PANDA Experiment. Nordic Winter Meeting on FAIR Björkliden Department of Physics and Astronomy Uppsala University

Transcription

1 Department of Physics and Astronomy Uppsala University Nordic Winter Meeting on FAIR Björkliden 1-3-6

2 1 3 pp Λ c Λ + c 4 5

3 pp ȲY What are the relevant degrees of freedom to describe a process? Quarks and gluons or hadronic degrees of freedom? ( GeV) is in the transition regime between the two descriptions.

4 Hyperon Spin Variables decay with a parity violating weak decay to a spin 1/ baryon and aspin meson L =, 1 (L = 1, for Ω). Decay asymmetry parameters α = Re(A S A P) A S + A P, β = Im(A S A P) A S + A P, γ = A S A P A S + A P (1) Polarisation P is given from angular distribution I (cos Θ) = 1 (1 + αp cos Θ) () In pp ȲY spin correlations are also be measured. For ΛΛ this relates to how the spins of the ss pair are correlated. (β and γ appears in the angular distribution of the decay of the daughter particle)

5 Definition of the Hyperon Rest System The hyperon rest systems are defined to make maximum use of C and P invariance 1 +P y (ᾱˆk py + αˆk py ) I pp (Θ Λ, ˆk p, ˆk p ) = I +C xx ᾱαˆk px ˆk px 64π 3 +C yy ᾱαˆk py ˆkpy (3) +C zz ᾱαˆk pz ˆkpz +C xz ᾱαˆk px ˆkpz +C zx ᾱαˆk pz ˆk px

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7 from PS185 at LEAR Largest amount of data, 4k events,from PS185 experiment at LEAR.

8 Spin Correlations

9 ΛΛ (and consequently the ss) are always produced with parallel spins. Singlet Fraction SF = 1 (1 + Cxx Cyy + Czz) (4) 4

10 Parameters D = Γ Γ Γ + Γ Γα + Γᾱ A = Γα Γᾱ α + ᾱ α ᾱ B = Γβ + Γ β Γβ Γ β β + β β β B = Γβ + Γ β β + β Γα Γᾱ α ᾱ Theoretical estimate A and (5).1O(B) O(B ) 1O(A) 1O(D) (6) Experimental limits: A Λ =.13 ±.1 (PDG average), A Ξ = (. ± 5.1 ± 4.4) 1 4 (HYCP, 158M events, p Cu, 8 GeV). No experimental limits on B Ξ and B Ξ

11 FAIR Facility for Antiproton and Ion Research Primary Beams 3 GeV protons (4)x1 13 s -1 pp Λ c Λ+ c 1 m HESR Storage and Cooler Ring 1 11 stored and cooled GeV/c antiprotons High resolution mode δp/p < x1 5 (electron cooling) Luminosity = x1 31 cm s 1 Secondary Beams Antiproton production target x1 7 s 3.8 GeV/c High luminosity mode Luminosity = x 1 3 cm s 1 δp/p ~ 1 4 (stochastic cooling)

12 Detector Target Spectrometer Muon Detectors Forward Spectrometer Dipole Magnet E. Thome Forward RICH Superconducting Solenoid p p Λ Λ p p Ξ + Ξ p p Ω + Ω + p p Λ c Λc DIRC p-beam Electromagnetic Calorimeters GEM Central Tracker Micro Vertex Detector Drift Chambers Muon/Hadron ID

13 New for pp Λ c Λ+ c Very large increase in statistics for Λ and Σ hyperons and possibility to measure at higher beam momenta Opens up new channels: Ξ, Ω, Λ c,... Increase in statistics for CP violation measurements and access to the unmeasured (more sensitive parameters) B Ξ and B Ξ

14 Hyperon Properties pp Λ c Λ+ c

15 pp Λ c Λ+ c Reconstruction efficiency between 14 and 4%, depending on beam momentum Between 1 and 1 reconstructable events/s Polarisation and spin correlations reconstructable Most severe background problem is to separate Λ from Σ

16 pp Λ c Λ+ c Only existing data from old bubble chamber experiments Ξ / Ξ + bent by magnetic field, must be corrected for Differential cross section not known, isotropic used for simulations Four displaced vertices low background Daughter Λ also decays weakly more parameters reconstructable

17 + Simulations at 4 GeV/c beam momentum Reconstruction efficiency 17% 3 reconstructable events/s Background from pp Σ (1385)Σ + (1385) investigated. Background/Signal smaller than 1 4 pp Λ c Λ+ c vertex in xy plane [cm] Ξ Λ vertex in xy plane [cm] Ξ vertex in z direction [cm] Decay histxipvtxzvsrmc vertices of Ξ + and Λ histlambarvtxzvsrmc Λ vertex in z direction [cm] 1 1

18 Reconstruction Efficiency Depending on Production and Decay Angles reconstruction efficiency cos Θ Ξ pp Λ c Λ+ c reconstruction efficiency.3.5. reconstruction efficiency.3.5. reconstruction efficiency k x k y k z

19 pp Λ c Λ+ c Ξ / Ξ + Spin Variables Spin variables can be calculated from averages of the reconstructed decay angles (ˆk). The acceptance depends on the angle in the hyperon decay need to use MC based acceptance functions P y = 3 α N n=1 k y,n A(k y,n ), C ij = 9 αᾱ N n=1 k i,n k j,n A( k i,n, k j,n ) Reconstructed spin variables from 35 reconstructed events. (P = sin Θ, C ij = sin Θ as input) Polarisation cos Θ Ξ Cxx Czz cos Θ Ξ cos Θ Ξ Cyy (Cxz+Czx)/ cos Θ Ξ cos Θ Ξ (7)

20 + Differential cross section not known, isotropic used for simulations Cross section estimate nb, branching ratio for Ω ΛK 68% Simulations at 1 GeV/c beam momentum Reconstruction efficiency 3% 8 reconstructable events/hour Acceptance for all production angles of Ω + pp Λ c Λ+ c vertex in xy plane [cm] Ω Λ vertex in xy plane [cm] Ω vertex in z direction Decay vertices of Ω + and Λ Λ vertex in z direction 1

21 Density Matrix of Ω spin 3/ particle 15 polarisation parameters r instead of only the vector polarisation as for spin 1/ Parity invariance 8 are equal to zero pp Λ c Λ+ c ρ = r i 3 5 r 1 1 3r 1 3r + i 3r 3 i 6r 3 3 i 3 r r 1 1 3r q i 35 r 1 1 q i3 5 r 1 3 3r i 3r 3 Degree of polarisation = r Compare spin 1/ ρ = 1 (I + P σ) = 1» 1 + Pz Px + ipy Px ipy 1 Pz 3r i 3r 3 q i 35 r 1 1 q + i3 5 r r i 3 5 r r 1 1» 1 ipy ipy 1 i 6r 3 3 3r + i 3r 3 i 3 r r r (8) (9) 3 7 5

22 Polarisation of Ω Angular distribution of Ω ΛK (α ) I (Θ, φ) = 1 4π 1 Angular distribution of Λ pπ! 3 (3 cos Θ 1)r sin Θ cos φr sin Θ cos φr 1 ) (1) I (Θ, φ) = α Λ sin Θ(16 15r 1 1 4π r 3 1 )(β1 cos φ + γ1 sin φ) (11) pp Λ c Λ+ c r cos Θ Ω Reconstructed r from 3 events. r = 1 3 sin Θ as input

23 pp Λ c Λ+ c pp Λ c Λ + c Treshold momentum 1. GeV/c, simulations at 1 GeV/c Differential cross section not known, isotropic used for simulations Acceptance for all production angles of Λ c Cross section.1 µb, branching ratio for Λ c pπ 1% Reconstruction efficiency 35% 5 reconstructable events/day Background from Σ resonances, not investigated yet Large asymmetry parameter α =.91, polarisation reasonably well reconstructed from a few thousand events (35) polarisation cos Θ Λ c

24 Other Charmed pp Λ c Λ+ c Ξ c and Ω c in principle also accessible Treshold momentum 1. and 14.6 GeV/c Assumption: Cross sections reduced by factors α s = 1/5 and α 4 s = 1/65 Branching ratios not known Ξ c maybe possible, Ω c probably not

25 pp Λ c Λ+ c CP violation parmeters can be measured by detecting if the decay particles go up or down with respect to the hyperon production plane b = N + N + = β + β N 4 Experimental considerations: Uncertainty P, choose right angular interval dσ dω (1) Only use events where the hyperons decay in the vacuum of the beam pipe to avoid depolarisation in material Use events close to beam axis to make acceptance symmetric b* radial length allowed [cm]

26 the Magnetic Field [ ( d Σ 1 dτ = ū dū ) + ge ] γ + 1 dτ m B () Σ (13) Uncharged hyperon: construct the coordinate system ˆB, ˆB ˆΣ, (ˆB ˆΣ) ˆB degrees The precession angle of the Λ polarisation vector at 4 GeV/c.

27 Effect on the Reconstruction of Polarisation x direction y direction z direction cos Θ Λ The difference in calculated polarisation using the Λ rest system at production and a rest system which has been rotated in the same way as the polarisation vector. Spin correlations are not affected.

28 High statistics for the lighter hyperons, low background in general Many observables for Ξ and Ω can be measured for the first time: differential cross section, polarisation, spin correlations, CP violation parameters,... Charmed hyperons: Λ + c is possible to study, maybe Ξ c and probably not Ω c A small effect from the strong magnetic field affecting the hyperon spins, for the uncharged hyperons this can be corrected for