Contribution of the QCD <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="normal">?</mml:mi></mml:math> -term to the nucleon electric dipole moment

We present a calculation of the contribution $\Theta$-term to neutron and proton electric dipole moments using seven 2+1+1-flavor HISQ ensembles. also estimate topological susceptibility for 2+1+1 theory be $\chi_Q = (66(9)(4) \rm MeV)^4$ in continuum limit at $M_\pi 135$ MeV. The nucleon three-point function is done Wilson-clover valence quarks. CP-violating form factor $F_3$ calculated by expanding small $\Theta$. show that lattice artifacts introduce term proportional $a$ does not vanish chiral limit, we include this our chiral-continuum fits. A perturbation analysis shows $N(0) \pi(0)$ state should provide leading excited contribution, study effect such state. Detailed contributions moment two strategies removing contamination are presented. Using spectrum from fits two-point function, find $d_n^\Theta$ small, $|d_n^\Theta| \lesssim 0.01 \overline \Theta e$ fm, whereas get $|d_p^\Theta| \sim 0.02 fm. On other hand, if dominant excited-state $N \pi$ state, then $|d_n^\Theta|$ could as large $0.05 fm 0.07 Our overall conclusion QCD calculations do reliable moments, ten higher statistics data needed better control over systematics possibly $3\sigma$ result.