J/ψ粒子衰变中σ、κ粒子的研究

Singa and kappa analysesat BESII

Ning Wu

Institute of High Energy Physics, CAS

Beijing, China

January 25-26, 2007

Introduction

The existence of  and  had been suggested from variousviewpints both theoretically and phenomenologically. Earlyanalysis of I=0  S-wave phase shift make the conclusionsagainst the existence of the σ particle. As a results, it had everdisappeared from PDG for about 20 years. But most re-analysis of ππ/πK scattering data support the existence of the and  particles.

In early studies, most evidences of the existence of  and come from ππ/πK scattering. If  and  particles exist, theyshould also be seen in the production processes. Searching andstudying  and  in production processes is also important forus to know their properties and structures.

Introduction(2)

We first found evidence of the existence of σand κparticles in7.8M BESI J/ψ data. After BESII obtain much larger J/ψ datasample, we moved our analysis to be based on BESII data.

Based on BES J/ψ decay data, a low mass enhancement in ππspectrum in J/ψωππ and a low mass enhancement in Kπspectrum in J/ψK*(892)Kπ are found. In order to prove thatthey are σand κparticles, we need not only to measure theirpole positions, but also to determine their spin-parity. So,PWA analyses are needed to study σand κparticles in these twochannels.

Introduction(3)

PWA analysis is widely used in BES physics analysis in pasta few years. It is used to determine mass, width andbranching ratio of a resonance, and to determine its spin-parity.

In this talk, we discuss PWA analyses of J/ψωππ andJ/ψK*(892)K.

Main contents of the talk are

1.Helicity Formalism

2.Maximum Likelihood Method

3.PWA analysis on J/ψωππ

4.PWA analysis on ψ′ππJ/ψ

5.PWA analysis on J/ψK*(892)K

6.Summary

Helicity Formalism

For a two-body decay process

a  b + c

spinJ sb sc

momentumpa pb pc

helicitym λb λc

paritya b c

Its S-matrix element is

Reltive momentum of two final state particles in center of mass syetem

Helicity Formalism(2)

The decay amplitude is

D-function

Helicity coupling amplitude

All angular information of the decay vertex are contained in the D-function,and helicity coupling amplitude is independent of all angular variables.

Helicity Formalism(3)

In J/ψ hadronic or radiative decay processes, parityconservation is hold. The heliclity coupling amplitude hasthe following symmetry

If two final state particle b and c are identical particles, thewave function of final state system should be symmetric orantisymmetric, and

Helicity Formalism(4)

In experimental physics analysis, most decays weencountered are sequential decays, and resonant statesappear as intermediate states.

The decay amplitude for this sequential decay is

Decay amplitude for

ab+c

Decay amplitude for

bd+e

Breit-Wigner function

of the resonance b

Maximum Likelihood Method

In experimental physics analysis, after we obtain a datasample, we first need to know how many resonances appearand what is the decay mechanism. Then we need tocalculate the differential cross-section

=(1,2,…)helicities of final state particles

=(1,2,…)helicities of intermediate resonances

mhelicity of the mother particle

dΦelement of phase space

BGnon-interference backgrounds

icomponents considered

Maximum Likelihood Method(2)

Normalized probability density function which is used todescribe the whole decay process is

σtotal cross section

W(Φ)effects of detection efficiency

xquantities which are measured by experiments

αunknown parameters which need to bedetermined in the PWA fit.

Maximum Likelihood Method(3)

Total cross-section is defined by

NMCthe total number of Monte Carlo events

( … )jthe quantity is calculated from the j-th MonteCarlo events

It is required that these Monte Carlo events are obtained throughreal detection simulation and have passed all cut conditions whichare used to to obtain the data sample of the process.

Maximum Likelihood Method(4)

The maximum likelihood function is given by the adjointprobability for all the data

Define

In the data analysis, the goal is to find the set of unknownparameters α by minimizing S. Mass and width of a resonanceare determined by mass and width scan. Spin-parity of aresonance is determined by comparing fit quality with differentsolution of different spin-parity.

Study of  Particle at BES

Clear signals of σ particle are found in two channels atBES:

1)J/ψ→ωππ

2)Ψ′→ππJ/ψ

 Pole in J/ψ→ωπ+π-

1)This channel was ever studied by MARKIII, DM2 andBES.

2)In the early studies, the low mass enhancement does notobtain enough attention.

3)Since 2000, BES had performed careful study on thestructure of the low mass enhancement, and measuredparameters of its pole position.

4)Data sample: BESI 7.8M J/ψ events

BESII 58M J/ψ events

Study of σ Based on58M BESII J/ψ Events

π0 and ω Signal

BESII

BESII

Invariant mass spectrumand Daliz plot

BESI

BESII

Possible Origin of the low mass enhancement

1.Backgrounds

2.Phase space effect

3.Threshold Effects

4.Resonance

Two different kinds of backgrounds

(1)Contain ωparticle in the decay sequence: J/ψωX

(2)Do not contain ωparticle in the decay sequence

ω side-band does not contain the low mass enhancement, so it does notcome from the second kind of backgrounds.

Background Study

BESII

After side-bandsubtraction

Monte Carlo simulation of some J/ψ decay channels. All these backgrounds cannot produced the low mass enhancement, so it can not also come from the firstkind of backgrounds.

Background Study

Generate 50M J/ψ  anything Monte Carlo events. The generator is based on

Lund-Charm model. It contain almost all known J/ψ decay channels.

It contains the backgrounds of inclusive J/ψ decays.

Backgound Study

Not a phase space effect.

Phase Space Effect

BESII

Enents are not unifromly scattered in the whole phase space, the shape of thelow mass enhancement is also different from that of phase space.

A clear peak is seen in the phase space and efficiency correctedspectrum. Threshold effect should decrease monotonically at thethreshold.

Threshold Effect

BESII

Summary on σ origin

•Not from backgrounds

•Not a phase space effect

•Not threshold effect

•It should be a resonance

PWA Analysis

Two Independent PWA analysis are performed:

1)Using the method of relativistic helicity couplingamplitude analysis to analyze the spectrum of lowermass region

2)Using the Zemach formalism to analyze the spectrumof the whole mass region.

Results obtained from two independent analysis arebasically consistent.

To avoid complicity in the higher mass region, and concentrate

our study on the low mass enhancement, PWA analysis isperformed only on the 0 — 1.5 GeV mass region.

PWA analysis：0-1.5 GeV

BESII

Components

The following components are considered:

 σ

 f2(1270)

 f0(980)

 b1(1235)

 Background

PWA Analysis

•The dominant backgrounds are phase spacebackgrounds and ρ3π backgrounds。

•Three different methods are used to fitBG.(free fit, directly side-band subtraction, fixBG to different level)

•Large uncertainties comes from the fit onbackgrounds, which is the main sources ofuncertainties.

0++

2++

4++

Angular distributions of the

low mass enhancement

Spin-Parity

Compare the fit quality

Spin-Parity

Parametrizations

There does not exist a maturemethod to parametrize a wideresonance near threshold, sodifferent parametrizations aretried in the fit.

Constant width

With contains ρ(s)

Zheng’s parametrization

Three different parametrizations are used in this fit. Mass and width areobtained through the fit, pole positions are calculated theoretically.

Mass, width and pole positions

Eq.(9)BW of constant width

Eq.(13)BW of width contains ρ

Eq.(14)Zheng’s parametrization

A 0++ resonance is used to fit σ particle.

Fit on the angular distributionsof the lower mass region

Contribution from σ particle

Fit on angular distributions

Fit on Dalitz Plot

Method II

Another independent PWA analysis is performed in this channel. Itanalyze the whole mass region and the following processes are addedinto the fit.

Method II (continued)

The σ particle is also needed in the fit of the low mass enhancement. Thedominant contribution of the low mass enhancement also comes from theσ particle.

Method II (continued)

Pole positions of the σ particle obtained by this method is consistent withabove. The combined results are (541±39) –i (252±42) MeV.

Constant

With ρ

σ particle in Ψ′→ππJ/ψ

•The ππ mass spectrum can be fit phenomenonlogically.

•It can also be fit by σ particle destructively interfere with a broad scalarstructure, i.e. |BW(σ)+IPS|2.

σ particle in Ψ’→ππJ/ψ

Strong destructiveinterference, so that theamplitude at threshold isalmost zero.

Three different BWparametrizations are also tried inthe fit. The shape of the BW givenby different parametrizations arealmost the same.

σ particle in Ψ’→ππJ/ψ

•Different parametrizations are tried in the PWA fit.

•Results on pole positions given by these parametrizations are quite consistent.

Summary on σ pole positions

BESI J/ψ data

BESII J/ψ data

ωππ system

BESII J/ψ data

5π system

BESII ψ′ data

Study of κ Particle at BES

Clear signal of κ particle is found in theKπ invariant mass spectrum in the decaychannel J/ψ→K*(892)0Kπ. It is seen atboth BESI and BESII data.

κ particle inJ/ψ→K*(892)0K+π-

BESII data

For our BESII data, the statistics are much larger.

Recoil mass spectrum againstK*(892)0

κ signal is clear in the invariant mass spectrum.

Dalitz Plot

κ signal isclear in theDalitz plot.

Charge conjugate channel

The spectrum is almost the same as that of the charge conjugate channel.

Charge conjugate channel

共轭道

1.Backgrounds

2.Phase space effects

3.Threshold effects

4.Resonance

Possible origin

Background Study

K*(892)0 side-band

Background Study

Monte Carlo simulation

Background Study

50M inclusive

Monte Carlo

Use the J/ψanythingMonte Carlo to study thebackgrounds from inclusiveJ/ψ decay.

Background Study

50M inclusive Monte Carlo

Data

Background Study

50M inclusive Monte Carlo

Data

All these results show that the low mass enhancement does not come fromthe backgrounds of inclusive J/ψ decay.

Phase space effect

Not a phase space effect

Summary on κ origin

•Not from backgrounds。

•Not a phase space effect。

•Threshold effect? (limit ststistics)

•Should be a resonance

Decay sequence

In the recoil mass spectrum against κ, only K*(892)0 can be clearlysee, so it is produced through J/ψ→ K*(892)0 κ。

Decay Mechanism

In the PWA analysis, the following four decay processes areconsidered.

Two IndependentPWA Analysis

•Method A is based on covariant helicity amplitude analysis.

•Method B is based VMW method.

•Two analyses are based on the same data sample.

•Two PWA analysis are performed independently.

Spin-parity

It is a 0+ resonance.

Statistical significance

Pole position

Poles given by different parametrizationsare close to each other.

Comparison

Δφ=φ(s)-φ(st)

Width contains ρ

Constant width

Zheng’s parametrization

Though mass and width parameters of different parametrizations aredifferent, the the shape given by them are almost the same.

Global fit

Global fit

Total 0++ contribution

Fit on Dalitz plot

PWA fit

Data

Method B

•Method B is based on VMW method.

•The least χ2 method is used in the fit.

•The fit is independently performed. Its theoretical formula of thedecay amplutude, fit method and components added into the fit aredifferent from those of method A.

•Final PWA results are consistent with those of Method A.