kinematics from gem hits for pvdis rich holmes march 2013 solid collaboration meeting
TRANSCRIPT
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Kinematics from GEM hitsfor pvdis
Rich HolmesMarch 2013 SoLID Collaboration Meeting
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• Trajectory determined by vertex (xv, yv, zv) and momentum (p, θ, ɸ). xv, yv ≈ 0.
• Hits in 2 GEM chambers give 4 quantities x1, y1, x2, y2
• Can we invert the mapping? Yes, if we parameterize with the right combinations of x1, y1, x2, y2.
What can we learn about resolution and calibration from four numbers?
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Parameters
In x-y plane:
ri = length of 2-vector ri
from vertex to hit iD = distance between hitsα = angle between vectors
Others (not illustrated)<r> = (r1+r2)/2Δr = r2–r1
(and so on)
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ParametersUniform field:Trajectory in x-y plane is a circular arc of radius ρ α pT
1/ρ ≈ (ψ+δ)/(r1+D) ≈ 2α/D
tan θ ≈ D/Δz(Δz = z2–z1, distance between GEM planes)
z1–zv ≈ Δz r1/D
Approximations hold for small angles.
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ParametersRealistic field:
1/pT = kα/D(1 + Fρ(...))
tan θ = D/Δz(1 + Fθ(...))(Δz = z2–z1, distance between GEM planes)
z1–zv = Δz r1/D(1 + Fz(...))
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PVDIS geometry, 1st 2 GEMs (inside magnet)Red points: Uniform fieldBlue points: Realistic field
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Red points: Uniform fieldBlue points: Realistic field
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Momentum correction Fρ is not a function of α.
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Resolution• Calibrate by fitting against truth values to obtain Fρ, Fθ, Fz
• Using these reconstruct p, θ, z and compare to truth values
• Resolution (using MC with target, window, GEM materials):
• p: 0.86%
• θ: 0.36%
• Q2: 1.23%
• x: 0.71%
• zv: 7.8 mm
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Calibrating real data
• For real data we have no truth values; how do we calibrate?
• Elastics: p is correlated with θ
• θ calibration is not very sensitive to details of B field
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Red points: Uniform fieldBlue points: Realistic field
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Calibrating real data
• Use MC (field map accurate to 1%) to get θ calibration
• Use θ calibration and elastic data to get p calibration
• This has been demonstrated using e.g. (90% CLEO + 10% uniform) field MC to stand in for real data
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summary
• Hits in 2 GEM chambers can be used to reconstruct scattering kinematics
• Resolution with multiple scattering and detector resolution is <1% for p, <0.5% for θ
• θ can be adequately calibrated with MC; p can then be calibrated with elastic data