Evaluation of « optimal » segmentation for neutrino factory far detectors

1. Evaluation of « optimal » segmentation for neutrino factory far detectors A. magnetized iron sampling calorimeter for muon chargemeasurement (not too controversial) B. segmented fine grained detector with external magnetic field (ex: LARG, ECC, TASD) for electron charge measurement (very very approximate) caution: results obtained with analytic formulae and some approximations. Determine scaling laws outlines issues (and initiate discussion) Excel Worksheet ==> can be updated online.

2. muon chargemeasurement in magnetized iron sampling calorimeter

3. tracking formulae from PDG curvature curvature error due to measurement curvature error due to multiple scattering We have a system with N planes of iron of thickness t and density d interspaced with N planes of scintillator of thickness t’ and density d’ of point measurements with precision e

4. The average density is d0 = (d.t+d’.t’)/(t+t’) The equivalent average energy loss Ê such that Ê0 (t+t’)d0 = Êtd+Ê’t’d’ Ê0= (Êtd+Ê’t’d’) /(dt+d’t’) The average magnetic field is B’’ = Biron t/(t+t’) The average radiation length is (t+t’) /X’’ = t/Xiron + t’/Xscint The total length of detector is N(t+t’) and mass is A*N(t*d + t’*d’)

6. Results A. resolution as a function of momentum t = 1cm iron t’= 2cm scint B= 1.4 T space resolution= 1cm t = 10 cm iron t’= 2cm scint B= 1.4 T space resolution= 1cm Notes: improvement with high momentum comes from number of points on longer tracks. MS always dominates. Range measurement not used.

7. resolution as a function of iron plate thickness (t’=2cm) For very thin plates, (t<t’) the average B field decreases and resolution worsens. B = 1.4 T, t’=2cm, res=1cm Best is [dP/P ~37% at 1 GeV] for 2-3 cm plates. remains within 10% of this for 1<t<6cm. no strong argument for going to anything better than 4cm plates.

8. electron charge separation

9. Electron charge separation Assume a fully active medium (Larg or TASD) with a given two-track resolution e’. The tricky question is to evaluate the probability that the tracking software is confused by secondary photons and cannot follow the primary electron in an electromagnetic shower. Gimmick: an electron will get confused if a HE photon (k >= E/3) materializes within a transverse distance less than e’ of the primary electron. Then in addition the track measurement resolution must be better than about 40%-50% over this length.

10. The typical length for radiating one photon with k> kmin = f.E is d1 ~ X0 / F(f) PDG: F(f)= Ng ( d=X0, kmax=1, kmin= f.E) for f=0.3, F(f)= 0.29 this is the critical number! Typical distance for materializing is 9/7 X0 ==> the typical length is L0 = X0 (9/7+1/F) ~ 4.7 X0 and the typical distance from the primary electron track will be d = L02 /2/R = L02 . B . 0.3/2/E which has to be compared with e’

11. If we wish to measure the sign of a significant electrons up to an energy Emax, B must be such that d = L02 /2/R = L02 . B . 0.3/2/Emax > e’ or B >~ 2 Emax e’ / 0.3 / (4.7 X0)2 The fractional resolution over this distance will be given by the previous formulae for tracking over this distance ! careful that this means that a fraction of electrons of energy Emax will be measurable (typically 1-1/e = 30%)

12. What Emax? I will take Emax = 10 GeV as it is sufficiently large to cover the first oscillation maximum (5 GeV at 2500 km) with good resolution and efficiency.

13. Results 1. TASD with scintillator (X0=43 cm) 1 measurement every t’= 3cm point resolution epsilon = 1cm two track separation epsilon’= 3cm 2. AIR-TASD of variable fraction f of length occupied with scint. same assumptions as above t’=3cm/f X0=43cm/f 3. Liquid Argon (X0=14cm) 1 measurement every 3mm point resolution 1mm two track separation 3mm or whatever number we would like to have above.

14. 1. TASD with scintillator (X0=43 cm)1 measurement every t’= 3cmpoint resolution epsilon = 1cm two track separation epsilon’= 3cm B needed for meast at 10 GeV is 0.52T resolution dominates badly.

15. 2. AIR-TASD of variable fraction f of length occupied with scint. same assumptions as above resolution = 1cm, ttsep = 3cm t’=3cm/fX0=43cm/f f= 0.5: B-Field required for meast at 10 GeV is 0.13 T and this scales as 1/f2 resolution still dominates

16. 3. Liquid Argon (X0=14cm)1 measurement every 3mmpoint resolution 1mmtwo track separation 3mm B = 0.49 T for measurability of electrons up to 10 GeVgood match MS-resolution MS dominates slightly

17. A better TASD would have better two track separation and resolution -- suppose we could improve these numbers by factor 2? result: B(10 GeV) required for full TASD is 0.26 T B(10 GeV) required for 50% TASD is 0.065 T etc… ex: 50% TASD ttsep=1.5cm res=0.5cm B=0.065T much better matched!

18. Main conclusions magnetized iron-scintillator detector -- fairly reliable results -- MS dominates, and -- the thickness of plates need not decrease below ~2-4 cm Electron charge ID -- not very reliable results: assumptions about ability of tracking program to follow an electron in the shower -- scaling law B >~ 2 Emax e’/ 0.3 / (4.7 X0)2 -- assumptions on resolutions etc… need to be checked -- for air+f.TASD, B scales down as 1/f2 -- TASD: better resolution would pay off quickly -- Larg: seems well matched for B field~0.5 T