Vertex and Kinematic fitting with Pandaroot Vishwajeet Jha PANDA Meeting : GSI December 09 1

Outline: 1. Introduction 2. PandaRoot Vertex Fitter and New Developments 3. Preliminary performance tests with New Vertex fitter 4. Tests of kinematic fitters in pandaroot 5. Summary and outlook

Introduction: Vertex fitters are implemented at the end of analysis chain To find the crossing point compatible with reconstructed tracks Output is the vertex position and its errors with fit probability Improvement in the resolution of track parameters In Pandaroot vertex fitters with Rho track candidates

New Vertex Fitter I: χ2 = (α – α0)T Vα0 -1 (α – α0) α0 Track parameters from track fit , Vα0 Covariance Matrix from track fit α New parameters , Iterations are needed to converge to the real vertex Algorithm same as BABAR Chi2Vertexer New Vertex Fitter II: Algorithm same as PndVtxFitter (Based on Belle Kfitter, a new implementation) A good start point is needed specially for displaced vertices. Start point : Vertex finder, ( crossing point , point of minimum distance) Propagation of the track parameters and covariance matrix to the start point

New Vertex Fitter II : Least Square minimization with lagrange multiplier for constraints. χ2 = (α – α0)T Vα0 -1 (α – α0)+ λ(D (α – αa )+ E(x – xa ) + d) The constraint equation H(α) =0 is linearized around suitable point (αa ,xa ) D is derivative w.r.t α, E is derivative w.r.t x, d is H (αa ,xa ) Minimize χ2 with respect to α , x and λ to determine track parameters and vertex Constraint : Tracks pass through an unknown point, For a solenoid field this leads to two constraints

Λ Reconstruction and Vertex Fitting: ppbar -> Λ Λbar 1.5 GeV/c, Λ-> pπ- Reconstructed Λ proper decay length (L*M/P) = 8.43 ± 0.313 cm PDG Value = 7.89 cm

Λ Reconstruction and Vertex Fitting: New Vertex Fitter PndVtxFitter

Ds Reconstruction and Vertex Fitting: ppbar -> Ds Ds*(2317) , Ds -> K+ K- π Reconstructed Ds (proper) Decay length = 185 ± 29 μm PDG Value =147 μm

Ds Reconstruction and Vertex Fitting:

Kinematic Fitting with other constraints: Same procedure can be used to apply additional constraints Global : All constraints are applied simultaneously Sequential : Constraints applied sequentially to build the decay chain Kinematic constraints: i) Invariant mass constraint ii) Total energy or momentum constraint iii) 4 vector constraint iv) Equal mass constraint Geometric Constraints : i) Pointing constraint ii) Back to back constraint

Kinematic Fitting Mass Constraint : PndMassFitter

Kinematic 4 Momentum Fitting: Pnd4CFitter ppbar -> J/ψ π+π- Full MC Simulation and reconstruction 4 Momentum fit for the ppbar system )

Summary and Outlook: New Vertex Fitters have been implemented Preliminary tests of its performance have been made. More detailed tests and improvements are in progress. Kinematic fitters with more constraints are planned to be included. 13

New Vertex Fitter I: χ2 = (α – α0)T Vα0 -1 (α – α0) α0 Track parameters from track fit , Vα0 Covariance Matrix from track fit α New parameters , Starting from parameters in cartesian coordinates α ( px,py,pz,E ,x,y,z) Gxx = Σ Txxi , Txxi = Wxxi –Di , Di = Wxpi * Wppi * Wxpi T x = GxxTx , Tx = Σ Txxi p = Σ pi =poi – Di T(x-x0i) Based on BABAR Chi2MinVertexer Iterations are needed to converge to the real vertex