From charm mesons to doubly-charmed baryons

Transcription

1 From charm mesons to doubly-charmed baryons Feng-Kun Guo Institute of Theoretical Physics, Chinese Academy of Sciences Peking University, Oct. 25, 2018 Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 29

2 Overview Charm-strange mesons: D s0(2317), D s1 (2460) Charm-nonstrange mesons: D 0(2400), D 1 (2430) Predictions: bottom-strange and nonstrange mesons doubly-charmed baryons with J P = 1/2 Suggestions for experiments Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 29

3 Charm-strange mesons Mass (MeV) D s * D s1 (2536) D s2 (2573) Ds ?? Charm-strange mesons Godfrey, Isgur, PRD32(1985)189 mesons discovered before 2003 Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 29

4 Charm-strange mesons Mass (MeV) DK threshold D * s0 (2317) D s1 (2460) ?? Charm-strange mesons D * K threshold Godfrey, Isgur, PRD32(1985)189 mesons discovered before 2003 mesons discovered after 2003 Ds0(2317): BaBar (2003) J P = 0 +, Γ< 3.8 MeV D s1 (2460): CLEO (2003) J P = 1 +, Γ< 3.5 MeV no isospin partner observed, tiny widths I = 0 Puzzle 1: Why are D s0(2317) and D s1 (2460) so light? Puzzle 2: Why M Ds1(2460) M D s0 (2317) M D ± M D ±? }{{}}{{} =(141.8±0.8) MeV =(140.67±0.08) MeV Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 29

5 Charm-strange mesons Mass (MeV) DK threshold D * s0 (2317) D s1 (2460) ?? Charm-strange mesons D * K threshold Godfrey, Isgur, PRD32(1985)189 mesons discovered before 2003 mesons discovered after 2003 Ds0(2317): BaBar (2003) J P = 0 +, Γ< 3.8 MeV D s1 (2460): CLEO (2003) J P = 1 +, Γ< 3.5 MeV no isospin partner observed, tiny widths I = 0 Puzzle 1: Why are D s0(2317) and D s1 (2460) so light? Puzzle 2: Why M Ds1(2460) M D s0 (2317) M D ± M D ±? }{{}}{{} =(141.8±0.8) MeV =(140.67±0.08) MeV Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 29

6 Charm-strange mesons Mass (MeV) DK threshold D * s0 (2317) D s1 (2460) ?? Charm-strange mesons D * K threshold Godfrey, Isgur, PRD32(1985)189 mesons discovered before 2003 mesons discovered after 2003 Ds0(2317): BaBar (2003) J P = 0 +, Γ< 3.8 MeV D s1 (2460): CLEO (2003) J P = 1 +, Γ< 3.5 MeV no isospin partner observed, tiny widths I = 0 Puzzle 1: Why are D s0(2317) and D s1 (2460) so light? Puzzle 2: Why M Ds1(2460) M D s0 (2317) M D ± M D ±? }{{}}{{} =(141.8±0.8) MeV =(140.67±0.08) MeV Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 29

7 Charm-nonstrange mesons (1) Obervations of charm-nonstrange excited mesons in 2003 B D ( )+ π π D0(2400): J P = 0 + Γ = (267 ± 40) MeV Mass (MeV): 2318 ± 29 PDG ± 22 BaBar B decays 2308 ± 36 Belle B decays 2401 ± 41 FOCUS γa 2360 ± 34 LHCb B 0 D 0 π K + Belle, PRD69(2004) [hep-ex/ ] D 1 (2430): J P = 1 + Γ = MeV M = (2427 ± 36) MeV Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 29

8 Charm-nonstrange mesons (2) Mass (MeV) D 1 (2430) D * 0 (2400) Godfrey, Isgur, PRD32(1985)189 mesons discovered before 2003 mesons discovered after ?? Charm-nonstrange mesons Puzzle 3: Why M D 0 (2400) M D s0 (2317) and M D1(2430) M Ds1(2460)? Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 29

9 Theoretical tools Lattice QCD Symmetries: Spontaneously broken chiral symmetry: π, K and η as the pseudo-goldstone bosons Heavy quark spin symmetry Heavy quark flavor symmetry Quark model, QCD sum rules,... Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 29

10 Lattice studies of the charmed scalar mesons: strange Early studies using only c s-type interpolators typically give mass larger than that for D s0(2317) Bali (2003); UKQCD (2003);... c s + DK interpolators: right mass Mohler et al., PRL111(2013) M D s0 1 4 ( MDs + 3M D s ) : Mohler et al. PDG2018 (266 ± 16) MeV (241.5 ± 0.8) MeV Calculation with M π = 150 MeV Bali et al. [RQCD Col.], PRD96(2017) Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 29

11 Lattice studies of the charmed scalar mesons: nonstrange (1) (S, I) = (0, 1 2 ): c q + Dπ interpolators: Mohler et al., PRD87(2013) M π 266 MeV, M D 1558 MeV, M D 1690 MeV Lüscher s formula Dπ phase shifts BW parameters of D 0(2400) consistent with PDG values Mohler et al. PDG2018 M D (M D + 3M D ) (351 ± 21) MeV (347 ± 29) MeV M D1 1 4 (M D + 3M D ) (380 ± 21) MeV (456 ± 40) MeV Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 29

12 Lattice studies of the charmed scalar mesons: nonstrange (2) (S, I) = (0, 1 2 ): first coupled-channel lattice calculation including interpolating fields for c q + Dπ + Dη + D s K: Moir et al. [Hadron Spectrum Col.], JHEP1610(2016)011 M π = 391 MeV, M D = 1885 MeV: for coupled channels: Dπ threshold ( ± 0.9) MeV parametrizing the T -matrix with the K-matrix formalism T 1 ij (s) = K 1 (s) + I ij(s) I ij (s): 2-point loop function evaluated with a subtracted dispersion integral K ij (s): different forms of the K-matrix were used, summarized as K ij (s) = ( g (0) i + g (1) i ) ( s g (0) ij j + g (1) j ) s 1 m 2 s + γ(0) ij + γ (1) ij s a pole below threshold ( ± 0.9) MeV. relation to D 0(2400)? Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 29

13 Interactions between charm and light mesons S-wave interactions between charm mesons (D, D s ) and light pseudoscalar mesons (π, K, η) not far from the thresholds chiral EFT for matter field Ds0/D 0 should appear as poles in scattering amplitudes: D s0 : DK, D s η; D 0 : Dπ, Dη, D s K needs a nonperturbative treatment: ChPT + unitarization T 1 (s) = V 1 (s) G(s) V (s): to be derived from SU(3) chiral Lagrangian, 6 LECs up to NLO G(s): 2-point scalar loop functions, regularized with a subtraction constant a(µ) Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 29

14 Fit to lattice data L. Liu, Orginos, FKG, Hanhart, Meißner, PRD86(2013) Fit to lattice data on scattering lengths in 5 simple channels: D K(I = 1, I = 0), D s K, Dπ(I = 3/2), D s π: no disconnected contribution 5 parameters: h 2, h 3, h 4, h 5 and a(µ) fm 1,1 a D K MΠ MeV fm 1,0 a D K MΠ MeV fm 0,3 2 a DΠ Π fm 1,1 a Ds Π MΠ MeV Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 29

15 Postdictions versus recent lattice results: charm-nonstrange In a finite volume: q = 2π L n, n Z3 ; loop integral G(s): d 3 q 1 L 3 q Postdicted I = 1/2 Dπ, Dη, D s K finite volume energy levels versus lattice QCD results by [G. Moir et al. [Hadron Spectrum Collaboration], JHEP1610(2016)011] NOT a fit! E (MeV) E free Dπ M. Albaladejo, P. Fernandez-Soler, FKG, J. Nieves, PLB767(2017)465 E free Dη E free D s K LQCD L/a s Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 29

16 Predictions for 0 + & 1 + heavy mesons Heavy-strange Du et al., arxiv: meson J P prediction (MeV) PDG2018 (MeV) lattice (MeV) D s ± [1] Heavy-nonstrange, two I = 1/2 states (M, Γ/2): Lower (MeV) Higher (MeV) PDG2018 (MeV) ( D , ) ( , ) (2318 ± 29, 134 ± 20) ( D , ) ( , ) (2427 ± 40, ( ) B , ) ( , 36 ± 5) ( B , ) ( , ) [1] Bali, Collins, Cox, Schäfer, PRD96(2017) [2] Lang, Mohler, Prelovsek, Woloshyn, PLB750(2015)17 Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 29

17 Predictions for 0 + & 1 + heavy mesons Heavy-strange Du et al., arxiv: meson J P prediction (MeV) PDG2018 (MeV) lattice (MeV) D s ± [1] D s ± ± 4[1] B s ± 23[2] B s ± 25[2] Heavy-nonstrange, two I = 1/2 states (M, Γ/2): Lower (MeV) Higher (MeV) PDG2018 (MeV) ( D , ) ( , ) (2318 ± 29, 134 ± 20) ( D , ) ( , ) (2427 ± 40, ( ) B , ) ( , 36 ± 5) ( B , ) ( , ) [1] Bali, Collins, Cox, Schäfer, PRD96(2017) [2] Lang, Mohler, Prelovsek, Woloshyn, PLB750(2015)17 Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 29

18 Predictions for 0 + & 1 + heavy mesons Heavy-strange Du et al., arxiv: meson J P prediction (MeV) PDG2018 (MeV) lattice (MeV) D s ± [1] D s ± ± 4[1] B s ± 23[2] B s ± 25[2] Heavy-nonstrange, two I = 1/2 states (M, Γ/2): Lower (MeV) Higher (MeV) PDG2018 (MeV) ( D , ) ( , ) (2318 ± 29, 134 ± 20) ( D , ) ( , ) (2427 ± 40, ( ) B , ) ( , 36 ± 5) ( B , ) ( , ) [1] Bali, Collins, Cox, Schäfer, PRD96(2017) [2] Lang, Mohler, Prelovsek, Woloshyn, PLB750(2015)17 Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 29

19 SU(3) analysis In the SU(3) limit, irreps: 3 8 = Evolution of the two poles from the physical to the SU(3) symmetric case Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 29

20 DK component from lattice QCD Compositeness (1 Z) related to the S-wave scattering length: Weinberg (1965) a 2 1 Z 1 2 Z 2µEB From the lattice energy levels in C. Lang et al., PRD90(2014) Ds0(2317) contains 70% DK Martínez Torres, Oset, Prelovsek, Ramos, JHEP1505,053 Latest lattice results in G. Bali et al., PRD96(2017) Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 29

21 DK component from lattice QCD Compositeness (1 Z) related to the S-wave scattering length: Weinberg (1965) a 2 1 Z 1 2 Z 2µEB From the lattice energy levels in C. Lang et al., PRD90(2014) Ds0(2317) contains 70% DK Martínez Torres, Oset, Prelovsek, Ramos, JHEP1505,053 Latest lattice results in G. Bali et al., PRD96(2017) Z = 1.04(0.08)(+0.30) M π [MeV] M D s0 (2317) [MeV] 2348 ± ± 3 M Ds [MeV] 1977 ± ± 1 strong M π dependence! curves: prediction in Du et al., EPJC77(2017)728 Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 29

22 [kev] Decay width of D s0(2317): smoking gun [2] [3] [1] measurement planned at PANDA [1] FKG et al.,plb666(2008)251; [2] L. Liu et al.,prd87(2013)014508; [3] X. Guo et al.,prd98(2018) non-molecular: e.g., P. Colangelo and F. De Fazio, PLB570(2003)180 Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 29

23 B D + π π (1) Angular moments: P L +1 1 LHCb, PRD94(2016) d cos θ P L (cos θ) dγ dm Dπ d cos θ Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 29

24 B D + π π (2) Du et al., arxiv: [hep-ph] Consider only S, P, D waves, up to around 2.5 GeV: A(B D + π π ) = A 0 (s) + 3A 1 (s)p 1 (z) + 5A 2 (s)p 2 (z); higher partial waves negligible: P 6 A 3 2 P -wave: D, D (2680) [M = 2681 MeV, Γ = 187 MeV]; D-wave: D 2 (2460) parametrized (with the same masses and widths) as in the LHCb paper: Breit Wigner with Bleit Weisskopf barrier factors, one constant phase for each as free parameters Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 29

25 B D + π π (3) M.-L. Du et al., arxiv: [hep-ph] S-wave: FSI, two new parameters P, D-wave: BWs from the LHCb fit Angular moments: P 0 A A A 2 2, P A A A 0 A 2 cos(δ 2 δ 0), P 13 P P3 2 3 A 0 A 1 cos(δ 1 δ 0) Data: LHCb, PRD94(2016) P0 /(20 MeV) MD + π - [GeV] ( P1-14 P3 /9) /(20 MeV) M D + π - [GeV] P2 /(20 MeV) MD + π - [GeV] Fast variation in [2.4, 2.5] GeV in P 13 : cusps at Dη and D s K thresholds Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 29

26 B D + π π (4) Dπ S-wave amplitude: comparison with the LHCb determination Coupled-channel thresholds, effects enhanced by the pole at (2.45 i 0.13) GeV Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 29

27 Puzzles solved Thanks for the recent experiment, lattice and EFT developments likely resolution to all 3 puzzles of positive-parity charm mesons: Q: Why are Ds0(2317) and D s1 (2460) much lighter than quark model predictions for c s mesons? A: They are dominantly DK and D K molecular states, respectively. Q: Why M Ds1(2460) ± M Ds0 M (2317)± D ± M D ±? A: Consequence of HQSS as dominantly DK and D K molecules. Q: Why M D 0 (2400) M D s0 (2317) and M D1(2430) M Ds1(2460)? A: Two D0 and two D 1, the SU(3) partners of D sj have smaller masses. Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 29

28 Puzzles solved Thanks for the recent experiment, lattice and EFT developments likely resolution to all 3 puzzles of positive-parity charm mesons: Q: Why are Ds0(2317) and D s1 (2460) much lighter than quark model predictions for c s mesons? A: They are dominantly DK and D K molecular states, respectively. Q: Why M Ds1(2460) ± M Ds0 M (2317)± D ± M D ±? A: Consequence of HQSS as dominantly DK and D K molecules. Q: Why M D 0 (2400) M D s0 (2317) and M D1(2430) M Ds1(2460)? A: Two D0 and two D 1, the SU(3) partners of D sj have smaller masses. Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 29

29 Puzzles solved Thanks for the recent experiment, lattice and EFT developments likely resolution to all 3 puzzles of positive-parity charm mesons: Q: Why are Ds0(2317) and D s1 (2460) much lighter than quark model predictions for c s mesons? A: They are dominantly DK and D K molecular states, respectively. Q: Why M Ds1(2460) ± M Ds0 M (2317)± D ± M D ±? A: Consequence of HQSS as dominantly DK and D K molecules. Q: Why M D 0 (2400) M D s0 (2317) and M D1(2430) M Ds1(2460)? A: Two D0 and two D 1, the SU(3) partners of D sj have smaller masses. Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 29

30 Searching for the higher nonstrange state Near-threshold enhancement in D s K? Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 29

31 Searching for the higher nonstrange state Near-threshold enhancement in D s K? BaBar, PRL100(2008)171803; Belle, PRD80(2009) Belle, PRD91(2015) Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 29

32 Searching for the higher nonstrange state: lattice Lattice QCD calculation with a SU(3) symmetric large quark mass: 2650 M6 [MeV] bound state virtual state resonance threshold Γ6/2 [MeV] m φ [MeV] Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 29

33 Doubly-charmed baryons Heavy anti-quark diquark symmetry (HADS): Savage, Wise (1990) m Q v Λ QCD, the diquark serves as a point-like color- 3 source, like a heavy anti-quark. doubly-heavy baryons anti-heavy mesons HADS + CHPT with virtual photons: Brodsky, FKG, Hanhart, Meißner, PLB698(2011)251 M D + M D 0 M Ξ ++ M cc Ξ + cc = (1.5 ± 2.7) MeV LHCb observation of Ξ ++ cc : M = ( ± 0.78) MeV LHCb, PRL119(2017) Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 29

34 Doubly-charmed baryons Heavy anti-quark diquark symmetry (HADS): Savage, Wise (1990) m Q v Λ QCD, the diquark serves as a point-like color- 3 source, like a heavy anti-quark. doubly-heavy baryons anti-heavy mesons HADS + CHPT with virtual photons: Brodsky, FKG, Hanhart, Meißner, PLB698(2011)251 M D + M D 0 M Ξ ++ M cc Ξ + cc = (1.5 ± 2.7) MeV LHCb observation of Ξ ++ cc : M = ( ± 0.78) MeV LHCb, PRL119(2017) Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 29

35 Doubly-charmed baryons Heavy anti-quark diquark symmetry (HADS): Savage, Wise (1990) m Q v Λ QCD, the diquark serves as a point-like color- 3 source, like a heavy anti-quark. doubly-heavy baryons anti-heavy mesons HADS + CHPT with virtual photons: Brodsky, FKG, Hanhart, Meißner, PLB698(2011)251 M D + M D 0 M Ξ ++ M cc Ξ + cc = (1.5 ± 2.7) MeV LHCb observation of Ξ ++ cc : M = ( ± 0.78) MeV LHCb, PRL119(2017) Candidates per 5 MeV/c LHCb 13 TeV Data Total Signal Background m ) [MeV/c 2 cand (Ξ cc ] Candidates per 5 MeV/c LHCb 8 TeV Data Total Signal Background m ) [MeV/c 2 cand (Ξ cc ] Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 29

36 Doubly-charmed baryons with J P = 1/2 P -wave QQ excitation energy Mehen, PRD96(2017) (M h c M J/ψ ) = O (200 MeV) Ξ P cc, Ω P cc as dynamical degrees of freedom S-wave QQ: spin s QQ = 1, P -wave QQ: spin s QQ = 0 = O ( ΛQCD m Q ) Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 29

37 Doubly-charmed strange baryons with J P = 1/2 : Ω P cc M.-J. Yan, X.-H. Liu, S. Gonzàlez-Solís, FKG, C. Hanhart, U.-G. Meißner, B.-S. Zou, arxiv: Very likely two states below the Ξ cc K threshold Inputs: bare M Ξ P cc = 3838 MeV from quark model D. Ebert et al., PRD96(2002) M Ωcc M Ξcc = M Ds M D, MΩ P cc M Ωcc = 217 MeV Tiny widths due to isospin breaking: Ω P cc Ω cc π 0 Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 29

38 Doubly-charmed strange baryons with J P = 1/2 : Ω P cc M.-J. Yan, X.-H. Liu, S. Gonzàlez-Solís, FKG, C. Hanhart, U.-G. Meißner, B.-S. Zou, arxiv: Very likely two states below the Ξ cc K threshold Inputs: bare M Ξ P cc = 3838 MeV from quark model D. Ebert et al., PRD96(2002) M Ωcc M Ξcc = M Ds M D, MΩ P cc M Ωcc = 217 MeV Γ [kev] Γ [kev] P,H (a) Ω cc P,L (b) Ω cc Tiny widths due to isospin breaking: Ω P cc Ω cc π 0 Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 29 λ

39 Doubly-charmed nonstrange baryons with J P = 1/2 : Ξ P cc M.-J. Yan, X.-H. Liu, S. Gonzàlez-Solís, FKG, C. Hanhart, U.-G. Meißner, B.-S. Zou, arxiv: Three 1 Ξ P cc states below 4.2 GeV: 2 Γ [MeV] λ=0.6 λ=0 λ=0.6 P,1 Ξ cc P,2 Ξ cc P,3 Ξ cc 0 λ= M [GeV] λ=0 λ=0.6 B(Ξ P,1 cc, Ξ P,2 cc Ξ cc π) 100%, searching for Ξ P,1 cc in Ξ ++ cc π λ Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 29

40 Doubly-charmed nonstrange baryons with J P = 1/2 : Ξ P cc M.-J. Yan, X.-H. Liu, S. Gonzàlez-Solís, FKG, C. Hanhart, U.-G. Meißner, B.-S. Zou, arxiv: Three 1 Ξ P cc states below 4.2 GeV: 2 Γ [MeV] λ=0.6 λ=0 λ=0.6 P,1 Ξ cc P,2 Ξ cc P,3 Ξ cc 0 λ= M [GeV] λ=0 λ=0.6 B(Ξ P,1 cc, Ξ P,2 cc Ξ cc π) 100%, searching for Ξ P,1 cc in Ξ ++ cc π λ Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 29

41 Summary and suggestions Puzzles of positive-parity charmed mesons naturally understood Suggestion for lattice: to study the flavor sextet at the SU(3) symmetric point at large quark masses Suggestions for exp.: D 0, D 1 : precise measurments of P P 3 for B D + π π and B D + π π the higher D 0, D 1 : D s K spectrum in processes such as B D ( )+ s K π, B D s ( )+ K K, B s 0 D s ( )+ K0 π,... to search for Bs0 (M 5.72 GeV) in B s γ, B s1 (M 5.77 GeV) in B s ( ) γ, not the B s1 (5830) to search for J P = 1/2 Ξ cc (M 3.82 GeV) in Ξ ++ cc π Suggestion for PDG: to reconsider the D 0 parameters Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 29

42 Thank you for your attention! Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 29

43 HQS for D s0(2317) and D s1 (2460) Heavy quark flavor symmetry: for a singly-heavy hadron, M HQ ( = m Q + A + O m 1 Q rough estimates of bottom analogues whatever the D sj states are ( ( 1 M B s0 = M D s0 (2317) + b c + O Λ 2 QCD 1 )) (5.65 ± 0.15) GeV m c m b ( ( 1 M Bs1 = M Ds1(2460) + b c + O Λ 2 QCD 1 )) (5.79 ± 0.15) GeV m c m b here b c m b m c M Bs M Ds 3.33 GeV, where M Bs = GeV, M Ds = GeV: spin-averaged g.s. Q s meson masses both to be discovered 1 more precise predictions can be made in a given model, e.g. hadronic molecules ) 1 The established meson B s1 (5830) is probably the bottom partner of D s1 (2536). Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 10

44 Easy predictions from HQFS Heavy quark flavor symmetry (HQFS) for any hadron containing one heavy quark: velocity remains unchanged in the limit m Q : v = p = Λ QCD m Q m Q heavy quark is like a static color triplet source, m Q is irrelevant Predicting the bottom-partner masses in 1 minute: M B s0 M B + M K 45 MeV GeV M Bs1 M B + M K 45 MeV GeV nice agreement with lattice results: Lang, Mohler, Prelovsek, Woloshyn, PLB750(2015)17 MB lat. s0 = (5.711 ± ± 0.019) GeV MB lat. s1 = (5.750 ± ± 0.019) GeV Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 10

45 Easy predictions from HQFS Heavy quark flavor symmetry (HQFS) for any hadron containing one heavy quark: velocity remains unchanged in the limit m Q : v = p = Λ QCD m Q m Q heavy quark is like a static color triplet source, m Q is irrelevant Predicting the bottom-partner masses in 1 minute: M B s0 M B + M K 45 MeV GeV M Bs1 M B + M K 45 MeV GeV nice agreement with lattice results: Lang, Mohler, Prelovsek, Woloshyn, PLB750(2015)17 MB lat. s0 = (5.711 ± ± 0.019) GeV MB lat. s1 = (5.750 ± ± 0.019) GeV Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 10

46 Energy levels in a finite volume Goal: predict finite volume (FV) energy levels for I = 1/2, and compare with recent lattice data by the Hadron Spectrum Col. in JHEP1610(2016)011 insights into D 0(2400) In a FV, momentum gets quantized: q = 2π L n, n Z3 Loop integral G(s) gets modified: d 3 q 1 L 3 q, and one gets G(s, L) = G(s) + I( q): loop integrand M. Döring, U.-G. Meißner, E. Oset, A. Rusetsky, EPJA47(2011)139 lim Λ + [ 1 L 3 q <Λ I( q ) FV energy levels obtained by as poles of T (s, L): n Λ 0 q 2 dq 2π 2 I( q ) } {{ } finite volume effect T 1 (s, L) = V 1 (s) G(s, L) ] Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 10

47 Chiral Lagrangian (I) The leading order Lagrangian: L (1) φp = D µp D µ P m 2 P P with P = (D 0, D +, D + s ) denoting the D mesons, and the covariant derivative being D µ P = µ P + P Γ µ, D µ P = ( µ + Γ µ )P, Γ µ = 1 ( u µ u + u µ u ), 2 where u µ = i [ u ( µ ir µ )u + u( µ il µ )u ], u = e iλaφa/(2f0) Burdman, Donoghue (1992); Wise (1992); Yan et al. (1992) this gives the Weinberg Tomozawa term for P φ scattering Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 10

48 Chiral Lagrangian (II) At the next-to-leading order O ( p 2) : FKG, Hanhart, Krewald, Meißner, PLB666(2008)251 L (2) φp = P [ h 0 χ + h 1 χ + + h 2 u µ u µ h 3 u µ u µ ] P +D µ P [h 4 u µ u ν h 5 {u µ, u ν }] D ν P, χ ± = u χu ± uχ u, χ = 2B 0 diag(m u, m d, m s ) LECs: h 1,3,5 = O ( ) Nc 0, h2,4,6 = O ( ) Nc 1 M Ds M D h 1 = 0.42 h 0 : can be fixed from lattice results of charmed meson masses h 2,3,4,5 : to be fixed from lattice results on scattering lengths Extensions to O ( p 3), see Y.-R. Liu, X. Liu, S.-L. Zhu, PRD79(2009)094026; L.-S. Geng et al., PRD82(2010)054022; D.-L. Yao, M.-L. Du, FKG, U.-G. Meißner, JHEP1511(2015)058; renormalization: M.-L. Du, FKG, U.-G. Meißner, D.-L. Yao, EPJC77(2017)728 PCB-term subtraction in EOMS scheme using path integral: M.-L. Du, FKG, U.-G. Meißner, JPG44(2017) M.-L. Du, FKG, U.-G. Meißner, JHEP1610(2016)122 Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 10

49 Chiral Lagrangian (II) At the next-to-leading order O ( p 2) : FKG, Hanhart, Krewald, Meißner, PLB666(2008)251 L (2) φp = P [ h 0 χ + h 1 χ + + h 2 u µ u µ h 3 u µ u µ ] P +D µ P [h 4 u µ u ν h 5 {u µ, u ν }] D ν P, χ ± = u χu ± uχ u, χ = 2B 0 diag(m u, m d, m s ) LECs: h 1,3,5 = O ( ) Nc 0, h2,4,6 = O ( ) Nc 1 M Ds M D h 1 = 0.42 h 0 : can be fixed from lattice results of charmed meson masses h 2,3,4,5 : to be fixed from lattice results on scattering lengths Extensions to O ( p 3), see Y.-R. Liu, X. Liu, S.-L. Zhu, PRD79(2009)094026; L.-S. Geng et al., PRD82(2010)054022; D.-L. Yao, M.-L. Du, FKG, U.-G. Meißner, JHEP1511(2015)058; renormalization: M.-L. Du, FKG, U.-G. Meißner, D.-L. Yao, EPJC77(2017)728 PCB-term subtraction in EOMS scheme using path integral: M.-L. Du, FKG, U.-G. Meißner, JPG44(2017) M.-L. Du, FKG, U.-G. Meißner, JHEP1610(2016)122 Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 10

50 Two I = 1/2 states! Masses M (MeV) Γ/2 (MeV) RS g Dπ g Dη g Ds K lattice (000) (110) M π = 391 MeV M D = 1885 MeV Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 10

51 Two I = 1/2 states! Masses M (MeV) Γ/2 (MeV) RS g Dπ g Dη g Ds K lattice (000) (110) physical (100) (110) Im E (MeV) Latt., Low Phys., Low EDπ (phy) Latt., High Phys., High Re E (MeV) EDπ (lat) PDG EDη (phy) E Ds K (phy) EDη (lat) E Ds K (lat) Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 10

52 Postdictions versus recent lattice results: charm-strange Postdicted finite volume energy levels for (S, I) = (1, 0) D ( ) K, J P = 1 + & 0 + versus lattice QCD results by [G. Bali, S. Collins, A. Cox, A. Schäfer, PRD96(2017)074501] M. Albaladejo, P. Fernandez-Soler, J. Nieves, P. G. Ortega, arxiv: E I: M π = 290 MeV E II: M π = 150 MeV E [GeV] (1 + ) E I 2.50 E [GeV] (1 + ) E [GeV] (0 + ) E II E free D ( ) K E free D s ( ) η LQCD E [GeV] (0 + ) L [fm] L [fm] 2.30 Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 10

53 Fit to LHCb data Du et al., arxiv: [hep-ph] B D + π π contains coupled-channel Dπ FSI consider S, P, D waves: A(B D + π π ) = A 0 (s) + A 1 (s) + A 2 (s) P -wave: D, D (2680); D-wave: D 2 (2460) as in the LHCb paper S-wave: use the coupled-channel (1: Dπ; 2 : Dη; 3 : D s K) amplitudes with all parameters fixed before only 2 parameters in S-wave: C and a subtraction constant in G i (s) ( 5 SU(3)+chiral A 0 (s) E π [2 + G Dπ (s) 3 T 1/2 11 (s) + 1 )] 3 T 3/2 (s) Im G i (s) = ρ i (s) Unitarity: E ηg Dη (s)t 1/2 21 (s) E KG Ds K(s)T 1/2 31 (s) +C E η G Dη (s)t 1/2 21, ImA 0,i (s) = j T ij (s)ρ j(s)a 0,j (s) Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 10

54 Fit to LHCb data Du et al., arxiv: [hep-ph] B D + π π contains coupled-channel Dπ FSI consider S, P, D waves: A(B D + π π ) = A 0 (s) + A 1 (s) + A 2 (s) P -wave: D, D (2680); D-wave: D 2 (2460) as in the LHCb paper S-wave: use the coupled-channel (1: Dπ; 2 : Dη; 3 : D s K) amplitudes with all parameters fixed before only 2 parameters in S-wave: C and a subtraction constant in G i (s) ( 5 SU(3)+chiral A 0 (s) E π [2 + G Dπ (s) 3 T 1/2 11 (s) + 1 )] 3 T 3/2 (s) Im G i (s) = ρ i (s) Unitarity: E ηg Dη (s)t 1/2 21 (s) E KG Ds K(s)T 1/2 31 (s) +C E η G Dη (s)t 1/2 21, ImA 0,i (s) = j T ij (s)ρ j(s)a 0,j (s) Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 10

55 More similar states? FKG, U.-G. Meißner, PRD84(2011) Chiral symmetry universal Weinberg Tomozawa term applicable to any hadrons with a small width Γ inverse of force range nice candidates: D 1 (2420) & D 2 (2460), Γ 30 MeV more speculative (using the same subtraction constant) predictions of D 1 (2420)K and D 2 (2460)K bound states Constituents D 1 (2420)K D 2 (2460)K B1 (5720)K B2 (5747)K J P Predictions 2870 ± ± ± ± 33 Decays D ( ) K, D s ( ) η D K, Dsη B( ) ( ) K, B s η B K, B s η D s1(2860) is probably the D 1 (2420)K bound state! Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 10

56 More similar states? FKG, U.-G. Meißner, PRD84(2011) Chiral symmetry universal Weinberg Tomozawa term applicable to any hadrons with a small width Γ inverse of force range nice candidates: D 1 (2420) & D 2 (2460), Γ 30 MeV more speculative (using the same subtraction constant) predictions of D 1 (2420)K and D 2 (2460)K bound states Constituents D 1 (2420)K D 2 (2460)K B1 (5720)K B2 (5747)K J P Predictions 2870 ± ± ± ± 33 Decays D ( ) K, D s ( ) η D K, Dsη B( ) ( ) K, B s η B K, B s η D s1(2860) is probably the D 1 (2420)K bound state! Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 10

57 What is Ds(2860)? Ds1(2860): puzzling decay pattern: Γ(D K)/Γ(DK) = 1.10 ± 0.24 Predictions from HQSS: P.Colangelo et al.,prd77(2008) but, better candidate for (2S, 1 ): D s1(2700) Γ(D K)/Γ(DK) = 0.91 ± 0.18 M(2P, 2 + ) 3.16 GeV A natural explanation of the decay pattern: : Γ(D s1(2860) D K) DK M. Di Pierro, E. Eichten, PRD64(2001) M D M D kd kd 3 = 1.23 Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 10

58 What is Ds(2860)? Ds1(2860): puzzling decay pattern: Γ(D K)/Γ(DK) = 1.10 ± 0.24 Predictions from HQSS: P.Colangelo et al.,prd77(2008) but, better candidate for (2S, 1 ): D s1(2700) Γ(D K)/Γ(DK) = 0.91 ± 0.18 M(2P, 2 + ) 3.16 GeV A natural explanation of the decay pattern: : Γ(D s1(2860) D K) DK M. Di Pierro, E. Eichten, PRD64(2001) M D M D kd kd 3 = 1.23 Feng-Kun Guo (ITP) From charm mesons to doubly-charmed baryons / 10