Electric dipole moments of light nuclei Emanuele Mereghetti - PowerPoint PPT Presentation

Electric dipole moments of light nuclei Emanuele Mereghetti November 4th, 2016

Outline Why EDMs of light ions? can we disentagle ¯ θ from BSM? 1. orthogonal to the nucleon EDM can we disentagle BSM models? direct connection between 2. theoretically clean EDMs and high energy parameters? (... not too dirty...) just a little expensive... 3. experimentally feasible

Storage Ring EDM experiments JEDI @ COSY (Julich) • measure spin precession relative to β ( η ∝ d ) � � � � ω e = η e a = g − 2 e 1 ω a = a B − a − β × E m [ E + β × B ] , γ 2 − 1 m 2

Storage Ring EDM experiments JEDI @ COSY (Julich) 10 − 16 e fm by 2020? • measure spin precession relative to β ( η ∝ d ) ❤❤❤❤❤❤❤❤❤❤❤❤❤ ✭ ✭✭✭✭✭✭✭✭✭✭✭✭✭ � � � � ω e = η e a = g − 2 ω a = e 1 a B − a − β × E m [ E + β × B ] , γ 2 − 1 m 2 ❤ a > 0: all electric ring a < 0: electric & magnetic ring ω a vanishes for “magic momentum” need both B & E to cancel ω a e.g. proton p = 0 . 7 GeV, E = 1 . 171 GeV case of deuteron, 3 He

CP violation at 1 GeV 1. Catalog possible / T operators in EFT • one dimension 4 operator: QCD ¯ θ term in principle ¯ θ = O ( 1 ) T 4 = m ∗ ¯ L / θ ¯ qi γ 5 q ... strong CP problem • 9 (+ 8 w. strangeness) dimension 6 operators: 1. 4 (+2) quark bilinears: qEDM and qCEDM c ( q ) c ( q ) m q ˜ m q ˜ qi σ µν g s G µν γ 5 q � γ qi σ µν γ 5 q eF µν − � g L / = − ¯ ¯ T 6 2 2 q = u , d , s q = u , d , s � � � � v 2 v 2 c ( q ) c ( q ) v 2 ˜ v 2 ˜ = O = O γ g Λ 2 Λ 2 Λ ≫ v

CP violation at 1 GeV 1. Catalog possible / T operators in EFT • one dimension 4 operator: QCD ¯ θ term in principle ¯ θ = O ( 1 ) T 4 = m ∗ ¯ L / θ ¯ qi γ 5 q ... strong CP problem • 9 (+ 8 w. strangeness) dimension 6 operators: 2. 1 pure glue: Weinberg three-gluon operator (gCEDM) C ˜ 6 f abc ǫ µναβ G a µρ G c ρ G αβ G b L / = ν T 6 � � v 2 v 2 C ˜ G = O Λ 2 Λ ≫ v

CP violation at 1 GeV 1. Catalog possible / T operators in EFT • one dimension 4 operator: QCD ¯ θ term in principle ¯ θ = O ( 1 ) T 4 = m ∗ ¯ L / θ ¯ qi γ 5 q ... strong CP problem • 9 (+ 8 w. strangeness) dimension 6 operators: 3. 4 (+ 6) four-quark (LR LR & LL RR) Σ ( ud ) (¯ u L u R ¯ d L d R ) + Ξ ( ud ) ¯ d L γ µ u L ¯ d L u R ¯ u L d R − ¯ L / = u R γ µ d R T 6 1 1 Σ ( us ) u L s R + Ξ ( us ) s L γ µ u L ¯ u R γ µ s R + Ξ ( ds ) s L γ µ d L ¯ + ¯ s L u R ¯ ¯ ¯ d R γ µ s R + color 1 1 1 � � � � v 2 v 2 v 2 Σ = O v 2 Ξ = O Λ 2 Λ 2 Λ ≫ v • I will neglect s quarks (but they are interesting!)

Connection to models • new physics models induce one, a subset or all these operators qEDM c ( u , d ) split SUSY γ qCEDM c ( u , d ) MSSM g gCEDM C ˜ 2 Higgs Doublet Model G LR LR Σ ud Leptoquarks LL RR Ξ ud LR symmetric models an incomplete list of possibilities... for more details M. Pospelov and A. Ritz, ‘05; W. Dekens et al , ‘14; J. Engel, M. Ramsey-Musolf and U. van Kolck, ‘13; • goal: identify the distinctive manifestations of EFT operators on nuclei

Chiral Perturbation Theory need to work here theory strongly coupled! PDG 2016 L = − 1 µν G a µν + ¯ 4 G a Dq L + ¯ Dq R − ¯ q L M q R − ¯ q R M q L + L / T 4 + L / q L i / q R i / T 6 • at the moment, we cannot compute nuclear EDMs directly from QCD . . . maybe not too far in the future . . . e.g. NPLQCD collaboration • chiral symmetry symmetries to the rescue! SU L ( 2 ) × SU R ( 2 ) & spontaneous breaking to SU V ( 2 ) • pions are Goldstone boson • strong constraints on low-energy interactions of pions with nucleons, photons etc.

Chiral Perturbation Theory L = − 1 µν G a µν + ¯ 4 G a Dq L + ¯ Dq R − ¯ q L M q R − ¯ q R M q L + L / T 4 + L / q L i / q R i / T 6 • at the moment, we cannot compute nuclear EDMs directly from QCD • chiral symmetry to the rescue! SU L ( 2 ) × SU R ( 2 ) → SU V ( 2 ) pions are Goldstone boson strong constraints m π ≪ Λ χ ∼ 1 GeV on pion-N interactions

Chiral Perturbation Theory Chiral Perturbation Theory • low-energy theory of nucleon and pions • consistent with the symmetries of QCD • organized in an expansion in powers of Q , m π / Λ χ (∆ / T ) � L (∆) � L [ π , N ] = [ π , N ] + L T , f [ π , N ] f / f , ∆ f , ∆ / T • ∆ : # of inverse powers of Λ χ in coefficients • f = 0 , 2 , 4: # of nucleon legs ∆ = d + 2 m + f / 2 − 2 ≥ 0 • d : # of derivatives or photon fields • m : # of quark mass insertions

Chiral Perturbation Theory Chiral Perturbation Theory • low-energy theory of nucleon and pions • consistent with the symmetries of QCD • organized in an expansion in powers of Q , m π / Λ χ Niv · DN − g A L ( 0 ) f = 2 + 4 = ¯ N τ S µ D µ π N + C 11 ¯ ¯ NN ¯ NN + C ττ ¯ N τ N · ¯ N τ N F π • ∆ : # of inverse powers of Λ χ in coefficients • f = 0 , 2 , 4: # of nucleon legs ∆ = d + 2 m + f / 2 − 2 ≥ 0 • d : # of derivatives or photon fields • m : # of quark mass insertions • e.g. ∆ = 0 1. interactions fixed by symmetry/power counting 2. low-energy constants (LECs) contain non-perturbative info O ( 1 ) numbers, fixed by experiments

Chiral Perturbation Theory. A = 1 A ≤ 1: • only one relevant scale Q ∼ m π • perturbative expansion of the amplitudes � Q � ν T ∼ Λ χ ν = 4 � ν = 2 L + ∆ i , Λ χ = 2 π F π i • more loops = ⇒ Q / Λ χ suppression • and/or insertions of subleading vertices • at a given ν , only finite number of diagrams

Chiral Perturbation Theory. A ≥ 2 g 2 ∼ A F 2 π • another relevant scale: binding energy Q 2 / m N

Chiral Perturbation Theory. A ≥ 2 g 2 g 4 m 2 Q 5 Q 4 ∼ A ∼ × A × N F 2 4 π m N F 4 ( Q 2 + m 2 π ) 2 Q 4 π π integration measure vertices & pion prop. nucleon prop. • another relevant scale: binding energy Q 2 / m N • in loops E N ∼ Q 2 / m N nucleon energy pion momentum p π ∼ Q nucleon momentum p N ∼ Q

Chiral Perturbation Theory. A ≥ 2 g 2 g 4 m 2 Q 5 Q 4 ∼ A ∼ × A × N F 2 4 π m N F 4 ( Q 2 + m 2 π ) 2 Q 4 π π integration measure vertices & pion prop. nucleon prop. • another relevant scale: binding energy Q 2 / m N • in loops E N ∼ Q 2 / m N nucleon energy pion momentum p π ∼ Q nucleon momentum p N ∼ Q loop ∼ g 2 g 2 ∼ g 2 A m N Q Q A A M NN ∼ 300 MeV F 2 4 π F 2 F 2 M NN π π π • loop not (at best barely) suppressed

Chiral Perturbation Theory. A ≥ 2 + . . . Weinberg’s recipe: follow χ PT power counting • identify “irreducible diagram”: nucleon prop. not “pinched” E N ∼ Q define the potential V

Chiral Perturbation Theory. A ≥ 2 Weinberg’s recipe: follow χ PT power counting • identify “irreducible diagram”: nucleon prop. not “pinched” E N ∼ Q define the potential V i.e. solve Lippmann-Schwinger • iterate the nucleon-nucleon potential equation

Chiral Perturbation Theory. A ≥ 2 Weinberg’s recipe: • identify “irreducible diagram”: follow χ PT power counting nucleon prop. not “pinched” E N ∼ Q define the potential V i.e. solve Lippmann-Schwinger • iterate the nucleon-nucleon potential equation • “non-perturbative pions” 1. pion exchange leading effect Q / M NN ∼ 1

Chiral Perturbation Theory. A ≥ 2 Weinberg’s recipe: • identify “irreducible diagram”: follow χ PT power counting nucleon prop. not “pinched” E N ∼ Q define the potential V i.e. solve Lippmann-Schwinger • iterate the nucleon-nucleon potential equation • “non-perturbative pions” 1. LO potential: contact S-wave operator • “perturbative pions” 2. pion exchange as perturbation: Q / M NN ≪ 1

The T -violating Chiral Lagrangian • 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 + ¯ ¯ F π π 3 ¯ � L / = d 1 τ 3 N NN T F π ¯ ¯ C 1 C 2 NN ∂ µ (¯ ¯ NS µ N ) + N τ N ∂ µ (¯ ¯ NS µ τ N ) + F 2 F 2 π π • at LO, nucleon/nuclear EDMs expressed in terms of a few couplings ¯ d 0 , ¯ d 1 neutron & proton EDM, one-body contribs. to A ≥ 2 nuclei ¯ g 0 , ¯ g 1 pion loop to nucleon & proton EDMs leading / T OPE potential ¯ C 1 , ¯ C 2 short-range / T potential relative size of the coupling ( ∆ / T ) depends on chiral/isospin properties of / T source

Low energy couplings. ¯ θ term ¯ ¯ ¯ g 0 / F π ¯ g 1 / F π d 0 , 1 × Q C 1 , 2 × Q m 2 m 2 ¯ θ × π ε π 1 NDA F π Λ χ Λ 2 χ ∆ / 1 3 T ¯ θ term: q τ 3 q + m ∗ ¯ L QCD = ¯ Dq − ¯ m ¯ qq + ¯ m ε ¯ θ ¯ qi γ 5 q qi / m u + m d m ε = m d − m u m u m d ¯ = , ¯ , m ∗ = m m u + m d 2 2 • ¯ θ breaks chiral symmetry = ⇒ non-derivative π - N couplings � • but not isospin = ⇒ need extra m u − m d to generate ¯ g 1