Lambda Weak Decay Constant – How to Assess Diﬀerent Results

Lambda Weak Decay Constant – how to assess diﬀerent results

D. G. Ireland Bayesian Inference in Subatomic Physics Gothenburg, 17-20 September, 2019

1 Objectives

Statistical Challenge:

Two independent measurements of same physical quantity - two results are (apparently) not compatible.

Discussion questions for talk today: Are there any obvious mistakes? • How should results be judged as compatible? • What are possible strategies for identifying sources of uncertainty? •

2 The Recent BESIII Result Nature Physics paper1

1M. Ablikim et al. “Polarization and entanglement in baryon-antibaryon pair production in electron-positron annihilation”. In: Nature Physics (May 2019), p. 1.

3 ΛΛ¯ Production

ΛΛ¯ production process.

4 ΛΛ¯ Production

BES Λ Λ¯ event Polarization signal... −

5 ΛΛ¯ Parameter Estimation

Intensity distribution of ΛΛ¯ events

Observations are counts in kinematic (ξ) space (total N 400000) • ∼ αψ, ∆Φ, α− and α+ are parameters to estimate • Maximise likelihood: • N N Y i i data = ξ ; αψ, ∆Φ, α−, α+ ξ L C W i=1

6 Λ Weak Decay Parameter- BES Results

7 Λ Weak Decay Parameter- BES Results

> 5σ diﬀerence between new result and PDG2.

2(Particle Data Group) Tanabashi, M. et al. “Review of Particle Physics”. In: Phys. Rev. D 98.3 (Aug. 2018), p. 030001.

7 So What? pp¯ ΛΛ¯ Polarization3 →

3E. Klempt et al. “Antinucleon nucleon interaction at low energy: Scattering and protonium”. In: Phys. Rept. 368 (2002), pp. 119–316.

8 Global Λ hyperon polarization in nuclear collisions4

STAR Au-Au collision Average Λ (Λ)¯ polarization in collisions...

4The STAR Collaboration. “Global Λ hyperon polarization in nuclear collisions”. In: Nature 548.7665 (2017), pp. 62–65.

9 Λ(Λ)¯ Transverse Polarization with ATLAS5

5ATLAS Collaboration, G. Aad, et al. “Measurement of the transverse polarization of Λ and Λ¯ hyperons produced in proton-proton...”. In: Phys. Rev. D 91 (2015), 10 p. 032004. Decay Parameters of Higher Mass States6

6(Particle Data Group) Tanabashi, M. et al. “Review of Particle Physics”. In: Phys. Rev. D 98.3 (Aug. 2018), p. 030001.

11 Light Baryon Spectrum - PDG 20187 List of N∗ Resonances

N Resonances 3000

2500 ) 2 c / V e

M 2000 (

s s a M 1500

**** 1996 **** 2018 *** *** 1000 ** ** * *

+ + + + + + 1 + 3 + 5 7 9 11 13 15 1− 3− 5− 7− 9− 11− 13− 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 Spin-Parity

7(Particle Data Group) Tanabashi, M. et al. “Review of Particle Physics”. In: Phys. Rev. D 98.3 (Aug. 2018), p. 030001. 12 Kaon Photoproduction Kaon Photoproduction - KΛ example

13 Fierz Identity for LUY plus CUY

Intensities for Experimental Polarization Conﬁgurations: LUY: Linear photon beam; unpolarized target; measured recoil

γ 1 + α− cos θy P Σ + α− cos θy T P cos 2(α φ) − { } L − γ + α− cos θx Ox + α− cos θz Oz P sin 2(α φ) { } L − CUY: Circularly photon beam; unpolarized target; measured recoil

γ 1 + α− cos θy P + (α− cos θx Cx + α− cos θz Cz) PC

Fierz identities connecting two experiments:

2 2 2 2 2 2 2 Ox + Oz + Cx + Cz + Σ T + P = 1 − ΣP CxOz + CzOx T = 0 . − −

14 Fierz Identities as a Statistical Ensemble

Generate pseudodata:

Pick random point in amplitude space • Calculate observables from amplitudes • Treat observables as independent and adjust value by a random • number sampled from (0, σ), N Single polarization observables have σ [0.01, 0.05] • ∈ Double polarization observables have 3 σ • × Writing 2 2 2 2 2 2 2 = Ox + Oz + Cx + Cz + Σ T + P F − Also deﬁne pull as 1 F − σF

15 Key Result: Histogram of Fierz Identities

3.0 Pseudodata

2.5

2.0

1.5

1.0

0.5

0.0 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2 2 2 2 2 2 2 Ox + Oz + Cx + Cz + T + P

16 Key Result: Histogram of Fierz Identities

3.0 Pseudodata Original 2.5

2.0

1.5

1.0

0.5

0.0 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2 2 2 2 2 2 2 Ox + Oz + Cx + Cz + T + P

16 Key Result: Histogram of Fierz Identities

3.0 Pseudodata Original Scaled 2.5

2.0

1.5

1.0

0.5

0.0 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2 2 2 2 2 2 2 Ox + Oz + Cx + Cz + T + P

16 Estimate α from KΛ data? − Parameter Estimation

Infer α− from KΛ data with: M. D¨oring,D. I. Glazier, J. Haidenbauer, R. Murray-Smith, M. Mai and D. R¨onchen8.

Fierz Identities as Random Variables

(1) =a2l 2 2 + 2 2 + a2c2 2 + 2 + l 2Σ 2 + a2 2 , Fi Ox,i Oz,i − Ti Cx,i Cz,i i Pi (2) =al [Σi i i ac( x,i z,i z,i x,i )] , Fi P − T − C O − C O PDG where a = α− /α− and c, l are relative calibrations (i.e. systematics) for circular and linear photon polarization, resp. Instances of (1) and (2) for given a, c and l are f (1) and f (2) Fi Fi i i

8D. G. Ireland et al. In: arXiv:1904.07616 (2019).

17 Parameter Estimation

Likelihood Function

 (1) !2 (2) !2 fi 1 fi pi (Oi a, l, c) exp  −  , | ∝ − σ (1) − σ (2) Fi Fi assuming observables are independent and identically distributed 7 (gaussian). Oi = j,i represents observables at point i ∪j=1O For observables from N bins:

n Y (O a, l, c) pi (Oi a, l, c) P | ∝ | i=1

n where O = Oi represents entire data set. ∪i=1 i.e. the probability that the observables obey Fierz identity

18 Parameter Estimation

Include knowledge of calibrations Calculate posterior PDF from likelihood and prior:

(a, l, c O) (O a, l, c) (l, c) . P | ∝ P | P

Impose α− 0 • ≥ Quoted systematic uncertainties in PL are 3-6% (use 5%) • γ Quoted systematic uncertainties in PC are 2% (use 2%) • γ Which PDF to use? Gaussian (1, σ)? Uniform (1 σ, 1 + σ)? • N U − Posterior PDF Function of a, c and l, (a, l, c O), calculations done by P | 1. Markov Chain Monte Carlo (MCMC) 2. Direct calculation on a c l grid − − 19 Gaussian Prior

�� (α-) �� Posterior looks �� PDG • �� III BES nice! � � Most probable • �(α-� �) �(�) value of l ��

�� questionable!

� ��

��

�� (α-� �) �(�� ) �� (�) �� α- � � 20 Uniform Prior

(α ) �� - �� Posterior in l • ��

PDG and c does not E III BES �� look nice! � Most probable �� (α-� �) �(�) �� • �� values are

� �� reasonable! ��

�(α-� �) �(�� ) �� (�) ��

� �� α- � � 21 Posterior PDFs for α− - Summary of results

120

100

Gaussian prior 20 Fixed l and c Uniform prior 0 0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78

22 Posterior PDFs for α− - Summary of results

120 PDG Value 100 BES III Value

Gaussian prior 20 Fixed l and c Uniform prior 0 0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78

22 Posterior PDFs for α− - Summary of results

120 PDG Value 100 BES III Value

Gaussian prior 20 Fixed l and c Uniform prior 0 0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78

α− = 0.721 0.006 (stat.) 0.005( sys.) ± ± 22 Estimates of α− - Summary of results

L C Source Value Prior Assumption Pγ , Pγ PDG 0.642 0.013 ± BES III 0.750 0.009 0.004 (new PDG value) ± ± 0.719 0.013 (1.0, 0.052), (1.0, 0.022) ± N N 0.721 0.006 (?) (0.95, 1.05), (0.98, 1.02) CLAS ± U U 0.727 0.007 (0.90, 1.10), (0.96, 1.04) ± U U 0.717 0.004 Both ﬁxed at 1.0 ± 0.721 0.006 0.005 Summary of our result ± ±

23 Conclusions Kaon photoproduction data can • independently determine α−

Our result: α− = 0.721 0.006 (stat.) • ± 0.005( sys.) ± Other analyses will have to be • reviewed!

Summary

New BES III result for α− is 17% • higher than PDG value

24 Our result: α− = 0.721 0.006 (stat.) • ± 0.005( sys.) ± Other analyses will have to be • reviewed!

Summary

New BES III result for α− is 17% • higher than PDG value Kaon photoproduction data can • independently determine α−

24 Other analyses will have to be • reviewed!

Summary

New BES III result for α− is 17% • 120 higher than PDG value PDG Value 100 BES III Value Kaon photoproduction data can • 80 independently determine α− 60

Our result: α = 0.721 0.006 (stat.) Gaussian prior − 20 Fixed l and c • ± Uniform prior 0.005( sys.) 0 ± 0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78

24 Summary

New BES III result for α− is 17% • 120 higher than PDG value PDG Value 100 BES III Value Kaon photoproduction data can • 80 independently determine α− 60

Our result: α = 0.721 0.006 (stat.) Gaussian prior − 20 Fixed l and c • ± Uniform prior 0.005( sys.) 0 ± 0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78 Other analyses will have to be • reviewed!

Details posted on arXiv9

9D. G. Ireland et al. In: arXiv:1904.07616 (2019).

24 Objectives

Statistical Challenge:

Two independent measurements of same physical quantity - two results are (apparently) not compatible.

Discussion questions for talk today: Are there any obvious mistakes? • How should results be judged as compatible? • What are possible strategies for identifying sources of uncertainty? •

25 Backup Slides

26 Light Baryon Spectrum - PDG 199610 List of ∆ Resonances

∆∗ Resonances: PDG 1996 3000

2500 ) 2

2000 Mass (MeV/c 1500

**** *** 1000 ** *

+ + + + + + + + 1 3 5 7 9 11 13 15 1− 3− 5− 7− 9− 11− 13− 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 Spin-Parity

10R.M. Barnett et al. In: Phys. Rev. D 54 (1996), p. 1.

26 Light Baryon Spectrum - PDG 201811 List of ∆ Resonances

∆∗ Resonances 3000

2500 ) 2

2000 Mass (MeV/c 1500

**** 1996 **** 2018 *** *** 1000 ** ** * *

+ + + + + + + + 1 3 5 7 9 11 13 15 1− 3− 5− 7− 9− 11− 13− 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 Spin-Parity

11(Particle Data Group) Tanabashi, M. et al. “Review of Particle Physics”. In: Phys. Rev. D 98.3 (Aug. 2018), p. 030001. 26 g8 K Λ Coverage −

1.00

0.75

0.50

0.25

s 0.00 o c

0.25

0.50

0.75 g8 g1c 1.00 1.7 1.8 1.9 2.0 2.1 2.2 W (GeV)

26 Gaussian Process Interpolation

26 Using Gaussian Process to Interpolate g1c to g8 Bins: Cx

W = 1.72 GeV W = 1.74 GeV W = 1.76 GeV W = 1.78 GeV W = 1.8 GeV W = 1.82 GeV 1 1

W = 1.84 GeV W = 1.86 GeV W = 1.88 GeV W = 1.9 GeV W = 1.92 GeV W = 1.94 GeV 1 x

C 1

W = 1.96 GeV W = 1.98 GeV W = 2.0 GeV W = 2.02 GeV W = 2.04 GeV W = 2.06 GeV 1 1

W = 2.08 GeV W = 2.1 GeV W = 2.12 GeV W = 2.14 GeV W = 2.16 GeV W = 2.18 GeV 1

1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 cos

26 Using Gaussian Process to Interpolate g1c to g8 Bins: Cz

W = 1.72 GeV W = 1.74 GeV W = 1.76 GeV W = 1.78 GeV W = 1.8 GeV W = 1.82 GeV 1 1

W = 1.84 GeV W = 1.86 GeV W = 1.88 GeV W = 1.9 GeV W = 1.92 GeV W = 1.94 GeV 1 z

C 1

W = 1.96 GeV W = 1.98 GeV W = 2.0 GeV W = 2.02 GeV W = 2.04 GeV W = 2.06 GeV 1 1

W = 2.08 GeV W = 2.1 GeV W = 2.12 GeV W = 2.14 GeV W = 2.16 GeV W = 2.18 GeV 1

1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 cos

26 Key Result: Pulls of Fierz Identities

0.9 Pseudodata 0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.0 3 2 1 0 1 2 3 Pull

26 Key Result: Pulls of Fierz Identities

0.9 Pseudodata 0.8 Original 0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.0 3 2 1 0 1 2 3 Pull

26 Key Result: Pulls of Fierz Identities

0.9 Pseudodata 0.8 Original Scaled 0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.0 3 2 1 0 1 2 3 Pull

26 MCMC Chain - no prior

1.05

0.90

a 0.75

0.60

1.20

1.05

0.90 l

0.75

0.60

1.75

1.50 c 1.25

1.00

0.75 0 500 1000 1500 2000 MCMC Time Step 26 MCMC Chain - gaussian prior

1.04

0.96 a 0.88

0.80

1.05

0.90 l

0.75

0.60

1.20

1.12

c 1.04

0.96

0.88 0 500 1000 1500 2000 MCMC Time Step 26 MCMC Chain - uniform prior

1.00

0.95 a 0.90

0.85

1.050

1.025

l 1.000

0.975

0.950

1.02

1.01

c 1.00

0.99

0.98 0 500 1000 1500 2000 MCMC Time Step 26 Light Baryon Spectrum - PDG 199612 List of N∗ Resonances

N∗ Resonances: PDG 1996 3000

2500 ) 2

2000 Mass (MeV/c 1500

**** *** 1000 ** *

+ + + + + + + + 1 3 5 7 9 11 13 15 1− 3− 5− 7− 9− 11− 13− 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 Spin-Parity

12R.M. Barnett et al. In: Phys. Rev. D 54 (1996), p. 1.

26 Resonance Hunting

Resonances found from πN scattering...

Coupling to other channels13?

13Simon Capstick and W. Roberts. “Strange decays of nonstrange baryons”. In: Phys. Rev. D 58 (1998), p. 074011.

26 Kaon Photoproduction - KΛ Experimental Database

Accumulated KΛ data points

26 Recent Experimental Data

Data also from ELSA, GRAAL, LEPS, MAMI,...

26 Fierz Identity Values for Original Data

2 Raw 2 P 1 + 2 T 0 W = 1.72 GeV W = 1.74 GeV W = 1.76 GeV W = 1.78 GeV W = 1.80 GeV W = 1.82 GeV 2 2 + 2 z

C 1 + 2 x C 0 W = 1.84 GeV W = 1.86 GeV W = 1.88 GeV W = 1.90 GeV W = 1.92 GeV W = 1.94 GeV + 2 z 2 O + 2 x 1 O

: y t

i W = 1.96 GeV W = 1.98 GeV W = 2.00 GeV W = 2.02 GeV W = 2.04 GeV W = 2.06 GeV

t 0 n

e 2 d I

z r 1 e i F 0 W = 2.08 GeV W = 2.10 GeV W = 2.12 GeV W = 2.14 GeV W = 2.16 GeV W = 2.18 GeV 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 cos

26 Fierz Identity Values for Scaled Data

2 Raw

2 Scaled P 1 + 2 T 0 W = 1.72 GeV W = 1.74 GeV W = 1.76 GeV W = 1.78 GeV W = 1.80 GeV W = 1.82 GeV 2 2 + 2 z

C 1 + 2 x C 0 W = 1.84 GeV W = 1.86 GeV W = 1.88 GeV W = 1.90 GeV W = 1.92 GeV W = 1.94 GeV + 2 z 2 O + 2 x 1 O

: y t

i W = 1.96 GeV W = 1.98 GeV W = 2.00 GeV W = 2.02 GeV W = 2.04 GeV W = 2.06 GeV

t 0 n

e 2 d I

z r 1 e i F 0 W = 2.08 GeV W = 2.10 GeV W = 2.12 GeV W = 2.14 GeV W = 2.16 GeV W = 2.18 GeV 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 cos

26 Reﬁt of J¨uBoCoupled Channels Model

Observable χ2/n (Reﬁts)

(# data points) α− = 0.642 0.75 0.721 dσ/dΩ (421) 1.11 1.03 0.95 Σ (314) 2.55 2.61 2.56 T (314) 1.75 1.74 1.69 P (410) 1.84 1.66 1.62

Cx (82) 2.15 1.72 1.34 Cz (85) 1.58 1.83 1.62 Ox (314) 1.44 1.53 1.51 Oz (314) 1.34 1.58 1.49 all (2254) 1.67 1.66 1.59

Improved ﬁt!