Charmed baryon spectroscopy in a quark model

Transcription

1 Charmed baryon spectroscopy in a quark model Tokyo tech RCNP A RIKEN B Tetsuya YoshidaMakoto Oka Atsushi Hosaka A Emiko Hiyama B Ktsunori Sadato A

2 Contents Ø Motivation Ø Formalism Ø Result ü Spectrum of single charmed baryon ü λ-mode and ρ-mode Ø Summary

3 Motivation Many unknown states in heavy baryons ü We know the baryon spectra in light sector but still do not know heavy baryon spectra well. ü Constituent quark model is successful in describing baryon spectra and we can predict unknown states of heavy baryons by using the model. Many unknown state Difference from light sector Λ C Σ C ü λ-mode state and ρ-mode state split in heavy quark sector ü Because of HQS we expect that there is spin-partner

4 Motivation light quark sector vs heavy quark sector How do spectrum and wave function change? What is the role of diquark? How is it in the heavy quark limit? heavy quark limit m q m Q λ ρ mode ü we can see how the spectrum and wave- funchon change ü Is charm sector near from heavy quark limit (or far)?

5 Hamiltonian Spin- Spin the cause of mass splipng + ij H = K i + (V conf i i< j ij + H hyp +V ij LS ) + C qqq = (m i + p i m i ) + π i 3 α " 1 con m + 1 % $ # i m ' δ(r) + i< j j & i< j ) + * + i< j α con 8π 3m i m j 1 + α SO 3m 3 q r ij 3 S i S j δ 3 (r ij )+ α ten 1 # 3S i r ij S j r & ij S 3 i S j 3m i m j r % ij $ r (. ij '-. ( ξ i +ξ j + 4ξ i ξ j )l ij s ij + C qqq i< j " $ # Spin orbit br ij α Coul 3r ij Tensor Confinement % ' & Coulomb ü We determined the parameter that the result of the Strange baryon will agree with experimental results. Using the parameter we performed spectral calcula@on of the charm baryon.

6 Heavy Quark Symmetry(HQS) If we take m Q heavy quark spin operator S Q m Q 0 ü In heavy quark limit the hamiltonian does not depend on heavy quark spin operator so the angular momentum of the light component become good quantum number. ü Two states that direction of heavy quark spin is different become degenerate. Σ Q doublet Σ Q Σ * 194MeV Σ C * Σ C 65MeV * Σ b Σ b 0MeV Σ

7 Heavy Quark Symmetry(HQS) Λ-particle (positive parity) Σ-particle (positive parity) s-wave j ρ 1 ( ) s-wave j ρ 1 ( 3 ) 1 p-wave j ρ ( ) 1 1 ( 3 ) 3 3 ( 5 ) 5 ( 7 ) 1 p-wave j ρ 1 1 ( ) 1 1 ( 3 ) 1 3 ( 5 ) 1 d-wave j ρ = 0 = 3 ( 5 ) d-wave j ρ ( 3 ) 3 ( 5 ) 5 ( 7 ) p-wave j ρ 1 ΛΣ-particle (negative parity) 1 1 ( ) 1 1 ( 3 ) j ρ 3 ( 5 ) 1 J = ± 1 = j ρ +

8 λ-mode and ρ-mode =0 q q ϕ Llλ Q q q ϕ Llλ =0 Q In heavy quark sector modes split ρ- mode λ- mode light sector heavy quark sector

9 Gaussian Expansion Method jacobi coodinate 3 r 1 3 R r R 3 R 3 1 r 3 Wave func@on Channel1 Channel Channel3 Trial func@on Ψ JM = Φ (C) JM (r 1 R 1 )+ Φ (C=) JM (r R )+ Φ (C=3) JM (r 3 R 3 ) φ G nlm (r) = N nl r l e ν nr Y lm (ˆr)! # # # # " Φ (C) JM = n C l C N C L C H 11 H 1 H 1N H 1 H H N H nn H nn H NN $! &# &# &# &# %" (C) A nc l C.N C L C Eigen value problem c 1 c c N " # φ G nc l C Hc = ENc $! & # & # & = E# & # % " G (r C )ψ NC L C N 11 N 1 N 1N N 1 N N N N nn N nn N NN $! &# &# &# &# %" (R C ) $ % c 1 c c N $ & & & & % (i) N ij = φ JM (i) H ij = φ JM ( j) φ JM ( j) H φ JM G ψ NLM (R) = N NL R L e λ Nr Y LM ( ˆR) ü We describe baryon wave func@on as sum of channels ü We use Gaussian basis func@on E. Hiyama Y. Kino and M. Kamimura Prog. Part. Nucl. Phys. 51 (003) 3

10 Result 1. Mass of charmed lambda charmed sigma ü we predict unkown states. Mass and wave function of single heavy baryon in the heavy quark limit ü We will see which states are doublet (or singlet) ü What is different from light sector 3. Wave function and baryon mass in different quark mass ü We will see how baryon mass and wave function change

11 Baryon spectroscopy of single charmed baryon Λ c 880MeV 940MeV 595MeV 65MeV 85MeV

12 Baryon spectroscopy of single charmed baryon Σ c 800MeV 455MeV 518MeV

13 Lambda baryon (negative parity) (heavy quark limit) = ( ) = C λ ψ λ + C ρ ψ ρ 5 ( ) = ψ ρ Φ Λ 1 3 Φ Λ λ-wave ρ-wave ΛΣ-particle (negative parity) p-wave j ρ ( ) ( ) ( ) Λ GR one singlet and three doublet

14 Lambda baryon (negative parity) C λ (heavy quark limit) = C ρ pure ρ-mode ( ) = C λ ψ λ + C ρ ψ ρ 5 ( ) = ψ ρ Φ Λ 1 3 Φ Λ λ-wave ρ-wave ΛΣ-particle (negative parity) C λ C ρ pure λ-mode p-wave j ρ ( ) ( ) ( ) Λ GR one singlet and three doublet

15 Lambda baryon (negative parity) Λ J Φ Λ 1 3 ( ) = C λ ψ λ + C ρ ψ ρ m s λ C λ m c P = 1 ρ C ρ J P = 1 E 1 m s m c E ρ C ρ λ C λ ρ C ρ J P = 1 λ J P = 3 m s m c E 3 E 1 C λ m s m c λ C λ ρ C ρ ρ C ρ J P = 3 ρ J P = 3 m s m c E E 3 m s m c λ C λ λ

16 Sigma baryon (negative parity) Φ Σ 1 3 ( ) = C λ ψ λ + C ρ ψ ρ Φ Σ 5 ( ) = ψ λ λ-wave ρ-wave ΛΣ-particle (negative parity) p-wave j ρ ( ) ( ) ( ) Λ GR one singlet and three doublet (heavy quark limit)

17 Sigma baryon (negative parity) Φ Σ 1 3 ( ) = C λ ψ λ + C ρ ψ ρ C λ C ρ pure ρ-mode Φ Σ 5 ( ) = ψ λ λ-wave ρ-wave ΛΣ-particle (negative parity) C λ = C ρ pure λ-mode Λ GR p-wave j ρ ( ) ( ) ( ) one singlet and three doublet (heavy quark limit)

18 Sigma baryon (negative parity) Φ Σ 1 3 ( ) = C λ ψ λ + C ρ ψ ρ λ C λ J P = 1 m s λ m c J P = 1 m s m c E 1 E ρ C ρ ρ ρ J P = 1 λ J P = 3 m s m c E 3 E 1 m s m c λ ρ λ J P = 3 ρ J P = 3 Σ m s m c E E 3 m s m c ρ λ

19 Lambda baryon (positive parity) = ( ) = C s ψ s + C p ψ p ( ) = C s ψ s + C p ψ p + C dρ ψ dρ + C d λψ d λ ( ) = ψ p Φ Λ 1 + Φ Λ Φ Λ 7 + s-wave p-wave dρ-wave dλ-wave = = = jl = 3 = =

20 Lambda baryon (positive parity) C s = C p = Cdλ Cdρ = dρ-wave state ( ) = C s ψ s + C p ψ p ( ) = C s ψ s + C p ψ p + C dρ ψ dρ + C d λψ d λ ( ) = ψ p Φ Λ 1 + Φ Λ Φ Λ 7 + s-wave p-wave dρ-wave dλ-wave = C s = C dλ = Cdρ Cp p-wave state = = = 3 = s-wave(1s) state and dλ state C s = C p = Cdρ Cdλ = C p = Cdλ = Cdρ Cs

21 Lambda baryon (positive parity) In charm sector (M841MeV) 1 + ( ) = C s ψ s + C p ψ p + ( ) = C p ψ p + C dρ ψ dρ + C d λψ d λ Φ Λ 1 + Φ Λ E C s.998 C p E 1 C p.0006 C dρ.0004 Cdλ E 1 C p.0007 C dρ.0001 Cdλ.9998

22 Sigma baryon (positive parity) ( ) = C s ψ s + C p ψ p ( ) = C s ψ s + C p ψ p + C dρ ψ dρ + C d λψ d λ ( ) = ψ p Φ Λ 1 + Φ Λ Φ Λ 1 + s-wave p-wave dρ-wave dλ-wave = = = 3 = = = = 3

23 Sigma baryon (positive parity) ( ) = C s ψ s + C p ψ p ( ) = C s ψ s + C p ψ p + C dρ ψ dρ + C d λψ d λ ( ) = ψ p Φ Λ 1 + Φ Λ Φ Λ 1 + s-wave p-wave dρ-wave dλ-wave = = C s = 3 = = C p = Cdλ Cdρ dρ-wave state C p = Cdλ = Cdρ Cs C s = C dλ = Cdρ Cp p-wave state s-wave state = s-wave(1s) state and dλ state C p = Cdλ = Cdρ Cs C s = C p = Cdρ Cdλ = = 3

24 Sigma baryon (positive parity) In charm sector (M841MeV) 1 + ( ) = C s ψ s + C p ψ p + C dρ ψ dρ + C d λψ d λ ( ) = C p ψ p + C dρ ψ dρ + C d λψ d λ Φ Σ Φ Σ 5 + E E 3 C s.9984 C p.001 C s.000 C p 3 + C dρ.0004 Cdλ.000 C dρ.0004 Cdλ.9994 E E 3 C s.05 C p.01 C s.944 C p.0005 C dρ.004 Cdλ.94 C dρ.0007 Cdλ.05 E 4 C s.008 C p C dρ.0006 Cdλ.991 E 1 E C p.011 C dρ.005 Cdλ.984 C p.000 C dρ.001 Cdλ.998

25 Summary ü We calculate charmed baryon spectra and our result reproduce experimental data. ü In heavy quark limit states separate into groups and each group do not mix each other. ü In charm sector the wave function is almost same in the heavy quark limit.

26 Change of state Ξ and Ω parhcle ρ ϕ ρ ϕ ρ J P = 1 ρ ϕ ρ ϕ ρ J P = 1 Ξ Ξ cc Ω Ω c λ ϕ λ ϕ λ λ ϕ λ ϕ λ m Q Figur9.Probability of two states(ξ par@cle) q q q Q q m Q Figur10.Probability of two states(ω par@cle) q Q s s

27 Λ and Σ spectrum Λ(P ρ χ S ) (without LSTENSOR force) Λ(P ρ χ λ ) Σ(P ρ χ ρ ) Σ(P λ χ S ) Σ(P λ χ λ ) Λ(P λ χ ρ ) Σ(S χ S ) Σ(S χ λ ) m Q [MeV ]

28 Harmonic oscillator

29 Baryon spectroscopy of double charmed baryon

30 Angular momentum ( ) Λ( 3 + ) Λ 1 + ( ) Λ 5 + N lρ lλ L s_qq S / / / / / N lρ lλ L s_qq S / N lρ lλ L s_qq S / / / / / / / / / / / s qq

31 Angular momentum ( ) Σ( 3 + ) Σ 1 + ( ) Σ 5 + N lρ lλ L s_qq S / / / / / N lρ lλ L s_qq S / N lρ lλ L s_qq S / / / / / / / 0 1 1/ / / / s qq

32 Angular momentum ( ) Λ( 5 ) Λ 1 3 N lρ lλ L s_qq S / / / N lρ lλ L s_qq S / ( ) Σ( 5 ) Σ 1 3 s qq N lρ lλ L s_qq S / / / N lρ lλ L s_qq S /

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37 λ-mode and ρ-mode What can we find from the analysis in two excitation modes? We can know the decay pawern of Λ Q Σ Q ρ- mode λ- mode Which is decay pattern?