### Recent Research Highlights

#### Older Publications

A mostly complete list of all publications, software, invited talks and seminars can be found in the following PDF.

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##### A New Paradigm for Hadronic Parity Nonconservation and its Experimental ImplicationsarXiv:1704.02617

For decades the primary experimental goal in studies of hadronic parity nonconservation (PNC) has been the isolation of the isovector weak nucleon-nucleon interaction, expected to be dominated by long-range pion exchange and enhanced by the neutral current. In meson-exchange descriptions this interaction together with an isoscalar interaction generated by rho and omega exchange dominate most observables. Consequently these two amplitudes have been used to compare and check the consistency of the field's experiments. Yet to date, despite sensitive searches like that performed with ${}^{18}$F, no evidence for isovector hadronic PNC has been found. Here we argue, based on recent large-$N_c$ treatments and new global analyses, that the emphasis on isovector hadronic PNC was misplaced. Large-$N_c$ provides an alternative and theoretically better motivated simplification of effective field theories (EFTs) of hadronic PNC, separating the five low-energy constants (LECs) into two of leading order (LO), and three others that are NNLO. This scheme pivots the isospin coordinates we have traditionally used, placing one dominant axis in the isoscalar plane, and a second along the isotensor direction. We show that this large-$N_c$ LEC hierarchy accurately describes all existing data on hadronic PNC, and we discuss opportunities to further test the predicted large-$N_c$ hierarchy of LECs, illustrating the kind of analyses experimentalists can use to better constrain the LO theory and to determine the size of NNLO corrections.

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##### An accurate calculation of the nucleon axial charge with lattice QCDarXiv:1704.01114

We report on a lattice QCD calculation of the nucleon axial charge, $g_A$, using Möbius Domain-Wall fermions solved on the dynamical $N_f=2+1+1$ HISQ ensembles after they are smeared using the gradient-flow algorithm. The calculation is performed with three pion masses, $m_\pi\sim{310,220,130}$ MeV. Three lattice spacings ($a∼{0.15,0.12,0.09}$ fm) are used with the heaviest pion mass, while the coarsest two spacings are used on the middle pion mass and only the coarsest spacing is used with the near physical pion mass. On the $m_\pi\sim220$ MeV, $a∼0.12$ fm point, a dedicated volume study is performed with $m_\pi L∼{3.22,4.29,5.36}$. Using a new strategy motivated by the Feynman-Hellmann Theorem, we achieve a precise determination of $g_A$ with relatively low statistics, and demonstrable control over the excited state, continuum, infinite volume and chiral extrapolation systematic uncertainties, the latter of which remains the dominant uncertainty. Our final determination at 2.6% total uncertainty is $g_A=1.278(21)(26)$, with the first uncertainty including statistical and systematic uncertainties from fitting and the second including model selection systematics related to the chiral and continuum extrapolation. The largest reduction of the second uncertainty will come from a greater number of pion mass points as well as more precise lattice QCD results near the physical pion mass.

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##### Stencil Computations for PDE-based Applications with Examples from DUNE and hypre

Concurrency and Computation: Practice and Experience, Wiley Online Library (2017)

Stencils are commonly used to implement efficient on-the-fly computations of linear operators arising from partial differential equations. At the same time the term “stencil” is not fully defined and can be interpreted differently depending on the application domain and the background of the software developers. Common features in stencil codes are the preservation of the structure given by the discretization of the partial differential equation and the benefit of minimal data storage. We discuss stencil concepts of different complexity, show how they are used in modern software packages like hypre and DUNE, and discuss recent efforts to extend the software to enable stencil computations of more complex problems and methods such as inf-sup-stable Stokes discretizations and mixed finite element discretizations.

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We describe a light-weight system of bash scripts for efficiently bundling supercomputing tasks into large jobs, so that one can take advantage of incentives or discounts for requesting large allocations. The software can backfill computational tasks, avoiding wasted cycles, and can streamline collaboration between different users. It is simple to use, functioning similarly to batch systems like PBS, MOAB, and SLURM.

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##### Möbius Domain-Wall fermions on gradient-flowed dynamical HISQ ensemblesarXiv:1701.07559
We report on salient features of a mixed lattice QCD action using valence Möbius Domain-Wall fermions solved on the dynamical $N_f=2+1+1$ HISQ sea-quark ensembles generated by the MILC Collaboration. The approximate chiral symmetry properties of the valence fermions are shown to be significantly improved by utilizing the gradient-flow scheme to first smear the HISQ configurations. The greater numerical cost of the Möbius Domain-Wall inversions is mitigated by the highly efficient QUDA library optimized for NVIDIA GPU accelerated compute nodes. We provide tuned parameters of the action and performance of QUDA using ensembles with the lattice spacings $a\simeq{0.15,0.12,0.09}$ fm and pion masses $m_\pi\simeq{310,220,135}$ MeV. With a fixed flow time of tgf=1 in lattice units, the residual chiral symmetry breaking of the valence fermions are kept below 10% of the light quark mass on all ensembles, $m_{res}≲0.1\times m_l$, with moderate values of the fifth dimension $L_5$ and a domain-wall height $M_5\leq 1.3$.

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##### Strong isospin violation and chiral logarithms in the baryon spectrumarXiv:1612.07733
We present a precise lattice QCD calculation of the contribution to the neutron-proton mass splitting arising from strong isospin breaking, $m_n-m_p|_{QCD}=2.32\pm0.17$ MeV. We also determine $m_{\Xi^-} - m_{\Xi^0}|_{QCD} = 5.44\pm0.31$ MeV. The calculation is performed at three values of the pion mass, with several values of the quark mass splitting and multiple lattice volumes, but only a single lattice spacing and an estimate of discretization errors. The calculations are performed on the anisotropic clover-Wilson ensembles generated by the Hadron Spectrum Collaboration. The omega-baryon mass is used to set the scale $a_t^{-1}=6111\pm127$ MeV, while the kaon masses are used to determine the value of the light-quark mass spitting. The nucleon mass splitting is then determined as a function of the pion mass. We observe, for the first time, conclusive evidence for non-analytic light quark mass dependence in lattice QCD calculations of the baryon spectrum. When left as a free parameter, the fits prefer a nucleon axial coupling of $g_A=1.24(56)$. Simultaneously including other lattice QCD results in the fit sharpens the value to $g_A = 1.08(33)$. To highlight the presence of this chiral logarithm in the nucleon mass splitting, we also compute the isospin splitting in the cascade-baryon system which is less sensitive to chiral dynamics. Finally, we update the best lattice QCD determination of the CP-odd pion-nucleon coupling that would arise from a non-zero QCD theta-term, $\bar{g}_0 / (\sqrt{2}f_\pi) = (14.7\pm1.8\pm1.4) \cdot 10^{-3} \bar{\theta}$.

The original lattice QCD correlation functions, analysis results and extrapolated quantities are packaged in HDF5 files made publicly available including a simple Python script to access the numerical results, construct effective mass plots along with our analysis results, and perform the extrapolations of various quantities determined in this work.

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##### On the Feynman-Hellmann Theorem in Quantum Field Theory and the Calculation of Matrix ElementsarXiv:1612.06963
The Feynman-Hellmann Theorem can be derived from the long Euclidean-time limit of correlation functions determined with functional derivatives of the partition function. Using this insight, we develop an improved method for computing matrix elements of external currents utilizing only two-point correlation functions. Our method applies to matrix elements of any external bi-linear current, including non-zero momentum transfer, flavor-changing, and two-current insertion matrix elements. The contamination from excited states is shown to be Euclidean-time dependent allowing for a significantly improved ability to reliably determine and control the systematics. We demonstrate the utility of our method with a calculation of the nucleon axial-charge using gradient-flowed domain-wall valence quarks on the $N_f=2+1+1$ MILC highly-improved staggered quark (HISQ) ensemble with lattice spacing and pion mass of approximately 0.15 fm and 310 MeV respectively. We show full control over excited state systematics with the new method and obtain value of $g_A=1.213(26)$ with a quark-mass dependent renormalization coefficient.

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##### Lattice QCD spectroscopy for hadronic CP violationPhys. Lett. B766 (2017) [arXiv:1612.01567]

The interpretation of nuclear electric dipole moment (EDM) experiments is clouded by large theoretical uncertainties associated with nonperturbative matrix elements. In various beyond-the-Standard Model scenarios nuclear and diamagnetic atomic EDMs are expected to be dominated by CP-violating pion-nucleon interactions that arise from quark chromo-electric dipole moments. The corresponding CP-violating pion-nucleon coupling strengths are, however, poorly known. In this work we propose a strategy to calculate these couplings by using spectroscopic lattice QCD techniques. Instead of directly calculating the pion-nucleon coupling constants, a challenging task, we use chiral symmetry relations that link the pion-nucleon couplings to nucleon sigma terms and mass splittings that are significantly easier to calculate. In this work, we show that these relations are reliable up to next-to-next-to-leading order in the chiral expansion in both SU(2) and SU(3) chiral perturbation theory. We conclude with a brief discussion about practical details regarding the required lattice QCD calculations and the phenomenological impact of an improved understanding of CP-violating matrix elements.

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##### Nuclear Physics without High-Momentum Potentials: Direct Construction of the Effective Interaction from Scattering ObservablesarXiv:1607.06863

The standard approach to nuclear physics encodes phase shift information in an NN potential, then decodes that information in forming an effective interaction, appropriate to a low-momentum Hilbert space. Here we show that it is instead possible to construct the effective interaction directly from continuum phase shifts and mixing angles, eliminating all reference to a high momentum potential. The theory is rapidly convergent and well behaved, yielding sub-keV accuracy.

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##### QUDA Features, Scaling and SolversLattice 2015

We describe recent developments to the QUDA software framework, a library aimed at deploying lattice QCD computations on GPUs. The library has ever broadening support for various LQCD actions and algorithms, as well as being integrated into many LQCD applications. Recent focus has been on improving strong scaling for multi-GPU calculations and developing an adaptive multigrid solver. We give updates on both of these efforts, and compare performance against other platforms. Lastly, we look to the future and discuss how upcoming technologies such as stacked memory and nvlink, a fast GPU interconnect, will bring disruptive changes to lattice QCD calculations.

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#### Older publications

##### Two-Nucleon Higher Partial-Wave Scattering from Lattice QCDPhys. Lett. B765 (2017)[arXiv:1508.00886]

We present a determination of nucleon-nucleon scattering phase shifts for $\ell \geq 0$. The S, P, D and F phase shifts for both the spin-triplet and spin-singlet channels are computed with lattice Quantum ChromoDynamics. For $\ell > 0$, this is the first lattice QCD calculation using the Lüscher finite-volume formalism. This required the design and implementation of novel lattice methods involving displaced sources and momentum-space cubic sinks. To demonstrate the utility of our approach, the calculations were performed in the SU(3)-flavor limit where the light quark masses have been tuned to the physical strange quark mass, corresponding to $m_\pi = m_K \sim 800$ MeV. In this work, we have assumed that only the lowest partial waves contribute to each channel, ignoring the unphysical partial wave mixing that arises within the finite-volume formalism. This assumption is only valid for sufficiently low energies; we present evidence that it holds for our study using two different channels. Two spatial volumes of $V \sim (3.5 fm)^3$ and $V \sim (4.6 fm)^3$ were used. The finite-volume spectrum is extracted from the exponential falloff of the correlation functions. Said spectrum is mapped onto the infinite volume phase shifts using the generalization of the Luscher formalism for two-nucleon systems.
##### Massive photons: an infrared regularization scheme for lattice QCD+QEDPhys. Rev. Lett. 117 (2016)[arXiv:1507.08916]

Standard methods for including electromagnetic interactions in lattice quantum chromodynamics calculations result in power-law finite-volume corrections to physical quantities. Removing these by extrapolation requires costly computations at multiple volumes. We introduce a photon mass to alternatively regulate the infrared, and rely on effective field theory to remove its unphysical effects. Electromagnetic modifications to the hadron spectrum are reliably estimated with a precision and cost comparable to conventional approaches that utilize multiple larger volumes. A significant overall cost advantage emerges when accounting for ensemble generation. The proposed method may benefit lattice calculations involving multiple charged hadrons, as well as quantum many-body computations with long-range Coulomb interactions.
##### Baryon mass splittings and strong CP violation in SU(3) Chiral Perturbation TheoryPhys. Rev. C92 (2015)[arXiv:1506.06247]

We study $SU(3)$ flavor-breaking corrections to the relation between the octet baryon masses and the nucleon-meson CP-violating interactions induced by the QCD $\bar{\theta}$ term. We work within the framework of $SU(3)$ chiral perturbation theory and work through next-to-next-to-leading order in the $SU(3)$ chiral expansion, which is $\mathcal{O}(m_q^2)$. At lowest order, the CP-odd couplings induced by the QCD $\bar{\theta}$ term are determined by mass splittings of the baryon octet, the classic result of Crewther et al. We show that for each isospin-invariant CP-violating nucleon-meson interaction there exists one relation which is respected by loop corrections up to the order we work, while other leading-order relations are violated. With these relations we extract a precise value of the pion-nucleon coupling $\bar{g}_0$ by using recent lattice QCD evaluations of the proton-neutron mass splitting. In addition, we derive semi-precise values for CP-violating coupling constants between heavier mesons and nucleons with ∼30% uncertainty and discuss their phenomenological impact on electric dipole moments of nucleons and nuclei.
##### High-Performance I/O: HDF5 for Lattice QCDarXiv:1501.06992

Practitioners of lattice QCD/QFT have been some of the primary pioneer users of the state-of-the-art high-performance-computing systems, and contribute towards the stress tests of such new machines as soon as they become available. As with all aspects of high-performance-computing, I/O is becoming an increasingly specialized component of these systems. In order to take advantage of the latest available high-performance I/O infrastructure, to ensure reliability and backwards compatibility of data files, and to help unify the data structures used in lattice codes, we have incorporated parallel HDF5 I/O into the SciDAC supported USQCD software stack. Here we present the design and implementation of this I/O framework. Our HDF5 implementation outperforms optimized QIO at the 10-20% level and leaves room for further improvement by utilizing appropriate dataset chunking.
##### Multichannel one-to-two transition amplitudes in a finite volumePhys. Rev. D91 (2015) [arXiv:1406.5965]

We perform a model-independent, non-perturbative investigation of two-point and three-point finite-volume correlation functions in the energy regime where two-particle states can go on-shell. We study three-point functions involving a single incoming particle and an outgoing two-particle state, relevant, for example, for studies of meson decays (e.g., B-to-pi Kll) or meson photo production (e.g., pi gamma-to-pi pi). We observe that, while the spectrum solely depends on the on-shell scattering amplitude, the correlation functions also depend on off-shell amplitudes. The main result of this work is a generalization of the Lellouch-Luscher formula relating matrix elements of currents in finite and infinite spatial volumes. We extend that work by considering a theory with multiple, strongly-coupled channels and by accommodating external currents which inject arbitrary four-momentum as well as arbitrary angular momentum. The result is exact up to exponentially suppressed corrections governed by the pion mass times the box size. We also apply our master equation to various examples, including the two processes mentioned above as well as examples where the final state is an admixture of two open channels.