# Detector Design Requirements

## Particle rates

The following figures show particle production rates for different eRHIC beam energy configurations, assuming an instantaneous luminosity of 1033 cm-2 s-1. All figures are produced from electron-proton events generated by PYTHIA 6. No cuts, for example on event Q2 or particle momentum, are applied. The η range (-4.5 to +4.5) covers the expected acceptance of the main eRHIC detector. "Charged" particles refers to electrons/positrons, and charged pions and kaons, while "neutrals" refers to photons, neutrons and K0L.

• Figures on the left show the distribution of particles per unit pseudorapidity (η) as a function of η. The left axis scale shows the mean number of particles per event per unit η as a function of η. The right axis shows the same distribution scaled to represent particle production per unit η and φ per second, assuming the aforementioned luminosity and the total event cross section reported by PYTHIA.
• Figures on the right show the distribution of particles per unit θ and φ per second as a function of η i.e. the η-dependent flux at a distance of 1m from the interaction point.

Click on the figures for a larger view. Data points are here.

 10 x 100 GeV 10 x 100 GeV 10 x 250 GeV 10 x 250 GeV 20 x 100 GeV 20 x 100 GeV 20 x 250 GeV 20 x 250 GeV

## Inclusive DIS

The following requirements are crucial to successfully reconstruct the scattered lepton:

• The lepton needs to be identified with high purity from the hadron and photon samples.
• The momentum resolution and angular resolution needs to guarantee a 80% survival probability in each x-Q2 bin.

### Lepton PID

The figure below shows the hadron and photon suppression required to ensure good lepton identification, in rapidity bins.
For this it is important to simulate MC samples without any Q2 cut, because this is what will be seen by the detector.

 5 GeV x 50 GeV 20 GeV x 250 GeV

In pseudo-rapidity bins

 5 GeV x 50 GeV 10 GeV x 250 GeV 20 GeV x 250 GeV
 5 GeV x 50 GeV 10 GeV x 250 GeV 20 GeV x 250 GeV

For increasing center-of-mass energy the hadron and photon suppression factor for the same rapidity bin needed is increased by a factor 100. For a given center-of-mass energy, the hadron and photon suppression factor needed increases going from negative rapidities (low Q2) to more central rapidities (high Q2). To ensure a minimal contribution to the systematic uncertainties due to misidentification of hadrons as leptons, the lepton purity should in the order of 99% for momenta bigger than 1 GeV. This purity can be also reached by trading statistics (=efficiency) for purity of the lepton sample if an PID algorithm as described as example in the following page

### Lepton Survival fraction per x-Q2 bin

Resolution in x and Q2 determines the probability for an event to be reconstructed in the correct (x, Q2) bin, and thus puts limits on how finely data can be binned.
Please see this study on Q2-x bin migration as an example of how bin migration varies for different kinematic reconstruction methods.
For any type of deep inelastic scattering event an unfolding in all kinematic variables is performed. This unfolding corrects for smearing due to radiative corrections as well as for detector effects.
The following page explains how the multi-dimensional unfolding is performed and what its consequences on the statistical uncertainties are.
Here is as example based on HERMES for smearing effects from radiative and and detector effects on the blow up of statistical uncertainties and bin migration.

## Semi-inclusive DIS

The following requirements are crucial to successfully reconstruct identified hadrons:

• The hadrons need to be identified with an efficiency of > 90% and a purity of 95%.
• The momentum resolution needs to be better than 3% for rapidities 1 to 3.

For the semi-inclusive physics it is extremely important to identify the hadron, distinguishing pions, kaons and protons over a wide range of momentum and rapidity. Identified hadrons will give the opportunity to tag the quark flavor through the hadron type using fragmentation functions. It is critical to have a high purity > 95% and identification efficiency > 90%, especially for kaons, which have a smaller yields than pions over all momentum and rapidity bins. The following plots show the pion, kaon and proton yields as function of momentum in bins of rapidity.

 5 GeV x 50 GeV 30 GeV x 250 GeV

The following plots show the pion, kaon and proton yields as function of momentum in bins of pseudo-rapidity.

 5 GeV x 50 GeV 10 GeV x 250 GeV 20 GeV x 250 GeV

Compared to other experiments, where PID to separate π, K and p is used to suppress background to have a cleaner signal for charmed mesons, for asymmetries you need to have a clena identification for single hadrons, which is much more challenging.

 SIDIS asymmetries as measured by COMPASS for a deuterium target

As we have have depending on the rapidity much more pions and/or protons as kaons and the pion asymmetries for pions are bigger then the ones for K- misidentification is a real problem to obtain the correct answer for the asymmetries. There is no way to correct this offline as we measure an unknown. In the following page are an example how to do an offline RICH unfolding. The plot for the measured double spin asymmetries above is a nice example the π- asymmetry is not small the K- asymmetry on the other hand is consistent with 0, with the different fluxes of π- to K- if there is a big misidentification, it will be very hard to measure the small K- asymmetry very accurately.

The momentum range to be covered at forward rapidities, Y > 1, requires a dual radiator RICH, because only this will allow identification of pions, kaons and protons from 1 GeV to 50 GeV. For this it is extremely critical to have a good momentum resolution at Y > 1. Possible radiators are Aerogel and C4F10; their cerenkov angles as function of momentum are shown in the following plot.

The right plot show the smearing of the correlation of the cerenkov angle for C4F10 as function of momenta for different momentum resolutions coming from the tracking detectors. A momentum resolution of δp/p ~ 3% will make a separation of kaons and protons at high momenta impossible.

## Exclusive Reactions

The additional requirements for an EIC detector, crucial to reconstructing the full final state in order to measure exclusive reactions are the following:

• Wide acceptance -4 < η < 4 for both the scattered lepton and the produced photon (or leptons coming from the produced vector meson's decay).
• The same rapidity coverage in electromagnetic calorimetry and tracking for lepton photon identification.
• The capability to discriminate two electromagnetic clusters down to a difference of 1 degree of polar angle in the rear endcap electromagnetic calorimeter.
• Separation of EM clusters from noise in the calorimeter down to 1 GeV.
• Good precision for momentum (energy) reconstruction.
• High acceptance for forward-going protons and neutrons from exclusive reactions as well as from heavy ion breakup (need for Roman Pots and a Zero Degree Calorimeter).

#### Calorimeter Requirements

To measure the DVCS cross-section in many x-Q2 bins it is important to suppress the Bethe-Heitler (BH) process, which for DVCS cross section measurements is the main background. The two plots below show the ratio of the DVCS cross section to the total Compton cross section as function of t for two different beam energy combinations and two different x-Q2 bins. For certain bins the BH process can be strongly dominant.

To suppress the BH process contribution the requirements shown in the following plots are important.

#### Requirements to detect the elastic protons

Measuring the final state of the proton is very important for exclusive DIS in ep. A Roman Pot spectrometer can be used, with its stations placed along the beam line at different distances from the IP, to measure the protons scattered at very small angles and thus escaping the main detector. Assuming a STAR-like RP spectrometer, each station consisting of four modules (up-down, left-right) and covering the whole φ-angle, the acceptance is limited externally by the quadrupole aperture and internally by keeping the modules as far as 10σ from the core of the beam to prevent radiation damages and guarantee a safe operation. The study shown in the following plots was done transporting the scattered protons from DVCS through the eRHIC IR design as described in the EIC WP chapter 5 (page 113+, fig. 5.4), to the RP stations. The total number of DVCS events (and thus scattered protons) generated is 100k and the hits on the different RP stations is shown below for 5x100 GeV (upper row) and 20x250 GeV (lower left) beam energy combinations. The lower right plot shows the DVCS t-distribution of exclusive protons for 20 GeV x 250 GeV as generated (black), those accepted after the quads (blue) and those in the RPs (red).

 5 GeV x 100 GeV 5 GeV x 100 GeV 20 GeV x 250 GeV] t-distribution at 20 GeV x 250 GeV]

One can see that an acceptance of ~68% (very high for a RP spectrometer) is expected for DVCS (in general for exclusive DIS) protons.
The following limitations exist for detecting the scattered proton from exclusive reactions:

• High‐|t| acceptance, mainly limited by magnet aperture.
• Low‐|t| acceptance, limited by beam envelop (~10σ).
• The |t|‐resolution is limited by:
• Beam angular divergence ~100μrad for small |t|.
• Uncertainties in vertex (x,y,z) and transport.

The EIC WP studies assumed ~<5-10% resolution in t (following RPs at STAR).

## Diffractive Reactions

#### Acceptance coverage

As we cannot tag coherent diffraction by detecting the outgoing intact nucleus, the other technique to tag on diffraction is to require a "rapidity gap" in the detector. This means that there is a region in the detector from the hadron beam towards the center of the detector in which there is no activity from the hadronic final state. The efficiency for detecting, and the purity of, diffractive events therefore depends strongly on the rapidity coverage of the detector. The left plot below shows the distribution for the most forward going particle (MVP) in DIS-events and in Diffractive events. The center (right) plot show the efficiency and purity for detection of diffractive events assuming a rapidity coverage of +5 to -5 (+4 to -4) assuming different cross section ratios for DIS to diffraction.
Note:: there is no Q2 cut applied for these plots

Attention: these plots have the rapidity definition reversed relative to all the other plots - negative rapidity is in the hadron beam direction (they will be redone).

 MVP for DIS and Diffractive events Detection efficiency and purity for diffractive events, acceptance -5 < η < 5. Detection efficiency and purity for diffractive events, acceptance -4 < η < 4.

A rapidity coverage of -4 to 2 is required to have a detection efficiency > 90% and a purity > 90% for diffractive events assuming a cross section ratio to DIS as measured at HERA (10:90). The following plots show the dependence of the detection efficiency and purity for diffractive events for different center-of-mass energies and assuming two different cross-section ratios DIS: Diffractive 90:10 and 66:34.

 Cross-section ratio: DIS:Diffractive 90:10 Cross-section ratio: DIS:Diffractive 66:34

The conclusion is the same as above; a rapidity coverage of -4 to 2 is required to have a detection efficiency > 90% and a purity > 90%.

#### ZDC neutron detection efficiency

The plot below shows the cross section as function of t for exclusive diffractive J/ψ and φ production for a specific x and Q2 bin. To suppress the incoherent part (open and blue filled circles) to access cleanly the coherent part at t > 0.1 GeV2 a rejection power of 1000 is needed; this requires highly efficient ZDCs.