Accelerators and particle detectors

Transkript

1 Accelerators and particle detectors Vincenzo Chiochia University of Zürich - Physik Institut Phenomenology of Particle Physics - HS010

2 Lecture outlook Introduction to particle accelerators and detectors Basic principles of particle accelerators Fixed target and collider experiments Luminosity Basic building blocks of a particle physics experiments Data analysis tools: Variables in the laboratory frame Momentum conservation: Transverse momentum and missing mass Examples: two jets events, three jet events, W discovery Method of invariant mass

3 Laboratory frame The momentum of each particle produced in a collision can be decomposed in: Component parallel to the beams (longitudinal, parallel to z) Component perpendicular to the beams (transverse, in x-y plane) The transverse component is: PT = P sin(θcm) Example: Longitudinal and transverse momentum in proton-antiproton scattering 3

4 Pseudorapidity To measure the longitudinal angle of the emerging particle jet one usually uses a variable called pseudo-rapidity The pseudorapidity (η) is Lorentz invariant under longitudinal boosts Momenta in the transverse plane are also invariant under longitudinal relativistic transformations Distance between particles or jets is usually measured in the (η,ϕ) plane 4

5 Pseudorapidity Particles produced at θ=90 have zero pseudorapidity High η values are equivalent to very shallow scattering angles Typical coverage of central detectors extends to η ~3. Coverage of high rapidities (θ<5 ) achieved with detectors at large z positions 5

6 Collider physics Experiments in hadron colliders usually deal with particles at high transverse momentum Reasons: Incoming particles collide head-on (no transverse momentum) Final state particles must have zero total transverse momentum Hard processes (large momentum transfer) produce particles in the center of the detector Example: proton + antiproton jet + jet 6

7 Two jets events in eta,phi plane The calorimeter measures the deposited energy in cells of the (η,ϕ) plane (including neutral particles) Histogram shows the energy in each cell The momentum of each charged particle in a jet is measured by the central tracking chamber 7

8 Two jets events Jet Total jet momentum P(1,)=ΣiPi(1,) Pz(1) = -Pz() PT(1) = -PT() Jet 1 8

9 Three jets in e+e- annihilation Electron-proton pairs can annihilate producing quark pairs (e.g. at LEP) In some cases, a gluon can be radiated from the out-coming quark In the latter case one observes three particle jets in the final state: Two quark jets and one gluon jet If no particle escapes the detector the three jets must have total transverse energy equal to zero 9

10 Missing mass A collision is characterized by an initial total energy and momentum (Ein, pin) In the final state we have n particles: E=ΣiEi, p=σipi Sometime we measure E<Ein and p pin In this case one of more particles have not been detected Typically: neutral particles Most often neutrinos, but also neutrons, 0, K 0 L (the latter for long decay time) We define the concept of missing mass: Missing mass = [(Ein-E) -(pin-p) ] 1/ If the spectrum of the missing mass has a well-defined peak one particle has escaped our detector 10

11 W boson decays The W boson is produced in proton collisions mainly via the following process: A u-quark collides with a anti-d quark producing a W+ boson The W+ decays into lepton (muon) and neutrino pairs The muon is detected and its momentum can be measured The neutrino escapes the detector undetected: The total sum of the transverse momenta is not zero! In other words, the experimental signature of the neutrino in the experiment is the missing transverse momentum 11

12 Example: W boson discovery 1

13 Invariant mass The invariant mass is a characteristic of the total energy and momentum of an object or a system of objects that is the same in all frames of reference. When the system as a whole is at rest, the invariant mass is equal to the total energy of the system divided by c. If the system is one particle, the invariant mass may also be called the rest mass. For a system of N particles: natural units (c=1): where W is the invariant mass of the decaying particle In a two body decay M 1+: 13

14 Invariant mass: applications Particles like ρ, ω, ϕ have average lifetime of s How do we know of their existence if they live so shortly? Example: reaction pp pp + - We identify all four particles in the final state and measure their momentum Let s focus on the pion pair, the total energy & momentum are: The invariant mass is: E=E++E- M = (E - p ) 1/ p=p++p- The event distribution for the variable M will look like: Evidence for ρ production! #Events #Events #Events M mρ Sparse pions pp ppρ All pions M mρ M 14

15 Example: Z discovery Z e + e - The Z boson was discovered in 1984 in proton-proton collisions. The boson decays into e+e- pairs (white dashed lines) The invariant mass of the two particles was ~9 GeV 15

16 Example: 0 reconstruction Neutral pions decay in photon pairs Measuring the angle and energy of the emitted photons one can reconstruct the mass of the decaying pion Entries per 1 MeV/c M = ± 0.03 MeV/c = 7.56 ± 0.03 MeV/c Exercise: calculate invariant mass formula for massless decay products (e.g. photons) p T >3 GeV/c Mass (GeV/c ) 16

17 Invariant mass: 3 body decay In case of a 3-body decay: R We can construct three invariant masses: m 1 (P 1 + P ), m 13 (P 1 + P 3 ), m 3 (P + P 3 ) For the three body case one finds: ante Masse ist als Norm eines m 1 + m 13 + m 3 = m 1 + m + m 3 +(P 1 + P + P 3 ) Only two independent invariant masses = m 1 + m + m 3 + M. 17

18 + g 159: Dalitzplot f u r K p + Λ. Die gestrichelte Kurve in der Projektion rechts zeigt den ung 159: Dalitzplot f ur K p In (61) f uλ. Die Kurve in der Projektion rechts zeigt den hren wirgestrichelte die Variablentransformation aus erder Intensit a t f u r phasenraumverteilte Ereignisse (nach [75]). Intensit at f ur phasenraumverteilte Ereignisse (nach [75]). + p Kurve in der Projektion rechts zeigt den Abbildung 159: Dalitzplot f ur Kd Λ. = Die gestrichelte R3 = de1 de F (m (640) 1, m13 )dm1 dm13. Verlauf der Intensit at f ur phasenraumverteilte Ereignisse (nach [75]). Example: Dalitz plot spiel Dalitzplot f die Reaktion Reaktion eispielzeigt zeigtabb. Abb den dendie Dalitzplot f uurr die Jacobi-Determinante ist zeigt (m m13 ) den Dalitzplot (E E E ) +f Als Beispiel Abb. 159 u(m r die Reaktion 1 E ) 1,+ + = (Λ = K p Λ p), (643) K p Λ p), (643) 0 (M E ) E As an Fexample, study the reaction: (E1, Elet s ), + =K4M (641) p Λ (643) + (Λ p), + GeV/c-Kaonen Impulsender der,, und undλλimimlaborlabor GeV/c-Kaonen[75]. [75].Aus Ausden den gemessenen gemessenen Impulsen alsomeasure ist mitmassen (640) two(635) We can invariant masses nnen invarianten (635) berechnet werden.die DieAnh Anh aufung mk ok onnendirekt direktdie die invarianten Massen berechnet werden. aufung + f u r 1. GeV/c-Kaonen [75]. Aus den gemessenen Impulsen der, und Labor +d R = dm dm. (64)Λ im rechts M Abbildung 159: Dalitzplot f ur Kmp1 m(λ Λ.))und Die gestrichelte Kurve in1.4 der Projektion zeigt den reignissen beiden den invarianten Massen ) ignissen bei invarianten Massen m(λ undm m1313 m(λ m(λ ) 1.4 system k o nnen direkt die invarianten Massen (635) berechnet werden. Die Anh a ufung der Intensit at Zwischenresonanz f ur phasenraumverteilte Ereignisse [75]). stammt ausdem dem Zerfall der Zwischenresonanz Die Dichte der Ereignisse im Dalitzplot m1 vs. m(nach konstant. mmtverlauf aus Zerfall der 13 ist also The so-called Dalitz plot shows the relation between (m13 (m1)+ ) 1.4 von Ereignissen bei den invarianten Massen m1 m(λ ) und m)13 and m(λ ± GeV stammt aus Zerfall der ±.Zwischenresonanz Σ±±dem (1387) Λ (644) Σ (1387) Λ. Als Beispiel zeigt Abb. 159 den Dalitzplot f ur die Reaktion (644) Σ± (1387) Λ ±. Massen (M (644) n der linearen Beziehung (638) zwischen den Quadraten der invarianten der linearen Beziehung (638) zwischen denquadraten der invarianten Massen (M + K p Λ (Λ p), (643) werpunktsenergie) w u rde eine Zwischenresonanz im -System mit Masse mm 3 erpunktsenergie) w urde eine Zwischenresonanz im -System mit Masse 3 WegenBand der linearen Beziehung (638) zwischen den Quadraten der invarianten Massen (M ) als ) alsdiagonales diagonales imdalitzplot Dalitzplot erscheinen. Band im erscheinen. = Schwerpunktsenergie) w urde eine Zwischenresonanz im -System+mitMasse m3 f ur 1. GeV/c-Kaonen [75]. Aus den gemessenen Impulsen der, und Λ im Laborm( + ) als diagonales Band im Dalitzplot erscheinen. system k onnen direkt die invarianten Massen (635) berechnet werden. Die Anh aufung + von Ereignissen bei den invarianten Massen m m(λ ) und m m(λ ) GeV stammt ausabbildung dem 159: Zerfall der Zwischenresonanz Dalitzplot f ur K p Λ. Die gestrichelte Kurve in der Projektion rechts zeigt den The + ± resonance appears as two bands in the ΣVerlauf der Intensit at f ur phasenraumverteilte Ereignisse (nach [75]). Dalitz plot around 1.4 GeV ± ± Σ (1387) Λ Als Beispiel zeigt Abb. 159 den Dalitzplot f ur die Reaktion. K p Λ + (Λ p), (644) (643) V. Chiochia (Uni. Zürich) Phenomenology ofder Particle Physics, HS Wegen der linearen Beziehung (638) zwischen den Quadraten invarianten Massen (M f ur 1. GeV/c-Kaonen [75]. Aus den gemessenen Impulsen der +, und Λ im Labor= Schwerpunktsenergie) w urde eine Zwischenresonanz im -System mit Masse m3