Contribution of the QCD Θ -term to the nucleon electric dipole moment

Bhattacharya, Tanmoy; Cirigliano, Vincenzo; Gupta, Rajan; Mereghetti, Emanuele; Yoon, Boram

doi:10.1103/PhysRevD.103.114507

Title: Contribution of the QCD $Θ$ -term to the nucleon electric dipole moment

Journal Article · Thu Jun 10 00:00:00 EDT 2021 · Physical Review D

DOI:https://doi.org/10.1103/PhysRevD.103.114507· OSTI ID:1787694

; Cirigliano, Vincenzo;

; Mereghetti, Emanuele; Yoon, Boram

We present a calculation of the contribution of the $Θ$ -term to the neutron and proton electric dipole moments using seven $2 + 1 + 1$ -flavor highly improved staggered quark ensembles. We also estimate the topological susceptibility for the $2 + 1 + 1$ theory to be $χ_{Q} = (66 (9) (4) MeV)^{4}$ in the continuum limit at $M_{π} = 135 MeV$ . The calculation of the nucleon three-point function is done using Wilson-clover valence quarks. The $CP$ form factor $F_{3}$ is calculated by expanding in small $Θ$ . We show that lattice artifacts introduce a term proportional to $a$ that does not vanish in the chiral limit, and we include this in our chiral-continuum fits. A chiral perturbation theory analysis shows that the $N (0) π (0)$ state should provide the leading excited-state contribution, and we study the effect of such a state. Detailed analysis of the contributions to the neutron and proton electric dipole moment using two strategies for removing excited-state contamination are presented. Using the excited-state spectrum from fits to the two-point function, we find $d_{n}^{Θ}$ is small, $| d_{n}^{Θ} | ≲ 0.01 \bar{Θ} e \cdot fm$ , whereas for the proton we get $| d_{p}^{Θ} | ~ 0.02 \bar{Θ} e \cdot fm$ . On the other hand, if the dominant excited-state contribution is from the $N π$ state, then $| d_{n}^{Θ} |$ could be as large as $0.05 \bar{Θ} e \cdot fm$ and $| d_{p}^{Θ} | ~ 0.07 \bar{Θ} e \cdot fm$ . Our overall conclusion is that present lattice QCD calculations do not provide a reliable estimate of the contribution of the $Θ$ -term to the nucleon electric dipole moments, and a factor of 10 higher statistics data are needed to get better control over the systematics and possibly a $3 σ$ result.

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Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: AC02-05CH11231; AC05-00OR22725; 89233218CNA000001

OSTI ID:: 1787694

Alternate ID(s):: OSTI ID: 1822795

Report Number(s):: LA-UR-20-30515; PRVDAQ; 114507

Journal Information:: Physical Review D, Journal Name: Physical Review D Vol. 103 Journal Issue: 11; ISSN 2470-0010

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

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Title: Contribution of the QCD $Θ$ -term to the nucleon electric dipole moment