Geometrical likelihood for Bs μ+μ-

PROGRAMA NACIONAL DEBECAS FPU

Diego Martínez SantosUniversidade de Santiago de Compostela (Spain)

Frederic Teubert, Jose Angel Hernando

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 bmu, bmu events.

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:

s1s2s3 .sn

b1b2b3 .bn

x1x2x3 .xn

n input variables(IP, pt…)

n variables which, for signal, are independent and gaussian (sigma 1) -distributed

χ2S = Σ si

2

same, but for background

χ2B = Σ bi

2

χ2 = χ2S - χ2

B

Decorrelated likelihood. Getting gaussians

Step 1: from normal variables to gaussian variables

xi -> ui (uniformized) -> ki (gaussian)

)(

')'(

')'(

max

min

mini

ii

xi

ii

i xI

dxx

dxx

u

ki = Ig-1(I(xi))

Making the ui transformed from a gaussian yiwe have: Ig(yi) so:

ki = errf-1(2*I(xi) - 1)

or, being the same

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

Correlation for signal (very small for background)

signal independentgaussina variables (for signal)

signal independentgaussina variables (for backgroundl)

Same procedure making a 2D gaussian for Background

Preselection. Background Sample

Mass window: 600 MeVVertex Chi2 < 14B 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) 22873From ~8M DC04v1 bmu, b mu events (generated with 400 mrad cut) 17243

Geometrical Variables

PID is related with kinematics:

muon pt - cut

After preselection + PID for both particles

Ratio of missidbackground(in b μ, b μ )

• 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

Only geometrical Variables:

DOCA/2(mm)

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 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)

signal

background

Geometrical Variables. IsolationSignal

Background

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)

• Geometrical

• ITEP

• RIO• CDF

ITEP cuts

RIO cuts

S

B

Efficiencies relative to preselection

PID applied only in one particle

Likelihood comparisons. Isolation Contribution

• Geometrical

• ITEP• no isolation

Isolation are workingNew degree of freedom which can be added to selections

• CDF – no iso.

• ITEP

• RIO• CDF

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

Requiring both muons with MuProb > 0:

Signal Efficiency: 84.7 % (19882 events)Background Retention: 7.77 % (1436 events)

π μ

DLL μ – π

PID & likelihoods

• Geometrical

• ITEP

• RIO• CDF

One event !

ITEP cuts

RIO cuts

After ITEP cuts: 15 events

The likelihood defined before MuProb cut continues working well

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

• Geometrical

• without lifetime

• without muIPS• without DOCA• without B IP

• Geometrical

• ITEP• no isolation

1. less IPS mu2. B iP (surprise)3. Isolation4. lifetime / DOCA

Red: Using chi2 instead of DOCA