JLAB-THY-18-2650 Vector Meson Photoproduction with a Linearly Polarized Beam V. Mathieu,1, ∗ J. Nys,1, 2, 3, 4 C. Fern´andez-Ram´ırez,5 A. Jackura,3, 4 A. Pilloni,1 N. Sherrill,3, 4 A. P. Szczepaniak,1, 3, 4 and G. Fox6 (Joint Physics Analysis Center) 1Theory Center, Thomas Jefferson National Accelerator Facility, Newport News, VA 23606, USA 2Department of Physics and Astronomy, Ghent University, Belgium 3Center for Exploration of Energy and Matter, Indiana University, Bloomington, IN 47403, USA 4Physics Department, Indiana University, Bloomington, IN 47405, USA 5Instituto de Ciencias Nucleares, Universidad Nacional Aut´onomade M´exico, Ciudad de M´exico 04510, Mexico 6School of Informatics, Computing, and Engineering, Indiana University, Bloomington, IN 47405, USA We propose a model based on Regge theory to describe photoproduction of light vector mesons. We fit the SLAC data and make predictions for the energy and momentum transfer dependence of 0 the spin-density matrix elements in photoproduction of !, ρ and φ mesons at Eγ ∼ 8:5 GeV, which are soon to be measured at Jefferson Lab. I. INTRODUCTION independently from the target, and conservation of parity reduces the number of helicity components at With the recent development of the 12 GeV electron each vertex. In the center-of-mass frame, the net helicity beam at Jefferson Lab (JLab) [1, 2], new precision mea- transfer between the vector meson and photon jλγ − λV j surements of light meson photoproduction and electro- can be 0, 1 or 2, which we refer to as helicity conserving, production are expected in the near future. These will single and double helicity flip respectively. Measurement provide constraints on resonance production dynamics, of the photon spin-density matrix elements (SDMEs) including production of gluonic excitations. For example, can be used to determine the relative strength of these the GlueX measurement of the photon beam asymme- components. try in the production of π0 and η mesons [3] established the dominance of natural-parity t-channel exchanges for production in the forward direction [4]. This measure- ment seems to contradict earlier SLAC data [5] that sug- gests significant contribution from unnatural-parity ex- changes. It was shown in [6] that the weak energy depen- dence of the axial-vector contributions suggested by the SLAC data is difficult to reconcile with predictions from Regge theory, while the GlueX data seem to be more in line with theory predictions. The GlueX measurement, however, was performed at fixed photon energy. Never- theless, more data from both GlueX and CLAS12 will FIG. 1. Schematic representation of the factorized amplitude be needed to refine our understanding of the production of a Regge exchange E in Eq. (3). The photon and nucleon mechanisms. vertices are denoted by T E and BE , respectively. The Regge We consider the reaction γ(k; λγ )N(p; λ) ! propagator of the exchange E is RE . 0 0 0 V (q; λV )N (p ; λ ). At high energies, the amplitude in the forward direction is dominated by exchange of Spin-density matrix elements can be reconstructed arXiv:1802.09403v1 [hep-ph] 26 Feb 2018 Regge poles (Reggeons). As illustrated in Fig. 1, the Reggeon amplitude factorizes into a product of two from the angular distributions of the vector meson de- vertices. The upper vertex describes the beam (photon) cay products [9]. The first measurements of neutral vec- interactions, and the lower vertex describes the target tor meson SDMEs were performed at SLAC [10], result- ing in the following qualitative conclusions: the natural (proton) interactions. The Mandelstam variables are 0 s = (k + p)2 and t = (k − q)2. Factorization of Regge exchanges contributing to ρ , ! and φ production are predominantly helicity conserving, and the unnatural- vertices follows from unitarity in the t-channel, where 0 Regge pole is a common pole in all partial waves related parity contributions are negligible for ρ production and by unitarity and its vertices determine residues of the consistent with a one-pion exchange for ! production. poles [7, 8]. Factorization of residues enables one to In this paper, we discuss the SLAC data in the context determine the helicity structure at the photon vertex of a Regge-pole exchange model, which allows us to as- sess contributions of individual exchanges to the SDMEs. Various models have been proposed in the past [11{20], with different descriptions of the momentum-transfer de- ∗ [email protected] pendence of the helicity amplitudes. In general these 2 exchanges can be characterized by the quantum num- 0.2 U 0.2 U 0.2 U bers of the lowest spin meson on the trajectory, namely r00 GJ Re r10 GJ r1-1 GJ à J 0.1 0.1 0.1 isospin I, naturality η = P (−1) (with the parity P ), æ à æ à à à à æ à à J à à à à à à à à signature τ = (−1) , charge conjugation C and G-parity 0.0 0.0 à à æ 0.0 à æ æ æ æ à à G = C(−1)I . The leading trajectories contributing to -0.1 -0.1 -0.1 æ gp®wp vector meson photoproduction are -0.2 gp®-r0.2p -0.2 0.0 0.2 0.4 0.6 0.8 0.0 0.2 0.4 0.6 0.8 0.0 0.2 0.4 0.6 0.8 Gητ PC Gητ PC Gητ PC -t HGeV2L -t HGeV2L -t HGeV2L I J I J I J −++ ++ −−+ −+ −−− ++ a2 : 1 2 π : 1 0 a1 : 1 1 0 +++ ++ +−+ −+ +−− ++ FIG. 2. Unnatural components of ! and ρ SDMEs at Eγ = f2 : 0 2 η : 0 0 f1 : 0 1 (1) 9:3 GeV. The dashed lines are the theoretical expectation for U U U a pseudoscalar exchange, ρ00 = ρ10 = ρ1−1 = 0. Data are In addition to the exchanges in Eq. (1), we also con- taken from Ref. [10]. sider the natural-parity Pomeron exchange, which domi- nates at high energies. In the ! photoproduction model from [20], a scalar exchange representing a σ meson tra- models reproduce the differential cross sections, but lack jectory was also considered. Since the σ meson trajectory a detailed discussion of the implication of the Regge pole is below the (leading) f2 trajectory, we do not include model for the SDMEs. it here. Among all unnatural exchanges, the π and η The paper is organized as follows. In Section II, we trajectories are expected to dominate, since they are the define the Regge amplitudes and discuss model param- closest to the scattering region. One can verify this by ex- U eters. In Section III, we discuss the fitting procedure. amining the SDMEs ρλ0λ, which in the Gottfried-Jackson Specifically, we first isolate the unnatural exchanges in (GJ) frame are determined by the unnatural exchanges ρ0 and ! production. We find that, within uncertain- (see Appendix A). The GJ frame is equivalent to the t- ties, these components are consistent with π and η ex- channel helicity frame where parity conservation implies changes so we neglect sub-leading trajectories. We de- a relation between helicity amplitudes and the natural- termine the residues of the dominant, natural exchanges ity of the exchanges. Inspecting the SLAC data [10], U U by the γp and γd total cross sections. Using the SLAC one finds that the matrix elements ρ00jGJ , Re ρ10jGJ and U data, the single and double helicity flip couplings are fit- ρ1−1jGJ for both ! and ρ production are all consistent ted to the three natural components of the SDMEs at with zero. Moreover, the unnatural component of the the laboratory frame (target rest frame) photon beam differential cross section is compatible with a π-exchange energy of Eγ = 9:3 GeV. The model is extrapolated to model [10]. Hence, we assume that the unnatural com- Eγ = 2:8 GeV and 4:7 GeV and compared to the three ponents of the SDMEs are dominated by either π or η natural components of the SLAC SDMEs at these ener- exchange. The η exchange is introduced to describe the gies. In Section IV, we compare the model to the nine ! SDMEs in production of the φ meson, while its contri- and ρ0 SDMEs obtained with a polarized beam at SLAC bution is negligible in ! and ρ0 production. As we will with Eγ = 9:3 GeV, to the nine φ SDMEs from LEPS [21] see in Sec. II, the normalization of these exchanges can and Omega-Photon [22], and to the three ! SDMEs ob- be determined by vector meson radiative decays. Re- tained with a unpolarized beam from CLAS [23, 24], garding axial vector exchanges, since the decay widths of 1 LAMP2 [25] and Cornell [26]. Furthermore, we test the f1; a1 ! γV are not known, their contribution is diffi- Pomeron normalization for the ! and ρ0 differential cross cult to evaluate. Within a specific quark model [20], the sections at Eγ > 50 GeV, and the Regge exchange nor- contribution of the f1 to ! photoproduction is found to malization for the !, ρ0 and φ differential cross sections at be negligible. As we will show, it is possible to saturate Eγ = 9:3 GeV from Ref. [10]. Lastly, we provide the pre- the unnatural components of the SDMEs by pseudoscalar dictions for the upcoming !, ρ0 and φ SDMEs measure- exchanges. We therefore neglect the axial vector trajecto- ments in JLab experiments. In Section V, we summarize ries. In summary, we consider the s-channel amplitudes our findings and give conclusions. Details regarding the in the form relations between the frames (helicity, Gottfried-Jackson, X E s- and t-channel frames) are summarized in Appendix A, MλV ,λγ (s; t) = MλV ,λγ (s; t); (2) 0 the definition of the SDMEs are detailed in Appendix B, λ ,λ E λ0,λ and further details on the amplitude parametrization are given in Appendix C.