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Confirming the Existence of the strong CP Problem in Lattice QCD with the Gradient Flow

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arxiv 1902.03254 v2 pith:GACYMP52 submitted 2019-02-08 hep-lat hep-ph

Jack Dragos , Thomas Luu , Andrea Shindler , Jordy de Vries , Ahmed Yousif This is my paper
classification hep-lathep-ph
keywords thetatexteffectsmomentnucleontimescalculationschiral
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We calculate the electric dipole moment of the nucleon induced by the QCD theta term. We use the gradient flow to define the topological charge and use $N_f = 2+1$ flavors of dynamical quarks corresponding to pion masses of $700$, $570$, and $410$ MeV, and perform an extrapolation to the physical point based on chiral perturbation theory. We perform calculations at $3$ different lattice spacings in the range of $0.07~{\rm fm} < a < 0.11$ fm at a single value of the pion mass, to enable control on discretization effects. We also investigate finite size effects using $2$ different volumes. A novel technique is applied to improve the signal-to-noise ratio in the form factor calculations. The very mild discretization effects observed suggest a continuum-like behavior of the nucleon EDM towards the chiral limit. Under this assumption our results read $d_{n}=-0.00152(71)\ \bar\theta\ e~\text{fm}$ and $d_{p}=0.0011(10)\ \bar\theta\ e~\text{fm}$. Assuming the theta term is the only source of CP violation, the experimental bound on the neutron electric dipole moment limits $\left|\bar\theta\right| < 1.98\times 10^{-10}$ ($90\%$ CL). A first attempt at calculating the nucleon Schiff moment in the continuum resulted in $S_{p} = 0.50(59)\times 10^{-4}\ \bar\theta\ e~\text{fm}^3$ and $S_{n} = -0.10(43)\times 10^{-4}\ \bar\theta\ e~\text{fm}^3$.

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Cited by 5 Pith papers

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  1. The Neutron Electric Dipole Moment from Lattice QCD using a Background Electric Field

    hep-lat 2026-07 conditional novelty 7.0 of 10

    Using background electric fields, local topological charge, and non-Hermitian GEVP, lattice QCD yields dn = -0.0050(4)stat(8)sys θ-bar e fm at the physical point.

  2. One-loop matching of the LEFT to the QCD gradient flow

    hep-ph 2026-01 conditional novelty 7.0 of 10

    All one-loop matching coefficients connecting the full baryon- and lepton-number-conserving low-energy effective field theory up to dimension six to the QCD gradient flow are computed.

  3. A particle on a ring or: how I learned to stop worrying and love $\theta$-vacua

    hep-ph 2026-01 accept novelty 6.0 of 10

    The ACGT order-of-limits prescription fails to reproduce the correct θ-dependent energy spectrum in the quantum rotor and quantum pendulum.

  4. Nucleon Electric Dipole Moments in Paramagnetic Molecules through Effective Field Theory

    hep-ph 2025-10 unverdicted novelty 6.0 of 10

    Introduces an EFT framework relating paramagnetic molecular EDMs to nucleon EDMs, computes the required nuclear matrix elements for BaF via shell model, and derives limits on nucleon EDMs from existing data.

  5. The landscape of QCD axion models

    hep-ph 2020-03 unverdicted novelty 2.0 of 10

    Review classifies QCD axion models extending the standard mass-coupling window and updates bounds from cosmology, astrophysics, and experiments.

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