D sJ mesons Jolanta Brodzicka (KEK) for Belle QWG5, DESY October 2007

Outline Introduction to cs multipletsIntroduction to cs multiplets Observation of new D sJ (2700) → D 0 K + in B + → D 0 D 0 K +Observation of new D sJ (2700) → D 0 K + in B + → D 0 D 0 K + Observation of D s1 (2536) → D + π - K +Observation of D s1 (2536) → D + π - K + Partial Wave Analysis of D s1 (2536) → D* + K 0 sPartial Wave Analysis of D s1 (2536) → D* + K 0 s SummarySummary J. Brodzicka for QWG5

cs multiplets Theory:  HQS based potential model predictions: (Godfrey-Isgur ‘85) two doublets for orbitally excited L=1 cs states: two doublets for orbitally excited L=1 cs states: 0 +, 1 + (j q =1/2) and 1 +, 2 + (j q =3/2) 0 +, 1 + (j q =1/2) and 1 +, 2 + (j q =3/2) M(j q =1/2), M(j q =3/2) > M D +M K M(j q =1/2), M(j q =3/2) > M D +M K Γ(j q =1/2) >> Γ(j q =3/2) Γ(j q =1/2) >> Γ(j q =3/2) J. Brodzicka for QWG5 spin-orbittensor s-o spin-spin L = 2 ….. j q = s q + L, J = j q + s QExperiment: j q =1/2 doublet j q =1/2 doublet 0 + : D * s 0 (2317) → D s π : D s 1 (2460) → D * s π 0 j q =3/2 doublet j q =3/2 doublet 1 + : D s 1 (2536) → D * K (Argus ‘89) 2 + : D s J (2573) → DK (CLEO ‘94) their properties need to be measured higher orbital/radial excitations? higher orbital/radial excitations? very narrow, masses below D ( * ) K → don’t match the model predictions → how to accommodate them within current models? BaBar CLEO ‘03 Belle L = 0 j q = 1/ Ds* Ds* Ds Ds mix? JPJP D*K D K D* s0 (2317) D s1 (2460) D s1 (2536) D sJ (2573) j q = 3/2 j q = 1/2 L = 1

b → ccs tree process; cs → D 0 K + and cc → D 0 D 0 states can contributeb → ccs tree process; cs → D 0 K + and cc → D 0 D 0 states can contribute B + → D 0 D 0 K + signal identified using:B + → D 0 D 0 K + signal identified using: ΔE=E B -E beam, E beam =√s/2 : cms energy difference ΔE=E B -E beam, E beam =√s/2 : cms energy difference M bc = √E 2 beam -p 2 B : beam-constrained mass M bc = √E 2 beam -p 2 B : beam-constrained mass S=399±40 for 449M BB usedS=399±40 for 449M BB used BF(B + → D 0 D 0 K + )=(22.2± ) x 10 -4BF(B + → D 0 D 0 K + )=(22.2± ) x Dalitz plot and mass projections Dalitz plot and mass projections different from 3-body Ph. Space different from 3-body Ph. Space New D sJ meson in B + → D 0 D 0 K + points: events from 1.5σ ΔE-Mbc signal box ■ :background from sidebands points: events from 1.5σ ΔE-Mbc signal box ■ :background from sidebands ΔEΔEΔEΔE M bc J. Brodzicka for QWG5 hep-ex/ (submitted to PRL)  (4160)  (3770) new D sJ

2D ΔE-M bc fits in invariant mass bins → B signal extracted2D ΔE-M bc fits in invariant mass bins → B signal extracted Obtained background-free mass spectra used to estimate the resonance contributions:Obtained background-free mass spectra used to estimate the resonance contributions: fitted B signal yield M(D 0 K + ) for M(D 0 D 0 )>3.85 GeV fitted with: Breit-Wigner ψ(4160) reflection + Ph. Space (shapes from MC) + ψ(4160) reflection + Ph. Space (shapes from MC) + exponential function (to describe the threshold enhancement (? ) ) Decomposition of B + → D 0 D 0 K + Dalitz plot D sJ (2700) J. Brodzicka for QWG5 ψ(4160) in ½ helicity distr. ψ(3770) Non-coherent approach; possible interference effects included in syst. errors

D sJ (2700) → D 0 K + in B + → D 0 D 0 K + Helicity angle distribution of D sJ (2700):Helicity angle distribution of D sJ (2700): ( background free and efficiency corrected; ( background free and efficiency corrected; reflections from threshold and ψ(4160) subtracted) reflections from threshold and ψ(4160) subtracted) J=1 preferred; 1 → decay implies P=-1J=1 preferred; 1 → decay implies P=-1 Contributions to the observed mass spectraContributions to the observed mass spectra Most observed features well describedMost observed features well described ■ D sJ (2700) ■ ψ(3770) ■ ψ(4160) ■ 3body ■ threshold component (MC predicted shapes) (MC predicted shapes) fitted B signal yield J. Brodzicka for QWG5 J=0  2 /ndf=112/5 J=1  2 /ndf= 11/5 J=2  2 /ndf=146/5

D sJ (2700) interpretation D sJ (2700) → D 0 K state can be:D sJ (2700) → D 0 K state can be: radial excitation 2 3 S 1radial excitation 2 3 S 1 (predicted by potential models at M~2720GeV) (predicted by potential models at M~2720GeV) chiral doubler state 1 - to 1 + D s1 (2536) (predicted from chiral symmetry considerationschiral doubler state 1 - to 1 + D s1 (2536) (predicted from chiral symmetry considerations at M=2721±10 MeV) at M=2721±10 MeV) BaBaR observed structure at M(DK)~2.69GeV producedBaBaR observed structure at M(DK)~2.69GeV produced in e + e - continuum. Is that due to D sJ (2700)? in e + e - continuum. Is that due to D sJ (2700)? D sJ (2860) observed by BaBar not seen in our data.D sJ (2860) observed by BaBar not seen in our data. Its production in B decays suppressed by its high spin? Its production in B decays suppressed by its high spin? BaBar Coll. PRL 97, (2006) BaBar Coll. PRL 97, (2006) J. Brodzicka for QWG5 Godfrey, Isgur PRD 32, 189 (1985) Close, Swanson PLB 647, 159 (2007) Nowak, Rho, Zahed Acta Phys. Polon. B 35, 2377 (2004)

Observation of D s1 (2536) → D + π - K + J. Brodzicka for QWG5 hep-ex/ (submitted to PRD) angular analysis performed for D s1 (2536) → D* + K s sample Known decay modes of D s1 (2536): D* + K s, D* 0 K +, D s π + π - (evidence)Known decay modes of D s1 (2536): D* + K s, D* 0 K +, D s π + π - (evidence) Study of e + e - → D s1 (2536)X using 462 fb -1,Study of e + e - → D s1 (2536)X using 462 fb -1, D s1 (2536) → D + π - K + and D s1 (2536) → D* + K s (normalization mode) D s1 (2536) → D + π - K + and D s1 (2536) → D* + K s (normalization mode) x P =p Ds1 / p max >0.8 in e + e - cms p max =√E 2 beam -M 2 Ds1x P =p Ds1 / p max >0.8 in e + e - cms p max =√E 2 beam -M 2 Ds1 Two-body mass spectra consistent with Phase SpaceTwo-body mass spectra consistent with Phase Space

Mixing of jq=1/2 and jq=3/2 states HQET prediction for P-wave cs states:HQET prediction for P-wave cs states: 1 + (j q =3/2) → D*K pure D-wave decay: D s1 (2536) → D*K 1 + (j q =3/2) → D*K pure D-wave decay: D s1 (2536) → D*K 1 + (j q =1/2) → D*K pure S-wave decay: but D s1 (2460) → D*K forbidden 1 + (j q =1/2) → D*K pure S-wave decay: but D s1 (2460) → D*K forbidden If HQET not exact: mixing of S-D waves possibleIf HQET not exact: mixing of S-D waves possible (by LS interaction, common decay channels, …) (by LS interaction, common decay channels, …) Exp. knowledge on the mixing:Exp. knowledge on the mixing: from BF’s ratio of D s1 (2460) radiative decays: D* s γ/D s γ=0.31 ± 0.14 from BF’s ratio of D s1 (2460) radiative decays: D* s γ/D s γ=0.31 ± 0.14 switch from |j q > to | 2S+1 L J > basis (from combined B decays switch from |j q > to | 2S+1 L J > basis (from combined B decays and e + e - study by Belle) and e + e - study by Belle) tan 2 (θ+θ 0 )=0.8 ± 0.4 where tan 2 θ 0 =2 (no-mixing case) tan 2 (θ+θ 0 )=0.8 ± 0.4 where tan 2 θ 0 =2 (no-mixing case) J. Brodzicka for QWG5 θθ0θ0 Measurement of mixing angle: test of HQS, way to understand jq=1/2 cs doublet unusual properties of jq=1/2 cs doublet

The decay described by α, β, γ angelsThe decay described by α, β, γ angels Prediction for 1 + statePrediction for 1 + state in the helicity formalism: in the helicity formalism: ρ: helicity density matrix ρ 00 : longitudinal polarization ρ 11 = ρ -1-1 =(1- ρ 00 )/2ρ: helicity density matrix ρ 00 : longitudinal polarization ρ 11 = ρ -1-1 =(1- ρ 00 )/2 z=√R Λ exp(iξ)=A 10 /A 00 A 10, A 00 : ampl. of D*‘s helicity= ±1, 0z=√R Λ exp(iξ)=A 10 /A 00 A 10, A 00 : ampl. of D*‘s helicity= ±1, 0 A 10 =(S+D/√2)/√3 A 00 =(S-√2D)/√3)A 10 =(S+D/√2)/√3 A 00 =(S-√2D)/√3) D, S : partial-wave ampl. in D s1 decay D, S : partial-wave ampl. in D s1 decay D/S= √2(z-1)/(1+2z) =√Γ D /Γ S exp(iη) D/S= √2(z-1)/(1+2z) =√Γ D /Γ S exp(iη) Partial Wave Analysis of D s1 (2536) → D* + K 0 s J. Brodzicka for QWG5 hep-ex/ (submitted to PRD) If no angle integrated → ξ-dependent term survives If no angle integrated → ξ-dependent term survives

Fit to angular distribution of D s1 (2536) → D* + K 0 s 3D maximum-likelihood fit with PDF: Background PDF: from M(D* + K s ) sidebands, normalized f bck : background fraction in M(D* + K s ) signal region: ~9% ε(α,β,γ)/ → efficiency correction Fit result projections (bckgd subtracted and efficiency corrected) : From χ 2 of the fit: goodness-of-fit probability: 60% J. Brodzicka for QWG5

Results of D s1 (2536) → D* + K 0 s PWA Results of D s1 (2536) → D* + K 0 s PWA Fit results (include systematic errors) :Fit results (include systematic errors) : Γ S /Γ TOT = 0.72 ± 0.05 (η=43.9 ± 1.7°) Γ S /Γ TOT = 0.72 ± 0.05 (η=43.9 ± 1.7°) S-wave dominates in D s1 (2536) → D * K, contradicts HQETS-wave dominates in D s1 (2536) → D * K, contradicts HQET D s1 (2460) and D s1 (2536) mixD s1 (2460) and D s1 (2536) mix How to calculate the mixing angle θ? Help from theoristsHow to calculate the mixing angle θ? Help from theorists needed to translate measurement to the j q =1/2, 3/2 states needed to translate measurement to the j q =1/2, 3/2 states D s1 ’s helicity=0 preferred D s1 ’s helicity=0 preferred A ligned production of j q =3/2 states is predicted by HQET (ρ 00 ~0.497). A ligned production of j q =3/2 states is predicted by HQET (ρ 00 ~0.497). First full analysis for P-wave cs mesonsFirst full analysis for P-wave cs mesons CLEO integrated over β in PWA of D 1 (2420) →D* π PLB 331, 236; PLB 340, 194. CLEO integrated over β in PWA of D 1 (2420) →D* π PLB 331, 236; PLB 340, 194. D 1 ’-D 1 mixing angle measured from B →D* ππ Dalitz plot analysis by Belle D 1 ’-D 1 mixing angle measured from B →D* ππ Dalitz plot analysis by Belle (-0.10±0.03±0.02±0.02 rad) PRD 69, (-0.10±0.03±0.02±0.02 rad) PRD 69, J. Brodzicka for QWG5

Summary New info to cs multiplets: New info to cs multiplets: new D sJ (2700) → D 0 K + meson observed:new D sJ (2700) → D 0 K + meson observed: M=2708± MeV Γ=108± MeV J P =1 - M=2708± MeV Γ=108± MeV J P =1 - It opens a box of higher radial/orbital excitations of cs states It opens a box of higher radial/orbital excitations of cs states new decay mode: D s1 (2536) → D + π - K + observednew decay mode: D s1 (2536) → D + π - K + observed from PWA of D s1 (2536) → D *+ Ks (first full analysis for cs mesons):from PWA of D s1 (2536) → D *+ Ks (first full analysis for cs mesons): S-wave dominates: Γ S /Γ TOT = 0.72 ± 0.05S-wave dominates: Γ S /Γ TOT = 0.72 ± 0.05 D s1 (2460) and D s1 (2536) mixD s1 (2460) and D s1 (2536) mix longitudinal polarization: ρ 00 = 0.490±0.013longitudinal polarization: ρ 00 = 0.490±0.013 → Falk-Peskin HQET parameter: w 3/2 = ± → Falk-Peskin HQET parameter: w 3/2 = ± …and to cc …and to cc Ψ(3770)[ → D 0 D 0 ] production in B decays confirmed Ψ(3770)[ → D 0 D 0 ] production in B decays confirmed Ψ(4160)[ → D 0 D 0 ] production in B decays not significant Ψ(4160)[ → D 0 D 0 ] production in B decays not significant J. Brodzicka for QWG5

Backup J. Brodzicka for QWG5 J. Brodzicka for QWG5

D s1 recoil mass study D s1 (2536) recoil mass: M rec spectrum indicates 2-body reactions: e + e - → D s1 (2536)X, where X=D s, D* s, higher D** s ’s M rec resolution: ~70MeV at 2GeV, 1/M rec dependence 3D fits to angular distribution in bins of M rec (R Λ and ξ fixed) Polarization at low M rec : show structures expected for: e + e - → D s1 (2536)D s, D s1 (2536)D* s J. Brodzicka for QWG5

HQET Falk-Peskin parameter w3/2 (prob. of light quark’s helicities) ρ00=2/3(1- w3/2) w3/2 = ± (w3/2 from D2*(2460) → Dπ by ARGUS)