EDMs, CP-odd Nucleon Correlators & QCD Sum Rules Adam Ritz - PowerPoint PPT Presentation

Hadronic Matrix Elements for Probes of CP Violation - ACFI, UMass Amherst - Jan 2015 EDMs, CP-odd Nucleon Correlators & QCD Sum Rules Adam Ritz University of Victoria Based on (older) work with M. Pospelov, see e.g. the review M. Pospelov & AR, Ann. Phys. 318, 119 (2005) [hep-ph/0504231] (plus some updates)

Experimental EDM Limits • EDMs are powerful (amplitude-level) probes for new � S (T,P) violating sources, motivated e.g. by baryogenesis. H = − d � E · S • Best current limits from neutrons, para- and dia-magnetic atoms and molecules Neutron EDM |d n | < 3 x 10 -26 e cm [Baker et al. ’06] |d Hg | < 3 x 10 -29 e cm [Griffith et al ’09] Diamagnetic EDMs |d Xe | < 4 x 10 -27 e cm [Rosenberry & Chupp ’01] Δ E ThO / ℇ ext < 3 x 10 -22 e cm [Baron et al. ’13] Paramagnetic EDMs Δ E YbF / ℇ ext < 1.4 x 10 -21 e cm [Hudson et al. ’11] Negligible SM (CKM) background - contribution is (at least) 4-5 orders of magnitude below the current neutron sensitivity, and lower for the atomic EDMs 2

Summary of the bounds log(d [e cm]) Real sensitivity to underlying sources -22 of CP violation depends on significant enhancement and suppression factors -24 ~ d q and d q from the neutron -26 ~ d q from Hg -28 impact of recent order of d e from ThO magnitude improvement in paramagnetic EDM sensitivity -30 The generic sensitivity to new physics -32 follows from taking d f ∝ m f -34 3

Multi-scale calculational scheme CP violation • Model-dependent (e.g. perturbative) • Nucleon matrix elements (focus of QCD scale this meeting), nucleon EDMs, pion- nucleon, nucleon-nucleon couplings nuclear/atomic scale • Nuclear scale, e.g. Schiff moment, magnetic quadrupole Observable • Atomic/Molecular EDM EDMs 4

Multi-scale calculational scheme Significant uncertainties for nucleon, nuclear and CP violation • Model-dependent diagmagnetic EDMs (e.g. perturbative) • Nucleon matrix elements (focus of QCD scale this meeting), nucleon EDMs, pion- nucleon, nucleon-nucleon couplings nuclear/atomic scale • Nuclear scale, e.g. Schiff moment, magnetic quadrupole Observable • Atomic/Molecular EDM EDMs 5

EDM Sensitivity to (short distance) CP-violation Fundamental Energy CP phases TeV θ -term, quark EDMs, semi-leptonic electron EDM CEDMs etc. qqee QCD pion-nucleon π NN Nucleon and NNNN µ semi-leptonic EDMs (n,p) EDM NNee nuclear EDMs of nuclei and ions (deuteron, etc) EDMs of paramagnetic atoms and molecules EDMs of (Tl,YbF, ThO, HfF + ,...) diamagnetic atoms Atoms in traps (Rb,Cs,Fr) atomic (Hg,Xe,Ra,Rn,...) solid state 6

EDM Sensitivity to (short distance) CP-violation Fundamental Energy CP phases TeV θ -term, quark EDMs, semi-leptonic electron EDM CEDMs etc. qqee QCD pion-nucleon π NN Nucleon and NNNN µ semi-leptonic EDMs (n,p) EDM NNee nuclear EDMs of nuclei and ions (deuteron, etc) EDMs of paramagnetic atoms and molecules EDMs of (Tl,YbF, ThO, HfF + ,...) diamagnetic atoms Atoms in traps (Rb,Cs,Fr) atomic (Hg,Xe,Ra,Rn,...) solid state 7

CP-odd operator expansion (at ~1GeV) (Flavor-diagonal) CP-violating operators at ~1GeV [ ➠ hadronic sector c n Λ d − 4 O ( n ) X L e ff = discussed in detail in d Jordy’s talk] n L dim 4 ⊃ ¯ θα s G ˜ G ¯ θ = θ 0 − ArgDet( M u M d ) ≡ θ 0 − θ q NB: (i) Basis at 1 GeV is simpler than at EW scale, after integrating out W,Z,h etc. (ii) Use of QCD dofs assumes that the new physics scale is above 1 GeV) 8

CP-odd operator expansion (at ~1GeV) (Flavor-diagonal) CP-violating operators at ~1GeV c n Λ d − 4 O ( n ) X L e ff = d n v d i ∼ cY i L dim 4 ⊃ ¯ θα s G ˜ G Λ 2 ⇣ ⌘ X X qF σγ 5 q + ˜ d l ¯ L “dim 6” ⊃ d q ¯ d q ¯ qG σγ 5 q lF σγ 5 l + q = u,d,s l = e,µ L dim 6 ⊃ wg 3 s GG ˜ G 9

CP-odd operator expansion (at ~1GeV) (Flavor-diagonal) CP-violating operators at ~1GeV c n Λ d − 4 O ( n ) X L e ff = d n L dim 4 ⊃ ¯ θα s G ˜ G ⇣ ⌘ X X qF σγ 5 q + ˜ d l ¯ L “dim 6” ⊃ d q ¯ d q ¯ qG σγ 5 q lF σγ 5 l + q = u,d,s l = e,µ s GG ˜ ff � ( ¯ f Γ f � ) LL ( ¯ � L dim 6 ⊃ wg 3 C � f Γ f � ) RR G + f,f � , Γ Schematic form of a few special 4-fermion operators, requiring no Higgs insertion - suppressed without new UV sources of LR mixing 10

CP-odd operator expansion (at ~1GeV) (Flavor-diagonal) CP-violating operators at ~1GeV c n Λ d − 4 O ( n ) X L e ff = d n L dim 4 ⊃ ¯ θα s G ˜ G ⇣ ⌘ X X qF σγ 5 q + ˜ d l ¯ L “dim 6” ⊃ d q ¯ d q ¯ qG σγ 5 q lF σγ 5 l + q = u,d,s l = e,µ s GG ˜ ff � ( ¯ f Γ f � ) LL ( ¯ � L dim 6 ⊃ wg 3 C � f Γ f � ) RR G + f,f � , Γ � L “dim 8” ⊃ C qq ¯ q Γ q ¯ q Γ i γ 5 q + C qe ¯ q Γ q ¯ e Γ i γ 5 e + · · · q, Γ v 2 C ij ∼ cY i Y j Λ 4 11

CP-odd operator expansion (at ~1GeV) (Flavor-diagonal) CP-violating operators at ~1GeV c n Λ d − 4 O ( n ) X L e ff = d n L dim 4 ⊃ ¯ θα s G ˜ G ⇣ ⌘ X X qF σγ 5 q + ˜ d l ¯ L “dim 6” ⊃ d q ¯ d q ¯ qG σγ 5 q lF σγ 5 l + q = u,d,s l = e,µ s GG ˜ ff � ( ¯ f Γ f � ) LL ( ¯ � L dim 6 ⊃ wg 3 C � f Γ f � ) RR G + f,f � , Γ � L “dim 8” ⊃ C qq ¯ q Γ q ¯ q Γ i γ 5 q + C qe ¯ q Γ q ¯ e Γ i γ 5 e + · · · q, Γ NB: Relative importance of different operators is very model-dependent, and the expansion can be misleading. E.g. for the SM (and SUSY and 2HDM regimes at large tanbeta), these 4-fermion sources are dominant 12

CP-odd operator expansion (at ~1GeV) (Flavor-diagonal) CP-violating operators at ~1GeV c n Λ d − 4 O ( n ) X L e ff = d n L dim 4 ⊃ ¯ θα s G ˜ G ⇣ ⌘ X X qF σγ 5 q + ˜ d l ¯ L “dim 6” ⊃ d q ¯ d q ¯ qG σγ 5 q lF σγ 5 l + q = u,d,s l = e,µ s GG ˜ ff � ( ¯ f Γ f � ) LL ( ¯ � L dim 6 ⊃ wg 3 C � f Γ f � ) RR G + f,f � , Γ � L “dim 8” ⊃ C qq ¯ q Γ q ¯ q Γ i γ 5 q + C qe ¯ q Γ q ¯ e Γ i γ 5 e + · · · q, Γ 13

CP-odd operator expansion (at ~1GeV) (Flavor-diagonal) CP-violating operators at ~1GeV c n Λ d − 4 O ( n ) X L e ff = d n L dim 4 ⊃ ¯ θα s G ˜ G ⇣ ⌘ X X qF σγ 5 q + ˜ d l ¯ L “dim 6” ⊃ d q ¯ d q ¯ qG σγ 5 q + lF σγ 5 l q = u,d,s l = e,µ s GG ˜ ff � ( ¯ f Γ f � ) LL ( ¯ � L dim 6 ⊃ wg 3 C � f Γ f � ) RR G + f,f � , Γ � L “dim 8” ⊃ C qq ¯ q Γ q ¯ q Γ i γ 5 q + C qe ¯ q Γ q ¯ e Γ i γ 5 e + · · · q, Γ nucleon/nuclear scales g (1) g (0) d ( n,p ) ¯ π NN ¯ π NN ¯ N π 0 N + ¯ NF σγ 5 N + ¯ N σ · π N + (4 − nucleon) + · · · eF σγ 5 e + C (0) ¯ d e ¯ NN ¯ ei γ 5 e + · · · S 14

EFT hierarchy Fundamental Energy CP phases TeV QCD pion-nucleon Nucleon couplings ( ) µ EDMs (n,p) EDM nuclear EDMs of nuclei and ions (deuteron, etc) EDMs of paramagnetic atoms and molecules EDMs of (Tl,YbF, ThO, HfF + ,...) diamagnetic atoms Atoms in traps (Rb,Cs,Fr) atomic (Hg,Xe,Ra,Rn,...) solid state 15

EFT hierarchy focus of the rest of this talk! Fundamental Energy CP phases TeV QCD pion-nucleon Nucleon couplings ( ) µ EDMs (n,p) EDM nuclear EDMs of nuclei and ions (deuteron, etc) EDMs of paramagnetic atoms and molecules EDMs of (Tl,YbF, ThO, HfF + ,...) diamagnetic atoms Atoms in traps (Rb,Cs,Fr) atomic (Hg,Xe,Ra,Rn,...) solid state 16

The QCD scale • Chiral EFT (chiral constraints) [ ➠ Emanuele’s talk] L = L ( π , ( K ) , N, · · · ) = − i N ( d n τ − + d p τ + ) F σγ 5 N − ¯ π NN τ a π a + ¯ g (0) g (1) ¯ π NN π 0 ) N + · · · N (¯ 2 { d N (¯ θ , d q , ˜ d q , w, C ij , . . . ) low energy constants g (0 , 1) π NN (¯ θ , ˜ ¯ d q , C ij , . . . ) [Crewther et al ’79; Hisano & Shimizu ’04; Stetcu et al ’08, de Vries et al ‘11,12; An et al ’12; Guo & Meissner ’12, Bsaisou et al ’14 ] 17

The QCD scale • Chiral EFT (chiral constraints) L = L ( π , ( K ) , N, · · · ) = − i N ( d n τ − + d p τ + ) F σγ 5 N − ¯ π NN τ a π a + ¯ g (0) g (1) ¯ π NN π 0 ) N + · · · N (¯ 2 { d N (¯ θ , d q , ˜ d q , w, C ij , . . . ) low energy constants g (0 , 1) π NN (¯ θ , ˜ ¯ d q , C ij , . . . ) • LEC’s related by IR loops (chiral logs) – still need input to fix counterterms e π NN ln Λ g (0) d n = g π NN ¯ + C ct 4 π 2 m n m π need UV threshold corrections 18

The QCD scale • Chiral EFT (chiral constraints) L = L ( π , ( K ) , N, · · · ) = − i N ( d n τ − + d p τ + ) F σγ 5 N − ¯ π NN τ a π a + ¯ g (0) g (1) ¯ π NN π 0 ) N + · · · N (¯ 2 { d N (¯ θ , d q , ˜ d q , w, C ij , . . . ) low energy constants g (0 , 1) π NN (¯ θ , ˜ ¯ d q , C ij , . . . ) • LEC’s related by IR loops (chiral logs) – still need input to fix counterterms • Simplest option is NDA - m q, av ∼ m 2 π / Λ had Λ had /f π ∼ g s ( µ ) ∼ 4 π ˜ θ q d q d q em q eg s O (1) d n Λ 2 4 π had Λ 2 m q g (0) had ¯ ∼ O ( α ) π NN f π f π 19