1. 1 Scalar Mesons in D and B Decays Scalar Mesons in D and B Decays Stefan Spanier University of Tennessee

2. 2 Scalars are special  understand non-perturbative QCD (meson spectrum)  understanding of QCD vacuum (quantum numbers 3 P 0 )

3. 3 Scalars are special f0f0 f0f0 K K _ u,d _ s s _ easy transitions:  As states are mixtures: a  nn  + b  ss  + c  qqqq  + d  glue  +  Decay obscures quark content need to study production and decay ____ Experimentally - broad states - often covered by tensors - featureless decay angle distributions too many / heavily shifted !

4. 4 Why Scalars in D, D S, and B Decays Initial state is single, isolated particle with well defined J B,D =0, J D s =1 Operators for decay have simple lorentz- and flavor quantum numbers Short range QCD properties are known (better) Weak decay defines initial quark structure; and rules (e.g.  I=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. B 0  f 0 K 0 - CP composition of 3-body modes, e.g. B 0  K 0 K + K - - hadronic phase for CP angle  in B  DK from D-Dalitz plot

5. 5 c.c. Experiments E791  - (500 GeV) [Pt, C]  charm  Focus  Brems [Be]  charm  BaBar 2008 Belle > 2008 CLEO-c e + e -   (3S)  DD 281pb -1 e + e -  qq @ Y(4S) _  B-factories are also D-factories: In each expect (2006) > 1 Million of – E791 - 35,400 1 – FOCUS - 120,000 2 – CLEO-c - D 0  K -  + : 51,200 3 BaBar 1. E791 Collaboration, Phys.Rev.Lett. 83 (1999) 32. 2. Focus Collaboration, Phys.Lett. B485 (2000) 62. 3. CLEO-c: hep-ex/0512063. 91fb -1 > 450 Million BB pairs take more than 10BB / sec _ _ D 0  K -  + _ +

6. 6 Formalism for X  3 body (Dalitz plot analysis) a b c d ll R L l Spectator ? d R c  assuming dominance by 2-body interaction (isobar model)  scalar resonances strongly overlap / decay channels open in vicinity Dynamic amplitude not just a simple Breit Wigner - Analytic - Unitary (2-body subsystem) - Lorentz-invariant  K-matrix formalism widely used: 2-body scattering production / decay R = (1-iK  ) -1   2-body PS 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 m   0 for p  =0: T = 0  near threshold; also/where for F ? Resonance: = pole in unphysical sheet of complex energy plane

7. 7 Content I = 1 Scalars I = 1/2 I = 0 Charmless 3-body B Decays

8. 8 D* +  D 0  + slow  K 0  +  - #92935  K 0 K + K - #13536 K 0  K 0 S   +  - _ _ _ D-flavor tag  D = 6.1 MeV/c 2  D = 3.4 MeV/c 2 I=1 Scalar a 0 (980) in D decays In 91.5 fb-1 @ Y(4S) BaBar finds: Ratio of branching fractions: BaBar 97.3% purity

9. 9 I=1 Scalar a 0 (980) in D decays  (1020) f 0 (980)  (770) K*(892) a 0 (980) f 0 (980) Efficiency: Data: BaBar D0K0S+ -D0K0S+ - D0K0SK+K-D0K0SK+K- a 0 (980) BaBar

10. 10 I=1 Scalar a 0 (980)  0  fixed by total BF  couplings g i (also tune lineshape) e.g. F 1 : X   F 2 : X   KK) Production amplitude 2    Flatte formula: Scattering amplitude 5 parameters

11. 11 I=1 Scalar a 0 (980) in D decays weight/ 5 MeV/c 2 Extract S-wave and describe Flatte’ formula with Crystal Barrel parameters [Abele et al., PRD 57, 3860 (1998)] Moment analysis  only S and P waves  Fix m 0 and coupling g , but float g KK  Best description of S-wave from moments and floated in PWA inconsistent with CBAR: BaBar: g KK = 473 + 29 + 40 MeV 1/2 CBAR: g KK = 329 + 27 MeV 1/2  need coupled channel analysis with D 0  K 0  PWA needs ~3% contribution from higher mass resonance tail (outside PS)  assume f 0 (1400) ; uniform distribution worse  what about a 0 (1450) ? _ BaBar DP projection D0K0SK+K-D0K0SK+K-

12. 12 I=1 Scalar a 0 (980) in D decays BaBar I=0,1 I=1 KK phase space corrected mass distribution normalized to the same PS area I=1 S-wave dominance D0K0S+ -D0K0S+ - [BaBar: hep-ex/0408088] [Belle : hep-ex/0411049] ~ 5.5 % f 0 (980) contribution  for f 0 (980) couplings need fix to better line-shape parameters BaBar

13. 13 I=1 Scalar a 0 (980) in B decays In 9 fb-1 @ Y(4S) CLEO finds: [PRL 93 (2004) 111801] Main contribution from a 0 K 0 S ; also a 2 (1320)K 0 S, K*(892) , K 0 *(1430)  B(D 0  K 0  0  ) = (1.05 ± 0.16 ± 0.14 ± 0.10) % fraction(a 0 (980)) = 1.19 ± 0.09 ± 0.20 ± 0.16 # (155 + 22) events _ CLEO

14. 14 I=1 Scalar a 0 (980) in B decays K+K+ For scalar mesons with {u,d} quark content theory expects suppression - all CKM suppressed (least a 0 K penguin  V ts ) - G-parity (W does not couple to scalar) [Laplace,Shelkov, EPJ C 22, 431 (2001)] - effective Hamiltonian  decay amplitude  1 - G(m i,m b,m q i ) (G  1) ( + for 0 - ) m i decay particle with quark content q i [Chernyak, PLB 509, 273 (2001)] BaBar determines in 81.9 fb-1 B(B  a 0 X, a 0   90% C.L. [10 -6 ] a 0 -  + < 5.1 a 0 - K + < 2.1 a 0 - K 0 < 3.9 a 0 0  + < 5.8 a 0 0 K + < 2.5 a 0 0 K 0 < 7.8

15. 15 I=1 Scalar a 0 (980) ! a 0 (1450) ?

16. 16 I=1/2 Scalar Data from: K - p  K -  + n and K - p  K 0  - p NPB 296, 493 (1988) No data below 825 MeV/c 2 K  Scattering LASS 0.7 0.9 1.1 1.3 1.5 M K  (GeV) 150 100 50 0 -50 Phase (degrees) 0.7 0.9 1.1 1.3 1.5 M K  (GeV) Most information on K -  + scattering comes from the LASS experiment (SLAC, E135) K  ’ threshold use directly in production if re-scattering is small require unitarity approach … LASS parameterization Disentangle I=1/2 and I=3/2 with K +  + [NPB133, 490 (1978)] Pennington ChPT compliant

17. 17 I=1/2 Scalar LASS experiment used an effective range expansion to parameterize the low energy behaviour:  : scattering phase q cot  = + a: scattering length b: effective range q: breakup momentum Turn into K-matrix : K -1 =  cot   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- (  ) and u-channel (K* ) [JPA:Gen.Phys 4,883 (1971), PRD 67, 034025 (2003)]  only K 0 *(1430) appears as s-pole   (K*) exchange important for S-waves in general 1 b q 2 a 2 ___ ______ a m g 0 2 + a b q 2 m 0 2 – m 2 ___________ __________ _

18. 18 I=1/2 Scalar D +  (K -  + )  +   K  system dominated by K*(892) Observe ~15% forward-backward asymmetry in K  rest frame Hadronic phase of 45 o corresponds to I=1/2 K  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 90 o would correspond to a kappa resonance, but …  Study semileptonic D decays  down to threshold ! FOCUS Reconstructed events: ~27,000 D+D+ K-K- ++ c s W+W+ [PLB 621, 72 (2005)] [PLB 535, 43 (2002)]  I=1/2 ?

19. 19 I=1/2 Scalar BaBar B  J/  K* in 81.9 fb-1 study K  mass from 0.8 – 1.5 GeV/c2 - weak process b  ccs is a pure  I=0 interaction  isospin(K  ) = ½ - P  VV 3 P-wave amplitudes (A 0,A ||,A  ) if no J/  – K* rescattering (Watson theorem) all P-waves are relatively real;  || -   -  > 7 standard deviations ! - according to LASS finding consider K  S wave and extract waves with moment analysis - use change of S-P interference near K*(892) to resolve phase ambiguity  S –  0   0 –  S - one solution does behave like  S (LASS) -  P (LASS) +  BaBar  S –  0  LASS _

20. 20 I=1/2 Scalar E791 K*(892) K*(1430) D+  K-++D+  K-++ #15090 Fit with Breit-Wigner (isobar model): ~138 % A ~89 % C  2 /d.o.f. = 0.73  2 /d.o.f. = 2.7 M  = (797  19  42) MeV/c 2    eV  c  D+D+ K-K- ++ W+W+ ++ [PRL 89, 121801 (2002)] unitarity ++ ++ K-K- W+W+ 

21. 21 I=1/2 Scalar Fit with Breit-Wigner + energy-independent fit to K  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 = a k e i  k bin-by-bin (40) E791 Phase Amplitude Compares well with BW Isobar fit S wave P wave D wave Mass projection  2 /NDF = 272/277 (48%)

22. 22 I=1/2 Scalar E791 Quasi-two body K  interaction (isobar model ) broken ? Watson theorem does not apply ? Isospin composition I=1/2 % I=3/2 in D decay same as in K   K  ? if not K  ’ threshold -75 o … but differs from LASS elastic scattering |F I | A(s) e i  s  = F 1/2 (s) + F 3/2 (s), s = m K  2 F I (s) = Q I (s) e i  I T 11 I (s) s – s 0 I Q-vector approach with Watson:  T 11 from LASS (  same poles ?)  Constraint: Q smooth functions  Adler zero s 0 I removed [Edera, Pennington: hep-ph/0506117] big !

23. 23 I=1/2 Scalar  (800) ? K*(1430) !

24. 24 f 0 (980)  (770) f 2 (1270) 0.10.8 m 13 2 (GeV 2 ) Extract S-wave phase  (s) from left-right asymmetry in f 2 (1270) F = a sin  (s) e i(  (s)+  ) Choose phase from 4 solutions   ( o ) E791 fit (  (500)) E791: BW fit +  (500) m  = (478  24  17) MeV   = (324  42  21) MeV FOCUS: use K-matrix A&S (no  pole) [PLB 633, 167 (2006)] m(  ) GeV I=0 Scalar Focus/E791 D+  -++D+  -++ E791 ~ 1680 events

25. 25 I=0 Scalar Au, Morgan, Pennington, Phys. Rev. D35, 1633 (1987) Anisovich, Sarantsev, Eur. Phys. A16, 229 (2003 ) 4 pole, 2  resonance 5 pole, 5 resonance I=0  S-wave parameterization (several on market) f 0 (980) f 0 (1500) … from fits to data from scattering, pp annihilation, … f 0 (980) : (988 – i 23) MeV (1024 – i 43) MeV describes    (  0  0 ) no  (500) pole, but feature included also with t (u) channel  (f 2,..) exchange [Li,Zou,Li:PRD 63,074003(2001)] (also I=2 phase shift) Coupled channel for pp-annihilation into 2 neutral PS, 3x3 K-matrix finds pole at low mass _ _

26. 26 I=0 Scalar FOCUS f 0 (980)  (1450) DS + - +DS + - + FOCUS(#1475) E791 (#848) S-wave 87% f 0 +f 0 (1370)+NR 90% K matrix,P vector* phase ~0,  f   MeV f 2 (1270) 10% 20%  (1450) 6% 6%  (770) 6% J/    FOCUS * not sensitive to Adler zero ss flavor tag _    c s _ s DSDS    f 2 (1270)

27. 27 Charmless 3-body B Decays Mode Events (1/fb -1 ) D 0 → K + K - K 0 ~140 B + →     K + Belle BABAR ~11 B + → K + K - K + Belle ~8 B0→ K+B0→ K+ BABAR ~5 B 0 →     K 0 Belle 2005 ~3 B 0 → K + K - K 0 BABAR 2005 ~2.5 B+→KSKS K+B+→KSKS K+ ~0.9 B0→ K0SB0→ K0S ~0.5 B0→KSKS KSB0→KSKS KS ~0.4 - B→odd # of K : penguin-dominated decays - large phase-space, limited number of events - Dalitz plot analyses at feasibility limit D0→K+K-K0D0→K+K-K0 B0→K+K-K0B0→K+K-K0 Dalitz Plot analysis

28. 28 Charmless B Decay Reconstruction Energy-substituted mass Energy difference Event shape Main background from continuum events: Some standard discrimination variables: * = e + e - CM frame  Likelihood fit

29. 29 B 0  K + K - K 0 S Dalitz Plot Results D +,D s +  reflections X(1500)  non-res [BABAR,hep-ex/0507094]  c0 ModeFraction (%)  (1020)K S 15.4  3.4  0.6 X(1500)K S 5.2  2.2  0.9 (<8.3) 38.9  7.3  0.9 Non-resonant70.7  3.8  1.7  c0 K S 3.1  1.6  0.8 (<5.5) f 0 (980)K S 5.7  3.2  1.0 (<9.7) Multiple solutions P-wave content consistent with isospin analysis Belle [ hep-ex/0208030 ] and moment analysis BaBar [ PhysRevD71:091102(2005) ]  (1020) no a 0 !

30. 30 B +  K + K - K + Dalitz Plot Results X(1500) non-res  c0 ModeFraction (%)  (1020)K S 15.0  1.3 X(1500)K S 8.2  1.9 63  7 Non-resonant70  5 Also penguin dominated ~ 4 times more events per fb -1 : 1089 signal events, 140 fb -1 [Belle,PRD71:092003(2005)] Multiple solutions  (1020)

31. 31 Charmless 3-body B Decays Parameterization of non-resonant S-wave background? - large excess of events at lower (higher) masses (~70% of total yield) - flat (phase-space) model found inadequate by all analyses - try a set of ad hoc models: Belle [PRD71,092003] BABAR [hep-ex/0507094] - little difference in fit quality with current statistics flat Contact terms KSKS K+K+ K-K- B0B0 KSKS K+K+ K-K- B0B0 Resonance tails [Cheng,Yang,Phys.Rev.D66:054015(2002)] What is it ? continuum

32. 32 X(1500) Is bump at 1.5GeV really f 0 (1500)? - PDG: BF( f 0 (1500)→  )/BF( f 0 (1500)→KK ) ≈ 4 K+K-KSK+K-KS K+K-KSK+K-KS Belle [PRD71] [hep-ex/0507094] K+K+K-K+K+K- K+K+K-K+K+K- - hard to assign a small excess of events in K  to f 0 (1500) -events assigned to f 0 (1370), f 2 (1270) - f 0 (1500) interferes with S- wave background constructively for KKK, destructively for K  ? [Minkowski,Ochs,EPJC 39,71(2005)] B A B AR KSKS KSKS K+K+ K+K+ Belle [hep-ex/0509001] [hep-ex/0507094] f 0 (980)  (770)

33. 33 I=0 Scalars  (500) ? f 0 (980) ! f 0 (1200-1500) ? f 0 (1500) !

34. 34 Summary / Outlook Since 40 years the scalar mesons are a puzzle ! Charm production experiments, but particularly the B-factories will provide input. Missing states are found, existing ones can be studied in greater detail. BaBar and Belle are continuing sources, SuperB at Frascati may be a future source for scalar meson spectroscopy in D, D S, and B decays.

35. 35  HQET m c >>  QCD  m c <<  QCD D0*D0* D1D1 D1’D1’ decays in HQET ‘hydrogen’ ‘positronium’ narrow Charmed Scalars

36. 36 2+ 0+ 2+/0+ M = ( 2308 ± 17 ± 15 ± 28 ) MeV/c 2  = ( 276 ± 21 ± 18 ± 60 ) MeV/c 2 B - D +  -  - K -  +  + D0*0D0*0 Regions in pion helicity angle Belle virtual Only pion S wave No resonance in  system Charmed Scalars

37. 37 I=0 Scalar K-matrix for coupled channel analysis - Adler zero (taken out for production – how P*Adler) - constant c=0.8 in K-matrix -> also propagator; allows 180o phase

38. 38 I=1/2 Scalar

39. 39 B 0 → KKK 0 : Moments Analysis [BABAR,PhysRevD71:091102(2005)] BABAR’s – analysis of angular moments: Compute wave strengths using moments of Legendre polynomials: Average moments computed using sPlot technique [Pivk, Le Diberder, physics/0402083] Describe decay in terms of S and P-waves decaying into K + K - Outside of  K S region Better errors with ½ statistics w.r.t. isospin analysis Not relying on any assumptions

40. 40 B 0 → KKK 0 : Isospin Analysis Belle’s – isospin analysis [hep-ex/0208030] - assume dominance of gluonic penguins - use SU(2) flav to relate rates for (K + K - )K 0 and (K 0  K 0 )K + K+K+ KK B0B0 KSKS L L’=L KSKS KSKS B0B0 K+K+ L Only L=even allowed All L allowed - fraction of L=even: Outside of  K S region Belle (386MBB)