Geometrical likelihood for Bs  μ + μ -

1. PROGRAMA NACIONAL DE BECAS FPU Geometrical likelihood for Bs  μ+μ- Diego Martínez Santos Universidade de Santiago de Compostela (Spain) Frederic Teubert, Jose Angel Hernando

2. Introduction • Can we extract more information from PID?, Can we use it in a better way than only a cut in preselection? •  Construct a selection ( via likelihood) without any (or minimal) information of PID • μ – PID is correlated with the momentum of μ – candidate  try to exclude kinematics when constructing the likelihood •  Attempt to make a likelihood (for S-B discrimination in Bs  μμ) only with geometrical information. (as independent of kinematics – PID as possible) • This likelihood (first version) combines: life time, muon IPS (from ITEP), DOCA (distance between tracks making the SV), Bs IP, and isolation. • As a background sample, we have taken ~8M bmu, bmu events.

3. s1 s2 s3 . sn b1 b2 b3 . bn x1 x2 x3 . xn n input variables (IP, pt…) Decorrelated likelihood • For constructing likelihoods, we have made some operations over the input variables. Trying to make them uncorrelated • A very similar method is described by Dean Karlen • “Using projections and correlations to aproximate probability distributions” • Computers in Physics Vol 12, N.4, Jul/Aug 1998 • The main idea: • n variables which, for signal, are independent and gaussian (sigma 1) -distributed • χ2S= Σ si2 • same, but for background • χ2B= Σ bi2 χ2 = χ2S - χ2B

4. Decorrelated likelihood. Getting gaussians Step 1: from normal variables to gaussian variables xi -> ui (uniformized) -> ki (gaussian) Making the ui transformed from a gaussian yi we have: Ig(yi) so: ki = Ig-1(I(xi)) or, being the same ki = errf-1(2*I(xi) - 1) Step 2: Rotation matrix Variables have all the same distribution  most of the correlations are linear with slope 1. (total correlation for original variables: y = f(x) traslated into g(y) = g(x))  Decorrelate them easily with a rotation matrix Step 3: from uncorrelated variables to final gaussian variables Same as in 1

5. Correlation for signal (very small for background) signal independent gaussina variables (for signal) signal independent gaussina variables (for backgroundl)  Same procedure making a 2D gaussian for Background

6. Preselection. Background Sample Mass window: 600 MeV Vertex Chi2 < 14 B IPS < 6 ( bug !! we wrote Bips2 < 6, a bit tight ( 82 % of efficiency over signal)) ----------------------------------------------------------------------------------------------------- Z (SV – PV) > 0 (Signal Eff = 97.5 %, Bkg Reten. = 63.7 %) pointing angle < 0.1 rad (Signal Eff. = 96.7 %, Bkg Reten. = 51.2 %) Muon PID required only for one of the particles From 100 000 DC04v2r3 signal events (generated with 400 mrad cut)  22873 From ~8M DC04v1 bmu, b  mu events (generated with 400 mrad cut) 17243

7. Geometrical Variables PID is related with kinematics: Ratio of missid background (in b μ, b μ ) After preselection + PID for both particles  Only geometrical Variables: • lifetime: Similar to distance of flight, but uncorrelated with boost • muon IPS: working well in ITEP selection • DOCA: distance between tracks making the vertex (used in Hlt : DOCA < 200 μm) • B IP • Isolation muon pt - cut DOCA/2 (mm)

8. Geometrical Variables. Isolation At the moment (after several attempts), we define: Isolation (for a muon – candidate): Number of generic SV’s ( DOCA < 200 microns, forward SV and pointing) which it can make with the other long tracks (excluding the other muon – candidate) signal background • Signal Tracks should be isolated • Primary Vertex Tracks also should be • designed to be independent of SV distance to PV • Only tracks from a SV (mainly a b – SV) shouldn’t be isolated (This background sample: Only one PID required  most of events are PV-track + b –muon  MuonIso = Isolation of the best muon candidate)

9. Geometrical Variables. Isolation Signal Background

10. S ITEP cuts RIO cuts B Likelihood comparisons We construct this geometrical likelihood, but also: “ITEP” – likelihood: muon IPS, muon pt, B IPS, pointing angle, chi 2 “RIO” – likelihood: SV DoFS, muon pt, B IPS, B pt, chi 2 “CDF” – likelihood: SV DoFS, pointing angle and B pt, “MuonIso”* *(CDF uses a combination between isolation and pt of B, but isolation defined by them – 1 rad conus from PV in the direction of B – flight- has no sense on LHCb detector  substitution by B –pt and our defintion of isolation) • Efficiencies relative to preselection • PID applied only in one particle • Geometrical • ITEP • RIO • CDF

11. Likelihood comparisons. Isolation Contribution • Isolation are working • New degree of freedom which can be added to selections • CDF – no iso. • ITEP • RIO • CDF • Geometrical • ITEP • no isolation

12. PID • Now: require PID for the 2nd muon, and look again at the likelihoods • DLL μ – π > -8 ?? Does not work. Why? • So, MuProb > 0 is our handle μ π Requiring both muons with MuProb > 0: Signal Efficiency: 84.7 % (19882 events) Background Retention: 7.77 % (1436 events) DLL μ – π

13. ITEP cuts RIO cuts PID & likelihoods  The likelihood defined before MuProb cut continues working well One event ! • Geometrical • ITEP • RIO • CDF After ITEP cuts: 15 events

14. Conclusions • PID is correlated with kinematics • A geometrical likelihood was presented, as an attempt to separate geometry and PID- kinematics information • This likelihood combines DOCA, life time, muon IPS, B IP, and isolation (new) • Isolation is adding extra information to our good – vertex definition, • This likelihood keep its performance even after PID cut for both muons

15. Geometrical • without lifetime • without muIPS • without DOCA • without B IP • less IPS mu • B iP (surprise) • Isolation • lifetime / DOCA • Geometrical • ITEP • no isolation

16. Red: Using chi2 instead of DOCA