Quark dynamics studied in charmed baryons April 20, 2015ASRC Seminar1 Atsushi Hosaka, RCNP, Osaka ASRC Seminar Contents 1. Introduction 2. Structure: How ρλ modes appear in the spectrum 3. Charmed baryon productions and decays Baryons with heavy quark(s) may disentangle light quark dynamics With Noumi, Shirotori, Kim, Sadato, Yoshida, Oka, Hiyama

1. Introduction April 20, 2015ASRC Seminar2 Quark model and EXOTICS: Now 51 years old But no colors ~ glues

Fermi Lab SLAC LHC April 20, 2015ASRC Seminar3 BES

Quarks bonding differently at LHCb April 20, 2015ASRC Seminar4 So until last week there were two known types of hadron LHCb has just confirmed what data from other experiments had already led us to suspect. There is a third way. Phys. Rev. Lett. 112, Z + (4430)

Z(3900) Z(4430) 5 X(3872) Above the threshold qq creation and rearrangement of multiquarks ? What governs them ? Constituent quarks, mesons, diquarks... Are heavy quarks useful to know it? April 20, 2015ASRC Seminar Meson-like Diquarks

April 20, Charmed baryons HO and no ss Degenerate λ and ρ Distinguished Isotope-shift: Copley-Isgur-Karl, PRD20, 768 (1979) A heavy quark may distinguish the fundamental modes λ and ρ  place to look at diquark correlations Mixing of ASRC Seminar

Harmonic oscillator April 20, 2015ASRC Seminar7 x1x1 x2x2 x3x3

String April 20, 2015ASRC Seminar8 ρ-mode λ-mode 120°

QCD sum rule April 20, 2015ASRC Seminar9 PRD91, (2015)

Diquark Density correlations April 20, 2015ASRC Seminar10 Alexandrou, deForcrand, Lucini PRL 97, (2006) cosθ 1.0 r θ r = 0.69 fm r = 0.47 fm r = 0.35 fm Good diquark Bad diquark Indicates significant attraction between quarks in good diquark pair See also recent QCD sum rule study, Chen et al arXiv: [hep-ph], To appear in PRD

S=3/2 S=1/2 1/2 + 1/2 – 1/2 + 3/2 + 1/2 – 1/2 + 3/2 + 3/2 – 5/2 + ? ΞCΞC [GeV] ? 1/2 + 3/2 + ΩCΩC csq css ΞCΞC Ξ’ C 1hω ? 1 Ξ + cc April 20, 2015ASRC Seminar11 Spectroscopy: More states at J-PARC Excited energies, decay widths are smaller Two distinct modes may be different

Spectrum and WF's as M Q is varied April 20, 2015ASRC Seminar12 Yoshida, Sadato, Hiyama, Oka, Hosaka Model Hamiltonian Solved by the Gaussian expansion method Roberts-Pervin, IJMPA, 23, 2817 (2008)

Excitation spectrum Σ(1/2 + ) Λ(1/2 + ) Σ(3/2 + ) Λ(1/2 , 3/2  ) Λ Σ  Σ Λ Hyperons April 20, Charmed baryons Σ c (1/2 + ) Λ c (1/2 + ) Σ c (3/2 + ) Λ c (1/2 , 3/2  ) ΛcΛc ΣcΣc ΛcΛc ΣcΣc ΣcΣc ASRC Seminar  l = 0, ground states   l = 1, excited states 

Excitation spectrum Σ(1/2 + ) Λ(1/2 + ) Σ(3/2 + ) Λ(1/2 , 3/2  ) Λ Σ  Σ Λ April 20, Σ c (1/2 + ) Λ c (1/2 + ) Σ c (3/2 + ) Λ c (1/2 , 3/2  ) ΛcΛc ΣcΣc ΛcΛc ΣcΣc ΣcΣc ASRC Seminar sc Hyperons Charmed baryons SU(3) HQ

Wave function April 20, 2015 ASRC Seminar 15 M Q [GeV] Probability |c| 2 Mixing of e.g. λ-mode dominant state: How much the other mode mixes? Λ c * is almost pure λ mode  Reflect more qq nature Λ solid Σ dashed

April 20, SU(3) spin Flavor Orbital u d s u d s..., To understand better -- Wave functions ASRC Seminar

April 20, SU(3) HQ To understand better -- Wave functions ASRC Seminar

April 20, SU(6) HQ mix To understand better -- Wave functions ASRC Seminar

Intermediate summary April 20, 2015ASRC Seminar19 Heavy quark spectroscopy will reveal uniquely the dynamics of constituents Isotope shift may resolve two diquark modes collective and internal Λ baryons may have more chance to see the two modes separately Systematic study from strange to heavy is needed

3. Productions April 20, 2015ASRC Seminar20 Production rate (Λ c /Λ) and Ratios (B c * /B c ) π + N  D * + Λ c reactions

Strategy: Forward peak (high energy)  t-channel dominant We look at: (1) Rates (Λ c /Λ s ) by the Regge model, D * Reggeon (2) Ratios of B c * (λ modes) / B c by a one step process of Qd picture for λ-mode 21 Pion-induced reaction π + p  D * + B c * π D*D* Bc*Bc* p D * Reggeon April 20, 2015 ASRC Seminar 21

p π, Lab = 4.5 GeV cosθ – D.J. Krennel et al PRD6, 1220 (1972) April 20, 2015ASRC Seminar22

Absolute values April 20, 2015ASRC Seminar23 Regge model (Sang-Ho Kim, in preparation) Charm/strangeness ratio: 10 –4 ~ 10 –6  several nb near the threshold strangeness charm ~ 10 –5 We have examined: K * (strange) productions D and D * Reggeon Angular dependence Small u-channels ~ Baryon Regge Normalizations

April 20, 2015ASRC Seminar24 Effective Lagrangian method Cross section does not fall off ↔ Unitarity

April 20, 2015ASRC Seminar25 Vector Reggeon dominance K(p-scalar) K * (vector) Angular dependence prefers vector-Reggeon Energy dependence seems There is some discrepancy in the very forward region

April 20, 2015ASRC Seminar26 Relative rates of (B c * /B c ) One step process for Qd λ-mode λ D*-exchanges π Bc*Bc* D * ~ Transverse = (Geometric) × (Dynamic) CG coefficients Quark model estimate N

Dynamical part ~ radial integral April 20, 2015ASRC Seminar27 GS Transitions to excited states are not suppressed Excited states q eff : the momentum transfer ~ Large

Results Strange k π CM = 1.59 [GeV], k π Lab = 5.8 [GeV] April 20, 2015ASRC Seminar Charm k π CM = 2.71 [GeV], k π Lab = 16 [GeV]

HQ doublet l = 1 l = 2 l = 0 1 : 2 3 : 2 April 20, 2015ASRC Seminar29

4. Decays April 20, 2015ASRC Seminar30 ρ -mode λ -mode Bc*Bc* McMc N π Bc*Bc* BcBc

Pion emission – quark model --on going April 20, 2015ASRC Seminar31 Λ c * (2595, 1/2 – ) Λ c * (2625, 3/2 – ) Σ c (2455, 1/2 + ) Σ c * (2520, 3/2 + ) π ~ 140 MeV Things to be looked at: Pion emission ~ very near the threshold Place to look at the two independent operators Λc*Λc* Σc*Σc*

ASRC Seminar Pion emission by the λ motion Pion emission – quark model --on going April 20, Diquark correlation may suppress pion emission λ-mode decay π Λ c * (2625, 3/2 – ) π Σ c (2455, 1/2 + ) overlap vanishes with strong correlation Σ c (2455, 1/2 + ) + π  Λ c * (2625, 3/2 – ) i f

Possible selection rules April 20, 2015ASRC Seminar33 ρ- modes Two conditions must be satisfied for baryons and for diquarks

Possible selection rules April 20, 2015ASRC Seminar34 Example: This is a forbidden process

Possible selection rules April 20, 2015ASRC Seminar35 Example:

April 20, 2015ASRC Seminar36 Radiative decay: 1/2 –  1/2 + E1 λ mode Good diquark 0 + l λ = 1 3P0 diquark 0 – lρ = 1 ρ mode 0 –  0 + is forbidden Good diquark 0 +

April 20, 2015ASRC Seminar37 Radiative decay: 5/2 –  1/2 + M2, E3 λ mode 3 S 1 diquark 1 + l λ = 1 3 P 2 diquark 2 – lρ = 1 ρ mode 2 –  0 + is only M2 Good diquark 0 + Both M2 E3

Summary Charmed baryons: yet unexplored region J-PARC plans to observe them Production rate: Charm/Strangeness: 10 –4 – 10 –6 Abundant production of excited states Decay selection rules are helpful April 20, 2015ASRC Seminar38