On large mass $γγ$ and $γ$-meson photoproduction
L. Szymanowski B. Pire S. Wallon



NCBJ, 02-093 Warsaw, Poland

^*E-mail: Lech.Szymanowski@ncbj.gov.pl 

CPHT, CNRS, École polytechnique, I.P. Paris, 91128-Palaiseau, France

LPT, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405, Orsay, France & 

Sorbonne Université, Faculté de Physique, 4 place Jussieu, 75252 Paris Cedex 05, France

Enlarging the set of hard exclusive reactions to be studied in the framework of QCD collinear
factorization opens new possibilities to access generalized parton distributions (GPDs). We
studied the photoproduction of a large invariant mass photon-photon or photon-meson pair in
the generalized Bjorken regime which may be accessible both at JLab and  at the EIC.




§ INTRODUCTION

Deeply virtual Compton scattering (DVCS) has proven to be a promising tool to study the three
dimensional arrangement of quarks and gluons in the nucleon <cit.>. The
crossed reaction, the photoproduction of a timelike highly virtual photon which materializes
in a large invariant mass lepton pair (dubbed TCS for timelike Compton scattering) is under
study at JLab. Its amplitude shares many features with the DVCS amplitude
<cit.> but with significant and interesting differences <cit.> due to the analytic behavior in the large scale Q^2
measuring the virtuality of the incoming (q^2 =-Q^2) or outgoing  (q^2 =+Q^2) photon. In
order to enlarge the set of experimental data allowing the extraction of GPDs, we studied the
generalization of TCS to the case of the photoproduction of large invariant mass photon-
photon and photon-meson pairs. Although factorization of GPDs from a perturbatively calculable coefficient function has not yet been proven for these processes, they are a natural 
extension of the current picture in the framework of collinear QCD factorization.


§ Γ N →ΓΓ N'


The photoproduction of a photon pair <cit.>
 shares with DVCS and TCS  the nice feature to be a purely electromagnetic amplitude at
the Born level. Charge parity however selects a complementary set of GPDs, namely the charge
parity - odd GPDs related to the valence part of quark PDFs, with no contribution from the
gluon GPDs. The analytic form of the Born amplitude calculated from the graphs shown on Fig. <ref> is very peculiar since the coefficient
function turns out to be proportional to δ(x±ξ) leading through the usual
momentum fraction integration to a scattering  amplitude  proportional to the GPDs taken at
the border values x=±ξ. For illustration, Fig. <ref> displays the  
diphoton invariant squared mass dependence of the unpolarized differential cross section on a proton at t = t_min and s_γ N= 20 (resp. 100, 10^6) GeV^2 (full, resp. dashed, dash-dotted multiplied by 10^5). 












§ Γ N →ΓΡ N' : THE QUEST FOR TRANSVERSITY GPDS

The photoproduction of a γρ pair <cit.>
has the rare feature of being sensitive to chiral-odd transversity quark GPDs at the leading
twist level, because of the leading twist chiral-odd distribution amplitude of the
transversely polarized vector meson. Indeed, except for higher twist amplitudes which suffer
from end-point divergences and heavy meson neutrino production amplitudes
<cit.>  which may be difficult to measure, one needs exclusive
processes with more particules in the final state to access transversity GPDs
<cit.>.


We show on Fig. <ref> the cross section for the production of a transversely polarized ρ in conjunction with a photon, on a proton or a neutron target. The curves show the  sensitivity to the transversity GPD parametrization. Cross sections are sufficiently high for the process to be measurable at JLab <cit.>.





§ Γ N →ΓΠ N'




Since deep electroproduction of a π meson has been shown to resist at moderate Q^2 to
leading twist dominance in the factorization framework, it has been tempting to  put the
blame on the peculiar chiral behavior of the higher twist (chiral-odd) pion DA as compared
with the leading twist (chiral even) pion DA. However, the dominance of higher twist contributions may not be a common feature of all exclusive amplitudes involving the pion DA. To check this idea, we propose <cit.>
 to study  the related process  γ N →γπ N'
where the same pion DAs appear. It turns out that the axial nature of the pion leading twist DA infers a high sensitivity of the amplitudes to the axial GPDs H̃(x,ξ,t) as shown on Fig. <ref> where the cross sections for the reaction γ p →γπ^+ n and γ n →γπ ^-p are displayed for two different sets of axial GPDs. The rates are of the same order as for the γρ case and we thus expect these reactions to be measurable at JLab.



§ CONCLUSIONS

The processes discussed here, because of the absence of gluon and sea quark contributions are not enhanced at high photon energy (or small skewness ξ) and they are thus more accessible at JLab than at EIC. However, since a high energy electron beam is also an intense source of medium energy quasi real photons (q^2≈ 0), with fractions of energy y = q.p/k.p=0(10^-3), (k and p being the initial electron  and nucleon momenta), one may expect the γγ and γρ_L channels to be accessible at moderate values of s_γ N. Prospects at higher values of s_γ N (and smaller values of the skewness ξ) are brighter for the γπ^0 channel which  benefits from the contributions of small ξ sea-quark and gluon GPDs. 


§ ACKNOWLEDGMENTS

We acknowledge the collaboration of R. Boussarie, G. Duplancic, K. Passek-Kumericki, A. Pedrak and J. Wagner for the works reported here. L. S. is supported by the grant 2017/26/M/ST2/01074 of the National Science Center in Poland. He thanks the French LABEX P2IO and the French GDR QCD for support. 



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