Challenges and future of three-body heavy meson decays Patricia C. - - PowerPoint PPT Presentation

SLIDE 1

p.magalhaes@bristol.ac.uk seminar @ Imperial College London, 30 October 2019

Challenges and future of three-body heavy meson decays

Patricia C. Magalhães

University of Bristol

SLIDE 2

30/10/2019

Patricia Magalhães

3-body hadronic decay 2

discussion topics

decay

can extract KK scattering amplitude

D+ → K−K+K−

What are the tools? Why we study 3-body hadronic decay? dynamics Dalitz plot 2-body x 3-body final remarks CP violation in B decays charm rescattering in B+ → K−K+K− Please stop me at any moment!

SLIDE 3

30/10/2019

Patricia Magalhães

3-body hadronic decay 3

Motivation

LHCb PRD90 (2014) 112004

CP-Violation

• 0.8
• 0.6
• 0.4
• 0.2

0.2 0.4 0.6 0.8 (DTF)

Low π π 2

m 2 4 6 8 10 12 14 (DTF)

High π π 2

m 5 10 15 20 25

massive localized Acp

ACP = Γ(M → f) − Γ( ¯ M → ¯ f) Γ(M → f) + Γ( ¯ M → ¯ f)

πππ

B± → h±h−h+

can lead to new physics

mixing

1st observation in charm

CPV on three-body?

D0( ¯ D0) → h−h+

dynamic effect !! Standard Model works quite well but... some gaps!

baryogenesis !

SLIDE 4

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Patricia Magalhães

3-body hadronic decay

D and B three-body HADRONIC decays are dominated by low E resonances

spectroscopy: new resonances, their properties…

4

Context

≠ scales!!! similar FSI B phase-space + FSI possibilities

B and D 3-body phase space …

information of MM interactions

no KK available

1st observation of 𝜏 [ ] and 𝜆 [ ] in D decays

f0(600)

K∗

0(700)

new high data sample from LHCb

more to come from LHCb and Belle II

simple models (only focus on two-body resonances) are not enough to explain data anymore theoretical challenge !

SLIDE 5

30/10/2019

Patricia Magalhães

3-body hadronic decay

bi-dimension phase-space information

A conservação da energia e momento

In three-body decay phase-space is NOT one-dimension!

5

Three-body kinematics : DALITZ plot

DALITZ PLOT : proposed by Richard Dalitz (1925-2006) in 1953

29

Mandelstam variables for 3-body

s12 + s13 + s12 = M 2 + m2

1 + m2 2 + m2 3

dynamics resonances

SLIDE 6

30/10/2019

Patricia Magalhães

3-body hadronic decay

common cartoon to described 3-body decay

6

Three-body kinematics : DALITZ plot

D0 → Ksπ−π+

Ks

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π+

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π−

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Ks

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π+

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π−

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+

Ks

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π+

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π−

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+

spin 0 spin 2 spin 1 (g , b)K∗(892)

K∗

2(1430)

(c , m) (r) (y)

f0(980) ρ(770)

mKπ

mKπ mππ

image credit:Tom Latham

If true, one expect 2-body resonances

)

4

/c

2

(GeV

• s

1 2 3

)

4

/c

2

(GeV

+

s

1 2 3

1 10

2

10

3

10

a)

BABAR Phys.Rev. Lett. 105 (2010) 081803

But in reality……. not all of them are clearly present

SLIDE 7

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Patricia Magalhães

3-body hadronic decay 7

Three-body kinematics : DALITZ plot

D0 → Ksπ−π+

18

Are methods used for D decay Dalitz plots also valid for B decays?

Same model Same model as D decay as D decay

D→K–π+π0 B→K–π+π0

Tim Gershon

Introduction to Dalitz Plot Analysis

D Dalitz plot

• n same scale

Image credit: Brian Meadows

image credit:Brian Meadows

D0 → K−π+π0 Similar final state but different interference pattern different dynamics to be understood new hight sample data cannot be described only by adding resonances!

)

4

/c

2

(GeV

• s

1 2 3

)

4

/c

2

(GeV

+

s

1 2 3

1 10

2

10

3

10

a)

to disentangle the interference we need amplitude analysis

SLIDE 8

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Patricia Magalhães

3-body hadronic decay 8

D+

s → π+π−π+

π−π+ → π−π+

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(I=J=0)

2-body x 3-body phases

+ +

If this picture is the reality:

Phys.Rev. D 79 (2009) 032003

scattering decay different phases!

phase from decay should be the same as scattering

Is not as simple as it look like!

3-body data: only spin! and dynamics

6=

2-body amplitude: spin and isospin well defined!

Quantum numbers:

It should only contain 2-body informations!

SLIDE 9

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Patricia Magalhães

3-body hadronic decay 9

hadronize

dynamics

Three-body heavy meson decay

D

F S I K K K K K K

D+ → K−K+K−

c q

W μ

• bserved

To extract information from data we need an amplitude MODEL

F S I

W

A = *

Final State Interactions - strong -

=

M

F S I

+ + +

+ + + + +

...

2-body is crucial!!!!

primary vertex - weak -

QCD, CKM coupling and phase

dynamics

(2+1)

3-body

SLIDE 10

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Patricia Magalhães

3-body hadronic decay 10

Models available

(2+1) approximation:

ignore the 3rd particle (bachelor)

isobar model: widely used by experimentalists

+ + +

=

M

F S I

= P c

weak vertex is not considered explicitly

e A = P ck Ak, + NR

BW(s12) = 1 m2

R − s12 − imRΓ(s12),

non-resonant as constant or exponential! each resonance as Breit-Wigner

{

• sum of BW violates two-body unitarity ( 2 res in the same channel);
• do NOT include rescattering and coupled-channels;
• free parameters are not connected with theory !

!

F S I

W

A = *

unitary, analytic,…

worst problems: ππ S-wave

isobar BW

0.6 0.7 0.8 0.9 1 1.1 1.2 s (GeV)

( )( *( +( ,( (-( ()(

moduli f0(980) f0(600) Mσ=0.6 Γσ=0.5 both

2

fit could change this interference more than 2 scalars

Pelaez, Yndurain PRD71(2005) 074016

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Patricia Magalhães

3-body hadronic decay 11

Models available

F S I

W

A = *

movement to use better 2-body (unitarity) inputs in data analysis

Anisovich PLB653(2007)

“K-matrix" : ππ S-wave 5 coupled-channel modulated by a production amplitude

used by Babar, LHCb, BES III

• analyticity problems !

contribution in

B± → π+π−π±

rescattering ππ → KK

Pelaez, Yndurain PRD71(2005) 074016

[arXiv:1905.09244]

LHCb

[arXiv:1909.05212; 1909.05211]

B± → K−K+π±

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new parametrization Pelaez, and Rodas EPJ. C78 (2018) 11, 897

• ther scalar and vector form factors available

< ππ|0 >

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< Kπ|0 >

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Moussallam EPJ C 14, 111 (2000); Daub, Hanhart, and B. Kubis JHEP 02 (2016) 009.

scalar vector

Hanhart, PL B715, 170 (2012); Dumm and Roig EPJ C 73, 2528 (2013). Moussallam EPJ C 53, 401 (2008); Jamin, Oller and Pich, PRD 74, 074009 (2006) Boito, Escribano, and Jamin EPJ C 59, 821 (2009). Albaladejo and Moussallam EPJ C 75, 488 (2015). Bruch,Khodjamirian, and Kühn , EPJ C 39, 41 (2005)

< KK|0 >

<latexit sha1_base64="2LGjA9Rl1OXWjhlYDhUNwV4dYk=">AB8HicbVBNSwMxEJ31s9avqkcvwSJ4KrtVsAeRghehlwr2Q9qlZNsG5pklyQrlLW/wosHRbz6c7z5b0zbPWjrg4HezPMzAtizrRx3W9nZXVtfWMzt5Xf3tnd2y8cHDZ1lChCGyTikWoHWFPOJG0YZjhtx4piEXDaCkY3U7/1SJVmkbw345j6Ag8kCxnBxkoPV6iGak/Ive4Vim7JnQEtEy8jRchQ7xW+uv2IJIJKQzjWuO5sfFTrAwjnE7y3UTGJMRHtCOpRILqv10dvAEnVqlj8JI2ZIGzdTfEykWo9FYDsFNkO96E3F/7xOYsKnzIZJ4ZKMl8UJhyZCE2/R32mKDF8bAkmitlbERlihYmxGeVtCN7iy8ukWS56Xy3UWxWsniyMExnMAZeHAJVbiFOjSAgIBneIU3RzkvzrvzMW9dcbKZI/gD5/MHkNuO6g=</latexit>

quark model with isospin symmetry

(no data)

extrapolate from unitarity model

scalar vector

Fit from 3-body data

PCM, Robilotta + LHCb JHEP 1904 (2019) 063

Limited to low E (2 GeV)!

SLIDE 12

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Patricia Magalhães

3-body hadronic decay 12

Models available

QCD factorization approach factorize the quark currents ex:

B+ → π+π−π+

A ~

• [π+(p2)π−(p3)]S|(¯

ub)V −A|B− π−(p1)|( ¯ du)V −A|0

• π−(p1)|( ¯

db)sc−ps|B− [π+(p2)π−(p3)]S|( ¯ dd)sc+ps|0

• +

challenging for 3-body

not all FSI and 3-body NR

scale issue with charm !

F S I

W

A = *

Boito et al. PRD96 113003 (2017)

parametrizations for B and D→3h naive factorization

R

FF

• FSI with scalar and vector form factors FF
• intermediate by a resonance R;

how to describe it?

• + C7γ(µ)O7γ(µ) + C8g(µ)O8g(µ)
• + h.c. ,

H∆B=1

eff

= GF √ 2

• p=u,c

V ∗

pqVpb

• C1(µ)Op

1(µ) + C2(µ)Op 2(µ) + 10

• i=3

Ci(µ)Oi(µ)

Klein, Mannel, Virto, Keri Vos JHEP10 117 (2017)

modern QDC factorization: improvement to include “long distance”

Chau [Phys. Rep. 95,1(1983)]

+

SLIDE 13

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3-body hadronic decay 13

Models available

Three-body FSI

+ =

M

F S I

+ + + +

...

shown to be relevant on charm sector

0.8 1 1.2 1.4 1.6

√s (GeV)

• 90

90 180

fase onda S

LASS

FOCUS/E791

D+ → K−π+π+

phase S-wave

F S I

W

A = *

(beyond 2+1)

SLIDE 14

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Patricia Magalhães

3-body hadronic decay

0.8 1 1.2 1.4 1.6 mK훑 (GeV)

• 90

90 180 Phase S-channel

14

Models available

Three-body FSI

+ =

M

F S I

+ + + +

...

shown to be relevant on charm sector

D+ → K−π+π+

phase S-wave

F S I

W

A = *

(beyond 2+1)

(2-body phase) (3)

PRD92 094005 (2015) Niecknig, Kubis, JHEP10 142 (2015)

3-body approaches

PCM et.al: PRD84 094001 (2011), S.Nakamura PRD93 014005 (2016)

3-body FSI play a role data analysis… can we extract 2-body information from 3-body?

SLIDE 15

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3-body hadronic decay 15

multi meson model -

D+ → K−K+K+

amplitude analysis for D decay

D+ → K−K+K+

<latexit sha1_base64="igVIRC5sdRAB3PpU+Mroqe7Zs8=">AB+nicbVDLSgMxFL1TX7W+prp0EyCUCwzVdBlRdCNxXsA9pyaSZNjTzIMkoZeynuHGhiFu/xJ1/Y9rOQlsPCRzOuZd73EjzqSyrG8js7K6tr6R3cxtbe/s7pn5/YMY0FonYQ8FC0XS8pZQOuKU5bkaDYdzltuqPrqd98oEKyMLhX4g6Ph4EzGMEKy31zPxNt4g6KkTV7m1W9SvZxaskjUDWiZ2SgqQotYzvzr9kMQ+DRThWMq2bUXKSbBQjHA6yXViSNMRnhA25oG2KfSWarT9CxVvrIC4X+gUIz9XdHgn0px76rK32shnLRm4r/e1YeZdOwoIoVjQg80FezJE+dZoD6jNBieJjTARTO+KyBALTJROK6dDsBdPXiaNcsk+K5XvzguVqzSOLBzCEZyADRdQgVuoQR0IPMIzvMKb8WS8GO/Gx7w0Y6Q9B/AHxucPYhWSIg=</latexit>

Multimeson model for the D + → K + K − K + decay amplitude

• R. T. Aoude,1,2 P. C. Magalhães,1,3,* A. C. dos Reis,1 and M. R. Robilotta4

1Centro Brasileiro de Pesquisas Físicas, 22.290-180 Rio de Janeiro, Brazil

PHYSICAL REVIEW D 98, 056021 (2018)

arXiv:1805.11764 [hep-ph]

Theoretical model fitted to data

JHEP 1904 (2019) 063

KK scattering amplitude

SLIDE 16

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Patricia Magalhães

3-body hadronic decay 16

multi meson model -

track the ingredients we include in our model!

parameters have physical meaning: resonance masses and coupling constants

Triple-M

depart from a fundamental theory Chiral Lagrangian

D+ → K−K+K+

K K K

+ +

−

3 2 1

K K K

+ +

−

3 2 1

K K K

+ +

−

3 2 1

= +

b a

W W

T

alternative to isobar model in amplitude analysis A

unitary scattering amplitude for ab → K+K−

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AJI

ab

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predict KK scattering amplitude

fitted to data

JHEP 1904 (2019) 063

K K K

+ +

−

3 2 1

T

full FSI: coupled channel,

SLIDE 17

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3-body hadronic decay 17

Triple - M

NLO

a0, f0, ρ, φ

width obtained through dynamics isobar

K K K

+ +

−

3 2 1

K K K

+ +

−

3 2 1 b a

+

Chiral symmetry

LO: non-resonant

3 1 2 3 1 2

= +

(1B) (1A)

3 3 2 1 2 1 (2A) (2B)

+ +

1 2 3 1 2 3 3 2 1 1 2 3

+

(4A)

+

(3B)

+

(4B) (3A)

+

K ¯ K coupled-channel unitary amplitude

isospin decomposition [J, I = (0, 1), (0, 1)]

ππ, ηη, πη, ρπ

SLIDE 18

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3-body hadronic decay 18

]

2

[GeV

−

K

+

K

s

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 )

2

candidates/(0.0095 GeV

500 1000 1500 2000 2500 3000

LHCb

]

2

[GeV

+

K

+

K

s

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 )

2

candidates/(0.0095 GeV

200 400 600 800 1000 1200 1400 1600 1800

LHCb

]

2

[GeV

high

−

K

+

K

s

1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 )

2

candidates/(0.009 GeV

200 400 600 800 1000 1200 1400 1600 1800 2000 2200

LHCb

]

2

[GeV

low

−

K

+

K

s

1 1.1 1.2 1.3 1.4 1.5 1.6 )

2

candidates/(0.007 GeV

500 1000 1500 2000 2500 3000 3500 4000 4500

LHCb Figure 11. Projections of the Dalitz plot onto (top left) sK+K−, (top right) sK+K+, (bottom left) shigh

K+K− and (bottom right) slow K+K− axes, with the fit result with the Triple-M amplitude superim-

posed, whereas the dashed green line is the phase space distribution weighted by the efficiency. The magenta histogram represents the contribution from the background.

Triple M LHCb fit

parameter value F 94.3+2.8

−1.7 ± 1.5 MeV

ma0 947.7+5.5

−5.0 ± 6.6 MeV

mSo 992.0+8.5

−7.5 ± 8.6 MeV

mS1 1330.2+5.9

−6.5 ± 5.1 MeV

mφ 1019.54+0.10

−0.10 ± 0.51 MeV

Gφ 0.464+0.013

−0.009 ± 0.007

cd −78.9+4.2

−2.7 ± 1.9 MeV

cm 106.0+7.7

−4.6 ± 3.3 MeV

˜ cd −6.15+0.55

−0.54 ± 0.19 MeV

˜ cm −10.8+2.0

−1.5 ± 0.4 MeV

T S = T S

NR + T 00 + T 01

T P = T P

NR + T 11 + T 10 .

K K K

+ +

−

3 2 1

K K K

+ +

−

3 2 1 b a

+

FFNR FF00 FF01 FF10 FF11 FFS−wave 14 ± 1 29 ± 1 131 ± 2 7.1 ± 0.9 0.26 ± 0.01 94 ± 1

strong destructive interference in S-wave

SLIDE 19

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3-body hadronic decay 19

Final State Interaction in B decays as a source of CP violation

SLIDE 20

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3-body hadronic decay 20

CPV on data: Puzzle!

Γ(M ! f) Γ( ¯ M ! ¯ f) = |hf | T | Mi|2 |h ¯ f | T | ¯ Mi|2 = 4A1A2 sin(δ1 δ2) sin(φ1 φ2)

∴

Charge Parity Violation

Γ(M ! f) 6= Γ( ¯ M ! ¯ f) hf | T | Mi = A1 ei(δ1+φ1) + A2 ei(δ2+φ2) h ¯ f | T | ¯ Mi = A1 ei(δ1−φ1) + A2 ei(δ2−φ2) CP

2 amplitudes, SAME final state with strong ( ) and weak ( ) phase

φi δi

6=

condition to CPV

q

φ2 φ1

weak phase: CKM Vub

BSS model

strong phase

+

Bander Silverman & Soni PRL 43 (1979) 242

SLIDE 21

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3-body hadronic decay 21

CPV on data: Puzzle!

not enough!!

BSS model

+

• 0.8
• 0.6
• 0.4
• 0.2

0.2 0.4 0.6 0.8 ) 4 c / 2 (GeV π π 2 m 2 4 6 8 10 12 14 16 18 20 22 ) 4 c / 2 (GeV π K 2 m 5 10 15 20 25

• 0.4
• 0.2

0.2 0.4 ) 4 c / 2 (GeV low

• K

+ K 2 m 2 4 6 8 10 12 14 ) 4 c / 2 (GeV high

• K

+ K 2 m 5 10 15 20 25

• 0.8
• 0.6
• 0.4
• 0.2

0.2 0.4 0.6 0.8 (DTF) Low π π 2 m 2 4 6 8 10 12 14 (DTF) High π π 2 m 5 10 15 20 25

• 0.8
• 0.6
• 0.4
• 0.2

0.2 0.4 0.6 0.8 (DTF) KK 2 m 5 10 15 20 25 (DTF) π K 2 m 5 10 15 20 25

Kππ KKK KKπ πππ

middle looks “empty" CPV

massive localized Acp

B± → h±h−h+

hadronic interactions

strong phase

low-energy CPV with opposite signs

Frederico, Bediaga, Lourenço PRD89(2014)094013

ππ → KK B± → π±π−π+

B± → π±K−K+

and

ACP = Γ(M → f) − Γ( ¯ M → ¯ f) Γ(M → f) + Γ( ¯ M → ¯ f)

suggest dynamic effect

SLIDE 22

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3-body hadronic decay 22

Parentheses…..

scattering data S-Wave

Inelasticity

• ne minus the probability of losing signal (1==elastic)

Pelaez, Yndurain PRD71(2011) 074016

ππ

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Inelasticity:

Phase-shift

^ f ls le2il 1 2i

• :

amplitude

el

l 1

2 1 2

l

2 cos2l

• ;

KK

SLIDE 23

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3-body hadronic decay 23

Гtotal = Г1 + Г2 + Г3 + Г4 + Г5 + Г6 + .... Гtotal = Г1 + Г2 + Г3 + Г4 + Г5 + Г6 + ...

_ _ _ _ _ _ _ Lifetime τ = 1 / Гtotal = 1 / Гtotal

CPV on data

• 0.8
• 0.6
• 0.4
• 0.2

0.2 0.4 0.6 0.8 ) 4 c / 2 (GeV π π 2 m 2 4 6 8 10 12 14 16 18 20 22 ) 4 c / 2 (GeV π K 2 m 5 10 15 20 25

• 0.4
• 0.2

0.2 0.4 ) 4 c / 2 (GeV low

• K

+ K 2 m 2 4 6 8 10 12 14 ) 4 c / 2 (GeV high

• K

+ K 2 m 5 10 15 20 25

• 0.8
• 0.6
• 0.4
• 0.2

0.2 0.4 0.6 0.8 (DTF) Low π π 2 m 2 4 6 8 10 12 14 (DTF) High π π 2 m 5 10 15 20 25

• 0.8
• 0.6
• 0.4
• 0.2

0.2 0.4 0.6 0.8 (DTF) KK 2 m 5 10 15 20 25 (DTF) π K 2 m 5 10 15 20 25

Kππ KKK KKπ πππ

FSI strong phase low-energy CPV

ππ → KK

Frederico, Bediaga & Lourenço PRD89(2014)094013

Wolfenstein PRD43 (1991) 151

CPT:

CPV in one channel should be compensated by another

• ne with opposite sign

[1 - 2] GeV

KKK Kππ KKπ πππ

SLIDE 24

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3-body hadronic decay 24

(a) (b) (c) (d)

Contribution Fit fraction (102) ACP (102) B+ phase () B phase () Isobar model ρ(770)0 55.5 ± 0.6 ± 2.5 +0.7 ± 1.1 ± 1.6 — — ω(782) 0.50 ± 0.03 ± 0.05 −4.8 ± 6.5 ± 3.8 −19 ± 6 ± 1 +8 ± 6 ± 1 f2(1270) 9.0 ± 0.3 ± 1.5 +46.8 ± 6.1 ± 4.7 +5 ± 3 ± 12 +53 ± 2 ± 12 ρ(1450)0 5.2 ± 0.3 ± 1.9 −12.9 ± 3.3 ± 35.9 +127 ± 4 ± 21 +154 ± 4 ± 6 ρ3(1690)0 0.5 ± 0.1 ± 0.3 −80.1 ± 11.4 ± 25.3 −26 ± 7 ± 14 −47 ± 18 ± 25 S-wave 25.4 ± 0.5 ± 3.6 +14.4 ± 1.8 ± 2.1 — — Rescattering 1.4 ± 0.1 ± 0.5 +44.7 ± 8.6 ± 17.3 −35 ± 6 ± 10 −4 ± 4 ± 25 σ 25.2 ± 0.5 ± 5.0 +16.0 ± 1.7 ± 2.2 +115 ± 2 ± 14 +179 ± 1 ± 95 K-matrix ρ(770)0 56.5 ± 0.7 ± 3.4 +4.2 ± 1.5 ± 6.4 — — ω(782) 0.47 ± 0.04 ± 0.03 −6.2 ± 8.4 ± 9.8 −15 ± 6 ± 4 +8 ± 7 ± 4 f2(1270) 9.3 ± 0.4 ± 2.5 +42.8 ± 4.1 ± 9.1 +19 ± 4 ± 18 +80 ± 3 ± 17 ρ(1450)0 10.5 ± 0.7 ± 4.6 +9.0 ± 6.0 ± 47.0 +155 ± 5 ± 29 −166 ± 4 ± 51 ρ3(1690)0 1.5 ± 0.1 ± 0.4 −35.7 ± 10.8 ± 36.9 +19 ± 8 ± 34 +5 ± 8 ± 46 S-wave 25.7 ± 0.6 ± 3.0 +15.8 ± 2.6 ± 7.2 — — QMI ρ(770)0 54.8 ± 1.0 ± 2.2 +4.4 ± 1.7 ± 2.8 — — ω(782) 0.57 ± 0.10 ± 0.17 −7.9 ± 16.5 ± 15.8 −25 ± 6 ± 27 −2 ± 7 ± 11 f2(1270) 9.6 ± 0.4 ± 4.0 +37.6 ± 4.4 ± 8.0 +13 ± 5 ± 21 +68 ± 3 ± 66 ρ(1450)0 7.4 ± 0.5 ± 4.0 −15.5 ± 7.3 ± 35.2 +147 ± 7 ± 152 −175 ± 5 ± 171 ρ3(1690)0 1.0 ± 0.1 ± 0.5 −93.2 ± 6.8 ± 38.9 +8 ± 10 ± 24 +36 ± 26 ± 46 S-wave 26.8 ± 0.7 ± 2.2 +15.0 ± 2.7 ± 8.1 — —

CPV: amplitude analysis B± → π−π+π±

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recent Amplitude analysis B± → π−π+π±

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(π−π+)S − W ave

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3 different model:

𝜏 as BW (!) + rescattering; P-vector K-Matrix; binned freed lineshape (QMI);

B± → π±K−K+

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ANA for

Contribution Fit Fraction(%) ACP(%) Magnitude (B+/B−) Phase[o] (B+/B−) K∗(892)0 7.5 ± 0.6 ± 0.5 +12.3 ± 8.7 ± 4.5 0.94 ± 0.04 ± 0.02 0 (fixed) 1.06 ± 0.04 ± 0.02 0 (fixed) K∗

0(1430)0

4.5 ± 0.7 ± 1.2 +10.4 ± 14.9 ± 8.8 0.74 ± 0.09 ± 0.09 −176 ± 10 ± 16 0.82 ± 0.09 ± 0.10 136 ± 11 ± 21 Single pole 32.3 ± 1.5 ± 4.1 −10.7 ± 5.3 ± 3.5 2.19 ± 0.13 ± 0.17 −138 ± 7 ± 5 1.97 ± 0.12 ± 0.20 166 ± 6 ± 5 ρ(1450)0 30.7 ± 1.2 ± 0.9 −10.9 ± 4.4 ± 2.4 2.14 ± 0.11 ± 0.07 −175 ± 10 ± 15 1.92 ± 0.10 ± 0.07 140 ± 13 ± 20 f2(1270) 7.5 ± 0.8 ± 0.7 +26.7 ± 10.2 ± 4.8 0.86 ± 0.09 ± 0.07 −106 ± 11 ± 10 1.13 ± 0.08 ± 0.05 −128 ± 11 ± 14 Rescattering 16.4 ± 0.8 ± 1.0 −66.4 ± 3.8 ± 1.9 1.91 ± 0.09 ± 0.06 −56 ± 12 ± 18 0.86 ± 0.07 ± 0.04 −81 ± 14 ± 15 φ(1020) 0.3 ± 0.1 ± 0.1 +9.8 ± 43.6 ± 26.6 0.20 ± 0.07 ± 0.02 −52 ± 23 ± 32 0.22 ± 0.06 ± 0.04 107 ± 33 ± 41

[arXiv:1905.09244] [arXiv:1909.05212(PRD); 1909.05211(PRL)]

???

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Patricia Magalhães

3-body hadronic decay 25 same observed in coupled-channels

high statistic nonresonant all phase-space

109k

B+ → K−K+K+

1 10

2

10

]

4

c /

2

[GeV

low

• K

+

K 2

m

5 10 15

]

4

c /

2

[GeV

high

• K

+

K 2

m

5 10 15 20 25

LHCb

presence of charm resonances: J/ψ

χc0

~ open channel

D ¯ D

D K+ K− D

, π , π

+

]

2

c [GeV/

high

)

−

K

+

(K m

2 3 4 5

yields

+

• B

−

B

800 − 600 − 400 − 200 − 200 400 600

LHCb

CPV high mass?

CPV high energy

charm intermediate processes as source of strong phase

dominated by penguin

_

u

_

s

_

c B+ K + K −

_

u K + c b u s s

(p )

3

B+ (p )

1

K+ (p )

2

D D 0 D*0

Κ

+

Κ

−

s

• I. Bediaga, PCM, T Frederico

PLB 780 (2018) 357

charm rescattering!

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3-body hadronic decay 26

hadronic loop

(p )

3

B+ (p )

1

K+ (p )

2

D D 0 D*0

Κ

+

Κ

−

s

hadronic loop three-body FSI - introduce new complex structures

arXiv:1512.09284

PCM & I Bediaga

_ K0

π+ π+ π 0

Ds*

(2) (1) (3) K−

W

T

B+ → π+π−π+

D+ → π+K−π+

PRD 92 094005 (2015) [arXiv:1504.06346]

PCM et al

PRD 84 094001 (2011 ) [arXiv:1105.5120]

PCM & M Robilotta

~1% 1000 x Br [B → DD∗

s]

Br [B → KKK]

scattering amplitude

D0 ¯ D0 → K+K−

phenomenological: weak transition

B+ → W + ¯ D0

form factor to regulate

C0 × form factor for W + → D0K+ S- matrix unitarity + Regge theory

+

• I. Bediaga, PCM, T Frederico

PLB 780 (2018) 357

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3-body hadronic decay 27

1 1.5 2 2.5 3 3.5 4 4.5

m(KK) GeV

• 1.5
• 1
• 0.5

0.5 1 Phase

hadronic loop

(p ) B+ (p ) K+ (p )

2

D D 0 D*0

Κ

+

Κ

−

s

A = iC m2

a

Z d4` (2⇡)4 T ¯

D0D0!KK(s23) [−2 p0 3 · (p0 2 − p1)]

∆D+∗∆D0 ∆ ¯

D0 ∆a

,

phase

]

2

c [GeV/

high

)

−

K

+

(K m

2 3 4 5

yields

+

• B

−

B

800 − 600 − 400 − 200 − 200 400 600

LHCb Phase change signal in the same region as Acp data

can explain change CPV signal in DP!!!

+

Promising mechanism !

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3-body hadronic decay 28

Charm rescattering elsewhere

D D 0 D (p )

1

(p )

2

(p )

3

B +

c

K K

π

*+ +

+ −

B+

c → K−K+π+

charm rescattering to

• I. Bediaga, PCM, T Frederico

PLB 785 (2018) 581

(p )

3

K

−

(p )

1

+

π

(p )

2

K

+

B +

c *

D D −

+

D

s

+ How much of the anomalies can be understood as hadronic effects?

vector meson dominance

V= all vector family psi, …

Next: investigating Hadronic effect in B → Kµµ

µ−

µ+

V

γ

D0 ¯ D0 B+ K+ D D 0 D*0

Κ

+

Κ

s

¯ D0D0 → γ → µ+µ−

µ+ µ−

+

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3-body hadronic decay 29

final remarks

superposition of resonant and non-resonant at low and high energy

FSI are important and play a major role in hadronic 3-body decays!

Lots of theoretical limitations to be developed:

need to merge the short and long distance descriptions!

extend the meson-meson interaction to high E, … Charm rescattering in under intense investigation : CPV on B, exotics, anomalies, …… Successful examples of cooperation between theory and experiment !!! Important tool !

Thank you very much!

image credit: unknown

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3-body hadronic decay 30

Backup slides

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3-body hadronic decay 31

FSI in three-body decay :

• I. Bediaga, I., T. Frederico, T. and O. Louren Phys. Rev. D89, 094013(2014),[arXiv:1307.8164]
• J. H. Alvarenga Nogueira, I. Bediaga, A. B. R. Cavalcante, T. Frederico and O. Louren ̧ Phys. Rev. D92,

054010 (2015) [ArXiv:1506.08332]. PC Magalhães and I Bediaga arXiv:1512.09284; P . C Magalhães and R.Robilotta, Phys. Rev. D92 094005 (2015) [arXiv:1504.06346] ; P .C.Magalhães et. al.

• Phys. Rev. D84 094001 (2011) [arXiv:1105.5120]; P

.C. Magalhães and Michael C. Birse, PoS QNP2012, 144 (2012).

• I. Caprini, Phys. Lett. B 638 468 (2006).

Bochao Liu, M. Buescher, Feng-Kun Guo, C. Hanhart, and Ulf-G. Meissner, Eur. Phys. J. C 63 93 (2009). F Niecknig and B Kubis - JHEP 10 142 (2015) ArXiv:1509.03188

• H. Kamano, S.X. Nakamura, T.-S.H. Lee and T. Sato, Phys. Rev. D 84, 114019 (2011).
• S. X. Nakamura, arXiv:1504.02557 (2015).
• J. -P

. Dedonder, A. Furman, R. Kaminski, L. Lesniak, L. and B. Loiseau, Acta Phys. Polon. B42, 2013 (2011), [Arxiv: 1011.0960] J.-P . Dedonder, R. Kaminski, L. Lesniak, and B. Loiseau, , Phys. Rev.D89, 094018 (2014). Donoghue et al., Phys. Rev Letters 77(1996) 2178; Suzuki,Wolfenstein, Phys. Rev. D 60 (1999)074019; Falk et al. Phys. Rev. D 57,4290(1998); Blok, Gronau, Rosner, Phys. Rev Letters 78, 3999 (1997). 


many more ... references

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3-body hadronic decay 32

1 10

2

10

]

4

c /

2

[GeV

• π

+

π 2

m

10 20

]

4

c /

2

[GeV

• π

+

K 2

m

5 10 15 20 25 30

LHCb

] c

Kpp KKK

1 10

2

10

]

4

c /

2

[GeV

low

• K

+

K 2

m

5 10 15

]

4

c /

2

[GeV

high

• K

+

K 2

m

5 10 15 20 25

LHCb

• 1

10 1 10

]

4

c /

2

[GeV

low

• π

+

π 2

m

5 10 15

]

4

c /

2

[GeV

high

• π

+

π 2

m

5 10 15 20 25

LHCb

]

• 1

10 1 10

]

4

c /

2

[GeV

• π

+

K 2

m

10 20

]

4

c /

2

[GeV

• K

+

K 2

m

5 10 15 20 25 30

LHCb

ppp Kpp KKp if needed