Role of Photoproduction in Exotic Meson Searches

We discuss two production mechanisms of the $J^{PC}=1^{-+}$ exotic meson, hadroproduction, using pion beams and photoproduction. We show that the ratio of exotic to non-exotic, in particular the $a_2$, meson production cross sections is expected to be by a factor of 5 to 10 larger, in photoproduction then in hadroproduction. Furthermore we show that the low-t photoproduction of exotic meson is enhanced as compared to hadronic production. This findings support the simple quark picture in which exotic meson production is predicted to be enhanced when the beam is a virtual $Q\bar Q$ pair with a spin-1 (photon) rather then with a spin-0 (pion).


Introduction. Present understanding of confinement is still mostly qualitative.
Even though in recent years significant progress has been made in lattice gauge studies of QCD, the dynamics of confinement, especially in association with light quarks, remains mysterious. Similarly, it remains to be verified whether soft gluonic excitations responsible for confinement are present in the low energy resonance spectrum.
In the past few years, a number of strong candidates for states lying outside the valence quark model spectrum have been reported. Examination of the scalar-isoscalar mesons produced in pp annihilation [1], central production and J/ψ [2] radiative decays [3] indicates that in the 1−2 GeV mass range there is an overpopulation of states as compared to predictions of the valence quark model. Furthermore analysis of the decay patterns seems to indicate that some of these states may have a significant non-QQ component. Since these states can mix with the regular QQ mesons the non-QQ components cannot be disentangled in a model independent way. A much cleaner signatures for non-QQ and/or gluonic excitations could come from exotic states. By definition, these are states which have combinations of spin, parity and charge conjugation quantum numbers that cannot be attributed to the valence quark degrees of freedom, e.g. J P C = 0 −− , 0 +− , 1 −+ , · · ·. Recently, the E852 BNL collaboration has reported an exotic, resonant signal with J P C = 1 −+ in the reaction π − p → Xp at 18 GeV in two decay channels, X → ρπ [4] and η ′ π [5] corresponding to the resonance mass of M X ≈ 1.6 GeV and width of Γ ≈ 170 MeV and Γ ≈ 340 MeV in the two channels respectively. The existence of the J P C = 1 −+ exotic meson below 2 GeV has been reported elsewhere [6]. Furthermore, lattice and model calculations indicate that the lightest exotic meson indeed should have J P C = 1 −+ and mass below 2 GeV [7,8,9].
The exotic resonance measured by the E852 collaboration is observed to be produced predominantly via natural parity exchange, and so is the nearby a 2 (1320) resonance. The later is a well established regular QQ state. Furthermore, in the ρπ decay channel the exotic wave is observed to be roughly 5% of the a 2 wave. In the η ′ π channel the exotic signal seems to be much stronger but it is also much broader.
It has been argued that real photons may be a better source of exotic mesons in high-s, low-t reactions [10]. The argument is based on a simple quark picture. At high energies photon couples to the QQ pair in total helicity-1 state, corresponding (in the QQ rest frame) to the quark-antiquark pair being in the spin-1 configuration.
The majority of models dealing with soft gluons predict that the low lying gluonic excitations are in the T E mode i.e. with J P C g = 1 +− [9,11]. This is also supported by the recent lattice calculations of the excited adiabatic potentials for heavy quarkonia [8]. As a consequence, the 1 −+ ground state has the QQ pair in S = 1, so that Thus, according to this simple quark picture one would expect exotic mesons production to be enhanced in reactions with real photon (QQ in spin-1) as compared to reactions with pseudoscalar (π, K) meson beams.
In this letter we show that this microscopic picture is supported by the standard, Regge phenomenology of high-s, low-t peripheral production. In particular we show that exotic meson production is expected to be comparable to production of other, non-exotic resonances in particular the a 2 meson, and to be enhanced at low-t as compared to hadronic production with pion beams.

Peripheral meson production.
We begin with the analysis of the reaction πN → XN → M 1 · · · M n N at high-s and low-t. In particular, a good candidate decay channel for exotic meson searches is M 1 · · · M n = (3π) ± . The charged 3π system has I = 1 and G = −1, thus assuming isospin invariance a resonating 3π P -wave belongs to the exotic 1 −+ isovector multiplet (a neutral 3π system will overlap with the isospin-0, i.e. non-exotic, 1 −− , ω-like resonance). The E852 data corresponds to π − p → π + π − π − p at the lab energy p L = 18 GeV [4]. The 3π mass spectrum is dominated by the a 2 (1320) J P C = 2 ++ resonance and at higher mass, the π 2 (1600) with J P C = 2 −+ is seen together with a small π 1 (1600), J P C = 1 −+ exotic signal. Both the a 2 and the exotic, π 1 resonances are observed to be produced via natural parity exchange and appear in the and P + waves respectively.
Here D M , P M , etc. refer to the t-channel (Gottfried-Jackson) amplitudes corresponding to the spin quantization axis along the direction of the beam in the resonance rest frame. In the following we will make a simplifying assumption that the natural parity exchange can be saturated by the ρ-trajectory. This is certainly a good assumption for the case of a charge exchange reaction e.g. π − p → π + π − π 0 n [12]. In the neutral case ρ-exchange should be supplemented by the f 0 and/or Pomeron exchange con-tributions [13]. In the later case, which, corresponds to the E852 measurement, the estimates for the exotic meson natural exchange amplitude should be considered as an upper bound. The ρ and scalar meson exchange contribute mainly to the nucleon helicity-flip and -nonflip respectively i.e. are essentially non-interfering. The E852 data lacks absolute normalization therefore we can only use it to establish the relative strength of the exotic to a 2 production yields. We will compare our predictions for the charge exchange a 2 production with the data from Ref. [12].
The t-channel amplitude for the reaction π − p → X 0 n producing a natural parity, where λ ′ N , λ N are the recoil and target nucleon helicities, G V and G T are the vector and tensor (helicity non-flip, and flip) ρNN couplings and R(t, s) is the ρ meson, Regge propagator, with α ρ (t) = 1 + α ′ (t − m 2 ρ ) and α ′ = 0.9 GeV −2 . The g Xρπ coupling is normalized so that the partial ρπ width of the natural parity resonance is given by with q being the on-shell breakup momentum, q = λ(M X , m π , m ρ ). Finally, the differential cross section is then given by For the a 2 , the ρπ partial width is known [14], Γ a2ρπ = 0.7 × 110 MeV. Since we are primarily interested in comparing the a 2 and the π 1 , exotic meson we will consider  Figure 1: Comparison of the a 2 (1320)-regular meson (solid) and π 1 (1600)-exotic meson (dashed) production cross sections in reaction π − p → Xπ + π − π 0 n at p π = 18 GeV. The data correspond to a 2 production at 15 GeV the production at p L = 18 GeV corresponding to the E852 data. Prediction for the differential cross section for the a 2 following from Eq. (1) is shown by the solid line in Fig. 1. This can be compared with the p L = 15 GeV charge exchange data from Ref. [12]. The vector and tensor ρNN couplings used are somewhat larger, G V = 5.9, G T = 27.7 then the "standard" parameters ( G V = 2.3, G T = 18.4) and come from what is referred to as the "theoretical" parameterization in Ref. [15]. One should note however, that even the "standard" parameters which come from the non-Regge ρ propagator after changing to the Regge propagators should be renormalized which enhances their values [16]. The characteristic dip at t ∼ −0.5 GeV 2 may be washed out by absorption (Regge+Pomeron) rescattering corrections. Finally the low value of slope parameter b ρ = 2 − 3GeV −2 in the residue function is typical to the ρ-exchange.
The E852 result indicates that the π 1 exotic wave found in the ρπ channel has the total width of Γ π 1 ≈ 170 MeV and corresponds to about 5% strength of the a 2 . The π 1 production is then expected to scale according to The above relation enables to determine the g π 1 ρπ coupling. We find that the Γ π 1 →ρπ partial width is approximately 40% of the total Γ π 1 = 170 GeV width. The tdependence of the differential cross-section for π 1 production is shown by the dashed line in Fig. 1. As expected it has a similar t-dependence to the a 2 production, since under assumption that the ρ-exchange dominates, the only difference comes from the angular momentum barrier factors, in agreement with the E852 result [4] scaled by the coupling to the ρπ decay channel.
Thus according the the E852 measurement the exotic pion-production cross section is a small fraction of the a 2 production cross section. The corresponding couplings are calculated to be g a2ρπ ≈ 75 and g π 1 ρπ ≈ 16.
We will now discuss charge exchange photoproduction. The dominant production amplitude is now expected to come from one-pion-exchange with the photon acting, through VMD as a vector meson-ρ beam. On the basis of VMD we would expect, The radiative, a 2 width is known [14], Γ a 2 γπ = 295 keV which gives g a 2 γπ = 1.55. The above VMD relation yields, Here C f = 1/ √ 2 = g X ± ρ 0 π ± /g Xρπ . Thus for the radiative widths we expect the VMD to be accurate within a factor of two. The charge-exchange, OPE photoproduction amplitude is given then by with R(s, t) = 1 2 1 + e iπαπ(t) Γ(−α π (t))α ′ (α ′ s) being the π Regge propagator with α ρ (t) = α ′ (t − m 2 ρ ) and g πN N = 35.5 GeV. The existing data on a 2 photoproduction comes from two SLAC bubble chamber experiments one at the average photon energy of E γ = p L = 4.8 GeV [17] and other at E γ = 19 GeV [18]. The corresponding total cross sections are measured to be σ γp→a + 2 n ≈ 2.6µb and 0.3µb respectively. The data for differential cross section for the lower energy experiment is shown in Fig. 2 after rescaling by a factor of 2.6 as explained in Ref. [18]. This should be compared with the cross section predicted from Eq. (9) (dashed line). The comparison is quite good, indicating, however need for some absorption corrections [17,19] We will now compare the prediction for the exotic π 1 photoproduction with that for the a 2 . We make the comparison for the photon energy, E γ = 8 GeV as proposed for the Hall D experiments at JLab. This is shown in Fig. 2. The solid line is the prediction for the a 2 production and the shaded region depicts the expected cross section for the π 1 using the radiative width in the range 300 keV < Γ π 1 γπ < 400 keV which covers the typical range of radiative widths of ordinary mesons in this mass range and includes the VMD prediction, . It is interesting to compare the predicted ratio of the π 1 to a 2 photoproduction cross section. In analogy to Eq. (6), we get ≈ 50%−100% (11) and for small-t, 3. Conclusions. We have estimated the exotic meson photoproduction rate based on the existing data on hadronic production with pion beams. From the E852 π − p → Xp → ρπp data it follows that the exotic production is suppressed by roughly a factor of 10 as compared to the a 2 (1320) production. We find, however, this is not the case in reactions with photon beams. Based on the rate estimate from the E852 data we conclude that in photoproduction the π 1 and a 2 production should be comparable.  Figure 2: Comparison of a 2 (1320) (solid) and exotic, π 1 (1600) (shaded region) production cross sections in reaction γp → X + n at p γ = 8 GeV. The data correspond to charge exchange a 2 production at 4.8 GeV and the theoretical prediction for a 2 at this energy is shown by the dashed line. The lowest (highest) prediction for exotic meson production given by the shaded region corresponds to Γ π 1 γπ = 200(400) keV respectively.
There main reasons for enhancement of exotic production is that the exotic meson photocoupling is not suppressed. This follows from simple kinematical constraints.
Secondly since the small-t behavior is determined by the helicity structure of the production amplitude, both the exotic and a 2 are enhanced at low-t in photoproduction via OPE as compared to hadronic production via ρ-exchange. This is due to the vector nature of the photon which transfers its helicity to the produced meson.
This is not the case for the pion beam, where helicity of the produced meson has to be transferred from the exchanged (vector) meson, and thus making the amplitude suppressed with √ −t ′ . These findings are important for exotic mesons searches in future photoproduction experiments in Hall D at the JLab.