Lattice QCD Spectroscopy for Hadronic CP Violation Andr Walker-Loud - PowerPoint PPT Presentation

Lattice QCD Spectroscopy for Hadronic CP Violation André Walker-Loud

Fundamental Symmetries and Low-Energy Nuclear Physics ๏ The Universe is matter dominated at roughly 1 ppb: η ≡ X p + n = 6 . 19(15) × 10 − 10 X γ APS/Alan Stonebraker ๏ Sources of CP-violation beyond the Standard Model (SM) are needed to generate this observed asymmetry ๏ Assuming nature is CPT symmetric, this implies T-violation which implies fermions will have permanent electric dipole moments (EDMs) ๏ This has motivated significant experimental efforts to search (or plan to search) for permanent EDMs in a variety of systems e, n, p, deuteron, triton, 3 He, ..., 199 Hg, 225 Ra, 229 Pa,...

Fundamental Symmetries and Low-Energy Nuclear Physics ๏ The Universe is matter dominated at roughly 1 ppb: η ≡ X p + n = 6 . 19(15) × 10 − 10 X γ APS/Alan Stonebraker ๏ There are now a number of groups working on computing EDMs from the QCD-theta term. If we can determine the couplings - they can be used in the chiral extrapolations, removing a free parameter from their analysis Mereghetti : Mon 10:00 Bhattacharya : Mon 14:40 Dragos : Tues 14:00 Kim : Tues 14:20 Liang : Tues 6:45 Walker-Loud : NOW Yoon : Thur 8:30 Syritsyn : Thur 8:50

Fundamental Symmetries and Low-Energy Nuclear Physics ๏ In a large nucleus, the long-range pion exchange will dominate the nuclear EDM ✓ ◆ g 0 g 1 g 2 ⌧ 3 − ⇡ 3 L CP V = − ¯ ⌧ N − ¯ N ⇡ 3 N − ¯ ¯ ¯ ⇡ 3 ¯ N ~ ⇡ · ~ ~ ⇡ · ~ ⌧ N N 2 F π 2 F π 2 F π F π ๏ For the QCD theta term m 2 { ¯ g 2 } ∼ ¯ π g 1 , ¯ g 0 Λ 2 χ ๏ For more generic CP Violating operators g 1 } m 2 g 2 ∼ { ¯ π ¯ g 0 , ¯ g 1 ∼ ¯ ¯ g 0 Λ 2 χ

Fundamental Symmetries and Low-Energy Nuclear Physics ๏ The nuclear EDM is proportional to the Schiff moment h Φ 0 | S z | Φ i ih Φ i | H CP V | Φ 0 i X S = + c.c. E 0 � E i i 6 =0 S = 2 M N g A ( a 0 ¯ g 0 + a 1 ¯ g 1 + a 2 ¯ g 2 ) F π ๏ The Schiff parameters are computed with nuclear { a 0 , a 1 , a 2 } models under the assumption the CPV operator does not significantly distort the nuclear wave-function ๏ For a QCD theta term only and thus a constraint g 1 ∼ ¯ ¯ g 2 ∼ 0 on can be made through the relation ¯ θ g 0 = δ M m d − m u 2 m d m u θ = α 2 m d m u n − p ¯ ¯ θ ¯ m d − m u m d + m u m d + m u

Fundamental Symmetries and Low-Energy Nuclear Physics ๏ The nuclear EDM is proportional to the Schiff moment h Φ 0 | S z | Φ i ih Φ i | H CP V | Φ 0 i X S = + c.c. E 0 � E i i 6 =0 S = 2 M N g A ( a 0 ¯ g 0 + a 1 ¯ g 1 + a 2 ¯ g 2 ) F π Gaffney et al. Nature 497 (2013) ๏ 225 Ra is interesting nucleus as it is pear- shaped (octupole deformed) ๏ “stiff ” core making nuclear model calculations more reliable ๏ nearly degenerate parity partner state 1 / 2 − E + E − 1 / 2 = 55 KeV ๏ 10 2 - 10 3 enhancement of a 0 , a 1 , a 2

Fundamental Symmetries and Low-Energy Nuclear Physics ๏ Sources of CP-Violation in quark sector: Operator [Operator] No. Operators 4 1 ¯ θ quark EDM 6 2 quark Chromo-EDM 6 2 Weinberg (GGG) 6 1 4-quark 6 2 4-quark induced 6 1

Fundamental Symmetries and Low-Energy Nuclear Physics ๏ Sources of CP-Violation in quark sector: Operator [Operator] No. Operators 4 1 ¯ θ quark EDM 6 2 quark Chromo-EDM 6 2 Weinberg (GGG) 6 1 4-quark 6 2 4-quark induced 6 1

Fundamental Symmetries and Low-Energy Nuclear Physics ๏ Sources of CP-Violation in quark sector: Operator [Operator] No. Operators 4 1 ¯ θ quark Chromo-EDM 6 2 s ¯ L CP V = − g 2 θ G µ ν G µ ν − i ⇣ ⌘ d 0 + ˜ ˜ 32 π 2 ˜ q σ µ ν γ 5 d 3 τ 3 G µ ν q 2 ¯ ✓ ◆ ⌧ 3 − ⇡ 3 L CP V = − ¯ g 0 ⌧ N − ¯ g 1 N ⇡ 3 N − ¯ g 2 ¯ ¯ ⇡ 3 ¯ N ~ ⇡ · ~ ~ ⇡ · ~ ⌧ N N 2 F π 2 F π 2 F π F π

QCD Isospin Violation and CP-violating 𝜌 -N ๏ A precise determination of the strong isospin breaking contribution to Mn-Mp teaches us about CP-violation 
 Crewther, Vecchia, Veneziano, Witten, Phys.Lett. 91B (1980) g 0 = δ M m d − m u 2 m d m u θ = α 2 m d m u n − p ¯ ¯ θ ¯ m d − m u m d + m u m d + m u

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 Phys. Rev. C92 (2015) [1506.06247] m 2 ✓ m 2 ⇢  ◆ � δ M m d − m u (4 π f π ) 2 (6 g 2 = δ α 1 − π A + 1) ln π n − p µ 2 ¯ g 0 = (14 . 7 ± 1 . 8 ± 1 . 4) · 10 − 3 ¯ θ 2 m 2 � √ 2 f π ( g A = 1 . 27 , f π = 130 MeV) + β ( µ ) π (4 π f π ) 2

Computational Strategy ๏ QCD Theta term s ¯ L CP V = − g 2 θ CP V = − ¯ g 0 32 π 2 ˜ G µ ν G µ ν ¯ L χ N ~ ⇡ · ~ ⌧ N 2 F π g 0 = δ M m d − m u 2 m d m u n − p Symmetries ¯ θ ¯ m d − m u m d + m u δ M m d − m u = α ( m d − m u ) n − p Simple spectroscopic calculation allows us to determine this long-range CP-Violating pion-nucleon coupling This relation holds to NNLO in the chiral expansion up to small corrections de Vries, Mereghetti, Walker-Loud 
 Phys. Rev. C92 (2015) [1506.06247]

Computational Strategy de Vries, Mereghetti, Seng, Walker-Loud 
 Phys. Lett. B766 (2017) [1612.01567] ๏ Quark Chromo-EDM Operators d 3 τ 3 ) G µ ν q − 1 qq = − i q σ µ ν γ 5 ( ˜ d 0 + ˜ L 6 2 ¯ 2 ¯ q σ µ ν (˜ c 3 τ 3 + ˜ c 0 ) G µ ν q ¯

Computational Strategy de Vries, Mereghetti, Seng, Walker-Loud 
 Phys. Lett. B766 (2017) [1612.01567] ๏ Quark Chromo-EDM Operators d 3 τ 3 ) G µ ν q − 1 qq = − i q σ µ ν γ 5 ( ˜ d 0 + ˜ L 6 2 ¯ 2 ¯ q σ µ ν (˜ c 3 τ 3 + ˜ c 0 ) G µ ν q ¯ ˜ ˜ ∆ q m 2 d 0 d 3 Symmetries g 0 = δ q M N + δ M N π ¯ m 2 c 3 c 0 ˜ ˜ π ◆ ˜ − ∆ q m 2 ✓ ∆ q M N d 3 π g 3 = − 2 σ π N ¯ m 2 c 0 ˜ σ π N π