A comprehensive interpretation of the D sj states
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1 A comprehensive interpretation of the D sj states Feng-Kun Guo Helmholtz-Institut für Strahlen- und Kernphysik, Universität Bonn Hadron 2011, München, June 13-17, 2011 Based on: F.-K.G., U.-G. Meißner, arxiv: [hep-ph] Feng-Kun Guo (Uni.Bonn) D sj / 12
2 Overview of charm-strange meson spectroscopy Mass MeV D 2600 K D K D K DK D s D s D s D s D s D s D s D sj 3040 D sj ?? All are listed in PDG 2010 See F. De Fazio s talk. Feng-Kun Guo (Uni.Bonn) D sj / 12
3 D s0 (2317), D s1(2460) and D s1 (2700) D s0 (2317) and D s1(2460): hadronic decay modes D sπ 0 and D s π 0 break isospin symmetry Masses much lower than quark model predictions Measured mass (MeV) Godfrey-Isgur quark model (MeV) Ds0 (2317) ± D s1 (2460) ± , 2570 They could be DK and D K bound states Barnes, Close, Lipkin, PRD68(2003) van Bevaren, Rupp, Kolomeistsev, Lutz, Hofmann, F.K.G., Shen, Gammermann, Oset, Faessler, Gutsche,... Explains naturally why M D M D = M Ds1 M D F.K.G., Hanhart, Meißner, PRL102(2009) s0 Feng-Kun Guo (Uni.Bonn) D sj / 12
4 D s0 (2317), D s1(2460) and D s1 (2700) D s0 (2317) and D s1(2460): hadronic decay modes D sπ 0 and D s π 0 break isospin symmetry Masses much lower than quark model predictions Measured mass (MeV) Godfrey-Isgur quark model (MeV) Ds0 (2317) ± D s1 (2460) ± , 2570 They could be DK and D K bound states Barnes, Close, Lipkin, PRD68(2003) van Bevaren, Rupp, Kolomeistsev, Lutz, Hofmann, F.K.G., Shen, Gammermann, Oset, Faessler, Gutsche,... Explains naturally why M D M D = M Ds1 M D F.K.G., Hanhart, Meißner, PRL102(2009) s0 D s1 (2700): discovered by Belle in B decays B+ D 0 DK PRL100(2008) M = MeV, Γ = 125 ± 30 MeV Decays into DK natural parity: positive (negative) parity for even (odd) spin Helicity angular distribution consistent with J = 1 J P = 1 Γ(D K )/Γ(DK ) = 0.91 ± 0.18 BABAR, PRD80(2009) Feng-Kun Guo (Uni.Bonn) D sj / 12
5 D s0 (2317), D s1(2460) and D s1 (2700) D s0 (2317) and D s1(2460): hadronic decay modes D sπ 0 and D s π 0 break isospin symmetry Masses much lower than quark model predictions Measured mass (MeV) Godfrey-Isgur quark model (MeV) Ds0 (2317) ± D s1 (2460) ± , 2570 They could be DK and D K bound states Barnes, Close, Lipkin, PRD68(2003) van Bevaren, Rupp, Kolomeistsev, Lutz, Hofmann, F.K.G., Shen, Gammermann, Oset, Faessler, Gutsche,... Explains naturally why M D M D = M Ds1 M D F.K.G., Hanhart, Meißner, PRL102(2009) s0 D s1 (2700): discovered by Belle in B decays B+ D 0 DK PRL100(2008) M = MeV, Γ = 125 ± 30 MeV Decays into DK natural parity: positive (negative) parity for even (odd) spin Helicity angular distribution consistent with J = 1 J P = 1 Γ(D K )/Γ(DK ) = 0.91 ± 0.18 Mass consistent with quark model prediction for the 2S 1 state BABAR, PRD80(2009) GeV in Godfrey-Isgur quark model S.Godfrey,N.Isgur,PRD32(1985)189 Leading order HMChPT predicts for 2S 1 : Γ(D K )/Γ(DK ) = 0.91 ± 0.04 P.Colangelo et al.,prd77(2008) Feng-Kun Guo (Uni.Bonn) D sj / 12
6 D sj (2860) and D sj (3040) Both discovered by BABAR. PRL97(2006)222001; PRD80(2009) D sj (2860) D sj (3040) Mass [width] (MeV) [48 ± 7] [239 ± 60] Decay modes DK, D K D K, so far not seen in DK Γ(D K )/Γ(DK ) = 1.10 ± 0.24 Quantum numbers natural parity? Feng-Kun Guo (Uni.Bonn) D sj / 12
7 D sj (2860) and D sj (3040) Both discovered by BABAR. PRL97(2006)222001; PRD80(2009) D sj (2860) D sj (3040) Mass [width] (MeV) [48 ± 7] [239 ± 60] Decay modes DK, D K D K, so far not seen in DK Γ(D K )/Γ(DK ) = 1.10 ± 0.24 Quantum numbers natural parity? LO HMChPT predictions: P.Colangelo et al.,prd77(2008) However, (2S, 1 ) has been assigned to D s1 (2700) M(2P, 2 + ) 3.16 GeV, M(1F, 3 ) 3.25 GeV M[D sj (2860)] M.Di Pierro, E.Eichten, PRD64(2001) n = 2, J P s l = 1 + 1/2 is the most possible assignment for D sj(3040) in the c s picture. P.Colangelo, F.De Fazio, PRD81(2010) Feng-Kun Guo (Uni.Bonn) D sj / 12
8 Resummation of the Weinberg-Tomozawa term Leading order interaction: Weinberg-Tomozawa term: chiral symmetric kinetic term Burdman, Donoghue, Wise, Yan,... i Tr[ H av D ba H b ] i Tr[ H av µh b ][Φ, µ Φ] ba 4Fπ 2 Heavy meson exchange: S wave projection vanishes or is tiny. Feng-Kun Guo (Uni.Bonn) D sj / 12
9 Resummation of the Weinberg-Tomozawa term Leading order interaction: Weinberg-Tomozawa term: chiral symmetric kinetic term Burdman, Donoghue, Wise, Yan,... i Tr[ H av D ba H b ] i Tr[ H av µh b ][Φ, µ Φ] ba 4Fπ 2 Heavy meson exchange: S wave projection vanishes or is tiny. Resummation: Oller, Oset, Pelaez, Meißner,... T (s) = V (s)[1 G(s)V (s)] 1 [ ( 1 M 2 G(s) = {E 16π 2 K a(µ)+ log K M µ 2 )] ( ) } + 2 p K cosh 1 EK 2πi p K M K Bound states and resonances as poles of the resummed amplitudes Ds0 (2317) is an S wave isoscalar DK bound state (using as an input to fix a(µ)) D s1 (2460) is an S wave isoscalar D K bound state Feng-Kun Guo (Uni.Bonn) D sj / 12
10 Narrow charmed mesons Excited states have nonvanishing widths, invalidate the use of WT term? The WT term can also be used for other narrow heavy hadrons, whose width is much smaller than the inverse of range of forces Γ M ρ or more conservatively 2M π. J P Nonstrange Width (MeV) Strange Width (MeV) 0 D 0 D s 0 1 D 0.1 Ds < D 1 (2420) 20.4 ± 1.7 D s1 (2536) < D2 (2460) 42.9 ± 3.1 D s2 (2573) 20 ± 5 0 (2S) D(2550) 130 ± 18 D s(?) Not observed 1 (2S) D (2600) 93 ± 14 Ds1 (2700) 125 ± 30 D(2550) and D (2600) were discovered in BABAR, PRD82(2010)111101R Feng-Kun Guo (Uni.Bonn) D sj / 12
11 Generated states Constituents DK D K D 1 (2420)K D (2600)K J P Predictions (input) 2458 ± ± ± 11 Data ± ± ± ± Decays D sπ Ds π D( ) K, D ( ) s η D K, Ds η,dsω,dk, Dφ Feng-Kun Guo (Uni.Bonn) D sj / 12
12 Generated states Constituents DK D K D 1 (2420)K D (2600)K J P Predictions (input) 2458 ± ± ± 11 Data ± ± ± ± Decays D sπ Ds π D( ) K, D ( ) s η D K, Ds η,dsω,dk, Dφ Heavy flavor hadronic molecules should have their spin partners Spin partners of the D sj (2860) and D sj (3040): Constituents D 2 (2460)K D(2550)K J P Predictions 2910 ± ± 10 Data?? Decays D K, Ds η DK, Dsη Feng-Kun Guo (Uni.Bonn) D sj / 12
13 Generated states Constituents DK D K D 1 (2420)K D (2600)K J P Predictions (input) 2458 ± ± ± 11 Data ± ± ± ± Decays D sπ Ds π D( ) K, D ( ) s η D K, Ds η,dsω,dk, Dφ Heavy flavor hadronic molecules should have their spin partners Spin partners of the D sj (2860) and D sj (3040): Very important question: Constituents D 2 (2460)K D(2550)K J P Predictions 2910 ± ± 10 Data?? Decays D K, Ds η DK, Dsη Can we understand the decay patterns of D sj (2860) and D sj (3040)? Feng-Kun Guo (Uni.Bonn) D sj / 12
14 Decays of D sj (2860) and D sj (3040) Sequential decays Rescattering Feng-Kun Guo (Uni.Bonn) D sj / 12
15 Decays of D sj (2860) and D sj (3040): qualitative features Three-body decays are suppressed: D sj (2860) D 1 (2420)K D πk : D 1 (2420) D π is in a D wave. [sl P = couples to s P l = 1 2 (D ) and J P = 0 (π)] D sj (3040) D (2600)K D ( ) πk : D (2600) D ( ) π is in a P wave. [sl P = 1 2 couples to s P l = 1 2 (D ( ) ) and J P = 0 (π)] Three-body phase space Feng-Kun Guo (Uni.Bonn) D sj / 12
16 Decays of D sj (2860) and D sj (3040): qualitative features Three-body decays are suppressed: D sj (2860) D 1 (2420)K D πk : D 1 (2420) D π is in a D wave. [sl P = couples to s P l = 1 2 (D ) and J P = 0 (π)] D sj (3040) D (2600)K D ( ) πk : D (2600) D ( ) π is in a P wave. [sl P = 1 2 couples to s P l = 1 2 (D ( ) ) and J P = 0 (π)] Three-body phase space Γ[D sj (3040)] Γ[D sj (2860)] Data: 239 ± 60 MeV 48 ± 7 MeV J P = 1 +, D sj (3040) D P, DV : S wave J P = 1, D sj (2860) D P, DP : P wave Feng-Kun Guo (Uni.Bonn) D sj / 12
17 Decays of D sj (2860) and D sj (3040): qualitative features Three-body decays are suppressed: D sj (2860) D 1 (2420)K D πk : D 1 (2420) D π is in a D wave. [sl P = couples to s P l = 1 2 (D ) and J P = 0 (π)] D sj (3040) D (2600)K D ( ) πk : D (2600) D ( ) π is in a P wave. [sl P = 1 2 couples to s P l = 1 2 (D ( ) ) and J P = 0 (π)] Three-body phase space Γ[D sj (3040)] Γ[D sj (2860)] Data: 239 ± 60 MeV 48 ± 7 MeV J P = 1 +, D sj (3040) D P, DV : S wave J P = 1, D sj (2860) D P, DP : P wave D sj (3040) with J P = 1 + cannot decay into DK (so far observed only in D K ) Feng-Kun Guo (Uni.Bonn) D sj / 12
18 Decays of D sj (2860) and D sj (3040): qualitative features Three-body decays are suppressed: D sj (2860) D 1 (2420)K D πk : D 1 (2420) D π is in a D wave. [sl P = couples to s P l = 1 2 (D ) and J P = 0 (π)] D sj (3040) D (2600)K D ( ) πk : D (2600) D ( ) π is in a P wave. [sl P = 1 2 couples to s P l = 1 2 (D ( ) ) and J P = 0 (π)] Three-body phase space Γ[D sj (3040)] Γ[D sj (2860)] Data: 239 ± 60 MeV 48 ± 7 MeV J P = 1 +, D sj (3040) D P, DV : S wave J P = 1, D sj (2860) D P, DP : P wave D sj (3040) with J P = 1 + cannot decay into DK (so far observed only in D K ) D sω is a signature channel of non-c s nature of the D sj (3040). c s D sω: disconnected, OZI violating. D (2600)K D sω: OZI allowed. Feng-Kun Guo (Uni.Bonn) D sj / 12
19 Decays of D sj (2860) and D sj (3040): quantitative predictions General structure of the P-wave decay amplitudes: Heavy quark spin symmetry M(D sj (2860) DK ) = g D G D1 K ε DsJ k D, M(D sj (2860) D K ) = g D G D1 K ɛ ijk k i D εj D sj ε k D R DsJ (2860) Predictions for the spin partners: = 2 M D M D = 1.23 kd 3 kd Data 1.10 ± 0.24 Amazing agreement! Γ D s2 (2910) Γ DsJ (2860) 0.2, Γ D s0 (2985) Γ DsJ (3040) < 1 Feng-Kun Guo (Uni.Bonn) D sj / 12
20 Summary Assuming dominance of the WT term for interaction between light pseudoscalar mesons and narrow heavy mesons, a family of kaonic bound states can be generated. Wonderful agreement with both the mass and decay pattern of D sj (2860) supports strongly the D 1 (2420)K bound state interpretation D sω can be used to distinguish the hadronic molecular picture of the D sj (3040) from the c s one. Their spin partners and more states are predicted: Constituents BK B K B1 (5720)K B2 (5747)K J P Predicted masses 5705 ± ± ± ± 33 Dominant decays Bsπ B s π B( ) ( ) K, B s η B K, B s η Feng-Kun Guo (Uni.Bonn) D sj / 12
21 Heavy quark spin symmetry For a heavy quark, spin-dependent quark gluon interaction suppressed by 1/m Q heavy quark spin symmetry The heavy quark spin and the total momentum of light degrees of freedom s l ( s l = s + l ) are conserved in the heavy quark limit m Q Heavy hadrons can be classified as spin multiplets sl P n 2s+1 l J J P Nonstrange Strange Nonstrange decays S 0 0 D D s Weak 1 3 S 1 1 D Ds Dπ P wave; radiative S 0 0 D(2550)? D π P wave 2 3 S 1 1 D (2600) D s1 (2700) D( ) π P wave 1 3 P D0 (2400)? Dπ S wave 1 3 P 1 (mixing) 1 + D 1 (2430)? D π S wave 1 1 P 1 (mixing) 1 + D 1 (2420) D s1 (2536) D π D wave 1 3 P D2 (2460) D s2 (2573) Dπ D wave Feng-Kun Guo (Uni.Bonn) D sj / 12
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