1 Recent results on charmed baryons at Belle

1 Recent results on charmed baryons at Belle Kiyoshi Tanida (Advanced Science Research Center, Japan Atomic Energy Agency) ELPH 研究会「様々なフレーバー領域で探る クォーク・ハドロン多体系の分光と構造」 4 Nov. 2020

2 Why charmed baryons? • Heavy quark in Baryon – Bare quark ≒ constituent quark – Makes a “static core”, light quarks play around Diquark correlation enhanced? – New symmetry – heavy quark symmetry Hyperfine doublet for heavy quark spin. Nucleon Charmed baryon HQS: spin Approximately conserved Indistinguishable pairs Light di-quark with inert charm?

Known charmed baryons • ~30 states are known • I(JP) are experimentally determined for very few states – none for charmed-strange baryons • Quark model predictions are quite good up to Ex～ 400 Me. V – assignment of I(JP) 3

4 Known charmed baryons (udc) (udc, uuc, ddc) (usc, dsc) (ssc)

Known charmed baryons • ~30 states are known • I(JP) are experimentally determined for very few states – none for charmed-strange baryons • Quark model predictions are quite good up to Ex～ 400 Me. V – assignment of I(JP) • There are many predicted states above that – Identification needs (at least) experimental determination of I(JP) – What are exotic and what are not? ? • Many other possible measurements 5

Belle experiment • √s~10. 6 Ge. V • Integrated Luminosity ~ 1 ab-1 • Almost 4 p, good momentum resolution (Dp/p～ 0. 1%), EM calorimeter, PID & Si Vertex detector • Finished ~10 years ago, still producing ~20 papers/year 6

Contents of the talk 0. Introduction 1. Spin-parity measurement of Xc(2970) [ar. Xiv: 2007. 14700, submitted to PRL] 2. Radiative decays of Xc(2790) & Xc(2815) [PRD 102, 071103(R)] 3. Λc → ηΛπ+ decay and L(1670) [ar. Xiv: 2008. 11575, submitted to PRD] 4. Future prospects 5. Summary 7

8 1. Spin-parity measurement of Xc(2970) [ar. Xiv: 2007. 14700, submitted to PRL]

9 Xc(2970) • Relatively low excitation energy – Good statistics & S/N ratio Belle, PRD 94, 05201 • Important decay mode: Xc(2970) Xc*(2645)p – Xc*(2645) has spin 3/2

Predictions by theory 10 Wide variety controversial

How to determine JP? • 11

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Angular distribution of Xc(2970) Xc*(2645)p 1/2 black 3/2 red 5/2 blue • Unfortunately, flat – any J can reproduce it 13

Angular correlation 14 • Cascade decay B 1 B 2 + p 1, B 2 B 3 + p 2 • B 1 may be unpolarized at initial state Decay angle distribution is uniform • If you take z to the direction of p 1 in the rest frame of B 2, B 2 is now polarized. • p 2 has angular dependence with respect to “z” (which is the direction of p 1) angular correlation.

Angular correlation of Xc(2970) Xc*(2645)p 1 Xcp 1 p 2 • Consistent with 1+3 cos 2 q J = 1/2 [see also: Arifi, Hosaka, Nagahiro, and Tanida, PRD 101, 111502(R)] 15

Heavy quark (spin) symmetry • For heavy quarks, spin effect becomes small Heavy quark spin symmetry – In quark model, this appears as 1/m. Q factor in spin dependent interactions. (spin-spin, spin-orbit, . . . ) – Directly derivable from QCD • Makes “fine-structure” – For J≠ 0 “core” (called brown-muck), J-1/2 and J+1/2 doublet appears J(=0) DE J+1/2 J-1/2 16

Heavy quark spin in decay • 17

Xc* and Xc’ • 18

Result • We got – Consistent with P=+ and brown-muck spin sℓ=0 only. • Therefore, the parity is + – with sℓ=0. 19

Discussion • We got JP=1/2+. What can we say from this? • This is the same as infamous Roper resonance, N(1440), the first excited state of nucleon. – Excitation energy (~500 Me. V) is also the same. • Difficult to explain Roper in quark model – Single quark excitation: 1 st excited state should be a negative parity state (ex. N(1530)). – Surprisingly, difficult even in Lattice QCD. – The present measurement gives a hint. • How about other flavors? 20

21 • Roper-like states are known for other light baryons.

Flavor universality? • Lc case: Yes, Lc(2765) • Lb case: seemingly yes with slightly smaller excitation energy (~450 Me. V) Arifi, Nagahiro, Hosaka, and Tanida, PRD 101, 111502 22

Flavor universality? • It seems the state is flavor independent – JP=1/2+ – Same excitation energy – although quark masses are very much different. • One possibility – collective excitation? (deformation, rotation, vibration, …) – Deformation case is known in nuclear physics • Anyway, very important information to understand the Roper resonance. 23

24 2. Radiative decays of Xc(2790) & Xc(2815) [PRD 102, 071103(R)]

Xc(2790) & Xc(2815) • Presumably, a HQS doublet with L=1 orbital excitation (l-mode). JP=1/2 - and 3/2 • Clearly seen in pion decays to Xc’ and Xc(2645) Xc(2790)+ Xc(2790)0 Xc(2815)+ Xc(2815)0 25

Radiative decays to ground Xc 26 • Signals are clearly seen for neutral ones, but not for charged ones.

Transition rates • 27

28 3. Λc → + ηΛπ decay and L(1670) [ar. Xiv: 2008. 11575, submitted to PRD]

+ Lhp Invariant mass Lc Lhp+ Lc S 0 hp+ (S 0 Lg, g missing) BG 29

Dalitz plot S*(1385)+ a 0(980) • Includes non-Lc BG • Resonances are clearly seen L*(1670) 30

Resonances: S(1385) & L(1670) • For each M(Lh)/M(Lp+) bin, count Lc in the Lhp+ mass spectrum – Non-Lc background is excluded L(1670) S(1385) 31

Results Branching ratios Mass & widths 32

Discussions • L(1670)p+, S 0 hp+ modes are measured for the first time. • BRs for Lhp+ and S(1385)+h are consistent with previous measurements, and more precise. • Mass & width of L(1670) and S(1385)+ – S(1385)+: consistent with PDG within uncertainty – L(1670): determined from peaking structure for the first time with a good accuracy. 33

5. Future prospects

a 0(980) • Clearly seen in Lc Lhp and Lc LK 0 SK+ Lc Lhp+ Lc LK 0 SK+ X(1690) 35

4 quark state? • 36

Super. KEKB and Belle II Goal: x 50 more statistics than Belle 37

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Belle II integrated luminosity Achieved Prospect • Instantaneous luminosity already exceeded Belle • Integrated luminosity will exceed Belle by 2022 • Goal: 50 ab-1 around 2031. 39

Belle II possibilities • 40

Summary 41 • JP of Xc(2970) – Angular correlation J=1/2, decay branch P=+ – same as infamous Roper resonance Gives a strong hint on the nature of enigmatic Roper • Radiative decays of Xc(2790) & Xc(2815) – Observed for neutral but not for charged – Quite strong transition, to be compared with theories • Lc Lhp+ decay – Measured branching ratios, L(1670) mass/width, etc. – a 0(980) also seen; interesting to confirm 4 -quark nature. • More measurements in future with Belle II

42 Backup

Old QM calc. • Old QM calc. by Copley et. Al. [PRD 20 (1979) 768] • A few states (1/2 -, 3/2+, …) are within 50 Me. V. • Still, more states were predicted for I=1 – ruled out. 43

Recent QM calc. 44 • Latest QM calc. by Yoshida et al. [PRD 92 114029] • No I=0 state within 50 Me. V. • Limitation of QM?

How to determine I(JP)? • 45

How to determine I(JP)? • 46

Reference mode: Lc/Sc(2765)+ Scp 47 Be lle pr el im in a ry (a) Inclusive Lcp+p(b) With Sc selection • Analyzed with full data of Belle (980 fb-1) • Clear peaks are observed • Fit with Breit-Wigner functions to extract yield.

48 Sc(2765)++/0 Sc++/0 p 0 [Belle-Conf-1905, Ar. Xiv: 1908. 06235] Sc++p 0 Belle preliminary Expectation for I=1 • No peak seen Isospin is not 1, but 0. The name is indeed Lc(2765) S c 0 p 0

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Prof. Hyodo’s slide 50

51 SPIN

Decay angle distribution • 52

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An example • Lc(2880) by Belle (PRL 98 (2007) 262001) • z-axis is taken to be missing momentum direction of e+e- Lc(2880) + X in the rest frame of Lc(2880) may not necessarily be polarized. • Fit needs 4 th order polynomial J=5/2 or higher 54

Example of correlation 55 • Determination of W spin by Babar (PRL 97 (2006) 112001) • Cascade process Xc 0 W- + K+ (1/2 ? + 0), W- L + K- (? 1/2 + 0) • If J=1/2 uniform 3/2 3 cos 2 q+1 J=3/2, as QM expects (note: parity violation is not significant and ignored)