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A study of the Kπ system

Mikhail Kozyulin, (CERN, BINP)

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Introduction

In the latest Bs J/ψK* paper the Kpi spectum was shown, but analysed only qualitatively

S-wave mass lineshape is still not well understood

https://twiki.cern.ch/twiki/bin/view/LHCbPhysics/Swave

We would like to have better control of the waves that can enter K* region

Some isobar test Some K-matrix test

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Introduction

In addition, a higher Kpi peak is clearly visible, but neither BR(branching rations) nor polarization fractions were reported

Mass fit favoured K*2(1430) rather than K*0(1430). But difficult to prove or extract exact yield without angular analysis that separates spin

My summer student project:

Perform an angular study of the Kpi spectrum in BdJ/psiKpi in order to see the actual mass shape of the different waves This will allow us to:

Search for an Spin-2 signal K*2See the mass lineshape of the S-wave….

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Strategy

Angular analysis in bins of Kpi mass.– MC test– data

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MCImplemented RooFit model (in helicity basis) with S and P waves and tested in MC @ generator level.Good agreement with true values for the amplitudes (including As compatible with 0).

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Angular acceptance

To make our life easy for this round, we fit using per event weight

In LHCb-ANA-2011-071 (published paper) we have the acceptance function evaluated in several binsusing MC10 BdJpsiK* MC(never used in old analysis, but maybe ok for this initial study)

1200-1650

We will use:

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We interpolate the coefficient values between different mass bins using error function parameterizations• Bin position in is taken as the mean of distribution in that bin• We add a loose asymptotic property for Acc(ψ): at high masses

• Acc(Psi) ~ 1 + c*cos(ψ)2 (inspired by the trend at lower masses as well as by the J/ψ acceptance)

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Data1. Fit in angular and B mass spectrum. Model=Bs+Bd+bkg, each Bs and Bd =Swave+Pwave. Acceptance with per event weights.

2. Cut in Bmass – M(Bd)+-20MeV

M(K*) +- 40 MeV

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Fit with S-,P-wave

Blue: fit functionRed: Bd Pink: backgroundBlack: Bs

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Blue: fit functionRed: Bd Pink: backgroundBlack: Bs

Fit with S-,P-wave

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Construct the fit model using Urania’s tools

Use Urania.Helicity to get symbolic pdf

given the spin list for intermediate XKπ states : 0, 1, 2

Use Urania.RooInterfaces to create a RooFit C++ class out of the symbolic pdf

op2 = D.RooClassGenerator(func, [x,y,z]+TransAmpModuli.values()+TransAmpPhases.values(),"RooB")op2.makePdf(integrable = kTRUE)op2.doIntegral(1,(x,-1,1))…..op2.doIntegral(7,(x,-1,1),(y,-1,1),(z,-Pi,Pi))op2.overwrite()

We can use this procedure for higher and higher waves if necessary

Adding now the D wave …..

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S - wave P - wave

fL = 0

fL = 1

fL = 0.5

D - wave

fL,2 = 0

fL,2 = 1

fL,2 = 0.5

Altogether

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Fit with S-,P-,D-waves

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P - wave

fL = 0

fL = 1

fL = 0.5

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P - wave

fL = 0

fL = 1

fL = 0.5

S - wave

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P - wave

fL = 0

fL = 1

fL = 0.5

S - wave

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D - wave

fL,2 = 0

fL,2 = 1

fL,2 = 0.5

S - wave

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D - wave

fL,2 = 0

fL,2 = 1

fL,2 = 0.5

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0.55

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Conclusion

• We have performed an angular analysis of Bd->J/ψKπ in bins of Kπ mass.

• Decided to neglect background.• Angular acceptance maybe not very accurate (MC10,

interpolated parameters,…) but hope is good enough to identify the dominant wave in each bin.

• Clear evidence of spin 2, favouring K*2(1430) instead of K*0(1430).

• S-wave seems to be the main amplitude in (1000-1300 MeV), but small variation in phases causes big changes in wave shapes, probably interferences play a dominant role in that region.