Spectrum of <math display="inline"><mi>S</mi></math>- and <math display="inline"><mi>P</mi></math>-wave <math display="inline"><mi>c</mi><mi>c</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><msup><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mo>′</mo></msup></math> <math display="inline"><mo stretchy="false">(</mo><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mo>,</mo><msup><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mo>′</mo></msup><mo>=</mo><mover accent="true"><mi>u</mi><mo stretchy="false">¯</mo></mover><mo>,</mo><mover accent="true"><mi>d</mi><mo stretchy="false">¯</mo></mover><mo>,</mo><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover><mo stretchy="false">)</mo></math> systems in a chiral SU(3) quark model - INSPIRE

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Spectrum of $S$ - and $P$ -wave $c c \bar{q} {\bar{q}}^{'}$ $(\bar{q}, {\bar{q}}^{'} = \bar{u}, \bar{d}, \bar{s})$ systems in a chiral SU(3) quark model

Mar 22, 2024

9 pages

Published in:

Phys.Rev.D 109 (2024) 7, 074026

Published: Apr 1, 2024

e-Print:

2403.15187 [hep-ph]

DOI:

10.1103/PhysRevD.109.074026 (publication)

View in:

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Abstract: (APS)

Inspired by the resonance

T_{c c}^{+} (3875)

recently observed by the LHCb Collaboration, we systematically explore the

S

- and

P

-wave

c c \bar{q} {\bar{q}}^{'}

(\bar{q}, {\bar{q}}^{'} = \bar{u}, \bar{d}, \bar{s})

systems in a chiral SU(3) quark model. The Hamiltonian contains the kinetic energy, the one-gluon-exchange (OGE) potential, the confinement potential, and the one-boson-exchange (OBE) potential stemming from the coupling of quark and chiral fields. The Schrödinger equation is solved by use of the variational method with the spacial trial wave functions chosen as Gaussian functions. It is found that the lowest state has a mass 3879 MeV, isospin and spin-parity

I J^{P} = 0 1^{+}

, and quark constituent

c c \bar{u} \bar{d}

, in agreement with the experimentally observed

T_{c c}^{+} (3875)

. This state is approximately at the calculated

D D^{*}

threshold and has a root-mean-square radius of about 0.48 fm. These demonstrate that the

T_{c c}^{+} (3875)

can be accommodated as a stable and compact tetraquark sate in the chiral SU(3) quark model. All the other

S

- and

P

-wave

c c \bar{q} {\bar{q}}^{'}

(\bar{q}, {\bar{q}}^{'} = \bar{u}, \bar{d}, \bar{s})

states lie about 100 to a few hundreds MeV higher than the corresponding meson-meson thresholds and thus are not suggested to be candidates of stable and compact tetraquark states due to their fall-apart decays to two mesons.

Note:

9 pages, 2 figures

potential: confinement
energy: kinetic
gluon: exchange
quark: constituent
chiral
quark model
SU(3)
tetraquark
multiquark
stability

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