Photoproduction of Vector Mesons on Nuclei with Gluex PR12-17-010

PR12-17-010 Photoproduction of vector mesons on nuclei with GlueX

H. Al Ghoul, B. E. Cannon, V. Crede, A. Ernst, P. Eugenio, A. I. Ostrovidov, and A. Tsaris Florida State University, Tallahassee, Florida 32306, USA

A. Ali, R. Dzhygadlo, K. Goetzen, A. Hamdi, F. Nerling, K. J. Peters, C. Schwarz, and J. Schwiening GSI Helmholtzzentrum f¨urSchwerionenforschung GmbH, D-64291 Darmstadt, Germany

E. G. Anassontzis, C. Kourkoumeli, and G. Vasileiadis National and Kapodistrian University of Athens, 15771 Athens, Greece

A. Austregesilo, F. Barbosa, T. Britton, E. Chudakov, M. M. Dalton, A. Deur, H. Egiyan, S. Furletov, M. M. Ito, D. Lawrence, D. Mack, P. T. Mattione, M. McCaughan, L. Pentchev, E. Pooser, E. S. Smith, A. Somov (spokesperson, contact person), S. Taylor, T. Whitlatch, and B. Zihlmann Thomas Jeﬀerson National Accelerator Facility, Newport News, Virginia 23606, USA

A. Barnes, R. T. Jones, J. McIntyre, F. Mokaya, and B. Pratt University of Connecticut, Storrs, Connecticut 06269, USA

T. D. Beattie, A. M. Foda, G. M. Huber, G. J. Lolos, Z. Papandreou, A. Yu. Semenov, I. A. Semenova, and A. Teymurazyan University of Regina, Regina, Saskatchewan, Canada S4S 0A2

V. V. Berdnikov, D. Romanov, and S. Somov National Research Nuclear University Moscow Engineering Physics Institute, Moscow 115409, Russia

T. Black and L. Gan (spokesperson) University of North Carolina at Wilmington,

1 Wilmington, North Carolina 28403, USA

W. Boeglin, L. Guo, M. Kamel, W. Phelps, and J. Reinhold Florida International University, Miami, Florida 33199, USA

W. J. Briscoe, F. J. Klein, and I. I. Strakovsky The George Washington University, Washington, D.C. 20052, USA

W. K. Brooks, H. Hakobyan, S. Kuleshov, and O. Soto Universidad T´ecnica Federico Santa Mar´ıa,Casilla 110-V Valpara´ıso,Chile

S. Dobbs, L. Robison, K. K. Seth, A. Tomaradze, and T. Xiao Northwestern University, Evanston, Illinois 60208, USA

A. Dolgolenko, V. S. Goryachev, V. Matveev, and V. Tarasov Institute for Theoretical and Experimental Physics, Moscow 117259, Russia

M. Dugger, B. G. Ritchie, and N. Sparks Arizona State University, Tempe, Arizona 85287, USA

C. Fanelli, J. Hardin, M. Patsyuk, M. Williams, and Y. Yang Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

J. Frye, R. E. Mitchell, M. R. Shepherd, A. Subedi, and J. Zarling Indiana University, Bloomington, Indiana 47405, USA

A. Gasparian (spokesperson), M. Levillain, and R. Pedroni North Carolina A&T State University, Greensboro, North Carolina 27411, USA

V. Gauzshtein, I. Kuznetsov, and V. Lyubovitskij Tomsk State University, 634050 Tomsk, Russia and Tomsk Polytechnic University, 634050 Tomsk, Russia

N. Gevorgyan, V. Kakoyan, and H. Marukyan

2 A. I. Alikhanian National Science Laboratory (Yerevan Physics Institute), 0036 Yerevan, Armenia

N. Gevorkyan (spokesperson) Joint Institute for Nuclear Research, 141980 Dubna, Moscow region, Russia

S. Han, N. Qin, Z. Zhang, and X. Zhou Wuhan University, Wuhan, Hubei 430072, People’s Republic of China

D. G. Ireland, K. Livingston, P. Pauli, and D. Werthm¨uller University of Glasgow, Glasgow G12 8QQ, United Kingdom

N. S. Jarvis, W. I. Levine, M. McCracken, W. McGinley, C. A. Meyer, R. A. Schumacher, and M. J. Staib Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA

G. Kalicy and D. I. Sober Catholic University of America, Washington, D.C. 20064, USA

I. Larin (spokesperson) University of Massachusetts, Amherst, Massachusetts 01003, USA and Institute for Theoretical and Experimental Physics, Moscow 117259, Russia

R. Miskimen University of Massachusetts, Amherst, Massachusetts 01003, USA

C. Salgado Norfolk State University, Norfolk, Virginia 23504, USA

J. R. Stevens College of William and Mary, Williamsburg, Virginia 23185, USA

3 Abstract

We propose to measure the photoproduction cross sections of vector mesons on 12C, 28Si, 120Sn, and 208Pb nuclear targets for the photon beam energy range between 6 GeV and 12 GeV with the GlueX experimental setup. The energy dependence of nuclear transparency for these nuclei will be extracted and used to test the theoretical models. Existing experimental data of the photoproduction of ρ mesons do not show the predicted dependence of the nuclear transparency on energy. Our data will test this. The cross section of the longitudinally polarized ω meson with nucleons σL = σ(ωLN) will be determined for the ﬁrst time. This information is important for the interpretation of color transparency eﬀects in electroproduction of vector mesons.

I. INTRODUCTION

We propose to study the photoproduction of light vector mesons with the GlueX detector using a set of nuclear targets: C, Si, Sn, and Pb. The nuclear transparency for these mesons will be measured in the large beam energy range between 6 GeV and 12 GeV and compared with predictions of the theoretical models. The primary goal of the experiment is to:

σA • Measure the nuclear transparency (T = , where σA and σN are production cross A σN sections on nuclei and nucleon, respectively) of ω mesons in photoproduction oﬀ complex nuclei, which will be used to study interactions of transversely and longitudinally polarized ω mesons with nucleons [1]. According to measurements at SLAC [2], at GlueX energies and modest transfer momenta, longitudinally polarized ω mesons will be produced due to the pion exchange process [42]. The total cross section for interactions of

the transversely polarized vector mesons with nucleons σT = σ(VT N) can be obtained from the coherent photoproduction. Measurements of ω meson photoproduction in the incoherent region provide a unique opportunity to extract the yet unmeasured total cross

section for longitudinally polarized vector mesons σL = σ(VLN).

The knowledge of σT (VN) and σL(VN) is particularly important in the interpretation of the effect of color transparency [3] in the electroproduction of vector mesons off nuclei, manifested in the decrease of the absorption due to the decrease of the size of a photon’s hadronic component with Q2. On the other hand, the number of longitudinally polarized 2 vector mesons grows [4] with Q and if σT σL color transparency screening effects

4 cannot completely account for the reduced absorption; some of the effect is due to the weaker absorption of longitudinally polarized vector mesons compared with the transversely polarized one. Measurement of the absorption of ω mesons in photoproduction by real photons has a certain advantage compared with the electroproduction. In the real photoproduction at modest transfer momenta | t |≤ 1 GeV2, the color transparency effect is absent. The reduced absorption will solely be a result of the difference between

σT and σL.

• Measure the dependency of the nuclear transparency of light vector mesons on the beam energy. These measurements are expected to shed light on disagreements between the theoretical predictions and experimental results [5, 6]. The decrease of the nuclear transparency with energy predicted by the theory [6] was not observed in ρ [7] and π±, π0 photoproduction [8, 9].

II. PHYSICS MOTIVATION

For particles with nonzero spin, such as vector mesons V (ρ, ω, φ), interactions with nucleons are represented by a set of polarization-dependent amplitudes and can result in different cross sections for transversely and longitudinally polarized vector mesons with nucleons. The meson- nucleon cross sections can be extracted by measuring the absorption of mesons in production off nuclei. The first indication that interaction of a vector mesons V (ρ, ω, φ) with a nucleon depends on the meson polarization comes from the ρ electroproduction data. The ratio of production cross 2 Q2 sections for a proton target can be represented as R = σ(γLp → ρLp)/σ(γT p → ρT p) = ξ 2 , mρ where the parameter ξ corresponds to the ratio of the longitudinal to transverse ρ0 total cross sections ξ = σL(ρp)/σT (ρp). The value of ξ obtained from measurements is ξ ≈ 0.7 [10], while the naive quark model predicts equal cross sections σL(ρp) = σT (ρp). In the case of φ electroproduction [11] this ratio is ξ ≈ 0.6. Some interpretations of the deep inelastic scattering data using the generalized vector dominance model [12] also allow for the large difference between σL(V p) and σT (V p)(ξ ≈ 0.25). The dependence of vector particle interactions on the particle’s polarization has been known for many years in the case when the constituents of the particle are in the D-wave state. A good example of such effect is the deuteron interaction with matter [13]. The D-wave component

5 in the deuteron wave function leads to different absorption in matter for transversely and longitudinally polarized deuterons. This effect was experimentally measured in Dubna [14] and Juelich [15]. There are also predictions that the interaction of mesons with nonzero orbital momentum with nucleons is strongly correlated with the meson polarization [16, 17]. For the ground-state S-wave vector mesons (ρ, ω, φ) the D-wave component in their wave functions can emerge as a result of the Lorentz transformation [18]. The origin of a difference between

σT (VN) and σL(VN) explained by the appearance of a D-wave contribution in the vector meson wave function in the infinite momentum frame. The only attempt to study the impact of the vector meson polarization on its absorption was made many years ago at ITEP [19] using the charge exchange reaction π− + A → ρ0 + A0. The incoherent cross section and polarization of ρ mesons were measured on a set of different nuclei: C, Al, Cu, Pb. Due to the dominance of the pion exchange in this process a large fraction of longitudinally polarized ρ mesons was produced. At first glance the experimental data supported the assumption that σT (ρN) = σL(ρN). However, there are reasons against such a conclusion. It was shown [20] that due to the low energy of the primary beam (Eπ = 3.7 GeV) and the large decay width of the ρ meson some mesons decay inside the nucleus, which complicates the interpretation of the experimental data. The total cross sections of ρ and f(1270) mesons with a nucleon were measured at Ar- gonne [21] using the charge exchange process on neon nuclei π+ + Ne → ρ(f) + Ne0. In order to account for decays of the ρ mesons in nuclei (pπ = 3.5 GeV/c) the total cross section is required to be σ(ρN) ≈ 12 mb, which contradicts to the value σ(ρN) ≈ 27 mb obtained from the ρ meson photoproduction on nuclei. From our point of view this difference is a result of distinction between σT (ρN) and σL(ρN). In the charge exchange process mainly longitudinally polarized ρ mesons are produced, whereas in the photoproduction ρ mesons are transversely polarized.

The knowledge of the cross section σL(VN) is important for interpreting the color screening eﬀect in leptoproduction [22]. The idea of the color transparency (CT) is that an object (hadron) produced in certain hard-scattering processes has a smaller probability to interact in the nuclear matter due to its smaller size compared with the physical hadron. As a result, the color transparency increases the nuclear transparency. On the other hand, the nuclear transparency depends on the values of σL(VN) and σT (VN). Fig. 1 represents the dependence of the nuclear transparency in the ρ meson electroproduction as a function of the virtuality of

6 the photon Q2. The ρ meson absorption in nuclei decreases with the increase of the Q2, which is accounted for the CT effect. At the same time, the fraction of longitudinally polarized vector 2 mesons also grows at large Q as shown on the right plot of Fig. 1. If we assume that σT (VN) 2 σL(VN), the effect of the absorption weakening at large Q cannot be entirely described by the CT; differences between interactions of longitudinally and transversely polarized vector mesons with nucleon have to be considered.

The total cross sections σT (VN) and σL(VN) can be calculated in the framework of the √ color dipole model [24, 25]. The dependence of σL(ρN) and σT (ρN) on the energy W = s CLAS Collaborationcomputed / Physics Letters B 712 for(2012) 326–330 diﬀerent choices of the ρ meson329 wave functions is shown in Fig. 2 [26]. The cross sections obtained for the boosted gaussian wave function [27] are shown on the left plot and ADC/QCD holographic [28] wave function [29, 30] are presented on the right plot. The cross

section σL(ρN) is predicted to be smaller than σT (ρN) for both wave functions. Study photoproduction of ω mesons on diﬀerent nuclei and beam energies provides a unique opportunity to measure energy dependence of the nuclear transparency predicted by theoretical models [1] and extract the total cross section of longitudinally polarized mesons with nucleon

Fig. 3. (Color online.) Nuclear transparency as a function of lc . The inner error bars σL = areσ( theωN statistical). uncertainties Unlike andρ the outerand onesφ aremesons, the statistical and point-which due to the s-channel helicity conservation in to-point (lc dependent) systematic uncertainties added in quadrature. There is an additional normalization systematic uncertainty of 1.9% for carbon and 1.8% for iron photoproduction(not shown in the figure) are with produced acceptance and background mainly subtraction transversely being the polarized, the pion exchange in the ω meson main sources. The carbon data has been scaled byEur. a factor Phys. 0.77 to fit J. in C the (2009) same 62: 659–695 683 figure with the iron data.

+ − Fig. 2. (Color online.) The (π , π ) invariant mass histogram for iron. Panel (a): Before applying kinematic cuts. Panel (b): After applying kinematic cuts. The blue shadow area represents the background contribution. Panel (c): After background + − subtraction. Panel (d): The (π , π ) invariant mass histogram for deuterium after background subtraction. The solid curves are non-relativistic Breit–Wigner fit to the data. the acceptance was defined in each elementary bin in all rele- 2 0 vant variables; Q , t, W ,theρ momentum Pρ0 , and the decay 0 angle in the ρ rest frame θπ + , as the ratio of accepted to generated events. Each event was then weighted with the inverse + − of the corresponding acceptance. The weighted (π , π )mass spectra were fitted as shown in Fig. 2(c)usinganon-relativistic Breit–Wigner for the shape of a ρ0 while the shape of the background was taken from the simulation. The magnitudes of each contributing process were taken as free parameters in the fit of the mass spectra. The acceptance correction to the transparency ratio was found to vary between 5 and 30%. Radiative corrections 2 were extracted for each (lc , Q ) bin using our MC generator in 2 conjunction with the DIFFRAD [34] code developed for exclusive Fig. 4. (Color online.) Nuclear transparency as a function of Q . The inner error bars are statistic uncertainties and the outer ones are statistic and point-to-point2 04 vector meson production. The radiative correction to the trans- (Q 2 dependent) systematic uncertainties added inFig. quadrature. 20 TheQ curvesdependence are pre- of the longitudinal-to-transverse cross-section grated over the xB acceptance. Right panel: R for ZEUS (trian- parency ratio was found to vary between 0.4 and 4%. An additionalFIG. 1:dictions Nuclear of the FMS transparency[39] (red) and GKM [38] (green) asratio a models function for with exclusive (dashed–dotted of Qρ20.production Experimental on the data proton. are Left from panel: CLAS,R04 calcu- JLab [23]gles (left).)andRNPE for HERMES (squares), fitted separately according correction of around 2.5% was applied to account for the contri- and dashed curves, respectively) and without (dotted and solid curves, respectively) 0 04 bution of deuterium target endcaps. The corrected t distributions CT. Both models include the pion absorption effectlated when the fromρ meson the decays SDME in- r according to (69). HERMES proton data to (76). For all data points, total uncertainties are shown. Theoretical − 00 for exclusive events were fit with an exponential form Ae bt .The2 side the nucleus. There is an additional normalization systematic uncertainty of 2.4% 0 2 2 Q dependencefor carbon and 2.1% of forthe iron (not ratio shown in of the figure). the longitudinal-to-transverse cross sections for exclusive ρ production R =|T | /|T | 2 ± ± (filled squares) are compared to measurements of CLAS [61, 62], Cor- calculations [38]of 0 00 11 are shown as a dashed line at slope parameters b for H(3.59 0.5), C (3.67 0.8) and Fe = (3.72 ± 0.6) were reasonably consistent with CLAS [35] hydro- nell [63], E665 [64], H1 [12], and ZEUS [10, 11]. The more recent W 5 GeV; the uncertainties arising from the uncertainties in the par- gen measurements of 2.63 ± 0.44takenwith5.75GeVbeamen-on protonthat in [4] the (right). absence of CT effects, hadronic Glauber calculations ton distribution functions are shown as a shaded band [38] 2 CLAS data2 [62](small squares) are from a narrow bin in xB with ergy. would predict no Q dependence of T A since any Q dependence 0 The transparencies for C and Fe are shown as a function of lc in the ρ production cross section wouldapproximately cancel in the ratio. the The same xB as the HERMES data, which are inte- 2 in Fig. 3. As expected, they do not exhibit any lc dependence be- rise in transparency with Q corresponds to an (11 ± 2.3)% and 0 cause lc is much shorter than the C and Fe nuclear radii of 2.7 (12.5 ± 4.1)% decrease in the absorption of the ρ in Fe and and 4.6 fm respectively. Consequently, the coherence length effect C respectively. The systematics uncertainties were separated into cannot mimic the CT signal in this experiment. point-to-point uncertainties, which are lc dependent in Fig. 3 and 7 Fig. 4 shows the increase of the transparency with Q 2 for both Q 2 dependent in Fig. 4 and normalization uncertainties, which C and Fe. The data are consistent with expectations of CT. Note are independent of the kinematics. Effects11.3 such as Comparison kinematic cuts, to world data and models RNPE, which is corrected for the UPE contributions shown in the previous section to be of substantial size at in- Results for R from different experiments can be com- termediate energy. The HERMES data are compared to pared only if either R is independent of t ,orthet de- the recent high-energy data on R04 from ZEUS [11], for dσL dσT pendences of the cross sections dt and dt and the t which the UPE contribution is expected to be strongly sup- intervals of the measurements of R are the same. The t pressed. dependence of R is determined essentially by the t de- In order to investigate a possible W dependence of the 04 pendence of the SDME r00 (see (A.1)), which is found longitudinal-to-transverse cross-section ratio, the HERMES t to be approximately flat in both at HERMES (see and ZEUS data are fitted separately to a Q2 dependence sug- Fig. 10) and at H1 [12] and ZEUS [11] kinematics. For gested by VMD models [2, 8, 65]: this case, the ratio of the total cross sections coincides with the ratio of the cross sections that are differential Q2 c1 in t (see (34)). R Q2 = c , 0 2 (76) The left panel of Fig. 20 shows HERMES results on the MV Q2 dependence of R04, as measured on the proton, in com-

parison to world data. Given the experimental uncertain- where c0 and c1 are free parameters and MV is the mass 0 ties, there is no discrepancy with the data at lower energies of the ρ meson. The fit results are c0 = 0.56 ± 0.08, from CLAS [61, 62] and CORNELL [63]. The HERMES c1 = 0.47 ± 0.12 for HERMES and c0 = 0.69 ± 0.22, c1 = data at intermediate energies are not expected to agree ex- 0.59 ± 0.15 for ZEUS, with χ2/d.o.f. = 0.45 and 0.15 re- actly with those at high energies because of the UPE con- spectively. These χ2 values indicate that the fits are domi- tributions observed in the HERMES data, as discussed in nated by systematic uncertainties. Sects. 9 and 10. We note that SCHC violating amplitudes A W dependence of the Q2 slope is consistent with recent are also observed in the new CLAS data [62]. Additional calculations using a GPD-based model [38]. We note the reasons may be the importance of valence-quark exchange = for NPE amplitudes and also a generally different W de- agreement of these calculations performed at W 5GeV 2 2 pendence of the longitudinal and transverse cross sections, for Q values down to 3 GeV (see dashed curve in Fig. 20) 2 2 as recently discussed in Ref. [38] in the context of a GPD- with the highest Q = 3GeV point of HERMES. Uncer- based model. tainties in the model calculations originating from uncer- The right panel of Fig. 20 presents the HERMES re- tainties in the parton distributions employed are shown as sults on the longitudinal-to-transverse cross-section ratio a shaded band superimposed on the curve. FIG. 2: Energy dependence of the total cross sections σL(ρN) and σT (ρN) computed for different ρ meson wave functions: boosted gaussian wave function [27] (left) and ADC/QCD holographic [28] wave function [29, 30](right). photoproduction leads to the noticeable production of longitudinally polarized ω mesons [2]. The dependence of the spin density matrix elements on the invariant momenta transfer in the process γ + p → ω + p measured by SLAC [2] is presented in Fig. 3. The fraction of the longitudinally polarized ω mesons determined by the value of ρ00 is significant even at large beam energies of Eγ = 10 GeV. The total cross sections of longitudinally and transversely polarized mesons with nucleon σL,T = σ(ωN) can be obtained from the incoherent and coherent photoproduction, respectively.

III. PHOTOPRODUCTION OF ω MESONS ON NUCLEI.

In the late 60’s and early 70’s many experiments were carried out to study vector mesons photoproduction on nuclei [5]. These experiments had two main goals:

• Extraction of vector meson-nucleon total cross sections σ(VN) in order to check quark model predictions.

• Veriﬁcation of the vector dominance model (VDM) and ﬁnding the limits of its validity.

8 The first ω photoproduction experiments at high energies using a large set of nuclei were carried out by the Rochester group at Cornell [31, 32] and the Bonn-Pisa group at DESY [33]. The mean photon energies used at Cornell were 6.8 GeV and 9.0 GeV. The ω mesons were detected via the 3π decay mode. The Bonn-Pisa group used beam photons with a mean energy of 5.7 GeV. The ω mesons were reconstructed using the π0γ decay mode. Both experiments confirmed the naive quark model prediction: σ(ωN) = σ(ρN) = (σ(π+N)+σ(π−N))/2. A later experiment on ω photoproduction off nuclei at a mean energy of 3.9 GeV was performed at the electron synchrotron NINA at Daresburry [34]. The nuclear absorption of ω mesons was found to be in agreement with the previous experiments. The total cross section σ(ωN) was extracted from the coherent part of the photoproduction cross section, whereas the incoherent part was considered to be an undesirable background. Experiments confirmed quark model predictions for total cross section of vector mesons interaction with nucleon, which is not strange as long as from the coherent part of the cross section one extracts [1] only the transversely polarized mesons cross section σT (ωN). Recently, the omega mesons photoproduction was measured by CBELSA/TAPS [35] collaboration via the decay ω → π0γ and at by the CLAS collaboration at Jefferson Lab [36]

FIG. 3: Spin density matrix elements of ω mesons in the helicity system measured by the SLAC experiment [2].

9 using the rare electromagnetic decay mode ω → e+e−. The main goal was to investigate the impact of the nuclear environment on the vector mesons mass and decay width. In order to have a significant fraction of the ω mesons decay in the nuclei, the mesons momentum in both experiments was low (pω ≥ 0.8 GeV in CLAS experiment and pω ≥ 0.2 GeV in CBELSA/TAPS experiment). At such low momenta the large contribution from nucleon resonances complicates the interpretation of experimental results [38]. The CLAS collaboration observed a significantly stronger absorption of the ω meson than measured by the CBELSA/TAPS collaboration[43]. Both experiments obtained a relatively large in-medium width of ω mesons and σ(ωN) total cross section, which disagrees with measurements of the KEK-E325 experiment [39], where ω mesons were produced using a 12 GeV proton beam. The KEK-E325 collaboration also reported the ω-meson mass shift, which is not confirmed by the CBELSA/TAPS and E01-112 experiments. Disagreements between the experimental measurements are not fully understood up to now. In all these experiments no attempt was done to separate the absorption of transversely and longitudinally polarized omega mesons. This effect can potentially be studied using the GlueX detector in Hall D, the new experimental facility constructed at Jefferson Lab. The Hall D facility provides a photon beam produced by 12 GeV electrons using the bremsstrahlung process. The experiment will allow to study photoproduction of mesons by reconstructing both neutral and charged final states in the beam energy range between 5 GeV and 12 GeV. Photoproduction of ω mesons on nuclear targets in the GlueX kinematic region is a unique way to study the dependence of the strong interaction on the polarization of vector mesons. The reasons look as follows:

• Photoproduction of ω mesons on nucleons γN → ωN at the photon energies of several GeV is determined by t-channel Pomeron exchange (diffraction, natural parity exchange) and one-pion-exchange (unnatural parity exchange). The pion exchange leads to production of longitudinally polarized ω mesons, unlike the diffraction process, which results in the production of transversely polarized mesons due to s-channel helicity conservation. The contributions from the diffraction and pion exchange are almost equal at a photon

energy of Eγ = 5 GeV [5]. Measuring the ω meson production at diﬀerent energies would provide data samples with diﬀerent contributions of the longitudinally polarized ω mesons.

10 • In the coherent photoproduction the unnatural exchange part of the elementary amplitude cancels out since in the coherent processes the amplitudes for interactions with protons and neutrons are added with the opposite signs. Therefore, from the coherent photoproduction one can extract only the total cross section of transversely polarized vector mesons on nucleons [1].

• In the incoherent photoproduction the cross section on the nucleus is the sum of the photoproduction cross sections on individual nucleons. As a result ω mesons with both polarizations can be produced. This can be used to study the interaction of longitudinally polarized vector mesons with the matter [1].

IV. COHERENT PHOTOPRODUCTION

The diﬀerential cross section of coherent photoproduction of ω (nuclear target remains in the ground state) γ + A → ω + A reads [1]:

dσ dσ (0) = N | F (q , q, σ ) |2, (1) dt dt A L T

dσN (0) where dt is the diﬀractive part of the forward cross section on the nucleon γ(k) + N →

ω(p) + N, and FA(qL, q, σT ) is the nucleus form factor, which accounts for the ω absorption in nucleus. The form factor depends on the photon energy through the longitudinal momentum 2 mω transferred qL = 2k . The two dimensional transverse momentum ~q is given by the standard 2 2 θ 2 2 2 relation ~q = 4kpsin 2 , thus the invariant transfer momenta: t = (k − p) = −qL − q . In the coherent photoproduction, where one has to sum the elementary amplitude from different nucleons the part of photoproduction amplitude on nucleon relevant to one pion exchange has a different signs for photoproduction on proton and neutron. This leads to cancellation of one pion exchange part[44] and to production of only transversely polarized ω mesons in coherent photoproduction on nuclei [1]. Figure 4 shows the dependence of the form factor on the transfer momentum for two nuclei and different values of σT (ωN).

V. INCOHERENT PHOTOPRODUCTION

We propose to study two main physics topics using incoherent photoproduction of vector mesons:

11 • measure energy dependence of the nuclear transparency of vector mesons,

• measure the nuclear transparency and spin density matrix elements for ω mesons with the aim to extract the yet unmeasured cross section of longitudinally polarized ω mesons with nucleons.

Measurements of A-dependence of the nuclear transparency of vector mesons at different energies relevant to GlueX are important because they will provide information related to the long standing problem: weak energy dependence of the nuclear transparency measured for ρ mesons at Cornel [7], which contradicts theoretical predictions [6]. The nuclear transparency measured at two photon energies Eγ = 4 GeV and Eγ = 8 GeV is shown in Fig. 5. In this figure, the nuclear transparency is defined as Aeff = σA/σN , and hereafter we will follow this definition. The transparencies are similar for these energies within the errors limit unlike the theoretical calculations [6], which predict the significant decrease of the transparency with energy due

1 2Eγ to the impact of the energy-dependent coherence length τc = = 2 on the incoherent qL mV photoproduction. Especially interesting are measurements of the incoherent photoproduction of ω mesons on a set of nuclei [1]. Unlike the coherent photoproduction from which one can extract only the value of the transverse cross section σT (ωN), measuring ω cross section and spin density matrix elements on nuclei in the incoherent photoproduction allows one to determine the value of

2 2 400 7000

|F(q)| σ |F(q)| 350 T = 22 mb 6000 σ T = 26 mb 300 5000 σ = 30 mb T 250 4000 200 Lead Aluminum 3000 150

2000 100

1000 50

0 0 0 0.005 0.01 0.015 0.02 0 0.005 0.01 0.015 0.02 0.025 t ( GeV2 ) t ( GeV2 )

FIG. 4: Dependence of the nuclear form factors on the invariant transfer momentum for diﬀerent cross sections of transversely polarized ω mesons with nucleons.

12 VOLUME 23, NUMBER 10 PHYSICAL REVIE%' LETTERS 8 SEPTEMBER 1969 tatively the important prediction of vector dom- For this discussion, low-level nuclear excitation inance is that A. ,ff should fal1 with energy in the and even low-energy nuclear breakup are to be transition region mentioned above, with the fall thought of as elastic while inelastic reactions being more dramatic for big nuclei. presumably include production of extra particles, The apparatus has been discribed in a previous such as r's. An unambiguous division of this publication. ' Deuterium, carbon, copper, and sort is difficult, but if we suppose the inelastic silver targets of approximate thickness 0.1 radi- rate to be proportional to kp-k& we get for carbon ation length were used. pG production was mea- the fit shown in Fig. 1. According to this fit, at sured at average energies, (kz), of 4.0 andunknown8.0 longitudinalthe point crosswhere section weσL(ωNactually). Theran, incoherentthe inelastic part of the photoproduction cross GeV, at average angles of 0.08 and 0.04sectionrad, re- of ω mesonsrate inwas the typical15% of rangethe total of therate. momentumThe data transfersuggest 0.1 GeV2 < t < 0.5 GeV2 spectively. In some cases we counted 7t pairs of a higher power of kp kp and hence a lower con- can be presented in the following form [1]: rest mass other than 750 MeV to check for pos- tamination. For the 8-GeV data kp-k& was twice sible non- p background. Since no significant dσA(q) asdσ0large(q) and hence the contamination was prob- = (ρ00N(0, σL) + (1 − ρ00)N(k, σT )) background was observed, all measurements todt ablydt lar ger. Z 1 − exp(−σ R ρ(b, z)dz) be discussed in what follows were obtained atN(0, σ) = Figure 2 shows the resultsd2b of the measure- the peak of the p' mass spectrum. ments from theσ different nuclei at the two ener- Z To investigate inelastic p' production we count-N(k, σ) = gies.ρ(b, zFor) | Ea(b,nucleus z) |2dzd2ofb mass number A, the ef- ed p"s of fixed energy, k~ = 4 GeV, for various fective number of nucleons A,ff is inferred from Z Z z Z our σ 0 0 σ 0 0 iq (z0−z) σ 00 00 values of the bremsstrahlung end-point energyE(b, z) = exp(measured− ρ(b, zcross)dz ) −sectionρ(b,on z )thedz enucleus,L exp(dv/− ρ(b, z )dz ) (2) kp from carbon and silver. The results are dQ(A), 2 andz the measured2 deuterium cross sec- 2 z0 shown in Fig. I. For elastic production, Heresinceρ(r) is the nucleartion, using density;thedσ0(formulaq) = dσN (q) + dσU (q) is the diﬀerential cross section of ω meson the nuclear recoil energy is negligible, the inci- dt dt dt photoproduction on nucleon, which1.85(do/dQ) accounts for(A) diﬀraction and unnatural parity exchanges; ρ dent-photon energy is equal to kz. The points 00 (do/dn)(a = 2) plotted in Fig. I are counting rates per isequiva- the spin density matrix element in the helicity system, relevant to the fraction of longitudinally = = lent quantum. This means that, if kp is polarizedabove mesonsHere in photoproductionwe have taken onA, nucleon.I~(A 2) In Fig.1.85 6 andfrom 7 weour present the A-dependence the k& aperture, the number of photons capable previous measurements of the deuterium-to-hy- A of elastically producing p's in our apertureof theis nuclear transparencydrogen ratio.Aeff' andThis theratio spin densityis consistent matrix elementwith theρ00 calculated according held constant. The resulting elastic ratetois Eq. (2) for twoproton energiesand andneutron threeamplitudes values of σL.being The inputequal. valuesThe of ρ00 = 0.2 and total therefore independent of k„and the increase of reduction from 2 to 1.85 is due to the Glauber transverse ω-nucleon cross section [33] σT (ωN) = 26 mb are taken from SLAC measurements [2]. the measured rate with k, implies a substantia1 correction. One can argue, even in the absence rate for inelastic events. The spin densityof matrixinformation elementsabout in photoproductionthe relative onmagnitude nuclei andof nucleons can be related as We shall argue below that the vector-dominance prediction applies also to these inelastic reactions. However, the data were taken with A ff (0) k, just above k& in order to minimize this rate. 4 GeV ~ 50- $ This Experiment 86eV ) I $ ~ N (A, O, 58) ~e r~A (e GeVJ ) Theory err + N (A, 38,38)' r 20- Corbon A II i8 GeV) aC Silver Iu I 0- IA eff eD 5- 0 2 ~ ~ 0' Normal i z LJLI Here Q I- 2- IS E lostic 02 C Cu Ag

I I (I G lo 20 50 l00 200 A 5 6 7 8 9 lo GeV Peok Brernsstrohlung Energy KO FIG. 2. The cross sections at )t )=0.1 GeV" for in- FIG. 5: Nuclear transparencycoherent p photoproduction for incoherent photoproductionfrom complex ofnucleiρ mesonsare at | t |= 0.1 GeV2 and FIG. 1. Dependence of counting rate from carbon given as ratios, &eff to the one-nucleon cross section. and silver on peak bremsstrahlung energy, ko.diﬀerentThe energies [7].The data are to be compared with the central two smooth curve is a fit including elastic and inelastic pro- curves calculated from the Gottfried- Yennie theory. duction. The dashed curve is the elastic component. Also shown are calculations 13by Kolbig and Margolis of The arrow indicates the point at which data were taken. the related quantity NQ, a~, 02).

555 follows [1]:

A N(0, σL) ρ00 = ρ00 (3) ρ00N(0, σL) + (1 − ρ00)N(k, σT )

A Fig. 8 demonstrates our predictions for the dependence of Aeff and ρ00 on σL for lead nuclei.

90 90 eff Eγ = 5 GeV eff Eγ = 9 GeV A 80 A 80 σ = 0 70 L 70 σ L = 13 mb 60 σ 60 L = 26 mb 50 50 40 40 30 30 20 20 10 10 Al Cu Pb Al Cu Pb 0 0 50 100 150 200 50 100 150 200 Mass number (A) Mass number (A)

FIG. 6: Dependence of the nuclear transparency Aeff on the mass number for (a) σL = 13 mb and

(b) σL = 26 mb.

0.7 0.7 A 00 A 00 Eγ = 9 GeV ρ (a) ρ (b) ρ (∞) 0.6 0.6 Eγ = 5 GeV

0.5 0.5 ρ (∞)

0.4 0.4

0.3 ρ(0)0.3

0.2 0.2 ρ(0)

Al Cu Ag Ta Pb Al Cu Ag Ta Pb 0.1 0.1 50 100 150 200 50 100 150 200 A A

A A FIG. 7: A-dependence of the spin density matrix element ρ00 for (a) σL=13 mb and (b) σL=26 mb. ρ00 is shown for diﬀerent photon energies. ρ(∞) ρ(0) correspond to inﬁnite energy and energy-independent

A ρ00, respectively.

14 VI. MONTE CARLO SIMULATION

We studied reconstruction efficiencies of ω mesons in the beam energy range between 6 GeV and 12 GeV using detailed GlueX detector simulation. The ω mesons were generated in a γp → ωp reaction using Pythia event generator (with the Fermi motion of nucleons taken into account). Generated events were passed through the Geant simulation and were reconstructed using the official GlueX reconstruction package. The distribution of the invariant momentum transfer generated by Pythia is presented in Fig. 9. The slope of the distribution is similar to SLAC measurements [2] (t = −7.5 ± 0.8 GeV−2 at the beam energy of 9 GeV). The typical GlueX reconstruction resolution on t for ω → π0γ decays in the range t > 0.1 GeV2 is 0.016 2 GeV . Invariant mass distributions mγγ and m3γ are presented on the bottom plots of Fig. 9. Invariant mass resolutions for reconstructed π0 and ω mesons constitute about 7.8 MeV and 33 MeV, respectively. The missing-mass resolution is 190 MeV. Reconstruction efficiencies for ω → π+π−π0 and ω → π0γ decays are listed in Table I. The efficiencies are computed for events where a recoil proton is required to be reconstructed and events where no proton reconstruction is required. The relative dependence of the reconstructed efficiency on the beam energy is found to be relatively small, on the level of 15%.

110 0.8 A 00 eff (a) E = 5 GeV γ ρ

A (b) 100 0.7 90 Eγ = 9 GeV 0.6 80 ρ ∞ 70 0.5 ( ) A (0) 60 eff 0.4

50 0.3 40 0.2 ρ(0) 30 A (∞) 20 eff 0.1 10 0 0 5 10 15 20 25 30 0 5 10 15 20 25 30 σ σ L (mb) L (mb)

A FIG. 8: (a) The nuclear transparency Aeff and (b) the spin density matrix element ρ00 as a function of σL for lead nucleus. The transverse ω- nucleon cross section σT and the spin density matrix element

ρ00 are taken to be 26 mb and 0.2 respectively.

15 VII. RECONSTRUCTION OF ω MESONS

We studied capabilities to reconstruct ω mesons produced on nuclear targets by using the GlueX data with an empty target acquired in Spring 2017. In these data ω mesons can be produced on the target walls and the air downstream the target. The walls and the window are made from Kapton with the total thickness of about 280 µm, which corresponds to about 2 · 1021 atoms/cm2 (assuming that Kapton consists mostly of Carbon). The target cell contains some cold H2 gas remaining after the liquid hydrogen was drained from the cell. The density −3 3 of the H2 gas is estimated to be about 1.8 · 10 g/cm , which can be compared with the air density of 1.2 · 10−3 g/cm3. The total number of hydrogen atoms in the cell corresponds to

Constant 6.663 ± 0.016 Constant 380.1 ± 7.4 3 Mean 0.0008513 ± 0.0002442 10 Slope −7.552 ± 0.088 450 Sigma 0.01695 ± 0.00022 (a) 400 (b) 350 102 300 250 10 200 150 100 1 50

0 0.2 0.4 0.6 0.8 1 1.2 0−0.15 −0.1 −0.05 0 0.05 0.1 0.15 2 2 | t | (GeV ) tgen - trec (GeV )

Constant 205.6 ± 4.1 Constant 295.6 ± 6.0 Mean 0.133 ± 0.000 400 Mean 0.7693 ± 0.0005 Sigma 0.007725 ± 0.000107 Sigma 0.03381 ± 0.00049 250 350

200 (c) 300 (d) 250 150 200

100 150 100 50 50

0 0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 00.5 0.6 0.7 0.8 0.9 1

mγ γ (GeV) m3γ (GeV)

FIG. 9: Monte Carlo simulation for the reaction γp → ωp, ω → π0γ (a) Distribution of the invariant transfer momentum generated by Pythia (b) Resolution of the transfer momentum, tgen − trec for

2 0 t > 0.1 GeV (c) Invariant mass Mγγ of reconstructed π candidates (d) Invariant mass M3γ.

16 Final state

p π+π−π0 π+π−π0 p π0γ π0γ

Eﬃciency (%) 12.9 21.4 28.5 51.9

TABLE I: Reconstruction efficiency of ω mesons produced in the γp → ωp reaction and decaying to ω → π+π−π0 and ω → π0γ final states. about 3.3 · 1022 atoms/cm2. We select ω → π+π−π0 candidates produced on the target walls or air by reconstructing the π± vertex. Z-coordinate of reconstructed vertices is presented in Fig. 10. Red arrows on this plot around the walls and air, denote Z-coordinates of vertices of ω candidates accepted for the analysis. We consider events with only two oppositely charged pion track candidates, a proton track consistent with the dE/dx of a proton hypothesis in the drift chambers, and a π0 candidate. Events with extraneous reconstructed tracks or clusters in the calorimeters are rejected. The energy of reconstructed ω mesons is required to be larger than 6 GeV. The invariant mass distribution Mπ+π−π0 is presented in Fig. 11 for two types of events: (1) proton is reconstructed in the event (right plot) and (2) no proton candidate is found (left plot). A relatively small background is observed for ω → π+π−π0 decays for events with and without a reconstructed proton. For reconstruction of ω → π0γ decays we don’t apply any constraints on the production vertex as there are no charged tracks in the final state except for some events with a recoil proton originating in the incoherent production on nuclei or in the γp → ωp reaction on the residual hydrogen gas in the target cell. The contribution to the production of ω mesons from the hydrogen gas is estimated to be smaller than that from nuclear photoproduction on the target walls and air. The invariant mass distribution M3γ is presented in Fig. 12. The ω peak on the mass distribution for events with no reconstructed proton (no vertex) is broad and shifted towards small masses. This can be accounted by the fact that ω mesons are produced on the air outside the target, at larger z, while in the reconstruction photons are assumed to originate from the center of the target, if vertex is not found. Under this assumption, the reconstruction angles between product decays are smaller than the real ones, resulting in the mass shift of π0 and ω mesons. In the proposed experiment with a nuclear target, there will be no mass shift,

17 Target cell walls Vacuum window

Air

Cold H2 gas target cell

Z (π+ π−) (cm)

Kapton Kapton Air

FIG. 10: Z-coordinate of reconstructed vertices of π± mesons originating from ω → π+π−π0 candidates in runs with an empty target. The target cell is 30 cm long with the center positioned at Z = 65 cm. as the position of the foil target is well defined. Background from ω production on air and the target walls will be subtracted using runs with an empty target. As expected, there is no ω mass shift when a proton is reconstructed (see the right plot in Fig. 12). In this case the proton defines the production point for π0γ. The signal to background ratio (S/B) for ω → π0γ is found to be relatively good, on the level of 2. In reality the S/B is expected to be better due to to the narrower mass distribution of reconstructed ω mesons on a thin target with a well-defined position.

VIII. RUN CONDITIONS

Photoproduction of vector mesons will be studied in the large beam energy range Eγ > 6 GeV using a photon beam produced by 11.6 GeV CEBAF electrons incident on an amorphous radiator. The energy of a beam photon is reconstructed by detecting bremsstrahlung electrons in the tagger hodoscope (TAGH) and microscope (TAGM) scintillator detectors. The tagging

18 300 60

250 50

200 40 Events / 20 MeV Events / 20 MeV 150 30

100 20

50 10

0 0 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 m (π+π-π0) (GeV) m (π+π-π0) (GeV)

FIG. 11: Invariant mass distribution Mπ+π−π0 for events produced on target walls and air in runs with an empty target. The right plot corresponds to events with reconstructed proton. The left plot corresponds to events when no proton is found. detectors provide a continuous energy coverage in the range between 7.8 GeV and 11.7 GeV and a typical electron detection efficiency of 90 − 95%. The TAGH counters are sampled below 7.8 GeV with an average sampling fraction of about 0.3. Reconstruction of the beam energy in the wide range is complicated due to the relatively large rate of accidental hits in the tagging detectors, i.e., hits originating from different events. In order to reduce the accidental rate, we are going to decrease the flux of uncollimated photons by a factor of 12 compared with the GlueX flux at high luminosity[45] and use larger collimator with a diameter of 5 mm. The fraction of events with multiple beam photons originating from the same beam bunch[46] in the energy between 6 GeV and 11.7 GeV is about 20%. The beamline conditions of the proposed experiment are listed in Table II. We propose to use four nuclear targets: C, Si, Sn, Pb, with a thickness of 7% radiation length

(the GlueX LH2 target thickness is 3.5%X0). Data will be taken on each individual target; multiple targets cannot be used in parallel due to the target misidentification in reconstruction of the multi-photon final state (π0γ). Properties of nuclear targets are listed in Table III. Reduction of the photon beam flux and using thin targets is also required by the electromagnetic and neutron backgrounds origination from nuclei. The neutron background is specifically

19 350 100 300 80 250 Events / 20 MeV Events / 20 MeV 200 60

150 40 100 20 50 0 0 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 m (3 γ) (GeV) m (3 γ) (GeV)

FIG. 12: Invariant mass distribution M3γ reconstructed in runs with an empty target. The right plot corresponds to events with reconstructed proton. The left plot corresponds to events when no proton is found. critical for Silicon photomultipliers used in the barrel calorimeter and start counter. For the proposed run conditions, the electromagnetic background level (which is proportional to the photon ﬂux and the target thickness in units of radiation lengths) is expected to be signiﬁcantly smaller than for GlueX. The neutron background in the GlueX experiment was simulated using

Geant provided by the RadCon group and Fluka for the LH2 and liquid He targets [40]. The background induced by heavier nuclear targets can be scaled to He [41] and is not expected to exceed the GlueX level.

IX. PRODUCTION RATES AND BEAM REQUEST

Reconstruction efficiencies for ω → π0γ and ω → π+π−π0 decays are described in Section 8. The number of reconstructed ω → π0γ decays produced in the incoherent process on a Carbon target as a function of the beam energy is presented in Fig. 13. The production rate is normalized to 1 day of taking data. In the simulation we used the realistic photon beam flux and efficiencies in the tagging detectors. The number of ω mesons reconstructed in the π0γ and π+π−π0 final states on the proposed nuclear targets is listed in Table IV.

20 Conditions GlueX Proposed Exp

Collimator (mm) 3.4 5

−4 −4 Radiator thickness (X0) 2 · 10 10

(Diamond) (Aluminum)

Beam current (µA) 1.1 0.18

Photon beam energy range of interest (GeV) 8.4 - 9.1 6 - 11.7

Rate of uncollimated photons (Hz) 1.2 · 108 5.3 · 107

Photon rate on target (Hz) 5 · 107 1.5 · 107

TABLE II: Beamline conditions of the proposed experiment compared with GlueX.

LH2 (GlueX) C Si Sn Pb

A 1 12 28 119 207

Target thickness (X0) 3.4% 7 %

Relative EM background 1 0.3

Number of atoms (N/cm2) 1.28 · 1024 1.5 · 1023 3.3 · 1022 3.1 · 1021 1.3 · 1021

N T arget · A/N LH2 1 1.4 0.7 0.3 0.2

Incoherent cross section (µb)

6 GeV 17 30 75 119

12 GeV 12 20 45 67

TABLE III: Properties of nuclear targets proposed for the experiment.

We propose to take data for 28 days on several nuclear targets including calibration runs and runs with empty target. The proﬁle of the requested beam time is shown in Table V. For each target, we plan to reconstruct about 103 ω → π0γ decays per 1 GeV beam energy range produced in the incoherent process. We expect that the total error on the nuclear transparency measurements for each nuclear

21 10000

8000 N reconstructed 6000

4000

2000

0 6 7 8 9 10 11 12 Beam energy (GeV)

FIG. 13: The number of reconstructed ω → π0γ candidates produced in the incoherent process on a carbon target with the momentum transfer t between 0.1 GeV2 and 0.5 GeV2 as a function of the beam energy. The yield is normalized to 1 day of taking data.

. target will be dominated by the systematic error, which should not exceed 5%. The list of possible main sources contributing to the systematic error is shown in Table VI. In the data analysis we will normalize the transparency to carbon data (or He data). This will allow us to avoid systematic uncertainties such as the ω production cross section on the nucleon and related reconstruction efficiencies. Expected errors on measurements of the energy dependence of the nuclear transparency (Aeff ) are presented on the left plot of Fig 14. The nuclear transparency for different values of σL with projected errors from the proposed experiment is shown on the right plot of Fig 14. The data sample acquired with the proposed experiment will allow to study nuclear transparency of other mesons decaying into different final states such as φ (φ → K+K− and + − 0 + − φ → π π π ) and Ks → π π with an expected statistical errors of a few percent.

X. SUMMARY

We propose to use the GlueX detector to study the photoproduction of the vector mesons ρ, ω, φ on a set of nuclear targets: C, Si, Sn, and Pb in the large photon beam energy range between 6 GeV and 12 GeV. The primary goal of the experiment is to:

22 3 Target Nrec per day (×10 )

ω → π0γ ω → π+π−π0

[6 - 9] GeV [9 - 12] GeV [6 - 9] GeV [9 - 12] GeV

C 35.2 (15.8) 24.5 (11.0) 176 (79) 122.5 (55)

Si 12.9 (5.8) 8.6 (3.9) 64.5 (29) 43 (19.5)

Sn 3.0 (1.4) 1.7 (0.8) 15 (7) 8.5 (4.0)

Pb 1.9 (0.9) 1.0 (0.5) 9.5 (4.5) 5 (2.5)

TABLE IV: The number of reconstructed ω → π0γ and ω → π+π−π0 decays produced in the incoherent process on diﬀerent nuclei targets. Numbers in parenthesis correspond to ω mesons reconstructed in the t range between [0.1 - 0.5] GeV2. The yield is normalized to 1 beam day.

Activity Time (days)

C production 3

Si production 4

Sn production 6

Pb production 10

Empty target 3

Calibration 2

Total 28

TABLE V: Beam time request.

1. Measure nuclear transparency of ω mesons using incoherent photoproduction on diﬀerent targets and extract the total cross section of longitudinally polarized ω mesons on a

nucleon, σL(ωN). This knowledge is important for many theoretical models. The ω mesons will be identiﬁed using the ω → π0γ and ω → π+π−π0 decay channels. The total error on the nuclear transparency measurements will be dominated by the systematic error, which is expected to be within 6% (see projected errors in Fig. 14).

23 Event selection and signal yield 3%

Measurements of ρ00 4%

Target thickness 0.5% − 1%

Photon ﬂux determination 1.5%

Reconstruction eﬃciencies 2%

Total 6%

TABLE VI: List of systematic errors expected in measurements of the nuclear transparency.

80 50 eff No E dependence σ L = 13 mb A 45 Eγ = 5 GeV σ 70 L = 26 mb Eγ = 9 GeV 40 GlueX 60 GlueX 35 50 30 40 25 30 20 20 15

10 10 Si Sn Pb Si Sn Pb 5 50 100 150 200 50 100 150 200 A A

FIG. 14: Dependence of the nuclear transparency Aeﬀ on the beam energy (left) and cross section σL (right). Markers correspond to the projected errors of the proposed experiment.

2. Measure spin density matrix elements for ω mesons using incoherent photoproduction, which will allow to unambiguously separate production of longitudinally and transversely polarized ω mesons. The dependence of the spin density matrix elements on the atomic weight A is the direct indication of the impact of the meson’s polarization on interactions with nucleons and nuclei. These measurements should provide an independent way to

extract σL(ωN).

24 3. Measure the nuclear transparency of light mesons such as ρ, ω, φ to study the dependency of the nuclear transparency on the beam energy and to compare measurements with the theoretical predictions. Such measurements will probe the degree of photon shadowing in nuclear matter and shed light on a long standing problem: the weak dependence of the measured nuclear transparency with energy, which contradicts theoretical predictions. Data samples acquired on each nuclear target will allow to measure the nuclear transparencies with statistical errors between 1% and 5%.

The data sample acquired with the experiment is expected to allow to study other physics topics. For example, the absorption of different projections of the total orbital momentum of a tensor meson f2(1270) can be measured[47]. Studies of the nuclear transparency in photoproduction of vector mesons can be extended to the region of the larger transfer momenta | t | > 1 − 2 GeV2, where the color transparency effects can be investigated [48]. The expected length of the experiment is 28 days of taking data. The detector will be operated at small luminosity. No modifications of the GlueX detector except replacing the LH2 target with the nuclear targets are required.

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[47] f2(1270) meson can be clearly reconstructed with the GlueX detector [48] The proposal to study the color transparency in photoproduction of mesons at large transfer momentum using the GlueX detector will be presented at PAC.