Photoproduction of hidden charm pentaquark states $P_c^{+}(4380)$ and $P_c^{+}(4450)$

We propose to study the pentaquark candidates of $P_c^{+}(4380)$ and $P_c^{+}(4450)$ in $J/\psi$ photoproduction and look for further experimental evidence for their nature. Since the photoproduction process does not satisfy the so-called “anomalous triangle singularity” condition their presence in $J/\psi$ photoproduction would conclude that they should be genuine states and provide further evidence for their existence.

Figure 1

The diffractive process via Pomeron exchange in $J/\psi$ photoptroduction.

Figure 2

The $s$ and $u$-channel production of pentaquark states $P_c^{+}$ in $J/\psi$ photoptroduction.

Figure 3

The total cross section of $\gamma p\to J/\psi p$ in terms of the c.m. energy. The red dashed, blue dotted, green dot-dashed and black solid curves are the contributions from Pomeron, $P_c$ with spin $3/2$, $P_c$ with spin $5/2$ and the coherent sum of all. (a) shows $(3/2^{+},5/2^{-})$ combination. (b) shows $(3/2^{-},5/2^{+})$ combination. The coupling constants [Eq. (21)] between $J/\psi p$ and the two $P_c$ states are extracted by assuming $J/\psi p$ saturates all their total widths. The experimental data are from Refs. [24, 25, 26].

Figure 4

The caption is the same as that of Fig. 3 except that the couplings are extracted by assuming $J/\psi p$ channel only accounts for 5% of their total widths.

Figure 5

Differential cross section of $\gamma p\to J/\psi p$ in terms of $\cos (\theta )$ with $\theta$ the relative angle between photon and $J/\psi$ in the c.m. frame. The red dashed, blue dotted, green dot-dashed and black solid curves are the contributions from Pomeron, $P_c$ with spin $3/2$, $P_c$ with spin $5/2$ and the coherent sum of all with the combination $(3/2^{+},5/2^{-})$. (a), (b), (c) and (d) are at the center energy $W=4.15\mathrm{GeV}$, 4.38 GeV, 4.45 GeV and 4.5 GeV, respectively.

Figure 6

Differential cross section of $\gamma p\to J/\psi p$ similar to Fig. 5 except that quantum numbers of these two pentaquark states are $(3/2^{-},5/2^{+})$.