Introduction Lattice Calculation SPC questions Conclusions Taming quark chromoEDM contribution to the neutron EDM Tanmoy Bhattacharya Vincenzo Cirigliano Rajan Gupta Yong-Chull Jang Huey-Wen Lin Boram Yoon Aprin 28, 2017 Tanmoy Bhattacharya nEDM from qCEDM
Introduction Form Factors Lattice Calculation Phase convention SPC questions BSM Operators Conclusions Introduction Form Factors Vector form-factors Dirac F 1 , Pauli F 2 , Electric dipole F 3 , and Anapole F A Sachs electric G E ≡ F 1 − ( q 2 / 4 M 2 ) F 2 and magnetic G M ≡ F 1 + F 2 � F 2 ( q 2 ) γ µ F 1 ( q 2 ) + i [ γ µ , γ ν ] � N | V µ ( q ) | N � = u N q ν 2 2 m N + (2 i m N γ 5 q µ − γ µ γ 5 q 2 ) F A ( q 2 ) m 2 N F 3 ( q 2 ) � + [ γ µ , γ ν ] q ν γ 5 u N 2 2 m N The charge G E (0) = F 1 (0) = 0 . G M (0) / 2 M N = F 2 (0) / 2 M N is the (anomalous) magnetic dipole moment. F 3 (0) / 2 m N is the electric dipole moment. F A violates PT; F 3 violates CP. Tanmoy Bhattacharya nEDM from qCEDM
Introduction Form Factors Lattice Calculation Phase convention SPC questions BSM Operators Conclusions Introduction Phase convention Theory does not have P symmetry, but asymptotic In and Out states do. Not necessarily implemented by γ 0 . In fact, � � σ · B iσ · E Σ · F ∝ , iσ · E σ · B which is σ · B in the rest frame only if ( i/ p + m ) = 0 . Previous calculations had missed this effect: including it reduces the signal. Tanmoy Bhattacharya nEDM from qCEDM
Introduction Form Factors Lattice Calculation Phase convention SPC questions BSM Operators Conclusions Introduction BSM Operators Standard model CP violation in the weak sector. Strong CP violation from dimension 3 and 4 operators anomalously small. Dimension 3 and 4: CP violating mass ¯ ψγ 5 ψ . Toplogical charge G µν ˜ G µν . Suppressed by v EW /M 2 BSM : Electric Dipole Moment ¯ ψ Σ µν ˜ F µν ψ . Chromo Dipole Moment ¯ ψ Σ µν ˜ G µν ψ . Suppressed by 1 /M 2 BSM : Weinberg operator (Gluon chromo-electric moment): G µν G λν ˜ G µλ . Various four-fermi operators. Tanmoy Bhattacharya nEDM from qCEDM
Introduction Three-point function Lattice Calculation Two-point function SPC questions Disconnected diagrams Conclusions Lattice Calculation Three-point function e i ε × P ¡ P ε ¡ P seq P ¡ P ¡ P P u ¡ u ¡ u ¡ u ¡ u u u u P ε ¡ P ε P ε ¡ P ε d ¡ d ¡ d ¡ d ¡ d d d d P ε ¡ P ε ¡ P ε P ε d ¡ d ¡ d ¡ d ¡ d d d d seq P ‐ε + P ε ¡ P ¡ P ‐ε seq P ε ¡ P ε P ε ¡ P ε u ¡ u ¡ u ¡ u ¡ u u u u P ¡ P P ¡ P d ¡ d ¡ d d d ¡ d ¡ d d P ¡ P P ¡ P d ¡ d ¡ d d d ¡ d ¡ d d seq P The chromoEDM operator is dimension 5. Uncontrolled divergences unless ǫ � 4 πa Λ QCD ∼ 1 . Need to check linearity. Tanmoy Bhattacharya nEDM from qCEDM
Introduction Three-point function Lattice Calculation Two-point function SPC questions Disconnected diagrams Conclusions Lattice Calculation Two-point function Find asymptotic Parity operator: e iαγ 5 γ 0 from two-point function. Preliminary; Connected Diagrams Only Tanmoy Bhattacharya nEDM from qCEDM
Introduction Three-point function Lattice Calculation Two-point function SPC questions Disconnected diagrams Conclusions Lattice Calculation Disconnected diagrams Reweighting (cEDM) 1500 N100 N800 1000 N5000 500 0 -500 -1000 0 50 100 150 200 250 Configurations Also calculate disconnected contribution to flavor diagonal (isoscalar) charges. Tanmoy Bhattacharya nEDM from qCEDM
Introduction Lattice Calculation Agreement between groups SPC questions Spatial versus Temporal Conclusions SPC questions Agreement between groups Ensembles PNDME CalLAT χ QCD a12m310 1.229(14) 1.237(07) 1.22(4) a12m220S 1.270(40) 1.272(28) a12m220 1.240(32) 1.259(15) a12m220L 1.255(16) 1.252(21) a09m310 1.231(33) 1.258(14) 1.21(3) Tanmoy Bhattacharya nEDM from qCEDM
Introduction Lattice Calculation Agreement between groups SPC questions Spatial versus Temporal Conclusions SPC questions Spatial versus Temporal ↔ ¯ D ν ψ ∝ ¯ D − m ) ψ + m ¯ ψγ 5 γ µ ( / ψγ 5 σ µν ψγ 5 γ µ ψ The first contributes O ( a 2 ) except for contact terms. The second is a mass dependent renormalization. We use space component and assign 2–3% for O ( a 2 ) . Our estimates agree. Tanmoy Bhattacharya nEDM from qCEDM
Introduction Lattice Calculation Request SPC questions Conclusions Conclusions Request Analyze 32 3 × 96 a09m310 Disconnected diagrams cEDM and Quark bilinears Axial form factors Vector form factors Flavor diagonal scalar and tensor charges 43M Jpsi core hours. Tanmoy Bhattacharya nEDM from qCEDM
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