### Speaker

Dr
Ballari Chakrabarti
(Jogamaya Devi College, Kolkata, India)

### Description

After the recent discovery of charmed pentaquarks $P_c^*$ (4380)
and, $P_c^*$ (4450) [1] quick search has been set in for
other pentaquarks. In the present work, the masses
of the cryptoexotic pentaquarks with hidden beauty
$P_b^*$ ($uudb\bar{b}$), and
strangeness $P_s^*$ ($uuds\bar{s}$) have been estimated
considering a di-hadronic
state consisting of a meson and a baryon. In addition to this,
other exotic heavy pentaquarks such as,
$\Theta_c^0$($uudd\bar{c}$), $\Theta_b^{+}$($uudd\bar{b}$),
$\Theta_{cs}^{++}$ ($cuud\bar{s})$, $\Theta_{bs}^{+}$ ($buud\bar{s}$)
and related family members have been probed. The results agree well with
the existing literature [2]. The interaction
between the meson and the baryon, i.e., the residual interaction of the
confined gluons has been taken to be Van der
Waals’ type of molecular interaction
$V(r_{12})=-(K_{mol}/r_{12})\exp(-c^2 r_{12}^2/2)$ , where, $K_{mol}$
is the residual strength of the
strong interaction molecular coupling, $c$ is the effective
color screening of the confined gluons. The mass formula for
calculating the heavy pentaquark masses now stands out to be,
\begin{equation}
M_ {pentaquark} = M_{meson} + M_{baryon} + E_{BE}+ E_{SD}
\end{equation}
Here, $E_{BE}$ and $E_{SD}$ represent the binding energy
and the hyperfine spin interaction of the system, which are being
estimated in the present work following the prescription
of a statistical model, and are given by,
$
E_{BE} = \frac{2.25 K_{mol}}{r_{12}} \left [_{2}F_2(1.5,1.0),(2.75,2.25),
-\beta \right ]
$,
with $\beta=c^2r_{12}^2/2$, and Re$\beta >0$, and
$
E_{SD} = \frac{8}{9} \frac{\alpha_s}{M_{meson} M_{baryon}}
(\vec{S_1}.\vec{S_2}) |\psi_0|^2
$. Here,
$\alpha_s$ is the strong interaction constant, taken to be equal to
0.59. $K_{mol}=0.65$, and $c=50$ MeV [3].
The masses of the cryptoexotic pentaquarks, as estimated
in our calculation, are given for $P_b^*$(1) ,
$P_b^*$(2) , $P_s^*$(1) , and
$P_s^*$(2) are 10.638, 10.881, 2.110, and 2.381 GeV respectively.
The masses of $\Theta_c^0$ , $N_c^0$ , $\Xi_c^0$ ,
$\Theta_{cs}^{++}$, $\Theta_b^+$, $N_b^+$, $\Xi_b^+$,
and $\Theta_{bs}^+$ have been estimated as, 2.656, 2.752, 2.905, 2.752,
6.043, 6.127, 6.366, and 6.128 GeV respectively.
The reported values for the masses of these exotic
pentaquarks may inspire furute experiments.
References:
[1] R. Aaij et al, (LHCb Collab.), Phys. Rev. Lett. 115 (2015),
072001.
[2] D. Diakonov, arXiv hep-ph/1003.2157; V. Kopeliovich et al,
arXiv hep-ph/1510.05958; R. Jaffe et al, Phys. Rev. Lett. 91
(2003), 232003; M. Karliner et al, arXiv hep-ph/1030.7343.
[3] B. Chakrabarti et al, Phys. Scr. 79 (2009), 025103.

### Primary author

Dr
Ballari Chakrabarti
(Jogamaya Devi College, Kolkata, India)