Constraining CP violation in the main decay of the neutral Sigma hyperon
Elisabetta Perotti S. Nair, S. Leupold
FAIRness 2019, Arenzano 20-24 May
(Elisabetta Perotti) Constraining CP violation in Σ0 → Λγ 1 / 18 Focus on: Σ0 and Λ hyperon
1 + Σ0 : I(JP ) = 1( ) 2 u d 1 + Λ: I(JP ) = 0( ) s 2
(Elisabetta Perotti) Constraining CP violation in Σ0 → Λγ 2 / 18 Focus on: Σ0 → Λγ BR: 100% Λ → pπ BR: 64%
p
Λ Σ0 π−
γ
(Elisabetta Perotti) Constraining CP violation in Σ0 → Λγ 3 / 18 Motivation
Look for baryonic CP violation → Might give us some insight into the origin of: p baryon asymmetry Λ strong CP problem Σ0 π−
γ
(Elisabetta Perotti) Constraining CP violation in Σ0 → Λγ 4 / 18 Strong CP problem in a nutshell
1 g2 L = − Ga Ga,µν + q¯(iD/ − M)q + θ Ga G˜ a,µν QCD 4 µν 32π2 µν
QCD doesn’t seem to break CP symmetry (in contrast to the electroweak theory) → i.e., no experimental evidence for strong CP violation
Our conservative approach:
1 allows strong CP violation via θ-term
2 stays faithful to the Standard Model (SM)
(Elisabetta Perotti) Constraining CP violation in Σ0 → Λγ 5 / 18 Two-step decay chain
Our starting point:
1 Σ0 → Λγ electromagnetic decay
parity conserving magnetic dipole transition moment κM parity violating electric dipole transition moment d ΣΛ p
Λ ν µ∗ 0 M1 = u¯Λ (a σµν − b σµν γ5) uΣ0 (−i)q Σ π− a and b related to transition moments κM and dΣΛ
final-state interaction leads to additional phase shift δF 2Re(a∗b) α 0 := decay asymmetry parameter Σ |a|2+|b|2 γ
Asymmetry in the angular distribution!
(Elisabetta Perotti) Constraining CP violation in Σ0 → Λγ 6 / 18 Two-step decay chain
2 Λ → pπ weak decay self-analyzing p
Λ M2 = u¯p(A − Bγ5) uΛ Σ0 π− A and B related to s- and p-wave 2Re(s∗p) αΛ := |s|2+|p|2 γ
To reveal CP violation compare particle and antiparticle decays
(Elisabetta Perotti) Constraining CP violation in Σ0 → Λγ 7 / 18 Three-body decay
¯ ν µ∗ 2 M3 = up (A − Bγ5)(p/Λ + mΛ)(a σµν − b σµν γ5) uΣ0 (−i)pγ DΛ(m12)
Λ resonance propagator 2 −1 DΛ(s) := (s − mΛ + imΛΓΛ) Λ is long-lived → displaced vertex!
in the Λ rest frame
dΓΣ0→γpπ− 1 = Γ 0 Br − (1 − αΛα 0 cosθ) dcosθ 2 Σ →γΛ Λ→pπ Σ
(Elisabetta Perotti) Constraining CP violation in Σ0 → Λγ 8 / 18 Constraining CP violation in Σ0 Λγ →
How?
In practice: Compare decay distributions of Σ0 and Σ¯ 0
dN N Vs dN¯ N¯ = (1 − αΛα 0 cosθ) = (1 − α¯Λα¯ 0 cosθ) dcosθ 2 Σ dcosθ 2 Σ
In theory: Exploit SU(3)F symmetry! i.e. from upper limit on neutron EDM → get upper limit for the angular asymmetry
Construct an observable to search for CP violation
OCP := αΣ0 +α ¯Σ0
→ vanishes if CP is conserved!
(Elisabetta Perotti) Constraining CP violation in Σ0 → Λγ 9 / 18 Theory approach
0 Σ -Λ EDM is related to nEDM via SU(3)F symmetry
use baryon chiral perturbation theory (incl. θ-term) to connect them calculate Σ0-Λ EDM at LO one-loop diagrams contribute! meson-baryon exchange pairs: π+Σ−, π−Σ+, K +Ξ−, K −p
Guo/Meißer, JHEP 12 (2012) 097
(Elisabetta Perotti) Constraining CP violation in Σ0 → Λγ 10 / 18 Tree-level contribution to EDM
NEUTRON Σ-Λ 4 tree 8 ¯ 0 tree ¯ 0 d = eθ (αw + w ) dΣΛ = − √ eθ0 (αw13 + w13) n 3 0 13 13 3 where:
0 w13 and w13 are low-energy constants from baryon NLO Lagrangian
α := (2) (1)/( )2 144V0 V3 F0Fπ Mη0
" (2) #−1 4V 4M2 −M2 ¯ 0 K π θ0 = 1 + θ0 F2 M2 (2M2 −M2 ) π π K π
(Elisabetta Perotti) Constraining CP violation in Σ0 → Λγ 11 / 18 Loop contribution to EDM
NEUTRON Σ-Λ ¯ (2) 4eθ¯ V (2) loop 8eθ0V X loop 0 0 X d = − 0 C J (0) d = − √ (Cce − Cdf) JMM (0) n 4 cd MM ΣΛ 4 F 3Fπ π {M,B} {M,B}
loops C C loops Ccd ce df − {π+, Σ−} −4Db 4Fb {π , p} 2(D + F)(bD + bF ) F D + − {π−, Σ+} −4Db 4Fb {K , Σ } −2(D − F)(bD − bF ) F D + − {K , Ξ } −(3F − D)(bD + bF ) (D + F)(3bF − bD ) − {K , p} −(D + 3F)(bD − bF ) (D − F)(3bF + bD )
where: Z d 2 d k 1 JMM (q ) = i (2π)d (k 2 − M2 + i)((k + q)2 − M2 + i) ! 1 M2 σ − 1 = 2L + ln − 1 − σln 16π2 µ2 σ + 1
0 L contains a divergence, absorbed into the renormalization of w13
(Elisabetta Perotti) Constraining CP violation in Σ0 → Λγ 12 / 18 Parameter estimates
Our calculations give: loop d dtree + d ΣΛ = ΣΛ ΣΛ ≈ −0.88 tree loop dn dn + dn
Use the experimental upper limit for the nEDM:
exp −26 |dn | ≤ 2.9 × 10 e cm ↓↓ to get an upper limit for the Σ0-Λ EDM:
−26 |dΣΛ| ≤ 2.5 × 10 e cm
(Elisabetta Perotti) Constraining CP violation in Σ0 → Λγ 13 / 18 Constraining CP violation in Σ0 Λγ →
Our result: 2dΣΛ sin δF α 0 ≈ − Σ a
−14 −14 |αΣ0 | ≤ 3.0 · 10 → |OCP| ≤ 6.0 · 10
far below any experimental resolution!
observation of CP violating angular asymmetry implies physics beyond the Standard Model
Nair/Perotti/Leupold, Phys.Lett. B788 (2019)
(Elisabetta Perotti) Constraining CP violation in Σ0 → Λγ 14 / 18 Summary and Outlook
So...What have we learned today?
Σ0 → Λpπ−: Observation of CP violating angular asymmetry would constitute physics BSM
And...What are other related projects?
Σ(∗)-Λ Transition Form Factors to NLO
Dalitz decays of decuplet hyperons to octet hyperons + dilepton
Branching ratios of spin-3/2 decuplet hyperons to octet hyperon + photon
(Elisabetta Perotti) Constraining CP violation in Σ0 → Λγ 15 / 18 Back-up slides
(Elisabetta Perotti) Constraining CP violation in Σ0 → Λγ 16 / 18 Electric and magnetic dipole moment
Baryon coupling to the EM current Jµ:
0 0 µ 0 µ 0 hB (p )|J |B(p)i = e u¯B0 (p )Γ (q) uB(p), with q := p − p
and µ i µν 2 1 µν 2 Γ (q) = − σ qν F2(q ) − σ qν γ5 F3(q ) + ... mB + mB0 mB + mB0
NEUTRON Σ-Λ
F2,n(0) = κn ≈ −1.91 κM := F2,ΣΛ(0) ≈ 1.98 e e dn = F3,n(0) dΣΛ := F3,ΣΛ(0) 2mn mΣ0 + mΛ
(Elisabetta Perotti) Constraining CP violation in Σ0 → Λγ 17 / 18 Decay parameters
The two decay parameters a and b are related to the transition moments via: e a = κM , b = i dΣΛ mΣ0 + mΛ For the second decay we have:
s := A and p := ηB with η := |~pp|/(mp + Ep)
(Elisabetta Perotti) Constraining CP violation in Σ0 → Λγ 18 / 18