Singa and kappa analyses at BESII

Ning Wu

Institute of High Energy Physics, CAS

Beijing, China

January 25-26, 2007

Introduction The existence of and had been suggested from various vie

wpints both theoretically and phenomenologically. Early analysis of I=0 S-wave phase shift make the conclusions against the existence of the σ particle. As a results, it had ever disappeared 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, they should also be seen in the production processes. Searching and studying and in production processes is also important for us to know their properties and structures.

Introduction(2) We first found evidence of the existence of σand κparticles in

7.8M BESI J/ψ data. After BESII obtain much larger J/ψ data sample, we moved our analysis to be based on BESII data.

Based on BES J/ψ decay data, a low mass enhancement in ππ spectrum in J/ψωππ and a low mass enhancement in Kπ spectrum in J/ψK*(892)Kπ are found. In order to prove that they are σand κparticles, we need not only to measure their pole positions, but also to determine their spin-parity. So, PWA analyses are needed to study σand κparticles in these two channels.

Introduction(3) PWA analysis is widely used in BES physics analysis in pas

t a few years. It is used to determine mass, width and branching ratio of a resonance, and to determine its spin-parity.

In this talk, we discuss PWA analyses of J/ψωππ and J/ψK*(892)K.

Main contents of the talk are

1. Helicity Formalism2. Maximum Likelihood Method3. PWA analysis on J/ψωππ4. PWA analysis on ψ′ππJ/ψ5. PWA analysis on J/ψK*(892)K 6. Summary

Helicity Formalism For a two-body decay process

a b + c

spin J sb sc

momentum pa pb pc

helicity m λb λc

parity a b c

Its S-matrix element isJJ

mcbaacbcb cbcbFDppp

J

p

sJmpSpp

)0()(

4

124)2( *

)(43

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

Helicity Formalism(2)

JJm

J

cbcbcbFDmM )0,,(),,( *

)(

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, parity conserv

ation is hold. The heliclity coupling amplitude has the following symmetry

If two final state particle b and c are identical particles, the wave function of final state system should be symmetric or antisymmetric, and

JssJcba

J

cb

cb

cbFF

)(

JJJ

bccbFF )(

Helicity Formalism(4) In experimental physics analysis, most decays we encounter

ed are sequential decays, and resonant states appear as intermediate states.

The decay amplitude for this sequential decay is),,(),,(),,( 2211 b

sbb

s b

ed

a

cbMMsBWmM

a

b

cd

e

Decay amplitude for ab+c

Decay amplitude for bd+e

Breit-Wigner functionof the resonance b

Maximum Likelihood Method In experimental physics analysis, after we obtain a data sam

ple, we first need to know how many resonances appear and what is the decay mechanism. Then we need to calculate the differential cross-section

=(1,2,…) helicities of final state particles=(1,2,…) helicities of intermediate resonancesm helicity of the mother particledΦ element of phase spaceBG non-interference backgroundsi components considered

BGmAd

di

im

2

,

),,(

Maximum Likelihood Method(2) Normalized probability density function which is used to de

scribe the whole decay process is

σ total cross sectionW(Φ) effects of detection efficiencyx quantities which are measured by experimentsα unknown parameters which need to be

determined in the PWA fit.

)(),(

Wdd

xf

Maximum Likelihood Method(3) Total cross-section is defined by

NMC the total number of Monte Carlo events( … )j the quantity is calculated from the j-th Monte

Carlo events

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

dd

dW

)(

j

iim

N

jMC

BGmAN

MC

2

,1

),,(1

Maximum Likelihood Method(4) The maximum likelihood function is given by the adjoint proba

bility for all the data

Define

In the data analysis, the goal is to find the set of unknown parameters α by minimizing S. Mass and width of a resonance are determined by mass and width scan. Spin-parity of a resonance is determined by comparing fit quality with different solution of different spin-parity.

),(1

xfeventsN

i

L

LlnS

Study of Particle at BES

Clear signals of σ particle are found in two channels at BES:

1) J/ψ→ωππ

2) Ψ′→ππJ/ψ

Pole in J/ψ→ωπ+π-

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

2) In the early studies, the low mass enhancement does not obtain enough attention.

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

4) Data sample: BESI 7.8M J/ψ events

BESII 58M J/ψ events

Study of σ Based on 58M BESII J/ψ Events

π0 and ω Signal

BESII

BESII

Invariant mass spectrum and Daliz plot

BESIBESI

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/ψωX

(2) Do not contain ωparticle in the decay sequence

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

Background Study

BESII

After side-band subtraction

Monte Carlo simulation of some J/ψ decay channels. All these backgrounds can not produced the low mass enhancement, so it can not also come from the first kind 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 the low mass enhancement is also different from that of phase space.

A clear peak is seen in the phase space and efficiency corrected spectrum. Threshold effect should decrease monotonically at the threshold.

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 coupling amplitude analysis to analyze the spectrum of lower mass region

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

Results obtained from two independent analysis are basically consistent.

To avoid complicity in the higher mass region, and concentrate

our study on the low mass enhancement, PWA analysis is performed 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 space backgrounds and ρ3π backgrounds。

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

•Large uncertainties comes from the fit on backgrounds, which is the main sources of uncertainties.

0++

2++

4++

Angular distributions of the

low mass enhancement

Spin-Parity

Compare the fit quality

Spin-Parity

Parametrizations

There does not exist a mature method to parametrize a wide resonance near threshold, so different parametrizations are tried in the fit.

Constant width

With contains ρ(s)

Zheng’s parametrization

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

Mass, width and pole positions

Eq.(9) BW of constant widthEq.(13) BW of width contains ρEq.(14) Zheng’s parametrization

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

Fit on the angular distributions of the lower mass region

Contribution from σ particle

Fit on angular distributions

Fit on Dalitz Plot

Method IIAnother independent PWA analysis is performed in this channel. It analyze the whole mass region and the following processes are added into the fit.

Method II (continued)

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

Method II (continued)

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

ConstantWith 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 scalar structure, i.e. |BW(σ)+IPS|2.

σ particle in Ψ’→ππJ/ψ

Strong destructive interference, so that the amplitude at threshold is almost zero.

Three different BW parametrizations are also tried in the fit. The shape of the BW given by different parametrizations are almost 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

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7mass(MeV)

width(MeV)

BESI J/ψ dataBESII J/ψ dataωππ system

BESII J/ψ data5π system

BESII ψ′ data

Study of κ Particle at BES

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

κ particle in J/ψ→K*(892)0K+π-

BESII dataFor our BESII data, the statistics are much larger.

Recoil mass spectrum against K*(892)0

κ signal is clear in the invariant mass spectrum.

Dalitz Plot

κ signal is clear in the Dalitz plot.

Charge conjugate channelThe 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 StudyMonte Carlo simulation

Background Study

50M inclusive

Monte Carlo

Use the J/ψanything Monte Carlo to study the backgrounds from inclusive J/ψ decay.

Background Study

50M inclusive Monte Carlo

DataMC

Background Study50M inclusive Monte Carlo

MC Data

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

Phase space effectNot 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 sequenceIn the recoil mass spectrum against κ, only K*(892)0 can be clearly see, so it is produced through J/ψ→ K*(892)0 κ 。

Decay Mechanism

In the PWA analysis, the following four decay processes are considered.

Two Independent PWA 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 parametrizations are 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 are different, 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 the decay amplutude, fit method and components added into the fit are different from those of method A. •Final PWA results are consistent with those of Method A.

VMW Method

Analysis formula is based on the Lagrangian of strong interactions.

VMW Method

Statistical significance

In the Mthod B, the κ particle is used to fit the low mass enhancement. Its statistical signigicance is also high.

VMW MethodComponents are different in two analysis.

Pole Position

Combined:

VMW Method

VMW Method

Summary

1) In BES J/ψ decay data, σ and κ particles are clearly seen in both invariant mass spectra and Dalitz plots.

2) The spin-parity of the low mass enhancements are determined to be 0++. They are considered to be the σ and κ particles respectively.

3) σ and κ particles are highly needed in the fit of the corresponding spectrum.

4) Different parametrizations are used to fit them. And the final pole positions given by these parametrizations are quite close to each other.

Thanks !