Four body charm amplitude analysis at LHCb T. Evans University of - - PowerPoint PPT Presentation

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Four body charm amplitude analysis at LHCb T. Evans University of - - PowerPoint PPT Presentation

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Four body charm amplitude analysis at LHCb T. Evans University of Oxford Institute of Physics APP and HEPP Annual Conference 2017 April 11, 2017 1/13 1 / 13 Motivation Amplitude analysis of Cabibbo favoured decay D 0 K + +

slide-1
SLIDE 1

1/13

Four body charm amplitude analysis at LHCb

  • T. Evans

University of Oxford Institute of Physics APP and HEPP Annual Conference 2017

April 11, 2017

1 / 13

slide-2
SLIDE 2

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Motivation

◮ Amplitude analysis of Cabibbo favoured decay

D0 → K−π+π+π− and suppressed decay D0 → K+π−π−π+.

◮ Interference between these amplitudes in

B → DX (see left hand example) can give access to γ → but need to know relative strong phase between amplitudes.

◮ Relative strong phase between DCS and CF

varies across phase-space of D decay - can benefit from “local-knowledge”.

◮ Also of interest for Charm CPV, mixing. ◮ Amplitudes models are also a rich laboratory of

strong and weak effects → very interesting in their own right.

2 / 13

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SLIDE 3

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Selection

]

2

) [MeV/c π π π m(K 1850 1900 N

exp

N-N 2 − 2 )

2

Candidates / (1.20 MeV/c 10 20 30 40 50 60

3

10 ×

Preliminary LHCb

]

2

) [MeV/c π π π ) - m(K

S

π π π π m(K 140 145 150 N

exp

N-N 2 − 2 )

2

Candidates / (0.12 MeV/c 20 40 60 80 100 120 140 160

3

10 ×

Preliminary LHCb

]

2

) [MeV/c π π π m(K 1850 1900 N

exp

N-N 2 − 2 )

2

Candidates / (1.20 MeV/c 50 100 150 200 250

Preliminary LHCb

]

2

) [MeV/c π π π ) - m(K

S

π π π π m(K 140 145 150 N

exp

N-N 2 − 2 )

2

Candidates / (0.12 MeV/c 100 200 300 400 500 600

Preliminary LHCb ◮ Reconstruct B → D∗(2010)+[D0π+]µX. ◮ Charge of π+, µ relative to D0 daughters gives

D0 flavour.

◮ Extremely clean (≈ 50% purity after initial

selection) source of D0 decays.

◮ Select offline with Boosted Decision Tree and

PID on the kaon.

◮ Get ≈ 3000 WS events @ 80% purity, 900,000

RS events @ > 99.9% purity.

◮ Plot m(Kπππ) and m(Kππππs) − m(Kπππ) for

both decay modes.

◮ Flat(ish) efficiency over phase-space - correct

using simulated events.

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SLIDE 4

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The Isobar Model

The “traditional” isobar model.

D0 K∗(892)0 ρ(770)0 K− π+ π− π+ D0 K− ρ(770)0 a1(1260)+ π− π+ π+

Extending to many bodies.

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SLIDE 5

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The Isobar Model (II)

D0 K− π+ π− π+

TK∗(p2

K∗)Lµ(pK∗, qK∗)

S : gµνjµ

1jν 2

P : εµναβpα

Dqβ Djµ 1jν 2

D : L2

µνjµ 1jν 2

Tρ(p2

ρ)Lµ(pρ, qρ)

◮ Divide multi-body process into chain of

quasi-independent two body processes.

◮ Express two body strong FSI with dynamical

functions T (s). For example, Breit-Wigners, K-matrices, Model Independent Partial Wave etc.

◮ Describe spin with covariant tensor formalism. ◮ Main free parameters in the fit are complex

coupling parameters between channels.

◮ In pictured case, there is an independent coupling

for three different orbital configurations (S,P,D) = ⇒ D0 → VV system has 6 free parameters.

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slide-6
SLIDE 6

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The Isobar Model (III)

D0 K− π− π+ π+

Tρ(p2

ρ)Lµ(pρ, qρ)

Ta1(p2

a)Sµν(pa, qa)jν ρ

Lµ(pD, qD)jµ

a1

◮ Cascade processes are a bit more complicated as

have to consider FSI between an isobar and a stable state. Consider the case of the a1(1260) :

◮ In the isobar model, express this in the width of

the a1 : Ta1(s)−1 = m2 − s − iΓ(s)m, where Γ(s) =

  • dx |Mπππ(x)|2 .

◮ The integral is over the three pion final state.

The matrix element coherently sums the different isobars that the a1 couples to.

◮ Need to compute this numerically. Dependence

  • f the width on couplings to isobars tends to be

quite weak, so the problem is tractable.

◮ Simplified model of quite a complicated system -

but works quite well.

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SLIDE 7

7/13

Amplitude Fitting

◮ Maximum unbinned likelihood fit of both datasets using AmpGen package. ◮ Exploits natural tree structure of the isobar model. Example :

D0{K*(892)bar0{K-,pi+},rho(770)0{pi+,pi-}} generates the tree shown on slide 4.

◮ Tree is used to generate the source code to evaluate the amplitude at runtime. ◮ Extremely fast, ≈ 106 amplitude evaluations /core/s. ◮ Can also pack up model, save the code for later :

◮ Plugin to MC generators (Gauss plugin = LbAmpGen) ◮ Distribute model code with documentation.

◮ Uses OpenMP for parallel evaluation of amplitudes, normalisation integrals. ◮ Correct for phase space acceptance variations by performing normalisation integrals for PDFs using MC

events that have been propagated through full LHCb simulation.

◮ Integration events are generated according to an approximate model fitted by neglecting efficiency

effects.

◮ Spin calculations verified against qft++, lineshapes against Laura++.

7 / 13

slide-8
SLIDE 8

8/13

RS Results (I)

]

4

/c

2

) [GeV

+

π

  • s(K

0.5 1 1.5 2 2.5 )

4

/c

2

Events / (0.02 GeV 5 10 15 20 25 30 35 40 45

3

10 ×

Unofficial LHCb

]

4

/c

2

) [GeV

  • π

+

π s( 0.5 1 1.5 )

4

/c

2

Events / (0.02 GeV 5 10 15 20 25 30

3

10 ×

Unofficial LHCb Signal Combinatorial

]

4

/c

2

) [GeV

  • π

+

π

  • s(K

1 2 3 )

4

/c

2

Events / (0.03 GeV 2 4 6 8 10 12 14 16 18 20 22

3

10 ×

Unofficial LHCb

]

4

/c

2

) [GeV

  • π

+

π

+

π s( 0.5 1 1.5 2 )

4

/c

2

Events / (0.02 GeV 2 4 6 8 10 12 14 16 18 20 22

3

10 ×

Unofficial LHCb

◮ Phase-space is five dimensional :

show fit by projecting onto invariant mass squared s to show resonant

  • contributions. From top left to

bottom right :

◮ K∗(892)0 ◮ ρ(770)0 ◮ K1(1270)− ◮ a1(1260)− (≈ 30% of the total

rate)

◮ χ2/ν ≈ 1.3 for ≈ ν ≈ 30, 000, ≈ 60

free parameters.

◮ Compare with BES III result with

≈ 16, 000 events.

◮ LHCb model has comparable with

quality with comparable number of free parameters with ≈ 60× the number of events.

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slide-9
SLIDE 9

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RS Results (II)

Fit Fraction R(g) I(g) K∗(892)0ρ(770)0 5.734 ± 0.057 0.184 ± 0.001 −0.079 ± 0.001

  • K∗(892)0ρ(770)0L=1

4.508 ± 0.038 0.062 ± 0.002 −0.309 ± 0.002

  • K∗(892)0ρ(770)0L=2

9.459 ± 0.063 1.000 ± 0.000 0.000 ± 0.000

D0 K− π+ π− π+

TK∗(p2

K∗)Lµ(pK∗, qK∗)

S : gµνjµ

1jν 2

P : εµναβpα

Dqβ Djµ 1jν 2

D : L2

µνjµ 1jν 2

Tρ(p2

ρ)Lµ(pρ, qρ)

◮ “Fit Fraction” defined for component i as :

Fi =

  • dx |giAi|2
  • ij
  • dxgig∗

j AiA∗ j

, (1) for coupling parameters g.

◮ Becomes branching ratio in limit of narrow

resonances - measure of the importance of a component in the model.

◮ Curious pattern in the D0 → VV

polarisation L = 2 contribution greater than the lower orbitals.

◮ Same pattern is seen in D0 → ρρ.

9 / 13

slide-10
SLIDE 10

10/13

WS Results (I)

]

4

/c

2

) [GeV

  • π

+

s(K 0.5 1 1.5 2 2.5 )

4

/c

2

Events / (0.05 GeV 50 100 150 200 250 300 350 400 450

Unofficial LHCb

]

4

/c

2

) [GeV

+

π

  • π

s( 0.5 1 1.5 )

4

/c

2

Events / (0.03 GeV 50 100 150 200 250

Unofficial LHCb Signal Combinatorial Mistag

]

4

/c

2

) [GeV

+

π

  • π

+

s(K 1 2 3 )

4

/c

2

Events / (0.05 GeV 20 40 60 80 100 120 140 160 180 200 220

Unofficial LHCb

]

4

/c

2

) [GeV

+

π

  • π
  • π

s( 0.5 1 1.5 2 )

4

/c

2

Events / (0.04 GeV 20 40 60 80 100 120 140 160 180 200

Unofficial LHCb

◮ K1(1270)− coupling and shape

parameters fixed from RS.

◮ χ2/ν ≈ 1.7 ( ν ≈ 250, 12 free

parameters) .

◮ Dominated by K∗(892)0, mostly from

cascades of the axial resonances K1(1270)−/K1(1400)−.

W a1/K1

◮ Connected to the a1(1260)−

contribution for the favoured mode.

◮ Key features are strongly constrained

  • but there are lots of possible

parameterisations of equivalent fit quality ..

10 / 13

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SLIDE 11

11/13

Coherence Factor and Binning

Coherence factor defined as : RK3πe−iδK3π =

  • dxAK−3π(x)AK+3π(x)
  • dx|AK−3π(x)|2
  • dx|AK+3π(x)|2

. Appears in calculations for B → Dh, D mixing. Can measure directly using a combination of charm threshold data @ CLEO and LHCb mixing results :

◮ Models can calculate coherence factor up to a

global phase offset. Look at the prediction with an ensemble of WS models with similar fit quality:

π K3

R 0.5 0.55 0.6 0.65 0.7 0.75 # Models 5 10 15 20 25

Unofficial LHCb ◮ Models are consistent with the direct

measurement.

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SLIDE 12

12/13

Local coherence

Can also defined coherence factor in ‘bins‘: Binning algorithm

◮ Divide data into “voxels” of equal

population using a decision tree.

◮ Group voxels by relative strong phase

between two modes, so we get N bins

  • f equal population where the phase

doesn’t vary much in each bin.

◮ Measure R and δ in bins from one

model for the ensemble of models. Phase description is rather stable w.r.t. model choice →

)

π K3

δ cos(

π K3

R 0.5 − )

π K3

δ sin(

π K3

R 0.8 − 0.6 − 0.4 − 0.2 −

Unofficial LHCb

12 / 13

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SLIDE 13

13/13

Conclusions

◮ Developed amplitude models of D0 → K−π+π+π−, D0 → K+π−π−π+. ◮ Analysis is currently under review by collaboration. ◮ Models provide rather stable predictions for phase variations → can reliably use this to optimise future

model independent measurements.

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