Taming quark chromoEDM contribution to the neutron EDM Tanmoy - - PowerPoint PPT Presentation

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 Lattice Calculation SPC questions Conclusions Form Factors Phase convention BSM Operators

Introduction

Form Factors

Vector form-factors

Dirac F1, Pauli F2, Electric dipole F3, and Anapole FA

Sachs electric GE ≡ F1 − (q2/4M2)F2 and magnetic GM ≡ F1 + F2

N|Vµ(q)|N = uN

• γµ F1(q2) + i[γµ, γν]

2 qν F2(q2) 2mN + (2i mNγ5qµ − γµγ5q2) FA(q2) m2

N

+ [γµ, γν] 2 qνγ5 F3(q2) 2mN

• uN

The charge GE(0) = F1(0) = 0. GM (0)/2MN = F2(0)/2MN is the (anomalous) magnetic dipole moment. F3(0)/2mN is the electric dipole moment. FA violates PT; F3 violates CP. Tanmoy Bhattacharya nEDM from qCEDM

Introduction Lattice Calculation SPC questions Conclusions Form Factors Phase convention BSM Operators

Introduction

Phase convention

Theory does not have P symmetry, but asymptotic In and Out states do. Not necessarily implemented by γ0. In fact, Σ · F ∝

• σ · B

iσ · E 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 Lattice Calculation SPC questions Conclusions Form Factors Phase convention BSM Operators

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 ¯ ψγ5ψ. Toplogical charge Gµν ˜ Gµν.

Suppressed by vEW/M 2

BSM:

Electric Dipole Moment ¯ ψΣµν ˜ F µνψ. Chromo Dipole Moment ¯ ψΣµν ˜ Gµνψ.

Suppressed by 1/M 2

BSM:

Weinberg operator (Gluon chromo-electric moment): GµνGλν ˜ Gµλ. Various four-fermi operators.

Tanmoy Bhattacharya nEDM from qCEDM

Introduction Lattice Calculation SPC questions Conclusions Three-point function Two-point function Disconnected diagrams

Lattice Calculation

Three-point function

eiε

×

      

u ¡ d ¡ d ¡ u ¡ d ¡ d ¡ Pε ¡ Pε ¡ P ¡ u ¡ d ¡ d ¡ u ¡ d ¡ d ¡ P ¡ P ¡ Pε ¡ u ¡ d ¡ d ¡ u ¡ d ¡ d ¡ P ¡ Pε ¡ Pε ¡ u ¡ d ¡ d ¡ u ¡ d ¡ d ¡ P ¡ P ¡ Pε ¡ P ¡ Pε ¡ Pε ¡ P ¡

+

u d d u d d Pε Pε P P

seq

u d d u d d P P P‐ε

seq

Pε u d d u d d P Pε Pε P‐ε

seq

u d d u d d P P P

seq

Pε

       The chromoEDM operator is dimension 5. Uncontrolled divergences unless ǫ 4πaΛQCD ∼ 1. Need to check linearity.

Tanmoy Bhattacharya nEDM from qCEDM

Introduction Lattice Calculation SPC questions Conclusions Three-point function Two-point function Disconnected diagrams

Lattice Calculation

Two-point function

Find asymptotic Parity operator: eiαγ5γ0 from two-point function.

Preliminary; Connected Diagrams Only

Tanmoy Bhattacharya nEDM from qCEDM

Introduction Lattice Calculation SPC questions Conclusions Three-point function Two-point function Disconnected diagrams

Lattice Calculation

Disconnected diagrams

• 1000
• 500

500 1000 1500 50 100 150 200 250

Reweighting (cEDM)

Configurations

N100 N800 N5000

Also calculate disconnected contribution to flavor diagonal (isoscalar) charges.

Tanmoy Bhattacharya nEDM from qCEDM

Introduction Lattice Calculation SPC questions Conclusions Agreement between groups Spatial versus Temporal

SPC questions

Agreement between groups

Ensembles PNDME CalLAT χQCD 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 SPC questions Conclusions Agreement between groups Spatial versus Temporal

SPC questions

Spatial versus Temporal

¯ ψγ5σµν

↔

Dν ψ ∝ ¯ ψγ5γµ( / D − m)ψ + m ¯ ψγ5γµψ The first contributes O(a2) except for contact terms. The second is a mass dependent renormalization. We use space component and assign 2–3% for O(a2). Our estimates agree.

Tanmoy Bhattacharya nEDM from qCEDM

Introduction Lattice Calculation SPC questions Conclusions Request

Conclusions

Request

Analyze 323 × 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