[PPT] - Charm IX Review of recent results on Amplitude Analyses PowerPoint Presentation

SLIDE 1

Review of recent results

n Amplitude Analyses

Charm IX

Novosibirsk

T. Evans

On behalf of the LHCb collaboration

SLIDE 2

IX International Workshop on Charm Physics, Novosibirsk, T. Evans 1/22

Why study amplitudes?

Window into CP violation, charm mixing .. Measurements of CP violating phase of the CKM matrix, γ. Learn about hadron physics along the way. Presenting results from the LHCb collaboration.

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IX International Workshop on Charm Physics, Novosibirsk, T. Evans 2/22

Studies of the resonance structure in D0 → K∓π±π±π∓ decays [3]

D0 →K−π+π+π−, largest contribution from:

u c s D0 u d W + Vcs Vud a1(1260)+ K−

Diagram is O(1) in terms of CKM matrix element → Cabibbo favoured (CF).

BR. ∼ 8%

Studied by Mark III [1] and BES III [2]. D0 →K+π−π−π+, largest contribution from:

u c d D0 s u W + Vcd Vus K1(1270/1400)+ π−

Diagram has two off-diagonal CKM elements → doubly-Cabibbo suppressed (DCS).

BR. ∼ 2 × 10−4

“Golden modes” for studies of γ and charm mixing.

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IX International Workshop on Charm Physics, Novosibirsk, T. Evans 3/22

Data samples

B PV D0 νµ X µ− π+

slow

K− π+ π− π+

≈ 1 c m ≈ 0.5cm

Reconstruct B → D∗+ D0π+ µ−X as a clean source of D0

decays. Charge of ‘slow’

pion and muon relative to kaon is used to infer D0 flavour at production. Uses 2011 + 2012 sample (3 fb−1 @ 7 and 8 TeV). mD∗ − mD0 peaks for ‘Right Sign’ (RS) and ‘Wrong Sign’ (WS). RS sample has ∼ 900, 000 candidates @ > 99.9% purity, WS has ∼ 3000@80% purity.

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IX International Workshop on Charm Physics, Novosibirsk, T. Evans 4/22

Phase space acceptance

0.5 1 1.5 2 2.5 sK−π+

GeV2/c4

10 20 30 40 50 60 70 ×103 Entries/(0.02GeV2/c4)

LHCb Fully Simulated Generator Level

0.5 1 1.5 2 2.5 sK−π+

GeV2/c4

0.6 0.8 1 1.2 1.4 ε(s) 1 2 3 sK−π+π−

GeV2/c4

5 10 15 20 25 30 35 ×103 Entries/(0.03GeV2/c4)

LHCb

1 2 3 sK−π+π−

GeV2/c4

0.6 0.8 1 1.2 1.4 ε(s) 0.5 1 1.5 2 2.5 sK+π−

GeV2/c4

10 20 30 40 50 60 ×103 Entries/(0.02GeV2/c4)

LHCb Fully Simulated Generator Level

0.5 1 1.5 2 2.5 sK+π−

GeV2/c4

0.6 0.8 1 1.2 1.4 ε(s)

Acceptance corrected using simulated events. Corrections are very small due to use of B sample / muonic trigger.

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IX International Workshop on Charm Physics, Novosibirsk, T. Evans 5/22

Quark level diagrams

u c s D0 u d W + Vcd Vud a1(1260)+ K− u

c s D0

d u

W +

K∗0, [K−π+]L=0 , ... ρ0, [π+π−]L=0 , ... Vcs Vud u c s D0 u d W + Vcd Vud π+ K1, K∗, K∗

2...

> >

↑ s ⇌ d ↓ ↑ s ⇌ d ↓ ↑ s ⇌ d ↓

u c d D0 u s W + Vcd Vus K1(1270/1400)+ π− u

c d D0

s u

W +

K∗0, [K+π−]L=0 , ... ρ0, [π+π−]L=0 , ... Vcd Vus u c d D0 u s W + Vcd Vus K+ a1, π, a2, ...

> >

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IX International Workshop on Charm Physics, Novosibirsk, T. Evans 6/22

The Isobar model

A(x) ∝ F(q2)S(x)TR(sR) where: F(q2) is a form-factor (Blatt-Weisskopf, exponential ...) S(x) accounts for the spin/angular momentum configuration TR(sR) is a dynamical function that parametrises the isobar (Breit-Wigner, K Matrix ...)

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IX International Workshop on Charm Physics, Novosibirsk, T. Evans 7/22

Extending to more bodies

Quasi two-body topology Cascade topology Turn one of the final state particles into a second isobar → leads to two different decay topologies. Very broadly: A(x) ∝ F(q2)S(x)TR(sR)TR′(sR′)

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IX International Workshop on Charm Physics, Novosibirsk, T. Evans 8/22

More about the cascade topology

a1(1260)+ ρ(770)0 π+ π+ π−

Three-body decays proceed a pair

f quasi two-body decays in isobar

model, for example: a1(1260)+ → ρ(770)0π+. Decay amplitude would be: Adecay = λµ(a1)∗qµTRBW (sπ+π−)

0.5 1 sπ+π−

GeV2/c4

0.2 0.4 0.6 0.8 1 1.2 sπ+π−

GeV2/c4

Spin-averaged decay rate for a1(1260) → ρπ But what about the dynamical function for the a1?

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IX International Workshop on Charm Physics, Novosibirsk, T. Evans 9/22

Dynamics of cascade resonances

Form of dynamical functions largely constrained by two-body unitarity: TRBW (s) ∝

m2 − s − imΓ(s)

−1 where Γ(s) ∝ q(s)2L× phase-space density. Can generalise to the case

f unstable decay products by:

Γ(s) ∝

pol
Dx |Adecay(x)|2

where the integral is over the phase space of the three body decay. Integrates out the second isobar in the width. Converges to two-body phase-space in limit of narrow resonances. Significantly simplifed model of complicated system → see talk of Mikhail for more advanced treatment.

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IX International Workshop on Charm Physics, Novosibirsk, T. Evans 10/22

Model building

Model(s) have O(100) possible contributing components (different resonances, different orbital configurations...) If model of “reasonable” complexity include O(20) contributions, number of possible models = 100C20 ≈ 1020. Select plausible contributions to the amplitude using an additive algorithm, results in “forest” of models of comparable fit quality. Models presented include components preferred by a simple majority in the ensemble.

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IX International Workshop on Charm Physics, Novosibirsk, T. Evans 11/22

D0 → K−π+π+π−

0.5 1 1.5 2 sπ+π+π−

GeV2/c4

2 4 6 8 10 12 14 16 18 20 22 ×103 Entries/ (0.02 GeV2/c4)

LHCb

Largest contributions from: D0 → a1(1260)+K− ∼ 40% D0 → K∗(892)0ρ(770)0 ∼ 20% D0 → [K−π+]L=0 [π+π−]L=0 ∼ 20% Width of bands indicate total systematic uncertainty on model.

0.5 1 1.5 2 2.5 sK−π+

GeV2/c4

5 10 15 20 25 30 35 40 45 ×103 Entries/ (0.02 GeV2/c4)

LHCb

0.5 1 1.5 sπ+π−

GeV2/c4

5 10 15 20 25 30 ×103 Entries/ (0.02 GeV2/c4)

LHCb

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IX International Workshop on Charm Physics, Novosibirsk, T. Evans 12/22

D0 → K−π+π+π− (II)

Fit Fraction [%]

K∗(892)0ρ(770)0L=0

7.34 ± 0.08 ± 0.47

K∗(892)0ρ(770)0L=1

6.03 ± 0.05 ± 0.25

K∗(892)0ρ(770)0L=2

8.47 ± 0.09 ± 0.67

ρ(1450)0K∗(892)0L=0

0.61 ± 0.04 ± 0.17

ρ(1450)0K∗(892)0L=1

1.98 ± 0.03 ± 0.33

ρ(1450)0K∗(892)0L=2

0.46 ± 0.03 ± 0.15 ρ(770)0 [K−π+]L=0 0.93 ± 0.03 ± 0.05 K∗(892)0 [π+π−]L=0 2.35 ± 0.09 ± 0.33 a1(1260)+K− 38.07 ± 0.24 ± 1.38 K1(1270)−π+ 4.66 ± 0.05 ± 0.39 K1(1400)−π+ 1.15 ± 0.04 ± 0.20 K∗

2(1430)−π+

0.46 ± 0.01 ± 0.03 K(1460)−π+ 3.75 ± 0.10 ± 0.37 [K−π+]L=0 [π+π−]L=0 22.04 ± 0.28 ± 2.09 Sum of Fit Fractions 98.29 ± 0.37 ± 0.84 χ2/ν 40483/32701 = 1.238

All two-body scalar contributions ([hh′]L=0) parametrised using K matrices → no ad-hoc nonresonant terms. Uncertainties dominated by systematics.

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IX International Workshop on Charm Physics, Novosibirsk, T. Evans 13/22

D0 → K+π−π−π+

1 2 3 sK+π−π+ [ GeV2/c4] 20 40 60 80 100 120 140 160 180 200 220 Entries/ (0.05 GeV2/c4)

LHCb

Largest contributions from: D0 → K1(1270/1400)+π− ∼ 40% D0 → K∗(892)0ρ(770)0 ∼ 20% D0 → [K+π−]L=0 [π+π−]L=0 ∼ 20% Backgrounds indicated by filled area (combinatorial + mistagged RS decays)

0.5 1 1.5 2 2.5 sK+π− [ GeV2/c4] 100 200 300 400 500 Entries/ (0.05 GeV2/c4)

LHCb

0.5 1 1.5 sπ−π+ [ GeV2/c4] 50 100 150 200 250 Entries/ (0.03 GeV2/c4)

LHCb

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IX International Workshop on Charm Physics, Novosibirsk, T. Evans 14/22

(quasi) Model Independent Partial Waves

0.5 1 1.5 s [ GeV2/c4]

4
3
2
1

1 2 3 4 R(A)

RBW Binned Linear interpolation Cubic interpolation

0.5 1 1.5 s [ GeV2/c4] 1 2 3 4 5 6 7 8 9 10 I(A)

RBW Binned Linear interpolation Cubic interpolation

How much do we really know about dynamics?

(quasi) Model independent

methods (QMIPWA). Real and imaginary parts of amplitude rn, in on a discrete set of points are free parameters. Different interpolation schemes (binned, linear, cubic) evaluate the amplitude everywhere else.

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IX International Workshop on Charm Physics, Novosibirsk, T. Evans 15/22

Example usage in other final states

)

+

(3/2 R Re

40 − 20 − 20 40

)

+

(3/2 R Im

40 − 30 − 20 − 10 − 10 20 30 40 1 2 3 4 5 LHCb

Λc(2860)+ argand diagram [4].

−

Z

Re A

0.6
0.4
0.2

0.2

−

Z

Im A

0.6
0.4
0.2

0.2

LHCb

Z(4430) argand diagram [5]. See presentations of Anton and Tomasz.

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IX International Workshop on Charm Physics, Novosibirsk, T. Evans 16/22

D0 → K(1460)−π+

First radial excitation the kaon, K(1460)−, is found to contribute significantly to RS decay mode (m ≈ 1.48 GeV /c2, Γ0 ≈ 0.35 GeV). Decays exclusively to three body final states, via K∗(892) and isoscalar amplitudes. Confirm using QMIPWA as K(1460)− is very broad in mK−π+π−.

0.5 1 Re (A)

0.2

0.2 0.4 0.6 0.8 1 1.2 Im (A)

m = 1.14 GeV /c2 m = 1.64 GeV /c2

LHCb

Argand diagram for the K(1460)− from QMIPWA → phase motion expected from a resonant state.

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IX International Workshop on Charm Physics, Novosibirsk, T. Evans 17/22

Parity violation

Generic amplitude for decays to a pair of vector mesons (for example, D0 → K∗(892)0ρ(770)0) is: AV1V2 = λµ(V1)λν(V2)

g0ηµν + g1εµναβpα

V1pβ V2 + g2pµ V2pν V1

where:

λµ, λν are polarisation vectors g0,1,2 are (energy-dependent) couplings. Terms with g0,2 are even under parity transformations, Term with g1 is odd under parity transformations. All three terms will generally be present in weak decays → observable parity (and charge conjugation) violations.

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IX International Workshop on Charm Physics, Novosibirsk, T. Evans 18/22

Parity violation (II)

100 200 300 φ [o] 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 ×103 Entries/ (7.2o)

cos(θA) < 0 cos(θB) < 0 D0 →K−π+π+π− D0 →K+π−π−π+

LHCb

100 200 300 φ [o] 50 100 150 200 250 300 350 400 Entries/ (7.2o)

cos(θA) > 0 cos(θB) > 0 D0 →K−π+π+π− D0 →K+π−π−π+

LHCb

Measure angle φ between the decay planes of the two particle systems, in the region of the K∗/ρ resonances. Divide into quadrants of helicity angle(s). Clear asymmetries about 180o → parity violation. Also clear asymmetries between D0 and D0 decays. But, P asymmetries equal and opposite to C asymmetries →CP is still good.

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IX International Workshop on Charm Physics, Novosibirsk, T. Evans 19/22

Coherence factor and ADS method

B− D0K− D0K−

rBei(δB−γ)

K+π−π−π+
D K−

rDeiδD

Both DCS and CF amplitudes contribute to B∓ → [K±π∓π∓π±]D K∓ with differing weak phases. Phase-space integrated rate is Γ ∝ r2

K3π + r2 B + 2rBRK3πrK3π cos(δB ∓ γ − δK3π)

Where the coherence factor RK3π and δK3π, the average strong-phase difference are defined by: RK3πe−iδK3π =

dxAD0→K+π−π−π+(x)A∗

D0→K+π−π−π+(x)

AD0→K+π−π−π+AD0→K+π−π−π+ So 0 RK3π 1

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IX International Workshop on Charm Physics, Novosibirsk, T. Evans 20/22

Coherence factor and ADS method (II)

Use models to calculate coherence factor: Rmod

K3π = 0.458 ± 0.010 ± 0.012 ± 0.020,

where the first uncertainty is statistical, the second systematic, the third from choosing a different model from the ensemble. Compare with direct determination[6] from CLEO-c + LHCb: RK3π = 0.43+0.17

−0.13

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IX International Workshop on Charm Physics, Novosibirsk, T. Evans 21/22

Conclusions and Outlook

LHCb has developed models of WS/RS D → K3π → these models are valuable inputs for charm mixing and CP violating phase γ. Amplitude studies of many other charm decays ongoing @ LHCb.

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IX International Workshop on Charm Physics, Novosibirsk, T. Evans 22/22

References

Mark III collaboration, D. Coffman et al., Phys. Rev. D45 (1992) 2196. BES III collaboration, M. Ablikim et al., Phys. Rev. D95 (2017) 072010, arXiv:1701.08591. LHCb, R. Aaij et al., Submitted to: Eur. Phys. J. C (2017) arXiv:1712.08609. LHCb, R. Aaij et al., JHEP 05 (2017) 030, arXiv:1701.07873. LHCb, R. Aaij et al., Phys. Rev. Lett. 112 (2014), no. 22 222002, arXiv:1404.1903.

T. Evans et al., Phys. Lett. B757 (2016) 520,

Review of recent results

Charm IX

Novosibirsk

On behalf of the LHCb collaboration

Why study amplitudes?

Window into CP violation, charm mixing .. Measurements of CP violating phase of the CKM matrix, γ. Learn about hadron physics along the way. Presenting results from the LHCb collaboration.

Studies of the resonance structure in D0 → K∓π±π±π∓ decays [3]

D0 →K−π+π+π−, largest contribution from:

Diagram is O(1) in terms of CKM matrix element → Cabibbo favoured (CF).

Studied by Mark III [1] and BES III [2]. D0 →K+π−π−π+, largest contribution from:

Diagram has two off-diagonal CKM elements → doubly-Cabibbo suppressed (DCS).

“Golden modes” for studies of γ and charm mixing.

Data samples

Reconstruct B → D∗+ D0π+ µ−X as a clean source of D0

pion and muon relative to kaon is used to infer D0 flavour at production. Uses 2011 + 2012 sample (3 fb−1 @ 7 and 8 TeV). mD∗ − mD0 peaks for ‘Right Sign’ (RS) and ‘Wrong Sign’ (WS). RS sample has ∼ 900, 000 candidates @ > 99.9% purity, WS has ∼ 3000@80% purity.

Phase space acceptance

Acceptance corrected using simulated events. Corrections are very small due to use of B sample / muonic trigger.

Quark level diagrams

> >

↑ s ⇌ d ↓ ↑ s ⇌ d ↓ ↑ s ⇌ d ↓

> >

The Isobar model

A(x) ∝ F(q2)S(x)TR(sR) where: F(q2) is a form-factor (Blatt-Weisskopf, exponential ...) S(x) accounts for the spin/angular momentum configuration TR(sR) is a dynamical function that parametrises the isobar (Breit-Wigner, K Matrix ...)

Extending to more bodies

Quasi two-body topology Cascade topology Turn one of the final state particles into a second isobar → leads to two different decay topologies. Very broadly: A(x) ∝ F(q2)S(x)TR(sR)TR′(sR′)

More about the cascade topology

Three-body decays proceed a pair

model, for example: a1(1260)+ → ρ(770)0π+. Decay amplitude would be: Adecay = λµ(a1)∗qµTRBW (sπ+π−)

0.5 1 sπ+π−

0.2 0.4 0.6 0.8 1 1.2 sπ+π−

Spin-averaged decay rate for a1(1260) → ρπ But what about the dynamical function for the a1?

Dynamics of cascade resonances

Form of dynamical functions largely constrained by two-body unitarity: TRBW (s) ∝

−1 where Γ(s) ∝ q(s)2L× phase-space density. Can generalise to the case

Γ(s) ∝

where the integral is over the phase space of the three body decay. Integrates out the second isobar in the width. Converges to two-body phase-space in limit of narrow resonances. Significantly simplifed model of complicated system → see talk of Mikhail for more advanced treatment.

Model building

D0 → K−π+π+π−

Largest contributions from: D0 → a1(1260)+K− ∼ 40% D0 → K∗(892)0ρ(770)0 ∼ 20% D0 → [K−π+]L=0 [π+π−]L=0 ∼ 20% Width of bands indicate total systematic uncertainty on model.

D0 → K−π+π+π− (II)

All two-body scalar contributions ([hh′]L=0) parametrised using K matrices → no ad-hoc nonresonant terms. Uncertainties dominated by systematics.

D0 → K+π−π−π+

Largest contributions from: D0 → K1(1270/1400)+π− ∼ 40% D0 → K∗(892)0ρ(770)0 ∼ 20% D0 → [K+π−]L=0 [π+π−]L=0 ∼ 20% Backgrounds indicated by filled area (combinatorial + mistagged RS decays)

(quasi) Model Independent Partial Waves

How much do we really know about dynamics?

methods (QMIPWA). Real and imaginary parts of amplitude rn, in on a discrete set of points are free parameters. Different interpolation schemes (binned, linear, cubic) evaluate the amplitude everywhere else.

Example usage in other final states

)

(3/2 R Re

)

(3/2 R Im

Λc(2860)+ argand diagram [4].

LHCb

Z(4430) argand diagram [5]. See presentations of Anton and Tomasz.

D0 → K(1460)−π+

First radial excitation the kaon, K(1460)−, is found to contribute significantly to RS decay mode (m ≈ 1.48 GeV /c2, Γ0 ≈ 0.35 GeV). Decays exclusively to three body final states, via K∗(892) and isoscalar amplitudes. Confirm using QMIPWA as K(1460)− is very broad in mK−π+π−.

0.5 1 Re (A)

0.2 0.4 0.6 0.8 1 1.2 Im (A)

Argand diagram for the K(1460)− from QMIPWA → phase motion expected from a resonant state.

Parity violation

Generic amplitude for decays to a pair of vector mesons (for example, D0 → K∗(892)0ρ(770)0) is: AV1V2 = λµ(V1)λν(V2)

λµ, λν are polarisation vectors g0,1,2 are (energy-dependent) couplings. Terms with g0,2 are even under parity transformations, Term with g1 is odd under parity transformations. All three terms will generally be present in weak decays → observable parity (and charge conjugation) violations.

Parity violation (II)

Coherence factor and ADS method

B− D0K− D0K−

Both DCS and CF amplitudes contribute to B∓ → [K±π∓π∓π±]D K∓ with differing weak phases. Phase-space integrated rate is Γ ∝ r2

Where the coherence factor RK3π and δK3π, the average strong-phase difference are defined by: RK3πe−iδK3π =

AD0→K+π−π−π+AD0→K+π−π−π+ So 0 RK3π 1

Coherence factor and ADS method (II)

Use models to calculate coherence factor: Rmod

where the first uncertainty is statistical, the second systematic, the third from choosing a different model from the ensemble. Compare with direct determination[6] from CLEO-c + LHCb: RK3π = 0.43+0.17

Conclusions and Outlook

LHCb has developed models of WS/RS D → K3π → these models are valuable inputs for charm mixing and CP violating phase γ. Amplitude studies of many other charm decays ongoing @ LHCb.

References

arXiv:1602.07430, [Erratum: Phys. Lett. B765 (2017) 402].