Juan Martin Otalora Goicochea - XXXV ENFPC 1/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

CP Violationin Charmless 3-body B decays

Juan Martin Otalora Goicochea(Campus Xerem, UFRJ)

XXXV Encontro Nacional de Fısica de Partıculas e Campos,September 17, 2014

B± → h+h−h± LHCb Brazilian Group

Juan Martin Otalora Goicochea - XXXV ENFPC 2/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

Outline

• Theory and Techniques

• The LHCb Detector

• B± → h+h−h± decays. (h = K , π)• B± → pph± decays.

Juan Martin Otalora Goicochea - XXXV ENFPC 2/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

Theory and Techniques

Juan Martin Otalora Goicochea - XXXV ENFPC 3/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

Introduction

• CP Violation (Sakharov, Baryogenesys)

• Discovered 1964 (neutral kaons)

• Standard Model CPV (CKM matrix)

• SM CPV (insufficient, Universe)

• CKM matrix: D (small or null), B (measurable)

• 3-body decays are interesting (signatures in Dalitz Plot)

Juan Martin Otalora Goicochea - XXXV ENFPC 4/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

Conditions for Direct CP Violation• In charged B decays, we have multiple amplitudes :

A(B → f ) = |A1|e i(δ1+φ1) + |A2|e i(δ2+φ2) + |A3|e i(δ3+φ3) + ...

• Strong phases (δi ) are invariant under CP Transformation: δi → δi• Weak phases (φi ) change sign under CP Transformation: φi → −φi

A(B → f ) = |A1|e i(δ1−φ1) + |A2|e i(δ2−φ2) + |A3|e i(δ3−φ3) + ...

• The Asymmetry can be calculated as:

ACP(B → f ) =|A|2 − |A|2

|A|2 + |A|2∝

∑ij

sin(δi − δj)sin(φi − φj)

• Conditions for Direct CP Violation:

1) At least two amplitudes.2) Non-zero weak phase difference, φi − φj 6= 03) Non-zero strong phase difference, δi − δj 6= 0

Juan Martin Otalora Goicochea - XXXV ENFPC 5/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

BSS Model for the B± → π+π−π±decay

b → duu

W

u

B−

b

u

ππ

u

dπ−

u

Vub

Vud

tree diagram

g

W

u

B−

b

uππ

u

uπ−d

Vqb Vqd

penguin diagram

1) At least two amplitudes. Tree x Pengin

• In both diagrams: Initial State: B meson, Final State: πππ

• BSS model: b is considered as free. u is considered an espectator (quark level)

2) Non-zero week phase difference: CKM: AT ∝ VubVud , AP ∝ VqbVqd , q = u, c, t.

3) Non-zero strong phase difference: (penguin: q on its mass shell (u, c for b decays)).

Source of δi − δj 6= 0 are Short Distance Effects.!!!

Juan Martin Otalora Goicochea - XXXV ENFPC 6/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

Dalitz Plot

Juan Martin Otalora Goicochea - XXXV ENFPC 7/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

Dalitz Plot

Isobar Model: the decay amplitude is a coherent sum of a non-resonant amplitude plusresonant amplitudes:

A(s12, s23) = cnrANR(s12, s23) +∑k

ckAk(s12, s23)

Juan Martin Otalora Goicochea - XXXV ENFPC 8/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

Amplitude Analysis

A(s12, s23) = cnrANR(s12, s23) +∑k

ckAk(s12, s23)

FB(s12, s23)FR(s12, s23)BW (s12, s23)M(s12, s23)

Fitting the model to data (DP plane) we obtain the complex coefficients cnr , ck wich tell usthe contribution of ressonances.

Asymmetry : In order to consider asymmetry we define a contribution for theparticle and the antiparticle:

A(s12, s23) =∑j

cjAj(s12, s23)︸ ︷︷ ︸B+sample

+∑j

cjAj(s12, s23)︸ ︷︷ ︸B−sample

, Aj (s12, s23) = Aj (s12, s23)

cj and cj contains weak and strong phases.

ACP =|cj |2−|cj |2|cj |2+|cj |2

Juan Martin Otalora Goicochea - XXXV ENFPC 9/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

Asymmetry Map from Mirandizing MethodPhys.Rev.D 86,036005(2012).I.Bediaga, J.Miranda, A.C.dosReis, I.I.Bigi, A.Gomes, J.M.Otalora Goicochea, and A.Veiga.

• Histogram performed by an adaptive binning algorithm.

• Each bin contains the same number of events.

• The asymmetry was calculated from the evens inside the bin.

• The vertical color scale tell us the asymmetry value.

Juan Martin Otalora Goicochea - XXXV ENFPC 9/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

LHCb Experiment

Juan Martin Otalora Goicochea - XXXV ENFPC 10/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

The LHCb Detector• Single-arm forward spectrometer (2 < η < 5),

• Designed to study particles containing b and c quarks

• Includes a High precision tracking system

• Ring Imaging Cherenkov Detectors (charged hadrons)

• Calorimeter System (photons, electrons and hadrons)

• Muon System, interleaved layers of iron and MWPC (muons)

2011: 1 fb−1,√s = 7 TeV

2012: 2 fb−1,√s = 8 TeV

Juan Martin Otalora Goicochea - XXXV ENFPC 10/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

The LHCb Detector• Single-arm forward spectrometer (2 < η < 5),

• Designed to study particles containing b and c quarks

• Includes a High precision tracking system

• Ring Imaging Cherenkov Detectors (charged hadrons)

• Calorimeter System (photons, electrons and hadrons)

• Muon System, interleaved layers of iron and MWPC (muons)

2011: 1 fb−1,√s = 7 TeV

2012: 2 fb−1,√s = 8 TeV

VertexDetector

Tracking Stations

Magnet

Juan Martin Otalora Goicochea - XXXV ENFPC 10/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

The LHCb Detector• Single-arm forward spectrometer (2 < η < 5),

• Designed to study particles containing b and c quarks

• Includes a High precision tracking system

• Ring Imaging Cherenkov Detectors (charged hadrons)

• Calorimeter System (photons, electrons and hadrons)

• Muon System, interleaved layers of iron and MWPC (muons)

2011: 1 fb−1,√s = 7 TeV

2012: 2 fb−1,√s = 8 TeV

Rich1 Rich2

Juan Martin Otalora Goicochea - XXXV ENFPC 10/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

The LHCb Detector• Single-arm forward spectrometer (2 < η < 5),

• Designed to study particles containing b and c quarks

• Includes a High precision tracking system

• Ring Imaging Cherenkov Detectors (charged hadrons)

• Calorimeter System (photons, electrons and hadrons)

• Muon System, interleaved layers of iron and MWPC (muons)

2011: 1 fb−1,√s = 7 TeV

2012: 2 fb−1,√s = 8 TeV

SP, PS

ECal

HCal

Juan Martin Otalora Goicochea - XXXV ENFPC 10/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

The LHCb Detector• Single-arm forward spectrometer (2 < η < 5),

• Designed to study particles containing b and c quarks

• Includes a High precision tracking system

• Ring Imaging Cherenkov Detectors (charged hadrons)

• Calorimeter System (photons, electrons and hadrons)

• Muon System, interleaved layers of iron and MWPC (muons)

2011: 1 fb−1,√s = 7 TeV

2012: 2 fb−1,√s = 8 TeV

MuonSystem

Juan Martin Otalora Goicochea - XXXV ENFPC 10/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

B±→ h+h−h± decays.

Juan Martin Otalora Goicochea - XXXV ENFPC 11/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

Inclusive CP asymmetry [arXiv:1408.5373]Measurement of the raw CP asymmetry from simultaneous mass fit to B+ and B−

candidates:Araw =

NB−−NB+

NB−+NB+

.

.

]2c) [GeV/−π+π−(Km

5.1 5.2 5.3 5.4 5.5

310×

)2 cC

andi

date

s / (

0.01

GeV

/

02468

1012141618

310× LHCb

]2c) [GeV/−π+π+(Km

5.1 5.2 5.3 5.4 5.5

310×

model−π+π± K→ ±B

combinatorial 4-body→B

±)Kγ0ρ'(η → ±B ±π−π+π → ±B

B− → K−π+π− B+ → K+π+π−Nsig = 181 074± 556

]2c) [GeV/−π+π−π(m

5.1 5.2 5.3 5.4 5.5

310×

)2 cC

andi

date

s / (

0.01

GeV

/

0

0.5

1

1.5

2

2.5

3310×

LHCb

]2c) [GeV/−π+π+π(m

5.1 5.2 5.3 5.4 5.5

310×

model±π−π+π → ±B

combinatorial

4-body→B −π+π± K→ ±B

Nsig = 24 907± 222B− → π−π+π− B+ → π+π+π−

]2c) [GeV/−K+K−(Km

5.1 5.2 5.3 5.4 5.5

310×

)2 cC

andi

date

s / (

0.01

GeV

/

0

2

4

6

8

10

12

310× LHCb

]2c) [GeV/−K+K+(Km

5.1 5.2 5.3 5.4 5.5

310×

model−

K+K± K→ ±Bcombinatorial

4-body→B ±π−

K+ K→ ±B−π+π± K→ ±B

B− → K−K+K− B+ → K+K+K−Nsig = 109 240± 354

]2c) [GeV/−π+K−(Km

5.1 5.2 5.3 5.4 5.5

310×

)2 cC

andi

date

s / (

0.01

GeV

/

0

0.2

0.4

0.6

0.8

1310×

LHCb

]2c) [GeV/−π+K+(Km

5.1 5.2 5.3 5.4 5.5

310×

model±π−

K+ K→ ±Bcombinatorial

4-body→ SB 4-body→B

−K+K± K→ ±B

−π+π± K→ ±B

B− → K−K+π− B+ → K+K+π−Nsig = 6 161± 172

Juan Martin Otalora Goicochea - XXXV ENFPC 11/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

Inclusive CP asymmetry [arXiv:1408.5373]Measurement of the raw CP asymmetry from simultaneous mass fit to B+ and B−

candidates:Araw =

NB−−NB+

NB−+NB+

.

.

]2c) [GeV/−π+π−(Km

5.1 5.2 5.3 5.4 5.5

310×

)2 cC

andi

date

s / (

0.01

GeV

/

02468

1012141618

310× LHCb

]2c) [GeV/−π+π+(Km

5.1 5.2 5.3 5.4 5.5

310×

model−π+π± K→ ±B

combinatorial 4-body→B

±)Kγ0ρ'(η → ±B ±π−π+π → ±B

B− → K−π+π− B+ → K+π+π−Nsig = 181 074± 556

]2c) [GeV/−π+π−π(m

5.1 5.2 5.3 5.4 5.5

310×

)2 cC

andi

date

s / (

0.01

GeV

/

0

0.5

1

1.5

2

2.5

3310×

LHCb

]2c) [GeV/−π+π+π(m

5.1 5.2 5.3 5.4 5.5

310×

model±π−π+π → ±B

combinatorial

4-body→B −π+π± K→ ±B

Nsig = 24 907± 222B− → π−π+π− B+ → π+π+π−

]2c) [GeV/−K+K−(Km

5.1 5.2 5.3 5.4 5.5

310×

)2 cC

andi

date

s / (

0.01

GeV

/

0

2

4

6

8

10

12

310× LHCb

]2c) [GeV/−K+K+(Km

5.1 5.2 5.3 5.4 5.5

310×

model−

K+K± K→ ±Bcombinatorial

4-body→B ±π−

K+ K→ ±B−π+π± K→ ±B

B− → K−K+K− B+ → K+K+K−Nsig = 109 240± 354

]2c) [GeV/−π+K−(Km

5.1 5.2 5.3 5.4 5.5

310×

)2 cC

andi

date

s / (

0.01

GeV

/

0

0.2

0.4

0.6

0.8

1310×

LHCb

]2c) [GeV/−π+K+(Km

5.1 5.2 5.3 5.4 5.5

310×

model±π−

K+ K→ ±Bcombinatorial

4-body→ SB 4-body→B

−K+K± K→ ±B

−π+π± K→ ±B

B− → K−K+π− B+ → K+K+π−Nsig = 6 161± 172

Juan Martin Otalora Goicochea - XXXV ENFPC 12/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

Inclusive CP asymmetry [arXiv:1408.5373]

• The raw asymmetry has to be corrected for the B-meson production asymmetry and thedetector asymmetry :

Araw ≈ ACP +AP +Ah′D

• Decays divided into two categories depending on the flavour of the unpaired hadron:

B± → h+h−K± ACP = Araw −AP(B±)−AD(K±)B± → h+h−π± ACP = Araw −AP(B±)−AD(π±)

• AP (B) from B → J/ψ(µµ)K studies and using AD (K) = (−0.126± 0.018)% [PRL 108 (2012) 201601]

• AD (π) = (0.00± 0.25)% from studies of prompt D∗ decays [PLB 713 (2012) 186]

• Acceptance correction to take into account non uniformity of efficiencies and rawasymmetries in the phase space

2.8σ

4.3σ

4.2σ

5.6σ

Juan Martin Otalora Goicochea - XXXV ENFPC 13/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

Dalitz Plot [arXiv:1408.5373]

Dalitz plots in the signal region with bkg: ±34 MeV/c2 (hhh and hhK), ±17 MeV/c2 (πKK)

]4c/2) [GeV−π+π(2m0 10 20

]4 c/2)

[GeV

− π+(K2

m

0

5

10

15

20

25

30

Ent

ries

1

10

210LHCb

Kππ

]4c/2 low) [GeV−π+π(2m0 5 10 15

]4 c/2 h

igh)

[G

eV− π+ π(2

m

0

5

10

15

20

25E

ntri

es

-110

1

10

LHCb

πππ

]4c/2 low) [GeV−K+(K2m0 5 10 15

]4 c/2 h

igh)

[G

eV−

K+(K2

m

0

5

10

15

20

25

Ent

ries

1

10

210

LHCb

KKK

]4c/2) [GeV−π+(K2m0 10 20

]4 c/2)

[GeV

−K+

(K2m

0

5

10

15

20

25

30

Ent

ries

-110

1

10LHCb

KKπ

Juan Martin Otalora Goicochea - XXXV ENFPC 13/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

Dalitz Plot [arXiv:1408.5373]

Dalitz plots in the signal region with bkg: ±34 MeV/c2 (hhh and hhK), ±17 MeV/c2 (πKK)

]4c/2) [GeV−π+π(2m0 10 20

]4 c/2)

[GeV

− π+(K2

m

0

5

10

15

20

25

30

Ent

ries

1

10

210LHCb

KππK∗0

]4c/2 low) [GeV−π+π(2m0 5 10 15

]4 c/2 h

igh)

[G

eV− π+ π(2

m

0

5

10

15

20

25E

ntri

es

-110

1

10

LHCb

πππ

]4c/2 low) [GeV−K+(K2m0 5 10 15

]4 c/2 h

igh)

[G

eV−

K+(K2

m

0

5

10

15

20

25

Ent

ries

1

10

210

LHCb

KKK

]4c/2) [GeV−π+(K2m0 10 20

]4 c/2)

[GeV

−K+

(K2m

0

5

10

15

20

25

30

Ent

ries

-110

1

10LHCb

KKπK∗0(892)

K∗0(1430)

Juan Martin Otalora Goicochea - XXXV ENFPC 13/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

Dalitz Plot [arXiv:1408.5373]

Dalitz plots in the signal region with bkg: ±34 MeV/c2 (hhh and hhK), ±17 MeV/c2 (πKK)

]4c/2) [GeV−π+π(2m0 10 20

]4 c/2)

[GeV

− π+(K2

m

0

5

10

15

20

25

30

Ent

ries

1

10

210LHCb

Kππρ0(770)

f0(980)

]4c/2 low) [GeV−π+π(2m0 5 10 15

]4 c/2 h

igh)

[G

eV− π+ π(2

m

0

5

10

15

20

25E

ntri

es

-110

1

10

LHCb

πππρ0(770)

ρ0(1450)

]4c/2 low) [GeV−K+(K2m0 5 10 15

]4 c/2 h

igh)

[G

eV−

K+(K2

m

0

5

10

15

20

25

Ent

ries

1

10

210

LHCb

KKK

]4c/2) [GeV−π+(K2m0 10 20

]4 c/2)

[GeV

−K+

(K2m

0

5

10

15

20

25

30

Ent

ries

-110

1

10LHCb

KKπ

Juan Martin Otalora Goicochea - XXXV ENFPC 13/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

Dalitz Plot [arXiv:1408.5373]

Dalitz plots in the signal region with bkg: ±34 MeV/c2 (hhh and hhK), ±17 MeV/c2 (πKK)

]4c/2) [GeV−π+π(2m0 10 20

]4 c/2)

[GeV

− π+(K2

m

0

5

10

15

20

25

30

Ent

ries

1

10

210LHCb

Kππχc0(1P)

]4c/2 low) [GeV−π+π(2m0 5 10 15

]4 c/2 h

igh)

[G

eV− π+ π(2

m

0

5

10

15

20

25E

ntri

es

-110

1

10

LHCb

πππ

]4c/2 low) [GeV−K+(K2m0 5 10 15

]4 c/2 h

igh)

[G

eV−

K+(K2

m

0

5

10

15

20

25

Ent

ries

1

10

210

LHCb

KKKχc0(1P)

]4c/2) [GeV−π+(K2m0 10 20

]4 c/2)

[GeV

−K+

(K2m

0

5

10

15

20

25

30

Ent

ries

-110

1

10LHCb

KKπ

Juan Martin Otalora Goicochea - XXXV ENFPC 13/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

Dalitz Plot [arXiv:1408.5373]

Dalitz plots in the signal region with bkg: ±34 MeV/c2 (hhh and hhK), ±17 MeV/c2 (πKK)

]4c/2) [GeV−π+π(2m0 10 20

]4 c/2)

[GeV

− π+(K2

m

0

5

10

15

20

25

30

Ent

ries

1

10

210LHCb

Kππ

]4c/2 low) [GeV−π+π(2m0 5 10 15

]4 c/2 h

igh)

[G

eV− π+ π(2

m

0

5

10

15

20

25E

ntri

es

-110

1

10

LHCb

πππ

]4c/2 low) [GeV−K+(K2m0 5 10 15

]4 c/2 h

igh)

[G

eV−

K+(K2

m

0

5

10

15

20

25

Ent

ries

1

10

210

LHCb

KKKφ(1020)

J/ψ

]4c/2) [GeV−π+(K2m0 10 20

]4 c/2)

[GeV

−K+

(K2m

0

5

10

15

20

25

30

Ent

ries

-110

1

10LHCb

KKπJ/ψ

Juan Martin Otalora Goicochea - XXXV ENFPC 14/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

CP asymmetries in the phase space [arXiv:1408.5373]

• Also background subtracted (SPlot) and efficiency corrected

N raw

A

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.81

]4c/2) [GeV−π+π(2m0 5 10 15 20

]4 c/2)

[GeV

− π+(K2

m

0

5

10

15

20

25

N raw

A

-1

-0.8

-0.6

-0.4

-0.2

0

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0.6

0.81

LHCb

Kππ

N raw

A

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.81

]4c/2 low) [GeV−π+π(2m0 5 10 15

]4 c/2 h

igh)

[G

eV− π+ π(2

m

0

5

10

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25

N raw

A

-1

-0.8

-0.6

-0.4

-0.2

0

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0.81

LHCb

πππ

N raw

A

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.81

]4c/2 low) [GeV−

K+(K2m0 5 10 15

]4 c/2 h

igh)

[G

eV−

K+(K2

m

0

5

10

15

20

25

N raw

A

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

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0.81

LHCb

KKK

N raw

A

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.81

]4c/2) [GeV−

K+(K2m0 10 20

]4 c/2)

[GeV

− π+(K2

m

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25

N raw

A

-1

-0.8

-0.6

-0.4

-0.2

0

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0.81

LHCb

KKπ

Juan Martin Otalora Goicochea - XXXV ENFPC 14/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

CP asymmetries in the phase space [arXiv:1408.5373]

Large asymmetries at low m2ππ Large asymmetries at low m2

KK

N raw

A

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.81

]4c/2) [GeV−π+π(2m0 5 10 15 20

]4 c/2)

[GeV

− π+(K2

m

0

5

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N raw

A

-1

-0.8

-0.6

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-0.2

0

0.2

0.4

0.6

0.81

LHCb

Kππ

N raw

A

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.81

]4c/2 low) [GeV−π+π(2m0 5 10 15

]4 c/2 h

igh)

[G

eV− π+ π(2

m

0

5

10

15

20

25N ra

wA

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.81

LHCb

πππ

N raw

A

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.81

]4c/2 low) [GeV−

K+(K2m0 5 10 15

]4 c/2 h

igh)

[G

eV−

K+(K2

m

0

5

10

15

20

25

N raw

A

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.81

LHCb

KKK

N raw

A

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.81

]4c/2) [GeV−

K+(K2m0 10 20

]4 c/2)

[GeV

− π+(K2

m

0

5

10

15

20

25

N raw

A

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.81

LHCb

KKπ

Juan Martin Otalora Goicochea - XXXV ENFPC 15/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

Interference

• Zoom at low mass region. Asymmetry is more evident.

N raw

A

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.81

]4c/2) [GeV−π+π(2m0 1 2 3

]4 c/2)

[GeV

− π+(K2

m

0

5

10

15

20

25 LHCb

Kππ

N raw

A

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.81

]4c/2 [GeVlow

)−π+π(2m0 1 2 3

]4 c/2 [

GeV

high

)− π+ π(2m

0

5

10

15

20

25 LHCb

πππ

N raw

A

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.81

]4c/2 [GeVlow

)−

K+(K2m1 2 3

]4 c/2 [

GeV

high

)−K+

(K2m

2468

1012141618202224

LHCb

KKK

N raw

A

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.81

]4c/2) [GeV−

K+(K2m1 2 3

]4 c/2)

[GeV

− π+(K2

m

02468

1012141618202224

LHCb

KKπ

Juan Martin Otalora Goicochea - XXXV ENFPC 15/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

Interference• The behavior of all channels change at midle of the vertical range

N raw

A

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.81

]4c/2) [GeV−π+π(2m0 1 2 3

]4 c/2)

[GeV

− π+(K2

m

0

5

10

15

20

25 LHCb

Kππ

N raw

A

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.81

]4c/2 [GeVlow

)−π+π(2m0 1 2 3

]4 c/2 [

GeV

high

)− π+ π(2m

0

5

10

15

20

25 LHCb

πππ

N raw

A

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.81

]4c/2 [GeVlow

)−

K+(K2m1 2 3

]4 c/2 [

GeV

high

)−K+

(K2m

2468

1012141618202224

LHCb

KKK

N raw

A

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.81

]4c/2) [GeV−

K+(K2m1 2 3

]4 c/2)

[GeV

− π+(K2

m

02468

1012141618202224

LHCb

KKπ

Juan Martin Otalora Goicochea - XXXV ENFPC 16/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

Interference: B± → π+π−π±

N raw

A

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.81

]4c/2 [GeVlow

)−π+π(2m0 1 2 3

]4 c/2 [

GeV

high

)− π+ π(2m

0

5

10

15

20

25 LHCb

πππ

Juan Martin Otalora Goicochea - XXXV ENFPC 16/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

Interference: B± → π+π−π±

N raw

A

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.81

]4c/2 [GeVlow

)−π+π(2m0 1 2 3

]4 c/2 [

GeV

high

)− π+ π(2m

0

5

10

15

20

25 LHCb

πππ

ρ0

Juan Martin Otalora Goicochea - XXXV ENFPC 16/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

Interference: B± → π+π−π±

N raw

A

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.81

]4c/2 [GeVlow

)−π+π(2m0 1 2 3

]4 c/2 [

GeV

high

)− π+ π(2m

0

5

10

15

20

25 LHCb

πππ

ρ0

I II

III IV

Juan Martin Otalora Goicochea - XXXV ENFPC 17/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

Interference: B± → π+π−π±co

sθ>

0co

sθ<

0

0.47 < mππlowGeV /c2 < 0.77

]2c) [GeV/−π+π−π(m

5.1 5.2 5.3 5.4 5.5

310×

)2 cC

andi

date

s / (

0.01

GeV

/

0

50100

150200

250

300350 LHCb

]2c) [GeV/−π+π+π(m

5.1 5.2 5.3 5.4 5.5

310×

model±π−π+π → ±B

combinatorial

4-body→B −π+π± K→ ±B

]2c) [GeV/−π+π−π(m

5.1 5.2 5.3 5.4 5.5

310×

)2 cC

andi

date

s / (

0.01

GeV

/

0

100

200

300

400

500

600 LHCb

]2c) [GeV/−π+π+π(m

5.1 5.2 5.3 5.4 5.5

310×

model±π−π+π → ±B

combinatorial

4-body→B −π+π± K→ ±B

0.77 < mππlowGeV /c2 < 0.92

]2c) [GeV/−π+π−π(m

5.1 5.2 5.3 5.4 5.5

310×

)2 cC

andi

date

s / (

0.01

GeV

/

0

50

100

150

200

250 LHCb

]2c) [GeV/−π+π+π(m

5.1 5.2 5.3 5.4 5.5

310×

model±π−π+π → ±B

combinatorial

4-body→B −π+π± K→ ±B

]2c) [GeV/−π+π−π(m

5.1 5.2 5.3 5.4 5.5

310×

)2 cC

andi

date

s / (

0.01

GeV

/

0

100

200

300

400

500 LHCb

]2c) [GeV/−π+π+π(m

5.1 5.2 5.3 5.4 5.5

310×

model±π−π+π → ±B

combinatorial

4-body→B −π+π± K→ ±B

I

III

II

IV

Juan Martin Otalora Goicochea - XXXV ENFPC 18/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

Interference: B± → π+π−π± (Simple Isobar Model)

B+: A+ = Aρ+eiΦρ+FBW

ρ cos θ + Anr+ e iΦ

nr+ Fnr

B−: A− = Aρ−eiΦρ−FBW

ρ cos θ + Anr− e

iΦnr−Fnr

The phase (Φ) contains the weak (φ) and strong (δ) phases.

FBWρ = 1

m2ρ−s−imρΓρ(s) Fnr = 1

Juan Martin Otalora Goicochea - XXXV ENFPC 19/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

Interference: B± → π+π−π± (Simple Isobar Model)

• Diference of magnitudes(Short Distance Effect)

∆|A+|2 = |A+|2 − |A−|2 = [(Aρ+)2 − (Aρ−)2] |FBWρ |2 cos2 θ + [(Anr

+ )2 − (Anr+ )2]|Fnr |2+

2 cos θ|FBWρ |2|Fnr |{

(m2ρ − s) [Aρ+Anr

+ cos(Φρ+ − Φnr+ )− Aρ−A

nr− cos(Φρ− − Φnr

−)]−

mρΓρ [Aρ+Anr+ sin(Φρ+ − Φnr

+ )− Aρ−Anr− sin(Φρ− − Φnr

−)]}

• Real part of the BW(Long Distance Effect)

• Imag part of the BW(Long Distance Effect)

Juan Martin Otalora Goicochea - XXXV ENFPC 20/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

Interference: B± → π+π−π± (Simple Isobar Model)

Monte Carlo simulation for the short distance term:

ACP ∝ [(Aρ+)2 − (Aρ−)2]|FBWρ |2 cos2 θ + ...

−2(m2ρ − s)|FBW

ρ |2|Fnr |2 cos θ...

+2mρΓρ|FBWρ |2|Fnr |2 cos θ...

• If it were the dominant term, we should see a peak at the ρ mass.

• The peak should has the same sign for cos θ > 0 and for cos θ < 0

Juan Martin Otalora Goicochea - XXXV ENFPC 21/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

Interference: B± → π+π−π± (Simple Isobar Model)

Monte Carlo simulation for the long distance term (Re BW):

ACP ∝ [(Aρ+)2 − (Aρ−)2]|FBWρ |2 cos2 θ + ...

−2(m2ρ − s)|FBW

ρ |2|Fnr |2 cos θ...

+2mρΓρ|FBWρ |2|Fnr |2 cos θ...

• In this case, we should see an interferent pattern with asymmetry zero at the ρ mass.

• For cos θ > 0 the asymmetry is (+) below the ρ mass and (-) above.

• For cos θ < 0 the behaviour is oposite.

Juan Martin Otalora Goicochea - XXXV ENFPC 22/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

Interference: B± → π+π−π± (Simple Isobar Model)

Monte Carlo simulation for the long distance term (Im BW):

ACP ∝ [(Aρ+)2 − (Aρ−)2]|FBWρ |2 cos2 θ + ...

−2(m2ρ − s)|FBW

ρ |2|Fnr |2 cos θ...

+2mρΓρ|FBWρ |2|Fnr |2 cos θ...

• In this case, also we should see a peak at the ρ mass.

• But the peak has oposite sign for cos θ > 0 and cos θ < 0.

Juan Martin Otalora Goicochea - XXXV ENFPC 23/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

Interference: B± → π+π−π± (Simple Isobar Model)

Long distance term (Re BW))

Juan Martin Otalora Goicochea - XXXV ENFPC 23/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

Interference: B± → π+π−π± (Simple Isobar Model)

Long-distance effectsplay an important rolegenerating strongphase.

Juan Martin Otalora Goicochea - XXXV ENFPC 24/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

Rescattering ππ → KK

Large asymmetries: 1 < mππ < 1.5 Large asymmetries: 1 < mKK < 1.5

N raw

A

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.81

]4c/2) [GeV−π+π(2m0 1 2 3

]4 c/2)

[GeV

− π+(K2

m

0

5

10

15

20

25 LHCb

Kππ

N raw

A

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.81

]4c/2 [GeVlow

)−π+π(2m0 1 2 3

]4 c/2 [

GeV

high

)− π+ π(2m

0

5

10

15

20

25 LHCb

πππ

N raw

A

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.81

]4c/2 [GeVlow

)−

K+(K2m1 2 3

]4 c/2 [

GeV

high

)−K+

(K2m

2468

1012141618202224

LHCb

KKK

N raw

A

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.81

]4c/2) [GeV−

K+(K2m1 2 3

]4 c/2)

[GeV

− π+(K2

m

02468

1012141618202224

LHCb

KKπ

Juan Martin Otalora Goicochea - XXXV ENFPC 25/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

Rescattering ππ → KK

Invariant masses with ππ and KK in the “rescattering region”: (1.0− 1.5)GeV /c2

ACP(Kππ) = +0.121± 0.012± 0.017± 0.007

]2c) [GeV/−π+π−(Km

5.1 5.2 5.3 5.4 5.5

310×

)2 cC

andi

date

s / (

0.01

GeV

/

00.20.40.60.8

11.21.41.61.8

310× LHCb

]2c) [GeV/−π+π+(Km

5.1 5.2 5.3 5.4 5.5

310×

model−π+π± K→ ±B

combinatorial 4-body→B

±)Kγ0ρ'(η → ±B ±π−π+π → ±B

ACP(πππ) = +0.172± 0.021± 0.015± 0.007

]2c) [GeV/−π+π−π(m

5.1 5.2 5.3 5.4 5.5

310×

)2 cC

andi

date

s / (

0.01

GeV

/

0

100

200

300

400

500 LHCb

]2c) [GeV/−π+π+π(m

5.1 5.2 5.3 5.4 5.5

310×

model±π−π+π → ±B

combinatorial

4-body→B −π+π± K→ ±B

ACP(KKK) = −0.211± 0.011± 0.004± 0.007

]2c) [GeV/−K+K−(Km

5.1 5.2 5.3 5.4 5.5

310×

)2 cC

andi

date

s / (

0.01

GeV

/

00.20.40.60.8

11.21.41.61.8

22.22.4

310× LHCb

]2c) [GeV/−K+K+(Km

5.1 5.2 5.3 5.4 5.5

310×

model−

K+K± K→ ±Bcombinatorial

4-body→B ±π−

K+ K→ ±B−π+π± K→ ±B

ACP(πKK) = −0.328± 0.028± 0.029± 0.007

]2c) [GeV/−π+K−(Km

5.1 5.2 5.3 5.4 5.5

310×

)2 cC

andi

date

s / (

0.01

GeV

/

050

100150200250300350400 LHCb

]2c) [GeV/−π+K+(Km

5.1 5.2 5.3 5.4 5.5

310×

model±π−

K+ K→ ±Bcombinatorial

4-body→ SB 4-body→B

−K+K± K→ ±B

−π+π± K→ ±B

All the asymmetries have more than 5σ of significance

Juan Martin Otalora Goicochea - XXXV ENFPC 26/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

Scattering and CPT constraintHigh local asymmetries not obviously associated to resonances.

positive for K± π+π− negative for K± K+K−

positive for π+π− π± negative for K+K−π±∑f

(i)α ∈Fi

Γ(P → f (i)α ) =

∑f

(i)α ∈Fi

Γ(P → f (i)α ) (Bigi & Sanda 2nd edition pp 57)

all fα in Fi connected via stronginteractions

for two modes ππ and KK : Γ(A+ππ) + Γ(A+

KK ) = Γ(A−ππ) + Γ(A−KK ) , then:

∆Γππ = −∆ΓKK

I.Bediaga, T.Frederico, O.Lourenco, Phys.Rev.D 89,094013 (2014)

∆ΓKK = (sinγ)√

1− η2cos(δKK + δππ + Φ)F (M2KK ) (Inelasticity and Unitarity)

Juan Martin Otalora Goicochea - XXXV ENFPC 26/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

B±→ pph± decays.

Juan Martin Otalora Goicochea - XXXV ENFPC 27/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

B± → pph± decays• Yields extracted with an unbinned maximum likelihood fit

]2 [GeV/c±Kppm5.1 5.2 5.3 5.4 5.5

)2C

and

idat

es /

(0.0

1 G

eV/c

0

500

1000

1500

2000

2500

3000

3500

4000

4500

LHCbB+ → ppK+

]2 [GeV/c±πppm5.1 5.2 5.3 5.4 5.5

)2C

and

idat

es /

(0.0

1 G

eV/c

0

100

200

300

400

500

600

700

LHCbB+ → ppπ+

• Background subtracted Dalitz distributions using sPlot technique

]4/c2 [GeV2ppm

5 10 15 20

]4/c2

[G

eV2 K

pm

2

4

6

8

10

12

14

16

18

20 )8/c4

Sig

nal

yie

ld /(

0.16

GeV

0

2000

4000

6000

8000

10000

12000LHCbB+ → ppK+

]4/c2 [GeV2ppm

5 10 15 20 25

]4/c2

[G

eV2 pπ

m

0

2

4

6

8

10

12

14

16

18

20 )8/c4

Sig

nal

yie

ld /(

0.20

GeV

0

500

1000

1500

2000

2500

3000

3500

LHCbB+ → ppπ+

• At low m2pp invariant mass the behaviour is differently distributed in the two modes

• Charmonium bands clearly visible:Jψ, ψ(2S) and ηc• At low m2

pk invariant mass we see Λ(1520)

N = 18721± 142 N = 1988± 74

Juan Martin Otalora Goicochea - XXXV ENFPC 27/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

B± → pph± decays• Yields extracted with an unbinned maximum likelihood fit

]2 [GeV/c±Kppm5.1 5.2 5.3 5.4 5.5

)2C

and

idat

es /

(0.0

1 G

eV/c

0

500

1000

1500

2000

2500

3000

3500

4000

4500

LHCbB+ → ppK+

]2 [GeV/c±πppm5.1 5.2 5.3 5.4 5.5

)2C

and

idat

es /

(0.0

1 G

eV/c

0

100

200

300

400

500

600

700

LHCbB+ → ppπ+

• Background subtracted Dalitz distributions using sPlot technique

]4/c2 [GeV2ppm

5 10 15 20

]4/c2

[G

eV2 K

pm

2

4

6

8

10

12

14

16

18

20 )8/c4

Sig

nal

yie

ld /(

0.16

GeV

0

2000

4000

6000

8000

10000

12000LHCbB+ → ppK+

]4/c2 [GeV2ppm

5 10 15 20 25

]4/c2

[G

eV2 pπ

m

0

2

4

6

8

10

12

14

16

18

20 )8/c4

Sig

nal

yie

ld /(

0.20

GeV

0

500

1000

1500

2000

2500

3000

3500

LHCbB+ → ppπ+

• At low m2pp invariant mass the behaviour is differently distributed in the two modes

• Charmonium bands clearly visible:Jψ, ψ(2S) and ηc• At low m2

pk invariant mass we see Λ(1520)

N = 18721± 142 N = 1988± 74

Juan Martin Otalora Goicochea - XXXV ENFPC 27/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

B± → pph± decays• Yields extracted with an unbinned maximum likelihood fit

]2 [GeV/c±Kppm5.1 5.2 5.3 5.4 5.5

)2C

and

idat

es /

(0.0

1 G

eV/c

0

500

1000

1500

2000

2500

3000

3500

4000

4500

LHCbB+ → ppK+

]2 [GeV/c±πppm5.1 5.2 5.3 5.4 5.5

)2C

and

idat

es /

(0.0

1 G

eV/c

0

100

200

300

400

500

600

700

LHCbB+ → ppπ+

• Background subtracted Dalitz distributions using sPlot technique

]4/c2 [GeV2ppm

5 10 15 20

]4/c2

[G

eV2 K

pm

2

4

6

8

10

12

14

16

18

20 )8/c4

Sig

nal

yie

ld /(

0.16

GeV

0

2000

4000

6000

8000

10000

12000LHCbB+ → ppK+

]4/c2 [GeV2ppm

5 10 15 20 25

]4/c2

[G

eV2 pπ

m

0

2

4

6

8

10

12

14

16

18

20 )8/c4

Sig

nal

yie

ld /(

0.20

GeV

0

500

1000

1500

2000

2500

3000

3500

LHCbB+ → ppπ+

• At low m2pp invariant mass the behaviour is differently distributed in the two modes

• Charmonium bands clearly visible:Jψ, ψ(2S) and ηc• At low m2

pk invariant mass we see Λ(1520)

N = 18721± 142 N = 1988± 74

Juan Martin Otalora Goicochea - XXXV ENFPC 28/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

B± → pph± decays: Dynamics

• Measurement of the forward-backward asymmetry

AFB =N(cos θp > 0)− N(cos θp < 0)

N(cos θp > 0) + N(cos θp < 0)

• Variation of the AFB as a function of mpp

B+ → ppK+

]2 [GeV/cppm2 2.2 2.4 2.6 2.8

FB

A

-1

-0.8

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B+ → ppπ+

]2 [GeV/cppm2 2.2 2.4 2.6 2.8

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• Opposite behaviour for the two decay modes

AFB(ppK+,mpp < 2.85GeV /c2) = 0.495± 0.012(stat)± 0.007(syst)AFB(ppπ+,mpp < 2.85GeV /c2) = −0.409± 0.033(stat)± 0.006(syst)

Juan Martin Otalora Goicochea - XXXV ENFPC 29/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

B± → pph± decays: CP asymmetries

• Variation of ACP as a function of the Dalitz-plot variables only for B± → ppK±

• Adaptive binning analysis

]2)2 [(GeV/cpp2m

5 10 15 20

]2 )2 [

(GeV

/cK

p2

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Raw

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Juan Martin Otalora Goicochea - XXXV ENFPC 29/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

B± → pph± decays: CP asymmetries

• Variation of ACP as a function of the Dalitz-plot variables only for B± → ppK±

• Adaptive binning analysis

m2Kp > 10 GeV 2/c4

]2 [GeV/c±Kppm5.1 5.2 5.3 5.4 5.5

)2C

and

idat

es /

(0.0

1 G

eV/c

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300

400

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B−

)4/c2 (GeVpp2m

4 6 8

)4/c2

)/(0

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Clear sign-flip pattern at low m2pp

]2)2 [(GeV/cpp2m

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eV/c

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)/(0

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LHCb

Juan Martin Otalora Goicochea - XXXV ENFPC 30/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

B± → pph± decays: CP asymmetries

• The raw CP is corrected for production and detection asymmetries as inB± → h+h−h±decays.

B± → ppK± ACP = Araw −AP(B±)−AD(K±)B± → ppπ± ACP = Araw −AP(B±)−AD(π±)

First evidence of CPV in baryonic B decays

4σ

3.5σ

• Systematics uncertainties dominated by the uncertainty on the ACP(J/ψK) measurement

Juan Martin Otalora Goicochea - XXXV ENFPC 31/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

B± → pph± decays: B.F. measurements

• Branching fraction of B+ → Λ(1520)(K+p)p relative to B+ → J/ψ(pp)K+

B(B+ → Λ(1520)(K+p)p)

B(B+ → J/ψ(pp)K+)=

NΛ→Kp

NJ/ψ→pp

×εgenJ/ψ→pp

εgenΛ→Kp

×εselJ/ψ→pp

εselΛ→Kp

• Similar equation for the ratio B+ → ppπ+ to B+ → J/ψ(pp)π+

• Resonant modes extracted with a 2D fit to pph+ and pp/K+p

B(B+→Λ(1520)(K+ p)p)B(B+→J/ψ(pp)K+)

= 0.033± 0.005(stat)± 0.007(syst)

B(B+→ppπ+),mpp<2.85GeV/c2

B(B+→J/ψ(pp)π+)= 12.0± 1.2(stat)± 0.3(syst)

• Using• B(B+ → J/ψK+) = (1.016± 0.033)× 10−3 [PDG]

• B(J/ψ → pp) = (2.17± 0.07)× 10−3 [PDG]• B(Λ(1520)→ K+ p) = 0.234± 0.016 [Eur.Phys.J. A47(2011)133]

B(B+ → Λ(1520)(K+p)p) = (3.15± 0.48(stat)± 0.07(syst)± 0.26(BF ))× 10−7

B(B+ → ppπ+,mpp < 2.85GeV /c2) = (1.07± 0.11(stat)± 0.03(syst)± 0.11(BF ))× 10−6

Juan Martin Otalora Goicochea - XXXV ENFPC 32/ 32

Theory and Techniques LHCb Experiment B± → h+h−h± B± → pph±

Summary

• New results with the full LHCb data set (3fb−1)

• B± → h+h−h±decays• Evidence of global direct CP violation• High localised CP asymmetries across the Dalitz plot• Long-distance effects play an important role in generating a

strong phase difference:• Interference between resonances.• Rescattering.

• B± → pph±decays• Large forward-backward asymmetries• First evidence CP violation in decays involving baryons• Sign-flip of CP asymmetry probably generated by interference of

long-distance pp waves

• Next Step: Amplitude Analyses.

Juan Martin Otalora Goicochea - XXXV ENFPC 33/ 32

Backup

BackUp Slides

Juan Martin Otalora Goicochea - XXXV ENFPC 34/ 32

Backup

BSS Model for the B± → π+π−π±decay

b → duu

W

u

B−

b

u

ππ

u

dπ−

u

Vub

Vud

b → duu

g

W

u

B−

b

uππ

u

uπ−d

Vqb Vqd

b → duu

• Strangeness = 0

• Penguin: q = u, c, t

• Tree Dominant.

• Different week phase (CKMmechanism).

• Different strong phase (for u and c inthe penguin).

Vud Vus Vub

Vcd Vcs Vcb

Vtd Vts Vtb

(1)

1− λ2

2λ Aλ3(ρ− iη)

−λ 1− λ2

2Aλ2

A[λ3(1− ρ− iη)] −Aλ2 1

, (2)

Juan Martin Otalora Goicochea - XXXV ENFPC 35/ 32

Backup

BSS Model for B± → K±π+π− & B± → K±K+K− decays

b → suu

W

u

B−

b

u

ππ

u

sK−

u

Vub

Vus

b → suu

g

W

u

B−

b

uππ

u

uK−s

Vqb Vqs

b → suu

• Strangeness = 1

• Penguin: q = u, c, t

• Penguin Dominant.

• CPV expected from interferencebetween tree and penguin diagrams

Vud Vus Vub

Vcd Vcs Vcb

Vtd Vts Vtb

(3)

1− λ2

2λ Aλ3(ρ− iη)

−λ 1− λ2

2Aλ2

A[λ3(1− ρ− iη)] −Aλ2 1

, (4)

Juan Martin Otalora Goicochea - XXXV ENFPC 36/ 32

Backup

Amplitude Analysis

Problems in the usual Isobar Model:

• Many broad states (scalars) squeezed in a narrow mass window

• For D mesons the Non-Resonant amplitude ANR0 is assumed to be constant (due to the

small phase space), but this is not the case for B meson decays.

• High Non-Resonant contribution in B meson decays.

• In Isobar Model, hard to disentangle the Non-Resonant and broad structures in theS-Wave.

The Partial Wave Analysis:

• This method was developed by E791 collaboration. PRD 73, 032004 (2006)

A = S −Wave︸ ︷︷ ︸a0(si)e

iφ0(si )

+ P −Wave + D −Wave︸ ︷︷ ︸Isobar Model

+

• The real functions a0(si) and φ0(si) are extracted directly from data.

• The measurement is inclusive: convolution of elastic, inelastic scattering, mixed isospin,FSI, etc...

• Accuracy depends on the features of P-(or D-waves) - an interferometry analysis.

Juan Martin Otalora Goicochea - XXXV ENFPC 37/ 32

Backup

Interference: B± → K±π+π−

N raw

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]4 c/2)

[GeV

− π+(K2

m

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Kππ

Juan Martin Otalora Goicochea - XXXV ENFPC 37/ 32

Backup

Interference: B± → K±π+π−

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[GeV

− π+(K2

m

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25 LHCb

Kππ

ρ0 f 0

Juan Martin Otalora Goicochea - XXXV ENFPC 38/ 32

Backup

Interference: B± → K±π+π− (Simple Isobar Model)

Juan Martin Otalora Goicochea - XXXV ENFPC 39/ 32

Backup

Interference: B± → K±π+π− (Simple Isobar Model)

Juan Martin Otalora Goicochea - XXXV ENFPC 40/ 32

Backup

Interference: B± → K±π+π− (Simple Isobar Model)

Juan Martin Otalora Goicochea - XXXV ENFPC 41/ 32

Backup

Interference: B± → K±K+K−

N raw

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]4c/2 [GeVlow

)−

K+(K2m1 2 3

]4 c/2 [

GeV

high

)−K+

(K2m

2468

1012141618202224

φ0?

LHCb

KKK

f 0(1500)f ′2(1525)

Juan Martin Otalora Goicochea - XXXV ENFPC 42/ 32

Backup

Scattering and CPT constraint• Scattering:

CERN-Munich collab: π+π− → π+π− scattering Nuclear Physics B64 (1973) 134-162Strongly coupled channels: π+π− → K+K− PRD 22 (1980) 2595

.

• CPT constraint:High local asymmetries not obviously associated to resonances.

positive for K± π+π− negative for K± K+K−

positive for π+π− π± negative for K+K−π±∑f

(i)α ∈Fi

Γ(P → f (i)α ) =

∑f

(i)α ∈Fi

Γ(P → f (i)α ) (Bigi & Sanda 2nd edition pp 57)

all fα in Fi connected via stronginteractions

for two channels α and β: Γ(A+α) + Γ(A+

β ) = Γ(A−α ) + Γ(A−β ) , then: ∆Γα = −∆Γβ