Neutron Electric Dipole. Moment. Boram Yoon Los Alamos Na.onal Lab. La0ce 2017 June 18-24, 2017, Granada

Transcription

1 Neutron Electric Dipole d + μ Moment - Boram Yoon Los Alamos Na.onal Lab La0ce 2017 June 18-24, 2017, Granada

2 Contents Introduc.on nedm induced by QCD θ-term nedm induced by Quark EDM nedm induced by Quark chromo EDM Other Related Results Summary

3 Neutron EDM and CP Viola6on Measures separa.on between centers of (+) and (-) charges δh = d N Ŝ! E Current bound: d n < e cm d + - S T P d d - + S Nonzero nedm violates P and T, so CP S + -

4 Neutron EDM Searches Neutron EDM Upper Limit (e cm) Previous Expts Future Expts Supersymmetry Predictions Standard Model Predictions Year of Publication Predic.ons Standard Model d n e cm Supersymmetry d n e cm Experiments targe.ng e cm precision PSI EDM Munich FRMII RCNP/TRIUMF SNS nedm JPARC

5 Tests of New source of CP viola.on CPV in SM is not sufficient to explain observed baryon asymmetry Supersymmetry and other BSM models nedm predicted to be at e cm

6 Effec6ve Lagrangian at 1 GeV L d 6 CPV = g 2 s 32π θ G G! 2 dim=4 QCD θ-term i 2 q=u,d,s d q q(σ F)γ 5 q dim=5 Quark EDM (qedm) i 2 q=u,d,s!d q g s q(σ G)γ 5 q dim=5 Quark Chromo EDM (CEDM) + d w g s 6 G! GG i + C i (4q) O i (4q) θ O( ): Strong CP problem dim=6 Weinberg 3g operator dim=6 Four-quark operators Dim=5 terms suppressed by d q v/λ BSM 2 ; effec.vely dim=6 La0ce QCD calcula.ons play important role

7 QCD θ-term g s 2 32π 2 θ G! G

8 QCD θ-term Calculate d N in presence of CP viola.ng θ-term S = S QCD + S θ S θ = iθ d 4 xg! G / 32π 2 = iθ Q top La0ce calcula.on strategies Expansion in θ External electric field method Simula.on with imaginary θ

9 Expansion in θ O (x) θ = 1 Z θ d[u, q, q]o (x) e S QCD +iθ Q top = O (x) θ=0 + iθ O (x)q top θ=0 +O( θ 2 ) Measurements performed on regular (θ=0) la0ces The effect of the QCD θ-term is included by reweigh.ng d n extracted from form-factor F 3 extrapolated to q 2 =0 N V µ N θ = u F 1 (q 2 )γ µ + i F 2(q 2 ) σ µν q ν F 3(q 2 ) σ µν q ν γ 5 u 2m N 2m N d N = F 3 (q2 = 0) 2m N

10 Form Factors with Parity Mixing Abramczyk, et al., arxiv: N = ε abc Dirac Eq. ( d Ta Cγ 5 u b )d c Parity Op. γ 4 e 2iαγ 5 γ 4 u! p γ 4 u! p!u" p e 2iαγ 5 γ 4 u! " p CPV interac.ons è phase in neutron mass γ 4 no longer parity op of neutron state Introduce new parity op or P, CP-even P, CP-viola6ng ( )!u = 0 ( ip µ γ µ + m)u = 0 ip µ γ µ + me 2iαγ 5 Rotate neutron state so that γ 4 is the parity op:!u = e iαγ 5 u,!u = ue iαγ 5 [Syritsyn@ Wed 9:00]

11 Form Factors with Parity Mixing Abramczyk, et al., arxiv: FF analysis used in La0ce QCD calcula.ons (since 2005)!N V µ! N! F1 (q 2 )γ µ + i! F 2 (q 2 ) 2m N σ µν q ν! F 3 (q 2 ) 2m N σ µν q ν γ 5 γ 4 is not parity op è!f 3 is not correct CP-odd FF of E S Correct analysis (Rotate: γ 4 is the parity operator) e iαγ 5!N V µ! N e iαγ 5 = N V µ N, e iαγ 5!N! N e iαγ 5 = N N F 1 (q 2 )γ µ + i F 2(q 2 ) σ µν q ν F 3(q 2 ) σ µν q ν γ 5 2m N 2m N Rota.on applies only to neutron not quark states [Syritsyn@ Wed 9:00]

12 Form Factors with Parity Mixing Abramczyk, et al., arxiv: Without rota.on, phase e iαγ 5 mixes F 2 and F 3 F 2 = cos(2α)!f 2 sin(2α)!f 3 F 3 = sin(2α)!f 2 + cos(2α)!f 3 F Phenomenology Shintani 2016 Alexandrou 2016 Guo 2015 Shintani Blue: Corrected F 3 Red : Old F ~ m π (MeV) Correc.ons calculated with assump.ons & approxima.ons Corrected la0ce data consistent with zero May resolve tension between phenomenology and la0ce results

13 Variance Reduc6on using Cluster Decomposi6on C R (t) = Q R (x) =! x x-y <R N(! x,t) N(G, 0) Q R (x) q(y) Liu, et al, arxiv: Wed 9:40] Calculate topological charge only in the vicinity of the sink F 3 (0) / 2m N [efm] m π 2 [GeV 2 ] Overlap on DWF n f = 2+1 a = fm m π = 330 MeV

14 External Electric Field Method! In the presence of uniform electric field E, a change of energy for the nucleon state due to the θ-term is E S! θ θ E! S 2d N θ! S! E Neutron correlator with θ-term via reweigh.ng NN θ (! E,t) = N(t)N(0)e iθq top! E Electric field applied only to valence quarks Does not need form-factor analysis and extrapola.on to q 2 =0

15 Simula6on with Imaginary θ Avoid imaginary ac.on (sign problem) by θ = i! θ S θ q =! θ m lm s x 2m s + m l Analy.c con.nua.on for small θ qγ 5 q d n is extracted from F 3 Fri 15:00] d n = (2)(9)[efmθ] F 3 θ,n R (0) θ m π 2 [GeV 2 ] Guo, et al, PRL 115 (2015) Stout Link Nonperturba.ve Clover, a = fm

16 Quark EDM i 2 q=u,d,s d q(σ F)γ q q 5

17 Quark EDM d q q(σ F)γ 5 q nedm from qedms wriven in tensor charges g T d N = d u g T u + d d g T d + d s g T s N qσ µν q N = g T q u N σ µν u N d q m q in many models; m u /m d 1/2, m s /m d 20 Precise determina.on of g T s is important

18 Tensor charges Quark EDM d q q(σ F)γ 5 q g T u = 0.23(3) g T d = 0.79(7) g T s = 0.008(9) N f =2+1+1 Clover-on-HISQ a 0, m π 135MeV Constraints on d q using d n < e cm d N = d u g u T + d d g d s T + d s g T Bhavacharya, et al., PRL (2015)

19 Quark Chromo EDM (cedm) i 2 q=u,d,s!d g q(σ G)γ q q s 5

20 Quark Chromo EDM Calculate d N in presence of CP viola.ng cedm term S = S QCD + S cedm S cedm = i 2 d 4 x! d q g s q(σ G)γ 5 q Three methods explored Expansion in!d q External electric field method Schwinger source method

21 Expansion in!d q NV µ N = NV CPV µ N + d! q NV µ N O cedm (x) +O( d! 2 q ) O cedm = i 2 g sq(σ G)γ 5 q x d n is extracted from the form-factor F 3 NV µ N = u F CPV 1 (q 2 )γ µ + i F 2(q 2 ) σ µν q ν F 3(q 2 ) σ µν q ν γ 5 u 2m N 2m N Needs calcula.on of four-point correlator N V µ N x O cedm (x)

22 Expansion in! d q Connected Diagrams Propagators Needed Four-point correlator is evaluated using Regular and backward props (F, B), cedm sequen.al prop (C) and doubly-sequen.al props (E, G) Abramczyk, et al., arxiv:

23 Expansion in! d q cedm U = 3.7(1.1) cedm D = 13.1(1.5) [Syritsyn@ Wed 9:00] Abramczyk, et al., arxiv: DWF a = 0.11fm m π =340 MeV

24 External Electric Field Method In the presence of uniform electric field!! i E! E cedm! E cedm! S S 2d N S i E Neutron correlator with CEDM term at leading order ( ) NN cedm (! E,t) = N(t)N(0)! E +! d q N(t)N(0) O cedm! E +O! d 2 q DWF a = 0.11fm m π =340 MeV E 0 = GeV 2 cedm U = 4.6(2.8) cedm D = 12.5(4.2) [Syritsyn@ Wed 9:00] Abramczyk, et al., arxiv:

25 Schwinger Source Method Quark chromo EDM operator is a quark bilinear iq(σ G)γ 5 q Include cedm term in valence quark propagators by changing Dirac op inversion rou.ne D clov D clov + iεσ µν γ 5 G µν Equivalently, c sw σ µν G µν σ µν (c sw + iεγ 5 )G µν No four-point correlators; d N extracted from F 3 Fermion determinant gives reweigh.ng factor det( D clov + iεσ µν γ 5 G ) µν det( D ) clov exp iε Tr σ µν 1 γ 5 G µν D clov ( )

26 Schwinger Source Method cedm u" P" Pε" Pε" P" seq" u" u" P" Pε" Pε" Pε" u" P u" Pε" P" P" seq" P)ε" u" u" Pε" P" P" P" u" Reweigh6ng Connected Diagrams Disconnected diagrams

27 Schwinger Source Method Calcula.on performed at small ε so that results are linear in ε cedm mixes with γ 5, so inves.gated both operators Bhavacharya, et al., arxiv: α N a12m310 cedm a09m310 cedm a12m310 γ 5 a09m310 γ 5 ε F 3 D, cedm, d-u Test at a = 0.09 fm, m π =310 MeV Q 2 = 0.18 GeV 2 ε = a09m310 t sep =10 t sep = τ - t sep /2 ε F 3 D, γ 5, d-u Q 2 = 0.18 GeV 2 ε = a09m τ - t sep /2 ε t sep =10 t sep =12

28 Renormaliza6on Renormaliza.on of cedm operator is studied 1-loop perturba.on on twisted-mass fermion [Constan.nou, et al, 2015] Nonperturba.ve RI- SMOM! [Bhavacharya, et al, 2015] Mixing with lower-dimensional operator Introduce 1/a 2 mixing O cedm = a 2 qσ µν γ 5 G µν q O P = qγ 5 q

29 Other Related Results Weinberg Three-gluon Operator d w g s 6 G! GG Wed 9:20] La0ce QCD spectroscopy for hadronic CPV Vries, et al., PLB (2017) ChPT for Neutron-An.neutron oscilla.ons [Bijnens@ Thur 16:00]

30 Summary QCD θ-term Ac.vely being calculated; need bever precision Quark EDM g T u,d given 10% error; bever g T s precision needed Quark Chromo EDM Exploratory studies started; need to address disconnected diagrams & renormaliza.on/mixing Weinberg Three-gluon Operator Just started Four-quark Operators Not explored

31 Acknowledgement: Compu.ng Resources USQCD Oak Ridge Leadership Compu.ng Facility at the Oak Ridge Na.onal Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC05-00OR Na.onal Energy Research Scien.fic Compu.ng Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231 Ins.tu.onal Compu.ng at the Los Alamos Na.onal Laboratory