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Unveiling New Insights into Scalar Mesons in D and B Decays

Discover the significance of scalar mesons in understanding non-perturbative QCD, with detailed examination of quark content through production and decay processes. Explore their role in the D, DS, and B decays for insights into CP violation and more. Cutting-edge experiments and formalisms play a crucial role in unraveling the mysteries of these intriguing particles.

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Unveiling New Insights into Scalar Mesons in D and B Decays

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

  2. Scalars are special  understand non-perturbative QCD (meson spectrum)  understanding of QCD vacuum (quantum numbers 3P0)

  3. 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 _ _ _ _ _ K f0 f0 K u,d s _ _ _ u,d s • Experimentally • broad states • often covered by tensors • featureless decay angle distributions • too many / heavily shifted ! easy transitions:

  4. Why Scalars in D, DS, and B Decays • Initial state is single, isolated particle with well defined JB,D=0, JDs=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. 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

  5. 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 (2006) > 1 Million of • E791 - 35,400 1 • FOCUS - 120,000 2 • CLEO-c - D0K-p+ : 51,200 3 D0 K-+ + BaBar 91fb-1 _ > 450 Million BB pairs take 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.

  6. 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

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

  8. I=1 Scalar a0(980) in D decays D-flavor tag In 91.5 fb-1 @ Y(4S) BaBar finds: D*+ D0p+slow  K0p+p- #92935  K0 K+K- #13536 K0  K0S  p+p- _ BaBar _ sD = 6.1 MeV/c2 _ Ratio of branching fractions: BaBar sD = 3.4 MeV/c2 97.3% purity

  9. I=1 Scalar a0(980) in D decays BaBar f(1020) Data: K*(892) D0K0Sp+p- D0K0SK+K- BaBar BaBar f0(980) r(770) a0(980) a0(980) f0(980) Efficiency:

  10. I=1 Scalar a0(980) 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

  11. 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)] • 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) ?

  12. I=1 Scalar a0(980) in D decays BaBar I=0,1 I=1 BaBar KK phase space corrected mass distribution normalized to the same PS area I=1 S-wave dominance D0K0Sp+p- ~ 5.5 % f0(980) contribution [BaBar: hep-ex/0408088] [Belle : hep-ex/0411049] • for f0(980) couplings need fix to better line-shape parameters

  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) % fraction(a0(980)) = 1.19 ± 0.09 ± 0.20 ± 0.16 _

  14. I=1 Scalar a0(980) in B decays BaBar determines in 81.9 fb-1 B(B a0 X, a0p h) 90% C.L. [10-6] a0-p+ < 5.1 a0- K+ < 2.1 a0- K0 < 3.9 a00p+ < 5.8 a00 K+ < 2.5 a00 K0 < 7.8 K+ • For scalar mesons with {u,d} quark content theory expects suppression • - all CKM suppressed (least a0K penguin  Vts) • G-parity (W does not couple to scalar) [Laplace,Shelkov, EPJ C 22, 431 (2001)] • effective Hamiltonian  decay amplitude  1 - G(mi,mb,mqi) (G1)( + for 0- ) • mi decay particle with quark content qi[Chernyak, PLB 509, 273 (2001)]

  15. I=1 Scalar a0(980) ! a0(1450) ?

  16. 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 …

  17. 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 • b q2 • a 2 ___ ______ a m g0 2 + a b q2 m02 – m2 ___________ __________ _

  18. 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)]

  19. I=1/2 Scalar BaBar BaBar • B  J/y K* in 81.9 fb-1 • study Kp mass from 0.8 – 1.5 GeV/c2 • weak process b ccs is a pure DI=0 interaction  isospin(Kp) = ½ • PVV 3 P-wave amplitudes (A0,A||,A) • if no J/y – K* rescattering (Watson theorem) • all P-waves are relatively real; • d||- d - p > 7 standard deviations ! • according to LASS finding • consider Kp S wave and extract • waves with moment analysis • use change of S-P interference • near K*(892) to resolve phase • ambiguity • dS – d0d0 – dS • one solution does behave like • dS(LASS) - dP (LASS) + p _ (dS – d0 )/p LASS

  20. 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)]

  21. 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) Compares well with BW Isobar fit Mass projection Amplitude Phase 2/NDF = 272/277 (48%) S wave P wave D wave

  22. 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 !

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

  24. 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) 0.1 0.8 m132 (GeV2) [PLB 633, 167 (2006)]

  25. 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 2 neutral PS, 3x3 K-matrix • finds pole at low mass _

  26. 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

  27. 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

  28. 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

  29. B0K+K-K0S Dalitz Plot Results f reflections D+,Ds+ f f(1020) [BABAR,hep-ex/0507094] X(1500) cc0 non-res f(1020) Multiple solutions no a0! • P-wave content consistent with isospin analysis Belle [hep-ex/0208030] • and moment analysis BaBar [PhysRevD71:091102(2005)]

  30. B+K+K-K+ Dalitz Plot Results [Belle,PRD71:092003(2005)] f(1020) X(1500) non-res f(1020) • Also penguin dominated • ~ 4 times more events per fb-1: • 1089 signal events, 140 fb-1 cc0 Multiple solutions

  31. Charmless 3-body B Decays Contact terms KS B0 K+ K- • 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: flat Belle [PRD71,092003] BABAR [hep-ex/0507094] continuum • - little difference in fit quality with current statistics What is it ? Resonance tails KS B0 K+ K- [Cheng,Yang,Phys.Rev.D66:054015(2002)]

  32. 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]

  33. I=0 Scalars s(500) ? f0(980) ! f0(1200-1500) ? f0(1500) !

  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, DS, and B decays.

  35. Charmed Scalars  HQET mc >> LQCD ‘hydrogen’ D1 D0* decays in HQET D1’  mc << LQCD ‘positronium’ narrow

  36. Charmed Scalars B-D+p-p- K- p+p+ Only pion S wave No resonance in pp system Regions in pion helicity angle Belle 2+ virtual 0+ 2+/0+ M = ( 2308 ± 17 ± 15 ± 28 ) MeV/c2 G = ( 276 ± 21 ± 18 ± 60 ) MeV/c2 D0*0

  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. I=1/2 Scalar

  39. B0→KKK0: Moments Analysis [BABAR,PhysRevD71:091102(2005)] • BABAR’s – analysis of angular moments: Describe decay in terms of S and P-waves decaying into K+K- Compute wave strengths using moments of Legendre polynomials: Average moments computed using sPlot technique [Pivk, Le Diberder, physics/0402083] Outside of fKS region Better errors with ½ statistics w.r.t. isospin analysis Not relying on any assumptions

  40. B0→KKK0: Isospin Analysis K+ L’=L B0 KS L K- KS L’=L B0 K+ L KS • Belle’s – isospin analysis [hep-ex/0208030] • assume dominance of gluonic penguins • use SU(2)flav to relate rates for (K+ K-)K0 and (K0K0)K+ Only L=even allowed All L allowed • fraction of L=even: Outside of fKS region Belle (386MBB)

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