Hidden-Charm Pentaquarks in Constituent Quark Models
Hidden-charm Pentaquarks in Constituent Quark Models
Makoto Oka
Tokyo Institute of Technology and Advance Science Research Center, JAEA Exotic Hadrons
Hadron is a color-singlet composite of quarks and gluons. q-qbar (meson): 3 3=1¯ 8 q-q-q (baryon) : 3 3 3=1 8 8 10 and MORE . . . g-g (glueball) : 8 8=1 8 8 10 10 27 q-qbar-g (hybrid): 3 3¯ 8=1 (3 8) 10 10 27 q2-qbar2 (tetra-quark): 3 3 3¯ 3¯ = (2 1) (4 8) 10 10 27 q4-qbar (penta-quark): 34 3¯ = (3 1) ... q6 (di-baryon) : 36 =(5 1) ...
!2 Multi-Quark (MQ) dynamics
“Extrapolation” to MQ hadrons is not trivial. “Color Confinement” is a key in the MQ dynamics. Exotic Hadrons are “Colorful” ! (Lipkin@YKIS06) bar (qq )8 or (qq)6 are allowed only in the MQ hadrons.
q q q q
8 6
q q q q Novel Dynamics
!3 What we learn from MQ hadrons?
CONFINEMENT of Quarks What is the Mechanism and Dynamics of quark confinement? Modeling of confinement Bag model v.s. Potential model
COUPLINGS of Resonances to Hadronic states How decay channels and widths are determined? Mechanisms of the strong decays Possibility of narrow resonances
!4 Bag Model
MIT Bag Model: Quarks (and gluons) are confined (and, in total, color-singlet) in a “Bag”. The bag is self-sustained by the “bag energy”. Two conditions at the bag surface - No outflow of color from the surface n j =0 · c |surface j µ =¯q µ q + (gluon color current) c 2
- Pressure balance of two phases Pin = Pout
Pin = (pressure by quarks and gluons)
Pout = (pressure by the bag energy)
Ebag = BV
!5 Bag Model
Energy of the hadron containing massless quarks 4 R3 4 BR3 E(R)=B + E = + i 3 i 3 R i i dE(R) n 1/4 = B4 R2 i i =0 R(n)= dR R2 4 B E = E(R(n)) = (const) B1/4n3/4 n
En is a convex function of n, that is E2n < 2En. If there is no other interaction, the binding energy is larger as the size of the system gets larger. The energy scale is B1/4 ~ 200 MeV. It is not surprising to have a bound state of binding energy ~ 100-200 MeV.
!6 Potential Model
Two-body confinement forces Force without color-cluster saturation is no good. n(n 1) V = v(rij) V v ~ gravity 2 i