/ T interactions and chiral symmetry Emanuele Mereghetti Los Alamos - PowerPoint PPT Presentation

/ T interactions and chiral symmetry Emanuele Mereghetti Los Alamos National Lab January 23th, 2015 ACFI Workshop, Amherst

Introduction M T ✟ • probing ✟ BSM CP with EDM entails physics at very different scales T ≫ v ew ≫ M QCD ≫ m π ≫ . . . M / ✟ • understanding nature of ✟ CP requires v EW � ❅ ✠ � ❅ ❘ • several, “orthogonal” • robust theoretical tools probes Nucleon d n , d p M QCD Light nuclei d d , d t , d h non- ptb d 199 Hg , d 205 Tl , . . . atoms QCD molecules d ThO , ... m π

Introduction M T ✟ • probing ✟ BSM CP with EDM entails physics at very different scales T ≫ v ew ≫ M QCD ≫ m π ≫ . . . M / ✟ • understanding nature of ✟ CP requires v EW � ❅ � ✠ ❅ ❘ • several, “orthogonal” • robust theoretical tools probes treated in same theory framework M QCD Nucleon d n , d p Chiral EFT non- ptb Light nuclei d d , d t , d h QCD m π

Introduction M T BSM v EW M QCD summary of recent calculations of light nuclei EDM, non- from U. van Kolck, EM, in preparation ptb QCD ∼ 10 % nuclear uncertainty m π . . . when expressed in hadronic couplings

Introduction M T ✟ • probing ✟ CP with EDM entails physics at very different scales BSM T ≫ v ew ≫ M QCD ≫ m π ≫ . . . M / ✟ • understanding nature of ✟ CP requires � ❅ v EW ✠ � ❘ ❅ • several, “orthogonal” • robust theoretical tools probes Nucleon d n , d p treated in same theory framework Light nuclei d d , d 3 H , d 3 He Chiral EFT M QCD non- • missing link: ptb LECs from QCD QCD What do we learn from symmetry ? m π

/ T at the quark-gluon level • QCD θ term − θ g 2 32 π 2 ε µναβ Tr G µν G αβ − ¯ s q L Me i ρ q R − ¯ q R Me − i ρ q L , L 4 = • dimension six − 1 q i σ µν γ 5 ( d 0 + d 3 τ 3 ) q F µν − 1 q i σ µν γ 5 � � ˜ d 0 + ˜ L 6 = 2 ¯ 2 ¯ d 3 τ 3 G µν q + 1 + d W � � 6 f abc ε µναβ G a αβ G b µρ G c ρ qi γ 5 q − ¯ q τ i γ 5 q ¯ qq ¯ q τ q · ¯ 4Im Σ 1 ( 8 ) ν + 1 4 Im Ξ 1 ( 8 ) ε 3 ij � � q γ µ τ i q ¯ qi γ µ γ 5 τ j q − ¯ q γ µ τ i q ¯ qi γ µ γ 5 τ j q ¯ see Jordy’s talk • quark electric (qEDM) and chromo-electric dipole moment (qCEDM) m ˜ d 0 , 3 = ¯ m δ 0 , 3 d 0 , 3 = ¯ δ 0 , 3 • chiral breaking, assume ∝ m u + m d ˜ , M 2 M 2 • δ 0 , 3 , ˜ δ 0 , 3 are O ( 1 ) / / T T

/ T at the quark-gluon level • dimension four: QCD θ term − θ g 2 32 π 2 ε µναβ Tr G µν G αβ − ¯ s q L Me i ρ q R − ¯ q R Me − i ρ q L , L 4 = • dimension six − 1 q i σ µν γ 5 ( d 0 + d 3 τ 3 ) q F µν − 1 q i σ µν γ 5 � � d 0 + ˜ ˜ L 6 = 2 ¯ 2 ¯ d 3 τ 3 G µν q + 1 + d W � � 6 f abc ε µναβ G a αβ G b µρ G c ρ qi γ 5 q − ¯ q τ i γ 5 q ¯ qq ¯ q τ q · ¯ 4 Im Σ 1 ( 8 ) ν + 1 4 Im Ξ 1 ( 8 ) ε 3 ij � � q γ µ τ i q ¯ qi γ µ γ 5 τ j q − ¯ q γ µ τ i q ¯ qi γ µ γ 5 τ j q ¯ see Jordy’s talk • gluon chromo-electric dipole moment (gCEDM) & χ I four-quark 1 ( d W , Σ 1 , 8 ) = { w , σ 1 , σ 8 } M 2 • chiral invariant / T

/ T at the quark-gluon level • dimension four: QCD θ term − θ g 2 32 π 2 ε µναβ Tr G µν G αβ − ¯ s q L Me i ρ q R − ¯ q R Me − i ρ q L , L 4 = • dimension six − 1 q i σ µν γ 5 ( d 0 + d 3 τ 3 ) q F µν − 1 q i σ µν γ 5 � � d 0 + ˜ ˜ L 6 = 2 ¯ 2 ¯ d 3 τ 3 G µν q + 1 + d W � � 6 f abc ε µναβ G a αβ G b µρ G c ρ qi γ 5 q − ¯ q τ i γ 5 q ¯ qq ¯ q τ q · ¯ 4Im Σ 1 ( 8 ) ν + 1 4 Im Ξ 1 ( 8 ) ε 3 ij � � q γ µ τ i q ¯ qi γ µ γ 5 τ j q − ¯ q γ µ τ i q ¯ qi γ µ γ 5 τ j q ¯ see Jordy’s talk • left-right four-quark (FQLR) operators Ξ 1 , 8 = ξ 1 • isospin breaking, M 2 not ∝ v ew / T

/ T at the hadronic level • include dim-four and dim-six / T in χ PT Lagrangian � � ¯ S µ v ν NF µν − ¯ N π · τ N − ¯ g 0 g 1 − 2 ¯ d 0 + ¯ ¯ π 3 ¯ � L / = N d 1 τ 3 NN T F π F π ¯ ∆ π 3 π 2 + ¯ C 1 ¯ NN ∂ µ (¯ NS µ N ) + ¯ C 2 ¯ N τ N ∂ µ (¯ NS µ τ N ) − F π • at LO, EDMs expressed in terms of a few couplings ¯ d 0 , ¯ d 1 neutron & proton EDM, one-body contribs. to A ≥ 2 nuclei g 1 , ¯ ¯ g 0 , ¯ ∆ pion loop to nucleon & proton EDMs leading / T OPE potential C 1 , ¯ ¯ C 2 short-range / T potential • relative size depends on / T source = ⇒ different signals for one, two, three-nucleon EDMs • Can we go beyond NDA?

QCD Theta Term − θ g 2 32 π 2 ε µναβ Tr G µν G αβ − ¯ q L Me i ρ q R − ¯ q R Me − i ρ q L , s L 4 = • rotate θ away physics depends on ¯ θ = θ − n F ρ • perform vacuum alignment T iso-breaking terms ¯ i.e. kill / qi γ 5 τ 3 q mr (¯ qq + r − 1 (¯ q τ 3 q + m ∗ sin ¯ � � L 4 = − ¯ θ )¯ θ ) ¯ m ε ¯ θ ¯ qi γ 5 q 2 ¯ m = m u + m d , • CP-even quark mass and mass difference 2 ¯ m ε = m d − m u • CP-odd isoscalar mass term

QCD Theta Term − θ g 2 32 π 2 ε µναβ Tr G µν G αβ − ¯ q L Me i ρ q R − ¯ q R Me − i ρ q L , s L 4 = • rotate θ away physics depends on ¯ θ = θ − n F ρ • perform vacuum alignment T iso-breaking terms ¯ i.e. kill / qi γ 5 τ 3 q mr (¯ qq + r − 1 (¯ q τ 3 q + m ∗ sin ¯ � � L 4 = − ¯ θ )¯ θ ) ¯ m ε ¯ θ ¯ qi γ 5 q m 1 − ε 2 m u m d • CP-even quark mass and mass difference m ∗ = = ¯ m u + m d 2 • CP-odd isoscalar mass term θ ) = 1 − 1 − ε 2 θ 2 + . . . r (¯ ¯ 2

The QCD Theta Term. Chiral Lagrangian and NDA ¯ ¯ ¯ d 0 , 1 × Q 2 C 1 , 2 × F 2 π Q 2 ¯ ¯ ∆ / F π g 0 g 1 m 2 ε m 2 Q 2 Q 2 ¯ Q θ × π 1 π ε NDA M 2 M 2 M 2 M QCD M QCD QCD QCD QCD Chiral properties of ¯ θ determine size of LECs • breaks chiral symmetry isoscalar ¯ g 0 at LO • but not isospin isobreaking requires insertion of ¯ m ε g 1 and ¯ ¯ ∆ suppressed • higher dimensionality of N γ and NN operators costs Q / M QCD

QCD Theta Term. Symmetry mr (¯ qq + r − 1 (¯ q τ 3 q + m ∗ sin ¯ � � L 4 = − ¯ θ )¯ θ ) ¯ m ε ¯ θ ¯ qi γ 5 q • ¯ θ term and mass splitting are chiral partners � ¯ � − ¯ qi γ 5 q � q α · τ q � SU A ( 2 ) − − − − → ¯ q τ q α ¯ qi γ 5 q • nucleon matrix elements are related • i.e. one spurion enough to construct iso- and T -breaking couplings isospin breaking = 1 − ε 2 T violation sin ¯ θ ≡ ρ ¯ θ 2 ε • powerful at LO • breaks down at O ( Q 2 / M 2 QCD ) × ignorance of CP-even LECs × too many operators when including EM

QCD Theta Term. ¯ g 0 1 − 2 π 2 � � NN + 1 � � τ 3 − π 3 π · τ � N π · τ � L ( 1 ) = ∆ m N ¯ ¯ θ ¯ 2 δ m N N − 2 ρ ¯ N N F 2 F 2 F π π π ∆ m N nucleon sigma term δ m N = ( m n − m p ) st , strong mass splitting 1 − ε 2 sin ¯ ¯ g 0 = δ m N θ 2 ε

QCD Theta Term. ¯ g 0 1 − 2 π 2 � � NN + 1 � � τ 3 − π 3 π · τ � N π · τ � L ( 1 ) = ∆ m N ¯ ¯ θ ¯ 2 δ m N N − 2 ρ ¯ N N F 2 F 2 F π π π ∆ m N nucleon sigma term δ m N = ( m n − m p ) st , strong mass splitting 1 − ε 2 sin ¯ ¯ g 0 = δ m N θ 2 ε • δ m N not directly accessible experimentally, δ em m N ∼ δ m N • accessible via existing lattice calculations δ m N = 2 . 39 ± 0 . 21 MeV ε = 0 . 37 ± 0 . 03 MeV A. Walker-Loud, ‘14; Borsanyi et al , ‘14. Aoki ‘13, FLAG Working group. • precise ( ∼ 10%) determination of ¯ g 0 ¯ g 0 = ( 15 ± 2 ) · 10 − 3 sin ¯ θ F π errors from lattice only

QCD Theta Term. ¯ g 0 + δ ( 3 ) m N ¯ ¯ � m 2 �� � log µ 2 �� θ + δ ¯ g 0 g 0 A + 1 A + 1 g 0 π 3 g 2 + g 2 = 1 + ρ ¯ ( 2 π F π ) 2 m 2 F π F π 2 2 F π F π π m 2 log µ 2 � �� A + 1 � A + 1 �� π 3 g 2 + g 2 + δ ( 3 ) m N ( m n − m p ) st = δ m N 1 + ( 2 π F π ) 2 m 2 2 2 π • same loop corrections to ¯ g 0 and δ m N • finite LEC δ ¯ g 0 only correct π N coupling ✭✭✭✭✭✭✭✭✭✭✭✭✭ ❤❤❤❤❤❤❤❤❤❤❤❤❤ isospin breaking = 1 − ε 2 T violation sin ¯ θ ≡ ρ ¯ . . . but . . . θ 2 ε • and are not log enhanced • corrections appear at NNLO

QCD Theta term. ¯ g 0 • what about strangeness? • in SU ( 3 ) χ PT m ( 1 − ε 2 ) ¯ δ m N ¯ = m Ξ − m Σ ¯ g 0 g 0 = 22 · 10 − 3 sin ¯ = ρ ¯ θ and θ F π F π F π m s − ¯ m 2 F π J. de Vries, EM, A. Walker-Loud, in progress • large O ( m K / M QCD ) corrections to m n − m p ( m K + − m K 0 , η - π mixing) and ¯ g 0 ( π KK , ππη CP-odd vertex)

QCD Theta term. ¯ g 0 • what about strangeness? • in SU ( 3 ) χ PT m ( 1 − ε 2 ) ¯ δ m N ¯ = m Ξ − m Σ ¯ g 0 g 0 = 22 · 10 − 3 sin ¯ = ρ ¯ θ and θ F π F π F π m s − ¯ m 2 F π (b) (a) (c) (d) (a) (b) (c) (d) (e) (f) (h) (g) (e) (f) (i) (l) (m) (n) • large (. ..too large ...) O ( m K / M QCD ) • under control NNLO corrections corrections to m n − m p ( m K + − m K 0 , η - π mixing) and ¯ g 0 ( π KK , ππη CP-odd vertex)