Diffractive Phi Analysis Note

Precision Extraction of Momentum Transfer in Diffractive Coherent Exclusive Vector Meson Production Maci Kesler1, Ashik Ikbal Sheikh1, Rongrong Ma2, Zhoudunming Tu2, Thomas Ullrich2, and Zhangbu Xu1,2 1Department of Physics, Kent State University, Kent, 44242, OH, USA 2Physics Department, Brookhaven National Laboratory, Upton, 11973, NY, USA December 15, 2025 Abstract Exclusive diffractive vector meson production is a critical component of the e+Aprogram at the EIC. The exclusivity of the event makes it an experimentally clean and ideal measurement to study the onset of saturation and other QCD phenomena. Diffractive processes, e+A→e′+A′+V M where V M =J/ψ, ϕ, etc., allow the measurement of momentum transfer (|t|). A Fourier-Bessel transformation of |t|enables us to extract the spatial distribution of the gluons inside the nucleus. This analysis focuses on improving the precision of the extraction of |t|. i Contents 1 Introduction 1 2 Simulation Overview 2 2.1 Event Generator Details . . . . . . . . . . . . . . . . . . . . . 3 3 Event Selection 4 3.1 TheCodeLogic.......................... 4 3.1.1 Breakdown: the analysis . . . . . . . . . . . . . . . . . 4 3.1.2 Breakdown: the transformation . . . . . . . . . . . . . 9 3.2 Cuts ................................ 9 3.2.1 Reconstruction Methods . . . . . . . . . . . . . . . . . 20 3.3 Systematic Uncertainies . . . . . . . . . . . . . . . . . . . . . 24 3.3.1 DIS Background . . . . . . . . . . . . . . . . . . . . . 27 3.3.2 ρProduction ....................... 31 3.3.3 Incoherent Production . . . . . . . . . . . . . . . . . . 32 3.4 AnalysisCode........................... 36 4 Results and Discussion 37 ii 1 Introduction The goal of this analysis is to advance the measurement of the nuclear momentum transfer distribution (|t|) through coherent exclusive vector meson (VM) production. Coherent exclusive VM production is considered a golden channel for imaging the gluon structure in nuclei and testing QCD properties, such as saturation [1]. Figure 1 shows the process of exclusive VM e A V M e′ A′ t γ∗(Q2) q ¯q Figure 1: Diagram of coherent exclusive VM production. production. The incoming electron (e) emits a virtual photon (γ∗) which then fluctuates into a quark-antiquark pair (qand ¯qrespectively) which interacts with the target (A) via a Pomeron and then recombines to form the final state VM (ϕ→K+K−in this analysis). The momentum transfer distribution forms a diffractive pattern that encodes information about the spatial distribution of gluons in the hadron wave function [2]. Since |t|is conjugate to the impact parameter, a Fourier-Bessel (Hankel) transformation of the distribution enables us to obtain the spatial profile of the gluon density. We define the Mandelstam variable |t|as |t|=−(PA′−PA)2,(1) where pA′and pAdenote the four-momenta of the outgoing and incoming nucleus. However, the |t|distribution is a challenging measurement, as it depends on the outgoing nucleus’ momentum, which, for heavy nuclei, we cannot access precisely. Consequently, we have to use different methods to reconstruct this measurement. There are two main complications with this: limited precision and a large background from incoherent production 1 where the nucleus breaks up. This analysis utilizes a projective technique, as demonstrated in [3], to reconstruct the |t|distribution. After constructing the momentum transfer profile, we can take a FourierBessel transformation to extract the spatial distribution of the gluons [4]. As shown in [5], a 2-dimensional transformation of the transverse |t|distribution gives the transverse distribution of the spatial profile. The transformation used is given by F(b)∝1 2πZ∞ 0 dqTqTJ0(bqT)sdσ d|t|,(2) where J0is a Bessel function of the first kind. This analysis confirms the improvement of the measurement of the tdistribution which facilitates gluon imaging. 2 Simulation Overview The Sartre event generator was used to simulate coherent exclusive ρ production for the purpose of a background study as well as coherent exclusive ϕproduction. All energy configurations in this analysis are for 10x100 GeV beams. The cross sections for the simulated datasets are listed in Table 1. For the ϕfiles, the detector geometry, CraterLake 25.10.2, can be found on the ePIC Campaign Simulation webpage [6]. The specific files used are under epic_craterlake/EXCLUSIVE/DIFFRACTIVE_PHI_ABCONV/ sartre1.39-1.0/eAu/coherent/bsat/10x100. These files are also accessible via eic-shell by the following commands: •xrdfsroot://dtn-eic.jlab.org •ls /volatile/eic/EPIC/RECO/25.10.2/epic_craterlake/ EXCLUSIVE/DIFFRACTIVE_PHI_ABCONV/sartre1.39-1.0/eAu/ coherent/bsat/10x100 A total of 2352 files were used under the base name of sartre1.39-1.0_ coherent_phi_eAu_bsat_10x100_ab.*.eicrecon.edm4eic.root, where ∗ indicates a wildcard. Similarly, for the ρfiles, the detector geometry is CraterLake 25.10.3 and the specific files are under 2 epic_craterlake/EXCLUSIVE/DIFFRACTIVE_RHO_ABCONV/sartre1.39-1. 1/eAu/coherent/bsat/10x100/q2_1to20. 2255 files were used in this analysis under the base name of sartre1.39-1.1_coherent_rho_eAu_ bsat_10x100_q2_1to20_hiAcc.*.eicrecon.edm4eic.root. The BeAGLE event generator was used to simulate inclusive DIS events for the purpose of a background study as well as for incoherent production of diffractive ϕ. These files are also accessible via eic-shell and retrieved in the same way as stated above. For the DIS files, the detector geometry is from CraterLake 25.10.2. The specific files used are under epic_craterlake_without_zdc/DIS/ BeAGLE1.03.02-1.0/eAu/10x100/q2_1to10, where 4998 files were used. The files have a base name of BeAGLE1.03.02-1.0_DIS_eAu_10x100_q2_ 1to10_ab_run*.eicrecon.edm4eic.root. For the incoherent files, the detector geometry is from CraterLake 25.10.3, with the file names being under epic_craterlake/EXCLUSIVE/DIFFRACTIVE_PHI_ABCONV/BeAGLE1.03.021.1/eAu/10x100/q2_1to10000, where 2599 files were used and have a base name of BeAGLE1.03.02-1.1_phi_eAu_10x100_q2_1to10000_hiAcc_ run*.eicrecon.edm4eic.root. Note that campaigns 10.25.2 and 10.25.3 were both used in this analysis. There was a memory issue in 10.25.2 but the results of the changes to 10.25.3 do not affect my analysis. Further information about this can be found on the Github [7]. Table 1: Cross sections for simulated datasets. Dataset Cross section (σ) [nb] Sartre coherent diffractive ϕ σϕ= 459.05 BeAGLE incoherent diffractive ϕ σ′ ϕ= 261.95 Sartre coherent diffractive ρ σρ= 5418.68 BeAGLE DIS background σDIS = 50184.8 2.1 Event Generator Details The version of Sartre used is 1.39-1.0 for coherent diffractive ϕproduction and 1.39-1.1 for coherent diffractive ρ. More details on the Sartre event generator can be found in [8, 9] while detailed information regarding the simulated 3 data set can be found on GitHub [10]. The versions of BeAGLE used for incoherent ϕproduction and DIS inclusive background are BeAGLE1.03.021.1 and BeAGLE1.03.02-1.0 respectively. They can both be found on GitHub [11]. For more information on the BeAGLE event generator, see [12]. 3 Event Selection 3.1 The Code Logic The code processes the events from the Sartre and BeAGLE files and reconstructs the kinematics for the beam particles, scattered electrons (e′), and produced VMs. This analysis uses different methods to reconstruct the |t| distribution by invoking cuts and momentum projection along the direction normal to the electron scattering plane (ˆn), as shown in Fig. 2, to resolve the diffractive pattern and the resulting gluon distribution through a FourierBessel transformation. Scattering Plane e′ eγ∗ ˆnˆs Production Plane V M A A′ Decay Plane X+ X− Figure 2: Diagram of exclusive VM production. The blue arrow indicates the normal direction, ˆn, from the electron scatting plane. The red arrow show the spin direction of the emitted virtual photon. The VM production and decay planes are also shown. 3.1.1 Breakdown: the analysis Each iteration of the event reading loop processes one event from the input tree. The events are processed in the following way: •We first check if there are hits in the off-momentum detectors (OMD), Roman Pots (RP), or zero-degree calorimeters (ZDC) to remove incoherent events. We do this by forming arrays from the OMDs, RPs, and 4 ZDC. These are used for incoherent or background event vetoes. Note that we do not have branches for the B0 detector at the time of writing this so it is omitted in this analysis. –If there are hits and we want to veto, we break out of the event loop. –This step is irrelevant for the Sartre files because they do not have the branches for the detectors as they are specifically for coherent events, thus, this step is only performed on the BeAGLE files. •Build Monte Carlo (MC) particles: –Loop over MC particles (which represent the truth) to identify the electron, beam particle, e′, and the VM decay daughters produced (in this analysis ϕ→K+K−). ∗In this loop, we also check if η > 3.5 and if it is we count it as incoherent. Again, this step is only done for the BeAGLE files as it is assumed that the Sartre files produce only coherent exclusive diffractive events. ∗Furthermore, we require 0.9383 <mass <0.9838 to be sure that we are not rejecting decay daughters when we use this as an incoherent check for the BeAGLE files. Sartre automatically sets this mass for the Abeam and scales the momentum appropriately. –We now make cuts on the MC phase space variables such that the virtuality of the photon (Q2) is 1 < Q2<10, and the inelasticity (y) is 0.01 < y < 0.85. –If the VM does not have zero energy or rapidity |yϕ|>3.5, we build our kinematic variables (i.e. Q2,y,x,|t|, etc). •Build reconstructed particles: –Technique for e′(Note that this method implements the electron finding method [13], but at the time of writing this, the energy isolation cut has not yet been implemented): ∗Find the highest energy cluster in the electron end cap by looping over the electromagnetic calorimeter (EMCal) clusters. This is then defined as the maximum energy and is used to define the positions xand y. 5 ∗Repeat this process, but instead look for the highest hit energy (above a threshold energy of 10 MeV) in the EMCal by looping over individual calorimeter cells and store that energy and position. ∗Build a 3x3 cluster around this position, mimicking calorimeter showers. ∗By summing nearby hit energies (within 70 mm of the maximum hit energy), we form a shower. This gives a better estimate of the total energy and position to reconstruct the particle energy and impact point. ∗Take the weighted average of this cluster position to define the final cluster position. ∗Add a 4.4% energy calibration to correct the EMCal energy response and define this as the final cluster energy. ∗Loop over the EMCal track to match the clusters to the track in xand y. This ensures that the EMCal cluster is associated with a particle track. ∗Lastly, we ensure that the reconstructed electron ID matches the MC electron ID and we require that the charge is negative. –Loop over the tracks to build the hadronic final state (HFS) from all tracks, excluding e′. ∗We check if η > 3.5 and ensure that we only have 2 particles, if these conditions are not met, we mark it as incoherent. ∗This identifies the VM daughters produced, in this case, the kaons. ∗The HFS should be ϕ→K+K−and e′since the event is coherent and exclusive. –We enforce cuts on the following reconstructed quantities: E−pz, E/p,Q2,y, and the VM which will be gone over in more detail in Section 3.2. –Figures 3–6 show the energy and θdistributions from the resulting scattered electron. 6 0 0.5 1 1.5 2 2.5 3 θ 10 2 10 3 10 4 10 5 10 6 10 counts MC RECO Truth vs Recoθ 1 10 2 10 3 10 4 10 5 10 2.7 2.8 2.9 3 3.1 MC θ 0.02− 0.015− 0.01− 0.005− 0 0.005 0.01 0.015 0.02 MC θ)/ MC θRECO θ ( Resolutionθ 1 10 2 10 3 10 4 10 5 10 6 10 2.7 2.8 2.9 3 3.1 RECO θ 2.7 2.75 2.8 2.85 2.9 2.95 3 3.05 3.1 MC θ Responseθ Figure 3: The leftmost plot shows the reconstruction of θein comparison with the truth. The middle plot shows the resolution and the rightmost plot shows the response. 1 10 2 10 3 10 4 10 5 10 6 10 2.7 2.75 2.8 2.85 2.9 2.95 3 3.05 MC θ 2.7 2.75 2.8 2.85 2.9 2.95 3 3.05 RECO θ Bin Migration 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 reco bin θ 0 0.2 0.4 0.6 0.8 1 Purity bin width=0.031 Purity 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 true bin θ 0 0.2 0.4 0.6 0.8 1 Stability bin width=0.031 Stability 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 θ 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Acceptance Acceptance 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 θ 0 0.2 0.4 0.6 0.8 1 Efficiency Efficiency 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 θ 4 10 5 10 6 10 Corrected Acceptance Corrected Figure 4: QA plots for θe. 7 1 10 2 10 3 10 4 10 5 10 6 10 0 0.02 0.04 0.06 0.08 0.1 MC x 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 RECO x Bin Migration 0 0.01 0.02 0.03 0.04 reco bin x 0 0.2 0.4 0.6 0.8 1 Purity bin width=0.005 Purity 0 0.05 0.1 0.15 0.2 true bin x 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Stability bin width=0.005 Stability 0 0.05 0.1 0.15 0.2 x 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Acceptance Acceptance 0 0.05 0.1 0.15 0.2 x 0 0.2 0.4 0.6 0.8 1 Efficiency Efficiency 0 0.05 0.1 0.15 0.2 x 3 10 4 10 5 10 6 10 Corrected Acceptance Corrected Figure 12: QA plots for x. –Stability: Ratio of events in a given MC bin that are reconstructed into the same bin. High stability corresponds to events staying in their bin. Stability = Ni→i ΣjNi→j (9) –Acceptance: Fraction of true events that are reconstructed anywhere and survive the selection cuts. This should be a smooth distribution whereas sharp fluctuations indicate a cut boundary or detector geometry edge. We want values to be close to 1. Acceptance = ΣjNi→j Ntrue i (10) –Efficiency: Ratio of true events that are reconstructed and pass final selection criteria. Efficiency = Nreco bin i Ntrue i (11) –Corrected: Acceptance-corrected yield per true bin. This should 14 be comparable to the MC truth distribution. Corrected = Nreco bin i Acceptance (12) •Vector Meson: We reject events where the VM has zero energy to confirm that we skip events without a produced VM. Furthermore, we want to look at regions where the VM is produced centrally to verify that we have a distinct diffractive event. This is done by placing a cut on the VM rapidity which defines how forward or backward a particle is moving in the beam direction. For this reason, we place a constraint on the VM rapidity to be |yϕ|<3.5. Lastly, we use the constraint |mVM −1.02|GeV/c2<0.02 GeV/c2to ensure that we are selecting ϕsince mϕ≈1.02 GeV/c2. VM reconstruction is discussed in more detail in Section 3.2.1 and is shown in Figs. 13 and 15 while the QA plots are presented in Figs. 14 and 16. 0 1 2 3 4 5 6 7 8 9 10 [GeV/c] T,VM p 1 10 2 10 3 10 4 10 5 10 6 10 counts MC RECO Truth vs Reco (VM) T p 0 0.5 1 1.5 2 2.5 3 [GeV/c] T,VM,MC p 0.1− 0.08− 0.06− 0.04− 0.02− 0 0.02 0.04 0.06 0.08 0.1 T,MC )/p T,MC -p T,RECO (p 1 10 2 10 3 10 4 10 Resolution (VM) T p 0 0.5 1 1.5 2 2.5 3 [GeV/c] T,VM,RECO p 0 0.5 1 1.5 2 2.5 3 [GeV/c] T,VM,MC p 1 10 2 10 3 10 4 10 5 10 Response (VM) T p Figure 13: The leftmost plot shows the reconstruction of pTfor the VM in comparison with the truth. The middle plot shows the resolution and the rightmost plot shows the response. •Momentum Distribution: For the new method presented in this analysis (projection method), we want to find the region of phase space where the four-momentum of the VM is dominate in the direction normal (ˆn) to the electron scattering plane [3]. The reason for this is that |t|component along the ˆndirection is unaffected by the momentum resolution e′. Therefore, we apply a cut on the angle between ˆnand 15 1 10 2 10 3 10 4 10 5 10 0 0.5 1 1.5 2 2.5 3 [GeV/c] T,VM,MC p 0 0.5 1 1.5 2 2.5 3 [GeV/c] T,VM,RECO p Bin Migration 0 0.5 1 1.5 2 2.5 3 [GeV/c] T,VM,reco bin p 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Purity bin width=0.05 GeV/c Purity 0 0.5 1 1.5 2 2.5 3 [GeV/c] T,VM,true bin p 0 0.2 0.4 0.6 0.8 1 Stability bin width=0.05 GeV/c Stability 0 0.5 1 1.5 2 2.5 3 [GeV/c] T,VM p 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Acceptance Acceptance 0 0.5 1 1.5 2 2.5 3 [GeV/c] T,VM p 0 0.2 0.4 0.6 0.8 1 Efficiency Efficiency 0 0.5 1 1.5 2 2.5 3 [GeV/c] T,VM p 3 10 4 10 5 10 6 10 Corrected Acceptance Corrected Figure 14: QA plots for the VMs pTdistribution. 0 2 4 6 8 10 12 14 16 18 20 [GeV] VM ) z (E-p 2 10 3 10 4 10 5 10 counts MC RECO Truth vs Reco (VM) z E-p 0 2 4 6 8 10 12 14 16 18 20 [GeV] VM,MC ) z (E-p 0.1− 0.08− 0.06− 0.04− 0.02− 0 0.02 0.04 0.06 0.08 0.1 VM,MC ) z ]/(E-p VM,MC ) z - (E-p VM,RECO ) z [(E-p 1 10 2 10 3 10 4 10 Resolution (VM) z E-p 1 10 2 10 3 10 4 10 5 10 0 2 4 6 8 10 12 14 16 18 20 [GeV] VM,RECO ) z (E-p 0 2 4 6 8 10 12 14 16 18 20 [GeV] VM,MC ) z (E-p Response (VM) z E-p Figure 15: The leftmost plot shows the reconstruction of the E−pzdistribution of the VM in comparison with the truth. The middle plot shows the resolution and the rightmost plot shows the response. 16 1 10 2 10 3 10 4 10 5 10 0 1 2 3 4 5 6 7 8 9 10 [GeV] VM,MC ) z (E-p 0 1 2 3 4 5 6 7 8 9 10 [GeV] VM,RECO ) z (E-p Bin Migration 0 2 4 6 8 10 12 14 16 18 20 [GeV] VM,reco bin ) z (E-p 0 0.2 0.4 0.6 0.8 1 Purity bin width=0.1 GeV Purity 0 2 4 6 8 10 12 14 16 18 20 [GeV] VM,true bin ) z (E-p 0 0.2 0.4 0.6 0.8 1 Stability bin width=0.1 GeV Stability 0 2 4 6 8 10 12 14 16 18 20 [GeV] VM ) z (E-p 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Acceptance Acceptance 0 2 4 6 8 10 12 14 16 18 20 [GeV] VM ) z (E-p 0 0.2 0.4 0.6 0.8 1 Efficiency Efficiency 0 2 4 6 8 10 12 14 16 18 20 [GeV] VM ) z (E-p 4 10 5 10 Corrected Acceptance Corrected Figure 16: QA plots for the VMs E−pzdistribution. the direction of the scattered electron (ˆx). This minimizes the VMs four-momenta in the direction of the electron scattering plane. We do this by defining the angle θmax = tan−1(qx/qy) where |t|⊥=q2 ⊥=q2 x+q2 y qx=q⊥sin θ qy=q⊥cos θ, (13) choosing the optimal angle needed for analysis. Figure 17 shows the 2-dimensional |t|distribution where a cut of θmax is shown. The following cuts have been made only on the reconstruction level of the events from the detector information (in addition to the cuts mentioned above). •Geometric acceptance: We place a constraint on the radius of clusters (r < 550 mm) that are too far from the detector to ensure that the electron lands within the detector’s sensitive region. The resulting distribution is shown in the rightmost plot of Figure 18. •Event selection: Here, we choose 15 < E−pz<25 GeV of the scattered electron to ensure exclusivity. Additionally, we implement a selection of 17 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 |t|x[GeV/c] 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 |t|y[GeV/c] 1 10 102 103 2D |t| Distribution θ max Figure 17: |t|=q2distribution in 2-dimensions. The wedge cut is shown by the angle θmax to demonstrate the projection technique. 18 1 10 2 10 3 10 4 10 Cluster Position Without Cut 800−600−400−200−0 200 400 600 800 x [mm] 800− 600− 400− 200− 0 200 400 600 800 y [mm] Cluster Position Without Cut 1 10 2 10 3 10 4 10 Cluster Position With Cut 800−600−400−200−0 200 400 600 800 x [mm] 800− 600− 400− 200− 0 200 400 600 800 y [mm] Cluster Position With Cut Figure 18: Distribution of cluster positions in EMcal with and with geometric cut. 19 0.9< E/p < 1.2 to confirm that the EMCal energy matches the track momentum and that we select true electrons. The results of these cuts are shown in Figures 21 and 19 while the QA plots are shown in Figs. 22 and 20. 15 16 17 18 19 20 21 22 23 24 25 ) [GeV] z (E - p 0 500 1000 1500 2000 2500 3 10× counts MC RECO ) Truth vs. Reco (e'+HFS) z (E-p 19.4 19.5 19.6 19.7 19.8 19.9 20 20.1 [GeV] MC ) z (E-p 0.3− 0.2− 0.1− 0 0.1 0.2 0.3 MC ) z )/(E-p MC ) z -(E-p REC ) z ((E-p 1 10 2 10 3 10 4 10 5 10 ) Resolution (e'+HFS) z (E-p 1 10 2 10 3 10 4 10 5 10 16 18 20 22 24 ) [GeV] z,trk - p EMCal (E 19.4 19.5 19.6 19.7 19.8 19.9 20 20.1 ) [GeV] z,MC -p MC (E ) Response (e'+HFS) z (E-p Figure 19: The leftmost plot shows the reconstruction of the E−pzdistribution from e′in comparison with the truth. We expect this to peak around 2Ee= 20 GeV. The middle plot shows the resolution and the rightmost plot shows the response. 3.2.1 Reconstruction Methods The MCParticles branch is used to reconstruct the MC particle momentum, generator status, mass, and PDG arrays for each MC particle. To reconstruct the EMCal endcap clusters, we use the position and energy arrays from the EcalEndcapNClusters and EcalEndcapNRecHits branches. The EcalEndcapNClusterAssociations branch is used for the rec and sim ID arrays. We also reconstruct calorimeter tracks using the _CalorimeterTrackProjections_points branch for the position and momentum arrays. The ReconstructedChargedParticles branch is used to reconstruct the charged particles’ momentum, rec and sim ID arrays, and charge. To reconstruct the ZDC events we use the branches HcalFarForwardZDCClusters and EcalFarForwardZDCClusters to get the position and energy arrays from the separate parts of the ZDC. The roman pots events are reconstructed using the branch ForwardRomanPotRecHits to get the position arrays. Lastly, we use 20 19 19.2 19.4 19.6 19.8 20 20.2 20.4 MC ) z (E-p 16 18 20 22 24 RECO ) z (E-p 1 10 2 10 3 10 4 10 5 10 Bin Migration 18 18.5 19 19.5 20 20.5 21 21.5 22 [GeV] reco bin ) z (E-p 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 Purity bin width=0.45 GeV Purity 18 18.5 19 19.5 20 20.5 21 21.5 22 [GeV] true bin ) z (E-p 0 0.02 0.04 0.06 0.08 0.1 0.12 Stability bin width=0.45 GeV Stability 18 18.5 19 19.5 20 20.5 21 21.5 22 ) [GeV] z (E-p 0 0.1 0.2 0.3 0.4 0.5 6− 10× Acceptance Acceptance 18 18.5 19 19.5 20 20.5 21 21.5 22 ) [GeV] z (E-p 0 0.2 0.4 0.6 0.8 1 Efficiency Efficiency 18 18.5 19 19.5 20 20.5 21 21.5 22 ) [GeV] z (E-p 9 10 10 10 11 10 12 10 Corrected Acceptance Corrected Figure 20: QA plots for the E−pzdistribution from e′. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 E/|p| 4 10 5 10 6 10 7 10 counts MC RECO E/|p| Truth vs. Reco 0.98 0.99 1 1.01 1.02 1.03 1.04 MC (E/|p|) 0.2− 0.15− 0.1− 0.05− 0 0.05 0.1 trk /|p| EEMC E 1 10 2 10 3 10 4 10 5 10 E/|p| Resolution 1 10 2 10 3 10 4 10 5 10 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 trk /|p| EEMC E 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 MC (E/|p|) E/|p| Response Figure 21: The leftmost plot shows the reconstruction of E/|p|for e′in comparison with the truth. We expect this to peak at one to demonstrate good matching of the EMcal with the track. The middle plot shows the resolution and the rightmost plot shows the response. 21 0.98 0.99 1 1.01 1.02 1.03 1.04 MC (E/|p|) 0.98 0.99 1 1.01 1.02 1.03 1.04 trk /|p| EEMC E 1 10 2 10 3 10 4 10 5 10 Bin Migration 0.98 0.99 1 1.01 1.02 1.03 1.04 reco bin (E/|p|) 0 0.2 0.4 0.6 0.8 1 Purity bin width=0.02 Purity 0.98 0.99 1 1.01 1.02 1.03 1.04 true bin (E/|p|) 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 Stability bin width=0.02 Stability 0.98 0.99 1 1.01 1.02 1.03 1.04 (E/|p|) 0 0.1 0.2 0.3 0.4 0.5 0.6 Acceptance Acceptance 0.98 0.99 1 1.01 1.02 1.03 1.04 E/|p| 0 0.2 0.4 0.6 0.8 1 Efficiency Efficiency 0.98 0.99 1 1.01 1.02 1.03 1.04 (E/|p|) 3 10 4 10 5 10 6 10 Corrected Acceptance Corrected Figure 22: QA plots for E/|p|for e′. the ForwardOffMTrackerRecHits branch to reconstruct the OMD position arrays. Some variables have special methods implemented for reconstruction, which will be explained in this section. –VM: We loop over the track array to select the decay daughters. After excluding the scattered electron, we check that |η|<3.0 to ensure the tracks are well measured because |η|>3 is too close to beamline. We then assign the positive and negative particles, in this case K±. –Scattered electron (Pe′ RECO ): This variable is derived by using the EMCal cluster energy, Ecal (obtained from the EM hits array as described in section 3.1). Ecal is used to calculate the momentum (p=pE2 cal −m2, where mis the mass of the electron). We then use that to calculate pT=psin θwhich allows us to define the scattered electron four-momentum in terms of m,η,ϕ, and pT, where η,ϕ, and θare resolved from the reconstructed track momentum array. –Momentum transfer distribution (|t|): There are three different ways in this analysis that are implemented to reconstruct the |t| 22 distribution, method E, method L, and the projection method. Given a coherent exclusive diffractive VM event, we have the following conservation of four-momenta equation Pe+PA→Pe′+PA′+PVM.(14) The derivation of the different methods of |t|=−(PA′−PA)2 reconstruction are based off of Eqn. 14 and given by the following: ∗Method E: Directly solves for PA′to arrive at the final formula for |t|and is used to generate MC events given by PA′=Pe+PA−Pe′−PVM |t|E=−(PA′−PA)2(15) =−(Pe−Pe′−PVM)2. ∗Method L: Uses a corrected outgoing ion momentum by using the mass as an additional constraint. We first change to lightcone variables defined as p±=pE±pz(16) p2=p+p−−p2 T=m2c4.(17) Solving for pEand pzgives pz=p+−pE(18) pE=p−+pz.(19) Using the above equations you can solve for pzand pEin terms of p+and p−resulting in pz=p+−p− 2(20) pE=p−+p+ 2.(21) Lastly, we use these new variables for Pcorr A′to arrive at our new |t|expressed as Pcorr A′= (px, py, pz, pE) =px, py,p+−p− 2,p−+p+ 2(22) |t|L=−(Pcorr A′−PA)2.(23) 23 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 2 |t| [GeV/c] 1− 10 1 10 2 10 3 10 4 10 5 10 ] 2 /d|t| [nb/(GeV/c)σd : MCφ /12π= max θ: φ DIS ePIC Simulation 25.10.2, 10x100 GeV - K + K→ φ φ e'Au'→eAu /A -1 = 10 fb int L Figure 28: |t|distribution with DIS background shown as the light blue plus signs, the MC truth is the black solid line and the projection method corresponds to the open pink stars. We see that the DIS curve only allows us to resolve the first minima. 30 Figure 29 shows the progression of DIS background removal from each detector veto and cut. For the detector vetoes, we use the ZDC, OMD, and RP detectors in this analysis. We also require that |η|<3.5 and that the HFS only contains the decay daughters. We see from Fig. 29 that the cuts on ηand HFS remove all DIS background. 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 2 |t| [GeV/c] 1− 10 1 10 2 10 3 10 4 10 5 10 ] 2 /d|t| [nb/(GeV/c)σd : MCφ/12π= max θ: φ DIS: no vetoes DIS: OMD only DIS: RP only DIS: only detectors onlyηDIS: DIS: all vetoes ePIC Simulation 25.10.2, 10x100 GeV - K + K→ φ φ e'Au'→eAu /A -1 = 10 fb int L Figure 29: |t|distribution with all vetoes and cuts applied. The solid black line corresponds to the MC truth, open pink stars to the projection method, light blue plus signs for DIS with no vetoes, solid green squares for DIS with only OMD vetoes, open red squares for DIS with only RP vetoes, orange stars for DIS with all detector vetoes, open purple circles for DIS with only ηand HFS cuts, and the gray open double diamonds represent DIS with all cuts and vetoes applied. 3.3.2 ρProduction Another source of systematic uncertainty is the production of the ρ VM. Figure 31 shows the |t|distribution with the included ρ contamination. After implementing PID using the branch 31 ReconstructedChargedParticles.PDG, we observe that the projection method is able to remove all of the ρproduction. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 ] 2 VM mass [GeV/c 2 10 3 10 4 10 5 10 6 10 counts Mass Distribution (no PID) MCρ RECρ REC before mass cutρ MCφ RECφ Mass Distribution (no PID) 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 ] 2 VM mass [GeV/c 0 500 1000 1500 2000 2500 3000 3500 3 10× counts Mass Distribution (with PID) MCρ RECρ REC before mass cutρ MCφ RECφ Mass Distribution (with PID) Figure 30: The leftmost plot shows the mass distributions of ρand ϕwith no PID while the rightmost plot shows the same distributions with PID. The orange dashed curve represents the ρMC mass distribution, the dashed blue curve is for ρreconstruction, the green long dash is for ρreconstruction before the ϕmass selection is applied, the solid black curve is for the ϕMC distribution, and the dashed purple curve is for the reconstructed ϕ. Figure 30 shows the VM mass distributions with and without PID. We see that without PID, the selection on the ϕmass successfully reduces the number of ρparticles but there still remains a significant amount of misidentified ρparticles. Figure 31 shows the |t|distribution of the misidentified ϕ. Again, we can only resolve the first minima. However, upon implementing PID, we are able to remove all of the ρ background as shown in Figs. 31 and 30. 3.3.3 Incoherent Production The dominate source of systematic uncertainty in this analysis arises from the incoherent production. As shown in Fig. 32, we see that the incoherent background dominates our diffractive pattern in the |t| distribution. After implementing the detector vetoes and cuts as mentioned in Section 3.3.1, we see some surpression, as shown in Fig. 33, but there is still an overwhelming amount of incoherent production remaining. Following the proposed spin-based technique in [3], we plan to statistically remove this background in the future. 32 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 2 |t| [GeV/c] 1− 10 1 10 2 10 3 10 4 10 5 10 ] 2 /d|t| [nb/(GeV/c)σd : MCφ /12π= max θ: φ /12π= max θ (no PID): ρ /12π= max θ (w. PID): ρ ePIC Simulation 25.10.2/3, 10x100 GeV - K + K→ φ φ e'Au'→eAu /A -1 = 10 fb int L Figure 31: |t|distribution with ρproduction. The solid black curve represents the ϕMC truth distribution, the open pink stars for the ϕdistribution projection method, the gray open crosses represent the ρdistribution with no PID, and the blue open double diamonds represent the ρdistribution with PID. 33 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 2 |t| [GeV/c] 1− 10 1 10 2 10 3 10 4 10 5 10 ] 2 /d|t| [nb/(GeV/c)σd : MCφCoherent /12 π= max θ: φCoherent /12π= max θ: φIncoherent ePIC Simulation 25.10.2, 10x100 GeV - K + K→ φ φ e'Au'→eAu /A -1 = 10 fb int L Figure 32: |t|distribution with incoherent production. No vetoes or cuts have been applied. The black solid curve represents the coherent MC truth, the open pink stars for the projection method for coherent ϕreconstruction, and the filled orange squares is the incoherent production distribution. 34 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 2 |t| [GeV/c] 1− 10 1 10 2 10 3 10 4 10 5 10 2 /d|t| [nb/(GeV/c)]σd : MCφ Coherent /12 π= max θ: φCoherent : no vetoesφIncoh. : RPφIncoh. : OMDφIncoh. : ZDCφIncoh. : all detectorsφIncoh. cutsη: φIncoh. : all vetoesφIncoh. ePIC Simulation 25.10.2, 10x100 GeV - K + K→ φ φ e'Au'→eAu /A -1 = 10 fb int L Figure 33: |t|distribution with incoherent production and individual detector vetoes and cuts. The black solid curve represents the coherent ϕMC distribution, the open pink stars are for the coherent ϕreconstruction using the projection method, the open four triangle x is for incoherent with no vetoes, the red star is for incoherent with only RP vetoes, the blue full cross x is for incoherent with only OMD vetoes, the green full diamond is for incoherent with only ZDC vetoes, the open gray circles are for incoherent with all detector vetoes, the black full down triangle is for incoherent with ηand HFS cuts, and the filled orange squares are for incoherent production with all vetoes applied. 35 3.4 Analysis Code –Code found on GitHub [15] where you will find: ∗model simulations: Simulations were developed and tested before the projection technique was implemented using the ePIC software. The files needed to reproduce the model are found in this folder. ∗EICreconOutputReader: An original simple analysis code based on [16]. ∗diffractive phi analysis: The final version of the analysis code (used to write this note) can be found here. This folder contains: ·All necessary header files in the ”header files” folder. Plot generators in the ”plot macros” folder. ·In this folder there are plot macros to generate: 1. Plots in this analysis note labeled ”AnalysisNote plots diffractive phi.C”. 2. Comprehensive plots of the |t|distribution scaled to Early Science and preTDR luminosities, different configurations of systematic uncertainties, and further detector analyses. This macro is labeled ”diffractive t plots.C” 3. Analysis plots that can be used for further investigation labeled ”plot QA.C”. ·The ”preTDR” folder contains all the information needed to reproduce the plots in the preTDR. ·The analysis code is found in the ”src” folder labeled ”diffractive vm full analysis.cxx”. Scripts in this folder are for submitting jobs to condor and preparing the file lists to be fed into the analysis code. To submit jobs and run multiple files from a list: 1. From eic-shell: ./prep file list.sh 2. Not in eic-shell: ./run analysis 2 To run the analysis for a single file: ·From the terminal: root ’diffractive vm full analysis.cxx (<input filename.root>,<output filename.root>)’ 36 4 Results and Discussion 0 0.05 0.1 0.15 2 |t| [GeV/c] 2− 10 1 2 10 4 10 6 10 ] 2 /d|t| [nb/(GeV/c)σd , 0.01 < y < 0.85 2 <10 GeV 2 1<Q | < 0.02 GeV φ M− inv |<3.5, |M φ |y ePIC Simulation 25.10.2 - K + K→ φ , 10x100 GeVφ e'Au'→eAu /A -1 = 10 fb int L MC φSartre /12π = max θ RECO φSartre Figure 34: |t|distribution after applying a cut of θ=π/12. This plot shows the improvement of the |t|measurement by comparing the coherent truth (MC reconstruction, black curve) with the new projection method (open pink stars). The results of the |t|distribution reconstruction are shown in Figs. 34 and 35. First, we can see a significant enhancement in resolving the diffractive pattern of the |t|distribution. Previously, the best method available for us to use was method L as stated in [14]. The projection method enables us to determine the peaks and minima with a much better resolution than before. The price we pay for making the wedge cut in the projection method is a loss of statistics. In this example, we use θmax =π/12 which results in ≈83% of lost coherent VM events. Second, Fig. 35 clearly indicates an improvement from the method L reconstruction. 37 10−5−0 5 10 b [fm] 0.05− 0 0.05 0.1 0.15 F(b) db ∫ F(b)/ ePIC Simulation 25.10.2, 10x100 GeV - K + K→ φ φ e'Au'→eAu MC Method L Projection method Figure 35: 2-dimensional Fourier-Bessel transformation of the |t|distribution with wedge cut of θ=π/12. This shows the gluon spatial distribution with a comparison from the transforms of the truth, method L, and the projection method distributions. The black solid curve represent the truth distribution, the blue filled circles correspond to |t|reconstruction using method L, and the pink open stars represent the reconstruction of |t|using the new projection technique. 38 This analysis demonstrates that the projection method used to reconstruct the momentum distribution is an effective approach to overcome the previous challenges of the |t|measurement and allows more precise spatial imaging of the gluons inside the nucleus. In future work we will statistically separate the coherent and incoherent events to reduce the incoherent background. The outcome will be a complete analysis technique for the measurement of the |t|distribution. References [1] A. Accardi, et al., Electron Ion Collider: The Next QCD Frontier: Understanding the glue that binds us all, Eur. Phys. J. A 52 (9) (2016) 268. arXiv:1212.1701,doi:10.1140/epja/i201616268-9. [2] N. Armesto, A. H. Rezaeian, Exclusive vector meson production at high energies and gluon saturation, Phys. Rev. D 90 (5) (2014) 054003. arXiv:1402.4831,doi:10.1103/PhysRevD.90.054003. [3] M. Kesler, A. I. Sheikh, R. Ma, Z. Tu, T. Ullrich, Z. Xu, Projective Imaging of High-Energy Nuclei via Coherent Exclusive Vector Meson Production in Electron-Nucleus Collisions (2 2025). arXiv:2502.15596. [4] T. Toll, T. Ullrich, Exclusive diffractive processes in electron-ion collisions, Phys. Rev. C 87 (2) (2013) 024913. arXiv:1211.3048, doi:10.1103/PhysRevC.87.024913. [5] L. Adamczyk, et al., Coherent diffractive photoproduction of ρ0 mesons on gold nuclei at 200 gev/nucleon-pair at the relativistic heavy ion collider, Phys. Rev. C 96 (2017) 054904. doi: 10.1103/PhysRevC.96.054904. URL https://link.aps.org/doi/10.1103/PhysRevC.96. 054904 [6] Reconstruction campaigns, accessed: November 10, 2025. URL https : / / eic . github . io / epic - prod / campaigns / campaigns_reco.html 39