Electric Dipole Moments: Phenomenology & Implications

Electric Dipole Moments: Phenomenology & Implications M.J. Ramsey-Musolf U Mass Amherst http://www.physics.umass.edu/acfi/ ACFI Workshop, Amherst May 015! 1

Outline I. Experimental situation II. Effective operators III. Illustrative examples IV. Paramagnetic & diamagnetic systems V. Theoretical issues

I. Experimental Situation 3

EDMs: New CPV? System Limit (e cm) * SM CKM CPV BSM SM CPV 199 Hg ThO n 3.1 x 10-9 8.7 x 10-9 ** 3.3 x 10-6 10-33 10-38 10-31 background well 10 below new CPV expectations 10 New expts: 10 to 10 3 more sensitive 10-6 CPV needed for BAU? * 95% CL ** e - equivalent 4

EDMs: New CPV? System 199 Hg ThO n Limit (e cm) * 3.1 x 10-9 8.7 x 10-9 ** 3.3 x 10-6 SM CKM CPV 10-33 10-38 10-31 BSM SM CPV background well 10 below new CPV expectations 10 New expts: 10 to 10 3 more sensitive 10-6 CPV needed for BAU? * 95% CL ** e - equivalent Mass Scale Sensitivity ψ e ϕ ϕ γ sinφ CP ~ 1! M > 5000 GeV M < 500 GeV! sinφ CP < 10-5

II. Effective Operators 7

Why Multiple Systems? 8

Why Multiple Systems? Multiple sources & multiple scales 9

EDM Interpretation & Multiple Scales Baryon Asymmetry Early universe CPV BSM CPV SUSY, GUTs, Extra Dim Collider Searches Particle spectrum; also scalars for baryon asym? Energy Scale QCD Matrix Elements d n, g πnn, Expt Nuclear & atomic MEs Schiff moment, other P- & T-odd moments, e-nucleus CPV 10

Effective Operators: The Bridge + 11

EDM Interpretation & Multiple Scales Baryon Asymmetry Early universe CPV BSM CPV SUSY, GUTs, Extra Dim Collider Searches Particle spectrum; also scalars for baryon asym d= 6 Effective Operators: CPV Sources fermion EDM, quark chromo EDM, 3 gluon, 4 fermion Energy Scale QCD Matrix Elements d n, g πnn, Expt Nuclear & atomic MEs Schiff moment, other P- & T-odd moments, e-nucleus CPV 1

Weinberg 3 gluon Operator Classification

Operator Classification ϕ + ϕ! υ θ-term renormalization

Operator Classification Quark chromo-edm

Operator Classification Fermion EDM

Wilson Coefficients: EDM & CEDM Chirality flipping ~ δ f, δ q appropriate for comparison with other d=6 Wilson coefficients 17

Operator Classification Semileptonic Nonleptonic Semileptonic Semileptonic: atomic & molecular EDMs

Operator Classification Nonleptonic: hadronic EDMs & Schiff moment

Operator Classification ϕ d L W + u R ϕ! υ u L d R ϕ Nonleptonic: hadronic EDMs & Schiff moment

Wilson Coefficients: Summary δ f fermion EDM (3) ~ δ q quark CEDM () C G ~ 3 gluon (1) C quqd non-leptonic () C lequ, ledq semi-leptonic (3) C ϕud induced 4f (1) 1 total + θ light flavors only (e,u,d) 1 65s

BSM Origins EDM: γff CEDM: gff Weinberg ggg: MSSM LRSM RS Four fermion udhh ϕ d L W + u R u L ϕ d R 3

III. Illustrative Examples 4

Complementarity: Three Illustrations CPV in an extended scalar sector (HDM): Higgs portal CPV Weak scale baryogenesis (MSSM) Model-independent 5

this symmetry general haveunder a di erent expression another basistoobtained by the transformatio ethough CPV complex phases will thatinare invariant a rephasing of theinscalar fields. 0 totaking a basis where the vacuum expectation value (vev) of the j = UY jk transformation L U(1) k. For example, complex: while that associated with the neutral component of is in general 1 1 1 For future purposes,+we emphasize U = p that the value, of is not invariant. ( 1 1 H1+ H Inoue, R-M, Zhang: tan = v / v1,0 the,minimization conditions in the(5) Hk0 and A0k directions give us the, Denoting = 1403.457 p1 (v1 + H 0 + ia0 ) p1 (v + H 0+ ia ) 1 1 thetransformation (1) corresponds to i i Higgs Portal CPV m11 = 1v cos +( 3 + 4 )v sin Re(m1 e ) tan + Re( 5e )v sin GeV, v1 = v1 and v = v ei. It is apparent that in0 general the relative $ +0( 3. +denotes m = v sin Re(m1 ei ) cot + Re( 5 ei )v cos (3 4 )v cos 1 CPV & HDM: Type I & II λ6,7 = 0 for simplicity lobal rephasing transformation i i Im(m e ) = v sin cos Im( 5 e ). We then take the Higgs i potential to have the1form 0 j (6) j = e j, h given the complex i parameters From the last equation, it is clear that the phase can be solved1 for 1 = the ( useful, ( to )express + 3 ( this )( ) +in terms however, 1) + 4 ( 1 of )(the 5 ( 1 ) + h.c. 1 1condition 1k): + e redefined tovabsorb 1global phases n h i o 0 m sin( sin( 0 i( 1 ) 1 i( 1 ) 1). 1 (4 (m1 ) = e m1m, 11 ( 15 = e m1 ( 1 5,) + h.c. + m ( ) 1.) = 5 v1 v(7) 1) + In the limit that the to small but non-vanishing that rephasing will be appropriate for our later phenomeno k are l is unchanged. It is then straightforward observe that there exist two eventually to EDMs. A repr work, only the scalar loop could contribute to C1 and The complex coefficientseq. in (1) the potential are m1 and 5. In general, the presence of the then implies 1 term, in conjunctio the right panel of Fig. 1. It is proportional to with the Z -conserving quartic interactions, will induce other Z -breaking quartic operators at one-loop order. Simp v sin ).. Give 5 v1 vim( 5 m1 v1 v ) = 5m1 v1/(16 EWSB power counting implies that the responding coefficients are finite with magnitude proportional to m 1 k = Arg (m ), 1 1 m1 5 1, isterm. our attention tousing 1 the 1/16 suppression, we thethe tree-level Z -breaking bilinear relationin Eq. (13), the above quantity indeed related to the unique CPV will restrict 5 v1 v = Arg (m )v v. (8) 1 1 The fermionic loops do not contribute because the Higgs and quar 5 1 m1a rephasing physical It is instructive to identify the CPV complex phases proportional that are toinvariant under of thecharge scalar fields. T the corresponding CKM element. As a result, the coefficients Cij are that end, we perform an SU()L U(1)Y transformationimaginary. to a basis vacuum expectation value (vev) of th They where contributethe to magnetic dipole moments instead of EDMs. so that there exists only one independent CPV phase in the theory after EWSB. neutral component of 1 is real while that associated with the neutral component of is in general complex: A special case arises when 1 = 0. In this case, Eq. (1) implies that + M at the electroweak scale without the Z symmetry flavor violation, flavor H1+ is to assume minimal H sin( ) = 0 5 v1 v0 sin(, = m1p1 studies., ), (5 not discuss this possibility, but refer [13 15] for recent phenomenological 1 0 0 1 = to p (v + H + ia ) (v + H + ia ) Viable EWB & CPV: 1 1 1 or H 0 /H + p H+ i where v = vedms + v = 46 GeV, v = v and v = v e. It is apparent that in general denotes the relativ 1 are -loop 1 1 1 m 1 H phase of v and v1. Under the global rephasing transformation cos W ±=. CPV is flavor non-diag the couplings m1 j =e i j 0 j, f 5 v1 v f f W+ H0 (6 When the right-hand side is less than 1, has solutions two solutions of equal magnitude and op to the presence of spontaneous CPV (SCPV) [17, 18]: and sponding 5 can be redefined to absorb the global phases FIG. 1: Left: quark or lepton EDM from W ± H exchange and CPV Higgs interactions. then contributes as the upper loop of t to W a B µ e ective operator, which to EDM 0 i( 1 ) 1 µ 01 i( m 1 m 1 ) 1 1 (m1 ) = e m arccos, (7 5 =e = 5±,. = ±1 cos sin v v v The gauge invariant to EDM 5 1 contributions 5 from this class of diagrams have been c a

Future Reach: Higgs Portal CPV CPV & HDM: Type II illustration λ 6,7 = 0 for simplicity Hg ThO n Ra Present sin α b : CPV scalar mixing Future: d n x 0.1 d A (Hg) x 0.1 d ThO x 0.1 d A (Ra) Future: d n x 0.01 d A (Hg) x 0.1 d ThO x 0.1 d A (Ra) Inoue, R-M, Zhang: 1403.457 68

EDMs & EW Baryogenesis: MSSM f ~ f ~ V f γ, g Heavy sfermions: LHC consistent & suppress 1-loop EDMs Sub-TeV EW-inos: LHC & EWB - viable but non-universal phases Compatible with observed BAU d e = 10-8 e cm ACME: ThO sin(µm 1 b * ) d n = 10-7 e cm sin(µm 1 b * ) d e = 10-9 e cm d n = 10-8 e cm Next gen d e Next gen d n Li, Profumo, RM 09-10 8

Wilson Coefficients: Model Independent δ f fermion EDM (3) ~ δ q quark CEDM () C G ~ 3 gluon (1) C quqd non-leptonic () C lequ, ledq semi-leptonic (3) C ϕud induced 4f (1) 1 total + θ light flavors only (e,u,d) 30 71

IV. Paramagnetic & Diamagnetic Systems 31

EDM Classification Paramagnetic: unpaired electron spin (ThO & YbF molecules, Tl atom ) Diamagnetic: no unpaired electron spin (neutron, 199 Hg, 5 Ra ) 3

Global Analysis: Input Chupp & R-M: 1407.1064 33

Global Analysis: Input Paramag Chupp & R-M: 1407.1064 34

Paramagnetic Systems: Two Sources e Electron EDM γ e N e γ (Scalar q) x (PS e - ) N e Tl, YbF, ThO 35

Paramagnetic Systems: Two Sources e Electron EDM γ e N e γ (Scalar q) x (PS e - ) N e Tl, YbF, ThO 36

Paramagnetic Systems: Two Sources e Electron EDM γ Chupp & R-M: 1407.1064 e N e γ (Scalar q) x (PS e - ) N e Tl, YbF, ThO 37

Paramagnetic Systems: Two Sources e Electron EDM γ Chupp & R-M: 1407.1064 e N e γ p (Scalar q) x (PS e - ) N e > (1.5 TeV) p sin CPV Electron EDM (global) > (1300 TeV) p sin CPV C S (global) Tl, YbF, ThO 38

Global Analysis: Diamagnetic Systems Chupp & R-M: 1407.1064 39

Diamagnetic Systems Nucleon EDMs Nonleptonic: hadronic EDMs, Schiff moment (atomic EDMs)

Diamagnetic Systems I = 0, 1, PVTV πn interaction π p n π π γ π +! Nonleptonic: hadronic EDMs, Schiff moment (atomic EDMs)

Hadronic CPV: Nucleons, Nuclei, Atoms PVTV πn p interaction π γ π +! n π π chromo EDM 3 gluon 4 quark θ QCD Nucleon EDM + quark EDM Nuclear EDM & Schiff moment + quark EDM Neutron, proton & light nuclei (future), diamagnetic atoms 4

Diamagnetic Systems: P- & T-Odd Moments Schiff Screening Atomic effect from nuclear finite size: Schiff moment Schiff moment, MQM, EDMs of diamagnetic atoms ( 199 Hg )

Nuclear Schiff Moment I Schiff Screening Nuclear Schiff Moment Nuclear EDM: Screened in atoms Atomic effect from nuclear finite size: Schiff moment EDMs of diamagnetic atoms ( 199 Hg ) π +!

Diamagnetic Systems Nuclear Moments P T P T P T P T C J T M J T E J E O O E O E EDM, Schiff MQM. Anapole 45

Diamagnetic Systems Nuclear Moments C J T M J P T P T P T P T E O O E EDM, Schiff MQM. Nuclear Enhancements T E J O E Anapole 46

Nuclear Schiff Moment Nuclear Enhancements Schiff moment, MQM, Nuclear polarization: mixing of opposite parity states by H TVPV ~ 1 / ΔE EDMs of diamagnetic atoms ( 199 Hg ) 47

Nuclear Enhancements: Octupole Deformation Nuclear Schiff Moment Opposite parity states mixed by H TVPV Nuclear amplifier EDMs of diamagnetic atoms ( 5 Ra ) Nuclear polarization: mixing of opposite parity states by H TVPV ~ 1 / ΔE Thanks: J. Engel 48 94

Diamagnetic Global Fit N e γ N π γ N e N Tensor eq TVPV πnn Short distance d n Chupp & R-M: 1407.1064 49

Diamagnetic Global Fit Isoscalar CEDM (+) q v < 0.01 > ( TeV) p sin CPV Caveat: Large hadronic uncertainty Chupp & R-M: 1407.1064 50

V. Theoretical Issues 51

Hadronic Matrix Elements Engel, R-M, van Kolck 13 5

Hadronic Matrix Elements Engel, R-M, van Kolck 13 53

Hadronic Matrix Elements (CEDM) Engel, R-M, van Kolck 13 54

Nuclear Matrix Elements Engel, R-M, van Kolck 13 55

Had & Nuc Uncertainties CPV & HDM: Type II illustration λ 6,7 = 0 for simplicity Present sin α b : CPV scalar mixing Inoue, R-M, Zhang: 1403.457 80

IV. Outlook Searches for permanent EDMs of atoms, molecules, hadrons and nuclei provide powerful probes of BSM physics at the TeV scale and above and constitute important tests of weak scale baryogenesis Studies on complementary systems is essential for first finding and then disentangling new CPV The interpretation of diamagnetic system EDMs (including the nucleon) is plagued by substantial hadronic and nuclear many-body uncertainties The advancing experimental sensitivity challenges hadronic structure theory to aim for an unprecedented level of reliability 57