^{1,2}

^{,*}

^{3,4}

^{,†}

^{5}

^{,‡}

^{6,7}

^{8}

^{9,10}

^{9,10,11}

^{3}.

Semi-inclusive processes are very promising to investigate

Appearance of the exotic

In a previous paper

In this paper, we focus on inclusive production of states that can process via one pion exchange. Modulo final state interactions, pion exchange is a rather well tested hypothesis and given its proximity to the physical threshold it usually results in large cross sections. We test our model by comparing with data on the

The paper is organized as follows. The following section, Sec.

We consider the process

Semi-inclusive photoproduction of an axial-vector

The extension of the single-particle exchange mechanism of the exclusive reactions to semi-inclusive production is given by the generalized optical theorem

We note that the discontinuity of a

Diagrammatic representation of the generalized optical theorem. The semi-inclusive amplitude squared summed over all possible final states is related to the discontinuity of the

The second line is identified with the nucleon pole contribution to the elastic scattering of an off-shell pion (

In the approach of

With an appropriately chosen pion propagator and parametrization for the (off-shell)

Examining the asymptotic behavior of Eq.

The aspect of the model in Eq.

To this end we use the formalism of Ref.

The SAID partial waves are provided up to

Parameters for Reggeon contributions to

The total cross section as a function of

Low-energy behavior of the pion-nucleon elastic scattering as a function of the

In order to incorporate the off-shell pion in a minimal way we will assume that the dependence on the virtuality enters only through a kinematic change of phase space factors. For the low-energy regime we modify Eq.

The rescaling in Eq.

The model in Eq.

Diagrammatic representation of the triple Regge formula of Eq.

If we consider Eq.

Seeing the emergence of triple Regge behavior in the appropriate limit is reassuring, as the formula Eq.

Another consistency test for the semi-inclusive cross section formula in Eq.

Additionally, in this

Because

Alternatively, in analogy to the exclusive formalism of Ref.

We may thus calculate the

Experimental data on the photoproduction of exotic quarkoniumlike states is virtually nonexistent. In order to benchmark the predictions for

We begin with the comparison with the differential cross section data in Ref.

The only undetermined parameter is the

For comparison purposes, we calculate the inclusive cross section with the pion-nucleon interaction described with the full

Inclusive

Away from the highest bin we note that single pion exchange severely underestimates the production. Indeed, since at high energies the upper limit of integration

By integrating over

Inclusive

Total

We now turn to the quarkoniumlike states in the hidden charm and bottom sectors. We use the couplings that were previously calculated from the observed hadronic decays of the

Total cross section predictions for charged, charmonium-like

Contributions to the total cross section of near-threshold

High-energy production cross sections of the total inclusive process

In Fig.

Differential distributions with respect to the transverse momentum of

We have calculated the semi-inclusive photoproduction rates of the axial-vector, charmoniumlike

The analysis indicates that the inclusion of semi-inclusive final states produces cross sections upwards of tens of nanobarn for the

Similar semi-inclusive electroproduction at electron-hadron facilities has been considered recently in

The predictions presented here, while likely a lower-bound of the total expected semi-inclusive production of

This work was supported by the U.S. Department of Energy under Grants No. DE-AC05-06OR23177 and No. DE-FG02-87ER40365, the U.S. National Science Foundation under Grant No. PHY-1415459. It was also supported by Deutsche Forschungsgemeinschaft (DFG) through the Research Unit FOR 2926 (Project No. 40824754). D. W. is supported by National Natural Science Foundation of China Grant No. 12035007 and the NSFC and the DFG through the funds provided to the Sino-German Collaborative Research Center TRR110 “Symmetries and the Emergence of Structure in QCD” (NSFC Grant No. 12070131001, DFG Project-ID 196253076-TRR 110). V. M. is a Serra Húnter fellow and acknowledges support from the Spanish national Grants No. PID2019–106080 GB-C21 and No. PID2020–118758 GB-I00. M. A. is supported by Generalitat Valenciana under Grant No. CIDEGENT/2020/002.

We use the standard notations for

Chew-Low plot marking physical semi-inclusive kinematic region in missing mass and momentum transfer at fixed

Another choice is to replace

Finally we may consider the Cartesian variables

Peyrou plot for

The Lorentz-invariant cross section can be given as:

For comparison to experimental papers it is convenient as well to look at the mixed variable combination:

For the triple Regge kinematics, where

At low energies, we appeal to the amplitudes provided by SAID, which provided partial-wave amplitudes up to orbital angular momentum,

Each partial wave contributes to the total cross section of Eq.

Finally these last