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MULTIQUARK STATES IN THE COVARIANT QUARK
CONFINEMENT MODEL
M.A. Ivanov 1†
(1) JINR, Dubna
† E-mail: ivanovm@theor.jinr.ru
We refine [1] the relativistic constituent quark model developed in our previous papers
to include the confinement of quarks. It is done, first, by introducing the scale integration
in the space of alpha-parameters, and, second, by cutting this scale integration on the
upper limit which corresponds to an infrared cut-off. Such trick allows one to remove all
possible thresholds available in the initial quark diagram. The cut-off parameter is taken
to be the same for all physical processes. We adjust other model parameters by fitting
the calculated quantities of the basic physical processes to available experimental data.
As an application, we calculate [2] in a parameter free way, the form factors of the
B(B s ) → P(V)-transitions in the full kinematical region of momentum transfer. By
using the calculated form factors, we evaluate the widths of the nonleptonic B s -decays
into Ds − D s + ,Ds ∗− D s + ,Ds − Ds
∗+ and Ds ∗− Ds ∗+ . These modes give the largest contribution
to ∆Γ for the B s − ¯B s system. We also treat the nonleptonic decay B s → J/ψ + φ.
Although this mode is color suppressed this decay has important implications for the
search of possible CP-violating New Physics effects in B s − ¯B s mixing.
We extend [3] our approach to the baryon sector. In our numerical calculation we use
the same values for the constituent quark masses and the infraredcutoff ashave been used
in the meson sector. In a first application we describe the static properties of the proton
and neutron, and the Λ-hyperon (magnetic moments and charge radii) and the behavior
of the nucleon form factors at low momentum transfers. We discuss in some detail the
conservation of gauge invariance of the electromagnetic transition matrix elements in the
presence of a nonlocal coupling of the baryons to the three constituent quark fields.
Wefurtherexplore[4-5]theconsequences oftreatingtheX(3872)mesonasatetraquark
bound state. We calculate the decay widths of the observed channels X → J/ψ+2π(3π),
X → ¯D 0 + D 0 + π 0 and X → γ + J/ψ. For a reasonable value of the size parameter
of the X(3872) meson we find consistency with the available experimental data. We also
calculate the helicity and multipole amplitudes of the process X → γ+J/ψ, and describe
howthey canbeobtainedfromthecovariant transition amplitude bycovariant projection.
References
[1] T. Branz, A. Faessler, T. Gutsche, M. A. Ivanov, J. G. Körner and V. E. Lyubovitskij,
Phys. Rev. D81, 034010 (2010).
[2] M. A. Ivanov, J. G. Körner, S. G. Kovalenko, P. Santorelli and G. G. Saidullaeva,
Phys. Rev. D85, 034004 (2012).
[3] T. Gutsche, M. A. Ivanov, J. G. Körner, V. E. Lyubovitskij and P. Santorelli,
arXiv:1207.7052 [hep-ph].
[4] S. Dubnicka, A. Z. Dubnickova, M. A. Ivanov and J. G. Körner, Phys. Rev. D D81,
114007 (2010).
[5] S. Dubnicka, A. Z. Dubnickova, M. A. Ivanov, J. G. Koerner, P. Santorelli and
G. G. Saidullaeva, Phys. Rev. D84, 014006 (2011).
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