RESCATTERING EFFECT IN UNDERSTANDING D DECAY PROCESSES

Zhi-Yong ZhouSoutheast university

2013.7.20Zhangjiajie

周智勇东南大学

MOTIVATION

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, =(657)o , from the difference of and decays is due to our inability to model the final state interactions.

D D

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.

qq

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.

2( / 2)poles M i

qq

A SIMPLE SCHEME

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

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

PROGRESS IN UNDERSTANDING LIGHT SCALARS

1, Most of states below 2.0 GeV could be described in a consistent and unified picture.

0 0 0

* * *0 0 0

0 0 0 0 0

I=1 states: a (980), a (1450), a (2020)(?)

I=1/2 states: K (800) or , K (1430),K (1950)

I=0 states:f (980) or σ f (980), f (1370), f (1500), f (2020)

，

Z.Zhou and Z.Xiao, Phys.Rev.D83,014010,2011

0PJ

0f (1710) might be the lightest scalar glueball candidate.

1. The masses of charmed and charmed-strange mesons and their decays could be described simultaneously.

2. The low mass puzzle of is solved naturally in this scheme.

3. In a prilliminary work, we obtained good results about charmonium spectra and their decays, which is consistent to the observed values in experiment.

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

PROGRESS IN UNDERSTANDING MESONS WITH CHARM QUARKS

* *0 0D (2318) and D (2317)s

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

P a b c

isobar picture

RESCATTERING EFFECTS IN DECAY PROCESS

Unitarity for P (c)

P

c

P

c

K

K

=P

c

Im

+c spectator

Or see Aitchson 1977, Caprini 2006, Pennington 2006

UNITARITY : decays in spectator picture

c spectator

T = K1 - iK

F = P

1 - iK = T

coupling function

P

c

=P

c

Im

P

c

K

K

+

If c is not a spectator?

Brian Meadows

Brian Meadows

1200

1000

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0

600

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0

0 0.5 1 1.5 2 2.5 3

m2(K-+low) (GeV/c2)2

m2(K-+high) (GeV/c2)2

Even

ts/0

.04

(GeV

/c2)2

Even

ts/0

.04

(GeV

/c2)2

0 0.5 1 1.5 2 2.5 3

non-resonant dominates

Brian Meadows

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0 0.5 1 1.5 2 2.5 3

0 0.5 1 1.5 2 2.5 3

m2(K-+low) (GeV/c2)2

m2(K-+high) (GeV/c2)2

Even

ts/0

.04

(GeV

/c2)2

Even

ts/0

.04

(GeV

/c2)2

Brian Meadows

E791 vs elastic scattering (LASS)

ph

ase

s (

deg

rees)

M (K) GeV

E791

LASS

Rescattering Rescattering

phases simply relatedif no rescattering

Watson’s theoremelastic

Rescattering : Unitarity

Including rescattering effect

Rescattering : Unitarity

Discontinuity relation of decay amplitude:

After making a partial wave projection,

Write it in short,

Elastic regionInelastic region

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

Pictorially represented as

Reproduced K\pi scattering phase by E791 result

22 2

12 13

| ( , ) | =|S+(P+D)|d

A s tds ds

2( , ) 2

12 13

| ( , ) | , if ( , ) is s-t symmetrici s tdA s t e s t

ds ds

+ +In processD K

( , )s tQ:Whether there is the phase ambiguity of ?A: Perhaps yes.

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

Building the following relations into analyses may help.

THANKS FOR YOUR PATIENCE!