在ψ´ J/ψ π+π-道中的相移测量(based on BESIII) 张振霞 (代表:张振霞, J.J.SANZ-CILLERO, 沈肖雁, 吴宁, 肖零亿,郑汉青) 第十届全国粒子物理学术会议 2008/04/27

motivation With the development of experiments, both experimental and theoretical studies on low energy ππand πK system produced in production processes have received interests. But there are few experimental data about the phase shift of ππand πK system in the region 0.4~0.6 GeV. It will be a good idea for our BESIII to measure it due to the proper energy. We re-investigate the ππ final state interactions in the ψ’ J/ψ π+π- process. Here s-wave dominates and the next contribution comes from the tiny d-wave. This is crucial for exploring the s-wave phase motion through interference effect in this process. The information on ππ,πk phase shift will provide a crucial ingredient in understanding the dynamics of goldstone boson and the spontaneous breaking of chiral symmetray. Cleo munich New Ke4 Zhang Zhenxia

Ψ’ J/Ψ π+π- Ψ’´ J/ψ π+π-是测量π+π-相移最好的衰变道 Hadronization Ψ’ J/Ψ 1 。在J/ψ→ω π+π-中, ω π的谱上有共振态,这会在理论上影响π+π-谱上的S波相移的提取.这是测量π+π-相移不可解决的困难. 其它道也存在类似情况。 2. 而在Ψ’´ J/ψ π+π-道中, J/Ψπ谱的能量非常底,不存在共振态.由末态定理,此过程的相移就是π+π-的相移. Zhang Zhenxia

在这个过程中,存在S波和D波,其中S波是主要的,D波占很小的成分. 理论模型Novikov-Shifman Model预言D波占4~20%左右. (hep-ex/9909038v1) D/S BESII Zhang Zhenxia M(π+π-)

衰变振幅是由Ψ’ 、 J/ψ的极化矢量和末态粒子的动量构成的所有的协变lorentz 结构组成,然后再根据极角 θπ*做分波展开 . 振幅的构造和相移的提取 衰变振幅是由Ψ’ 、 J/ψ的极化矢量和末态粒子的动量构成的所有的协变lorentz 结构组成,然后再根据极角 θπ*做分波展开 . Zhang Zhenxia

From S.U.Chung,Phys.Rev.D48(1993)1225, we get: Zhang Zhenxia

Zhang Zhenxia

总振幅： D 和 S波之间的相移差是: |δ0-δ2|.最后通过拟合形状因子I1~I7和 相移来获取它们的值. For S wave For D wave δ0 ,δ2 : phase shift D 和 S波之间的相移差是: |δ0-δ2|.最后通过拟合形状因子I1~I7和 相移来获取它们的值. Zhang Zhenxia

由手征对称性和重夸克对称性构成的拉氏量出发,振幅可以被写成: T.Mannel,R.Urech. Z.Phys.C73(1775)541 I4,I5,I6消失了,表明它们是小量,这个可以在将来的BESIII实验中被检验. Zhang Zhenxia 这里Gklm,G0,G2都是I1~I7的函数

Zhang Zhenxia

可见,我们这种相移的提取,并不依赖于任何模型,是更一般的参数化方法,相比之下更准确. 下面是基于BESIII的MC研究 Zhang Zhenxia

样本产生: 用BESIII模拟软件产生一个有固定相移的ψ’ J/ψ π+π- 模拟样本,再用上面推导的相移公式去拟合. The generated MC sample is similar to the real BESII data with: σ, 0+phase space, f2(1270) 产生公式: D波占48%: D波占2%,4%, 8%,20%: 事例挑选: All the charged tracks are required to be within the polar angle region: cosθ<0.9 Vertex cut: Z<5.0cm , r<1.0cm Particle ID: 1. if P<0.5, identified as pion. 2. use TOF,DE/DX, Muon id . Require all π+π- μ+μ- are identified out. 4-constrait kinematic fit. Mass of μ+μ- Zhang Zhenxia

Study result (ratio of D-wave is about 45%) ( in bin of 0.5-0.51GeV π+π- mass spectrum) Blue: D-wave Green: S-wave cosθπ 用相移公式拟合 cosθ3 Phase shift difference (rad) Input: 1.03radian Output: 1.04 ±0.04radian 用相移公式拟合得到的输出值和输入值是一致的.验证了公式的可靠性. Zhang Zhenxia

Phase shift Input: 1.17radian Study result (ratio of D-wave is about 2%, 4%,8%,20%) ( in bin of 0.5-0.51GeV π+π- mass spectrum) Phase shift Input: 1.17radian D wave 2% Phase shift: 1.52±0.04; 1.28±0.08 D wave 8% Phase shift: 1.24±0.08 D wave 4% Phase shift: 1.10±0.15 D wave 20% Phase shift: 1.18±0.02 这里用了大约50倍的ψ’数据的统计量 Zhang Zhenxia

总结 这里不仅验证了我们推导的相移公式的可靠性,而且为BESIII测量相移提供了可行性的预言. 这将是首次由BES提供0.3Gev~0.6GeV区间的ππ相移的数据. BESIII收集的数据将要比BESII多出约200倍,这会使得统计误差会变的更小,测量的更准确. Zhang Zhenxia

thanks! Zhang Zhenxia