An Effective Approach to Hadronic Electric Dipole Moments. Jordy de Vries, Nikhef, Amsterdam

Transcription

1 An Effective Approach to Hadronic Electric Dipole Moments Jordy de Vries, Nikhef, Amsterdam

2 Outline Part I: The Standard Model EFT and EDMs Part II: Chiral considerations Part III: EDMs of nucleons and nuclei

3 Standard Model suppression Upperbound nedm 10^ [e cm] Quarks Neutron/ Proton 10-33,-34 e cm 10-31,-32 e cm 199 Hg 10-32,-34 e cm Electron Baker et al ,-38 e cm Here be dragons 5 to 6 orders below upper bound Out of reach! With linear extrapolation: CKM neutron EDM in Note: actual size of SM nedm is unclear (factor >10 uncertainty)

4 The strong CP problem If θ ~ 1 Upperbound nedm 10^ [e cm] More details on calculation later Sets θ upper bound: θ < Is there a reason for this suppression? Axions? Is θ=0 exact, or merely very small?

5 Measurement of a nonzero EDM? Standard Model: θ-term BSM sources of CP-violation SUSY, Left-Right, 2HDM, Forseeable future: EDMs are background-free searches for new physics Can we pinpoint the microscopic source of CPV from EDM measurements alone?

6 Measurement of a nonzero EDM? Standard Model: θ-term BSM sources of CP-violation SUSY, Left-Right, 2HDM, Collider/ Flavor/. input Matter/Antimatter asymmetry

7 The EDM metromap

8 EFT for new physics Energy M CP? TeV Probing models of CP violation via EDMs, involves a large hierarchy in scales M EW ~ v ~ M Z,W,H,t M CP > v >> m N > m π >> m e Λ χ ~ 2π F π ~ M N All scales involve new dynamics or even new degrees of freedom (QCD phase transition) F m Strategy: Use a cascade of effective field theories to go from one scale to the next em m e

9 Separation of scales Energy M CP? TeV BSM physics? Integrate out heavy degrees of freedom M EW ~ v ~ M Z,W,H,t 100 GeV L EFF L' EFF RG flow RG flow Integrate out heavy SM degrees of freedom Λ χ ~ 2π F π ~ M N 1 GeV Nonperturbative QCD regimes

10 Separation of scales Energy M CP? TeV BSM physics? Integrate out heavy degrees of freedom M EW ~ v ~ M Z,W,H,t 100 GeV L EFF L' EFF RG flow RG flow Integrate out heavy SM degrees of freedom Λ χ ~ 2π F π ~ M N 1 GeV F m 100 MeV em m e 1 kev Nonperturbative QCD regimes Nonperturbative methods: Lattice + chiral EFT Chiral EFT Hadronic and nuclear EDMs Atomic/Molecular observables Schiff theorem

11 Separation of scales Energy BSM physics M CP? TeV? Model dependent Integrate out heavy degrees of freedom L EFF RG flow M EW ~ v ~ M Z,W,H,t 100 GeV Λ χ ~ 2π F π ~ M N 1 GeV L' EFF RG flow Can be done once and for all! F m 100 MeV em m e 1 kev

12 Step 1: SM as an EFT Assume any BSM physics lives at scales >> Match to full set of CP-odd operators (model independent *) 1) Degrees of freedom: Full SM field content 2) Symmetries: Lorentz, SU(3)xSU(2)xU(1) L new = 1 L M L 6 +! CP M CP dim-5 generates neutrino masses/mixing, neglected here M EW 3) Few operators generate EDMs directly But SM loops 4) Discuss only a subset. More general set : W. Dekens et al * Assumption: no new light fields Buchmuller & Wyler 86 Gradzkowski et al 10 Many others

13 Fermion dipole operators M CP? TeV B, W q, l q, l One-loop QCD mixing Quark chromo-edm Quark EDM electron EDM 1 GeV e e

14 Gluon chromo-edm Weinberg PRL 89 Braaten et al PRL 90 Weinberg operator M CP? TeV d w f abc ε µναβ G a b c λ αβ G µλ G ν d w f abc ε µναβ G a b c λ αβ G µλ G ν 1 GeV

15 Gluon chromo-edm Weinberg PRL 89 Braaten et al PRL 90 Weinberg operator M CP? TeV d w f abc ε µναβ G a b c λ αβ G µλ G ν m Q Q Threshold contributions from heavy CEDMs d w f abc ε µναβ G a b c λ αβ G µλ G ν 1 GeV

16 Dipole mixing Numerical solu8on of the three dipole operators C q (1 GeV) = 0.39 C q (1 TeV) C q (1 TeV) C W (1 TeV) O( 2 s) C q (1 GeV) = C q (1 TeV) 0.29 C W (1 TeV) C W (1 GeV) = C W (1 TeV) 1) Diagonal terms are all suppressed 2) Suppressions are moderate 3) Mixing is important, e.g. if qcedm at low energy then also qedm (unless cancellations.) * 2-loop running in Degrassi et al, JHEP 05, few % correc8ons to LO running

17 Top electromagnetic dipoles What if the BSM physics couples mainly to third generation? Example: top EDM Concero-Cid et al 08 1-loop suppressed by V td 2 ~ 10-5 d t t d Two-loop path to electron EDM Cirigliano et al 16 Mckeen et al 12 H 2 F! F Much more stringent constraints! Far better than LHC. Talk by Vincenzo Cirigliano

18 Four-quark operators Ng & Tulin 12 Mereghetti et al 12 Fermion-Higgs interactions (appears in left-right models) Energy ū R µ d R ( ' id µ ')+h.c. v 2 g (ū R µ d R W ± µ +h.c.) W µ + M CP A right-handed quark-w coupling d R ` u R < M W d L u L L = i (ū R µ d R )(ū L µ d L )+h.c. u R d R Λ χ QCD RGE induces another operator Two four-quarks terms (FQLR operators) Ng & Tulin 12 Mereghetti et al 12 Maiezza et al 14

19 Many more But when the dust settles.. γ Few GeV QCD (θ-term) Quark EDM Quark C-EDM Gluon C-EDM FQ Without SU(2) invariance it would be > 20 operators (semi-)leptonic interactions e γ e Electron EDM e q ` e q ~ 1 2 M CP m e 2 m h 2

20 Intermediate summary I Parametrized BSM CP violation in terms of dim6 operators Evolved them to lower energies to ~ 1 GeV Several operators left: theta, (C)EDMs, Weinberg, Four-fermion Important: different BSM models -> different EFT operators

21 Intermediate summary I Parametrized BSM CP violation in terms of dim6 operators Evolved them to lower energies to ~ 1 GeV Several operators left: theta, (C)EDMs, Weinberg, Four-fermion Important: different BSM models -> different EFT operators Mohapatra et al 75 Giudice et al 06 Dekens et al 14 Pich & Jung Standard Model: only theta has a chance to be measured 2. 2-Higgs doublet model: quark+electron EDM, CEDMs, Weinberg (exact hierarchy depends on detail of models) 3. Split SUSY: only electron + quark EDMs (ratio fixed) 4. Left-right symmetric models: FQLR operators, way smaller (C)EDMs 5 Leptoquarks: Semi-leptonic four-fermion and four-quark (tree-level) Main question: can we unravel these scenarios with EDMs? Can EDMs compete with high-energy experiments?

22 Onwards to hadronic CPV Few GeV QCD (θ-term) γ q q q q Quark EDM Quark chromo- EDM Gluon chromo- EDM FQLR Hadronic/Nuclear CP-violation Lattice/Chiral perturbation theory 100 MeV π 0,± γ N N N N N N N N

23 CPV in hadrons and nuclei Goal is to calculate CPV properties of hadrons and nuclei o Electric dipole moments o Higher moments (Schiff moments/magnetic quadrupole ) Wishlist o Link to underlying theory (QCD + CPV operators) o Power counting o General (several observables in one framework) o Require nucleon quantities and CPV nuclear forces/currents

24 An ultrashort intro to Chiral EFT Use the symmetries of QCD to obtain chiral Lagrangian L QCD L chipt = L ππ + L πn + L NN +! Quark masses = 0 à SU(2) L xsu(2) R symmetry Spontaneously broken to SU(2)-isospin (pions = Goldstone) Explicit breaking (quark mass) à pion mass ChPT has systematic expansion in Q Λ χ ~ m π Λ χ Λ χ 1GeV Form of interactions fixed by symmetries Each interactions comes with an unknown constant (LEC) Extended to include CP violation Weinberg, Gasser, Leutwyler, and many many others Mereghetti et al 10, JdV et al 12, Bsaisou et al 14 Review: Meißner/JdV 15

25 ChiPT with CP violation γ q q + QCD (θ-term) q q They all break CP. But transform differently under chiral/isospin symmetry Different CP-odd chiral Lagrangians Different hierarchy of EDMs

26 Theta and chiral perturbation theory After axial U(1) and SU(2) rotations, complex CP-odd quark mass: L +m? qi 5 QCD = L kin m qq " m q 3 q q Crewther et al 79 Baluni 79

27 Theta and chiral perturbation theory After axial U(1) and SU(2) rotations, complex CP-odd quark mass: m = m u + m d 2 L QCD = L kin m qq " m q 3 q +m? qi 5 q Crewther et al 79 Baluni 79 L 0 = L m m N N 3 N +ḡ 0 N N Pion mass

28 Theta and chiral perturbation theory After axial U(1) and SU(2) rotations, complex CP-odd quark mass: " = m u m d m u + m d L QCD = L kin m qq " m q 3 q +m? qi 5 q Crewther et al 79 Baluni 79 L 0 = L m m N N 3 N +ḡ 0 N N Strong proton-neutron mass splitting

29 Theta and chiral perturbation theory After axial U(1) and SU(2) rotations, complex CP-odd quark mass: L +m? qi 5 QCD = L kin m qq " m q 3 q q Crewther et al 79 Baluni 79 m? = m um d m u + m d L 0 = L m m N N 3 N +ḡ 0 N N π 0,± g 0 CP-odd pion-nucleon interaction

30 Theta and chiral perturbation theory After axial U(1) and SU(2) rotations, complex CP-odd quark mass: L +m? qi 5 QCD = L kin m qq " m q 3 q q Crewther et al 79 Baluni 79 Linked via SU A (2) rotation m? = m um d m u + m d L 0 = L m m N N 3 N +ḡ 0 N N π 0,± Nucleon mass splitting (strong part, no EM!) g 0 CP-odd pion-nucleon interaction Use lattice for mass splitting Walker-Loud 14, Borsanyi 14, Aoki (FLAG) 13 1 ε 2 g 0 = δm N 2ε θ = (15.5± 2.5) 10 3 θ

31 Trust issues The relations are no longer unique if we use SU(3) chpt m g 0 = δm * N mε θ 2m g 0 = (m Ξ m Σ ) * (m s m) θ Numerically: LO relations differ by more than 100% ( sometimes sign...) g 0 = (15.5± 2.5) 10 3 θ Can this be trusted??

32 Trust issues The relations are no longer unique if we use SU(3) chpt m g 0 = δm * N mε θ 2m g 0 = (m Ξ m Σ ) * (m s m) θ Numerically: LO relations differ by more than 100% ( sometimes sign...) g 0 = (15.5± 2.5) 10 3 θ Can this be trusted?? Investigate higher-order corrections to left- right-sides of relations g NLO Mass NLO (c) (a)

33 Protected relations g NLO Mass NLO (c) m g 0 = δm * N mε θ 2m g 0 = (m Ξ m Σ ) * (m s m) θ Relation 1: All corrections obey the relation Relation 2: Explicit violation already at NLO g 0 (m Ξ m Σ ) = 1+ (D2 6DF 3F 2 ) [ 1 0.7] (m K m π ) 2 (m K + m π ) 2m * 6(4π f π ) 2 (m Ξ m Σ ) (m s m) θ 2m * (m s m) θ JdV, Mereghetti, Walker-Loud 15 (a)

34 Wrap-up Identify protected relations (including N2LO) for various couplings JdV et al 15 Values recommended for lattice extrapolations of neutron EDM Used to estimate short-range CPV NN forces Similar couplings appear in axion phenomenology Stadnik et al 14 Isospin-violating coupling g 1 has no protected relation. g 1 = (3± 2) 10 3 θ Partially based on Bsaisou et al 12 resonance saturation

35 Back to pion-nucleon couplings 2 relevant CP-odd structures L = g 0 Nπ τ N + g 1 Nπ 0 N π 0,± g 0 g 1,2 π 0 θ-term conserves isospin! So g 1 is suppressed. g 0 = (15.5± 2.5) 10 3 θ g 1 = (3± 2) 10 3 θ Pospelov et al 01, 04 Mereghetti et al 10, 12, Bsaisou et al 12 g 1 g 0 = (0.2 ± 0.1) Large uncertainty for g 1 due to pion mass splitting and unknown LEC g 0 relation protected from higher-order SU(2) and SU(3) corrections

36 Back to pion-nucleon couplings Dominant CPV force from: L = g 0 Nπ τ N + g 1 Nπ 0 N π 0,± π 0 g 0 g 1 Dimension-six qcedms have isospin-odd component! ChPT gives no direct info about size. Both g 0,1 are LO QCD sum rules to the rescue Pospelov 02 ḡ 0 =(5± 10)( d u + d d )fm 1 ḡ 1 = ( )( d u dd )fm 1 Large uncertainties. But generally: ḡ 1 ḡ 0

37 Back to pion-nucleon couplings 2 CP-odd structures π 0,± π 0 L = g 0 Nπ τ N + g 1 Nπ 0 N g 0 g 1 Quark Chromo-EDM is chiral partner of chromo-mdm Pospelov -Ritz 05 Hisano et al 12 d q q µ 5 qg µ c q q µ 3 qg µ SU A (2) Relations protected up to N2LO Promising way to get g 0, g 1 from lattice JdV, Mereghetti, Seng, Walker-loud in prep

38 Back to pion-nucleon couplings 2 CP-odd structures π 0,± π 0 L = g 0 Nπ τ N + g 1 Nπ 0 N g 0 g 1 Mohapatra, Senjanovic, Pati 75 Four-quark left-right operator breaks isospin! Maiezza et al 14 L = i (ū R µ d R )(ū L µ d L )+h.c. Absolute sizes of g 0,1 are not given by ChPT. No sum rules either. ChPT gives ratio of couplings g 1 g 0 = 2 8c 1 m π = (68± 25) strong (m n m p ) JdV et al 12 Bsaisou et al 14

39 Back to pion-nucleon couplings 2 CP-odd structures π 0,± π 0 L = g 0 Nπ τ N + g 1 Nπ 0 N Key idea g 0 g 1 The theta-term and dim-6 operators have different chiral properties Different models -> Different g0/g1 ratios Theta Theta term 2HDM Quark CEDMs mlrsm FQLR g 1 g Quark EDM and Weinberg Both couplings are suppressed! But how to experimentally probe these ratios?

40 The Nucleon EDM Nucleon EDM + γ π ± γ d n = d 0 d 1 eg A g F d p = d 0 + d 1 + eg A 4 2 F ln m2 MN 2 2 appleg 0 ln m2 M 2 N m M N g 0 2 m M N g 1 2 m M N g A absorbed UV divergences in d 0, d 1 LO counterterms. No ChPT prediction for size. For all CPV sources, neutron and proton EDM of same order More can be said with lattice and/or model calculations Crewther et al., 79, Pich, Rafael, 91, Borasoy 00 Guo et al, , Mereghetti et al

41 The Nucleon EDM Nucleon EDM + γ π ± γ d n = d 0 d 1 eg A g F d p = d 0 + d 1 + eg A 4 2 F ln m2 MN 2 2 appleg 0 ln m2 M 2 N m M N g 0 2 m M N g 1 2 m M N g A ḡ0 = (15.5 ± 2.5) 10 3 d n ' e cm Experimental constraint: < Lattice + ChPT Guo et al d n = (3.9 ± 1.0) e cm O Connell /Savage 06 See also: Shindler et al 15, Shintani et al 15, Alexandrou et al 15

42 Extracting g 0 ChPT makes a robust prediction Lattice Test ḡ 0 = (15.5 ± 2.5) 10 3 F( Q 2 ) 2 4 = d + Q S + Q H +... EDM Radius (Schiff moment) Schiff moments are ChPT predictions S n = S p = eg g A π π F π m π 4 m π m N

43 Extracting g 0 ChPT makes a robust prediction Lattice Test ḡ 0 = (15.5 ± 2.5) 10 3 F( Q 2 ) 2 4 = d + Q S + Q H Neutr Proton EDM Radius (Schiff moment) Schiff moments are ChPT predictions S n = S p = eg g A π π F π m π 4 m π m N F3(Q 2 )/2MN Signs of slopes agree Magnitudes larger then ChPT (larger g0 by factor 5) However, quenched + large pion masses + large Q 2.. Andrea Shindler et a Q 2 [GeV 2 ] Similar pattern in Shintani et al, PRD 16. Need higher precison.

44 And dim-6 sources? Quark EDM accurately determined recently! Bhattacharya et al d n = (0.22 ± 0.03)d u +(0.74 ± 0.07)d d +(0.008 ± 0.01)d s Quark CEDM no lattice calculations yet. But in progress. QCD sum rules: nucleon EDMs ~ 50-75% uncertainty Weinberg (and four-quark) only estimates d n = ±[(50 ± 40) MeV] ed W Pospelov, Ritz Hisano et al Weinberg 89 Demir et al 03 Ratio of proton/neutron EDM ~O(1) for all sources Need more input to unravel the models

45 Probe these ratios with nuclear EDMs g 0 γ π ± π ±,0 g 0, g 1 Nucleon EDM Nuclear EDM Tree-level: no loop suppression Orthogonal to nucleon EDMs, sensitive to different CPV structures d A = < Ψ A! J CP Ψ A > (E H PT ) Ψ (E H PT ) Ψ A > = 0 A > = V CP Ψ A > + 2 < Ψ A CP-even forces + currents from chiral EFT Need to describe the CPV nuclear force!! J CP " Ψ A >

46 A quick look at the P- and T-odd potential How do we know that pion exchange (long-range) dominates? CP-even g A N (! σ 2F π N N N N! D π a )τ a N π ±,0 ~ (g A Q)2 Q 2 ~ Q 0 ~ Q 0

47 A quick look at the P- and T-odd potential How do we know that pion exchange (long-range) dominates? If CPV + chiral breaking then nonderivative pi-n couplings CP-even g A N (! σ 2F π! D π a )τ a N CP-odd g 0 Nπ τ N + g 1 Nπ 0 N N N N N π ±,0 ~ (g A Q)2 Q 2 ~ Q 0 ~ Q 0 π ±,0 ~ (g A Q)g 0,1 Q 2 NN i (Nσ i N) ~ Q 1 ~ Q 1

48 A quick look at the P- and T-odd potential Apply this to the theta term LO g 0 g 0 NLO LO g 1 LO only g 0 pion exchange, NLO two-pion-exchange + g 1 O NLO O short-range estimated by resonance saturation (eta, kaon couplings) 10% contributions in 3He EDM JdV et al 11 Bsaisou et al 14 N 2 LO

49 A quick look at the P- and T-odd potential Quark CEDMs FQLR JdV et al 11 LO g 0 LO g 1 NLO NLO Both pion exchange at Nleading 2 LO order (but LECs not well known yet) Short-range expected to be small (good!) TPE g 1 diagrams vanish, g 0 work in same channel as OPE For FQLR only: three-nucleon force at NLO Found to be small in 3He

50 A quick look at the P- and T-odd potential Weinberg operator + chiral-invariant FQ operators JdV et al 11 LO LO NLO NLO LO g 0 g 1 LO N 2 LO NLO NLO Pion-exchange suppressed because of chiral symmetry Short-range NN terms not suppressed compared to OPE! Large uncertainties N 2 LO in N 2 both LO LECs and nuclear matrix elements

51 EDM of the deuteron Target of storage ring measurement Three contribu8ons (NLO) 1. Sum of nucleon EDMs 2. CP-odd pion exchange 3. CP-odd NN interactions π g0 g1 C 1,2

52 EDM of the deuteron Target of storage ring measurement Three contribu8ons (NLO) 1. Sum of nucleon EDMs 2. CP-odd pion exchange 3. CP-odd NN interactions π g0 g1 Deuteron is a special case due to N=Z C 1,2 3 S1 3 S1 g0 g 1 γ 1 P 3 S 1 1 γ 3 P 3 S 1 1

53 The chiral filter Deuteron EDM results Chiral filter Liu/Timmermans 04 JdV et al 11 Bsaisou et al 14 d D = 0.9(d n + d p )+ [(0.18± 0.02) g 1 + (0.0028± ) g 0 ] e fm Error estimate from cut-off variations + higher-order terms ` Theta term Quark CEDMs Four-quark operator Quark EDM and Weinberg d D d n d p 0.5± 0.2 5± 3 20 ±10 0 d n Ratio suffers from hadronic (not nuclear!) uncertainties (need lattice) EDM ratio hint towards underlying CP-odd operator!

54 The chiral filter Deuteron EDM results Stetcu et al 08 JdV et al 11 Song et al 13 Bsaisou et al 14 d D = 0.9(d n + d p )+ [(0.18± 0.02) g 1 + (0.0028± ) g 0 ] e fm d 3He = 0.9 d n 0.05 d p + [(0.14 ± 0.04) g 1 + (0.10 ± 0.03) g 0 ] e fm +... ` Theta term Quark CEDMs Four-quark operator Quark EDM and Weinberg d D d n d p 0.5± 0.2 5± 3 20 ±10 0 d n Ratio suffers from hadronic (not nuclear!) uncertainties (need lattice) EDM ratio hint towards underlying CP-odd operator! 3He is complementary but also short-range corrections. Extended to 6Li, 13C, 19F? (nuclear cluster model) Yamanaka et al 15, 16

55 Uuugh. Plot from Bsaisou et al JHEP 14 EDM contribution (some units) Av18 CD-Bonn Chiral EFT Cut-off varia8on Quite a large spread. Av18 very repulsive at short distances Heavy meson mass (GeV) Only 10-30% for theta/qcedm (but unknown for Weinberg)

56 Unraveling models Dekens et al 14 Theta term: quantitative predictions d n = (3.9 ±1.0) θ e cm d D d n d p = (0.89 ± 0.3) θ e cm d 3He 0.9d n = (1.0 ± 0.4) θ e cm Left-right symmetry d 2H d n, p = 20 ±10 d 3He = (0.8± 0.1)d D Identifying Aligned 2HDM more difficult. Need lattice input. d 3He ~ d D ~ 5 d n, p Complementary info from electron EDM (assuming similar phases) d e Theta: = 0 mlrsm: ~ HDM: d n d n d e d e d n ~ 10 2

57 Onwards to heavy systems Strongest bound on atomic EDM: New measurements expected: Ra, Xe,. Graner et al, 16 d 199 Hg < e cm Schiff Theorem: EDM of nucleus is screened by electron cloud if: 1. Non-relativistic kinematics 2. Point particles Schiff, 63

58 Onwards to heavy systems Graner et al, 16 Strongest bound on atomic EDM: New measurements expected: Ra, Xe,. d 199 Hg < e cm Schiff Theorem: EDM of nucleus is screened by electron cloud if: 1. Non-relativistic kinematics 2. Point particles Schiff, 63 Screening incomplete: nuclear finite size (Schiff moment S) Typical suppression: Atomic part well under control d Atom d nucleus 10Z 2 " $ # R N R A % ' & d 199 Hg = ( 2.8 ± 0.6 ) 10 4 S Hg e fm 2 Dzuba et al, 02, 09 Sing et al, 15

59 EFT and many-body problems Need to calculate Schiff Moment (or MQM) of Hg, Ra, Xe. Issue: no power counting... Do pions dominate? Say we assume so: S = g(a 0 g 0 + a 1 g 1 ) e fm 3 g =13.5 a 0 range (best) a 1 range (best) 199 Hg 0.03±0.025 (0.01) 0.030±0.060 (±0.02) 225 Ra -3.5±2.5 (-1.5) 14±10 (6) 129 Xe -0.03±0.025 (-0.008) -0.03±0.025 (-0.009) Flambaum, de Jesus, Engel, Dobaczewski,,. Uncertainties would make interpretation more difficult Great challenge: connect chiral-eft approach to heavier nuclei table from review: Engel et al, 13

60 Role of uncertainties Im Y 0 d Im Y 0 u The Higgs Yukawa couplings to quarks can be complex (2HDM, SUSY, ) Central values matrix elements v 2 Im Y 0 u,d < 10 6 Plots from Chien, Cirigliano, Dekens, JdV, Mereghetti, 15

61 Role of uncertainties Im Y 0 d Im Y 0 u The Higgs Yukawa couplings to quarks can be complex (2HDM, SUSY, ) Central values matrix elements v 2 Im Yu,d 0 < 10 6 Once uncertainties are included. Free direction appears! Modest hadronic+nuclear theory improvements (50%) would help a lot Plots from Chien, Cirigliano, Dekens, JdV, Mereghetti, 15

62 Role of uncertainties Im Y 0 d Im Y 0 u The Higgs Yukawa couplings to quarks can be complex (2HDM, SUSY, ) Central values matrix elements v 2 Im Yu,d 0 < 10 6 Once uncertainties are included. Free direction appears! Modest hadronic+nuclear theory improvements (50%) would help a lot Or new experiments! Plots from Chien, Cirigliano, Dekens, JdV, Mereghetti, 15

63 The EDM metromap

64 Conclusion/Summary/Outlook EDMs ü Very powerful search for BSM physics (probe the highest scales) ü Heroic experimental effort and great outlook ü Theory needed to interpret measurements and constraints ü ü EFT framework Framework exists for CP-violation (EDMs) from 1 st principles Keep track of symmetries (gauge/cp/chiral) from multi-tev to atomic scales ü ü The chiral filter Chiral symmetry determines form of hadronic interactions Different models à different dim6 à different EDM hierarchy ü Need theory improvement to fully exploit the experimental program