A Proposed Forward Silicon Tracker for the Future Electron-Ion Collider and Associated Physics Studies
Cheuk-Ping Wong, Xuan Li, Melynda Brooks, Matthew J. Durham, Ming Xiong Liu, Astrid Morreale, Cesar da Silva, Walter E. Sondheim
LLANL Report:
LA-UR-20-26642
A Proposed Forward Silicon Tracker for the FutureElectron-Ion Collider and Associated Physics Studies
Cheuk-Ping Wong, Xuan Li, Melynda Brooks, Matthew J. Durham, Ming Xiong Liu,Astrid Morreale, Cesar da Silva and Walter E. Sondheim
Los Alamos National Laboratory,Los Alamos, NM, USA
E-mail: [email protected], [email protected]
The future Electron-Ion Collider (EIC) will explore several fundamental questions in a broad Bjorken-x( x BJ ) and Q phase space. Heavy flavor and jet products are ideal probes to precisely study the tomographyof nucleon/nuclei structure, help solve the proton spin puzzle and understand the hadronizaton processes invacuum or in the QCD medium. Due to the asymmetric collisions at the EIC, most of the final state hadronsare produced in the nucleon/nuclei beam going (forward) direction. A silicon vertex/tracking is critical toprecisely measure these forward hadrons at the EIC. Details of different conceptual designs of the proposedForward Silicon Tracker (FST) and the relevant detector performance are presented in this technical note.The associated heavy flavor and jet studies with the evaluated FST performance are discussed as well. Primary Author and contact person Primary Author and contact person a r X i v : . [ nu c l - e x ] S e p roposed EIC FST and Associated Physics Contents
1. Introduction
The future Electron-Ion Collider (EIC) [1] at Brookhaven National Laboratory will open a new QCDfrontier to explore fundamental questions in nuclear physics. Heavy flavor and jet measurements will help us1) precisely determine the initial nucleon/nuclei parton distribution functions, especially in the highBjorken-x ( x BJ ) region.2) explore the hadronization processes in vacuum and medium.3) improve the understanding of the proton spin structure including study of the gluon Sivers function.4) characterize new exotic states, which may be pentaquarks, tetraquark or glueballs.To realize the heavy flavor and jet measurements, a silicon vertex/tracking detector is essential for thefuture EIC. The LANL LDRD 20200022DR project focuses on the proposed forward silicon tracker design,R&D, and simulation studies together with studies of how heavy flavor and jet probes can be used for the2 roposed EIC FST and Associated Physics future EIC physics program. In this techinical note, we discuss details of the kinematic distributions offinal particle production, the Forward Silicon Tracker (FST) design and the tracking performance, and heavyflavor and jet physics performance projections.
2. Kinematics distributions
The kinematic distributions of inclusive K ± , π ± and e − obtained from Pythia6 simulation with radiativecorrections [2, 3] as shown in Figure 1 and Figure 2. Momenta of these inclusive products are plotted as afunction of pseudorapidity in Figure 1, while momenta plotted versus polar angle, θ , is shown in Figure 2.Figure 1 and Figure 2 show that the low momentum ( p ≤
10 GeV) inclusive charged meson products dominatein 0 < η < η <
Figure 1:
Inclusive decay π ± (top row), K ± (second row) and e − (bottom row) momenta as a function of pseudorapidityfrom electron-proton collisions at 10 ×
100 GeV (left column), 18 ×
100 GeV (center column) and 18 ×
275 GeV (rightcolumn) using Pythia6 simulations. roposed EIC FST and Associated Physics Figure 2:
Inclusive decay π ± (top row), K ± (second row) and e − (bottom row) momentum distributions in polarcoordinates from electron-proton collisions at 10 ×
100 GeV (left column), 18 ×
100 GeV (center column) and 18 ×
275 GeV(right column) using Pythia6 simulations. roposed EIC FST and Associated Physics Figure 3: B meson decay π ± (top row), K ± (second row) and B meson (bottom row) momentum as a function ofpseudorapidity from electron-proton collisions at 10 ×
100 GeV (left column), 18 ×
100 GeV (center column) and18 ×
275 GeV (right column) using Pythia8 simulations.
Figure 4: B meson p T and η distributions from electron-proton collisions at 10 ×
100 GeV (left column), 18 ×
100 GeV(center column) and 18 ×
275 GeV (right column) using Pythia8 simulations. roposed EIC FST and Associated Physics Figure 5: B meson decay π ± (top row), K ± (second row), e − (third row) and B meson (bottom row) momentumdistributions in polar coordinates from electron-proton collisions at 10 ×
100 GeV (left column), 18 ×
100 GeV (centercolumn) and 18 ×
275 GeV (right column) using Pythia8 simulations. roposed EIC FST and Associated Physics Figure 6: D meson decay π ± (top row), K ± (second row) and D meson (bottom row) momentum as a function ofpseudorapidity from electron-proton collisions at 10 ×
100 GeV (left column), 18 ×
100 GeV (center column) and18 ×
275 GeV (right column) using Pythia8 simulations. roposed EIC FST and Associated Physics Figure 7: D meson p T and η distributions from electron-proton collisions at 10 ×
100 GeV (left column), 18 ×
100 GeV(center column) and 18 ×
275 GeV (right column) using Pythia8 simulations.
Figure 8: D meson decay π ± (top row), K ± (second row), e − (third row) and D meson (bottom row) momentumdistributions in polar coordinates from electron-proton collisions at 10 ×
100 GeV (left column), 18 ×
100 GeV (centercolumn) and 18 ×
275 GeV (right column) using Pythia8 simulations. roposed EIC FST and Associated Physics
3. Detector Design
Due to the asymmetric collisions that will occur at the future EIC, the majority of the final hadrons areproduced in the pseudorapity region of −
4. Fun4all Simulation
The EIC Fun4all simulation is a modified version of the sPHENIX simulation. Both the Babar andBeAST magnets are tested in the simulation. The Babar magnetic field peaks at 1 .
4T and the BeASTmagnetic field peaks at 3T. A 95% detection hit efficiency is used in both track and vertex reconstructions. Intrack reconstruction, the Kalman Filter algorithm is used and a 20 µ m vertex Gaussian smearing is appliedto both x and y directions. In vertex reconstruction, no vertex smearing is applied and 10 charged pionsare launched per event. The number of degrees of freedom is set to 1 in vertex reconstruction for the initialstudies.This section will show the the tracking performance from simulations with the preliminary detectordesigns detailed in Section 4.1. These simulation results, including momentum resolution and distance ofclosest approach resolution, are applied to heavy meson reconstruction in physics simulation discussed inSection 6. Both detector and physics simulation results will help evaluate and improve different designs. The initial implementation of the FST simulation in Fun4all includes both the barrel detector system andthe FST as shown in Figure 9. This section will detail three different FST designs, including geometry andmaterial. The parameters of detector geometries are listed in Table 1 and Table 2.•
Version 0 is the initial FST design. There are five-layer barrel detector and five-plane FST detectorimplemented in the Fun4all simulation as shown on the left of Figure 9. The inner radius of the FSTplanes increases along the z positions to accommodate the ion beam pipe which gets larger at large z . The structure of each plane of FST and layer of barrel detector, which is illustrated on the right ofFigure 9, includes a silicon wafer with a sheet of aluminum support, a thin layer of kapton followed bythe cooling wafer and the supporting structure of graphite. The silicon wafer (including the aluminumbase) implemented in both the barrel detector and the FST has a 100 µ m thickness in this initial design.• Version 1 design is derived from the version 0 design. Two changes are made in version 1 comparedto version 0. First, the outer radii of plane 0 and plane 1 of the FST were changed as listed in Table 2.Plane 0 is smaller to reduce material budget at mid pseudorapidity while plane 1 is slightly larger by1 cm to improve the forward acceptance. Secondly, the thickness of the silicon wafer is different thanin version 0. In the outer two layers (layer 3 and layer 4) of the barrel detector, the silicon wafer has a100 µ m thickness. In the rest of the barrel detector and all five planes of the FST, the silicon wafer hasa 50 µ m thickness.• Version 2 , which is shown on the left of Figure 10, is also derived from the version 0 design. Thisversion moved the last plane of the FST, that is plane 4, from z = .
25 m to z = . η = µ m thickness. In the rest of the barreldetector and all five planes of the FST, the silicon wafer has a 50 µ m thickness.• Version 3 is derived from the version 1 design. The silicon thickness of the barrel detector is set to35 µ m in version3. The last two planes, plane 3 and 4, of the FST have a 36 . µ m pixel pitch and a100 µ m thick silicon wafer. 9 roposed EIC FST and Associated Physics • Version 4 , which is shown on the right of Figure 10, is derived from version 2 design. Instead ofmoving plane 4 to the far-z location ( z = . z = . Table 1:
Barrel detector geometry parameters
Version 0Layer half length (cm) radius (cm) pixel Pitch ( µ m) silicon thickness ( µ m)0 20 3.64 20 1001 20 4.81 20 1002 25 5.98 20 1003 25 16 20 1004 25 22 20 100Version 1Layer half length (cm) radius (cm) pixel Pitch ( µ m) silicon thickness ( µ m)0 20 3.64 20 501 20 4.81 20 502 25 5.98 20 503 25 16 20 1004 25 22 20 100Version 2Layer half length (cm) radius (cm) pixel Pitch ( µ m) silicon thickness ( µ m)0 20 3.64 20 501 20 4.81 20 502 25 5.98 20 503 25 16 20 1004 25 22 20 100Version 3Layer half length (cm) radius (cm) pixel Pitch ( µ m) silicon thickness ( µ m)0 20 3.64 20 351 20 4.81 20 352 25 5.98 20 353 25 16 20 354 25 22 20 35Version 4, 4.1 and 4.2Layer half length (cm) radius (cm) pixel Pitch ( µ m) silicon thickness ( µ m)0 20 3.64 20 501 20 4.81 20 502 25 5.98 20 503 25 9.2 20 1004 25 17 20 1005 25 27 20 10010 roposed EIC FST and Associated Physics Table 2:
Forward plane detector geometry parametersVersion 0Plane z (cm) inner radius (cm) outer radius (cm) pixel Pitch ( µ m) silicon thickness ( µ m)0 35 4 30 20 1001 53 4.5 35 20 1002 77 5 36 20 1003 101 6 38.5 20 1004 125 6.5 45 20 100Version 1Plane z (cm) inner radius (cm) outer radius (cm) pixel Pitch ( µ m) silicon thickness ( µ m)0 35 4 25 20 501 53 4.5 36 20 502 77 5 36 20 503 101 6 38.5 20 504 125 6.5 45 20 50Version 2Plane z (cm) inner radius (cm) outer radius (cm) pixel Pitch ( µ m) silicon thickness ( µ m)0 35 4 30 20 501 53 4.5 35 20 502 77 5 36 20 503 101 6 38.5 20 504 270 6.5 45 20 50Version 3Plane z (cm) inner radius (cm) outer radius (cm) pixel Pitch ( µ m) silicon thickness ( µ m)0 35 4 25 20 501 53 4.5 36 20 502 77 5 36 20 503 101 6 38.5 36.4 1004 125 6.5 45 36.4 100Version 4Plane z (cm) inner radius (cm) outer radius (cm) pixel Pitch ( µ m) silicon thickness ( µ m)0 35 4 25 20 501 53 4.5 36 20 502 77 5 36 20 503 101 6 38.5 20 504 125 6.5 45 20 505 270 15 45 20 50Version 4.1Plane z (cm) inner radius (cm) outer radius (cm) pixel Pitch ( µ m) silicon thickness ( µ m)0 35 4 25 20 501 53 4.5 36 20 502 77 5 36 20 503 101 6 38.5 36.4 1004 125 6.5 45 36.4 1005 270 15 45 36.4 100Version 4.2Plane z (cm) inner radius (cm) outer radius (cm) pixel Pitch ( µ m) silicon thickness ( µ m)0 35 4 25 20 501 53 4.5 36 20 502 77 5 36 20 503 101 6 38.5 20 504 125 6.5 45 36.4 1005 270 15 45 36.4 100 roposed EIC FST and Associated Physics Figure 9:
Left: initial detector implementation in Fun4all simulation includes the five-plane FST system (right) alongwith the five-layer barrel system (left). Right: illustration of each layer of barrel detector and FST.
Layer 0Layer 4Plane 0 1 2 3 Plane 4
Version 2
Plane 0 1 2 3 Plane 54
Version 4
Figure 10:
Left: version 2 of FST design. Right: version 4 of FST design which is the same for version 4.1 and 4.2.
Different thicknesses of the silicon wafer are considered. The material scan with no silicon wafer showsthe material budget of the supporting and cooling structures of the detector. The scan with the silicon waferof a conservative 100 µ m thickness gives the upper bound estimation for the material budget. The mixed useof thickness of silicon wafers shows the realistic estimation. In the material scan of mixed silicon thicknesses,the silicon wafers in the outer layers (layer 3 and 4) of the barrel detector are set to 100 µ m thick, while therest of the barrel detector layers as well as the FST have silicon wafers with a 50 µ m thickness.Figure 11, which shows the material budget of the version 0 FST design, shows that the highest materialbudget occurs at θ ≈ ◦ ( η ≈ .
1) with about 2 . x , 1 . x and 1 . x when using the 100 µ m siliconwafers in both barrel and FST systems, different thicknesses of silicon wafer in both barrel and FST systemsand no silicon wafer in the detector systems, respectively.Version 1 and version 2 designs give slightly different material budgets at different polar angles. Thematerial budget of version 1 at θ ≈ ◦ ( η ≈ .
2) is about 0 .
2% higher than version 0, as shown in Figure 12,due to the larger size of plane 1 in version 1. However, at θ > ◦ ( η < . .
2% lower in version 1 than in version 0 because of the smaller plane 0 in version 1. The material budgetof version 2 design is about 0 .
2% lower than version 0 design between 10 ◦ < θ < ◦ (1 . < η < . z = .
25 m to z = . roposed EIC FST and Associated Physics q x no wafer100um100um in Layer 3,4 / rest 50um q l h x h l Figure 11:
Material budget of the version 0 FST design. q x ver 0 ver 1 no wafer100um in Layer 3,4 / rest 50um q l h x h l Figure 12:
Material budget of the version 1 FST design compared to version 0 design. roposed EIC FST and Associated Physics q x ver 0 ver 2 no wafer100um in Layer 3,4 / rest 50um q l h x h l Figure 13:
Material budget of the version 2 FST design compared to version 0 design.
The momentum resolution is defined as the width of the distribution of the relative difference betweenthe reconstructed and the input (true) momenta, that is ∆ pp input = p reco − p input p input , (1)where p reco and p input are the reconstructed momentum and input momentum, respectively. This sectionwill discuss the effects on the momentum resolution of different magnetic fields, detector geometry and pixelpitch. With uniform 1 . . Figure 15 and 16 show the momentum resolution comparisons of different FST designs with the use ofBabar and BeAST magnets, respectively. The comparison of version 0 to version 1 shows the momentumresolution decreases as the material budget is reduced in version 1. Version 1 and version 3 share the samegeometry, but version 3 uses thinner (35 µ m) silicon wafers in the barrel detector than version 1. However,there are no significant differences in momentum resolution at η =
1. Version 3 also use thicker siliconwafers (100 µ m) and larger pixel pitches (36 . µ m) for the plane 3 and 4 of the FST than version 1 whichcauses a small increase ( < . η ≥ roposed EIC FST and Associated Physics m o m r e s ( % ) uniform 3TBeASTuniform 1.4TBabar =1.5 h =2.0 h input p11.522.5 =2.5 h input p1234 =3.0 h Figure 14:
Comparison of Momentum resolution of the tracking system in different magnetic field in Fun4all simulation.Version 0 of FST design with 100 µ m thickness of silicon wafers are used in the simulation. The comparison between version 0 and version 2 shown in Figure 15 and 16 demonstrates that with aplane at a far-z location ( z = . η = .
8% (1 . .
8% (1 . ≤ η ≤ .
5. Therefore, version 4 withan additional FST plane at a far-z location is introduced to maintain the performance at 2 ≤ η ≤ .
5, whileimproving the performance at large pseudorapidity ( η = η = . . Version 4 detector design is used in the simulation to study pixel pitch size effect on momentum resolution.Three pixel pitch sizes, 10 µ m, 20 µ m and 30 µ m, are used in the simulation with the implementation ofthe Babar magnet. Figure 17 shows the pixel pitch dependence of momentum resolution in differentpseudorapidity. At η =
1, the momentum resolution is highly dependent on the pixel pitch size at the barreldetector as tracks with a η = . ≤ η ≤
2, themomentum resolution also relies on the pixel pitch size at the FST detector. At η ≥
2, the momentumresolution becomes dependent on the pixel pitch size of the FST alone as the track with large pseudorapidityonly passes through the FST. Figure 18 shows the same results as figure 17, but zoom in to the 0–10 GeVregion. The same pixel pitch dependency shown at high momentum ( >
10 GeV) is also found at lowmomentum ( <
10 GeV). However, at η =
3, there is no noticeable pixel pitch dependence shown at lowmomentum. 15 roposed EIC FST and Associated Physics m o m r e s ( % ) babar magnet=1.0 h ver 0 ver 1ver 2 ver 3ver 4 =1.5 h =2.0 h input p =2.5 h input p =3.0 h Figure 15:
Comparison of Momentum resolution of the different FST design from Fun4All simulation with the Babarmagnet. m o m r e s ( % ) beast magnet=1.0 h ver 0 ver 1ver 2 ver 3ver 4 =1.5 h =2.0 h input p =2.5 h input p =3.0 h Figure 16:
Comparison of Momentum resolution of the different FST design from Fun4All simulation with the BeASTmagnet.
Figure 19 shows the comparison of momentum resolutions between version 4, 4.1 and 4.2 from simulationwith the implementation of the BeAST magnet. The latter two versions of FST design use larger pixel pitchand thicker silicon wafer in the last few planes as listed in Table 2. The momentum resolutions of version 4,4.1 and 4.2 are consistent at η ≤ η ≥ .
5, but limited within0 . roposed EIC FST and Associated Physics m o m r e s ( % ) Barrel pitch=10um
Barrel pitch=20um (GeV) input p FST pitch10um20um30um
Barrel pitch=30um = . h = . h = . h = . h = . h Figure 17:
Momentum resolution as a function input (true) momentum from Fun4all simulation using version 4 of FSTdesign and Babar magnet. roposed EIC FST and Associated Physics m o m r e s ( % ) FST pitch10um20um30um
Barrel pitch=10um
Barrel pitch=20um (GeV) input p Barrel pitch=30um = . h = . h = . h = . h = . h Figure 18:
Momentum resolution as a function input (true) momentum from Fun4all simulation using version 4 of FSTdesign and Babar magnet. roposed EIC FST and Associated Physics m o m r e s ( % ) ver4 ver4.1ver4.2 beast magnet=1.0 h =1.5 h =2.0 h (GeV) input p5 10 15 20 25 30 =2.5 h (GeV) input p5 10 15 20 25 30 =3.0 h Figure 19:
Momentum resolution as a function input (true) momentum from Fun4all simulation using version 4, 4.1and 4.2 of FST design and BeAST magnet.
Four distance of the closest approach (DCA) values,
DC A r , DC A φ , DC A z and DC A D are measuredin the simulations. These DCA values are defined as DC A r = ( pca − v t x ) · p T , (2) DC A φ = ( pca − v t x ) × p T , (3) DC A z = ( pca z − v t x z ) · p z , (4) DC A D = ( pca − v t x ) · ( p T × ˆ z ) , (5)where pca is the point of closest approach of the tracks to the primary vertex and v t x is the reconstructedvertex. Different DC A resolutions from Fun4All simulations using version 0, version 4 FST designs andBeAST are shown in Figure 20 to Figure 23. With the additional layer of barrel detector and plane detectorat far-z location, the DCA resolutions of version 4 are lower than version 0 especially at 3 ≤ η ≤ . To study effect from different silicon sensor technologies, version 4.1 and version 4.2 FST designs areintroduced. Version 4.1 (Version 4.4) and version 4 use the same detector geometry as version 4, but largerpixel pitch (36 . µ m) and thicker silicon wafer (100 µ m) are implemented in the last three (two) planes asshown in Table 2. The comparisons of DCA resolutions of version 4, version 4.1 and version 4.2 are shownin Figure 24 to 27. These figures show that the changes of pixel pitch and silicon wafer thickness at the lasttwo or three planes do not affect the resolutions at η ≤ . η > .
5, the effect of pixel pitch and silicon wafer thickness become. noticeable. Version 4.1with three planes that have a pixel pitch (36 . µ m) and 100 µ m thick silicon wafer fives the highest DCAresolutions, while version 4 gives the lowest DCA resolutions amount these three designs. The differencesbetween Version 4 and Version 4.1 are about 2 µ m in DC A r , 7 µ m in DC A φ , 20 µ m in DC A z and 5 µ m in DC A D . 19 roposed EIC FST and Associated Physics r e s ( u m ) r DC A ver 0 ver 4 Barrel pitch=20umFST pitch=20um £h£ £h£ £h£
T,input p £h£ T,input p £h£ Figure 20:
DC A r resolution as a function input (true) transverse momentum from Fun4all simulation using version 0and version 4 FST design with BeAST magnetic field. r e s ( u m ) f DC A ver 0 ver 4 Barrel pitch=20umFST pitch=20um £h£ £h£ £h£
T,input p £h£ T,input p £h£ Figure 21:
DC A φ resolution as a function input (true) transverse momentum from Fun4all simulation using version 0and version 4 FST design with BeAST magnetic field. roposed EIC FST and Associated Physics r e s ( u m ) z DC A ver 0 ver 4 Barrel pitch=20umFST pitch=20um £h£ £h£ £h£
T,input p £h£ T,input p £h£ Figure 22:
DC A z resolution as a function input (true) transverse momentum from Fun4all simulation using version 0and version 4 FST design with BeAST magnetic field. DC A D r e s ( u m ) ver 0 ver 4 Barrel pitch=20umFST pitch=20um £h£ £h£ £h£
T,input p £h£ T,input p £h£ Figure 23:
DC A D resolution as a function input (true) transverse momentum from Fun4all simulation using version 0and version 4 FST design with BeAST magnetic field. roposed EIC FST and Associated Physics r e s ( u m ) r DC A ver4 ver4.1ver4.2 £h£ £h£ £h£ (GeV) T,input p5 10 15 20 25 30 £h£ (GeV)
T,input p5 10 15 20 25 30 £h£
Figure 24:
DC A r resolution as a function input (true) transverse momentum from Fun4all simulation using version 4,4.1 and 4.2 FST design. r e s ( u m ) f DC A ver4 ver4.1ver4.2 £h£ £h£ £h£ (GeV) T,input p5 10 15 20 25 30 £h£ (GeV)
T,input p5 10 15 20 25 30 £h£
Figure 25:
DC A φ resolution as a function input (true) transverse momentum from Fun4all simulation using version 4,4.1 and 4.2 FST design. roposed EIC FST and Associated Physics r e s ( u m ) z DC A ver4 ver4.1ver4.2 £h£ £h£ £h£ (GeV) T,input p5 10 15 20 25 30 £h£ (GeV)
T,input p5 10 15 20 25 30 £h£
Figure 26:
DC A z resolution as a function input (true) transverse momentum from Fun4all simulation using version 4,4.1 and 4.2 FST design. DC A D r e s ( u m ) ver4 ver4.1ver4.2 £h£ £h£ £h£ (GeV) T,input p5 10 15 20 25 30 £h£ (GeV)
T,input p5 10 15 20 25 30 £h£
Figure 27:
DC A D resolution as a function input (true) transverse momentum from Fun4all simulation using version 4,4.1 and 4.2 FST design. roposed EIC FST and Associated Physics Vertex resolutions in x, y and z directions are defined as the Gaussian width of the difference of thereconstructed vertex ( v t x x , reco , v t x y , reco and v t x z , reco ) and input (true) vertex ( v t x x , input , v t x y , input and v t x z , input ), that is written as ∆ v t x x = v t x x , reco − v t x x , input , (6) ∆ v t x y = v t x y , reco − v t x y , input , (7) ∆ v t x z = v t x z , reco − v t x z , input . (8)The vertex resolutions of version 0 and version 4 FST designs from Fun4All simulation with BeAST magneticfield are shown in Figure 28 to Figure 30. The x vertex and y vertex resolutions shown in Figure 28 andFigure 29 are consistent because of the symmetric detector geometry. The x and y vertex resolutions arebelow 14 µ m at η < = .
5, they increase to about 26 µ m (16 µ m) at 1 GeV when version 0 (version 4) designis implemented. The z vertex resolution shown in Figure 30 increases from about 18 µ m to about 200 µ mfor version 0 design and 150 µ m for version 4 design at 1 GeV as pseudorapidity increases. r e s ( u m ) x V t x ver 0 ver 4 Barrel pitch=20umFST pitch=20um £h£ £h£ £h£ (GeV)
T,input p5 10 15 20 25 30 £h£ (GeV)
T,input p5 10 15 20 25 30 £h£
Figure 28: x vertex resolution as a function input (true) transverse momentum from Fun4all simulation using version 0and version 4 FST design with BeAST magnetic field. r e s ( u m ) y V t x ver 0 ver 4 Barrel pitch=20umFST pitch=20um £h£ £h£ £h£ (GeV)
T,input p5 10 15 20 25 30 £h£ (GeV)
T,input p5 10 15 20 25 30 £h£
Figure 29: y vertex resolution as a function input (true) transverse momentum from Fun4all simulation using version 0and version 4 FST design with BeAST magnetic field. roposed EIC FST and Associated Physics r e s ( u m ) z V t x ver 0 ver 4 Barrel pitch=20umFST pitch=20um £h£ £h£ £h£ (GeV)
T,input p5 10 15 20 25 30 £h£ (GeV)
T,input p5 10 15 20 25 30 £h£
Figure 30: z vertex resolution as a function input (true) transverse momentum from Fun4all simulation using version 0and version 4 FST design with BeAST magnetic field.
Version 4.1 and version 4.2, which are described in Section 4.4.1 and Table 2, are also tested for vertexresolutions as shown in Figure 31 to 33. Similar to DCA resolutions shown in Section 4.4.1, the vertexresolutions are the same between version 4, 4.1 and 4.2 at η ≤
3. At η >
3, the differences are about 1 . µ min x and y vertex resolutions, and about 10 µ m in z vertex resolution. r e s ( u m ) x V t x ver4 ver4.1ver4.2 £h£ £h£ £h£ (GeV) T,input p5 10 15 20 25 30 £h£ (GeV)
T,input p5 10 15 20 25 30 £h£
Figure 31: x vertex resolution as a function input (true) transverse momentum from Fun4all simulation using version 4,4.1 and 4.2 FST design. roposed EIC FST and Associated Physics r e s ( u m ) y V t x ver4 ver4.1ver4.2 £h£ £h£ £h£ (GeV) T,input p5 10 15 20 25 30 £h£ (GeV)
T,input p5 10 15 20 25 30 £h£
Figure 32: y vertex resolution as a function input (true) transverse momentum from Fun4all simulation using version 4,4.1 and 4.2 FST design. r e s ( u m ) z V t x ver4 ver4.1ver4.2 £h£ £h£ £h£ (GeV) T,input p5 10 15 20 25 30 £h£ (GeV)
T,input p5 10 15 20 25 30 £h£
Figure 33: z vertex resolution as a function input (true) transverse momentum from Fun4all simulation using version 4,4.1 and 4.2 FST design.
5. Eicroot Simulation
Tracking performance with additional GEM detectors studies were done using Eicroot simulation witha five-plane silicon detector setup.
The position and radii of the silicon disks are summarized in Table 3. The addition of large gaseousdetectors (GEMS [5]) at large z ( > roposed EIC FST and Associated Physics Table 3:
Silicon detector planes geometrical configurations. disk 1 disk 2 disk 3 disk 4 disk 5r
40 mm 40 mm 50 mm 60 cm 65mmr
300 mm 350 mm 400mm 400mm 440 mmz z z z z Config 1 (default) 48cm 63cm 78cm 93cm 113cmConfig 2 35cm 63cm 78cm 93cm 113cmConfig 3 25cm 63cm 78cm 93cm 113cm
Table 4:
GEM detector planes geometrical configuration. z r r To evaluate the effect of the z position of the first plane (closest to the interaction point), three z positionswere evaluated as described in Table 3. Figure 34 (left panel) shows that a first plane positioned at 25 cmfrom the interaction point gives the best overall relative resolution beyond momentum of 10 GeV. The rightpanel of the same figure on the other hand shows that the inclusion of the GEMS reduces the overall effect ofthis plane position. Using a magnetic field of 3T as it is shown in Figure 35 shows similar trends as beforebut with an improved resolution across all momentum.
Figure 34:
Relative resolution under 1.5T. The left panel shows the dispersion obtained when varying the first plane z position. The right panel shows the equivalent result when adding the GEMS in addition to the 3 silicon plane detector. roposed EIC FST and Associated Physics Figure 35:
Relative resolution under 3T. The left panel shows the dispersion obtained when varying the first plane z position. The right panel shows the equivalent result when adding the GEMs in addition to the 3 silicon plane detector. Momentum of a charged particle is determined by the degree of curvature of a track. To evaluate thecurvature one can look at the azimuth location of a single track hit in sequential or alternating plane locationsas it is illustrated in Figure 36. The larger the difference between the azimuth location in two planes thelarger the curvature. In the following azimuth difference studies, three silicon planes were used at a startingdistance of 1.8 m from the interaction region (Figure 37 left panel). Pions were generated at a vertex positionof (0,0,0) with a flat p T distribution ranging 2-25 GeV. The plane positions were shifted in z and the azimuthdifference was re-evaluated. Figure 37 (right) shows the difference of azimuth position between the third andfirst plane as a function of 1 / p . Figure 36:
Illustration of the trajectory of a charged particle whose curvature depends on the magnetic field strength.
Figure 38 shows the results of the difference in azimuth of two adjacent planes while moving the planescloser to the vertex. Plane 1 was shifted from 1.8 m to 0.3 m while plane 2 was shifted from 1.95 m to0.45 m. The two-plane configurations considered before assume equidistant silicon planes. An asymmetricplane spacing was also studied and the results are given in Figure 39. Finally, Figure 40, which summarizesall results indicates that equivalent results can be obtained with both field strengths if different z positionsare considered in each case. The distance from the interaction point to the vertex tracker has a significant effect on the pointingresolution from tracks back to the collision vertex. In general, a tracking detector with angular resolution d θ that is a distance r from the vertex will produce a pointing uncertainty r d θ when projecting tracks back tothe vertex. Therefore, minimizing the distance to the vertex as well as enhancing the angular resolution areboth necessary for optimal vertexing performance. Momentum resolution improves as particles are tracked28 roposed EIC FST and Associated Physics Figure 37:
Left: illustration of a pion beam tracked by three-plane tracker. The first plane is positioned at 1.8 m from thevertex. Right: track curvature evaluations in two magnetic field strengths. Ordinate is the hit azimuth position differencein radians. Abscissa is 1 / p average reconstructed of the track. - - - - - - (r ad ) - D i sk D i sk fD + p -Disk Disk -Disk -Disk -Disk
3T Disk -Disk
3T Disk o o Figure 38:
Azimuth difference between two adjacent planes sitting at 1.8 m and 1.95 m (black). Re-evaluation after ashifting closer to z both planes. Two magnetic fields were considered with 3T (blue triangles and open black circles)giving a larger difference as expected. Figure 39:
Comparison of azimuth differences between the third and first plane assuming equidistant planes as presentedbefore (red and black markers) and with non equidistant planes (blue markers) 0. 3m and 0.9 m over a longer lever arm. However, the silicon area required to cover a given angular acceptance increaseswith the square of the distance from the vertex, so minimizing that distance also reduces the detector area andtherefore cost and complexity. A compromise between lever arm and detector size must therefore be made.Simulations are used to study the track pointing resolution to the vertex as a function of the silicon planepositions. Five planes of silicon tracker are placed at 50, 63, 78, 93, and 113 cm from the vertex. Tracks arelaunched at 22.5 ◦ above the z axis, and the hit positions at the planes are smeared with a 30 µ m Gaussian29 roposed EIC FST and Associated Physics Figure 40:
Summary of results
Figure 41:
Cartoon illustrating the relative position of the GEM detectors with respect to the silicon detectors resolution. The smeared points are fit with a straight line, and the resulting tracks are projected back tothe collision vertex z position. The distance from the projected track to the actual origin are collected intohistograms and fit with a Gaussian. The width of that Gaussian is taken as the vertex pointing resolution foreach detector configuration. Figure 42:
Effects of moving the first (left) and last (right) planes in the tracker along the z axis In the nominal case, where the first plane of the tracker is 50 cm from the vertex, a vertex pointingresolution of 50 µ m is found. To examine the effect of distance on the pointing resolution, the position ofthe first plane is varied while the positions of the other planes are held constant. The resulting resolutionsare shown on the right of Figure 42 which shows that a vertex pointing resolution of approximately 35 µ m isobtained when the first plane is 25 cm from the vertex.30 roposed EIC FST and Associated Physics The effect of the position of the last plane was also evaluated, with results shown on the right of Figure 42.Here positions of the first four planes were held constant at 25, 63, 78, and 93 cm from the vertex, and the lastplane was moved. Plot on the right of Figure 42 shows that the resolution varies by 4 µ m from approximately38 µ m to 32 µ m when the last plane is moved away from z =100 cm to 140 cm. This would, however,necessitate an increase in size of the last detector by a factor of 2 to have the same angular acceptance. Asthe position of this last plane has relatively little effect on the vertex pointing resolution, detailed studies ofthe trade-off between plane position, area and momentum resolution are needed to fully evaluate this detectordesign. 31 roposed EIC FST and Associated Physics
6. Heavy Flavor and Jet Physics studies
As shown in the various kinematic distributions of heavy flavor hadrons and their decay daughters insection 2, majority of the final state particles produced at the future EIC are within pseudorapidity regionfrom -2 to 4 (see example in Figure 43 which use one EIC collision combination). The EIC recommendcollision energy combinations are listed below:• E e = 5 GeV, E p / A = 41 GeV• E e = 5 GeV, E p = 100 GeV• E e = 10 GeV, E p / A = 100/110 GeV• E e = 18 GeV, E p / A = 100/110 GeV• E e = 18 GeV, E p = 275 GeV VS y T Reconstructed D p − − rapidity y ( G e V / c ) T p VS y T Reconstructed D p η Reconstructed D p VS − − η pseudorapidity p ( G e V / c ) η Reconstructed D p VS η Reconstructed D daughter p VS − − η pseudorapidity p ( G e V / c ) η Reconstructed D daughter p VS
Figure 43:
Kinematic distributions for reconstructed D-meson and its daughters in 10 f b −
10 GeV electron and 100GeV protons collisions. Reconstructed D-meson p T VS rapidity y is shown in the left. Reconstructed D-meson p T VSpseudorapidity η is shown in the middle. D-meson decayed daughter p T VS pseudorapidity η is shown in the right. VS x for hadron measurements η η hadron − − − pa r t on x ± π VS x for hadron measurements η VS x for hadron measurements η η hadron ± K VS x for hadron measurements η VS x for hadron measurements η η hadron )pp ( VS x for hadron measurements η VS x for hadron measurements η η hadron − − − pa r t on x ± D VS x for hadron measurements η VS x for hadron measurements η η hadron ± B VS x for hadron measurements η Figure 44:
Pseudorapidity versus Bjorken-x for different flavor hadrons at generation level in 10 f b −
10 GeV electronand 100 GeV protons collisions. roposed EIC FST and Associated Physics We use one collision energy combination which is the 10 GeV electron and 100 GeV protons collisionsas our reference system to study the heavy flavor and jet measurements. This energy can access a wideBjorken-x region especially for the high-x region as shwon in Figure 44. Initial heavy flavor studies havebeen carried out with detector performance in fast simulation [4, 6]. In the following sections, we will startwith the open heavy flavor hadron studies (see section 6.2), then followed by the heavy flavor jet tagging andjet angularity studies (in section 6.3). Beyond the normal heavy flavor and jet observable, new exotic statessuch as the X(3872) will be explored at the future EIC. Section 6.4 will introduce the ongoing work of theexotic states. p / p VS p ∆ Track p (GeV/c) p / p ∆ T r a ck in FST π = 1.0 1.5 η = 1.5 2.0 η = 2.0 2.5 η = 2.5 3.0 η = 3.0 3.5 η p / p VS p ∆ T resolution VS p DCA (GeV/c) T Track p m ) µ ( D T r a ck DC A in FST π = 1.0 1.5 η = 1.5 2.0 η = 2.0 2.5 η = 2.5 3.0 η = 3.0 3.5 η T resolution VS p DCA T resolution VS p z DCA (GeV/c) T Track p m ) µ ( z T r a ck DC A in FST π = 1.0 1.5 η = 1.5 2.0 η = 2.0 2.5 η = 2.5 3.0 η = 3.0 3.5 η T resolution VS p z DCA
Figure 45:
Tracking performance for FST version 0 design with the Beast magnetic field. Pixel pitch for both barrellayers and forward planes are selected at 20 µ m . Left panel shows the momentum dependent momentum resolution indifferent pseudorapidity regions. Middle panel shows the transverse momentum dependent DC A D resolution and theright panel shows the transverse momentum dependent DC A z resolution in the associated pseudorapidity regions. p / p VS p ∆ Track p (GeV/c) p / p ∆ T r a ck in FST π = 1.0 1.5 η = 1.5 2.0 η = 2.0 2.5 η = 2.5 3.0 η = 3.0 3.5 η p / p VS p ∆ T resolution VS p DCA (GeV/c) T Track p m ) µ ( D T r a ck DC A in FST π = 1.0 1.5 η = 1.5 2.0 η = 2.0 2.5 η = 2.5 3.0 η = 3.0 3.5 η T resolution VS p DCA T resolution VS p z DCA (GeV/c) T Track p m ) µ ( z T r a ck DC A in FST π = 1.0 1.5 η = 1.5 2.0 η = 2.0 2.5 η = 2.5 3.0 η = 3.0 3.5 η T resolution VS p z DCA
Figure 46:
Tracking performance for FST version 4 design with the Beast magnetic field. Pixel pitch for both barrellayers and forward planes are selected at 20 µ m . Left panel shows the momentum dependent momentum resolution indifferent pseudorapidity regions. Middle panel shows the transverse momentum dependent DC A D resolution and theright panel shows the transverse momentum dependent DC A z resolution in the associated pseudorapidity regions. In our current studies, we use PYTHIA8 event generator for our heavy flavor and jet studies in e + p collisions. A N coll scaling is applied for the e + A collisions. In additional to the physics e + p collisions,a 12 kHz p + p collision background is embedded in to the simulated events with the same proton beamenergy. The evaluated tracking performance of the barrel and foward silicon vertex/tracking detector (seedifferent design parameters in section 4.1) in both the central and forward pseudorapidity regions are usedto smear charged tracks in generated events. In addition to the tracking performance provided by the siliconvertex/tracking detectors, 20-35 micron primary vertex resolution which depends on the track multiplity,95% K/ π /p separation and 95% electron identification efficiency are included.33 roposed EIC FST and Associated Physics Heavy flavor products have strong a discriminating power between different model predictions of nucleartransport coefficients. In the factorizaton frame, the covolution function of the heavy flavor hadron cross-section includes the hadronization process. This results in that heavy flavor hadron production will be anideal probe to map out the hadronization process in vacuum and nuclear medium by comparing to the otherchannels such as jet production.In these simulation studies, the open heavy flavor hadrons including D-meson and B-meson are recon-structed by matching the charged tracking transverse Distance Closest Approach (
DC A D ) within a certainvalue. The cuts are varied depending on the reconstructed particle species, the average value is set at 100 µ m . The simulation analysis chain is the following:1. event generation in PYTHIA.2. Detector performance smearing of generated particles.3. Heavy flavor hadron and jet reconstruction.4. Physics projection scaled with the integrated luminosity. GeV/c × ± Reconstructed D
MCTotal fit fit ± Rec. DBKG fit
SIG/BKG: 1.718 ± D : 10 GeV e E : 100 GeV p ETrack cut:<4 η ± Reconstructed D GeV/c ) D ( Reconstructed D
MCTotal fit ) fit D ( Rec. DBKG fit ) SIG/BKG: 2.348 D ( D ) D ( Reconstructed D GeV/c ± s Reconstructed D
SIG/BKG: 0.351 ± s D MCTotal fit fit s ± Rec. DBKG fit ± s Reconstructed D GeV/c
Reconstructed B meson w/ Det. performanceMC SIG fit ± B : 10 GeV e E : 100 GeV p E Int. Lumi: 10 fb
Reconstructed B meson GeV/c
Reconstructed B meson w/ Det. performanceMC ) SIG fit B ( B ) SIG fit B ( B Reconstructed B meson
Figure 47:
Reconstructed D-mesons and B-mesons using the FST version 0 design with the Barbar magnetic field.Pixel pitch for both barrel layers and forward planes are selected at 20 µ m . The integrated luminosity of e + p collisionsat √ s =
63 GeV is 10 f b − . Different geometries of the proposed Forward Silicon Tracker (FST) have been studies in section 4,impacts on the open heavy flavor hadron by their tracking performances are studied. We start with theparameterization of the tracking performance for one version of the barrel and forward silicon vertex/trackingdetector design. Figure 45 shows the tracking performance with the FST version 0 design using the Beastmagnetic field. Figure 46 shows the tracking performance with the FST version 4 design using the Beastmagnetic field. Better tracking momentum and DCA resolutions are achieved by the FST version 4 design.34 roposed EIC FST and Associated Physics GeV/c ) D ( Reconstructed D
MCTotal fitBKG fit : 2 to 4.0 η D :0.5 1.5 GeV/c T pSIG/BKG: 2.579 ) D ( Reconstructed D GeV/c ) D ( Reconstructed D
MCTotal fitBKG fit : 2 to 4.0 η D :1.5 2.5 GeV/c T pSIG/BKG: 6.009 ) D ( Reconstructed D GeV/c ) D ( Reconstructed D
MCTotal fitBKG fit : 2 to 4.0 η D :2.5 4.0 GeV/c T pSIG/BKG: 5.336 ) D ( Reconstructed D GeV/c ) D ( Reconstructed D
MCTotal fitBKG fit : 2 to 4.0 η D : >4.0 GeV/c T pSIG/BKG: 6.487 ) D ( Reconstructed D GeV/c ) D ( Reconstructed D
MCTotal fitBKG fit >0.5 GeV/c T p D: 2 to 0 η SIG/BKG: 4.204 ) D ( Reconstructed D GeV/c ) D ( Reconstructed D
MCTotal fitBKG fit >0.5 GeV/c T p D: 0 to 1 η SIG/BKG: 4.563 ) D ( Reconstructed D GeV/c ) D ( Reconstructed D
MCTotal fitBKG fit >0.5 GeV/c T p D: 1 to 2 η SIG/BKG: 1.974 ) D ( Reconstructed D GeV/c ) D ( Reconstructed D
MCTotal fitBKG fit >0.5 GeV/c T p D: 2 to 4.0 η SIG/BKG: 0.782 ) D ( Reconstructed D
Figure 48:
Reconstructed D ( ¯ D ) mesons using the FST version 0 design with the Barbar magnetic field. Pixel pitchfor both barrel layers and forward planes are selected at 20 µ m . The integrated luminosity of e + p collisions at √ s = f b − . Top four panels present the invariant mass distributions of reconstructed D ( ¯ D ) in different p T bins.The bottom four panels show the Figure 47 shows the mass spectrum of fully reconstructed D ± , D ( ¯ D ), D ± s , B ± , B ( ¯ B ) and B s ( ¯ B s )based on the tracking performance shown in Figure 46. For these heavy flavor hadron reconstructions,35 roposed EIC FST and Associated Physics charged tracks are required to have pseudorapidity within -2 to 4. Clear D-meson signals have been obtainedon top of the combinatorial backgrounds. The signal over background ratios and the reconstruction efficiencyare listed in the associated panels. Clean B-mesons can be reconstructed with this FST design, while thewidth of reconstructed B s ( bar B s ) is a bit wide and could not get separation from the reconstructed B ( ¯ B )mass peak.The kinematic dependence of the reconstructed D-meson has been studied. The top four panels ofFigure 48 present the mass distributions of reconstructed D ( ¯ D ) with − < η < p T regions. The p T bins are 0.5-1.5 GeV/c, 1.5-2.5 GeV/c, 2.5-4.0 GeV/c, > D ( ¯ D ) with p T > . η regions. The pseudorapidty η bins are -2 to 0, 0 to 1, 1 to 2 and 2 to 4.0. GeV/c )p+p ( ± +K ± π Cluster mass of w/ Det. performanceMC + BKG) c Λ Total fit ( SIG fit c Λ BKG fit
SIG/BKG: 0.061 c Λ : 10 GeV e E : 100 GeV p E )p+p ( ± +K ± π Cluster mass of
Figure 49:
Reconstructed Λ c mass spectrum using the FST version 0 design with the Babar magnetic field. Pixel pitchfor both barrel layers and forward planes are selected at 20 µ m . The integrated luminosity of e + p collisions at √ s = f b − . In addition to heavy flavor meson reconstruction, we also looked for the heavy flavor hadron recon-struction (e.g. Λ c ). Although the combinatorial background is significantly higher than the D-meson massspectrum, clear Λ c signal can be obtained as shown in Figure 49.36 roposed EIC FST and Associated Physics GeV/c × ± Reconstructed D
MCTotal fit fit ± Rec. DBKG fit
SIG/BKG: 2.298 ± D : 10 GeV e E : 100 GeV p ETrack cut:<4 η ± Reconstructed D GeV/c ) D ( Reconstructed D
MCTotal fit ) fit D ( Rec. DBKG fit ) SIG/BKG: 3.199 D ( D ) D ( Reconstructed D GeV/c × ± s Reconstructed D
SIG/BKG: 0.392 ± s D MCTotal fit fit s ± Rec. DBKG fit ± s Reconstructed D GeV/c × ± Reconstructed D
MCTotal fit fit ± Rec. DBKG fit
SIG/BKG: 2.367 ± D : 10 GeV e E : 100 GeV p ETrack cut:<4 η ± Reconstructed D GeV/c ) D ( Reconstructed D
MCTotal fit ) fit D ( Rec. DBKG fit ) SIG/BKG: 3.624 D ( D ) D ( Reconstructed D GeV/c × ± s Reconstructed D
SIG/BKG: 0.402 ± s D MCTotal fit fit s ± Rec. DBKG fit ± s Reconstructed D
Figure 50:
Reconstructed D-meson mass spectrum using the FST version 0 and version 4 designs with the Beastmagnetic field. Pixel pitch for both barrel layers and forward planes are selected at 20 µ m . The integrated luminosity of e + p collisions at √ s =
63 GeV is 10 f b − . GeV/c
Reconstructed B meson w/ Det. performanceMC SIG fit ± B : 10 GeV e E : 100 GeV p E Int. Lumi: 10 fb
Reconstructed B meson GeV/c
Reconstructed B meson w/ Det. performanceMC ) SIG fit B ( B ) SIG fit B ( B Reconstructed B meson GeV/c
Reconstructed B meson w/ Det. performanceMC SIG fit ± B : 10 GeV e E : 100 GeV p E Int. Lumi: 10 fb
Reconstructed B meson GeV/c
Reconstructed B meson w/ Det. performanceMC ) SIG fit B ( B ) SIG fit B ( B Reconstructed B meson
Figure 51:
Reconstructed B-meson mass spectrum using the FST version 0 and version 4 designs with the Beastmagnetic field. Pixel pitch for both barrel layers and forward planes are selected at 20 µ m . The integrated luminosity of e + p collisions at √ s =
63 GeV is 10 f b − . roposed EIC FST and Associated Physics GeV/c ) D ( Reconstructed D
MCTotal fitBKG fit >0.5 GeV/c T p D: 2 to 0 η SIG/BKG: 4.738 ) D ( Reconstructed D GeV/c ) D ( Reconstructed D
MCTotal fitBKG fit >0.5 GeV/c T p D: 0 to 1 η SIG/BKG: 4.720 ) D ( Reconstructed D GeV/c ) D ( Reconstructed D
MCTotal fitBKG fit >0.5 GeV/c T p D: 1 to 2 η SIG/BKG: 1.921 ) D ( Reconstructed D GeV/c ) D ( Reconstructed D
MCTotal fitBKG fit >0.5 GeV/c T p D: 2 to 4.0 η SIG/BKG: 1.030 ) D ( Reconstructed D GeV/c ) D ( Reconstructed D
MCTotal fitBKG fit >0.5 GeV/c T p D: 2 to 0 η SIG/BKG: 4.668 ) D ( Reconstructed D GeV/c ) D ( Reconstructed D
MCTotal fitBKG fit >0.5 GeV/c T p D: 0 to 1 η SIG/BKG: 4.772 ) D ( Reconstructed D GeV/c ) D ( Reconstructed D
MCTotal fitBKG fit >0.5 GeV/c T p D: 1 to 2 η SIG/BKG: 1.940 ) D ( Reconstructed D GeV/c ) D ( Reconstructed D
MCTotal fitBKG fit >0.5 GeV/c T p D: 2 to 4.0 η SIG/BKG: 1.069 ) D ( Reconstructed D
Figure 52:
Reconstructed D ( ¯ D ) meson mass spectrum in different pseudorapidity regions using the FST version 0and version 4 designs with the Beast magnetic field. Pixel pitch for both barrel layers and forward planes are selected at20 µ m . The integrated luminosity of e + p collisions at √ s =
63 GeV is 10 f b − . roposed EIC FST and Associated Physics GeV/c )p+p ( ± +K ± π Cluster mass of w/ Det. performanceMC + BKG) c Λ Total fit (BKG fit
SIG/BKG: 0.073 c Λ : 10 GeV e E : 100 GeV p E )p+p ( ± +K ± π Cluster mass of
GeV/c )p+p ( ± +K ± π Cluster mass of w/ Det. performanceMC + BKG) c Λ Total fit (BKG fit
SIG/BKG: 0.072 c Λ : 10 GeV e E : 100 GeV p E )p+p ( ± +K ± π Cluster mass of
Figure 53:
Reconstructed Λ c mass spectrum using the FST version 0 and version 4 designs with the Beast magneticfield. Pixel pitch for both barrel layers and forward planes are selected at 20 µ m . The integrated luminosity of e + p collisions at √ s =
63 GeV is 10 f b − . GeV/c )p+p ( ± +K ± π Cluster mass of w/ Det. performanceMC + BKG) c Λ Total fit ( SIG fit c Λ BKG fit
SIG/BKG: 0.075 c Λ : 10 GeV e E : 100 GeV p E <1 η )p+p ( ± +K ± π Cluster mass of GeV/c )p+p ( ± +K ± π Cluster mass of
SIG/BKG: 0.080 c Λ : 10 GeV e E : 100 GeV p E<2 η )p+p ( ± +K ± π Cluster mass of GeV/c )p+p ( ± +K ± π Cluster mass of
SIG/BKG: 0.058 c Λ : 10 GeV e E : 100 GeV p E<4 η )p+p ( ± +K ± π Cluster mass of
Figure 54:
Reconstructed Λ c mass spectrum in different pseudorapidity regions using the FST version 4 designs withthe Beast magnetic field. Pixel pitch for both barrel layers and forward planes are selected at 20 µ m . The integratedluminosity of e + p collisions at √ s =
63 GeV is 10 f b − . Different FST detector geometries and magnetic field maps are used for the open heavy flavor hadronreconstruction. Figure 50 shows the comparison of the reconstructed D-meson with using the FST version0 and version 4 designs with the Beast magnetic field in 10 f b − e + p collisions at √ s =
63 GeV. Withthe same simulation sample, comparison for reconstructed B-mesons are shown in Figure 51, comparisonfor reconstructed D-mesons in different pseudorapidity regions are shown in Figure 52 and comparison forreconstructed Λ c are shown in Figure 53. Pseudorapidity dependent reconstructed Λ c mass spectrum withthe FST version 4 design and the Beast magnetic filed have been shown in Figure 54.These results indicate adding one outer barrel layer and one outer forward plane on top of the 5 barrel layerand 5 forward plane silicon vertex/tracker detector does not significantly change the signal over backgroundratio for reconstructed D-mesons, B-mesons and Λ c hadrons. Including a more forward and low materialbudget tracking detector such as a GEM tracker could further improve the tracking momentum resolutionand provide better mass resolutions in the more forward pseudoradity region. These studies will be carriedout once the detector design and performance evaluation is done.39 roposed EIC FST and Associated Physics Signal/Background VS FST design version
FST design version S i g / B k g r a t i o Sig/Bkg ratio ± D ) D ( D s ± D = 63.2 GeVse+p collisions at Signal/Background VS FST design version
Figure 55:
Comparison of signal/background ratios for reconstructed D-mesons with different FST designs. Thesevalues are determined in simulation of e + p collisions at √ s =
63 GeV with integrated luminosity of 10 f b − . Signal/Background VS FST design version
FST design version S i g / B k g r a t i o ) D ( Rec. D <0 η
2< <1 η
0< <2 η
1< <4 η = 63.2 GeVse+p collisions at Signal/Background VS FST design version
Figure 56:
Comparison of reconstructed D ( ¯ D ) in different pseudorapidity regions with different FST designs. Thesevalues are determined in simulation of e + p collisions at √ s =
63 GeV with integrated luminosity of 10 f b − . roposed EIC FST and Associated Physics Signal/Background VS FST design version
FST design version S i g / B k g r a t i o ) c Λ ( c Λ Rec. <1 η
2< <2 η
1< <4 η Signal/Background VS FST design version
Figure 57:
Comparison of reconstructed Λ c ( ¯ Λ c ) in different pseudorapidity regions with different FST designs. Thesevalues are determined in simulation of e + p collisions at √ s =
63 GeV with integrated luminosity of 10 f b − . Table 5:
FST version corresponding geometries and magnet options
Name FST index 1 FST index 2 FST index 3 FST index4geometry version in Table 2 version 0 version 0 version 1 version 4Magnet options Babar Beast Beast Beast h vs z eA Projected hadron R h hadron momentum fraction z e A N u c l ea r m od i f i c a t i on f a c t o r R ± B ± D ± π : 2 to 4 η Track = 63.2 GeVs e+p Int. Lumi.: 10 fb e+Au Int. Lumi. : 500 pb h vs z eA Projected hadron R h vs z eA ) R D ( Projected D h ) momentum fraction z D ( D e A N u c l ea r m od i f i c a t i on f a c t o r R : 2 to 4.0 η ) D ( D : 1 to 2 η ) D ( D : 0 to 1 η ) D ( D : 2 to 0 η ) D ( D = 63.2 GeVs e+p Int. Lumi.: 10 fb e+Au Int. Lumi. : 500 pb h vs z eA ) R D ( Projected D
Figure 58:
Projections of nuclear modification factor R eAu for reconstructed flavor dependent hadron versus the hadronmomentum fraction z h (left panel). R eAu projections of reconstructed D ( ¯ D ) in different pseudorapidity bins are shownin the right panel. Detector performance from FST version 0 design in Babar magnetic filed is used. The statisticaluncertainties are projected with signal yields in e + p and e + Au collisions at √ s =
63 GeV.
Summary of the signal over background ratio for the reconstructed D-meson within pseudorapidity of -2to 4 is shown in Figure 55. The pseudorapidity separated reconstructed D ( ¯ D ) signal over background ratio41 roposed EIC FST and Associated Physics with different FST designs are shown in Figure 56. Pseudorapidity dependent reconstructed Λ c signal overbackground ratios are shown in Figure 57. The corresponding FST geometries and the magnet selections arelisted in Table 5. The signal over background ratios for reconstructed D-mesons have dominant impacts bythe tracking momentum resolutions which is associated with the magnetic filed options. h vs z eA Projected hadron R h hadron momentum fraction z e A N u c l ea r m od i f i c a t i on f a c t o r R ± B ± D ± π : 2 to 4 η Track = 63.2 GeVs e+p Int. Lumi.: 10 fb e+Au Int. Lumi. : 500 pb h vs z eA Projected hadron R h vs z eA ) R D ( Projected D h ) momentum fraction z D ( D e A N u c l ea r m od i f i c a t i on f a c t o r R : 2 to 4.0 η ) D ( D : 1 to 2 η ) D ( D : 0 to 1 η ) D ( D : 2 to 0 η ) D ( D = 63.2 GeVs e+p Int. Lumi.: 10 fb e+Au Int. Lumi. : 500 pb h vs z eA ) R D ( Projected D
Figure 59:
Projections of nuclear modification factor R eAu for reconstructed flavor dependent hadron versus the hadronmomentum fraction z h (left panel). R eAu projections of reconstructed D ( ¯ D ) in different pseudorapidity bins areshown in the right panel. Detector performance from FST version 0 design in Beast magnetic filed is used. The statisticaluncertainties are projected with signal yields in e + p and e + Au collisions at √ s =
63 GeV. h vs z eA Projected hadron R h hadron momentum fraction z e A N u c l ea r m od i f i c a t i on f a c t o r R ± B ± D ± π : 2 to 4 η Track = 63.2 GeVs e+p Int. Lumi.: 10 fb e+Au Int. Lumi. : 500 pb h vs z eA Projected hadron R h vs z eA ) R D ( Projected D h ) momentum fraction z D ( D e A N u c l ea r m od i f i c a t i on f a c t o r R : 2 to 4.0 η ) D ( D : 1 to 2 η ) D ( D : 0 to 1 η ) D ( D : 2 to 0 η ) D ( D = 63.2 GeVs e+p Int. Lumi.: 10 fb e+Au Int. Lumi. : 500 pb h vs z eA ) R D ( Projected D
Figure 60:
Projections of nuclear modification factor R eAu for reconstructed flavor dependent hadron versus the hadronmomentum fraction z h (left panel). R eAu projections of reconstructed D ( ¯ D ) in different pseudorapidity bins areshown in the right panel. Detector performance from FST version 4 design in Beast magnetic filed is used. The statisticaluncertainties are projected with signal yields in e + p and e + Au collisions at √ s =
63 GeV. roposed EIC FST and Associated Physics Nuclear modification factor R eA measurements for different flavor hadrons at the future EIC will notonly explore both initial and final state effects on hadron production in nuclear medium [7–9] but also providefurther information on hadronization process and its flavor dependence [10]. Figure 58 to 60 present theprojected nuclear modification factor for reconstructed flavor dependent hadron versus the hadron momentumfraction z h with detector performance from different FST designs and different magnetic filed options in e + p and e + Au collisions at √ s =
63 GeV. Projected R eAu for reconstructed D ( ¯ D ) in different pseudorapiditybins are also shown in these figures.Comparing Figure 58 and Figure 59, smaller projection uncertainties have been achieved for moreforward D ( ¯ D ) measurements with the same FST design by using the Beast magnetic field which producesa better signal over background ratio. Good statistics can be achieved for inclusive D-meson measurementsat the future EIC, and different FST design and different magnet options have little impacts on their projectedstatistical uncertainties. These reconstructed heavy flavor hadrons provide a good discriminating powerto separate different theoretical predictions on the nuclear transport coefficients. Forward heavy flavormeasurements to be carried out at the EIC can provide better constraints on the hadron fragmentationprocesses in medium as discussed in [10]. The future EIC will provide a clean environment for jet studies as well. Initial jet reconstructionshave been achieved based on true particle information. Inclusive jets are reconstructed with the anti- k T jet algorithm with cone radius at 1.0. Then jets are tagged with fully reconstructed heavy flavor meson byrequiring these reconstructed heavy flavor hadrons be within the associated jet cone [6]. If there is not areconstructed heavy flavor hadron can be found within the jet cone, this jet is labeled as light flavor jet.Figure 61 show the spectrum of reconstructed light flavor jets and heavy flavor (charm and bottom) jets.These distributions are not corrected by the corresponding reconstruction efficiencies. (GeV/c) T p spectrum T Jet p
Light jetCharm jetBottom jet spectrum T Jet p
Figure 61: p T spectrum of reconstructed light flavor jets (black open circles), charm jets (red closed triangles) andbottom jets (blue closed triangles). The statistical uncertainties are projected with 10 f b − e + p at √ s =
63 GeV.
Jet substructure observable can image the nucleon/nuclei 3D structure and help map out the hadronizationprocess in vacuum and nuclear medium. Recent theoretical developments [11] suggest the jet angularityobservable has a better discriminating power to distinguish quark or gluon originated jets. Following the43 roposed EIC FST and Associated Physics same definition in [11], we have studied the jet angularity for light flavor jets and charm tagged jets withdifferent power order a value selections. Figure 62 shows the jet angularity distributions of light flavor jetsand charm tagged jets and ratio distributions of their shapes in 10 f b − e + p at √ s =
63 GeV. Charm jetshave a broader jet shape which causes a increasing trends in the jet angularity ratio distributions presented inthe bottom panels of Figure 62. Nuclear modification effects for different flavor jets are under study. τ (a = 0.5) a τ Jet angularity
Light jetCharm jet (a = 0.5) a τ Jet angularity τ (a = 1) a τ Jet angularity
Light jetCharm jet (a = 1) a τ Jet angularity τ (a = 2) a τ Jet angularity
Light jetCharm jet (a = 2) a τ Jet angularity τ s hape r a t i o a τ c j e t/ l j e t (a = 0.5) a τ Jet angularity (a = 0.5) a τ Jet angularity τ s hape r a t i o a τ c j e t/ l j e t (a = 1) a τ Jet angularity (a = 1) a τ Jet angularity τ s hape r a t i o a τ c j e t/ l j e t (a = 2) a τ Jet angularity (a = 2) a τ Jet angularity
Figure 62:
Jet angularity distributions for light flavor jets (black open points) and charm tagged jets (blue closed points)with different power order a value selections are shown in the top panel. Distributions with a = . a = a = − a value selection. The statistical uncertainties are projected with 10 f b − e + p at √ s =
63 GeV.
Hadronization inside the nucleus is expected to play an important role on particle production in e Acollisions at the EIC [9]. Hadrons that propagate through the nucleus are subject to interactions with partonsthat lead to energy loss and, in the case of bound quarkonium states, dissociation via breakup. This will leadto reduction in the nuclear modification factor R eA .Quarkonium production has been studied extensively in fixed-target p A collisions, where hadronizationinside the nucleus also occurs. Experiments at Fermilab [12] and the SPS [13] have measured differencesbetween the suppression of the ψ ( S ) state compared to the J / ψ . Since these two states have the same quarkcontent, the interactions of the primordial c ¯ c pair prior to hadronization are identical, regardless of the finalstate the pair eventually projects onto. Therefore, the suppression mechanism must occur after the pair hashadronized into a final state. This effect can be quantitatively explained when considering the different radiiof the final states: the relatively large ψ ( S ) state samples a larger volume of nuclear matter while passingthrough the nucleus, and has a correspondingly higher probability of encountering a partons an undergoingbeakup than the relatively tightly bound J / ψ [14]. Similar effects are expected to occur in e A collisions.While the spectrum of charmonia states is well understood [15], the ever-expanding list of
XY Z exoticstates remain a mystery [16]. Various explanations of these unexpected states have been put forth, includingtetraquarks, hadroncharmonium, hadronic molecules, and other exotic hybrid states. Given the large number44 roposed EIC FST and Associated Physics of states that have been found, and their various properties, it is unlikely that a single model will be able todescribe them all. Additional data is needed to discriminate between various model calculations.Similar to conventional charmonia, exotics produced in e A collisions will also undergo interactionsinside the nucleus, which can lead to disruption. From our experience in fixed target p A experimentsdiscussed above, we expect that the magnitude of these disruption effects will depend on the size of the finalstate. A weakly-bound hadronic molecule with a large radius would suffer significantly more disruption thata tightly bound tetraquark (see Fig. 63 for a conceptual drawing). Therefore measurements of the nuclearmodification of exotic states can provide discrimination between models of their structure.
Figure 63:
The ratio of nuclear modification factors R eA for X(3872) to psi ( S ) , for two different assumptions of theX(3872) structure. We extend the charmonium breakup model from Ref. [14] to also consider the exotic tetraquark candidateX(3872). A Glauber model of the nucleus is prepared in simulation, and the starting point of the X(3872) israndomly selected inside the nucleus. The state expands as it crosses the nucleus and considered disruptedif it approaches a nucleon within a distance of less than √ σ c ¯ c π , where σ c ¯ c is a breakup cross section thatdepends on the size of the state. These simulations are run for two different models of the X(3872), one whereit is considered a compact tetraquark with a final radius of 1 fm, and one where the X(3872) is modeled as aweakly bound hadronic molecule with a radius of 7 fm. Since the X(3872) and the well-known conventionalcharmonium state ψ ( S ) are both measureable through their decays to J / ψπ + π − , the ψ ( S ) is also modeled,with a radius of 0.84 fm. ( S ) y e A / R X ( ) e A R Compact X(3872)Molecular X(3872) e+ Cu e+ Au e+WORK IN PROGRESS Figure 64:
The ratio of nuclear modification factors R eA for X(3872) to psi ( S ) , for two different assumptions of theX(3872) structure. The ratio of nuclear modification factors for the X(3872) and the ψ ( S ) taken from this model is shownin Fig. 64, for three different nuclear targets. We see that, for a compact X(3872) with a radius similar to45 roposed EIC FST and Associated Physics the psi ( S ) , there is approximately a 10% difference between the species R eA . However, for the molecularX(3872), the nuclear modification is different by a factor of approximately 2, showing that measurementsof this ratio at the EIC can be used to discriminate between various structure models. We note here thatX(3872) is only used as an example; the technique is equally applicable to the charged Z ± states (which arestrong candidates for compact tetraquarks) and the P ± c pentaquark states (which are baryon-meson hadronicmolecule candidates).
7. Summary
Detailed studies have been performed for the proposed forward silicon tracker detector and its associatedheavy flavor and jet measurements. Different conceptual detector designs and their tracking performancewith different silicon sensor options and magnet options have been implemented. Full analysis frameworkhas been developed for open heavy flavor and jet reconstruction. New physics observables such as theflavor dependent nuclear modification factor, flavor dependent jet angularity and exotic structure have beenexplored. These studies significantly enrich the ongoing EIC physics developments and will help provideguidance on the detector technology down selection and associated detector design.
8. Acknowledgements
This work is supported by the Los Alamos National Laboratory LDRD office 20200022DR project.46 roposed EIC FST and Associated Physics
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