Rescattering effect in understanding D decay processes

1. 周智勇 东南大学 Zhi-Yong Zhou Southeast university Rescattering effect in understanding D decay processes 2013.7.20 Zhangjiajie

2. How to precisely model the final state strong interaction is important to understand the weak interactions in shorter distance. • The biggest uncertainties in determining the CKM angle, =(657)o, from the difference of and decays is due to our inability to model the final state interactions. Motivation

3. Rescattering In calculation of Dyson-Schwinger equation, the propagator of the ρ-meson expressed in terms of quark line graphs. At lowest order it is assumed to be a meson, which decays at higher order by coupling to pion pairs.

4. The analytic structure of the ρ-propagator in the complex s-plane. At lowest order, the propagator is real with a pole on the real axis corresponding to a bare meson. The corrections at higher orders, dominated by pion loops, give the full propagator with a pole on the nearby unphysical sheet.

5. Start by considering a simple model at the hadron level, in which the inverse meson propagator could be represented as Πn(s) is the self-energy function for the n-th decay channel. Here, the sum is over all the opened channels or including nearby virtual channels. Πn(s) is an analytic function with only a right-hand cut starting from the n-th threshold, and so one can write its real part and imaginary part through a dispersion relation A Simple Scheme

6. Based on Cutkosky rule, the imaginary part of the self-energy function could be represented pictorially as

7. 1, Most of states below 2.0 GeV could be described in a consistent and unified picture. Progress in understanding light scalars Z.Zhou and Z.Xiao, Phys.Rev.D83,014010,2011

8. The masses of charmed and charmed-strange mesons and their decays could be described simultaneously. • The low mass puzzle of is solved naturally in this scheme. • In a prilliminary work, we obtained good results about charmonium spectra and their decays, which is consistent to the observed values in experiment. Progress in understanding mesons with charm quarks Z.Zhou and Z.Xiao, Phys.Rev.D84,034023,2011

9. Z.Zhou and Z.Xiao, Phys.Rev.D84,034023,2011

10. Rescattering effects in Decay process isobar picture

11. Unitarity for P  (c) Or see Aitchson 1977, Caprini 2006, Pennington 2006

12. K 1 - iK T = P 1 - iK = T F = coupling function UNITARITY : decays in spectator picture If c is not a spectator?

13. Brian Meadows

14. 1200 1000 800 Events/0.04(GeV/c2)2 600 400 200 0 0 0.5 1 1.5 2 2.5 3 m2(K-+low) (GeV/c2)2 600 500 400 Events/0.04(GeV/c2)2 300 200 100 non-resonant dominates 0 0 0.5 1 1.5 2 2.5 3 m2(K-+high) (GeV/c2)2 Brian Meadows

15. 1200 1000 800 Events/0.04(GeV/c2)2 600 400 200 0 0 0.5 1 1.5 2 2.5 3 m2(K-+low) (GeV/c2)2 600 500 400 Events/0.04(GeV/c2)2 300  200 100 0 0 0.5 1 1.5 2 2.5 3 m2(K-+high) (GeV/c2)2 Brian Meadows

16. Brian Meadows

17. E791 vselastic scattering (LASS) LASS phases (degrees) E791 M (K) GeV

18. Rescattering

19. Rescattering : Unitarity Watson’s theorem elastic phases simply related if no rescattering

20. Rescattering : Unitarity Including rescattering effect

21. Discontinuity relation of decay amplitude: After making a partial wave projection, Write it in short,

22. Pictorially represented as Elastic region Inelastic region Unitarity requires four points on Argond diagram, t*, a + h, (0, 1) and (0, Im[a]), stay on a circle.

23. Reproduced K\pi scattering phase by E791 result

24. Q:Whether there is the phase ambiguity of ? A: Perhaps yes.

26. How to obtain a better Dalitzanalysis for the processes with strong final state interaction? Building the following relations into analyses may help.

27. Thanks for your patience!