Teilchenphysik mit höchstenergetischen Beschleunigern (Higgs & Co) 4. Detectors II 13.11.2017 Prof. Dr. Siegfried Bethke Dr. Frank Simon
Detectors: Overview • Lecture Detectors I • Introduction, overall detector concepts • Detector systems at hadron colliders • Basics of particle detection: Interaction with matter • Methods for particle detection • Lecture Detectors II • Tracking detectors: Basics • Semiconductor trackers • Calorimeters Teilchenphysik mit höchstenergetischen Beschleunigern: 2 Frank Simon (fsimon@mpp.mpg.de) WS 17/18, 04: Detectors II
Momentum Measurement with Trackers Teilchenphysik mit höchstenergetischen Beschleunigern: 3 Frank Simon (fsimon@mpp.mpg.de) WS 17/18, 04: Detectors II
Tracking: Momentum Measurement in B-Field • Charged particles are deflected in magnetic field • only acts on the component transverse to the field p T GeV /c = 0 . 3 B r The radius of the trajectory gives transverse momentum: T m Example: 45 GeV µ, 4 T field: r = 37.5 m Teilchenphysik mit höchstenergetischen Beschleunigern: 4 Frank Simon (fsimon@mpp.mpg.de) WS 17/18, 04: Detectors II
Tracking: Momentum Measurement in B-Field • Charged particles are deflected in magnetic field • only acts on the component transverse to the field p T GeV /c = 0 . 3 B r The radius of the trajectory gives transverse momentum: T m Example: • parallel to the field there is no deflection 45 GeV µ, 4 T field: r = 37.5 m ➫ the particle moves on a helix given by field and p T magnetic field Teilchenphysik mit höchstenergetischen Beschleunigern: 4 Frank Simon (fsimon@mpp.mpg.de) WS 17/18, 04: Detectors II
Tracking: Momentum Measurement in B-Field • Charged particles are deflected in magnetic field • only acts on the component transverse to the field p T GeV /c = 0 . 3 B r The radius of the trajectory gives transverse momentum: T m Example: • parallel to the field there is no deflection 45 GeV µ, 4 T field: r = 37.5 m ➫ the particle moves on a helix given by field and p T The total momentum is determined with the “dip angle” in addition to p T : p T p p = p T /sin λ λ p L magnetic field Teilchenphysik mit höchstenergetischen Beschleunigern: 4 Frank Simon (fsimon@mpp.mpg.de) WS 17/18, 04: Detectors II
Momentum Measurement in B-Field II • In real-world applications one does not measure a full circle, but just a slightly bent track segment • Characteristic variable: sagitta Teilchenphysik mit höchstenergetischen Beschleunigern: 5 Frank Simon (fsimon@mpp.mpg.de) WS 17/18, 04: Detectors II
Momentum Measurement in B-Field II • In real-world applications one does not measure a full circle, but just a slightly bent track segment • Characteristic variable: sagitta Mathematical calculation: � r 2 − L 2 s = r − 4 2 + L 2 L 2 s ⇤ r = 8 s ( s ⇥ L ) � 8 s Teilchenphysik mit höchstenergetischen Beschleunigern: 5 Frank Simon (fsimon@mpp.mpg.de) WS 17/18, 04: Detectors II
Momentum Measurement in B-Field II • In real-world applications one does not measure a full circle, but just a slightly bent track segment • Characteristic variable: sagitta Mathematical calculation: � r 2 − L 2 s = r − 4 2 + L 2 L 2 s ⇤ r = 8 s ( s ⇥ L ) � 8 s Taking the relation of radius, momentum and B-field gives: 0 . 3 B L 2 p T 0 . 3 B ⇒ s = r = 8 p T Teilchenphysik mit höchstenergetischen Beschleunigern: 5 Frank Simon (fsimon@mpp.mpg.de) WS 17/18, 04: Detectors II
Momentum Measurement in B-Field III • A minimum of 3 points are required to determine the sagitta • Taking into account the point-by-point measurement uncertainty: N � σ 2 ( x ) 1 σ 2 ( s ) = für N = 3 there are 2 degrees of freedom N − 1 i =1 sagitta error uncertainty of a single point σ ( s ) Sagitta − Fehler , σ ( x ) Messfehler eines Punktes Teilchenphysik mit höchstenergetischen Beschleunigern: 6 Frank Simon (fsimon@mpp.mpg.de) WS 17/18, 04: Detectors II
Momentum Measurement in B-Field III • A minimum of 3 points are required to determine the sagitta • Taking into account the point-by-point measurement uncertainty: N � σ 2 ( x ) 1 σ 2 ( s ) = für N = 3 there are 2 degrees of freedom N − 1 i =1 sagitta error uncertainty of a single point σ ( s ) Sagitta − Fehler , σ ( x ) Messfehler eines Punktes 0 . 3 B L 2 with p T = 8 s √ � 3 2 σ ( x ) 8 p T σ ( p T ) σ ( s ) 3 σ ( s ) = 2 σ ( x ) ⇒ = = 0 . 3 B L 2 p T s Teilchenphysik mit höchstenergetischen Beschleunigern: 6 Frank Simon (fsimon@mpp.mpg.de) WS 17/18, 04: Detectors II
Momentum Measurement in B-Field III • A minimum of 3 points are required to determine the sagitta • Taking into account the point-by-point measurement uncertainty: N � σ 2 ( x ) 1 σ 2 ( s ) = für N = 3 there are 2 degrees of freedom N − 1 i =1 sagitta error uncertainty of a single point σ ( s ) Sagitta − Fehler , σ ( x ) Messfehler eines Punktes 0 . 3 B L 2 with p T = 8 s √ � 3 2 σ ( x ) 8 p T σ ( p T ) σ ( s ) 3 σ ( s ) = 2 σ ( x ) ⇒ = = 0 . 3 B L 2 p T s generalization to an arbitrary number of points: σ ( p T ) σ ( x ) � R.L. Gluckstern, = 720 / ( N + 4) p T NIM 24, 381 (1963) 0 . 3 B L 2 p T Teilchenphysik mit höchstenergetischen Beschleunigern: 6 Frank Simon (fsimon@mpp.mpg.de) WS 17/18, 04: Detectors II
Momentum Measurement in B-Field III • A minimum of 3 points are required to determine the sagitta • Taking into account the point-by-point measurement uncertainty: N � σ 2 ( x ) 1 σ 2 ( s ) = für N = 3 there are 2 degrees of freedom N − 1 i =1 sagitta error uncertainty of a single point σ ( s ) Sagitta − Fehler , σ ( x ) Messfehler eines Punktes 0 . 3 B L 2 with p T = 8 s √ � 3 2 σ ( x ) 8 p T σ ( p T ) σ ( s ) 3 σ ( s ) = 2 σ ( x ) ⇒ = = 0 . 3 B L 2 p T s generalization to an arbitrary number of points: σ ( p T ) σ ( x ) � R.L. Gluckstern, = 720 / ( N + 4) p T NIM 24, 381 (1963) 0 . 3 B L 2 p T ➠ The bigger B, lever arm L and the number of measurements and the better the spatial resolution, the higher is the accuracy of the momentum measurement example (ATLAS Si-Tracker): N =7, L = 0.5, B = 2T, σ (x) = 20 µm, p t = 5 GeV/c: Δ p t /p t = 0.5 %, r = 8.3 m, s = 3.75 mm Teilchenphysik mit höchstenergetischen Beschleunigern: 6 Frank Simon (fsimon@mpp.mpg.de) WS 17/18, 04: Detectors II
Conflicting Effect: Multiple Scattering • Charged particles are deflected when traversing matter: Multiple scattering via Coulomb interaction θ 0 = 13 . 6 MeV 1 � θ 0 = θ rms 2 θ rms z x/X 0 [1 + 0 . 038 ln( x/X 0 )] plane = space β c p √ • valid for relativistic particles ( β = 1), the central 98% of the distribution, for layer thicknesses from 10 -3 X 0 to 100 X 0 with an accuracy of better than 11% Teilchenphysik mit höchstenergetischen Beschleunigern: 7 Frank Simon (fsimon@mpp.mpg.de) WS 17/18, 04: Detectors II
Multiple Scattering vs Spatial Resolution • Two e ff ects influence the momentum resolution σ (p T )/p T of tracking systems: • Momentum resolution of the tracker: σ ( p T ) ∝ p T Teilchenphysik mit höchstenergetischen Beschleunigern: 8 Frank Simon (fsimon@mpp.mpg.de) WS 17/18, 04: Detectors II
Multiple Scattering vs Spatial Resolution • Two e ff ects influence the momentum resolution σ (p T )/p T of tracking systems: • Momentum resolution of the tracker: σ ( p T ) ∝ p T • Influence of multiple scattering θ ∝ 1 and with that also the spatial σ ( x ) MS ∝ 1 inaccuracy due to scattering: p p Teilchenphysik mit höchstenergetischen Beschleunigern: 8 Frank Simon (fsimon@mpp.mpg.de) WS 17/18, 04: Detectors II
Multiple Scattering vs Spatial Resolution • Two e ff ects influence the momentum resolution σ (p T )/p T of tracking systems: • Momentum resolution of the tracker: σ ( p T ) ∝ p T • Influence of multiple scattering θ ∝ 1 and with that also the spatial σ ( x ) MS ∝ 1 inaccuracy due to scattering: p p σ ( p T ) We know: (taking the spread induced by multiple ∝ σ ( x ) MS × p T scattering as a “spatial resolution”) p T � σ ( p T ) and with that: � = const � p T � MS Teilchenphysik mit höchstenergetischen Beschleunigern: 8 Frank Simon (fsimon@mpp.mpg.de) WS 17/18, 04: Detectors II
Multiple Scattering vs Spatial Resolution • Two e ff ects influence the momentum resolution σ (p T )/p T of tracking systems: • Momentum resolution of the tracker: σ ( p T ) ∝ p T • Influence of multiple scattering θ ∝ 1 and with that also the spatial σ ( x ) MS ∝ 1 inaccuracy due to scattering: p p σ ( p T ) We know: (taking the spread induced by multiple ∝ σ ( x ) MS × p T scattering as a “spatial resolution”) p T � σ ( p T ) and with that: � = const � p T � MS The measurement of low-momentum particles is limited by multiple scattering! At higher momenta the intrinsic resolution of the detector dominates. Teilchenphysik mit höchstenergetischen Beschleunigern: 8 Frank Simon (fsimon@mpp.mpg.de) WS 17/18, 04: Detectors II
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