Photoproduction of Exotic Baryon Resonances

We point out that the new exotic resonances recently reported by LHCb in the $J/\psi p$ channel are excellent candidates for photoproduction off a proton target. This test is crucial to confirming the resonant nature of such states, as opposed to their being kinematical effects. We specialize to an interpretation of the heavier narrow state as a molecule composed of $\Sigma_c$ and $\bar D^*$, and estimate its production cross section using vector dominance. The relevant photon energies and fluxes are well within the capabilities of the GlueX and CLAS12 detectors at Thomas Jefferson National Accelerator Facility (JLAB). A corresponding calculation is also performed for photoproduction of an analogous resonance which is predicted to exist in the $\Upsilon p$ channel.


Introduction
The LHCb experiment [1] has observed two new exotic resonances in the J /ψ p channel, a broad one with mass 4380 ± 8 ± 29 MeV, width 205 ± 18 ± 86 MeV, and statistical significance 9σ , and a narrower one with mass 4449.8 ± 1.7 ± 2.5 MeV, width 39 ± 5 ± 19 MeV, and statistical significance 12σ . In the present note we point out that these states are excellent candidates for photoproduction off a proton target, an observation made by others [2,3] as a preliminary version of this Letter was being prepared. Specializing to an interpretation in which the heavier state is regarded as a molecule of c and D * [4], we estimate the cross section for its production using vector dominance. A corresponding calculation is also performed for a molecule of b and B * forming an ϒ p resonance. Observation of the states observed by LHCb in photoproduction is crucial to their confirmation as resonances as opposed to their being kinematic enhancements.

The reaction γ p → X → J /ψ p
We calculate the cross section for photoproduction of a resonance X decaying to J /ψ p by assuming it is dominated by the elastic process J /ψ p → X → J /ψ p. The photon-J /ψ coupling * Corresponding author. is estimated from the J /ψ leptonic width: ( J /ψ → + − ) = 5.55 ± 0.14 ± 0.02 keV [5]. The Breit-Wigner cross section for production of a resonance with spin J by particles of spins S 1 and S 2 is [5] where k in,out are the center-of-mass (CM) 3-momenta in the (incoming γ p, outgoing J /ψ p) channel, E = E cm is the total CM energy, E R is the resonance energy, B in and B out are the resonance branching fractions into the incoming and outgoing channels, and tot is the resonance total width. For E R = 4380 MeV, in,out = (2126, 820) MeV. (We shall denote these resonances X A and X B , respectively.) In the preferred fits of Ref. [1], one of these resonances has spin 3/2, the other has spin 5/2, and they are of opposite parity. One theoretical interpretation of the narrow higher-lying state as a cD * molecule bound by pion exchange [4] assigns its spin and parity to be J P B = 3/2 − and therefore J P A = 5/2 + . For an incident photon, with only transverse polarizations, the 2S 1 + 1 factor in the denominator is to be multiplied by 2/3.
We define the decay constant f V of a vector meson V in terms of the matrix element between the one-V state and the vacuum: where q, , and M V are the four-momentum, polarization vector, and mass of the vector meson. Then dominance of the photoproduction cross section by the J /ψ pole implies 1 where f L is the fraction of decays P c → J /ψ p in a relative partial wave L that give rise to a transversely polarized J /ψ . With our J P assignments, L = 1, 3 for X A = P c (4380) and L = 0, 2 for X B = P c (4450).
The leptonic width of the J /ψ (neglecting lepton masses) is from which, using the experimental central value [5], we find For subsequent purposes we shall consider only the photoproduction of the state X B decaying to J /ψ p with relative orbital angular momentum L = 0, so henceforth f L ≡ f 0 . It may be easily seen that the cases L = 2 for X B and L = 1, 3 for X A production lead to higher predicted cross sections, so our estimate may be regarded as a lower bound. The quantity f 0 is given by counts for the relativistic enhancement of the longitudinally polar- Then the cross section for X B production is where is the magnitude of the incoming 3-momentum in the CM. For a photon on a proton target yielding C B = 1.35 μb. This is a substantial cross section, considering that the diffractive cross section for γ p → J /ψ p is below 1 nb at E = 4.4 GeV [6][7][8][9][10]. We will return to this subject at the end of the current Section. The size of the resonant cross sections is illustrated by Fig. 1 which shows the cross section for case (B), i.e., resonant photopro- The CM energies of 4.38 and 4.45 GeV correspond to laboratory photon energies of 9.75 and 10.08 GeV, respectively, well within the capabilities of the GlueX and CLAS12 detectors at Thomas Jefferson National Accelerator Facility (JLAB) [11,12].
For example, CLAS12 will produce a tagged photon spectrum via bremsstrahlung from an electron beam, yielding a total of 5 × 10 7 photons per second with 6.5 < E γ < 10.5 GeV and having a spectrum dN/dE γ = A/E γ [13]. Demanding that the integral of dN γ /dE γ from 6.5 to 10.5 GeV be 5 × 10 7 photons per second, we find dN γ /dE γ = 1.0 × 10 8 photons/s/E γ . (8) This spectrum may be used to estimate the signal [using Eq. (6)] and background for the resonances X A and X B with arbitrary spin. 1 We thank M. Voloshin for a correction to a preliminary version of this Letter.
Since the photon beam intensity is given in terms of number of photons per second, rather than in the usual units of luminosity, we shall use here the GlueX rule of thumb that an intensity of 10 5 γ /s will produce about 10 4 events per 1 μb of cross section per day of running [11]. So with a peak cross section of 1.35 (B out ) 2 μb, a branching fraction B( J /ψ → e + e − ) = (5.971 ± 0.032)% [5] and the photon flux (9) we should expect 1.6 × 10 4 (B out ) 2 events per day of running. While this looks large, we do not know the magnitude of B out .
In the region of interest the E γ resolution is 20-30 MeV, corresponding to 4-6 MeV resolution in E. This is much less than the 39 MeV width (in E) of the P c (4450) resonance, so it should be possible to resolve the peak in Fig. 1. It is likely that in the future the E γ resolution will be even better [13]. For details of a specific CLAS12 proposal to study J /ψ production with a tagged polarized photon beam of energy 11 GeV, see Ref. [14]. Such a beam enables useful measurements of resonance spin-parity via angular distributions of the final e + e − pair in J /ψ decay [15].
In the future the GlueX detector [11,16] will complement the reach of CLAS12. A specific proposal to study γ p → J /ψ p with 8.7 < E γ < 11.5 GeV [17], optimized for a peak in the photon spectrum at 10 GeV [18], leads one to expect about 6 × 10 −4 events/MeV/s/μb (with J /ψ → e + e − ). Integration with respect to CM energy E over a Breit-Wigner resonance with maximum σ peak and width multiplies σ peak by a factor of π /2 = 61.26 MeV. But we want to integrate with respect to laboratory photon energy E γ , so we have to multiply by dE γ /dE = E/m p = 4.743, giving a factor of 290.5 MeV. Multiplying by σ peak = 1.35 μb(B out ) 2 one estimates a rate of about 2 × 10 4 (B out ) 2 events of the 4450 MeV state per day, roughly consistent with our estimate for CLAS12. As for energy resolution, GlueX expects a RMS tagged photon uncertainty around 6 MeV. On a proton target, this translates into an uncertainty in E of 1 MeV for a 10 GeV photon [16], which should enable an accurate scan of the resonance lineshape.
The branching fraction B out cannot be too small, as the with P c decaying to final states other than J /ψ p, becomes unreasonably large in comparison with B( b → K − J /ψ p) = 3 × 10 −4 [15].

Comparison with J /ψ photoproduction data near threshold
The elastic J /ψ photoproduction cross section for 10 < E γ < 13 GeV has been measured by SLAC and Cornell teams in 1975 and is quite small, below 1 nb [6][7][8][9][10]. This raises an obvious question: Why wasn't the P c (4450) resonance observed by these experiments? There are several effects, all working in the same direction, as listed below. a) Smearing by poor energy resolution: The P c (4450) width is quite small, 39 MeV, corresponding to 180 MeV in terms of photon energy. The photon energy in the early experiments had a rather large spread. For example, in the Cornell study [7] the photon energy was divided into three intervals: 9.3-10.4, 10.4-11.1, 11.1-11.8 GeV. The narrow peak is smeared out when convoluted with such a wide energy distribution. b) Mostly forward scattering: Experiments [6,7] focused on the forward cross section, which is mostly due to diffractive scattering, while resonance scattering tends to be much more isotropic. Therefore only a small fraction of the resonant cross section is in the forward direction. c) B out 1: The branching fraction of the resonance into J /ψ p might be significantly less than 1. In this context it is interesting to point out that Ref. [6] used vector dominance to derive the estimate dσ (γ p → J /ψ p) dt t=0 25 μb/GeV 2 . (10) Assuming that the forward J /ψ p scattering amplitude is purely imaginary, they then used the optical theorem to derive the bound σ tot ( J /ψ p) ≤ 0.8 mb.

The reaction γ p → X → ϒ p
It was suggested in Ref. [4] that an exotic doubly-heavy meson or baryon resonance should exist near any threshold if pion exchange is allowed between the two constituent hadrons. In particular, there should exist a relatively narrow J P = 3/2 − resonance near b B * threshold, or 11.14 GeV, decaying to ϒ(nS)p. We shall estimate the cross section for photoproduction of such a resonance, denoted by P b (11140). The corresponding photon energy in the laboratory is E γ = 65.66 GeV. In principle such an energy could be achieved using tagged photons from HERA.
The calculation for resonant ϒ(1S) p photoproduction is entirely analogous to the one for J /ψ . Using the experimental value [5] (ϒ(1S) → e + e − ) = 1.34 keV, we obtain f ϒ(1S) = 238 MeV . (11) We then find, for a ϒ(1S) p resonance of mass E R = 11.14 GeV, with k R in,out = (5.530, 1.287) GeV the (incoming, outgoing) CM 3-momentum for E = E R , The photoproduction cross section for such a resonance with width tot is given by where, for J = 3/2, The cross section for resonant photoproduction γ p → ϒ(1S)p Fig. 2 as a function of the incident photon energy E γ . Here we have assumed the same width as P c (4450), i.e., = 39 MeV. The actual width is likely to be narrow, but its precise value is unknown. It is given by the product of the square of the matrix element and the phase space. Under the assumption that B out is close to 1, the phase space scales as k R out for an S-wave decay. If the matrix element remained unchanged, out /k P c out ) = 61 MeV. The matrix element is given by the overlap of the ϒ p and b B * molecule wave functions. This overlap is likely to be less than the overlap of that between the J /ψ p and cD * wave functions as a result of the more compact nature of the ϒ , but we do not have a quantitative estimate. In the more likely case that B out is much less than 1, (P b ) will depend on details of the molecular binding The corresponding background is the diffractive process γ p → ϒ(nS)p. A few events of γ p → ϒ(1S)p were seen in 1995-7 data by the ZEUS Collaboration at HERA [19]. They quoted a ratio At 11 GeV, Ref. [10] estimated σ el (γ p → J /ψ p) 10 nb, yielding σ el (γ p → ϒ p) 50 pb. In later ZEUS data with 62 ± 12 ϒ(1S) events [20], σ (γ p → ϒ p) was measured in various ranges of center-of-mass energy W to be 160 ± 51 +48 −21 pb 60 < W < 130 GeV Central W 0 = 100 GeV 321 ± 88 +46 −114 pb 130 < W < 220 GeV Central W 0 = 180 GeV 235 ± 47 +30 −40 pb 60 < W < 220 GeV .
Comparing cross sections at W 0 = 100 and 180 GeV, they scale as W 1.18 . Assuming this dependence to extrapolate to 11 GeV gives a cross section of 12 pb at that energy.

Conclusions
The discovery in the LHCb experiment of a narrow resonance of mass 4450 MeV and a broader enhancement at 4380 MeV, both of which decay to J /ψ p, suggests that one search for photoproduction of these states on proton targets using photons of energy near 10 GeV. Predicted cross sections are at an encouraging level above diffractive γ p → J /ψ p background. On the basis of proximity to the b B * threshold, a predicted state [4] near 11.14 GeV should be photoproduced with photons of energy ∼ 66 GeV. The observation of signals in the γ p → J /ψ p channel would provide important confirmation of the resonant nature of the LHCb states.
The observation of a narrow resonance in the γ p → ϒ p channel would be a major new discovery and would strongly indicate existence of yet additional resonances, along the lines advocated in Ref. [4].