On large mass γγ and γ -meson photoproduction
SSeptember 30, 2019 0:29 ws-procs961x669 WSPC Proceedings - 9.61in x 6.69in INT18˙Szymanowski page 1 On large mass γ − γ and γ − meson photoproduction L. Szymanowski ∗ NCBJ, 02-093 Warsaw, Poland ∗ E-mail: [email protected]
B. Pire
CPHT, CNRS, ´Ecole polytechnique, I.P. Paris, 91128-Palaiseau, France
S. Wallon
LPT, CNRS, Univ. Paris-Sud, Universit´e Paris-Saclay, 91405, Orsay, France & Sorbonne Universit´e, Facult´e de Physique, 4 place Jussieu, 75252 Paris Cedex 05, France
Enlarging the set of hard exclusive reactions to be studied in the framework of QCDcollinear factorization opens new possibilities to access generalized parton distributions(GPDs). We studied the photoproduction of a large invariant mass photon-photon orphoton-meson pair in the generalized Bjorken regime which may be accessible both atJLab and at the EIC.
Keywords : GPD, transversity, EIC
1. Introduction
Deeply virtual Compton scattering (DVCS) has proven to be a promising tool tostudy the three dimensional arrangement of quarks and gluons in the nucleon . Thecrossed reaction, the photoproduction of a timelike highly virtual photon which ma-terializes in a large invariant mass lepton pair (dubbed TCS for timelike Comptonscattering) is under study at JLab. Its amplitude shares many features with theDVCS amplitude but with significant and interesting differences due to theanalytic behavior in the large scale Q measuring the virtuality of the incoming( q = − Q ) or outgoing ( q = + Q ) photon. In order to enlarge the set of ex-perimental data allowing the extraction of GPDs, we studied the generalization ofTCS to the case of the photoproduction of large invariant mass photon- photonand photon-meson pairs. Although factorization of GPDs from a perturbativelycalculable coefficient function has not yet been proven for these processes, theyare a natural extension of the current picture in the framework of collinear QCDfactorization. γN → γγN (cid:48) The photoproduction of a photon pair shares with DVCS and TCS the nice featureto be a purely electromagnetic amplitude at the Born level. Charge parity howeverselects a complementary set of GPDs, namely the charge parity - odd GPDs related a r X i v : . [ h e p - ph ] S e p eptember 30, 2019 0:29 ws-procs961x669 WSPC Proceedings - 9.61in x 6.69in INT18˙Szymanowski page 2 γγ production at the Born level. to the valence part of quark PDFs, with no contribution from the gluon GPDs. Theanalytic form of the Born amplitude calculated from the graphs shown on Fig. 1 isvery peculiar since the coefficient function turns out to be proportional to δ ( x ± ξ )leading through the usual momentum fraction integration to a scattering amplitudeproportional to the GPDs taken at the border values x = ± ξ . For illustration,Fig. 2 displays the diphoton invariant squared mass dependence of the unpolarizeddifferential cross section on a proton at t = t min and s γN = 20 (resp. 100 , )GeV (full, resp. dashed, dash-dotted multiplied by 10 ). M gg @ GeV D d s d t d M gg @ pb G e V - D Fig. 2. M γγ dependence of the unpolarized differential cross-section for the photoproduction ofa diphoton on a proton (left panel) or neutron (right panel) at t = t min and s γN = 20 (resp.100 , ) GeV (full, resp. dashed, dash-dotted multiplied by 10 ). γN → γρN (cid:48) : the quest for transversity GPDs The photoproduction of a γρ pair has the rare feature of being sensitive to chiral-odd transversity quark GPDs at the leading twist level, because of the leading twistchiral-odd distribution amplitude of the transversely polarized vector meson. In-deed, except for higher twist amplitudes which suffer from end-point divergencesand heavy meson neutrino production amplitudes which may be difficult to mea-sure, one needs exclusive processes with more particules in the final state to accesstransversity GPDs .We show on Fig. 3 the cross section for the production of a transversely polarized eptember 30, 2019 0:29 ws-procs961x669 WSPC Proceedings - 9.61in x 6.69in INT18˙Szymanowski page 3 ρ in conjunction with a photon, on a proton or a neutron target. The curves show thesensitivity to the transversity GPD parametrization. Cross sections are sufficientlyhigh for the process to be measurable at JLab . Introduction Access to GPDs through a 3 body final state Non-perturbative ingredients Computation Results Conclusion
Integrated cross-section
Chiral odd cross section S γN (GeV ) σ odd (pb) S γN (GeV ) σ odd (pb) proton neutron solid red: “valence” scenariodashed blue: “standard” one Fig. 3. Energy dependence of the integrated cross section for a photon and a transversely polarized ρ meson production, on a proton (left panel) or neutron (right panel) target. The γρ pair isrequired to have an invariant mass squared larger than 2 GeV . The solid red and dashed bluecurves correspond to different parametrization of the transversity GPDs. γN → γπN (cid:48) − u ′ (GeV ) dσ γπ + dM γπ + d ( − u ′ ) d ( − t ) (pb · GeV − ) − u ′ (GeV ) dσ γπ − dM γπ − d ( − u ′ ) d ( − t ) (pb · GeV − ) Fig. 4. Left panel : the differential cross section for γπ + production on a proton target at s γN = 20 GeV , t = t min , and M γπ = 3 (resp.4 , ,
6) GeV for the black (resp. red, blue, green)curves. The solid and dashed curves correspond to two different parametrization of the axialGPDs. Right panel : the same curves for γπ − production on a neutron target. Since deep electroproduction of a π meson has been shown to resist at moderate Q to leading twist dominance in the factorization framework, it has been temptingto 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, thedominance of higher twist contributions may not be a common feature of all exclu-sive amplitudes involving the pion DA. To check this idea, we propose to study eptember 30, 2019 0:29 ws-procs961x669 WSPC Proceedings - 9.61in x 6.69in INT18˙Szymanowski page 4 the related process γN → γπN (cid:48) where the same pion DAs appear. It turns outthat the axial nature of the pion leading twist DA infers a high sensitivity of theamplitudes to the axial GPDs ˜ H ( x, ξ, t ) as shown on Fig. 4 where the cross sectionsfor the reaction γp → γπ + n and γn → γπ − p are displayed for two different sets ofaxial GPDs. The rates are of the same order as for the γρ case and we thus expectthese reactions to be measurable at JLab.
5. Conclusions
The processes discussed here, because of the absence of gluon and sea quark contri-butions are not enhanced at high photon energy (or small skewness ξ ) and they arethus more accessible at JLab than at EIC. However, since a high energy electronbeam is also an intense source of medium energy quasi real photons ( q ≈ y = q.pk.p = 0(10 − ), ( k and p being the initial electron and nucleonmomenta), one may expect the γγ and γρ L channels to be accessible at moderatevalues of s γN . Prospects at higher values of s γN (and smaller values of the skewness ξ ) are brighter for the γπ 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 supportedby the grant 2017/26/M/ST2/01074 of the National Science Center in Poland. Hethanks the French LABEX P2IO and the French GDR QCD for support.
References
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