Feasibility of measuring the magnetic dipole moments of the charm baryons at the LHC using bent crystals

Transcription

1 Feasibility of measuring the magnetic dipole moments of the charm baryons at the LHC using bent crystals Alex Fomin Laboratoire de l Accélérateur Linéaire Université Paris-Sud/IN2P3, Orsay, France NSC Kharkiv Institute of Physics and Technology, Kharkiv, Ukraine / French-Ukrainian Workshop c French-Ukrainian Workshop / 23

2 Outline Magnetic dipole moment of charm baryons Introduction Principals of measurement 2 Deflection by a bent crystal Planar channeling Computational model Phenomenological formula 3 Sensitivity study Error of measured g-factor Crystal parameters optimization Data taking time c French-Ukrainian Workshop 2 / 23

3 Outline Magnetic dipole moment of charm baryons Introduction Principals of measurement 2 Deflection by a bent crystal Planar channeling Computational model Phenomenological formula 3 Sensitivity study Error of measured g-factor Crystal parameters optimization Data taking time c French-Ukrainian Workshop 3 / 23

4 c magnetic dipole moment measurement µ = g 2 e m S, ~ S = 2 Particle g-factor electron (52) muon (3) neutron (9) proton (7) 2.458() not measured for charmed, beauty baryons g 2 æ apoint-like(diracparticle) g 2 æ a composite structure g! c (u, d, c) " g c g c = 2 æ g! " c = How? Induce the precession of the polarization vector by the strong magnetic field Problem: c ( c ) 6 µm fartooshortformeasuring Solution: conventional B replaced by bent crystal V.G. Baryshevsky, Pis ma Zh. Tekh. Fiz., 5 (979) c French-Ukrainian Workshop 4 / 23

5 Precession of magnetic dipole moment: principals of measurement ~ i x ~ f µ! g 2 " x ~p i µ y z ~E rotation axis ~E z ~p f rotation axis = L crys R i = (,, ) f = (cos µ,, sin µ ) Angular distribution of decay products: N dn d cos Ë k = 2 ( - k cos Ë k ) - k=x,y,z Need: = c polarized at the production = keep polarization at the decay Cos(θ x) Cos(θ y) Cos(θ z) c French-Ukrainian Workshop 5 /

6 Precession of magnetic dipole moment: angular analysis g = j Û t j ( j) det 2 s ˆNtarcrys polarization proton flux t datatakingtime Decay channel dependent j weak-decayparameter Crystal dependent deflection angle j/ branching fraction ( j) det detection e ciency ˆN tarcrys normalizedspectra of deflected particles (per incident proton) c French-Ukrainian Workshop 6 / 23

7 c magnetic dipole moment measurement: Exp. setup This double crystal scheme is now under study with a 2 years program by UA9 at SPS. Halo Beam core Crystal 5 µrad c æ (232) (pfi )K c æ Tungsten Target Crystal 2 5 mrad 7TeVprotons c LHCb EOI (CERN 26): L. Burmistrov et al., Tech. Rep. CERN-SPSC SPSC-EOI-2; Physics Beyond Colliders Kicko Workshop (CERN 26): A. Stocchi et al.; W. Scandale et al. c French-Ukrainian Workshop 7 / 23

8 Outline Magnetic dipole moment of charm baryons Introduction Principals of measurement 2 Deflection by a bent crystal Planar channeling Computational model Phenomenological formula 3 Sensitivity study Error of measured g-factor Crystal parameters optimization Data taking time c French-Ukrainian Workshop 8 / 23

9 Channeling in a bent crystal x z x E ective potential U e (x) =U ± (x) x Á R c U eff R c z Critical radius R cr = Á Á d Ux Õ p 4 U U -4U R c = R cr R c R cr R c = 3R cr Acceptance angle Ú 2 U e acc = Á Á R 2 Ux Õ 2 3 x, d p c French-Ukrainian Workshop 9 / 23

10 Computational model Analytical approach Accurate model z z b i b i i bi ~p ~p ~p ~p Binary collision model (scattering on atoms) Most natural way of taking into account the thermal vibration of atoms Deflection angle of particle is calculated on each consequent atom Displacement of nearest atom due to the thermal vibration is drawn by normal distribution Aggregate collisions model (scattering on electrons) Multiple scattering with modified radiation length c French-Ukrainian Workshop / 23

11 Computational model Binary collision model Deflection angle of particle on each consequent atom: 3q Ë a ( r) = Ze2 r Á r 2 i i 2 q K ( i r), Ën = N Ë a ( r k ). i= k= Displacement of nearest atom due to the thermal vibration: P(u x ) du x = apple 2 fi ux 2 exp( u2 x ) du x 2 ux 2 L dech, cm Aggregate collisions model Multiple scattering on the electron subsystem Ò Ò 2È Ë MeV l l x = Á X Ë.38 ln X, l X s = 4 l e6 m ln(md 2 p ) n e (l) dl. 3 2 Si 293K Si 28K..2 E, TeV Forster J S et al. Nucl. Phys. B 38 3 (989) c French-Ukrainian Workshop / 23

12 Channeling in a bent crystal: primary vs secondary beams Primary particle beam 6 TeV 5 TeV 4 TeV 3 TeV 2 TeV TeV.2 TeV N/ ε, ev ε, ev Secondary particle beam Primary particle beam N/ ε, ev- - Parallel beam. - Monochromatic Secondary particle beam.5 x, A - Uniform angular distribution - Wide energy distribution 5 5 ε, ev - Populated high energy states c French-Ukrainian Workshop 2 / 23

13 Deflection e ciency: phenomenological formula def (Á, R, L) = ang ch ( dech ) deflected fraction of secondary beam Angular acceptance ang = erf!ô 2 acc " acc = Ú 2 Ue Á Channeling acceptance ch (Á, R) = 3 Á 4 R Ux Õ 3 Á R str U Õ x k 4 2 Dechanneling probability Ú dech (Á, R, L) = e Dechanneling length L dech (Á, R) =L max L L dech (Á, R) E Á max e E Emax L max = k dech R! " R bdech R Á max = R F dech U e, U Õ x, str, k, k dech, R, b dech, F dech were found for Si, Ge and Ge* crystals c French-Ukrainian Workshop 3 / 23

14 Spectra of deflected c produced by 7 TeV protons Initial spectra (Pythia v8.) credit to Leonid Burmistrov p - N collision in a fixed target normalized to one produced c Spectra after the target ˆN tar = fl N A A tar ˆN M c tar Ls tar e L c dl N ε N tar ε -4-5 TeV - L = cm L = 4 cm L = 8 cm L = 2 cm ε,tev - L tar = 4 cm TeV L tar = 2 cm L tar = cm L tar =.5 cm normalized to one initial proton ε,tev Spectra of deflected ˆN tarcrys = ˆN tar c def e Lcrys c N/ ε TeV day Ge L = 8 cm Ge L = 2 cm Si L = 8 cm 4 Si L = 2 cm ε,tev c French-Ukrainian Workshop 4 / 23

15 Outline Magnetic dipole moment of charm baryons Introduction Principals of measurement 2 Deflection by a bent crystal Planar channeling Computational model Phenomenological formula 3 Sensitivity study Error of measured g-factor Crystal parameters optimization Data taking time c French-Ukrainian Workshop 5 / 23

16 Sensitivity study: error of measured g-factor. List of parameters. g = j Û t j ( j) det 2 s ˆNtarcrys polarization proton flux t datatakingtime Decay channel dependent j weak-decayparameter Crystal dependent deflection angle j/ branching fraction ( j) det detection e ciency ˆN tarcrys normalizedspectra of deflected particles (per incident proton) Optimization of the crystal parameters c French-Ukrainian Workshop 6 / 23

17 Sensitivity study: Crystal parameters optimization g = j Û t j ( j) det 2 s ˆNtarcrys Relative crystal e ciency: rel = t t = 2 2 ˆNtarcrys ˆNtarcrys, t data taking time ( indicates the reference crystal) deflection angle ˆN tarcrys normalized spectra of deflected particles (per incident proton) c French-Ukrainian Workshop 7 / 23

18 Optimal crystal for measuring the MDM of c Relative crystal e rel = t t = ciency 2 ˆNtarcrys 2 ˆNtarcrys, Optimal Length: L crys = 8 cm Optimal Curvature: Si 293K R = 22 m 3.6 mrad Ge 293K R = 5 m 5.3 mrad Ge 8K R = 3 m 6.2 mrad Optimal Crystal: rel (Ge) rel (Si) 2.5!! rel (Ge) 4.5!!!! rel (Si) η rel R, m Ge 8K Ge 293K Si 293K Lcrys, cm Lcrys, cm c French-Ukrainian Workshop 8 / 23

19 Optimal crystal for measuring the MDM of c at LHCb Relative crystal e ciency rel = t t = 2 ˆNtarcrys 2 ˆNtarcrys, - η rel 2 5 Θ = 5 mrad Si 293K relative to the reference Si configuration: Si 293K L = 8cm 3.6 mrad But: silicon is more mature technology 2 Ge 293K 5 Ge 8K L, cm 8 cm is possible (di culties with longer crystals) work is ongoing Acceptance of LHCb 5 mrad rel (Si) 5 2 rel (Ge) 8 22 rel (Ge) 3 8 c French-Ukrainian Workshop 9 / 23

20 Absolute statistical error of measured g-factor. Decay channel parameters g = j Û t j ( j) det 2 s ˆNtarcrys c ( ) 8cm Weak-decay Branching Detection Decay channel parameter fraction e ciency j j /, % ( j) det, % c æ (p fi ) fi.9(5).7(2).2 c æ (p fi ) e (µ ) e(µ).86(4).3(4).2 c æ (232) (p fi ) K.67(3).9(3) 3 c æ K ú (892) (K fi ) p.55(35).6(5) 3 c æ (52)(pK ) fi.(6).8(3) 3 c French-Ukrainian Workshop 2 / 23

21 Absolute statistical error of measured g-factor. Polarization as a function of transverse momentum. g = j Û t j ( j) det 2 s ˆNtarcrys Ò 2 th =.37 Ò 2 ex =.4(5) N ch / p t, (GeV/c) ξ Polarization J. G. Korner, et al. Z. Phys., C2:7,979 E. M. Aitala et al. Phys. Lett., B47:449, Fitted exp. data Gary R. Goldstein. FNAL, Batavia, Illinois p.32 36, p t, GeV/c c French-Ukrainian Workshop 2 / 23

22 Absolute statistical error of measured g-factor as a function of data taking time g = j Û t j ( j) det 2 s ˆNtarcrys Reference crystal: Si L = 8cm R = 22 m Δg Λ c Δ(232) K -.5 g =.. t 3 days.5 t 5days t, days This proposal is now considered in LHCb and so we use the required parameters c French-Ukrainian Workshop 22 / 23

23 Absolute statistical error of measured g-factor as a function of data taking time g = j Û t j ( j) det 2 s ˆNtarcrys Ge L = 2 cm R = 8m Δg.8.6 Ge L = 2 cm g = t, days t 4 days t 5days Work is going on both UA9 and LHCb c French-Ukrainian Workshop 23 / 23