Toy Monte-Carlo for Ke4

1. Toy Monte-Carlo for Ke4 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 + Ke4 generator from CMC (M. De Beer, R.Turlay)

2. Geometry: • Strow sizes and layout inside chamber – from the current NA62MC • 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-GeV pi- from Ke4, => 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

3. Simulation: • Kaon momentum (Gaussian centered at 75 GeV, sigma: 0.76 GeV) • Kaon transversal position (parallel beam X : ±2.5 cm, Y: ±1.0 cm). • Kaon flight from the last steering magnet to the decay point • Ke4 decay (and boost from SCM to lab system) • Calculation of decay product positions @ every chamber, view, layer • Pt kicks at the TRIM5 -0.09 GeV (for kaon), and at MNP33 +0.270 GeV for positive particles (and -0.270 for negative ones). • Only stright flight of Ke4 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. 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: Track is regarded as reconstructable, if in every chamber there are hits in at least 2 views X, cm

5. 4-th chamber near the hole Z, cm (Too) Simple VETO Conditions Not too X(Y,U,V)-close hits in Z-close layers of the same view. OR Two hits in the same layer Trivial inefficiency is also possible If pi+ and pi- hit the same or close straws in 4-th chamber X, cm

6. One layer, X-coordinate, All hits, 107 Ke4 decays

8. V-coordinate, one layer

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

10. Ke4 background with pi+ detected (e+ is detectable by LKr) Only < (2Mpi)2 are dangerous 2pi+- mass Missing mass

11. Simulation results: 10 mln Ke4, 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 But an essential part of background is just due to the pi- missing 4-th chamber.

12. Simulation results: 10 mln Ke4, 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 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.

13. Last check : full statistics (100 mln Ke4 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 < 2pi+ : 24 • In decay volume (Z<16200 cm) : 16 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. Bkg missing mass