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

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

May 31, 2023 288 likes •596 views

Challenges and future in three-body heavy meson decays Patricia C. Magalhes p.magalhaes@bristol.ac.uk #BlackLifesMatter Seminar at Birmingham Particle Physics Group 17/6/20 <latexit

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SLIDE 1

p.magalhaes@bristol.ac.uk

Patricia C. Magalhães #BlackLifesMatter

Challenges and future in three-body heavy meson decays

Seminar at Birmingham Particle Physics Group 17/6/20

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SLIDE 2

Birmingham - 17/06/2020

Patricia Magalhães

3-body hadronic decay 2

Motivation

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

baryogenesis !

  • 1967, the Russian physicist Andrey Sakharov proposed

three conditions for generating the observed matter/ anti-matter asymmetry of the Universe: 1) baryon number violation 2) C and CP violation 3) departure from thermal equilibrium

CP-Violation on Hadronic decays

massive phase-space localized Asymmetry in B± → h±h−h+

SM predicts CPV in B sector but ….. lot to be understood

can lead to new physics

CPV on three-body?

2019 1st observation in charm D0( ¯

D0) → π+π− − K+K−

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SLIDE 3

Birmingham - 17/06/2020

Patricia Magalhães

3-body hadronic decay

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

3

Context

spectroscopy: new resonances, their properties… information of MM interactions

build up the idea that the main dynamic in 3-body is driven by 2-body resonances

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

f0(600)

K∗

0(700)

image credit:Brian Meadows

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

D0 → K−π+π0

new high data sample from LHCb

more to come from LHCb, BelleII, BESIII

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

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SLIDE 4

Birmingham - 17/06/2020

Patricia Magalhães

3-body hadronic decay 4

Three-body kinematics : DALITZ plot

How to describe the kinematics of three-body HADRONIC decays? + + = M p1

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p2

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p3

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s13

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s12

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s23

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Mandelstam variables for 3-body

s12 + s13 + s12 = M 2 + m2

1 + m2 2 + m2 3

decay rate can be written as: dΓ =

1 (2π)3 1 32M 2 ¯ |M|2s12s23

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In the rest frame of M (P=0): final particle are in the same plane

final particle distribution in the phase-space will depend on: - average of spin

  • Euler angles

Amplitude, dynamic!

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SLIDE 5

Birmingham - 17/06/2020

Patricia Magalhães

3-body hadronic decay

The phase-space is NOT one-dimension!

5

Three-body kinematics : DALITZ plot

A conservação da energia e momento

a b c

DP proposed by Richard Dalitz (1925-2006) in 1953

  • the perimeter depends on the masses

min: max: in ,

sij > (mi + mj)2

sij (M − mk)2

  • inside this contour there are all

combinations of momenta distribution

  • The probability of each point inside is

given by the dynamic amplitude A

tool for analyse data DALITZ PLOT

sab sbc

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SLIDE 6

scalar vector tensor besides the amplitude bump (intensity/probability) the resonance will have a spin signature in DP: (same as spherical harmonics)…

(s)Pj(cos(◊))

credit: knowino.org

Birmingham - 17/06/2020

Patricia Magalhães

3-body hadronic decay 6

Two-body resonances signature in DP

2-body resonances have spin and isospin well defined: RJ,I

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+ +

RJ,I

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∑

RJ,I

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=

this pattern in Dalitz Plot

ρ(770) f0(980) K*(890)

typically amplitudes are bumps (like the Breit-Wigner) contribute to a specific partial wave

Mba(s, t) =

∞

ÿ

j=0

(2j + 1)Mj

ba(s)Pj(cos(◊))

credit:hyperphysics.phy

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SLIDE 7

Birmingham - 17/06/2020

Patricia Magalhães

3-body hadronic decay

common cartoon to described 3-body decay

7

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

<latexit sha1_base64="fnucIWfnCn9YSdQUiMBJOqBvQF0=">AB63icbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF8FLBfsBbSib7aZdursJuxOhlP4FLx4U8eof8ua/MWlz0NYHA4/3ZpiZF8RSWHTdb6ewtr6xuVXcLu3s7u0flA+PWjZKDONFsnIdAJquRSaN1Gg5J3YcKoCydvB+Dbz20/cWBHpR5zE3Fd0qEUoGMVMu/bUr9cavuHGSVeDmpQI5Gv/zVG0QsUVwjk9TarufG6E+pQcEkn5V6ieUxZWM65N2Uaq49afzW2fkLFUGJIxMWhrJXP09MaXK2okK0k5FcWSXvUz8z+smGF7U6HjBLlmi0VhIglGJHucDIThDOUkJZQZkd5K2IgayjCNJwvBW35lbRqVe+iWnu4rNRv8jiKcAKncA4eXEd7qABTWAwgmd4hTdHOS/Ou/OxaC04+cwx/IHz+QNhpY3N</latexit>

π+

<latexit sha1_base64="IMOk3oLNkoIsz8quODvMO/AvzE=">AB7XicbVBNSwMxEJ2tX7V+VT16CRZBEMpuFfRY9OKxgv2Adi3ZNvGZpMlyQpl6X/w4kERr/4fb/4bs+0etPXBwO9GWbmBTFn2rjut1NYWV1b3yhulra2d3b3yvsHLS0TRWiTSC5VJ8CaciZo0zDaSdWFEcBp+1gfJP57SeqNJPi3kxi6kd4KFjICDZWavVi9nBW6pcrbtWdAS0TLycVyNHol796A0mSiApDONa67mx8VOsDCOcTku9RNMYkzEe0q6lAkdU+ns2ik6scoAhVLZEgbN1N8TKY60nkSB7YywGelFLxP/87qJCa/8lIk4MVSQ+aIw4chIlL2OBkxRYvjEkwUs7ciMsIKE2MDykLwFl9eJq1a1Tuv1u4uKvXrPI4iHMExnIHl1CHW2hAEwg8wjO8wpsjnRfn3fmYtxacfOYQ/sD5/AGjKo6C</latexit>

π−

<latexit sha1_base64="Xjl1uYBWGIU+cspQjvtMRkw7a04=">AB7XicbVBNSwMxEJ2tX7V+VT16CRbBi2W3CnosevFYwX5Au5Zsm1js8mSZIWy9D948aCIV/+PN/+N2XYP2vpg4PHeDPzgpgzbVz32ymsrK6tbxQ3S1vbO7t75f2DlpaJIrRJeqE2BNORO0aZjhtBMriqOA03Ywvsn89hNVmklxbyYx9SM8FCxkBsrtXoxezgr9csVt+rOgJaJl5MK5Gj0y1+9gSRJRIUhHGvd9dzY+ClWhFOp6VeomMyRgPadSgSOq/XR27RSdWGWAQqlsCYNm6u+JFEdaT6LAdkbYjPSil4n/ed3EhFd+ykScGCrIfFGYcGQkyl5HA6YoMXxiCSaK2VsRGWGFibEBZSF4iy8vk1at6p1Xa3cXlfp1HkcRjuAYTsGDS6jDLTSgCQe4Rle4c2Rzovz7nzMWwtOPnMIf+B8/gCmNI6E</latexit>

+

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

  • ne expect to see all 3 channels res:

)

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

Two-body resonances signature in DP

RJ,I

<latexit sha1_base64="K9hITRCzJH+w0NwgW8nENoftCs=">AB7nicbVBNSwMxEJ2tX7V+VT16CRbBg5TdKuhJCl7UxX7Ae1asm2DU2yS5IVytIf4cWDIl79Pd78N6btHrT1wcDjvRlm5gUxZ9q47reTW1peWV3Lrxc2Nre2d4q7ew0dJYrQOol4pFoB1pQzSeuGU5bsaJYBJw2g+HVxG8+UaVZJB/MKa+wH3JQkawsVLz/jG9PbkZd4slt+xOgRaJl5ESZKh1i1+dXkQSQaUhHGvd9tzY+ClWhFOx4VOomMyRD3adtSiQXVfjo9d4yOrNJDYaRsSYOm6u+JFAutRyKwnQKbgZ73JuJ/Xjsx4YWfMhknhkoyWxQmHJkITX5HPaYoMXxkCSaK2VsRGWCFibEJFWwI3vzLi6RKXun5crdWal6mcWRhwM4hGPw4ByqcA01qAOBITzDK7w5sfPivDsfs9ack83swx84nz+5bo8n</latexit>

∑

RJ,I

<latexit sha1_base64="K9hITRCzJH+w0NwgW8nENoftCs=">AB7nicbVBNSwMxEJ2tX7V+VT16CRbBg5TdKuhJCl7UxX7Ae1asm2DU2yS5IVytIf4cWDIl79Pd78N6btHrT1wcDjvRlm5gUxZ9q47reTW1peWV3Lrxc2Nre2d4q7ew0dJYrQOol4pFoB1pQzSeuGU5bsaJYBJw2g+HVxG8+UaVZJB/MKa+wH3JQkawsVLz/jG9PbkZd4slt+xOgRaJl5ESZKh1i1+dXkQSQaUhHGvd9tzY+ClWhFOx4VOomMyRD3adtSiQXVfjo9d4yOrNJDYaRsSYOm6u+JFAutRyKwnQKbgZ73JuJ/Xjsx4YWfMhknhkoyWxQmHJkITX5HPaYoMXxkCSaK2VsRGWCFibEJFWwI3vzLi6RKXun5crdWal6mcWRhwM4hGPw4ByqcA01qAOBITzDK7w5sfPivDsfs9ack83swx84nz+5bo8n</latexit>

= D0 → Ksπ−π+

slide-8
SLIDE 8

Birmingham - 17/06/2020

Patricia Magalhães

3-body hadronic decay 8

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

credit:Brian Meadows

D0 → K−π+π0 Similar final state but different interference pattern different dynamics to be understood

)

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-9
SLIDE 9

Birmingham - 17/06/2020

Patricia Magalhães

3-body hadronic decay 9

D+

s → π+π−π+

π−π+ → π−π+

<latexit sha1_base64="h1soNZu6bGDYSDKND4KMHtOrxs=">ACAXicdVDLSgMxFL3js9bXqCtxEyCIJZpEXysCm5cVnBsoTOWTJpQzOZIckIZShu/BU3LlTc+hfu/BszbcX3gSQn59xLck+QcKa047xZU9Mzs3PzhYXi4tLyq9tn6p4lQS6pKYx7IZYEU5E9TVTHPaTCTFUcBpI+if5n7jmkrFYnGhBwn1I9wVLGQEayO17U0vYVf7+baHPB2jz2vbLjnlqpMD/SaV8uh0SjBvW2/ep2YpBEVmnCsVKviJNrPsNSMcDoseqmiCSZ93KUtQwWOqPKz0QhDtGOUDgpjaZbQaKR+7chwpNQgCkxlhHVP/fRy8S+vlerwyM+YSFJNBRk/FKYcmVnzPFCHSUo0HxiCiWTmr4j0sMREm9SKJoSPSdH/xK2Wj8vO+UGpdjJowBbsA27UIFDqMEZ1MEFAjdwBw/waN1a9aT9TwunbImPRvwDdbLO8/VlfE=</latexit><latexit sha1_base64="h1soNZu6bGDYSDKND4KMHtOrxs=">ACAXicdVDLSgMxFL3js9bXqCtxEyCIJZpEXysCm5cVnBsoTOWTJpQzOZIckIZShu/BU3LlTc+hfu/BszbcX3gSQn59xLck+QcKa047xZU9Mzs3PzhYXi4tLyq9tn6p4lQS6pKYx7IZYEU5E9TVTHPaTCTFUcBpI+if5n7jmkrFYnGhBwn1I9wVLGQEayO17U0vYVf7+baHPB2jz2vbLjnlqpMD/SaV8uh0SjBvW2/ep2YpBEVmnCsVKviJNrPsNSMcDoseqmiCSZ93KUtQwWOqPKz0QhDtGOUDgpjaZbQaKR+7chwpNQgCkxlhHVP/fRy8S+vlerwyM+YSFJNBRk/FKYcmVnzPFCHSUo0HxiCiWTmr4j0sMREm9SKJoSPSdH/xK2Wj8vO+UGpdjJowBbsA27UIFDqMEZ1MEFAjdwBw/waN1a9aT9TwunbImPRvwDdbLO8/VlfE=</latexit><latexit sha1_base64="h1soNZu6bGDYSDKND4KMHtOrxs=">ACAXicdVDLSgMxFL3js9bXqCtxEyCIJZpEXysCm5cVnBsoTOWTJpQzOZIckIZShu/BU3LlTc+hfu/BszbcX3gSQn59xLck+QcKa047xZU9Mzs3PzhYXi4tLyq9tn6p4lQS6pKYx7IZYEU5E9TVTHPaTCTFUcBpI+if5n7jmkrFYnGhBwn1I9wVLGQEayO17U0vYVf7+baHPB2jz2vbLjnlqpMD/SaV8uh0SjBvW2/ep2YpBEVmnCsVKviJNrPsNSMcDoseqmiCSZ93KUtQwWOqPKz0QhDtGOUDgpjaZbQaKR+7chwpNQgCkxlhHVP/fRy8S+vlerwyM+YSFJNBRk/FKYcmVnzPFCHSUo0HxiCiWTmr4j0sMREm9SKJoSPSdH/xK2Wj8vO+UGpdjJowBbsA27UIFDqMEZ1MEFAjdwBw/waN1a9aT9TwunbImPRvwDdbLO8/VlfE=</latexit>

(I=J=0)

2-body x 3-body phases

+ +

If this is the “nature” picture

Phys.Rev. D 79 (2009) 032003

scattering decay different phases!

decay phase should be the same as scattering

Is not as simple as it look like!

  • nce it only contain 2-body information,

3-body data: only spin! and dynamics

6=

2-body amplitude: spin and isospin well defined!

Quantum numbers:

slide-10
SLIDE 10

Birmingham - 17/06/2020

Patricia Magalhães

3-body hadronic decay 10

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-11
SLIDE 11

Birmingham - 17/06/2020

Patricia Magalhães

3-body hadronic decay 11

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

slide-12
SLIDE 12

Anisovich PLB653(2007)

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

used by Babar, LHCb, BES II

Birmingham - 17/06/2020

Patricia Magalhães

3-body hadronic decay 12

Models available

F S I

W

A = *

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

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±

<latexit sha1_base64="mMSZdFn27wxwpC513G8OSJwjQA=">ACAHicbVDLSgMxFM3UV62vURcu3ASLIhlpgp2WXQjdFPBPqAzLZk04ZmMiHJCGXoxl9x40IRt36GO/GTNuFth4IHM65l5tzAsGo0o7zbeVWVtfWN/Kbha3tnd09e/+gqeJEYtLAMYtlO0CKMpJQ1PNSFtIgqKAkVYwus381iORisb8QY8F8SM04DSkGkj9eyjm64nIujpGNa6F7XuSdopvTsolNypoDLxJ2TIpij3rO/vH6Mk4hwjRlSquM6QvspkpiRiYFL1FEIDxCA9IxlKOIKD+dBpjAU6P0YRhL87iGU/X3RoipcZRYCYjpIdq0cvE/7xOosOKn1IuEk04nh0KEwZN3KwN2KeSYM3GhiAsqfkrxEMkEdams4IpwV2MvEya5ZJ7WSrfXxWrlXkdeXAMTsAZcME1qI7UAcNgMEPINX8GY9WS/Wu/UxG81Z851D8AfW5w/9CZVZ</latexit>

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

  • ther scalar and vector form factors available

< ππ|0 >

<latexit sha1_base64="gUu68W5qwO70FhPZfBHdBnWtQS8=">AB83icbVDLSgMxFL1TX7W+qi7dBIvgqsxUwS5ECm5cVrAP6Awlk2ba0EwmJBmhjP0Ny4UcevPuPNvTNtZaOvhXjicy+5OaHkTBvX/XYKa+sbm1vF7dLO7t7+QfnwqK2TVBHaIglPVDfEmnImaMsw2lXKorjkNOL6d+Z1HqjRLxIOZSBrEeChYxAg2VvKvkS+ZrSfk3vTLFbfqzoFWiZeTCuRo9stf/iAhaUyFIRxr3fNcaYIMK8MIp9OSn2oqMRnjIe1ZKnBMdZDNb56iM6sMUJQo28Kgufp7I8Ox1pM4tJMxNiO97M3E/7xeaqJ6kDEhU0MFWTwUpRyZBM0CQAOmKDF8YgkmitlbERlhYmxMZVsCN7yl1dJu1b1Lq1+8tKo57HUYQTOIVz8OAKGnAHTWgBAQnP8ApvTuq8O/Ox2K04OQ7x/AHzucPodeQvA=</latexit>

< Kπ|0 >

<latexit sha1_base64="fOTlH0biGPa2vQwvTJLeNg/uAVo=">AB8nicbVBNSwMxEM36WetX1aOXYBE8ld0q2INIwYvgpYL9gO1Ssm2Dc0mSzIrlLU/w4sHRbz6a7z5b0zbPWjrg4HezPMzAsTwQ247rezsrq2vrFZ2Cpu7+zu7ZcODltGpZqyJlVC6U5IDBNcsiZwEKyTaEbiULB2OLqZ+u1Hpg1X8gHGCQtiMpA84pSAlfwrfIe7CX/C7nWvVHYr7gx4mXg5KaMcjV7pq9tXNI2ZBCqIMb7nJhBkRAOngk2K3dSwhNARGTDfUkliZoJsdvIEn1qljyOlbUnAM/X3REZiY8ZxaDtjAkOz6E3F/zw/hagWZFwmKTBJ54uiVGBQePo/7nPNKIixJYRqbm/FdEg0oWBTKtoQvMWXl0mrWvHOK9X7i3K9lsdRQMfoBJ0hD12iOrpFDdREFCn0jF7RmwPOi/PufMxbV5x85gj9gfP5A0Ppj+g=</latexit>

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-13
SLIDE 13

Birmingham - 17/06/2020

Patricia Magalhães

3-body hadronic decay 13

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 = *

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)

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

+

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;

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

modern QDC factorization: improvement to include “long distance” still developing

slide-14
SLIDE 14

Birmingham - 17/06/2020

Patricia Magalhães

3-body hadronic decay 14

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)

Decay projected in one pair mass

Scattering

MKπ(

<latexit sha1_base64="Kuz5+3V/HOApzoIx3eLt5T/U+k=">AB9XicbVDLSgNBEOyNrxhfUY9eBoMQL2E3CnoMelAQIYJ5QLKG2UknGTL7YGZWCUv+w4sHRbz6L978GyfJHjSxoKGo6qa7y4sEV9q2v63M0vLK6lp2PbexubW9k9/dq6swlgxrLBShbHpUoeAB1jTXApuROp7Ahve8HLiNx5RKh4G93oUoevTfsB7nFtpIfbTnLTjviYFK+wftzJF+ySPQVZJE5KCpCi2sl/tbshi30MNBNUqZjR9pNqNScCRzn2rHCiLIh7WPL0ID6qNxkevWYHBmlS3qhNBVoMlV/TyTUV2rke6bTp3qg5r2J+J/XinXv3E14EMUaAzZb1IsF0SGZREC6XCLTYmQIZKbWwkbUEmZNkHlTAjO/MuLpF4uOSel8t1poXKRxpGFAziEIjhwBhW4hirUgIGEZ3iFN+vJerHerY9Za8ZKZ/bhD6zPHyeMkaE=</latexit>

sKπ

<latexit sha1_base64="jIRE4d7f9YTNOpHo365eHI4ygXM=">AB8HicbVDLSgNBEOz1GeMr6tHLYBA8hd0o6DHoRfASwTwkWcLsZDYZMo9lZlYIS7CiwdFvPo53vwbJ8keNLGgoajqprsrSjgz1ve/vZXVtfWNzcJWcXtnd2+/dHDYNCrVhDaI4kq3I2woZ5I2LOcthNsYg4bUWjm6nfeqLaMCUf7DihocADyWJGsHXSo+ld92ETVCvVPYr/gxomQ5KUOeq/01e0rkgoqLeHYmE7gJzbMsLaMcDopdlNDE0xGeEA7jkosqAmz2cETdOqUPoqVdiUtmqm/JzIsjBmLyHUKbIdm0ZuK/3md1MZXYcZkloqyXxRnHJkFZp+j/pMU2L52BFMNHO3IjLEGhPrMiq6EILFl5dJs1oJzivV+4ty7TqPowDHcAJnEMAl1OAW6tAgKe4RXePO29eO/ex7x1xctnjuAPvM8flJqQg=</latexit>
slide-15
SLIDE 15

Birmingham - 17/06/2020

Patricia Magalhães

3-body hadronic decay

0.8 1 1.2 1.4 1.6 mK훑 (GeV)

  • 90

90 180 Phase S-channel

15

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…

slide-16
SLIDE 16

Birmingham - 17/06/2020

Patricia Magalhães

3-body hadronic decay 16

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

#BlackLifesMatter

slide-17
SLIDE 17

Birmingham - 17/06/2020

Patricia Magalhães

3-body hadronic decay 17

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-18
SLIDE 18

Birmingham - 17/06/2020

Patricia Magalhães

3-body hadronic decay 18

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+

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

suggest dynamic effect

LHCb PRD90 (2014) 112004

hadronic interactions

strong phase

FSI strong phase

Wolfenstein PRD43 (1991) 151

slide-19
SLIDE 19

Birmingham - 17/06/2020

Patricia Magalhães

3-body hadronic decay 19

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

KKK Kππ KKπ πππ

ππ → KK

and B± → h±K−K+

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B± → h±π−π+

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low-energy CPV with opposite signs

Frederico PRD89(2014)094013

CPT:

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

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

CPV in one channel should be compensated by another

  • ne with opposite sign
slide-20
SLIDE 20

Birmingham - 17/06/2020

Patricia Magalhães

3-body hadronic decay 20

(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±

<latexit sha1_base64="/4i6/M8/7rC2AfozhVs2W7AmYcg=">ACBHicdVDLSgMxFM3UV62vUZfdBIsgiMNMW2m7K3XjsoJ9QGdaMmDc08SDJCGbpw46+4caGIWz/CnX9jpi1FRQ/kcjnXm7ucSNGhTNTy2ztr6xuZXdzu3s7u0f6IdHbRHGHJMWDlnIuy4ShNGAtCSVjHQjTpDvMtJxJ1ep37kjXNAwuJXTiDg+GgXUoxhJQ30fKNvRz60ZQjtiPYv0nKeFqUO9IJp1EoV0ypDyzDngKZRLdes6uVKYAlmgP9wx6GOPZJIDFDQvQsM5JOgrikmJFZzo4FiRCeoBHpKRognwgnmR8xg6dKGUIv5OoFEs7V7xMJ8oWY+q7q9JEci9eKv7l9WLpVZ2EBlEsSYAXi7yYQXVymgcUk6wZFNFEOZU/RXiMeIS5VbToWwuv1/0i4aVsko3pQL9cYyjizIgxNwBixQAXVwDZqgBTC4B4/gGbxoD9qT9q9LVoz2nLmGPyA9v4F1GXmw=</latexit>

recent Amplitude analysis B± → π−π+π±

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(π−π+)S − W ave

<latexit sha1_base64="PDdGMaoGDzRQIYD1a3Wq4XadZxA=">ACAnicbVDLSsNAFJ3UV62vqCtxEyxCxbYkVdCVFNy4rGgf0MQwmU7aoZNJmJkUSihu/BU3LhRx61e482+ctFlo64F7OZxzLzP3eBElQprmt5ZbWl5ZXcuvFzY2t7Z39N29lghjnAThTkHQ8KTAnDTUkxZ2IYxh4FLe94Xqt0eYCxKyezmOsBPAPiM+QVAqydUPSnZEHipOz1xkzu7XLHLbTjCE1cvmlVzCmORWBkpgwNV/+yeyGKA8wkolCIrmVG0kglwRPCnYscAREPYx1FGQywcJLpCRPjWCk9w+5KiaNqfp7I4GBEOPAU5MBlAMx76Xif143lv6lkxAWxRIzNHvIj6khQyPNw+gRjpGkY0Ug4kT91UADyCGSKrWCsGaP3mRtGpV6xauz0v1q+yOPLgEByBErDABaiDG9ATYDAI3gGr+BNe9JetHftYza07KdfAH2ucPEYiV7g=</latexit>

3 different model:

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

B± → π±K−K+

<latexit sha1_base64="eUwjRfnBgbL7gOTLjd2CKu5lHaQ=">ACAXicbVDLSgMxFM3UV62vUTeCm2ARBLHMVEFXUnQjdFPBPqAzLZk04ZmMiHJCKXUjb/ixoUibv0Ld/6N6XQWj0QOJxzLzfnBIJRpR3ny8otLC4tr+RXC2vrG5tb9vZOQ8WJxKSOYxbLVoAUYZSTuqakZaQBEUBI81geD31m/dEKhrzOz0SxI9Qn9OQYqSN1LX3rjqeiKCnY+gJmvJq56TaOe7aRafkpIB/iZuRIshQ69qfXi/GSUS4xgwp1XYdof0xkpiRiYFL1FEIDxEfdI2lKOIKH+cJpjAQ6P0YBhL87iGqfpzY4wipUZRYCYjpAdq3puK/3ntRIcX/phykWjC8exQmDBo8k7rgD0qCdZsZAjCkpq/QjxAEmFtSiuYEtz5yH9Jo1xyT0vl27Ni5TKrIw/2wQE4Ai4BxVwA2qgDjB4AE/gBbxaj9az9Wa9z0ZzVrazC37B+vgGYJuViQ=</latexit>

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)]

???

slide-21
SLIDE 21

Birmingham - 17/06/2020

Patricia Magalhães

3-body hadronic decay 21

B+ → K−K+K+

CPV high energy

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

J/ψ

χc0

+

K−

D D

K

]

2

c [GeV/

high

)

−

K

+

(K m

2 3 4 5

yields

+

  • B

−

B

800 − 600 − 400 − 200 − 200 400 600

LHCb

change sign ~ open channel

D ¯ D

Acp

<latexit sha1_base64="zuEzrHy9JpfAuQMo/pRi+Z2nTs4=">AB+XicbVDLSsNAFL3xWesr6tLNYBFclaQKuqy6cVnBPqANYTKdtEMnkzAzKZSQP3HjQhG3/ok7/8ZJm4W2Hhg4nHMv98wJEs6Udpxva219Y3Nru7JT3d3bPzi0j47Kk4loW0S81j2AqwoZ4K2NdOc9hJcRw2g0m94XfnVKpWCye9CyhXoRHgoWMYG0k37YHEdZjgnl2m/sZSXLfrjl1Zw60StyS1KBEy7e/BsOYpBEVmnCsVN91Eu1lWGpGOM2rg1TRBJMJHtG+oQJHVHnZPHmOzo0yRGEszRMazdXfGxmOlJpFgZkscqplrxD/8/qpDm+8jIk1VSQxaEw5UjHqKgBDZmkRPOZIZhIZrIiMsYSE23KqpoS3OUvr5JOo+5e1huPV7XmXVlHBU7hDC7AhWtowgO0oA0EpvAMr/BmZdaL9W59LEbXrHLnBP7A+vwBJ2T6A=</latexit>

_

u

_

s

_

c B+ K + K −

_

u K + c b u s s

charm intermediate processes as source of strong phase

  • I. Bediaga, PCM, T Frederico

PLB 780 (2018) 357

(p )

3

B+ (p )

1

K+ (p )

2

D D 0 D*0

Κ

+

Κ

−

s+

~1% 1000 x Br [B → DD∗

s]

Br [B → KKK]

even dynamically suppressed hadronic loop technique

PCM & M Robilotta PRD 92 094005 (2015) PCM et al PRD 84 094001 (2011)

D+ → π+K−π+

slide-22
SLIDE 22

Birmingham - 17/06/2020

Patricia Magalhães

3-body hadronic decay

Triangle hadronic loop with charm rescattering can generate a phase that change signal near DD threshold

22

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 results for

(p )

3

B+ (p )

1

K+ (p )

2

D D 0 D*0

Κ

+

Κ

−

s

+

B± → K±K−K+

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how this can be translated to the observable CPV?

we need inference with weak-phase!

slide-23
SLIDE 23

Birmingham - 17/06/2020

Patricia Magalhães

3-body hadronic decay 23

charm rescattering in

B± → π±π−π+

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high mass CPV study in

B± → π±π−π+

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Focus on m2

ππ > 3 GeV 2

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avoid low energy resonances

) c / (GeV

π π

m

  • 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

Bediaga, Frederico, PCM - PLBX (2020)[arXiv:2003.10019]

χc0

include data shows a huge CP asymmetry around m2

χc0 = 11.65 GeV 2

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wide CP asymmetry: same source for a nonresonant amplitude and χc0

charm loop and χc0

Important data features

{

wide

m2

χc0

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(expected in Run II)

slide-24
SLIDE 24

Birmingham - 17/06/2020

Patricia Magalhães

3-body hadronic decay 24

Amplitude model

AB±→π−π+π±(s12, s23) = A±

tree(s12, s23) + AD ¯ D(s12, s23)

B± → π±π−π+

<latexit sha1_base64="L7GrbI7DHMzjdOIxJvB/zP3phxo=">ACBXicbVDLSgMxFM3UV62vUZe6CBZBEMtMFXQlRTcuK9gHdMaSTNtaDITkoxQhm7c+CtuXCji1n9w59+YaWehrReSezjnXpJzAsGo0o7zbRUWFpeWV4qrpbX1jc0te3unqeJEYtLAMYtlO0CKMBqRhqakbaQBPGAkVYwvM701gORisbRnR4J4nPUj2hIMdKG6tr7V/e4NDTMfQEnWLT7LruGuXnYozKTgP3ByUQV71rv3l9WKcBJpzJBSHdcR2k+R1BQzMi5iSIC4SHqk46BEeJE+enExRgeGqYHw1iaE2k4YX9vpIgrNeKBmeRID9SslpH/aZ1Ehxd+SiORaBLh6UNhwqDxnEUCe1QSrNnIAIQlNX+FeIAkwtoEVzIhuLOW50GzWnFPK9Xbs3LtMo+jCPbATgCLjgHNXAD6qABMHgEz+AVvFlP1ov1bn1MRwtWvrML/pT1+QPgLpeF</latexit>

Amplitude Model for

u u u b

Nonresonant (only resonances tails) high mass

A±

tree = a0 e±iγ

Amplitude projection - Nonresonant

: weak phase γ from the dominant tree diagram

b → u

<latexit sha1_base64="2GL3ZU/1271rUfHzDMlxGknUG0=">AB7nicbVDLSgMxFL1TX7W+qi7dBIvgqszUQl0W3LisYB/QDiWTZtrQTGZI7ghl6Ee4caGIW7/HnX9j2s5CWw8EDufcS+45QSKFQdf9dgpb2zu7e8X90sHh0fFJ+fSsY+JUM95msYx1L6CGS6F4GwVK3ks0p1EgeTeY3i387hPXRsTqEWcJ9yM6ViIUjKVugEZYEzSYbniVt0lyCbxclKBHK1h+WswilkacYVMUmP6npugn1GNgk+Lw1SwxPKpnTM+5YqGnHjZ8tz5+TKiMSxto+hWSp/t7IaGTMLArsZERxYta9hfif108xvPUzoZIUuWKrj8JUEhtxkZ2MhOYM5cwSyrSwtxI2oZoytA2VbAneuRN0qlVvZtq7aFeadbzOopwAZdwDR40oAn30I2MJjCM7zCm5M4L86787EaLTj5zjn8gfP5A5wxjw=</latexit>

is complex (strong phase)

a0

<latexit sha1_base64="B92gF+4eEy6QsyahYeGdEX2oFc=">AB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lqQY8FLx4r2g9oQ9lsN+3SzSbsToQS+hO8eFDEq7/Im/GbZuDtj4YeLw3w8y8IJHCoOt+O4WNza3tneJuaW/4PCofHzSNnGqGW+xWMa6G1DpVC8hQIl7ya0yiQvBNMbud+54lrI2L1iNOE+xEdKREKRtFKD3TgDsoVt+ouQNaJl5MK5GgOyl/9YczSiCtkhrT89wE/YxqFEzyWamfGp5QNqEj3rNU0YgbP1ucOiMXVhmSMNa2FJKF+nsio5Ex0yiwnRHFsVn15uJ/Xi/F8MbPhEpS5IotF4WpJBiT+d9kKDRnKeWUKaFvZWwMdWUoU2nZEPwVl9eJ+1a1buq1u7rlUY9j6MIZ3AOl+DBNTgDprQAgYjeIZXeHOk8+K8Ox/L1oKTz5zCHzifP+QrjX4=</latexit>

m2

ππ > 3 GeV 2

<latexit sha1_base64="Jw5Kcpgpf6V8jzlnq8HCN+NaA=">ACAnicbVDLSgMxFM34rPU16krcBIvgQspMK+iqFzosoJ9QGcsmfROG5rMDElGKENx46+4caGIW7/CnX9j+lho6+FeOJxzL8k9QcKZ0o7zbS0tr6yurec28ptb2zu79t5+Q8WpFCnMY9lKyAKOIugrpnm0EokEBFwaAaDq7HfACpWBzd6WECviC9iIWMEm2kjn0o7kudzEuYqRGuYFzG3tk1NIxqF5yiMwFeJO6MFNAMtY795XVjmgqINOVEqbrJNrPiNSMchjlvVRBQuiA9KBtaEQEKD+bnDCJ0bp4jCWpiONJ+rvjYwIpYiMJOC6L6a98bif1471eGln7EoSTVEdPpQmHKsYzOA3eZBKr50BCJTN/xbRPJKHapJY3IbjzJy+SRqnoloul2/NCtTKLI4eO0DE6RS6QFV0g2qojih6RM/oFb1ZT9aL9W59TEeXrNnOAfoD6/MHVEaVbg=</latexit>

*+(0)

0(−)

D D 0(+) B+

+

D

+ −

π π π

charm rescattering with : source of strong phase variation

χc0

0(+)

π

+

π

0(−) −

D D

r simu d AD ¯

D

e integr

NEW!

χc0 is a pole bellow threshold

similar triangle loop

slide-25
SLIDE 25

Birmingham - 17/06/2020

Patricia Magalhães

3-body hadronic decay 25

Results

*+(0)

0(−)

D D 0(+) B+

+

D

+ −

π π π

+

= a0 e±iγ

AB±→π−π+π±(s12, s23) =

the goal was to reproduce the main observed CPV characteristics γ = 70o

<latexit sha1_base64="O/sueISK23c0NLbXRTVbvh0DFPM=">AB+HicbVDLSsNAFJ3UV42PRl26GSyCq5JUoW6UghuXFewD2lgm0k7dB5hZiLU0C9x40IRt36KO/GaZuFth64cDjnXu69J0oY1cb3v53C2vrG5lZx293Z3dsveQeHLS1ThUkTSyZVJ0KaMCpI01DSCdRBPGIkXY0vpn57UeiNJXi3kwSEnI0FDSmGBkr9b1Sb4g4R/AK1vwH6cK+V/Yr/hxwlQ5KYMcjb731RtInHIiDGZI627gJybMkDIUMzJ1e6kmCcJjNCRdSwXiRIfZ/PApPLXKAMZS2RIGztXfExniWk94ZDs5MiO97M3E/7xuauLMKMiSQ0ReLEoThk0Es5SgAOqCDZsYgnCitpbIR4hbCxWbk2hGD5VXSqlaC80r17qJcv87jKIJjcALOQABqoA5uQM0AQYpeAav4M15cl6cd+dj0Vpw8pkj8AfO5w84LpF7</latexit>

a0 = 2 ei(δs=45o)

<latexit sha1_base64="QU+cSdSBW1Yhv6a7OED6Jvua6w=">ACD3icbVDJSgNBEO1xjXGLevTSGJQIczEiF6UgBePEcwCmcnQ01NJmvQsdPcIYcgfePFXvHhQxKtXb/6NneWgiQ8KHu9VUVXPizmTyjS/jaXldW19cxGdnNre2c3t7fkFEiKNRpxCPR8ogEzkKoK6Y4tGIBJPA4NL3BzdhvPoCQLArv1TAGJyC9kHUZJUpLbu4EY+Ka+AqXsV2ETsoKtg9cEVdqrXLeiU5HdhFn3VzeLJkT4EVizUgezVBzc1+2H9EkgFBRTqRsW2asnJQIxSiHUdZOJMSEDkgP2pqGJADpJN/RvhYKz7uRkJXqPBE/T2RkDKYeDpzoCovpz3xuJ/XjtR3UsnZWGcKAjpdFE34VhFeBwO9pkAqvhQE0IF07di2ieCUKUjHIdgzb+8SBrlknVWKt9V8tXrWRwZdIiOUAFZ6AJV0S2qoTqi6BE9o1f0ZjwZL8a78TFtXTJmMwfoD4zPH9cnmMA=</latexit>

5 10 15 20 25

)

4

/c

2

high (GeV

  • π

+

π 2

m

50 100 150 200 250 300 350 400

Amplitude projection B+ B- Amplitude projection

0.5 − 0.4 − 0.3 − 0.2 − 0.1 − 0.1 0.2 0.3 0.4 0.5

N raw

A

5 10 15

]

4

c /

2

[GeV

low

)

−

π

+

π (

2

m

5 10 15 20 25

]

4

c /

2

[GeV

high

)

−

π

+

π (

2

m

0.5 − 0.4 − 0.3 − 0.2 − 0.1 − 0.1 0.2 0.3 0.4 0.5

N raw

A

Acp signature

slide-26
SLIDE 26

Birmingham - 17/06/2020

Patricia Magalhães

3-body hadronic decay 26

*+(0)

0(−)

D D 0(+) B+

+

D

+ −

π π π

+

= a0 e±iγ

AB±→π−π+π±(s12, s23) =

a0 = 2 e(δs=45o)

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γ = 70o

<latexit sha1_base64="O/sueISK23c0NLbXRTVbvh0DFPM=">AB+HicbVDLSsNAFJ3UV42PRl26GSyCq5JUoW6UghuXFewD2lgm0k7dB5hZiLU0C9x40IRt36KO/GaZuFth64cDjnXu69J0oY1cb3v53C2vrG5lZx293Z3dsveQeHLS1ThUkTSyZVJ0KaMCpI01DSCdRBPGIkXY0vpn57UeiNJXi3kwSEnI0FDSmGBkr9b1Sb4g4R/AK1vwH6cK+V/Yr/hxwlQ5KYMcjb731RtInHIiDGZI627gJybMkDIUMzJ1e6kmCcJjNCRdSwXiRIfZ/PApPLXKAMZS2RIGztXfExniWk94ZDs5MiO97M3E/7xuauLMKMiSQ0ReLEoThk0Es5SgAOqCDZsYgnCitpbIR4hbCxWbk2hGD5VXSqlaC80r17qJcv87jKIJjcALOQABqoA5uQM0AQYpeAav4M15cl6cd+dj0Vpw8pkj8AfO5w84LpF7</latexit>

0.5 − 0.4 − 0.3 − 0.2 − 0.1 − 0.1 0.2 0.3 0.4 0.5

N raw

A

5 10 15

]

4

c /

2

[GeV

low

)

−

π

+

π (

2

m

5 10 15 20 25

]

4

c /

2

[GeV

high

)

−

π

+

π (

2

m

0.5 − 0.4 − 0.3 − 0.2 − 0.1 − 0.1 0.2 0.3 0.4 0.5

N raw

A

  • ur model
  • 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

Run I mimic some of the CPV pattern at high mass

Results

not the same binning and scale

should be included in amplitude analysis of Run II data to confirm or disprove

slide-27
SLIDE 27

Birmingham - 17/06/2020

Patricia Magalhães

3-body hadronic decay 27

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

+ interference between charm loop and nonresonant can give a similar CPV signature observed in data Charm rescattering triangles is an important FSI mechanism

final remarks

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−

+

slide-28
SLIDE 28

Birmingham - 17/06/2020

Patricia Magalhães

3-body hadronic decay 28

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!

Successful examples of cooperation between theory and experiment !!! Important tool ! Lots of theoretical limitations to be developed:

need to merge the short and long distance descriptions!

extend the meson-meson interaction to high E, …

  • brigada!!

Thank you!

#staysafe #BlackLifesMatter

slide-29
SLIDE 29

Birmingham - 17/06/2020

Patricia Magalhães

3-body hadronic decay 29

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

slide-30
SLIDE 30

Birmingham - 17/06/2020

Patricia Magalhães

3-body hadronic decay 30

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 KKp if needed