Mitglied der Helmholtz-Gemeinschaft. Theory IV: Electric Dipole Moments Hadron Physics Summer School 2012

Transcription

1 Mitglied der Helmholtz-Gemeinschaft Theory IV: Electric Dipole Moments Hadron Physics Summer School 2012 August 29, 2012 Andreas Wirzba

2 Motivation: Matter Excess in the Early Universe matter antimatter as Problem Standard Model falls short by several orders of magnitude! What is missing? T m B O(1 GeV): (n B n B)/(n B +n B) 10 9 [A.D. Dolgov (1997)] Bad Honnef: August 29, 2012 HPSS2012 Theory IV: EDM Andreas Wirzba 2 28

3 Motivation: Matter Excess in the Present Universe Matter-Antimatter Asymmetry Sakharov Conditions: 1 baryon number B violation 2 C- and CP(T)-symmetry violation 3 no thermal equilibrium JETP Lett. 5 (1967) 24 observed asymmetry (n B n B)/n γ = vs. Standard Cosmological Model: (n B n B)/n γ = Investigation of CP induced by SM extensions required Complementary approaches: high energy high precision WMAP + COBE (2003): n B /n γ =( ) 10 10, n γ 411cm CMB K Bad Honnef: August 29, 2012 HPSS2012 Theory IV: EDM Andreas Wirzba 3 28

4 Outline: 1 Motivation: Matter Antimatter Asymmetry 2 The Permanent EDM and its Features 3 CP-Violating Sources beyond the Standard Model 4 CP-Violating Sources at the Hadronic Level 5 Electric Dipole Moments of Neutron and Proton 6 Nuclear Electric Dipole Moments: the EDM of the Deuteron 7 Outlook Bad Honnef: August 29, 2012 HPSS2012 Theory IV: EDM Andreas Wirzba 4 28

5 Outline: 1 Motivation: Matter Antimatter Asymmetry 2 The Permanent EDM and its Features 3 CP-Violating Sources beyond the Standard Model 4 CP-Violating Sources at the Hadronic Level 5 Electric Dipole Moments of Neutron and Proton 6 Nuclear Electric Dipole Moments: the EDM of the Deuteron 7 Outlook Come to the dark side of the force! Bad Honnef: August 29, 2012 HPSS2012 Theory IV: EDM Andreas Wirzba 4 28

6 The Electric Dipole Moment (EDM) EDM: d = i r i e i (polar) subatomic particles H = µ σ B d σ E T: H = µ σ B + d σ E P: H = µ σ B + d σ E d σ (axial) Assuming CPT to hold, CP is violated as well a non-vanishing permanent EDM of a stable subatomic particle is P- and T-violating Strongly suppressed in SM (CKM-matrix): d n e cm Current bounds: d n < e cm, d p < e cm n: Baker et al. (2006), p: Dimitriev and Sen kov (2003) calculation with input from Hg atom measurement: Griffith et al. (2009) Bad Honnef: August 29, 2012 HPSS2012 Theory IV: EDM Andreas Wirzba 5 28

7 A naive estimate of the natural EDM scale Khriplovich & Lamoreaux (1997) CP & P conserving magnetic moment nuclear magneton µ N µ N = e 2m p e cm EDM demands for parity P violation : pay the price EDM demands for CP violation : Scale for CP from K-decays is 10 3 Pay this price. In summary: d N µ N e cm GF mπ with G F GeV 2, η + A(K L 0 π+ π ) A(K 0 S π+ π = (2.232 ± 0.011) 10 3 ) Bad Honnef: August 29, 2012 HPSS2012 Theory IV: EDM Andreas Wirzba 6 28

8 Upper bounds on dn in the course of time Upper bounds on the neutron EDM Smith, Purcell, Ramsey (1957) Baker et al. (2006) Bad Honnef: August 29, 2012 HPSS2012 Theory IV: EDM Andreas Wirzba 7 28

9 (Permanent) EDMs of (stable) non-selfconjugate particles with spin EDM operator d = d 3 x xρ( x) in stationary state j of definite parity j d j = d j J j time reversal: d d, J J, space reflection: d d, J J If d 0 and state j has no degeneracy (besides rotations), then P& T. j can be elementary particle (quark, charged lepton, W ± boson, Dirac neutrino,... ) or a composite neutron, proton, nuclei, atom, molecule Do not confuse with huge EDM of H 2O or NH 3 molecules no P & T: Ground state of these molecules at non-zero temperatures is mixture of 2 opposite parity states: above theorem does not apply If the interactions are described by a local, Lorentz-invariant, hermitian Lagrangian, then CPT invariance holds: then T CP Thus, under very mild assumptions: EDM d 0 P and CP self-conjugate particle particle equal to its antiparticle: all its charges" are zero Bad Honnef: August 29, 2012 HPSS2012 Theory IV: EDM Andreas Wirzba 8 28

10 Permanent EDMs and Form Factors Consider here s = 1 fermions: f = quark, lepton or nucleon 2 p f (p ) J µ em f (p) = ū f (p ) Γ µ (q 2 ) u f (p) q q 2 = (p p) 2 Γ µ (q 2 ) = γ µ F 1 (q 2 ) iσ µν q ν F 2 (q 2 ) 2m f + σ µν q ν γ 5 F 3 (q 2 ) 2m f + (/q q µ q 2 γ µ )γ 5 F a (q 2 )/m 2 f p Dirac F 1(q 2 ), Pauli F 2(q 2 ), electric dipole F 3(q 2 ) and anapole F a(q 2 ) FFs quark, lepton or nucleon EDM d f = F 3,f (0)/(2m f ) H eff = i d f f σ µν γ 5 f F µν d f σ E linear Stark effect 2 Likewise CP chromo (color quark) EDM in quark-gluon vertex i d cq 2 qσµν γ 5 T a q G a µν etc. or weak dipole moment (WDM) in ffz -boson vertex i d Z f 2 f σ µν γ 5 f Z µν. Bad Honnef: August 29, 2012 HPSS2012 Theory IV: EDM Andreas Wirzba 9 28

11 Generic features of EDM, chromo EDM or WDM L EDM = i d f 2 f σ µν γ 5 f F µν = i d f 2 f L σ µν f R F µν + i d f 2 f R σ µν f L F µν has mass dimension 5 (i.e. dim(d f ) = e length = e mass 1 ) non-renormalizable effective interaction In renormalizable theories, L EDM must be induced by quantum corrections, i.e. at 1-loop order or higher If EDM or chromo EDM or WDM non-zero, then CP in flavor-diagonal amplitudes Note: CP in SM model via CKM matrix is flavor changing. Thus extra P 10 7 factor multiplying naive estimate d e cm. L EDM flips fermion chirality 1 2 (11 γ 5)f = f L f R = 1 2 (11+γ 5)f fermion mass m F term (e.g. via Higgs) must be involved: d F mf n, n = 1, 2, 3 i.e. mass scaling depends on model of CP Bad Honnef: August 29, 2012 HPSS2012 Theory IV: EDM Andreas Wirzba 10 28

12 CP violation in the Standard Model (SM) 3 generations of up/down quarks (& el./neutrino leptons) with interactions with gluons, the photon, W ±, Z, and Higgs boson Empirical facts: 0 < m u < m d < m s < m c < m b < m t and m e < m µ < m τ quarks & leptons in mass basis quarks & leptons in weak-interaction basis L SM = L gauge + L gauge fermion + L gauge Higgs + L Higgs fermion CP invariant, except θ term of QCD (see below) and charged-weak-current interaction L cc L gauge fermion L cc = gw 2 3 ij=1 d Liγ µ V ij u Lj W µ gw 2 3 ij=1 l Liγ µ U ij ν Lj W µ + h.c. V : CKM (Cabibbo-Kobayashi-Maskawa matrix), U: lepton-mixing (Maki-Nakagawa-Sakata m.) 3 angles + 1 CP phase δ KM 3 angles +1(3) CP phase(s) for Dirac (Majorana) ν i s Bad Honnef: August 29, 2012 HPSS2012 Theory IV: EDM Andreas Wirzba 11 28

13 EDMs in the SM CP effects i>i ( m2 u m 2 i u j ) MEW 2 k>l ( m2 d m 2 k d l ) J MEW 2 KM J KM with J KM = Im(V ud V ubv cb V cd)= Im(V cb V cdv td V tb) and, especially, flavor-changing (!) EDM flavor-neutral predictions of KM mechanism tiny ( G 2 F ) 1-loop: O(g 2 w) γ d W V dq u, c, t W V dq d CP phase δ KM cancels prefactor real d 1 loop q =0 2-loop: d 2 loop q = d 2 loop cq = 0 Shabalin (1978) 3-loop: O(g 4 W gs 2 ), δ KM induces d q only at 3 loops: dn KM e cm Shabalin (1978); Khriplovich & Zhitnitsky (1982); Czarnecki & Krause (1997) Bad Honnef: August 29, 2012 HPSS2012 Theory IV: EDM Andreas Wirzba 12 28

14 Effective Lagrangian on the quark/gluon level Construction of an effective (low-energy) Lagrangian that incorporates the relevant CP (light) quark, gluon & electromagnetic interactions SM (light quarks w. Higgs integrated out) with at most marginal(dim=4) terms: L SM = L EW + L QCD L CP SM + L cc = L EW + q c f (iγ µ Dµ cc δ cc m f ) q c f 1 4 Ga µν µνga f =u,d,s Bad Honnef: August 29, 2012 HPSS2012 Theory IV: EDM Andreas Wirzba 13 28

15 Effective Lagrangian on the quark/gluon level Construction of an effective (low-energy) Lagrangian that incorporates the relevant CP (light) quark, gluon & electromagnetic interactions SM (light quarks w. Higgs integrated out) with at most marginal(dim=4) terms: L SM = L EW + L QCD + L θ QCD L CP SM + L cc + L CP dim=4 = L EW + q c f (iγ µ Dµ cc δ cc m f ) q c f 1 4 Ga µν Ga µν + θ g2 s f =u,d,s 32π 2 Ga a µν µν G Bad Honnef: August 29, 2012 HPSS2012 Theory IV: EDM Andreas Wirzba 13 28

16 Effective Lagrangian on the quark/gluon level Construction of an effective (low-energy) Lagrangian that incorporates the relevant CP (light) quark, gluon & electromagnetic interactions SM (light quarks w. Higgs integrated out) with at most marginal(dim=4) terms: L SM = L EW + L QCD + L θ QCD L CP SM + L cc + L CP dim=4 = L EW + q c f (iγ µ Dµ cc δ cc m f ) q c f 1 4 Ga µν Ga µν + θ g2 s f =u,d,s 32π 2 Ga a µν µν G Add CP non-relevant (dim=5 and higher) effective terms to L SM : L SM L SM + L CP dim=5 + L CP dim=6 + L CP SM + L cc + L CP L CP = L CP dim=4 + L CP dim=5 + L CP dim=6 + with = θg 2 s 32π 2 Ga µν G a µν i f =u,d,s d q 2 q f σ µν γ 5q f F µν i f =u,d,s d cq + w 3G 3 f abc G a G b νρ µν G c µ ρ + C fg ( q f q f ) ( q giγ 5q g) f,g=u,d,s 2 q f σ µν γ 5T a q f G a µν Bad Honnef: August 29, 2012 HPSS2012 Theory IV: EDM Andreas Wirzba 13 28

17 Effective Lagrangian on the quark/gluon level Construction of an effective (low-energy) Lagrangian that incorporates the relevant CP (light) quark, gluon & electromagnetic interactions SM (light quarks w. Higgs integrated out) with at most marginal(dim=4) terms: L SM = L EW + L QCD + L θ QCD L CP SM + L cc + L CP dim=4 = L EW + q c f (iγ µ Dµ cc δ cc m f ) q c f 1 4 Ga µν Ga µν + θ g2 s f =u,d,s 32π 2 Ga a µν µν G Add CP non-relevant (dim=5 and higher) effective terms to L SM : L SM L SM + L CP dim=5 + L CP dim=6 + L CP SM + L cc + L CP L CP = L CP dim=4 + L CP dim=5 + L CP dim=6 + = θg 2 s 32π 2 Ga µν G a µν i f =u,d,s d q 2 q f σ µν γ 5q f F µν i f =u,d,s d cq + w 3G 3 f abc G a G b νρ µν G c µ ρ + C fg ( q f q f ) ( q giγ 5q g) f,g=u,d,s Note: because of d q and d cq m f L CP with 2 q f σ µν γ 5T a q f G a µν effectively dim=6! dim=5 Bad Honnef: August 29, 2012 HPSS2012 Theory IV: EDM Andreas Wirzba 13 28

18 Strong CP violation: dimension 4 QCD has non-trivial vacua with topological quantum number n : Cluster decomposition theorem QCD vacuum characterized by the parameter θ value: θ = n= e inθ n with n = g2 s 32π 2 d 4 x E Ga µν G a µν Z P & T (= CP ) term in QCD Lagrangian (remember ɛ µναβ 0 only if µνρσ = 0123 modulo permutations) L QCD = L CP QCD + θ g2 s 32π 2 Ga µν G a,µν = L CP QCD + θ g2 s 32π ɛµνρσ G a µν Ga αβ Bad Honnef: August 29, 2012 HPSS2012 Theory IV: EDM Andreas Wirzba 14 28

19 Strong CP violation: dimension 4 QCD has non-trivial vacua with topological quantum number n : Cluster decomposition theorem QCD vacuum characterized by the parameter θ value: θ = n= e inθ n with n = g2 s 32π 2 d 4 x E Ga µν G a µν Z P & T (= CP ) term in QCD Lagrangian (remember ɛ µναβ 0 only if µνρσ = 0123 modulo permutations) L QCD = L CP QCD + θ g2 s 32π 2 Ga µν G a,µν = L CP QCD + θ g2 s 32π ɛµνρσ G a µν Ga αβ Under U A (1) rotation of the quark fields q f e iαγ 5/2 q f (1 + i 1 2 αγ5)q f : L QCD L str CP SM L CP QCD α f m f qiγ 5 q + (θ N f α) g2 s 32π 2 Ga µν G a,µν = L CP SM θm f q f iγ 5 q f with θ = θ+arg det M and m = mum d m u+m d Bad Honnef: August 29, 2012 HPSS2012 Theory IV: EDM Andreas Wirzba 14 28

20 Strong CP violation: dimension 4 QCD has non-trivial vacua with topological quantum number n : Cluster decomposition theorem QCD vacuum characterized by the parameter θ value: θ = n= e inθ n with n = g2 s 32π 2 d 4 x E Ga µν G a µν Z P & T (= CP ) term in QCD Lagrangian (remember ɛ µναβ 0 only if µνρσ = 0123 modulo permutations) L QCD = L CP QCD + θ g2 s 32π 2 Ga µν G a,µν = L CP QCD + θ g2 s 32π ɛµνρσ G a µν Ga αβ Under U A (1) rotation of the quark fields q f e iαγ 5/2 q f (1 + i 1 2 αγ5)q f : L QCD L str CP SM L CP QCD α f m f qiγ 5 q + (θ N f α) g2 s 32π 2 Ga µν G a,µν = L CP SM θm f q f iγ 5 q f with θ = θ+arg det M and m = mum d m u+m d Estimate of natural θedm size (note θ 0 if one m f 0): dn θ θ e m q θ e cm 10 2 θ e cm 2m N m N Bad Honnef: August 29, 2012 HPSS2012 Theory IV: EDM Andreas Wirzba 14 28

21 CP-violating sources beyond SM: dimension 6 CP-violation from extensions of the standard model SUSY, multi-higgs, Left-Right Symmetric Models,... Treatment of SM as an effective field theory: All higher d.o.f. than those of a given scale are integrated out: Theory contains only relevant d.o.f. and non-relevant contact terms governed by symmetry: Lorentz + SM gauge symmetries All information about the physics beyond this scale are collected in the values of the low-energy constants (LECS) g q g 1/ M 2 q 1T ev 100GeV Bad Honnef: August 29, 2012 HPSS2012 Theory IV: EDM Andreas Wirzba 15 28

22 CP-violating sources beyond SM: dim. 6 Add to SM all possible T- and P-odd contact interactions 100GeV g q q, G, γ, H H H qedm qcedm gcedm 4q 10GeV q q, γ, G 1GeV N... N, π, γ,... Bad Honnef: August 29, 2012 HPSS2012 Theory IV: EDM Andreas Wirzba 16 28

23 EDM-Translator from quarkish to hadronic" language? Bad Honnef: August 29, 2012 HPSS2012 Theory IV: EDM Andreas Wirzba 17 28

24 EDM-Translator from quarkish to hadronic" language? Symmetries, esp. Chiral Symmetry and Goldstone Theorem Low-Energy Effective Field Theory with External Sources Bad Honnef: August 29, 2012 HPSS2012 Theory IV: EDM Andreas Wirzba 17 28

25 Effective CP-violating sources on the hadronic level: Non perturbative techniques required: e.g. 2-flavor-ChPT J. DeVries et.al. (2010, 2011) J. Bsaisou, C. Hanhart, U.-G. Meißner, A.W. (2012, in preparation) Symmetries of QCD preserved by the effective field theory Association of terms by chiral transformation properties (each source transforms differently under chiral symmetry) P & T hadronic θ qedm qcedm gcedm operator 1 τ 3 1 τ 3 4q N τ πn ( ) N π 3 N ( ) N S µ v ν NF µν N S µ v ν τ 3 NF µν ( ): Suppressed by Goldstone theorem All sources contribute to nucleon EDMs Measurement of nuclear EDMs required for disentanglement! Bad Honnef: August 29, 2012 HPSS2012 Theory IV: EDM Andreas Wirzba 18 28

26 θ-term at the hadronic level: θ-term related to charge symmetry breaking (CSB) mass term: Crewther et al. (1979); Ottnad et al. (2010); Mereghetti et al. (2011); de Vries et al. (2011) ɛ = (m u m d)/(m u + m d), m = mum d m u+m d = (m u + m d)(1 ɛ 2 )/4 m u m d 2 qτ 3 q s s+ip m θ qiγ5 q δm str 2 N (τ 3 1 τ ππ 2Fπ 2 3 ) N m m+im θ δm str 2 (1 ɛ 2 ) θ 2Fπ 2 ɛ N τ πn δm str = (M n M p) str Non-perturbative part of πnn-vertex fixed by CSB studies: δm str = (2.0 ± 0.3) MeV [Gasser, Leutwyler (1982)] Bad Honnef: August 29, 2012 HPSS2012 Theory IV: EDM Andreas Wirzba 19 28

27 θ-term induced Nucleon EDM: complete 1-loop calculation chiral L: Crewther, di Vechia, Veneziano & Witten (1979/80) complete 1-loop: Ottnad, Kubis, Meißner & Guo (2010) = d n = dn tree + d loop n = ([2.9 ± 1.1] + [( 3 5) ± 2]) θ e cm θ < (using d n < e cm) Counter term at LO: estimate is model dependent Lattice calculation required for reliable prediction EDM of p and n not related by isovector symmetry Nuclear EDMs might be larger and simpler Sushkov, Flambaum, Khriplovichv (1984) Bad Honnef: August 29, 2012 HPSS2012 Theory IV: EDM Andreas Wirzba 20 28

28 Loop contributions to neutron EDM d n Ottnad, Kubis, Meißner & Guo, PLB 687 (2010) 42 π (K + ) π (K + ) n p (Σ ) n p (Σ ) n p (Σ ) n p (Σ ) n n n n π (K + ) π (K + ) p (Σ ) p (Σ ) n n n n π (K + ) π (K + ) Note that the participating baryons and mesons in the loops are both charged and the baryons and mesons are the same in both loop topologies Bad Honnef: August 29, 2012 HPSS2012 Theory IV: EDM Andreas Wirzba 21 28

29 Loop contributions to the proton EDM d p Ottnad, Kubis, Meißner & Guo, PLB 687 (2010) 42 π + (K + ) π + (K + ) p n (Σ 0, Λ) p p n (Σ 0, Λ) p p (Σ + ) p (Σ + ) p p p p π 0, η, η (K 0 ) π 0, η, η (K 0 ) p n (Σ 0, Λ) p p n (Σ 0, Λ) p π + (K + ) π + (K + ) In contradistinction to d n, the graphs relevant for d p are not symmetric with respect to the photon coupling Note the additional neutral mesons in the second loop topology Bad Honnef: August 29, 2012 HPSS2012 Theory IV: EDM Andreas Wirzba 22 28

30 Why d n d p? d p has additional (counter) terms due to the contributions of additional neutral loop baryons and contributions of additional neutral loop mesons and the electric charge of the proton: additional LECs since [Q, B p ] 0 while [Q, B n ] = 0. In the lattice calculation, additional noise because the charge form factor F 1 (q 2 ) and the electric dipole form factor F 3 (q 2 )/2m N mix in the electromagnetic current of the proton. Bad Honnef: August 29, 2012 HPSS2012 Theory IV: EDM Andreas Wirzba 23 28

31 First lattice results for the nucleon EDM R. Horsley et al., arxiv: v2 simulation details: V = , a 0.11 fm, m π /m ρ 0.8 (!) proton and neutron dipole form factors: (here θ I = 0.2 with θ = i θ I ) extract: d n = 0.049(5) θ e fm, d p = 0.080(10) θ e fm θ < Note: no isovector symmetry, d p d n! d p noisy since F 1 (0) has to be subtracted from p, s J µ p, s Bad Honnef: August 29, 2012 HPSS2012 Theory IV: EDM Andreas Wirzba 24 28

32 Nuclear EDM Two-Nucleon Contribution for gcedm and 4q; changes for θ-term and qcedm in [... ]; eδq 1 1 mπ 2 f π mπ 2 E Λf π [ 1] 1 [1] eδq Λ eδq Λ 1 E 1 E 1 [ m2 π ] fπ 2 Λ 2 1 [ m2 π ] fπ 2 Λ 2 1 [ln( m2 π ) m2 π µ 2 Sushkov, Flambaum, Khriplovich (1984) 1 [ m2 π Λ 2 ] Λ 2 +C] eδq f πm 1 mπ 2 mπ 2 Λf π [ 1] E [ E ] Λ Λ pion ranged operators enhanced for θ-term and qcedm Bad Honnef: August 29, 2012 HPSS2012 Theory IV: EDM Andreas Wirzba 25 28

33 Two-Nucleon Contribution to the Deuteron EDM at LO 3 S 1 3 S 1 N π τn: N π 3 N : 3 S 1 CP 1 P 1 γ 3 S/ 1 3 CP S 1 3 γ P 1 3 S 1 = ie(1 + τ 3) No θedm contribution to 2 H at LO θedm contribution to 3 He at LO in G π (1) e fm State CDBonn [U] (3) AV18 [U] (3) Reid93 [U] (2) ZRA [U] (1) 3 S D 1-adm Total (1): Khriplovich, Korkin (2000), J. de Vries et al. (2011) (2): Afnan, Gibson (2010) (3): Bsaisou, Hanhart, Meißner, Wirzba,... (2012, in prep.) Bad Honnef: August 29, 2012 HPSS2012 Theory IV: EDM Andreas Wirzba 26 28

34 Two-Nucleon Contribution to the Deuteron EDM at LO 3 S P 1 S 1 N π τn: N π 3 N : 3 S 1 CP 1 P 1 γ 3 S/ 1 3 CP S 1 3 γ P 1 3 S 1 = ie(1 + τ 3) No θedm contribution to 2 H at LO θedm contribution to 3 He at LO in G π (1) e fm State CDBonn [U] (3) AV18 [U] (3) Reid93 [U] (2) ZRA [U] (1) 3 S D 1-adm Total P 1-int Total (1): Khriplovich, Korkin (2000), J. de Vries et al. (2011) (2): Afnan, Gibson (2010) (3): Bsaisou, Hanhart, Meißner, Wirzba,... (2012, in prep.) Bad Honnef: August 29, 2012 HPSS2012 Theory IV: EDM Andreas Wirzba 26 28

35 Two-Nucleon Contribution to the Deuteron EDM at NLO =N π 3 N (qcedm) Bsaisou, Hanhart, Meißner, Wirzba... (2012, in prep.) LO N 2 LO 1% N 4 LO Finite: Ren.: All other topologies yield no EDM contribution, blue: also θedm contr. Consistent power counting scheme Bad Honnef: August 29, 2012 HPSS2012 Theory IV: EDM Andreas Wirzba 27 28

36 Outlook: source θ qedm qcedm gcedm 1 τ 3 1 τ 3 4q p n 2 H 3 He EDMs are ideal probes for CP violation in the hadronic sector EDMs of light nuclei provide independent information to p and n EDMs of light nuclei may be larger & simpler than nucleon EDMs qedm dominates if nuclear EDM is sum of nucleon EDMs Nuclear calculation possible up to accuracy of a few % Deuteron is a filter for the isospin-dependent qcedm θedm: d 3 He 2d p d n θ p-,n-edm Bad Honnef: August 29, 2012 HPSS2012 Theory IV: EDM Andreas Wirzba 28 28

37 Outlook: May the force be with us! source θ qedm qcedm gcedm 1 τ 3 1 τ 3 4q p n 2 H 3 He EDMs are ideal probes for CP violation in the hadronic sector EDMs of light nuclei provide independent information to p and n EDMs of light nuclei may be larger & simpler than nucleon EDMs qedm dominates if nuclear EDM is sum of nucleon EDMs Nuclear calculation possible up to accuracy of a few % Deuteron is a filter for the isospin-dependent qcedm θedm: d 3 He 2d p d n θ p-,n-edm A measurement of p, n, d, and 3 He EDM is necessary to learn about the underlying physics Bad Honnef: August 29, 2012 HPSS2012 Theory IV: EDM Andreas Wirzba 28 28