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# Rescattering effect in understanding D decay processes - PowerPoint PPT Presentation

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Zhi-Yong Zhou

Southeast university

### Rescattering effect in understanding D decay processes

2013.7.20

Zhangjiajie

Motivation

Rescattering important to understand the weak interactions in shorter distance.

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.

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.

Start by considering a simple model at the 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 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

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

1, Most of states below 2.0 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 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

• The masses of charmed and charmed-strange mesons 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 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

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

Rescattering 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 effects in Decay process

isobar picture

Unitarity for P 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  (c)

Or see Aitchson 1977, Caprini 2006, Pennington 2006

K 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

1 - iK

T =

P

1 - iK

= T

F =

coupling function

UNITARITY : decays in spectator picture

If c is not a spectator?

Brian Meadows 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

1200 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

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

1200 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

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 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

E791 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 vselastic scattering (LASS)

LASS

phases (degrees)

E791

M (K) GeV

Rescattering 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

Rescattering : Unitarity 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

Watson’s theorem

elastic

phases simply related

if no rescattering

Rescattering : Unitarity 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

Including rescattering effect

Discontinuity relation of decay amplitude: 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

After making a partial wave projection,

Write it in short,

Pictorially represented as 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

Elastic region

Inelastic region

Unitarity requires four points on Argond diagram, t*, a + h, (0, 1) and (0, Im[a]), stay on a circle.

Reproduced K\pi scattering phase by E791 result 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

Q:Whether there is the phase ambiguity of ? 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

A: Perhaps yes.

How to obtain a better 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 Dalitzanalysis for the processes with strong final state interaction?

Building the following relations into analyses may help.

Thanks for your patience! 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