Ψ(3686)和J/ψγη’K+K-的分波分析 博士论文答辩 Ψ(3686)和J/ψγη’K+K-的分波分析 孙振田 导师：张子平，沈肖雁 近代物理系 2014.5.26

Outline Introduction to BEPCII and BESIII Motivation ψ’γη’ K+ K- 1. The branching fraction of χcJ η’K+K- 2. PWA of χc1 η’K+K- J/ψγη’ K+ K- 1. The branching fraction of J/ ψ γη’K+K- 2. PWA of ηc η’K+K- Summary

北京正负电子对撞机(BEPCII)实验区 电子直线注入器 储存环 北京谱仪 e+ e- 北京同步辐射装置

北京谱仪(BESIII) 由内而外： 主漂移室(MDC),飞行时间探测器 (TOF), 电磁量能器(EMC), 超导磁铁，μ子探测器(MUC)

Dataset Data Samples: BesII: 58M J/ψ, 14M ψ(2S) BesIII round one: 225M J/ψ, 106M ψ(2S) The result in this talk are mainly based on the two data samples. BesIII round two: 1billion J/ψ, 0.4billion ψ(2S)

Motivation BES Ⅲ BES Ⅱ History: Similar process，J/ψγη’π+π- has been studied at BESII. γη’K+K- has never been studied。The η’K+K- mass threshold is 1.95GeV, some higher resonance may be observed. BES Ⅲ BES Ⅱ X(1835) X(2120) X(2370)

Motivation Measure the decay χcJ : color-octet mechanism(COM) Color singlet χc0, χc2 (cc)(gg) Color singlet χc1 (cc)(gqq) Color octet (ccg)(gqq)

Motivation Search for exotic states: glueball, hybrid… The QCD allow the existence of glueballs. The glueball mass spectrum predicted by LQCD. PRD 60, 034509 (1999)

Motivation The abundance of scalar mesons: We observed much more scalar than theoretical predicted. Some of them may be exotic states. Radiative ψ decay is glueball rich process. Experimental light flavoured meson spectrum. Phys. Rept.454, 2007

motivation Glueball is flavor blindness. Most of the glueball is expected to mix with nearby mesons. χc1PS is sensitive to the glueball-qq mixing scheme

Motivation Q. Wang, G. Li, Q. Zhao, Int. J. Mod. Phys. A27, 1250135 (2012) Scheme 1 Scheme 2 𝜸 𝜼 ′ = 𝑩𝒓(𝝌𝒄𝟏→ 𝜼 ′ 𝒇𝟎 𝑿 ) 𝑩𝒓(𝝌𝒄𝟏→𝑲∗𝟎 𝟏𝟒𝟑𝟎 𝑲) ， R is the the SU(3) flavor breaking parameter K*0(1430) η’K hasn’t been observed by now. χc1 η’KK and ηc η’KK might be the most suitable channel to observe K*0(1430) η’K.

Selection criteria for (ψ’γη’ K+ K-,η’ γρ0, ρ0π+π-) Ngood=4, Q=0 Vr<1cm,|Vz|<10cm |cosθ|<=0.93 Ngamma>=2 Eγ>=25MeV,For Barrel Eγ>=50MeV,For Endcap angleγ-ch>=50 0<=TDC time<=14 PID for K:prob(K)>prob(π) &&prob(K)>prob(p) NK+=NK-=1 Select 2 gamma χ4c2(γγππKK)<40 select 1 gamma of η’ Minimize |m(γππ)-m(η’)| veto π0 |m(γγ)-m(π0)|>=15MeV Veto J/psi |m(γγ)recoil-m(J/ψ)|>22MeV |m(ππ)recoil-m(J/ψ)|>8MeV Mass windows cut |m(γππ)-m(η’)|<15MeV

Several invariant mass spectrum ρ0 η’ ηc, χcJ

Selection criteria for (ψ’γη’ k+ k-,η’ ηπ+π-, ηγγ) Ngood=4, Q=0 Vr<1cm,|Vz|<10cm |cosθ|<=0.93 Ngamma>=3 Eγ>=25MeV,For Barrel Eγ>=50MeV,For Endcap angleγ-ch>=50 0<=TDC time<=14 PID for K:prob(k)>prob(π) &&prob(k)>prob(p) Nk+=Nk-=1 Select 3 gamma χ2(γγγππk k)<50 select 2 gamma of η Minimize |m(γγ)-m(η)| veto π0 any combination of two γ |m(γγ)-m(π0)|>20MeV Mass windows cut |m(γγ)-m(η)|<25MeV |m(ηππ)-m(η’)|<25MeV

Several invariant mass spectrum η η’ ηc, χcJ

The peaking background η’γρ0 mode η’ηππ mode χcJ χcJ η’ η’ There are clear χcJ band out of η’ range. There are peaking background within η’ range.

The main background For η’γρ0 mode: The main background is χcJK+K-π+π- : peak higher χcJK+K-π+π-π0: peak lower A gauss function is used to represent the overlap of this two kinds of background. For η’ηππ mode: The main background is χcJηπ+π-K+K-

Simultaneous fit for η’ signal events and sideband events η’γρ0 mode Signal range Sideband The signal PDF: MC shape gauss. Use the shape and event number of peaking background in sideband to constrain the peaking background in η’ signal range. η’ηππ

DIY MC to get the selection efficiency with PWA result DIY MC: 用分波给出的截面为权重对PHSP事例进行舍选法抽样 The comparison between data and DIY MC. The red dot is real data. The black histogram is the MC. 数据与MC的不变质量谱和角分布都符合的很好

The systematic uncertainties

The combination of the measured result from two η’ mode The measured branching fraction from two measurements We use the weighted χ2 method to combine the result. And take the relation of uncertainties between two mode into consideration. σi 是两次测量各自独立的误差， εf 是两次测量相同的误差

The combination of the measured result from two η’ mode The formula for the combination of two measurement. The combined result

PWA for χc1 η’K+K- 分波公式 反应截面: 𝒅𝝈 𝒅𝝓 = |𝑨 𝟎++ +𝑨 𝟐++ …| 𝟐 = |∑𝑨𝒊| 𝟐 反应截面: 𝒅𝝈 𝒅𝝓 = |𝑨 𝟎++ +𝑨 𝟐++ …| 𝟐 = |∑𝑨𝒊| 𝟐 采用最大似然法拟合数据。 拟合目标函数的构造： 1. 概率函数 2. likelihood value: 3. 目标函数： 采用协变张量公式写不同自选宇称态的振幅Ai

分波公式 4. 本底的扣除: S= Ssig - Sbkg 我们用二维sideband的事例 来表示本底 5. 两个η’ 衰变道同时拟合。将两个道的目标函数相加。 拟合数据，找 Stotal 最小值

The line-shape of states All the line-shape of the states involved in the analysis are fixed in the fit. f0(980), flatte formula, M=0.965GeV, g1=0.165GeV, g2/g1=4.21(BES2’s result) K*0(1430), flatte formula, cleo’s measurement All other states are fixed to PDG value with constant width Breit-Wigner.

The projection result of PWA η’γρ0 mode f2(1525) K*0(1430) f0(980) η’ηππ mode Only four states are included in nominal fit.

The angular distribution comparison The χ2 check for the projection result.

The dalitz plot η’γρ0 mode fit data η’ηππ mode fit data

The branching fraction of intermediate process 对过程 i 的微分截面和总截面进行数值积分，得出过程 i 占总过程的比例 Fi. Fi乘上总的 χcJ η’K+K- 的分支比，即得过程 i 的分支 比

The systematic uncertainty of PWA The banching fraction result with systematic uncertainty

Selection criteria for (J/ψγη’ k+ k-,η’ γρ0, ρ0π+π-) Ngood=4, Q=0 Vr<2cm,|Vz|<20cm |cosθ|<=0.93 Ngamma>=2 Eγ>=40Mev angleγ-ch>=50 0<=TDC time<=14 PID for π:prob(π)>prob(K) &&prob(π)>prob(P) for K:prob(K)>prob(π) &&prob(K)>prob(P) Nk+=Nk-=1 Select 2 gamma χ4c2(γγππKK)<40 select 1 gamma of η’ Minimize |m(γππ)-m(η’)| veto π0 |m(γγ)-m(π0)|>=20MeV veto η |m(γγ)-m(η)|>=15MeV Mass windows cut 0.55<m(ππ)<0.9GeV |m(γππ)-m(η’)|<15MeV Optimized with the largest S/√(S+B)

Selection criteria for (J/ψγη’ k+ k-,η’ ηπ+π-, ηγγ) Ngood=4, Q=0 Vr<2cm,|Vz|<20cm |cosθ|<=0.93 Ngamma>=3 Eγ>=40Mev angleγ-ch>=50 0<=TDC time<=14 PID for π:prob(π)>prob(K) &&prob(π)>prob(P) for K:prob(K)>prob(π) &&prob(K)>prob(P) Nk+=Nk-=1 Select 3 gamma χ2(γγγππK K)<40 select 2 gamma of η Minimize |m(γγ)-m(η)| veto π0 any combination of two γ |m(γγ)-m(π0)|>10MeV Mass windows cut |m(γγ)-m(η)|<25MeV |m(ηππ)-m(η’)|<25MeV Optimized with the largest S/√(S+B)

The fit of η’ peak η’ηππ mode η’γρ0 mode Blue line: fit result, the signal is represented by Double Gaussian function Red line: background of J/ψη’K+K- (Br(J/ψη’K+K- ) is measured simply) blackline: background of J/ψπ0η’K+K- (Br(J/ψπ0η’K+K- ) is measured simply) Combined result: Br(J/ψγη’K+K- )=(3.65±0.35 ) ×10-4

The m(η’K+K-) spectrum The black dot is real data. The red histogram is the PHSP shape from MC. There is no clear structure at the lower mass range.

The fit of ηc Method 1： the fit is not so good. Method 2: The mass and width of ηc is fixed to cleo’s measurement. M=2.9822GeV, Γ=31.5MeV.

The fit of ηc Method 3: consider the interference between ηc and non- ηc process. The phase angle The blue line is global fit result. The red line is signal. The green line is the interference

The branching fraction of ηc We use method 2 to give the preliminary result η’γρ0 mode η’ηππ mode Combined result

PWA for ηc η’K+K- 2D plot M(η’K+K- ) vs. M(K+K- ) The distribution is trival out of ηc range, we only perform PWA within ηc range. The method is very like χc1 η’K+K- . 根据角动量以及宇称守恒. M(KK)谱上可能的态: f0(0++), f2(2++) M(η’K)谱上可能的态:K*0(0+), K*0(1-), K*0(2+)

The PWA projection result f0(1710) Black dot is realdata. Red histogram is fit result. f0(980) K*0(1555) Dalitz plot f0(1710) f0(980) fit data The projection of individual state. K*0(1555)

The problems The pole position of K*(1555) is much higher than PDG’s K*(1430). PDG value of K*(1430): M=1.425GeV, Γ=0.27GeV The ηc line shape is greatly influenced by the barrier factor , R is the radius of the centrifugal barrier. R=1fm R=0.1fm

PWA result with systematic uncertainty The parameters of resonance with systematic uncertainty The non-pwa part of systematic uncertainty The branching fraction with systematic uncertainty

Summary We measured the branching fraction of χcJ η’K+K- for the first time with η’γρ0 and η’ηππ mode. We performed the PWA for χc1 η’K+K- , the intermediate process χc1 η’f0(980), χc1 η’f0(1710), χc1 η’f2(1525)， χc1 K*0(1430)K is observed. K*0(1430)η’K is observed for the first time. A preliminary result of J/ψ γη’K+K- is also given. The branching fraction of J/ψ γη’K+K- and ηc η’K+K- are measured . PWA for ηc η’K+K- are performed. ηc  η’f0(980), ηc  η’f0(1710), ηc  K*0(x)K.

Other works Other works during the period for Ph.D degree. The partial wave analysis for Y(4260)D*Dπ. The partial wave analysis for Yπ0π0J/ψ to determine the JPC of Zc(3900) The TOF electronic on-call.