero: at mp 0 for pp=0: T = 0 near threshold; also/where for F ? • Resonance: = pole in unphysical sheet of complex energy plane

8. Scalars in D, DS, and B Decays • Initial state is single, isolated particle with well defined JB,D=0, JDs=1 • Decay-operators have simple lorentz and flavor structure • Short range QCD properties are known (better) • Weak decay defines initial quark structure; and rules (e.g. DI=1/2) • Large variety of transitions to different flavor and spin states with • large mass differences of the constituent quarks • - combined/coupled channel analyses • - isospin relations (simple BF measurements) • - semileptonic decays (true spectator, form factors) • Access to higher mass scalar states in B (?) • Input for B CP – physics • - add penguin modes for New Physics Search, e.g. B0 f0 K0 • - CP composition of 3-body modes, e.g. B0K0K+K- • - hadronic phase for CP angle g in BDK from D-Dalitz plot

9. Experiments • E791 p-(500 GeV) [Pt, C]  charm  • Focus gBrems [Be]  charm  • BaBar 2008 • Belle > 2008 • CLEO-c e+e- y(3S) DD 281pb-1 e+e- qq @ Y(4S) c.c. _ _ • B-factories are also D-factories: In each expect >> 2 Million of • E791 - 35,400 1 • FOCUS - 120,000 2 • CLEO-c - D0K-p+ : 51,200 3 D0 K-+ + BaBar 91fb-1 _ > 500 Million BB pairs took more than 10BB / sec _ • 1. E791 Collaboration, Phys.Rev.Lett. 83 (1999) 32. • 2. Focus Collaboration, Phys.Lett. B485 (2000) 62. • 3. CLEO-c: hep-ex/0512063.

10. I=1 Scalar a0(980) in D decays BaBar ~100fb-1 f(1020) Data: K*(892) D0K0Sp+p- D0K0SK+K- #92935 #13536 BaBar BaBar 97.3% purity f0(980) r(770) a0(980) a0(980) f0(980) Efficiency:

11. I=1 Scalar a0(980) / a0(1450) Flatte formula: 5 parameters |b0 | fixed by total BF  couplings gi(also tune lineshape) e.g. F1 : X  p (p h) F2 : X  p (KK) Scattering amplitude Production amplitude2 phph

12. I=1 Scalar a0(980) in D decays BaBar weight/ 5 MeV/c2 D0K0SK+K- • Moment analysis  only S and P waves • Extract S-wave and describe Flatte’ formula • with Crystal Barrel parameters • [Abele et al., PRD 57, 3860 (1998)] f(1020) • Fix m0 and coupling gph, but float gKK • Best description of S-wave from moments and floated in PWA inconsistent with CBAR: BaBar: gKK = 473 + 29 + 40 MeV1/2 CBAR: gKK = 329 + 27 MeV1/2  need coupled channel analysis with D0 K0p h DP projection _ • PWA needs ~3% contribution from higher mass • resonance tail (outside PS) •  assume f0(1400) ; uniform distribution worse •  what about a0(1450) ?

13. I=1 Scalar a0(980) in B decays CLEO In 9 fb-1 @ Y(4S) CLEO finds: [PRL 93 (2004) 111801] # (155 + 22) events Main contribution from a0K0S; also a2(1320)K0S, K*(892)h, K0*(1430)h B(D0K0p0h ) = (1.05 ± 0.16 ± 0.14 ± 0.10) % _

14. I=1/2 Scalar 150 100 50 0 -50 Phase (degrees) 0.7 0.9 1.1 1.3 1.5 0.7 0.9 1.1 1.3 1.5 MKp (GeV) MKp (GeV) Kp Scattering LASS Data from: K-pK-p+n and K-pK0p-p NPB 296, 493 (1988) • Most information on K-p+ scattering comes from the • LASS experiment (SLAC, E135) • Disentangle I=1/2 and I=3/2 with K+p+[NPB133, 490 (1978)] Pennington ChPT compliant LASS parameterization Kh’ threshold No data below 825 MeV/c2 • use directly in production if re-scattering is small • require unitarity approach …

15. I=1/2 Scalar • LASS experiment used an effective range expansion to • parameterize the low energy behaviour: • d: scattering phase • q cot d = + a: scattering length • b: effective range • q: breakup momentum • Turn into K-matrix: K-1 = r cot d • K = +and add a pole term (fits also pp annihilation data) Both describe scattering on potential V(r) (a,b predicted by ChPT) • Take left hand cuts implicitly into account • Instead treat with meson exchange in t- (r ) and u-channel (K* ) [JPA:Gen.Phys 4,883 (1971), PRD 67, 034025 (2003)]  only K0*(1430) appears as s-pole • r (K*) exchange important for S-waves in general % kappa ? • b q2 • a 2 ___ ______ a m g0 2 + a b q2 m02 – m2 ___________ __________ _

16. I=1/2 Scalar FOCUS s D+ (K-p+) m+ nm W+ K- c Reconstructed events: ~27,000 D+ p+ DI=1/2 ? • Kp system dominated by K*(892) • Observe ~15% forward-backward • asymmetry in Kp rest frame • Hadronic phase of 45o corresponds to • I=1/2 Kp wave measured by LASS • required by Watson theorem in semileptonic • decay below inelastic threshold • S-wave is modeled as constant • (~7% of K*(892) Breit-Wigner at pole). • a phase of 90o would correspond to a • kappa resonance, but … • Study semileptonic D decays • down to threshold ! [PLB 621, 72 (2005)] [PLB 535, 43 (2002)]

17. I=1/2 Scalar E791 Fit with Breit-Wigner (isobar model): D+K-p+p+ K- p+ #15090 p+ A ~138 % c2/d.o.f. = 2.7 K*(892) K*(1430) C ~89 % c2/d.o.f. = 0.73 Mk = (797  19  42) MeV/c2 Gk = (410  43  85) MeV/c2 p+ W+ K- D+ p+  W+ unitarity [PRL 89, 121801 (2002)]

18. I=1/2 Scalar E791 Fit with Breit-Wigner + energy-independent fit to Kp S-wave (P(K*(892), K*(1680)) and D-waves (K*2(1430))act as interferometer) Model P- and D-wave (Beit-Wigner), S-wave A = ak eifk bin-by-bin (40) Phase S wave 0.75 1.5 M(Kp) / GeV/c2 Compares well with BW Isobar fit

19. I=1/2 Scalar E791 -75o Kh’ threshold A(s) eif(s) = F1/2(s) + F3/2(s) , s = mKp2 FI(s) = QI(s) eibI T11I(s) s – s0I [Edera, Pennington: hep-ph/0506117] … but differs from LASS elastic scattering • Quasi-two body Kp interaction • (isobar model ) broken ? • Watson theorem does not apply ? • Isospin composition • I=1/2 % I=3/2 in D decay • same as in Kp Kp ? if not if not |FI | Q-vector approach with Watson: • T11 from LASS ( same poles ?) • Constraint: Q smooth functions •  Adler zero s0I removed big !

20. I=0 Scalar D+p-p+p+ f0(980) r(770) f2(1270) Focus/E791 • E791: BW fit + s(500) • ms = (478 24  17) MeV • Gs = (324  42  21) MeV • FOCUS: use K-matrix A&S • (no s pole) m(pp) GeV ~ 1680 events E791 Extract S-wave phase d(s) from left-right asymmetry in f2(1270) F = a sind(s) ei(d(s)+g) Choose phase from 4 solutions  E791 fit (s(500)) d (o) [PLB 633, 167 (2006)] 0.1 0.8 m132 (GeV2)

21. I=0 Scalar I=0 pp S-wave parameterization (several on market) Au, Morgan, Pennington, Phys. Rev. D35, 1633 (1987) Anisovich, Sarantsev, Eur. Phys. A16, 229 (2003) 5 pole, 5 resonance 4 pole, 2resonance f0(1500) f0(980) _ • … from fits to data from scattering, pp annihilation, … • f0(980) : (988 – i 23) MeV (1024 – i 43) MeV • describesfg (p0p0) • no s(500) pole, but feature included • also with t (u) channel r (f2,..) exchange [Li,Zou,Li:PRD 63,074003(2001)] (also I=2 phase shift) • Coupled channel for pp-annihilation into 3 neutral PS, 3x3 K-matrix finds pole at low mass _

22. I=0 Scalar p c p s _ f0(980) s p DSp+p-p+ FOCUS FOCUS(#1475) E791 (#848) S-wave 87% f0+f0(1370)+NR 90% K matrix,P vector*phase ~0,p; G(f0) = 44 MeV f2(1270) 10% 20% r(1450) 6% 6% r(770) 6% r(1450) f2(1270) * not sensitive to Adler zero pppp FOCUS DS _ ss flavor tag J/yf pp

23. Charmless 3-body B Decays B0→K+K-K0 Dalitz Plot analysis D0→K+K-K0 • B→odd # of K : penguin-dominated decays • large phase-space, limited number of events • Dalitz plot analyses at feasibility limit

24. Charmless B Decay Reconstruction Main background from continuum events: Some standard discrimination variables: Event shape Energy-substituted mass Energy difference * = e+e-CM frame  Likelihood fit

25. X(1500) • Is bump at 1.5GeV really f0(1500)? • - PDG: BF(f0(1500)→pp )/BF( f0(1500)→KK ) ≈ 4 f0(980) K+p+p- K+K+K- • hard to assign a • small excess of • events in Kpp • to f0(1500) • events assigned • to f0(1370), • f2(1270) • f0(1500) • interferes with S-wave background constructively for KKK, • destructively for Kpp ? • [Minkowski,Ochs,EPJC 39,71(2005)] Belle [hep-ex/0509001] Belle [PRD71] r(770) p+p-KS K+K-KS BABAR [hep-ex/0507094] [hep-ex/0507094]

26. Initial State Radiation – ISR BaBar gISR e+ hadrons g* e- hadrons e+ (3 GeV) e- (9 GeV) gISR The radiative process effectively varies the CM energy of the e+e- collider  access to processes at energies below Y(4S) If the ISR photon is detected in BaBar the hadrons are found in opposite direction • Precision test of Standard Model (hadronic vacuum polarization)  Low mass particle spectroscopy

27. ISR BaBar • The hard photon must be detected and well measured: • Eg > 3 GeV ( s < 4.68 GeV ) • only directional information used in kinematic fit • Acceptance ~ 10 – 15 % • polar angle range 30o – 150o • BaBar runs an open trigger (lot of storage), high luminosity • e.g. visible cross section: e s(e+e- m+ m-g ) ~ 1.2 pb _ • pp PRD 73, 012005 (2006)‏ •  PRD 70, 072004 (2004)‏ • , K+K-, PRD 71, 052001 (2005)‏ • K+K- K+K-, 2K+2K- PRD 76, 012008 (2007) • K+K- PRD 73, 052003 (2006)‏ Most Recent results: • K+KKSKK+K BaBar Preliminary • arXiv:0709.1988 (submitted to PRD)  •  BaBar Preliminary •  arXiv:0708.2461 (submitted to PRD)

28.  • e+e-  K+K-p0 / KKh / KsKp(g) BaBar 232fb-1 KSK+p- ECM < m(J/y) BABAR 4.6 Disentangle I=0 (f-like), I=1 (r-like) components in Dalitz plot Split at ECM = 2GeV into K*(892)K and K*2(1430)K dominated region From interference find I=0 and I=1 K*K Fit to K*(892)K, K+K-p0/h (f, no-f (symmetric DP)), fp0, and fh …

29. e+e-  fp0 / fh BaBar Mass fits simultaneously to s(e+e-  K*K) f’(1680) M= 1710 MeV G = 325 MeV fh ? fp0 BABAR r `` BABAR r``` f’’M= 2125 MeV G = 60 MeV 3.3s 2.5s +K+K-p+p-p0 IG=1+ IG=0- OZI suppressed r’’’: consistent with dip in multi-pion data! r’’: m=1570 G=145 == C(1480) ? or r(1700) ?

30. Evidence for X(2175) 232fb-1 BABAR BABAR (+10% fpp) PS model Very rich substructure K*(892), K1(1270), K2*0(1430), K1(1400) Select f0(980) + f(1020) from invariant mass spectra ? Phys.Rev.D 76 012008 2007

31. Study of Charmonia at B-Factories • Colour-suppressed (Y(4S)) bc decay • Predominantly from B-meson decays • e+e- annihilation/Initial State Radiation (ISR) • e+e- collision below nominal c.m. energy • JPC = 1-- • Double charmonium production • Typically one J/y or y, plus second ccbar state • Two-photon production • Access to C = +1 states

32. ISR Study of Charmonia BaBar discovers peaks in Y(4260)J/y p+p-and Y(4320)y(2S)p+p- 298fb-1 211fb-1 PRL 95, 142001 (2005) PRL 98, 212001 (2007) 673fb-1 • States confirmed by Belle, in addition to claims for two others • Too many JPC = 1— No evidence for YD(*)D(*) from BaBar or Belle (no fpp)  difficult to accommodate as cc arXiv:0707:3699 -

33. Study of Charmonia < 2004

34. The DSJ States - strange charmed mesons DsJ*(2860) * X(2690) DsJ(2700) Ds1(2460) Ds0*(2317) S wave P wave D wave • Ds*, Ds1(2536)+,Ds2(2573)+: well known, but JP only inferred (not measured!) • Ds0*(2317)+, Apr. 2003: unexpected observation of a narrow resonance in BaBar • Ds1(2460)+, May 2003: CLEO, BaBar observed a new narrow resonance • DsJ*(2860)+, Jul. 2006: new state discovered by BaBar (2112) • X(2690)+, Jul. 2006: broad enhancement seen in BaBar • DsJ(2700)+, Jul. 2006: new state discovered by Belle (== X(2690) ? )

35. Summary B-Factories are a rich source of mesons in many production modes

36. Ds0*(2317) and Ds1(2460) Update • Discovered 4 years ago in e+e-  cc events; subsequentlyobserved inB decays • Ds0*(2317) and Ds1(2460) very well established and known experimentally • Masses andtight upper limits on widths • JP: 0+ for Ds0*(2317) and 1+ for Ds1(2460) • decay modes and branching fractions • Interpretation of these new states still unclear! • One possibility: identify these 2 states as the 0+ and 1+ cs states • However strong difficulties within the potential model • Other possibilities • 4 quark states? DK molecule? D atom? Chiral symmetry? Belle: Phys. Rev. Lett. 91 (2003) 262001 BaBar: Phys. Rev. D74 (2006) 032007 Belle: Belle-Conf-0461 (2006) BaBar: Phys. Rev. D74 (2006) 031103

37. DsJ*(2860): Another New State 240 fb-1 • Reconstruct from cc continuum: e+e-  D0(K-+,K-+0)K+X ande+e-  D+(K-++)K0sX • New state at 2860 MeV/c2! (fit with a Breit-Wigner) • Bump at 2690 MeV/c2? (better fit with a Gaussian than a Breit-Wigner) D+(K-+ +)K0s D0(K-+)K+ D0(K-+ 0)K+ p* > 3.5 GeV/c2

38. DsJ*(2860) … and X(2690) • Combining the 3 modes • M = (2856.6 ± 1.5 ± 5.0) MeV/c2 •  = (47 ± 7 ± 10) MeV • JP = 0+, 1-, 2+, … • Final state is DK, i.e. two pseudoscalars • Interpretation of DsJ*(2860)? • Radial excitation of Ds0*(2317)? hep-ph/0606110 • cs with JP = 3-? hep-ph/0607245 • cs with JP = 0+? hep-ph/0608139 • Another structure at 2690 MeV/c2? • M = (2688 ± 4 ± 3) MeV/c2 •  = (112 ± 7 ± 36) MeV • Needs confirmation by other experiments or in other channels… Sum of 3 modes X(2690) bkg subtracted DsJ*(2860) m(DK) GeV/c2 BaBar: Phys. Rev. Lett. 97 (2006) 222001

39. DsJ (2700) - a Different State ? 347 fb-1 • New resonance decaying to D0K+ discovered by Belle in B+ D0(D0K+) : DsJ(2700) • Same resonance as seen by BaBar in continuum, X(2690)? • Mass and width consistent, same decay mode • Study of B  D(*)D(*)K decays in BaBar • Construct 8 DK + 8 D*K invariant masses • Enhancement observed around 2700 MeV/c2in DK and D*K • Full Dalitz plot analysis ongoing Belle: hep-ex/0707.3491 Summing all 8 DK modes Summing all 8 D*K modes Ds1(2536) Phase space Background (generic MC) Background (generic MC)