CP-symmetry tests in sequential decays of

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𝒆 + 𝒆 → J/𝝍 → 𝚲ഥ 𝚲

J/𝝍(𝝍 ) → 𝚺 + ഥ 𝚺

PRL125 (2020) 052004

J/𝝍 → 𝚵ഥ 𝚵

arXiv:2105.11155

𝝍 → 𝛀 𝛀 ഥ +

PRL126 (2021) 092002

Polarization and spin correlations Sequential decays

Determination of hyperon decay parameters CP tests

Nature Phys. 15 (2019) 631

1. G.Fäldt, AK PLB772 (2017) 16

2. E.Perotti,G.Fäldt,AK,S.Leupold,JJ.Song PRD99 (2019)056008 3. P.Adlarson, AK PRD100 (2019) 114005

4. P.Adlarson,V.Batozskaya,AK,N.Salone, S.Leupold, J. Tandean in preparation

NCBJ, 20 December 2021

Methods (UU&NCBJ):

CP-symmetry tests in sequential decays of entangled strange baryons

Andrzej Kupsc (UU&NCBJ)

Precision hyperon physics at Τ 𝐽 𝜓 and 𝜓′ factories:

NCBJ from 30/6:

V. Batozskaja*

M. Berłowski A. Kupść*

A. Ukleja N. Salone

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𝒆 + 𝒆 → J/ψ → Bഥ 𝑩

𝒆

+

𝒆

→ J/ψ→ 𝚵ഥ 𝚵 𝒆

+

𝒆

→ J/ψ→ 𝚲ഥ 𝚲

𝜦 → 𝒑𝝅

𝜦 𝒑

𝝅

Weak phases and CP-symmetry tests in

sequential decays of entangled double-strange

baryons arXiv:2105.11155

Nature Phys. 15 (2019) 631

#94 citations

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Introduction: Direct CP violation in kaon decays

Notation: 𝒜

2∆𝐼,𝐼 ∆𝐼 Τ1 2 , Τ3 2

CPV phases

∆𝑰 = Τ 𝟏 𝟐 𝐚𝐧𝐝 Τ 𝟑 𝟐 amplitudes

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𝑛(𝑢𝑑𝑑) 𝑝(𝑢𝑢𝑑)

Λ (𝑢𝑑𝑠)

Ξ (𝑑𝑠𝑠)

Σ + (𝑢𝑢𝑠) Σ (𝑑𝑑𝑠) Σ 0 (𝑢𝑑𝑠)

Ξ 0 (𝑢𝑠𝑠)

Spin ½ baryon octet

Spin Τ 𝟑 𝟐 Ground-state strange baryons

Ω (𝑠𝑠𝑠)

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∆𝐼 = Τ1 2

weak CP-odd phases

strong phases

Decay amplitudes in hyperon decays

P and S transitions

Admixture of ∆𝐼 = Τ3 2 (~1/22)

Λ → 𝑝𝜋 Ξ → Λ𝜋

Measurable: BF and

two decay parameters

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𝑝 𝑛 ො 𝑃

Λ

𝜋

Measurement of hyperon decay parameters

p=100 MeV/c

𝑑Γ

𝑑Ω = 1

4𝜋(1 + 𝛼Λ𝑛 തො 𝑃Λ)

𝛼

Ξ=-0.392(8)

𝜙

Λ=-0.113(61)

𝛼

Λ= 0.750(10)

𝜙

Ξ=-0.042(16)

Accesible if daughter baryon polarization measured eg in decay sequence:

𝚵 → 𝚲𝝅, 𝚲 → 𝒑𝝅

Λ rest frame 𝜦 → 𝒑𝝅

𝚵 → 𝚲𝝅, 𝚲 → 𝒑𝝅

𝜎𝜇Λ → ෍

𝜇=0 3

𝒂𝝁,𝝁′𝜦 𝜎𝜇′𝑝

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CP violation observables in hyperon decays

weak P-S phase diff.

CP-test :

* Tandean,Valencia PRD67 (2003) 056001

SM ref *

for c.c. decay modes if CP conserved:

Leading order Δ𝐼 = Τ

1 2

:

𝛼 = −𝛼 and ҧ 𝛽 = −𝛽

** Tandean Phys.Rev.D 69 (2004) 076008

BSM ref **

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Γ 𝜇

F

1

(Dirac) and F

2

(Pauli) Form Factors

Sachs Form Factors (FFs) ⇔ helicity amplitudes:

𝒆 + 𝒆 → 𝜸 → 𝑩ഥ 𝑩 (𝐬𝐩𝐢𝐧 𝟏/𝟐 )

helicity non-flip helicity flip

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𝑒 + Λ

𝑒

Ƹ𝑧

Baryon polarization in 𝒆 + 𝒆 𝑦

𝛼𝜓 = 0.469

𝑃 ത

ΔΦ ≠ 0

𝜃 Λ

Λ ഥ

Unpolarized e+e- beams ⇨ transverse polarization:

Ex. 𝑒

+

𝑒

→ Τ 𝐽 𝜓 → Λഥ Λ

𝑃

𝑦

ΔΦ=42.3

o

Angular distribution:

−1 ≤ 𝜶

𝝍

≤ 1

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𝜌

1 2, ΤΤ 1 2

= 1

4 ෍

𝜇ഥ𝜈

𝐶

𝜇ഥ𝜈

𝜎

𝜇𝐵1

⨂𝜎

𝜈𝐵2

General two spin ½ particle state:

Baryon-antibaryon spin density matrix 𝒆 + 𝒆 → 𝑩 𝟏 𝑩 ഥ 𝟐

𝐶 𝜇ഥ 𝜈 =

(𝜎0= 𝟏2, 𝜎1 = 𝜎𝑥, 𝜎2 = 𝜎𝑦, 𝜎3 = 𝜎𝑧)

E.Perotti, G.Faldt, AK, S.Leupold,JJ.Song PRD99 (2019)056008

∝ 𝑃 𝑦

𝛽𝜓 = 1 − 𝛼𝜓2 sin ΔΦ 𝛾𝜓 = 1 − 𝛼𝜓2 cos ΔΦ

∝ 𝐶 𝑖 ҧ𝑗

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BESIII 10

10

J/ψ

PRD 93, 072003 (2016) PLB770,217 (2017)

PRD 95, 052003 (2017)

𝒆 + 𝒆 → 𝑱/𝝍, 𝝍(𝟐𝑺) → 𝑩ഥ 𝑩

#events at BESIII (estimate)

ℬ Τ 𝐽 𝜓 → 𝑝 ഥ 𝑝 = (21.21 ± 0.29) × 10

−4

ST

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Exclusive (Double Tag - DT)

𝒆 + 𝒆 → (𝜦 → 𝒑𝝅 )(ഥ 𝜦 → ഥ 𝒑𝝅 + )

Λ → 𝑝π

: ෝ 𝐧

1

→ (cos 𝜃

1

, 𝜙

1

) : 𝜶

𝚲

Λ → ҧ ഥ 𝑝π

+

: ෝ 𝐧

2

→ (cos 𝜃

2

, 𝜙

2

)

Fäldt, Kupsc PLB772 (2017) 16

: 𝜶 ഥ

𝚲

5D PhSp

1 + 𝜶

𝝍

cos

2

𝜃

Λ

+𝜶

𝚲

𝜶 ഥ

𝚲

𝒊, ҧ𝒋=𝟏 𝟑

𝑪

𝒊 ҧ𝒋

𝑛

1,𝑧

𝑛

2,𝑧

+ 𝜶

𝚲

𝑛

1,𝑦

− 𝜶 ഥ

𝚲

𝑛

2,𝑦

𝑷

𝒚

𝝃 ∶ (cos 𝜃

Λ

, ෝ 𝐧

1

, ෝ 𝐧

2

)

𝑑Γ ∝ 𝑊 𝝃; 𝜶 𝝍 , 𝜟𝜱, 𝜶 𝚲 , 𝜶 ഥ 𝜦 =

𝑊 = 𝑇𝑟𝜌

𝑝, ҧ𝑝

= ෍

𝜇,ഥ𝜈=0 3

𝐶

𝜇ഥ𝜈

𝑎

𝜇,0Λ

𝑎

𝜈,0Λ

Modular angular distribution:

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BESIII measurement

BESIII Nature Phys. 15 (2019) 631 421k events

𝒆

+

𝒆

→ (𝜦 → 𝒑𝝅

)(ഥ 𝜦 → ഥ 𝒑𝝅

+

)

399 background

based on 1.31x10

9

J/ψ

4 fit

parameters

𝜶 ഥ

𝚲

𝜶

𝚲

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𝒆 + 𝒆 → Τ 𝑱 𝝍 → 𝚵 ഥ 𝚵 + → 𝚲𝝅 𝚲𝝅 ഥ + → 𝐩𝛑 𝛑 𝐩𝛑 ഥ + 𝛑 +

9 kinematical variables, 9D PhSp

𝑑Γ ∝ 𝑊 𝝃; 𝝎 𝝃

Parameters: 2 production + 6 for decay chains

E.Perotti, G.Faldt, AK, S.Leupold,JJ.Song PRD99 (2019)056008 P.Adlarson, AK PRD100 (2019) 114005

𝑊 = ෍

𝜇,ഥ𝜈=0 3

𝐶

𝜇ഥ𝜈

𝜇,ഥ𝜈=0 3

𝑎

𝜇,𝜇′Ξ

𝑎

𝜈,ഥΞ𝜈′

𝑎

𝜇′,0Λ

𝑎

𝜈′,0Λ

𝝎 = 𝜶

𝝍

, 𝚫𝚽, 𝜶

𝜩

, 𝝓

𝜩

, 𝜶

𝚲

, 𝜶 ഥ

𝜩

, 𝝓 ഥ

𝜩

, 𝜶 ഥ

𝚲

Modular angular distribution:

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p [GeV/c]

𝜋

+

Τ 𝜋

𝑝 Τ 𝑝 ҧ

𝑱 𝝍 → 𝚵 Τ ഥ 𝚵 +

421k events 399 bkg

Exclusive (DT) analyses based on 1.31x10

9

J/ψ

73k events 190 bkg

𝜋

+

Τ 𝜋

𝑝 Τ 𝑝 ҧ

p [GeV/c]

arXiv:2105.11155 Nature Phys. 15 (2019) 631

9D PhSp 5D PhSp

Unbinned MLL fit

4 parameters 8 parameters

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Preliminary

arXiv:2105.11155

8 fit

parameters

3 CP

tests

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Conclusions

first direct measurement of weak phase difference: 𝜉

𝑃

− 𝜉

𝑆

𝛼

Ξ

= 0.373 5 2

𝐽 𝜓 → Ξത Τ Ξ (prel. )

three independent CP tests

0.72 0.74 0.76 0.78 0.80

20 40 60 80 100

𝛼Λ = 0.754 3 2 𝐽 𝜓 → ΛഥΤ Λ

𝛼Λ = 0.760 6 3 prel Τ𝐽 𝜓 → ΞതΞ 𝛼Λ

0.721(6)(5) CLAS

J/ψ and ψ’ decays into hyperon-antihyperon unique spin entangled system:

• determination of (anti-)hyperon decay parameters

• CP tests

• polarization observed for J/ψ,(𝜓

) → Λഥ Λ, Σ

+

Σ ത

, Ξ

Ξ ത

+

, Ω

Ω ഥ

+

𝜶 𝚲

More data: 10

10

J/ψ

3x10

9

ψ(2S)

Results using:

1.3 × 109 J/ψ 4.5 × 108 ψ(2S)

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Outlook I:Polarized 𝒆 beam 𝑒 + 𝑒 → Τ 𝐽 𝜓 → 𝛬 ҧ 𝛬

𝐶 𝜇ഥ 𝜈 =

𝑃 ത Λ

| ത 𝑃

Λ

|

𝑃(𝑒

)

𝜎

𝐴

Λ

𝑁

𝜎

𝛼

Λ

𝑁

𝝈 𝑨𝜦 = 𝟐. 𝟎 𝑵 𝜎 𝐴Λ = 8.8

𝑁

+ 80% longitudinal 𝑒 polarization

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Outlook II: Sequential decays of charmed baryons at LHCb

Precision values of hyperon decay parameters fixed from our BESIII measurements.

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ΔΦ=(69.5±2.6±0.9)

o

Polarization and 𝑪 𝒊𝒊 𝐟𝐨𝐫 𝒆 + 𝒆 → Τ 𝑱 𝝍 → 𝚵 ഥ 𝚵 + 𝑪 𝒙𝒙

𝑪 𝒚𝒚 𝑪 𝒛𝒛

𝑷 𝒚

arXiv:2105.11155

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