arXiv subjects

Martin J. Savage

Publications and source records attributed to Martin J. Savage.

At least 73 records · Page 4Linked to original sources

arXiv2017

First lattice QCD study of the gluonic structure of light nuclei

The role of gluons in the structure of the nucleon and light nuclei is investigated using lattice quantum chromodynamics (QCD) calculations. The first moment of the unpolarised gluon distribution is studied in nuclei up to atomic number $A=3$ at quark masses corresponding to pion masses of $m_π\sim 450$ and $806$ MeV. Nuclear modification of this quantity defines a gluonic analogue of the EMC effect and is constrained to be less than $\sim 10$% in these nuclei. This is consistent with expectations from phenomenological quark distributions and the momentum sum rule. In the deuteron, the combination of gluon distributions corresponding to the $b_1$ structure function is found to have a small first moment compared with the corresponding momentum fraction. The first moment of the gluon transversity structure function is also investigated in the spin-1 deuteron, where a non-zero signal is observed at $m_π\sim 806$ MeV. This is the first indication of gluon contributions to nuclear structure that can not be associated with an individual nucleon.

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arXiv2017

The isotensor axial polarisability and lattice QCD input for nuclear double-$β$ decay phenomenology

The potential importance of short-distance nuclear effects in double-$β$ decay is assessed using a lattice QCD calculation of the $nn\rightarrow pp$ transition and effective field theory methods. At the unphysical quark masses used in the numerical computation, these effects, encoded in the isotensor axial polarisability, are found to be of similar magnitude to the nuclear modification of the single axial current, which phenomenologically is the quenching of the axial charge used in nuclear many-body calculations. This finding suggests that nuclear models for neutrinoful and neutrinoless double-$β$ decays should incorporate this previously neglected contribution if they are to provide reliable guidance for next-generation neutrinoless double-$β$ decay searches. The prospects of constraining the isotensor axial polarisabilities of nuclei using lattice QCD input into nuclear many-body calculations are discussed.

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arXiv2017

Baryon magnetic moments: Symmetries and relations

Magnetic moments of the octet baryons are computed using lattice QCD in background magnetic fields, including the first treatment of the magnetically coupled Sigma-Lambda system. Although the computations are performed for relatively large values of the up and down quark masses, we gain new insight into the symmetries and relations between magnetic moments by working at a three-flavor mass-symmetric point. While the spin-flavor symmetry in the large Nc limit of QCD is shared by the naive constituent quark model, we find instances where quark model predictions are considerably favored over those emerging in the large Nc limit. We suggest further calculations that would shed light on the curious patterns of baryon magnetic moments.

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arXiv2017

On the Statistics of Baryon Correlation Functions in Lattice QCD

A systematic analysis of the structure of single-baryon correlation functions calculated with lattice QCD is performed, with a particular focus on characterizing the structure of the noise associated with quantum fluctuations. The signal-to-noise problem in these correlation functions is shown, as long suspected, to result from a sign problem. The log-magnitude and complex phase are found to be approximately described by normal and wrapped normal distributions respectively. Properties of circular statistics are used to understand the emergence of a large time noise region where standard energy measurements are unreliable. Power-law tails in the distribution of baryon correlation functions, associated with stable distributions and "Levy flights", are found to play a central role in their time evolution. A new method of analyzing correlation functions is considered for which the signal-to-noise ratio of energy measurements is constant, rather than exponentially degrading, with increasing source-sink separation time. This new method includes an additional systematic uncertainty that can be removed by performing an extrapolation, and the signal-to-noise problem re-emerges in the statistics of this extrapolation. It is demonstrated that this new method allows accurate results for the nucleon mass to be extracted from the large-time noise region inaccessible to standard methods. The observations presented here are expected to apply to quantum Monte Carlo calculations more generally. Similar methods to those introduced here may lead to practical improvements in analysis of noisier systems.

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arXiv2017

Proton-proton fusion and tritium $β$-decay from lattice quantum chromodynamics

The nuclear matrix element determining the $pp\to d e^+ ν$ fusion cross section and the Gamow-Teller matrix element contributing to tritium $β$-decay are calculated with lattice Quantum Chromodynamics (QCD) for the first time. Using a new implementation of the background field method, these quantities are calculated at the SU(3)-flavor-symmetric value of the quark masses, corresponding to a pion mass of $m_π$ ~ 806 MeV. The Gamow-Teller matrix element in tritium is found to be 0.979(03)(10) at these quark masses, which is within $2σ$ of the experimental value. Assuming that the short-distance correlated two-nucleon contributions to the matrix element (meson-exchange currents) depend only mildly on the quark masses, as seen for the analogous magnetic interactions, the calculated $pp\to d e^+ ν$ transition matrix element leads to a fusion cross section at the physical quark masses that is consistent with its currently accepted value. Moreover, the leading two-nucleon axial counterterm of pionless effective field theory is determined to be $L_{1,A}=3.9(0.1)(1.0)(0.3)(0.9)\ {\rm fm}^3$ at a renormalization scale set by the physical pion mass, also in agreement with the accepted phenomenological range. This work concretely demonstrates that weak transition amplitudes in few-nucleon systems can be studied directly from the fundamental quark and gluon degrees of freedom and opens the way for subsequent investigations of many important quantities in nuclear physics.

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arXiv2017

Baryon-Baryon Interactions and Spin-Flavor Symmetry from Lattice Quantum Chromodynamics

Lattice quantum chromodynamics is used to constrain the interactions of two octet baryons at the SU(3) flavor-symmetric point, with quark masses that are heavier than those in nature (equal to that of the physical strange quark mass and corresponding to a pion mass of $\approx 806~\tt{MeV}$). Specifically, the S-wave scattering phase shifts of two-baryon systems at low energies are obtained with the application of Lüscher's formalism, mapping the energy eigenvalues of two interacting baryons in a finite volume to the two-particle scattering amplitudes below the relevant inelastic thresholds. The values of the leading-order low-energy scattering parameters in the irreducible representations of SU(3) are consistent with an approximate SU(6) spin-flavor symmetry in the nuclear and hypernuclear forces that is predicted in the large-$N_c$ limit of QCD. The two distinct SU(6)-invariant interactions between two baryons are constrained at this value of the quark masses, and their values indicate an approximate accidental SU(16) symmetry. The SU(3) irreducible representations containing the $NN~({^1}S_0)$, $NN~({^3}S_1)$ and $\frac{1}{\sqrt{2}}(Ξ^0n+Ξ^-p)~({^3}S_1)$ channels unambiguously exhibit a single bound state, while the irreducible representation containing the $Σ^+ p~({^3}S_1)$ channel exhibits a state that is consistent with either a bound state or a scattering state close to threshold. These results are in agreement with the previous conclusions of the NPLQCD collaboration regarding the existence of two-nucleon bound states at this value of the quark masses.

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arXiv2017

Octet Baryon Magnetic Moments from Lattice QCD: Approaching Experiment from a Three-Flavor Symmetric Point

Lattice QCD calculations with background magnetic fields are used to determine the magnetic moments of the octet baryons. Computations are performed at the physical value of the strange quark mass, and two values of the light quark mass, one corresponding to the three-flavor symmetric point, where the pion mass is 800 MeV, and the other corresponding to a pion mass of 450 MeV. The moments are found to exhibit only mild pion-mass dependence when expressed in terms of appropriately chosen magneton units- the natural baryon magneton. A curious pattern is revealed among the anomalous baryon magnetic moments which is linked to the constituent quark model, however, careful scrutiny exposes additional features. Relations expected to hold in the large-Nc limit of QCD are studied; and, in one case, a clear preference for the quark model over the large-Nc prediction is found. The magnetically coupled Lambda-Sigma system is treated in detail at the three-flavor symmetric point, with the lattice QCD results comparing favorably with predictions based on SU(3)F symmetry. This analysis enables the first extraction of the isovector transition magnetic polarizability. The possibility that large magnetic fields stabilize strange matter is explored, but such a scenario is found to be unlikely.

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arXiv2017

Taming the Signal-to-Noise Problem in Lattice QCD by Phase Reweighting

Path integrals describing quantum many-body systems can be calculated with Monte Carlo sampling techniques, but average quantities are often subject to signal-to-noise ratios that degrade exponentially with time. A phase-reweighting technique inspired by recent observations of random walk statistics in correlation functions is proposed that allows energy levels to be extracted from late-time correlation functions with time-independent signal-to-noise ratios. Phase reweighting effectively includes dynamical refinement of source magnitudes but introduces a bias associated with the phase. This bias can be removed by performing an extrapolation, but at the expense of re-introducing a signal-to-noise problem. Lattice Quantum Chromodynamics calculations of the $ρ$ and nucleon masses and of the $ΞΞ$ binding energy show consistency between standard results obtained using earlier-time correlation functions and phase-reweighted results using late-time correlation functions inaccessible to standard statistical analysis methods.

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arXiv2017

Double-$β$ Decay Matrix Elements from Lattice Quantum Chromodynamics

A lattice quantum chromodynamics (LQCD) calculation of the nuclear matrix element relevant to the $nn\to ppee\overlineν_e\overlineν_e$ transition is described in detail, expanding on the results presented in Ref. [1]. This matrix element, which involves two insertions of the weak axial current, is an important input for phenomenological determinations of double-$β$ decay rates of nuclei. From this exploratory study, performed using unphysical values of the quark masses, the long-distance deuteron-pole contribution to the matrix element is separated from shorter-distance hadronic contributions. This polarizability, which is only accessible in double-weak processes, cannot be constrained from single-$β$ decay of nuclei, and is found to be smaller than the long-distance contributions in this calculation, but non-negligible. In this work, technical aspects of the LQCD calculations, and of the relevant formalism in the pionless effective field theory, are described. Further calculations of the isotensor axial polarizability, in particular near and at the physical values of the light-quark masses, are required for precise determinations of both two-neutrino and neutrinoless double-$β$ decay rates in heavy nuclei.

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arXiv2016

Nuclear Physics

Lattice QCD is making good progress toward calculating the structure and properties of light nuclei and the forces between nucleons. These calculations will ultimately refine the nuclear forces, particularly in the three- and four-nucleon sector and the short-distance interactions of nucleons with electroweak currents, and allow for a reduction of uncertainties in nuclear many-body calculations of nuclei and their reactions. After highlighting their importance, particularly to the Nuclear Physics and High-Energy Physics experimental programs, I discuss the progress that has been made toward achieving these goals and the challenges that remain.

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arXiv2016

Axial-Current Matrix Elements in Light Nuclei from Lattice QCD

I present results from the first lattice QCD calculations of axial-current matrix elements in light nuclei, performed by the NPLQCD collaboration. Precision calculations of these matrix elements, and the subsequent extraction of multi-nucleon axial-current operators, are essential in refining theoretical predictions of the proton-proton fusion cross section, neutrino-nucleus cross sections and $ββ$-decay rates of nuclei. In addition, they are expected to shed light on the phenomenological quenching of $g_A$ that is required in nuclear many-body calculations.

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arXiv2016

Unitary Limit of Two-Nucleon Interactions in Strong Magnetic Fields

Two-nucleon systems are shown to exhibit large scattering lengths in strong magnetic fields at unphysical quark masses, and the trends toward the physical values indicate that such features may exist in nature. Lattice QCD calculations of the energies of one and two nucleons systems are performed at pion masses of $m_π\sim 450$ and 806 MeV in uniform, time-independent magnetic fields of strength {\bf B}| \sim 10^{19}$-$10^{20}$ Gauss to determine the response of these hadronic systems to large magnetic fields. Fields of this strength may exist inside magnetars and in peripheral relativistic heavy ion collisions, and the unitary behavior at large scattering lengths may have important consequences for these systems.

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arXiv2015

Nuclear Physics from Lattice Quantum Chromodynamics

Quantum Chromodynamics and Quantum Electrodynamics, both renormalizable quantum field theories with a small number of precisely constrained input parameters, dominate the dynamics of the quarks and gluons - the underlying building blocks of protons, neutrons, and nuclei. While the analytic techniques of quantum field theory have played a key role in understanding the dynamics of matter in high energy processes, they encounter difficulties when applied to low-energy nuclear structure and reactions, and dense systems. Expected increases in computational resources into the exascale during the next decade will provide the ability to determine a range of important strong interaction processes directly from QCD using the numerical technique of Lattice QCD. This will complement the nuclear physics experimental program, and in partnership with new thrusts in nuclear many-body theory, will enable unprecedented understanding and refinement of nuclear forces and, more generally, the visible matter in our universe. In this presentation, I will discuss the state-of-the-art Lattice QCD calculations of quantities of interest in nuclear physics, progress that is expected in the near future, and the anticipated impact.

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arXiv2015

Magnetic properties of light nuclei from lattice QCD

After a short review of Lattice QCD methodology and techniques, I summarize recent results of Lattice QCD calculations of the interactions of nucleons and light nuclei with magnetic fields at pion masses of 805 MeV and 450 MeV. Interestingly, the magnetic moments are found to be consistent with the experimental values when given in terms of natural nuclear magnetons. The very low-energy cross section for $np\rightarrow dγ$ is calculated and found to agree with the experimental measurement. First calculations of the magnetic polarizabilities of light nuclei are presented, with a large isovector polarizability observed for the nucleon at these heavier pion masses.

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arXiv2015

The Magnetic Structure of Light Nuclei from Lattice QCD

Lattice QCD with background magnetic fields is used to calculate the magnetic moments and magnetic polarizabilities of the nucleons and of light nuclei with $A\le4$, along with the cross-section for the $M1$ transition $np\rightarrow dγ$, at the flavor SU(3)-symmetric point where the pion mass is $m_π\sim 806$ MeV. These magnetic properties are extracted from nucleon and nuclear energies in six uniform magnetic fields of varying strengths. The magnetic moments are presented in a recent Letter. For the charged states, the extraction of the polarizability requires careful treatment of Landau levels, which enter non-trivially in the method that is employed. The nucleon polarizabilities are found to be of similar magnitude to their physical values, with $β_p=5.22(+0.66/-0.45)(0.23) \times 10^{-4}$ fm$^3$ and $β_n=1.253(+0.056/-0.067)(0.055) \times 10^{-4}$ fm$^3$, exhibiting a significant isovector component. The dineutron is bound at these heavy quark masses and its magnetic polarizability, $β_{nn}=1.872(+0.121/-0.113)(0.082) \times 10^{-4}$ fm$^3$ differs significantly from twice that of the neutron. A linear combination of deuteron scalar and tensor polarizabilities is determined by the energies of the $j_z=\pm 1$ deuteron states, and is found to be $β_{d,\pm 1}=4.4(+1.6/-1.5)(0.2) \times 10^{-4}$ fm$^3$. The magnetic polarizabilities of the three-nucleon and four-nucleon systems are found to be positive and similar in size to those of the proton, $β_{^{3}\rm He}=5.4(+2.2/-2.1)(0.2) \times 10^{-4}$ fm$^3$, $β_{^{3}\rm H}=2.6(1.7)(0.1) \times 10^{-4}$ fm$^3$, $β_{^{4}\rm He}=3.4(+2.0/-1.9)(0.2) \times 10^{-4}$ fm$^3$. Mixing between the $j_z=0$ deuteron state and the spin-singlet $np$ state induced by the background magnetic field is used to extract the short-distance two-nucleon counterterm, ${\bar L}_1$, of the pionless effective theory for $NN$ systems (equivalent to the meson-exchange current contribution in nuclear potential models), that dictates the cross-section for the $np\to dγ$ process near threshold. Combined with previous determinations of NN scattering parameters, this enables an ab initio determination of the threshold cross-section at these unphysical masses.

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arXiv2015

Ab initio calculation of the $np \to d γ$ radiative capture process

Lattice QCD calculations of two-nucleon systems are used to isolate the short-distance two-body electromagnetic contributions to the radiative capture process $np \to dγ$, and the photo-disintegration processes $γ^{(\ast)} d \to np$. In nuclear potential models, such contributions are described by phenomenological meson-exchange currents, while in the present work, they are determined directly from the quark and gluon interactions of QCD. Calculations of neutron-proton energy levels in multiple background magnetic fields are performed at two values of the quark masses, corresponding to pion masses of $m_π\sim 450$ and 806 MeV, and are combined with pionless nuclear effective field theory to determine these low-energy inelastic processes. Extrapolating to the physical pion mass, a cross section of $σ^{lqcd}(np\to dγ)=332.4({\tiny \begin{array}{l}+5.4 \\ - 4.7\end{array}})\ mb$ is obtained at an incident neutron speed of $v=2,200\ m/s$, consistent with the experimental value of $σ^{expt}(np \to dγ) = 334.2(0.5)\ mb$.

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arXiv2014

Uncertainty Quantification in Lattice QCD Calculations for Nuclear Physics

The numerical technique of Lattice QCD holds the promise of connecting the nuclear forces, nuclei, the spectrum and structure of hadrons, and the properties of matter under extreme conditions with the underlying theory of the strong interactions, quantum chromodynamics. A distinguishing, and thus far unique, feature of this formulation is that all of the associated uncertainties, both statistical and systematic can, in principle, be systematically reduced to any desired precision with sufficient computational and human resources. We review the sources of uncertainty inherent in Lattice QCD calculations for nuclear physics, and discuss how each is quantified in current efforts.

nucl-th↗

arXiv2014

Finite-Volume Electromagnetic Corrections to the Masses of Mesons, Baryons and Nuclei

Now that Lattice QCD calculations are beginning to include QED, it is important to better understand how hadronic properties are modified by finite-volume QED effects. They are known to exhibit power-law scaling with volume, in contrast to the exponential behavior of finite-volume strong interaction effects. We use non-relativistic effective field theories describing the low-momentum behavior of hadrons to determine the finite-volume QED corrections to the masses of mesons, baryons and nuclei out to O(1/L^4) in a volume expansion, where L is the spatial extent of the cubic volume. This generalizes the previously determined expansion for mesons, and extends it by two orders in 1/L to include contributions from the charge radius, magnetic moment and polarizabilities of the hadron. We make an observation about direct calculations of the muon g-2 in a finite volume.

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