1 Few thoughts on PFA, from the calorim etric point of view discussing pad siz e, M oliere radius, distance from the interaction point. H enri Videau
2 H ave you had anytim e a close view at show ers? I had not until w e sim ulated show ers in the LDC calorim eter but w ith a pad siz e of 1x1 m m 2 and..
3 In this design the EC AL has 20 layers w ith 2.1 m m of W and 2.1 m m of stuff 10 layers w ith 4.2 m m of W and.. stuff being 0.5 m m of silicium w ith G10.. The study is done w ith photons at 2, 10, 5 0 and 20 0 GeV along y
4 First, have a look at show ers w ith such a cell siz e at 2, 10, 5 0 GeV along the photon direction or perpendicular. The intensity of blue is related to energy the energy rising w ith the fraction of w hite The cylinder draw n in the figure corresponds to the M oliere radius estim ated from these sim ulations as containing 90% of the show er energy. The cells are draw n after sorting by ascending energy
5 2 GeV 10 GeV 5 0 GeV
6 100 GeV T he tw o 's are 21 and 17 GeV and are at 1.2 cm apart
D epo sited energy as a fu nctio n o f its distan ce to the ph o to n ax is H isto gram o f the in tegral o f the previo us o n e norm a lised to u nity. 90% pro vides the M o liere radiu s draw n as a c yan line RM = 1.65 c m 7 H enri V ideau LLR-Eco le po lytechnique 50 GeV photons
But the previous inform ation is m eaningless for separating photon show ers from a near by pion. W hat has a m eaning is the probability to be hit for a cell at a given distance of a photon. 8 at 13 m m the pro bability to h ave a 1m m 2 c ell hit by the sh o w er is abo ut 5% it is sm aller at lo w er energies.
Another view : 90% of the energy is on one side of a plane at 5m m in x. 9
10 It m ay be educative to illustrate the separation cap ab ilities of cells of different w idths. 1x1m m 2 3x3 m m 2 H enri V ideau LLR-Eco le po lytechnique 5x5 m m 2 7x7 m m 2
11 Educated guess: the granularity continues to bring you efficiency w ell below the M oliere radius. If you are not able to go dow n to 3x3 m m 2, w hy w ould you bother reducing your M oliere radius below 2cm? W ould you abandon tungsten? for lead? W ould'nt you sell a bit of M oliere radius to im prove the granularity?
12 U sing lead
13 U sing lead R M = 2.1
14 But does any physics need it? stay for Jean-C laude's talk
A m ore statistical point of view 15 It is reasonable to think that it is possible to reconstruct photons at distances larger than 1.5 pad siz e from charged tracks. A s an exam ple,, at 100 GeV JC.B events w ith pions are in red, those w ith rhos are in blue Full reconstruction tracks and photons for a 1 cm pad siz e jet m ass
16 Good photons Fake photons JC.B JC.B Energy in GeV versus distance in cm to the closest track
Tungsten design 17 Few characteristics of the design at 3 energies 2, 10 and 50 GeV. Energy resolution: 15% 16 % 17% E E Position resolu tion: x E independent of E 0.84 at 1m m, 0.86 at 3, 0.91 at 5, 0.94 at 7 A ngular precision: E 5 5 m rad independent of energy does not depend on cell siz e
18
19 Occupancy norm alised to 7m m 7 5 3 1 2 10 5 0 1. 1.2 4 1.71 2.2 4 1. 1.3 3 2.2 6 3.2 1 1. 1.3 6 3.04 4.59
Lead design sam e sam pling and num ber of layers 2 0 Few characteristics of the design at 3 energies 2, 10 and 50 GeV. Energy resolution: E E 17% 16 % 17% sam e as W as ex pected Position resolu tion: x E independent of E 1.09 at 1m m, sc ales w ith R M A ngular precision: E 59 m rad independent of energy
2 1 The m ost im portant is the pad siz e!! M uch m ore than the M oliere radius m ore than the distance? You w ill learn about it in the next episode H enri V ideau LLR-Eco le po lytechnique com e to th e L D C m eeting
A rem inder The jet energy ergy resolution δ E J = a E J b E J + c 2 2 A L E P H M ethod q uasi PFA a 0.59 b 0 c (G ev ) 0.6 A TL A S 0.6 0.03 0 H 1 0.5 0.05 0 PFL O W - IL C 0.3 0 0.5 And the Angular Dependence!! * N IM A360 (1994 ),4 80
A rem inder 2 3 resolu tion H 1 A tlas A leph g o al fo r ILC G ev
2 4 A quick com parison of the three concepts for three different reactions Fraction of the total event photon energy closer to a charged track than the abcissa JC.B H enri V ideau LLR-Eco le po lytechnique Distance in cm
2 5 Fraction of the total event photon energy closer to a charged track than the abcissa JC.B JC.B Energy fraction Distance in cm