Production of pentaquarks in $pA$-collisions

We argue that a hidden-charm pentaquark recently observed in weak decays of ${\mathrm{\Lambda }}_b$ can be produced in proton-nucleus collisions without electroweak intermediaries. We analyze the production cross section for the case when a pentaquark is a molecule of charmonium and a light baryon, as suggested by some models of pentaquark structure, and find that the cross section is sizable. This process can be studied both in collider and in fixed-target experiments. In the former case, the pentaquarks are produced at very forward rapidities, whereas in the latter case, pentaquarks are produced with relatively small rapidities and can be easily detected via invariant mass distribution of a forward $J/\psi$ and a comoving proton. Additionally, the suggested process allows us to check the existence of a neutral pentaquark $P_c^0$ (an isospin partner of $P_c^{+}$) predicted in several models. The rapidity and transverse momentum distributions of pentaquarks could provide comprehensive information about the $\overline{c}c$ component of this exotic baryon.

Figure 1

Perturbative diagrams contributing to the pentaquark production if the $\overline{c}c$ pair is in a color singlet state. Diagrams shown in the diagrams (a) and (b) probe the $P$-wave and $S$-wave component of the $\overline{c}c$ dipole in a pentaquark. Each squared block implies a sum of diagrams with a gluon attached to each of the quarks. In diagram (b) both emissions before and after interaction with a target are possible.

Figure 2

Comparison of the effective two-nucleon wave function ${\mathrm{\Phi }}_{2N}$ (30) (green solid lines) with components of a realistic deuteron wave function evaluated with Argonne $v_{18}$ potential [59] (blue dashed lines). The function ${\mathrm{\Phi }}_{2N}$ is scaled by an arbitrary factor to match the peak value of the deuteron wave function component $u(r)$.

Figure 3

Left: $\alpha$ dependence of the light-cone correlator ${\mathrm{\Phi }}_{2N}(\alpha ,r_{\perp })$ for several fixed values of $r$. As we can see, the peak is very narrow. Right: Comparison of the light-cone wave function ${\mathrm{\Phi }}_{LC}^{2D}(r_{\perp })$ from (33) (solid line) and 3D wave function (30) (dashed line). $\sqrt{m_N}$ is added to match dimensions.

Figure 4

Dependence of the overlap of proton and pentaquark wave functions on $x_1$ and ${\alpha }_c$.

Figure 5

Rapidity dependence of the cross section $d\sigma /dy$ [if the pentaquark has a $\overline{c}c$ pair in the color singlet $S$-wave (left) and $P$-wave (right)]. $y$ is a pentaquark rapidity in a nucleon-nucleon center of mass (8); $y_{RF}$ is a rapidity in the nucleus rest frame (11).

Figure 6

Dependence of the integrated cross section ${\sigma }^{(a)}$ (singlet $P$-wave $\overline{c}c$ pair) on pentaquark parameters $⟨r_{cc}⟩$ and $⟨R_{cc}⟩$ for $\sqrt{s}\approx 7\mathrm{TeV}$.

Figure 7

Diagrams (1–6) contributing to $\overline{c}c$ production in color singlet $S$-wave.