Toy MonteCarlo for Ke 4 D Madigozhin Motivation

Toy Monte-Carlo for Ke 4 D. Madigozhin Motivation: To investigate rare veto-inefficient events (millions of attempts needed, full scale MC is too heavy) Task: to check the sensitivity of veto inefficiency to the straw effective radius – even if the model in general is too simple, specific sensitivity may be correct. Code: ~ 500 lines of FORTRAN + cernlib + Ke 4 generator from CMC (M. De Beer, R. Turlay)

Geometry: Strow sizes and layout inside chamber – from the current NA 62 MC Chambers Z positions – from the last BEACH file (standard version) Hole center follows the central 75 Gev K+ path (4 -th chamber is not tuned additionally to catch <60 -Ge. V pi- from Ke 4, => some part of veto inefficiency is trivial). So chamber X-displacements: ( -9. 765, -11. 038, -9. 869, -6. 360 ) cm Hole radius: 6 cm – if straw touches hole, straw is removed

Simulation: Kaon momentum (Gaussian centered at 75 Ge. V, sigma: 0. 76 Ge. V) Kaon transversal position (parallel beam X : ± 2. 5 cm, Y: ± 1. 0 cm). Kaon flight from the last steering magnet to the decay point Ke 4 decay (and boost from SCM to lab system) Calculation of decay product positions @ every chamber, view, layer Pt kicks at the TRIM 5 -0. 09 Ge. V (for kaon), and at MNP 33 +0. 270 Ge. V for positive particles (and -0. 270 for negative ones). Only stright flight of Ke 4 products and momentum kick on the magnet plane, no pi-mu decays, no cascades, no scattering, no smearing of coordinate measurements Efficiency of the straw as a function of radius – from GARFIELD To check the effect of radius decrease as an over-worsened model of straw curvature (upper limit of the effect)

4 -th chamber near the hole Z, cm Position of the track is calculated at the layer Z, then distance R to closest straw wire is calculated taking into account the flight direction. R Hits are shown here as a tracks position on the corresponding layer plane. No reconstruction: X, cm Track is regarded as reconstructable, if in every chamber there are hits in at least 2 views

Z, cm (Too) Simple VETO Conditions 4 -th chamber near the hole Not too X(Y, U, V)-close hits in Z-close layers of the same view. OR Two hits in the same layer X, cm Trivial inefficiency is also possible If pi+ and pi- hit the same or close straws in 4 -th chamber

One layer, X-coordinate, All hits, 107 Ke 4 decays

V-coordinate, one layer

Number of efficient hits Efficiency variation: 0, 200, 400 mkm of lost radius Distance to wire

Ke 4 background with pi+ detected (e+ is detectable by LKr) Only < (2 Mpi)2 are dangerous 2 pi+- mass Missing mass

Simulation results: 10 mln Ke 4, include trivial inefficiency (pi- is in the hole). Events are the same (random value sequence is repeated), just efficiency detection is different. Number of background events Lost straw radius (mkm) All background events Dangerous (missing mass < 2 pi+- mass) 0 150 8 200 163 8 400 182 10 But an essential part of background is just due to the pi- missing 4 -th chamber.

Simulation results: 10 mln Ke 4, main trivial inefficiency excluded (4 -th chamber is moved by 2 cm to catch pi- near the hole, so displacement is changed from -6. 36 to -4. 36 cm) Number of background events Lost straw radius (mkm) All background events Dangerous (missing mass < 2 pi+- mass) 0 64 3 200 70 3 400 70 3 Preliminary conclusion : no need to change straw layout for curvature-caused losses compensation at least up to 400 mkm-curved case, as the sensitivity to effective radius is rather moderate.

Last check : full statistics (100 mln Ke 4 decays, corresponds approximately to 100 signal events), 4 -th chamber is shifted by 2 cm to catch pi-. 400 mkm of effective radius is lost. The absolute value is not very reliable (it is just a toy), but may be the order of magnitude is correct? Results: Total bkg: 755 events With missing mass < 2 pi+ : 24 In decay volume (Z<16200 cm) : 16 Bkg missing mass These 16 events can be suppressed further (even by the order of magnitude) if we will apply offline veto to check the completely reconstructed pi+ track for the possibility to cross the straw tube in another layer – current veto is too simple and soft, it doesn't reject all the cases of hits in neighboring straws of different neighboring layers.