Probing Novel CP Violation
Using Lattice QCD (CPV)

The quest of high energy and nuclear physicists is to understand the universe in terms of fundamental interactions and particles and address questions such as: What extension of the standard model describes nature at the TeV scale? Where do the masses of fundamental particles come from? Why is the observed universe predominately matter? What is the nature of dark matter and dark energy? These questions are being addressed both at the high energy frontier at the LHC and through high precision experiments at scales all the way from ultracold neutrons, to physics of c and b quarks, to neutrinos from accelerators, astrophysical events, and nuclear decays. On the theory side, to constrain the many candidate extensions of the standard model one needs to calculate the predictions of the standard model and look for deviations due to possible novel interactions. A key challenge to calculations involving quarks and gluons (they also impact processes mediated by elctromagnetic and weak interactions through quantum corrections) are the corrections due to strong interactions described by Quantum Chromodynamics (QCD). In the hadronic world (below few GeV), these corrections can be large since the coupling constant is order unity and non-perturbative methods are needed. For many quantities large scale simulations of Lattice QCD are providing (or can provide) estimates with control over all systematics and of accuracy required to interpret experiments and test candidate theories. This project is focused on calculating the matrix elements of novel CP violating operators within the neutron state and using bounds on the neutron electric dipole moment to constrain theories beyond the standard model at the TeV scale.

Goal

Our goal is to provide increasingly high precision calculations of matrix elements (ME) of bilinear quark operators within nucleon states to probe new physics beyond the standard model (BSM) of elementary particles and their interactions. The basic idea is that new interactions at the TeV and higher energy scales give rise to tiny corrections to the properties of nucleons (protons and neutrons) in low energy processes involving them. By the combined effort, measuring these possible subtle deviations from predictions of the standard model in ongoing and upcoming low-energy precision experiments and calculating the matrix elements of novel interactions, one can constrain the parameter space of possible BSM theories. This approach to discovery is complementary to experiments being done at the highest energies at the LHC at CERN, where one aims to directly detect new particles and interactions, such as the recent discovery of the Higgs boson.

Method

The proposed calculations of matrix elements are being done using large scale simulations of lattice Quantum Chromodynamics (QCD). We will derive precise estimates of QCD corrections to a variety of matrix elements of bilinear quark operators between nucleon states on ensembles of gauge configurations generated with 2+1+1-flavors of dynamical HISQ fermions at multiple values of lattice spacing and quark masses. These calculations will allow us to extract a variety of low-energy observables that will elucidate the structure of nucleons and probe the presence of new interactions beyond the Standard Model at the TeV scale. By performing simulations at multiple values of lattice spacings and quark masses, including the physical mass, we will demostrate control over all sources of systematic errors. The toolkit being used includes:

• The truncated solver method with bias correction (also called the all-mode-averaging (AMA) method) {collins:2007mh,Blum:2012uh}. We show that inverting the quark propagator with the residual set to r = (solution-source)/source = 10^-3 gives rise to no detectable bias in the estimates of 2-point and 3-point functions. Our results, nevertheless, include the possible bias correction term. The lower precision calculations are, however, a factor of about 17 faster.
• The multigrid method was used to invert the Dirac operator. It significantly reduces the critical slowing down, i.e., the increase in the number of iterations is small as the light quark mass is reduced to its physical value.
• The coherent source sequential propagator method was used to reduce the number of inversions required. We demonstrated that this approach does not significantly increase the errors. Processing 4 source points in a single computer job with 5 values of the source-sink separation t_sep reduced the number of inversions from (4+4x2x5=44) to (4+2x5=14).
• A number of values (3—5) of the source-sink separation t_sep are analyzed in each calculation to understand and reduce excited-state contamination.
• A simultaneous 2-state fit to the 3-point function data at all the different source-sink separation t_sep was made. These fits allowed us to estimate the transition matrix elements <0 | O_A | 1 > and <1 | O_A | 1 > in addition to the desired ground state matrix element <0 | O_A | 0 > . The 2-state fit, by taking into account the excited-state contamination provides, provides an estimate of the t_sep → ∞ value. Three state analysis is being tested.
• The nine HISQ ensembles analyzed covered the range 0.012—0.06 fm in lattice spacing a, 320—135 MeV in the pion mass M_π, and 3.3—5.5 in M_π L. With high statistics measurements on each of the 9 ensembles we made the first simultaneous fit in the three variables a, M_π and M_π L to obtain results in the limit a → 0, M_π L → ∞ and the physical light quark mass defined by M_π = 135 MeV.

Ongoing Calculations

The matrix elements within nucleon states are being calculated using ensembles of 2+1+1-flavor HISQ fermions generated by the MILC Collaboration and 2+1-flavor Clover fermions generated by the JLab/W&M collaboration. They will provide estimates of:

• Contributions of new CP violating interactions (the quark EDM, the quark Chromo EDM and the Θ-term) to the electric dipole moment of the neutron.
• Axial form factors that are needed to improve estimates of neutrino cross-section with nuclear matter as required by precision neutrino oscillation experiments.
• The isovector tensor and scalar charges that are needed to probe possible scalar and tensor interactions at the TeV scale in beta-decay of [ultra]cold-neutrons. The tensor charge also gives the lowest moment of the transversity parton distribution.
• The axial charge of the nucleons that encapsulates the strength of weak interactions of the nucleons.
• Electromagnetic form-factors of the nucleons, from which their charge radii will be extracted and compared with measurements made in electron scattering and muon capture experiments.
• Spatial, momentum, and angular distribution of quark and gluons within nucleons and how each constituent contributes to the nucleon spin.

Results and Expected Results

• Results for the flavor diagonal charges of the proton are g_T^u=0.792(42), g_T^d=-0.194(14) and g_T^s=0.008(9). These have been used to bound the quark EDM couplings.
  [Phys. Rev. D92 (2015) 094511; Phys. Rev. Lett115 (2014) 212002]
• We are working to reduce the uncertainty in the contribution of the disconnected diagrams to O(10%) and overall uncertainty to O(20%) in the charges g_T^s and g_T^c that get enhanced relative to g_T^u, g_T^d in Higgs-like theories by the ratio of quark masses.
• Carried out 1-loop calculation of the mixing of the CEDM operator with operators of equal and lower dimensions. Developed The RI-sMOM scheme for calculating teh renormalization constants non-perturbatively.
  [Phys. Rev. D92 (2015) 114096]
• Presented a new method and demonstrated its efficacy to carry out the full calculation of the quark chromo EDM operator and to obtain results with O(1) uncertainty.
• Current lattice QCD estimates of the axial charge g_A systematically lie about 7% below the precisely measured experimental value 1.276(2). Our goal is to reduce the uncertainty to about 2%.
  [Phys. Rev. D94 (2016) 054508]
• We aim to reduce the uncertainty in the tensor charge g_T to 2% and the uncertainty in g_S to 10% as needed to complement experimental precision of 10⁻³ in the measurement of b and B₁ parameters in neutron beta-decay.
• Results for the electric and magnetic form factors with O(10%) accuracy up to momentum transfers of 1 GeV. Resolve the factor of two discrepancy between current lattice results for the charge radii and experimental determination. Eventually resolve the difference between charge radii extracted from electron scattering and muonic hydrogen.
• Results for the axial vector form factors with O(10%) accuracy up to momentum transfers of 1 GeV.

The Neutron Electric Dipole Moment (nEDM)

The neutron electric dipole moment (nEDM) is a measure of the distribution of positive and negative charge inside the neutron. To generate a finite nEDM, one needs processes that violate CP-symmetry. In the standard model there are two sources of CP violation: a CP-odd θ-term and the complex phase in the quark mixing matrix. The standard model contribution of the CP violating phase is too small, O(10⁻³² e⋅cm), to explain baryogenesis, i.e., why the observed universe is predominately made up of matter and not equal parts of matter and anti-matter. The current bound on θ~10⁻¹⁰ comes from the current bound on the nEDM and is is an un-naturally small number. New sources of CP violation arise in almost all extensions of the standard model and the bound on the nEDM can be used to constrain these theories provided matrix elements of the new interactions within the neutron state are calculated with commensurate precision. Our goal is to calculate the matrix elements of the two leading interactions, the quark EDM and quark chromo EDM.

Resources

• Jan 01, 2014 – Dec 31, 2016: ERCAP allocation at NERSC of 40M core-hours
• Jul 01, 2014 – Jun 30, 2016: Los Alamos Institutional Computing allocation of 20M core-hours

Last updated: 2016 September 21