The electric dipole moment of light nuclei in effective field theory

Transcription

1 Mitglied der Helmholtz-Gemeinschaft The electric dipole moment of light nuclei in effective field theory Jülich-Bonn Collaboration (JBC): Jan Bsaisou, Christoph Hanhart, Susanna Liebig, Ulf-G. Meißner, David Minossi, Andreas Nogga, Jordy de Vries, A.W. Tbilisi 23 September 2013 Andreas Wirzba

2 Permanent EDMs and Form Factors p f (p ) J µ em f (p) = ū f (p ) Γ µ (q 2 ) u f (p) q 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 q 2 = (p p ) 2 p Dirac F 1 (q 2 ), Pauli F 2 (q 2 ), electric dipole F 3 (q 2 ), and anapole F a(q 2 ) FFs (here for a fermion of mass m f with spin s = 1/2) F 3 (q 2 ) d = lim, (q p p, electron charge e < 0) q 2 0 2m f Andreas Wirzba 2 24

3 EDMs from CP Formfactor F 3 (q 2 =0)/(2m) γ n, D, 3 He n, D, 3 He Outline: CP-violation beyond CKM matrix in the SM: L QCD θ-term (dim. 4) EDM of the deuteron / EDM of helium-3 strategies of testing the θ-term CP-violation from physics beyond the SM: SUSY, multi-higgs, dim. 6 sources: qedm, qcedm, gcedm, 4qEDMs EDM of the deuteron / EDM of helium-3 disentangling dim. 6 sources Andreas Wirzba 3 24

4 The L QCD θ-term topologically non-trivial vacuum CP term in L QCD : L = L CP QCD + θ g2 S 32π 2 Ga a,µν µν G... + θ g2 S 32π 2 Ga a,µν µν G U A (1)... θm q f iγ 5 q f f =u,d with θ = θ+arg Det M, naive dim. analysis (NDA): θ O(1) M: quark mass matrix, m = mum d m u+m d Andreas Wirzba 4 24

5 New Physics Beyond Standard Model (BSM) SUSY, multi-higgs, Left-Right-Symmetric models,... Effective field theory approach: All degrees of freedom beyond a specified scale are integrated out: Only SM degrees of freedom remain: q, g, H, W ±,... Relics of eliminated BSM physics remembered by the values of the low-energy constants (LECs) of the CP-violating contact terms, e.g. g q g 1/ M 2 q 1T ev 100GeV Andreas Wirzba 5 24

6 BSM physics continued: CP-violating dim. 6 sources Removal of the Higgs and transition to hadronic fields (plus mixing) Add to SM all possible T- and P-odd contact interactions 150GeV g d L u L q H W ± H H H qedm qcedm 4qLR u R d R gcedm 4q d L u L 10GeV q u R d R 1GeV N γ N π π N... Andreas Wirzba 6 24

7 θ-term on the Hadronic Level hadronic level: non perturbative techniques required: e.g. 2-flavor ChPT Symmetries of QCD preserved by the effective field theory (EFT) L θ QCD = θm f q f iγ 5q f : CP, I CP, I M M+ θm iγ 5 m = mum d m u+m d CP, I CP, I + I L ChPT θ = g θ 0 N π τn + g θ 1 N π 3N + N (b 0+b 1τ 3)S µ v ν F µνn + g θ 0 g θ 1 dominating for n, p & 3 He dominating for D important for n, p Lebedev et al. (2004), Mereghetti et al. (2010), Bsaisou et al. (2013) Andreas Wirzba 7 24

8 θ-term: CP πnn vertices determined from LECs Leading g θ 0 coupling (from c 5) Crewther et al. (1979); Ottnad et al. (2010); Mereghetti et al. (2011); de Vries et al. (2011); Bsaisou et al. (2013) g θ 0 : N π τn-vertex L πn =... + c 5 2B N ((m u m d ) τ 3 + 2m θ F π π τ)n +... δm str np = 4B(m u m d )c 5 g θ 0 = θ δm str np (1 ɛ 2 ) 1 4F π ɛ δm em np δm str np = (2.6 ± 0.5)MeV Walker-Loud et al. (2012) g θ 0 = ( ± 0.007) θ ɛ = (m u m d)/(m u + m d), 4Bm = M 2 π(1 ɛ 2 ), m = mum d m u+m d Andreas Wirzba 8 24

9 θ-term: subleading g θ coupling (from c1 LEC) 1 g θ 1 : π 3NN-vertex ɛ = (m u m d)/(m u+m d) L πn =... + c 1 4B N ((m u + m d ) + (δm2 π) QCD (1 ɛ 2 ) θ π 3 )N BF π ɛ 1 c 1 σ πn : c 1 = ( 1.0 ± 0.3) GeV 1 Compilation: Baru et al. (2011) M 4 π 2 (δmπ) 2 QCD ɛ2 4 MK 2 M2 π π 0 = π 0 η, η g θ 1 = (0.003 ± 0.002) θ Bsaisou et al. (2013) g θ 1 g θ 0 = 0.20 ± 0.13 M π ɛ M2 π 0.01 m N (NDA) mn 2 Bsaisou et al. (2013) de Vries et al. (2011) g θ 0 (δmstr np ) is unnaturally small! Andreas Wirzba 9 24

10 Scalings of CP hadronic vertices (from θ and BSM sources) In BSM case: reliance on Naive Dimensional Analysis (NDA), lattice,... g 0: CP, I g1: CP, I d 0, d 1: CP, I + I C 3π: CP, I L CP EFT: N π ±, π 0 N π 0 N γ π θ-term: O(1) O(M π/m N) O(Mπ/m 2 N) 2 O(ɛMπ/m 2 N) 2 qedm: O(α EM/(4π)) O(α EM/(4π)) O(1) O(α EM/(4π)) qcedm: O(1) O(1) O(Mπ/m 2 N) 2 O(ɛMπ/m 2 N) 2 4qLR: O(Mπ/m 2 n) 2 O(1) O(Mπ/m 2 N) 2 O(1) gcedm: O(Mπ/m 2 N) 2 O(Mπ/m 2 N) 2 O(1) O(ɛMπ/m 2 N) 2 4q: O(Mπ/m 2 N) 2 O(Mπ/m 2 N) 2 O(1) O(ɛMπ/m 2 N) 2 *: Goldstone theorem relative O(Mπ/m 2 n) 2 suppression of Nπ interactions Andreas Wirzba 10 24

11 θ-term Induced Nucleon EDM single nucleon EDM: controlled d n isovector loop = e g πnn g θ 0 ln(mn 2 /m2 π) 4π 2 2M N isovector isoscalar θ m 2 π ln m2 π two unknown coefficients Guo & Meißner (2012): also in SU(3) case Crewther, di Vecchia, Veneziano & Witten (1979); Pich & de Rafael (1991); Ottnad et al. (2010) g θ 0 = (m n m p ) strong (1 ɛ 2 ) 4F π ɛ θ ( ± 0.007) θ (where ɛ mu m d m u+m d ) d n isovector loop (2.1 ± 0.9) θ e cm Ottnad et al. (2010); Bsaisou et al. (2013) Andreas Wirzba 11 24

12 θ-term Induced Nucleon EDM single nucleon EDM: controlled d n isovector loop = e g πnn g θ 0 ln(mn 2 /m2 π) 4π 2 2M N isovector isoscalar θ m 2 π ln m2 π two unknown coefficients Guo & Meißner (2012): also in SU(3) case Crewther, di Vecchia, Veneziano & Witten (1979); Pich & de Rafael (1991); Ottnad et al. (2010) g θ 0 = (m n m p ) strong (1 ɛ 2 ) 4F π ɛ θ ( ± 0.007) θ (where ɛ mu m d m u+m d ) d n isovector loop (2.1 ± 0.9) θ e cm Ottnad et al. (2010); Bsaisou et al. (2013) But what about the two unknown" coefficients of the contact terms? Andreas Wirzba 11 24

13 We ll always have... the lattice Don t mention the... light nuclei Andreas Wirzba 12 24

14 We ll always have... the lattice However, It s a long way to Tipperary... Results from full QCD calculations (no systematical errors!) for the neutron EDM and proton EDM 0.1 PRELIMINARY Θ = PRELIMINARY d N (e fm) CP-PACS, N f =2 clover, "E(#) CP-PACS, N f =2 clover, F 3 (#) RBC, N f =2 DW, F 3 (#) QCDSF, N f =2 clover, F 3 (i#) Current algebra N f =3 DWF, F 3 (#) d P (e fm) N f =3 DWF, F 3 (#) CP-PACS, N f =2 clover, F 3 (#) m! 2 (GeV 2 ) m! (GeV ) (adapted from Taku Izubuchi (BNL), Lattice-QCD calculations for EDMs, Fermilab, Feb. 14, 2013) Don t mention the... light nuclei Andreas Wirzba 12 24

15 We ll always have... the lattice However, It s a long way to Tipperary... Results from full QCD calculations (no systematical errors!) for the neutron EDM and proton EDM 0.1 PRELIMINARY Θ = PRELIMINARY d N (e fm) CP-PACS, N f =2 clover, "E(#) CP-PACS, N f =2 clover, F 3 (#) RBC, N f =2 DW, F 3 (#) QCDSF, N f =2 clover, F 3 (i#) Current algebra N f =3 DWF, F 3 (#) d P (e fm) N f =3 DWF, F 3 (#) CP-PACS, N f =2 clover, F 3 (#) m! 2 (GeV 2 ) m! (GeV ) (adapted from Taku Izubuchi (BNL), Lattice-QCD calculations for EDMs, Fermilab, Feb. 14, 2013) Don t mention the... light nuclei Andreas Wirzba 12 24

16 θ-term Induced Nucleon EDM: single nucleon EDM: Crewther, di Vecchia, Veneziano & Witten (1979); Pich & de Rafael (1991); Ottnad et al. (2010) controlled isovector isoscalar unknown" coefficients lattice QCD required Guo, Meißner (2012) two nucleon EDM: Sushkov, Flambaum, Khriplovich (1984) controlled unknown coefficient Andreas Wirzba 13 24

17 θ-term Induced Nucleon EDM: single nucleon EDM: Crewther, di Vecchia, Veneziano & Witten (1979); Pich & de Rafael (1991); Ottnad et al. (2010) controlled isovector isoscalar unknown" coefficients lattice QCD required Guo, Meißner (2012) two nucleon EDM: Sushkov, Flambaum, Khriplovich (1984) controlled unknown coefficient Andreas Wirzba 13 24

18 EDM of the Deuteron at LO: quantitative θ-term results 3 S 1 3 P 1 3 S 1 ( 3 D 1 ) ( 3 D1) LO: g θ 0 N π τn ( CP,I) Isospin excl. NLO: g θ 1 N π 3 N ( CP, I) LO in units of g θ 1 e fm (g A m N/F π) Ref. potential no 3 P 1-int with 3 P 1-int total JBC (2013)* Av JBC (2013) CD Bonn JBC (2013)* ChPT (N 2 LO) Song (2013) Av Liu (2004) Av Afnan (2010) Reid *: in preparation : cutoffs at 600 MeV (LS) and 700 MeV (SFR) BSM CP sources: LO g1 πnn-vertex also exists in qcedm and 4qLR cases Andreas Wirzba 14 24

19 EDM of the Deuteron: NLO- and N 2 LO-Potentials g θ 0 g θ 1 LO NLO N 2 LO Andreas Wirzba 15 24

20 EDM of the Deuteron: NLO- and N 2 LO-Potentials g θ 0 g θ 1 LO NLO N 2 LO : vanishing by selection rules, : sum of diagrams vanishes : vertex correction Andreas Wirzba 15 24

21 EDM of the Deuteron: NLO- and N 2 LO-Currents g θ 0 g θ 1 LO NLO N 2 LO : de Vries et al. (2011), Bsaisou et al. (2013) Andreas Wirzba 16 24

22 EDM of the Deuteron: NLO- and N 2 LO-Currents g θ 0 g θ 1 LO NLO N 2 LO : de Vries et al. (2011), Bsaisou et al. (2013) : vanishing by selection rules, : sum of diagrams vanishes Andreas Wirzba 16 24

23 Deuteron EDM from the θ-term Bsaisou et al. (2013) total deuteron EDM: d D = d n + d p + d D (2N) single-nucleon contribution: EFT alone has no predictive power Experiment or Lattice QCD needed in addition two-nucleon contribution d D (2N): EFT has predictive power d D (2N) = (0.59 ± 0.39) θ e cm LO + (0.05 ± 0.02) θ e cm N 2 LO Andreas Wirzba 17 24

24 3 He EDM: quantitative results for g 0 exchange 3 He 3 He g 0 N π τn ( CP, I) θ-term, qcedm LO 4qLR N 2 LO units: g 0(g Am N/F π)e fm author potential no int. with int. total JBC (2013)* Av 18UIX JBC (2013)* CD BONN TM JBC (2013)* ChPT (N 2 LO) Song (2013) Av 18UIX Stetcu (2008) Av 18 UIX *: in preparation : cutoffs at 600 MeV (LS) and 700 MeV (SFR) Results for 3 H also available (not shown) Note: calculation finally under control! Andreas Wirzba 18 24

25 3 He EDM: quantitative results for g 1 exchange 3 He 3 He g 1 N π 3 N ( CP, I) θ-term NLO qcedm, 4qLR LO! units: g 1(g Am N/F π)e fm Ref. potential no int. with int. total JBC (2013)* Av 18UIX JBC( 2013)* CD BONN TM JBC (2013)* ChPT (N 2 LO) Song (2013) Av 18UIX Stetcu (2008) Av 18 UIX *: in preparation : cutoffs at 600 MeV (LS) and 700 MeV (SFR) Results for 3 H also available (not shown) In the pipeline: CP 3π-vertex contribution (4qLR: LO ) Andreas Wirzba 19 24

26 Quantitative EDM results in the θ-term scenario Single Nucleon (with adjusted signs for consistency; note here e < 0): d loop (d n d p ) loop = (2.1 ± 0.9) θ e cm (Bsaisou et al. (2013)) Deuteron: d n = +(2.9 ± 0.9) θ e cm (Guo & Meißner (2012)) d p = (1.1 ± 1.1) 0 16 θ e cm (Guo & Meißner (2012)) d D = d n + d p [(0.59 ± 0.39) (0.05 ± 0.02)] θ e cm Helium-3: = d n + d p (0.54 ± 0.39) θ e cm (Bsaisou et al. (2013)) d 3 He = dn + [(1.52 ± 0.60) (0.46 ± 0.30)] θ e cm = dn + (1.06 ± 0.67) θ e cm (JBC (2013)) with dn = 0.88d n 0.047d p (de Vries et al. (2011)) Andreas Wirzba 20 24

27 Testing Strategies in the θ EDM scenario Remember: d D = d n + d p (0.54 ± 0.39) θ e cm (Bsaisou et al. (2013)) d 3 He = dn + (1.06 ± 0.67) θ e cm (JBC (2013)) Testing strategies: plan A: measure d n, d p, and d D d D (2N) θ test d 3 He plan A : measure d n, (d p ), and d 3 He d 3 He (2N) θ test d D plan B: measure d n (or d p) + Lattice QCD θ test d D plan B : measure d n (or d p) + Lattice QCD θ test d p (or d n) Andreas Wirzba 21 24

28 If θ-term tests fail: use effective BSM dim. 6 sources de Vries et al. (2011) qedm qcedm 4qLR gcedm + 4qEDM d > d + d d > d + d d d + d d D d p + d n d 3 He d n D p n d 3 He > d n D p n d 3 He > d n D p n d 3 He d n g 0, g 1 α/(4π) 2N contribution suppressed by photon loop! here: only absolute values considered Andreas Wirzba 22 24

29 If θ-term tests fail: use effective BSM dim. 6 sources de Vries et al. (2011) qedm qcedm 4qLR gcedm + 4qEDM d > d + d d > d + d d d + d d D d p + d n d 3 He d n D p n d 3 He > d n D p n d 3 He > d n D p n d 3 He d n g 0, g 1 2N contribution enhanced! here: only absolute values considered Andreas Wirzba 22 24

30 If θ-term tests fail: use effective BSM dim. 6 sources de Vries et al. (2011) qedm qcedm 4qLR gcedm + 4qEDM d > d + d d > d + d d d + d d D d p + d n d 3 He d n D p n d 3 He > d n D p n d 3 He > d n D p n d 3 He d n g 1 g 0 ; 3π-coupling (unsuppressed) 2N contribution enhanced! here: only absolute values considered Andreas Wirzba 22 24

31 If θ-term tests fail: use effective BSM dim. 6 sources de Vries et al. (2011) qedm qcedm 4qLR gcedm + 4qEDM d > d + d d > d + d d d + d d D d p + d n d 3 He d n D p n d 3 He > d n D p n d 3 He > d n D p n d 3 He d n g 1, g 0, 4N coupling 2N contribution difficult to asses! here: only absolute values considered Andreas Wirzba 22 24

32 Summary and Outlook θedm: relevant low-energy couplings quantifiable d D (2N) strategy A: measure d n, d p, d D θ test d 3 He d strategy A : measure d n, (d p ), d 3 He (2N) 3 He θ test d D strategy B: measure d n (or d p) + Lattice QCD θ test d D test strategy B : measure d n (or d p) + Lattice QCD θ d p (or d n) qedm, qcedm, 4QLR: NDA required to asses sizes of low-energy couplings disentanglement possible by measurements of d n, d p, d D & d 3 He gcedm, 4quark chiral singlet: controlled calculation/disentanglement difficult (lattice?) Ultimate progress may eventually come from Lattice QCD the CP NNπ couplings may be accessible even for dim-6 sources then quantifiable d D (d 3 He) EFT predictions feasible in BSM case Andreas Wirzba 23 24

33 Conclusions (Hadronic) EDMs play a key role in probing new sources of CP Measurements of hadronic EDMs are low-energy measurements Predictions have to be given in the empirical language of hadrons only reliable methods predicting uncertainties as well: ChPT/EFT and/(or ultimately) Lattice QCD EDMs of light nuclei provide independent information to nucleon EDMs and may be even larger and even simpler Deuteron and helium-3 nuclei serve as isospin filters for EDMs At least the EDMs of p, n, d, and 3 He have to be measured to disentangle the underlying physics by applying methods of EFT and lattice QCD Andreas Wirzba 24 24

34 Many thanks to my colleagues in Jülich: Jan Bsaisou, Christoph Hanhart, Susanna Liebig, Ulf-G. Meißner, Andreas Nogga, and Jordy de Vries in Bonn: Feng-Kun Guo, Bastian Kubis, Ulf-G. Meißner and: Werner Bernreuther, Bira van Kolck, Kolya Nikolaev J. Bsaisou, C. Hanhart, S. Liebig, U.-G. Meißner, A. Nogga and A. Wirzba, The electric dipole moment of the deuteron from the QCD θ-term, Eur. Phys. J. A 49 (2013) 31 [arxiv: [hep-ph]]. K. Ottnad, B. Kubis, U.-G. Meißner and F.-K. Guo, New insights into the neutron electric dipole moment, Phys. Lett. B 687 (2010) 42 [arxiv: [hep-ph]]. F.-K. Guo and U.-G. Meißner, Baryon electric dipole moments from strong CP violation, JHEP 1212 (2012) 097 [arxiv: [hep-ph]]. W. Dekens and J. de Vries, Renormalization Group Running of Dimension-Six Sources..., JHEP 1305 (2013) 149 [arxiv: [hep-ph]]. J. de Vries, R. Higa, C.-P. Liu, E. Mereghetti, I. Stetcu, R. Timmermans, U. van Kolck, Electric Dipole Moments of Light Nuclei From Chiral Effective Field Theory, Phys. Rev. C 84 (2011) [arxiv: [hep-ph]]. Andreas Wirzba 25 24