EDMs and CP Violation (in the LHC Era)

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1 Lepton Moments - Cape Cod - July 2014 EDMs and CP Violation (in the LHC Era) Adam Ritz University of Victoria w/~ D. McKeen, M. Pospelov [ , , ] w/~ M. Le Dall, M. Pospelov [to appear] Reviews: M. Pospelov & AR [hep-ph/ ] T. Fukuyama [ ] J. Engel, M. Ramsey-Musolf, U. van Kolck [ ] 1

2 CP (or T) Violation in the Standard Model H ΨL ΨR Yf sin( KM ) Arg Det[Y u Y u,y d Y d ] sin( QCD ) ArgDet[Y u Y d ] (in a basis where θ0 rotated 0) δ KM ~ O(1) Explains CP-violation in K and B meson mixing and decays θ QCD < 10-10! Constrained experimentally (strong CP problem) Motivations for new CP-odd sources? Required for baryogenesis (Sakharov conditions) Generic with extra degrees of freedom 2

3 Experimental EDM Limits H = de S S EDMs are powerful (amplitude-level) probes for new (T,P) violating sources, motivated e.g. by baryogenesis. Best current limits from neutrons, para- and dia-magnetic atoms and molecules. Neutron EDM dn < 3 x e cm [Baker et al. 06] Diamagnetic EDMs dhg < 3 x e cm [Griffith et al 09] Paramagnetic EDMs ΔEThO/ℇext < 3 x e cm [Baron et al. 13] Negligible SM (CKM) background - contribution is (at least) 4-5 orders of magnitude below the current neutron sensitivity, and lower for the atomic EDMs 3

4 Experimental EDM Limits H = de S S EDMs are powerful (amplitude-level) probes for new (T,P) violating sources, motivated e.g. by baryogenesis. Best current limits from neutrons, para- and dia-magnetic atoms and molecules Neutron EDM dn < 3 x e cm [Baker et al. 06] Diamagnetic EDMs Paramagnetic EDMs dhg < 3 x e cm [Griffith et al 09] dxe < 4 x e cm [Rosenberry & Chupp 01] ΔEThO/ℇext < 3 x e cm [Baron et al. 13] ΔEYbF/ℇext < 1.4 x e cm [Hudson et al. 11] dtl < 9 x e cm [Regan et al. 02] Negligible SM (CKM) background - contribution is (at least) 4-5 orders of magnitude below the current neutron sensitivity, and lower for the atomic EDMs 4

5 Schematic view of the bounds log(δe/ℇext [e cm]) -22 ThO n }Difference of 7 orders of magnitude is very misleading! Hg Real sensitivity to underlying sources of CP violation, depends on significant enhancement and suppression factors to be discussed shortly... 5

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

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

8 CP-odd operator expansion (at ~1GeV) Choose to start by parametrizing new (flavor-diagonal) CP-violating new physics with an operator expansion at ~1GeV L e = X n c n d 4 O(n) d NB: (ii) Basis at ~1GeV simpler than EW scale, after integrating out W,Z,h, assuming L-R chirality structure of the Standard Model (i) Assumes new physics is heavier than ~1 GeV Will return to this later, as empirical evidence for new physics (dark matter, neutrino mass) does not necessarily suggest a particular mass scale... 8

9 CP-odd operator expansion (at ~1GeV) (Flavor-diagonal) CP-violating operators at ~1GeV L e = X n c n d 4 O(n) d L dim 4 s G G = 0 ArgDet(M u M d ) 0 q 9

10 CP-odd operator expansion (at ~1GeV) (Flavor-diagonal) CP-violating operators at ~1GeV L e = X n c n d 4 O(n) d L dim 4 L dim 6 L dim 6 s G G X q=u,d,s wg 3 sgg G d i cy i v d q qf 5 q + d q qg 5 q + X l=e,µ 2 d l lf 5 l 10

11 CP-odd operator expansion (at ~1GeV) (Flavor-diagonal) CP-violating operators at ~1GeV L e = X n c n d 4 O(n) d L dim 4 s G G L dim 6 X d q qf 5 q + d q qg 5 q + X d l lf 5 l q=u,d,s l=e,µ L dim 6 wg 3 sgg G + C ff ( f f ) LL ( f f ) RR f,f, Suppressed without new sources of LR mixing 11

12 CP-odd operator expansion (at ~1GeV) (Flavor-diagonal) CP-violating operators at ~1GeV L e = X n c n d 4 O(n) d L dim 4 s G G L dim 6 X d q qf 5 q + d q qg 5 q + X d l lf 5 l q=u,d,s l=e,µ L dim 6 wg 3 sgg G + C ff ( f f ) LL ( f f ) RR f,f, L dim 8 q, C qq q q q i 5 q + C qe q qē i 5 e + C ij cy i Y j v

13 CP-odd operator expansion (at ~1GeV) (Flavor-diagonal) CP-violating operators at ~1GeV L e = X n c n d 4 O(n) d L dim 4 s G G L dim 6 X d q qf 5 q + d q qg 5 q + X d l lf 5 l q=u,d,s l=e,µ L dim 6 wg 3 sgg G + C ff ( f f ) LL ( f f ) RR f,f, L dim 8 q, C qq q q q i 5 q + C qe q qē i 5 e + 13

14 CP-odd operator expansion (at ~1GeV) (Flavor-diagonal) CP-violating operators at ~1GeV L e = X n c n d 4 O(n) d L dim 4 s G G L dim 6 X d q qf 5 q + d q qg 5 q + X d l lf 5 l q=u,d,s l=e,µ L dim 6 wg 3 sgg G + C ff ( f f ) LL ( f f ) RR f,f, L dim 8 q, C qq q q q i 5 q + C qe q qē i 5 e + nuclear scales d (n,p) NF 5 N +ḡ (1) NN N 0 N +ḡ (0) NN N N + d e ēf 5 e + C (0) S NNēi 5 e + 14

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

16 Paramagnetic EDMs - Schiff enhancement Atoms (e.g. Tl [Berkeley]) [Regan et al 02] (relativistic violation of Schiff screening which naively implies dneutral atom(de)=0 at the non-rel level) [Salpeter 58; Sandars 65] d Tl 20 2 Z 3 d e + O(C S ) O( ) for Tl [e.g. Liu & Kelly 92] 16

17 Paramagnetic EDMs - Schiff enhancement Polar molecules (e.g. ThO [Harvard/Yale], YbF [Imperial]) [Baron et al 13, Hudson et al 11] E ThO E e (E ext )d e + O(C S ) Nonlinear function of Eext E ThO E ext d ThO 10 2 Z 3 µ nuc m e d e + O(C S ) [Sandars; Sushkov & Flambaum, 78] 17

18 Paramagnetic EDMs - Schiff enhancement Polar molecules (e.g. ThO [Harvard/Yale], YbF [Imperial]) [Baron et al 13, Hudson et al 11] E ThO E YbF 84 GeV 15 GeV d e e cm + O(C S(C qe )) d e e cm + O(C S(C qe )) [Kozlov et al ; Quiney et al 98; Parpia 98; Chaudhuri & Nayak 08, Meyer & Bohn 08; Dzuba et al 11; Skripnikov et al 13] 18

19 Diamagnetic EDMs - Schiff suppression Atoms (e.g. Hg [Washington], also Xe) [Griffith et al 09] charge distribution (finite size violation of Schiff screening, which implies dneutral atom(dnuc)=0) d Hg 10Z 2 (R N /R A ) 2 d nuc nuclear dipole d Hg S[e fm 2 ]+O(d e,c qe,c qq ) [Flambaum et al 86; Dzuba et al. 02] ~S = S ~ I I = 1 10 Schiff moment [Schiff 63] applez e (~r)~rr 2 d 3 r 5 3Z ~ d Z (~r)r 2 d 3 r Schiff moment is dominant CP-odd source for large atoms (magnetic quadrupole important for small nuclei) 19

20 Diamagnetic EDMs - Schiff suppression Atoms (e.g. Hg [Washington], also Xe) [Griffith et al 09] nuclear dipole S = S(ḡ (i) NN,d N,...) charge distribution ḡ (1) NN (3 ± 2)( d u d Hg S[e fm 2 ]+O(d e,c qe,c qq ) Schiff moment g NN O(0.1)ḡ (0) NN + O(0.1)ḡ(1) NN + [Flambaum et al. 86; Dmitriev & Senkov 03; de Jesus & Engel 05; Ban et al 10] NB: concerns over precision for Hg dd )+O( d u + d d, d s,w) Octopole enhancements (e.g. Ra, Rn) (finite size violation of Schiff screening) [Flambaum et al 86; Dzuba et al. 02] [Pospelov 01] fm 3 + [R. Holt, Z.-T. Lu, et al, T. Chupp et al] - Schiff moment O( ) larger than Hg [Flambaum et al.] 20

21 Nuclear EDMs - avoiding Schiff screening Neutron EDM via UCN bottles [..., PSI, SNS, PNPI, TRIUMF, TUM, J-PARC...] (Calculations using: chiralpt, NDA, QCD sum rules, ) d n ( ) ecm Nuclear EDMs (e.g. p,d, 3 He,...) in storage rings d (PQ) n (0.4 ± 0.2)[4d d d u +2.7e( d d +0.5 d d )+ ]+O(d s,w,c qq ) - proton - similar sensitivity to the neutron (d u) - deuteron [BNL, FNAL? COSY/Julich] [Pospelov & AR 99, 00; Hisano et al 12] via η-π mixing [Lebedev, Olive, Pospelov, AR 04] d D =(d n + d p )(,d q, d q )+d NN D [ḡ (1) NN (, d q ),...] 5e( d d du )+ [Khriplovich & Korkin 00; Liu & Timmermans 04; de Vries et al 11; Bsaisou et al 12] - extended to other light nuclei (e.g. 3 H, 3 He) in recent work [Stetcu et al 08, de Vries et al 11] [ hadronic EDMs covered in next talk by Rob Timmermans]

22 EFT hierarchy Energy Fundamental CP phases TeV QCD nuclear µ EDM pion-nucleon coupling ( ) EDMs of nuclei and ions (deuteron, etc) Nucleon EDMs (n,p) atomic EDMs of paramagnetic atoms and molecules (Tl,YbF, ThO, HfF +,...) Atoms in traps (Rb,Cs,Fr) solid state EDMs of diamagnetic atoms (Hg,Xe,Ra,Rn,...) 22

23 Constraints on CP-violation Energy Fundamental CP phases TeV QCD nuclear pion-nucleon coupling ( ) EDM constraints EDMs of nuclei and ions (deuteron, etc) Nucleon EDMs (n,p) atomic EDMs of paramagnetic atoms and molecules (Tl,YbF, ThO, HfF +,...) Atoms in traps (Rb,Cs) EDMs of diamagnetic atoms (Hg,Xe,Ra,Rn,...) 23

24 Resulting Bounds on fermion EDMs & CEDMs ThO EDM [±20%] d e + e(26 MeV) 2 3 C ed m d + 11 C es m s +5 C eb m b < e cm n EDM [±50%?] Hg EDM [±O(few)?] e d d du + O(d e, d s,c qq,c qe ) < e cm Generic scaling: See also recent compilation of limits: [Engel, Ramsey-Musolf, van Kolck 13 ] 24

25 Resulting Bounds on fermion EDMs & CEDMs ThO EDM YbF EDM Tl EDM [±20%] d e + e(26 MeV) 2 d e + e(21 MeV) 2 3 C ed m d + 11 C es m s +5 C eb m b d e + e(26 MeV) 2 3 C ed m d + 11 C es m s +5 C eb < e cm m b < ecm 3 C ed m d + 11 C es m s +5 C eb m b < e cm n EDM [±50%?] Hg EDM [±O(few)?] e d d du + O(d e, d s,c qq,c qe ) < e cm Generic scaling: See also recent compilation of limits: [Engel, Ramsey-Musolf, van Kolck 13 ] 25

26 log(δe/ℇext [e cm]) -22 ThO Summary of the bounds n }Difference of 7 orders of magnitude is very misleading! Hg Real sensitivity to underlying sources of CP violation, depends on significant enhancement and suppression factors to be discussed shortly... 26

27 Summary of the bounds log(d [e cm]) ~ dq and dq from the neutron ~ dq from Hg de from ThO impact of recent order of magnitude improvement in paramagnetic EDM sensitivity The generic sensitivity to new physics follows from taking df mf 27

28 EDMs in the Standard Model (CKM phase) log(d [e cm]) d(ckm) / J Im(VVVV) neutron EDM limit Next generation sensitivity? d n (CKM) / C qq (J) / JG 2 F [Khriplovich & Zhitnitsky 82; McKellar et al 87; Mannel & Uraltsev 12] 28

29 EDMs in the Standard Model (CKM phase) log(d [e cm]) d(ckm) / J Im(VVVV) Hg EDM limit d Hg (CKM) / C qq (J) / JG 2 F [Flambaum et al 84; Donoghue et al 87] 29

30 EDMs in the Standard Model (CKM phase) log(d [e cm]) d(ckm) / J Im(VVVV) ThO EDM limit Paramagnetic EDMs in the SM determined by CS rather than de d ThO (CKM) / C S (J) / JG 2 F [Pospelov & AR 13] 30

31 LHC-era tests of CP-violating new physics Expectation of new EW-scale physics is (or was) primarily associated with stabilizing the Higgs sector... This predominantly suggests new physics coupling strongly to the Higgs, 3rd generation,... EDMs at 2-loops SUSY provides new physics with strong coupling to 1st generation EDMs at 1-loop! 31

32 Example 1 - CP-odd Higgs couplings Hints in 2012 that Br(h γγ) > BrSM (have since dissipated) EDMs significantly constrain any CP-odd contribution to h γγ L = 1 e 2 2 H H a h g 2 1B µ Bµ + b h g 2 2W µ W µ c h v 2 hf µ F µ + This interaction shifts Br(h γγ), but also generates EDMs! 2 SM 1+ c h v 2 8 A SM 2 Current bound on de limits ΔBr(h γγ)/brsm < O(10-5 ) from this CP-odd operator! [McKeen, Pospelov & AR 12] [Harnik et al 12; Fan & Reece 13] 32

33 LHC-era tests of CP-violating new physics Expectation of new EW-scale physics is (or was) primarily associated with stabilizing the Higgs sector... This predominantly suggests new physics coupling strongly to the Higgs, 3rd generation,... EDMs at 2-loops SUSY provides new physics with strong coupling to 1st generation EDMs at 1-loop! 33

34 LHC-era tests of CP-violating new physics Expectation of new EW-scale physics is (or was) primarily associated with stabilizing the Higgs sector... This predominantly suggests new physics coupling strongly to the Higgs, 3rd generation,... EDMs at 2-loops SUSY provides new physics with strong coupling to 1st generation EDMs at 1-loop! SUSY CP problem! 34

35 Example 2a - (LHC era) SUSY CP Problem (pre-lhc) (2012/13) Msusy = 500 GeV Msusy = 2 TeV 0.4 d YbF d Hg d n 0.4 d YbF d Hg d n q A p st gen squarks excluded by direct searches at ~1 TeV q A p q m p q m p EDMs have for many years required (tuned) O(10-3 ) CP-odd phases for generic weak-scale SUSY. The LHC appears to have resolved this by pushing mass limits on 1st generation sfermions above a TeV. Now tuning (at a TeV) being re-introduced via ThO limit on de. 35

36 Example 2a - (LHC era) SUSY CP Problem (pre-lhc) Msusy = 500 GeV (now) Msusy = 2 TeV 0.4 d YbF d Hg d n 0.4 d ThO d Hg d n q A p q A p st gen squarks excluded by direct searches at ~1 TeV q m p q m p EDMs have for many years required (tuned) O(10-3 ) CP-odd phases for generic weak-scale SUSY. The LHC appears to have resolved this by pushing mass limits on 1st generation sfermions above a TeV. Now tuning (at a TeV) being re-introduced via ThO limit on de. 36

37 Example 2b - PeV-scale SUSY sensitivity Within minimal SUSY, mh>>mz points to PeVscale s-partners ( tuning, no soln to little hierarchy problem) [e.g. Arkani-Hamed et al 12] m 2 h M 2 Z G F m 4 t ln m2 t v 2 Need a large log correction msquark > TeV 37

one of the few observables able to probe this scale via log-enhanced quark CEDMs [McKeen,

38 Example 2b - PeV-scale SUSY sensitivity Within minimal SUSY, mh>>mz points to PeVscale s-partners The PeV scale allows a generic flavour structure and, with TeV gauginos, EDMs are one of the few observables able to probe this scale via log-enhanced quark CEDMs [McKeen, Pospelov & AR; Altmannshofer et al 13; Fuyuto et al 13] [Altmannshofer et al 13] e-edm limit from ThO 38

39 LHC-era tests of CP-violating new physics Expectation of new EW-scale physics is (or was) primarily associated with stabilizing the Higgs sector... This predominantly suggests new physics coupling strongly to the Higgs, 3rd generation,... EDMs at 2-loops SUSY provides new physics with strong coupling to 1st generation EDMs at 1-loop! Hidden sectors are also empirically motivated EDMs at 2-loops 39

40 LHC-era tests of CP-violating new physics Expectation of new EW-scale physics is (or was) primarily associated with stabilizing the Higgs sector... This predominantly suggests new physics coupling strongly to the Higgs, 3rd generation,... EDMs at 2-loops SUSY provides new physics with strong coupling to 1st generation EDMs at 1-loop! Hidden sectors with light (sub-gev) states EDMs at 2-loops 40

41 EFT hierarchy TeV QCD nuclear atomic Energy Fundamental CP phases pion-nucleon coupling ( ) EFT hierarchy can be modified if µ EDM EDMs of paramagnetic atoms and molecules (Tl,YbF, ThO, HfF +,...) Atoms in traps (Rb,Cs,Fr) solid state EDMs of nuclei and ions (deuteron, etc) EDMs of diamagnetic atoms (Hg,Xe,Ra,Rn,...) Nucleon EDMs (n,p) new CP-violating physics is light (sub-gev) 41

Mediating (IR) CP-violation - Portals Empirical evidence for new physics (neutrino mass, dark matter) points to very weak interactions, but not to a specific mass scale.

42 Mediating (IR) CP-violation - Portals Empirical evidence for new physics (neutrino mass, dark matter) points to very weak interactions, but not to a specific mass scale... EFT parametrization of couplings to neutral hidden sector Standard Model Hidden Sector Only a small number of new (light) dofs can couple via relevant or marginal interactions (given SM SU(2)xU(1) structure), e.g. Vector portal (V) [Okun 82, Holdom 86] O 4 = 2 V µ B µ V µ J µ em (also shifts muon g-2) Can mediate IR hidden sector CP-violation observable EDMs

43 Example 3 - EDM Sensitivity to hidden sectors Would a nonzero EDM necessarily imply new short distance physics? No! L = L SM + L portals (O 3, O 4 )+L hid [Le Dall, Pospelov & AR, to appear] V γ 5 ψ h S V O 4 = V µ B µ V µ J µ 2 em O 3 = ASH H! = Av m 2 S (m q h qqi + ) h γ γ CP-violation EDMS are also competitive probes of weakly coupled hidden sectors 43

44 Summary EDMs are an important class of flavour-diagonal CP-odd observables, probing new physics (motivated by the need for baryogenesis) Disentangling CP-odd operators at 1 GeV requires multiple EDM observables recent applications Useful complementarity between EDM constraints and precision LHC tests of CP-odd Higgs couplings The SUSY CP problem, hinted at by (1-loop) EDMs for more than 20 years, has been confirmed by the LHC, with no squarks seen near the weak scale (thus far). EDMs probe the very high (PeV) sfermion scales characteristic of the large observed Higgs mass Baryogenesis requires new CP-odd physics, but are the new states at or above the weak scale? EDMs can also probe light (CP-violating) hidden sectors [NB: Also MHz EDMs from light axion DM dn θeff(ρdm)cos(mat) [Graham, Rajendran, Budker et al] 44

EDMs, CP-odd Nucleon Correlators & QCD Sum Rules

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,