Nucleon EDMs on a Lattice at the Physical Point Sergey N. - PowerPoint PPT Presentation

Nucleon EDMs on a Lattice 
 at the Physical Point Sergey N. Syritsyn, Stony Brook University & RIKEN / BNL Research Center together with LHP and RBC collaborations LATTICE 2018 East Lansing, MI, July 22-28, 2018

Outline Nucleon Electric Dipole Moments: Introduction • Motivation • Experimental status & outlook • Lattice methodology Physical point calculations with chiral quarks • Form Factors → [T.Izubuchi's talk, July 27 5:30pm @106 (Hadron Structure)] • Electric dipole moments induced by quark chromo-EDM Studies of θ QCD -induced nucleon EDM • Noise reduction with subvolume top.charge sampling • Results from m 𝜌 ≳ 330 MeV lattices • Outlook for physical point calculations Sergey N. Syritsyn Nucleon EDMs on a Lattice at the Physical Point LATTICE2018, East Lansing, MI, July 22-28

Nucleon Electric Dipole Moments ~ S H = − ~ d N · ~ ~ E d N = d N S µ V µ OR L int = eA em (P,T-even) µ A µ + eA em (P,T-odd) EDMs are the most sensitive probes of CPv: Signals for beyond SM physics (SM = 10 -5 of the current exp.bound) Prerequisite for Baryogenesis θ QCD -induced EDM : Strong CP problem F 1 γ µ + ( F 2 + iF 3 γ 5 ) σ µ ν ( p 0 � p ) ν h N p 0 | J µ | ¯ u p 0 ⇥ ⇤ N p i � CP = ¯ u p � 2 m N Dirac Electric dipole Pauli (anom.magnetic) Sergey N. Syritsyn Nucleon EDMs on a Lattice at the Physical Point LATTICE2018, East Lansing, MI, July 22-28


 
 Experimental Outlook Future nEDM sensitivity : Current nEDM limits: | d n | < 2 . 9 × 10 − 26 e · cm 1–2 years : next best limit? [Baker et al, PRL97: 131801(2006)] 3–4 years : x10 improvement | d n | < 1 . 6 × 10 − 26 e · cm 7-10 years : x100 improvement [Graner et al, PRL116:161601(2016)] 10 -28 e cm [B.Filippone's talk, KITP 2016] CURRENT LIMIT <300 Spallation Source @ORNL < 5 Ultracold Neutrons @LANL ~30 PSI EDM <50 (I), <5 (II) ILL PNPI <10 Munich FRMII < 5 RCMP TRIUMF <50 (I), <5 (II) JPARC < 5 Standard Model (CKM) < 0.001 Other experiments: light nuclei in storage rings, octupole-deformed 225 Ra, etc Sergey N. Syritsyn Nucleon EDMs on a Lattice at the Physical Point LATTICE2018, East Lansing, MI, July 22-28


 
 Nucleon EDMs: a Window into New Physics Experiments: Nucleon dim=4: QCD θ -term Neutron EDM; 
 EDMs d n, d p Proton EDM?? dim=5(6): effective SUSY? GUT? 
 quark-gluon interactions: 
 Experiments: CP-odd 𝛒 NN 
 Extradimensions? quark (chromo)EDM, Nuclear EDMs 
 2 Higgs Doublets? couplings g 0,1,2 4-quark, 3-gluon, ... 199 Hg, 225 Ra, ... [ E. Mereghetti's plenary talk (Mon)] Effective quark-gluon CPv interactions organized by dimension c i [ J.Engel, M. Ramsey-Musolf, U. van Kolck, [ Λ ( i ) ] d i − 4 O [ d i ] X L eff = Prog.Part.Nucl.Phys. 71 (2013), pp. 21-74] i i d=4 : θ QCD d n,p d=5(6) : quark EDM, quark-gluon chromo EDM ( Q 2 ) F n,p d=6 : 4-fermion CPv, 3-gluon (Weinberg) 3 d n,p = d θ n,p θ QCD + d cEDM c cEDM + . . . n,p ? c i ⇐ ⇒ d n,p lattice QCD calculations are needed 
 to constrain θ QCD, c cEDM, ... Sergey N. Syritsyn Nucleon EDMs on a Lattice at the Physical Point LATTICE2018, East Lansing, MI, July 22-28

CP-odd Nucleon Structure on a Lattice CP = h O . . . i CP − even � i θ h Q · O . . . i CP − even + O ( θ 2 ) h O . . . i � � CP coupling CP operator: GG ̃ , cEDM, GGG ̃ (Weinberg), etc � � � � CPv interaction induces a chiral phase in fermion fields: CP = e i αγ 5 u p, σ = ˜ h vac | N | p, σ i � u p, σ � u [ u T C γ 5 d ] ∂ + m N e − 2 i αγ 5 )˜ ( / u p = 0 X u p, σ ¯ p E + m N e 2 i αγ 5 � � u p, σ ∼ − i/ ˜ ˜ σ To determine F 2,3 correctly, one has to use positive-parity spinors [M.Abramczyk, S.Aoki, S.N.S, et al (2017) arXiv:1701.07792] F 1 γ µ + ( F 2 + iF 3 γ 5 ) i σ µ ν ( p 0 � p ) ν γ 4 u = + u q γ µ q | N p i � u p 0 ⇥ ⇤ , with h N p 0 | ¯ CP = ¯ u p � 2 m N u γ 4 = +¯ ¯ u “ F 3 ” ≈ [ F 3 ] true − 2 α [ F 2 ] true Prior to 2017, lattice determinations of EDM 
 “ d n,p ” ≈ [ d n,p ] true − 2 α κ n,p were subject to large bias from F 2,3 mixing 2 m N Sergey N. Syritsyn Nucleon EDMs on a Lattice at the Physical Point LATTICE2018, East Lansing, MI, July 22-28

Quark Chromo-EDM on a Lattice ˜ δ q X q [ G µ ν σ µ ν γ 5 ] q L cEDM = 2 ¯ q = u,d dim-5 operator : O(a -2 ) mixing with dim-3 pseudoscalar density 
 ⇒ evaluate&subtract p,nEDM induced by PS density P = ¯ q γ 5 q [T.Bhattacharya et al, 1502.07325] Chiral symmetry is important: 
 O(a) clover term in, e.g., Wilson fermion action ≣ chromo-magnetic DM L clover = a c 4 ¯ q [ G µ ν σ µ ν ] q q → e i γ 5 Ω q In presense of CPv, condensate is realigned 
 CP | π a i = 0 so that h vac |L m + L � � leading to mixing (chromo)EDM ⟺ (chromo)MDM: q [ ˜ q [ { Ω , ˜ δ L cEDM = δ (¯ D q G µ ν σ µ ν γ 5 ] q ) = ¯ D q } G µ ν σ µ ν ] q ) ∼ δ L cMDM Sergey N. Syritsyn Nucleon EDMs on a Lattice at the Physical Point LATTICE2018, East Lansing, MI, July 22-28

Quark-Gluon EDM: Insertions of dim-5 Operators Z h N ( y ) ¯ d 4 x ¯ N (0) q ( G · σ ) γ 5 q i L (5) = ˜ X d q ¯ q ( G · σ ) γ 5 q Z h N ( y ) [ ¯ ψγ µ ψ ] z ¯ d 4 x ¯ N (0) q ( G · σ ) γ 5 q i q This work: Only quark-connected insertions δ d → d d δ d → d u δ u → d d δ u → d u } } } } u u d u u d u u d u u d u u d u u d u u d u u d u u d u u d u u d u u d u u d u u d In future: Single- and double-disconnected diagrams 
 (contribute to isosinglet cEDM, mix with θ -term) u u d u u u u d d u u d u u d u u d u u u u d d u u d u u d Sergey N. Syritsyn Nucleon EDMs on a Lattice at the Physical Point LATTICE2018, East Lansing, MI, July 22-28

Nucleon Vector (Sachs) Form Factors Physical point 
 1 . 2 0 . 10 DWF N f =2+1 1 . 0 48 3 x96, a =0.114 fm 0 . 05 0 . 8 0 . 6 [Alberico] G Ep G En 0 . 00 T = 8 a 0 . 4 T = 9 a T = 10 a 0 . 2 − 0 . 05 T = 11 a 0 . 0 T = 12 a fit-c3 − 0 . 2 − 0 . 10 4 . 0 0 . 0 3 . 5 − 0 . 5 3 . 0 2 . 5 − 1 . 0 2 . 0 G Mn G Mp − 1 . 5 1 . 5 1 . 0 − 2 . 0 0 . 5 − 2 . 5 0 . 0 − 0 . 5 − 3 . 0 0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 Q 2 [GeV 2 ] Q 2 [GeV 2 ] G E = F 1 − Q 2 F 2 See [T.Izubuchi's talk, Fri 5:30pm 4 m 2 @106 (Hadron Structure)] N G M = F 1 + F 2 Sergey N. Syritsyn Nucleon EDMs on a Lattice at the Physical Point LATTICE2018, East Lansing, MI, July 22-28

Parity Mixing : cEDM and pseudoscalar(*) Physical point 
 N δ = ✏ abc u a δ ( u aT C � 5 d c ) DWF N f =2+1 48 3 x96, a =0.114 fm p + m N e 2 i α 5 γ 5 CP = � i/ h N ( t ) ¯ e − E N t N (0) i � � 2 m N T + γ 5 · C CP ⇥ ⇤ = − ReTr 2 pt ( t ) α 5 = α 5 ˆ ⇤ , t → ∞ ˜ ⇥ T + · C CP ReTr 2 pt ( t ) d (flavor labels for the proton uud ) 100 100 0 0 mixing from d-cEDM mixing from d-PS − 100 − 100 volpsc.U α 5 α 5 volpsc.D − 200 − 200 mixing from u-cEDM mixing from u-PS − 300 − 300 volcedm.orig.U volcedm.orig.D − 400 − 400 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 t t (*)connected-only, bare cEDM and PS operators Sergey N. Syritsyn Nucleon EDMs on a Lattice at the Physical Point LATTICE2018, East Lansing, MI, July 22-28

Proton & Neutron EDM Form Factors (*) Physical point 
 200 150 Proton, u-cEDM Neutron, u-cEDM DWF N f =2+1 F 3 p , (cEDM) u F 3 p , (cEDM) d 100 50 48 3 x96, a =0.114 fm 0 − 50 − 100 − 150 − 200 200 Neutron, d-cEDM 150 Proton, d-cEDM F 3 n , (cEDM) u F 3 n , (cEDM) d 100 50 0 − 50 − 100 − 150 − 200 0 . 00 0 . 05 0 . 10 0 . 15 0 . 20 0 . 00 0 . 05 0 . 10 0 . 15 0 . 20 Q 2 [GeV 2 ] Q 2 [GeV 2 ] 200 Proton, u-PS 150 Neutron, u-PS 100 q γ 5 q ] u q γ 5 q ] d 50 F 3 p , [¯ F 3 p , [¯ 0 − 50 − 100 − 150 − 200 200 150 100 q γ 5 q ] u q γ 5 q ] d 50 F 3 n , [¯ F 3 n , [¯ 0 − 50 − 100 Proton, d-PS Neutron, d-PS − 150 − 200 0 . 00 0 . 05 0 . 10 0 . 15 0 . 20 0 . 00 0 . 05 0 . 10 0 . 15 0 . 20 (*)connected-only, bare cEDM and PS operators Q 2 [GeV 2 ] Q 2 [GeV 2 ] Sergey N. Syritsyn Nucleon EDMs on a Lattice at the Physical Point LATTICE2018, East Lansing, MI, July 22-28

Neutron EDM from Isovector Quark cEDM Physical point 
 DWF N f =2+1 100 neutron EDM from 48 3 x96, a =0.114 fm T = 8 a isovector cEDM T = 9 a 80 F 3 n , (cEDM) d − u T = 10 a 60 40 20 0 0 . 00 0 . 05 0 . 10 0 . 15 0 . 20 Q 2 [GeV 2 ] Outlook for cEDM-induced p,nEDM Renormalization & mixing subtractions : work underway 
 using position-space scheme Flavor-dependent CPv from cEDM : disconnected diagrams are required, 
 will be challenging due to noise and mixing with θ QCD term Sergey N. Syritsyn Nucleon EDMs on a Lattice at the Physical Point LATTICE2018, East Lansing, MI, July 22-28