arXiv subjects

Jared Vanasse

Publications and source records attributed to Jared Vanasse.

At least 19 recordsLinked to original sources

arXiv2026

Coulomb Corrections to Three-Nucleon Moments

The Helium-3 (${}^3\mathrm{He}$) magnetic moment and Gamow-Teller (GT) matrix element in triton (${}^3\mathrm{H}$) $\beta$-decay are calculated in pionless effective field theory ($\mathrm{EFT}(/\!\!\!\pi)$) to next-to-leading order (NLO). Coulomb corrections are included perturbatively to $\mathcal{O}(\alpha)$ in this framework and should naively be $\alpha M_n/p^*\!\!\sim\!8\%$ corrections, where $p^*\!\!\sim\!88.5$ MeV is related to the three-nucleon binding momentum. Fitting the two-nucleon iso-vector magnetic current low-energy constant (LEC), $L_1$, to the ${}^3\mathrm{H}$ magnetic moment and the two-nucleon iso-scalar magnetic current LEC, $L_2$, to the deuteron magnetic moment we find the NLO ${}^3\mathrm{He}$ magnetic moment in units of nuclear magnetons is -2.130 and the surprisingly small $\mathcal{O}(\alpha)$ correction is 0.00335, $\approx\!0.18\%$ of the LO $\mathrm{EFT}(/\!\!\!\pi)$ prediction. The leading-order (LO) GT matrix element for ${}^3\mathrm{H}$ $\beta$-decay is 0.9806 while again it has a surprisingly small $\mathcal{O}(\alpha)$ Coulomb correction of $-0.000740$, $\approx\!0.08\%$ of the LO $\mathrm{EFT}(/\!\!\!\pi)$ prediction. At NLO we calculate the GT matrix element of ${}^3\mathrm{H}$ $\beta$-decay, including the $\mathcal{O}(\alpha)$ Coulomb correction, in terms of the two-nucleon axial current LEC $l_{1,A}$. Fitting $l_{1,A}$ to the ${}^3\mathrm{H}$ half-life we make a prediction for the proton-proton fusion reduced matrix element of $\Lambda(0)=2.776(331)$. Finally, we attempt to explain the unusually small size of the $\mathcal{O}(\alpha)$ corrections by investigating the Wigner-SU(4) expansion of these observables.

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arXiv2024

Two-Body Triton Photodisintegration and Wigner-SU(4) Symmetry

We calculate the two-body triton photodisintegration cross section as a function of photon energy to next-to-next-to leading order (NNLO) in pionless effective field theory (EFT($\pi \!\!/$)) and show good agreement with experiment. In addition we calculate the polarization asymmetry $R_C=-0.441(15)$ in cold neutron-deuteron capture to NNLO in EFT($\pi \!\!/$), in agreement with the experimental value of $R_C=-0.42\pm 0.03$ [M. W. Konijnenberg et al. in Phys. Lett. B 205, 215 (1988)]. We also assess the dependence of $R_C$ on different fits of the two-nucleon magnetic currents. Finally, we consider the impact of Wigner-SU(4) symmetry and demonstrate that starting from the Wigner-SU(4) symmetric limit and including perturbative corrections to the breaking of Wigner-SU(4) symmetry does a good job of describing two-body triton photodisintegration.

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arXiv2024

Tritium $\beta$-decay and Proton-Proton Fusion in Pionless Effective Field Theory

The Gamow-Teller and Fermi matrix elements, ${\left<\mathbf{GT}\right>}$ and ${\left<\mathbf{F}\right>}$, respectively, for tritium $\beta$-decay are calculated to next-to-leading order (NLO) in pionless effective field theory in the absence of Coulomb and isospin violation giving the leading order predictions ${\left<\mathbf{GT}\right>}_{0}=0.9807$ and ${\left<\mathbf{F}\right>}_{0}=1$. Using an experimentally determined value for the tritium-$\beta$ decay GT matrix element, the two-body axial current low energy constant is fixed at NLO yielding $L_{1,A}=6.01\pm2.08$ fm$^{3}$ at the renormalization scale of the physical pion mass, which agrees with predictions based on naive dimensional analysis. Finally, the consequences of Wigner-SU(4) spin-isospin symmetry are considered for the Gamow-Teller matrix element.

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arXiv2022

Cold Neutron-Deuteron Capture and Wigner-SU(4) Symmetry

We calculate the cold neutron-deuteron ($nd$) capture cross section, $\sigma_{nd}$, to next-to-next-to leading order (NNLO) using the model-independent approach of pionless effective field theory (EFT($\pi\!\!\!/$)). At leading order we find $\sigma_{nd} = 0.315 \pm 0.217$ mb, while the experimental result is 0.508(15) mb [Jurney, Bendt and Browne in Phys. Rev. C 25, 2810 (1982)] for a laboratory neutron velocity of 2200 m/s. At next-to-leading-order (NLO), we show that $\sigma_{nd}$ is sensitive to the low energy constant (LEC), $L_1^{(0)}$, of the two-nucleon isovector current appearing at NLO. A fit of $L_1^{(0)}$ at NLO to the triton magnetic moment yields a NLO prediction of $\sigma_{nd}=0.393 \pm 0.164$ mb, where the error comes from propagating the error from the $L_1^{(0)}$ fit. At next-to-next-to-leading-order (NNLO), we find that a new three-nucleon magnetic moment counterterm is required for renormalization group invariance of both $\sigma_{nd}$ and the triton magnetic moment. Fitting the NNLO correction to $L_1^{(0)}$ (denoted $L_1^{(1)}$) to cold neutron-proton capture ($\sigma_{np}$) yields a NNLO prediction of $\sigma_{nd}=0.447 \pm 0.130$ mb, where the error comes from propagating the error from the $L_1^{(1)}$ fit. We also study different fittings of $L_1^{(0)}$ and $L_1^{(1)}$ to $\sigma_{np}$, $\sigma_{nd}$, and/or the triton magnetic moment. For example, fitting $L_1^{(0)}$ simultaneously to $\sigma_{np}$, $\sigma_{nd}$, and the triton magnetic moment at NLO, and fitting $L_1^{(1)}$ simultaneously to $\sigma_{np}$ and $\sigma_{nd}$ at NNLO, yields $\sigma_{nd} = 0.480 \pm 0.114$ mb and $0.511 \pm 0.042$ mb, respectively, where errors are naively estimated from EFT($\pi\!\!\!/$) power counting. In addition, we discuss how Wigner-SU(4) symmetry may alter the naive EFT($\pi\!\!\!/$) expansion of $\sigma_{nd}$.

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arXiv2020

Large-$N_c$ and renormalization group constraints on parity-violating low-energy coefficients for three-derivative operators in pionless effective field theory

We extend from operators with one derivative to operators with three derivatives the analysis of two-body hadronic parity violation in a combined pionless effective field theory (EFT$_{\pi\!/}$) and large-$N_c$ expansion, where $N_c$ is the number of colors in quantum chromodynamics (QCD). In elastic scattering, these operators contribute to $S$-$P$ and $P$-$D$ wave transitions, with five operators and their accompanying low energy coefficients (LECs) characterizing the $S$-$P$ transitions and six operators and LECs those in $P$-$D$ transitions. We show that the large-$N_c$ analysis separates them into leading order in $N_c$, next-to-leading order in $N_c$, etc. Relationships among EFT$_{\pi\!/}$ LECs emerge in the large-$N_c$ expansion. We also discuss the renormalization scale dependence of these LECs. Our analysis can complement lattice QCD calculations and help prioritize future parity-violating experiments.

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arXiv2020

Electric dipole moments of three-nucleon systems in the pionless effective field theory

We calculate the electric dipole moments (EDMs) of three-nucleon systems at leading order in pionless effective field theory. The one-body contributions that arise from permanent proton and neutron EDMs and the two-body contributions that arise from CP-odd nucleon-nucleon interactions are taken into account. Neglecting the Coulomb interaction, we consider the triton and ${}^3$He, and also investigate them in the Wigner-SU(4) symmetric limit. We also calculate the electric dipole form factor and find numerically that the momentum dependence of the electric dipole form factor in the Wigner limit is, up to an overall constant (and numerical accuracy), the same as the momentum dependence of the charge form factor.

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arXiv2020

Effective field theory analysis of boson-trimer bond lengths to next-to-leading order

Cold Helium atoms are a unique system where a single excited three-body Efimov state occurs, naturally, without the need for an external magnetic field. While three-body bound state energies of cold Helium atoms have previously been investigated, recent experimental techniques have allowed their structure to also be studied. The weak interaction between Helium atoms leads to a helium-helium (dimer) scattering length, $a$, much larger than the helium-helium effective range of interaction, $r$. This feature is exploited in a theory that systematically expands observables in powers of $r/a$, known as short range effective field theory (srEFT), which has been used successfully to investigate properties of cold atom systems. Using srEFT we investigate the average bond length of atoms in the three-body ground state and excited Efimov state of cold Helium atoms. At leading-order (next-to-leading order) in srEFT, we find the average bond length of the $^4$He trimer ground state is 8.35(33) \r{A} (10.29(2) \r{A}) and the average bond length of the excited $^4$He trimer Efimov state is 103(4) \r{A} (105.3(2) \r{A}).

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arXiv2019

Time-Reversal-Invariance Violation in the $N\!d$ System and Large-$N_C$

A minimal set of five low energy constants (LECs) for time-reversal and parity violating ($\not{T}\!\!\!\not{P}$) nucleon-nucleon ($N\!N$) interactions at low energies ($E\!<\!m_{\pi}^2/M_N$) is given. Using a large-$N_C$ (number of colors in QCD) analysis we show that one linear combination of LECs is $\mathcal{O}(N_C)$, three LECs are $\mathcal{O}(N_C^{0})$, and one linear combination of LECs is $\mathcal{O}(N_C^{-1})$. We also calculate the $\not{T}\!\!\!\not{P}$ observables of neutron spin rotation through a polarized deuteron target and a spin correlation coefficient in nucleon-deuteron scattering using pionless effective field theory. Using the large-$N_C$ analysis we show that the spin correlation coefficient and the neutron spin rotation are predominantly determined by same two LECs in the large-$N_C$ basis.

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arXiv2019

Parity-Violating Three Nucleon Interactions at Low Energies and Large-$N_{C}$

The parity-violating (PV) nucleon-nucleon ($N\!N$) interaction in the three-nucleon system is investigated using pionless effective field theory ($\mathrm{EFT}(/\!\!\!π)$). This work shows that a next-to-leading order (NLO) PV three-body force is necessary in contradiction with a previous claim [Griesshammer and Schindler in Eur. Phys. J. A 46, 73 (2010)]. Including three-body $P$ to $D$-wave transitions PV three-nucleon observables are calculated to higher energies than previously considered. Using the recent large-$N_{C}$ analysis of the PV $N\!N$ interaction in $\mathrm{EFT}(/\!\!\!π)$ the current understanding of low energy PV few-body measurements is reassessed. The recent measurement of the asymmetry $A_γ$ in $\vec{n}p\to dγ$ from the NPDGamma collaboration [D. Blyth et al. (NPDGamma), Phys. Rev. Lett. 121, 242002 (2018)], gives the value $g_{4}^{(N_{C}^{-1})}=(-1.4\pm 0.63(stat.)\pm 0.09(syst.))\times 10^{-10}~\mathrm{MeV}^{-1}$ for a next-to-next-to-leading order (N$^{2}$LO) in large-$N_{C}$ low energy constant (LEC). Using the large-$N_{C}$ hierarchy of LECs the sizes of the leading order (LO) in large-$N_{C}$ LECs are estimated using an experimental bound on a parity violating asymmetry in $\vec{p}d$ scattering at $E_{\mathrm{lab}}=15$ MeV and a measurement of $\vec{pp}$ scattering at $E_{\mathrm{lab}}=13.6$ MeV. Comparing the size of the resulting LO in large-$N_{C}$ LECs to the N$^{2}$LO in large-$N_{C}$ LEC $g_{4}^{(N_{C}^{-1})}$ shows they are roughly the same size in contradiction with current large-$N_{C}$ counting.

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arXiv2018

Large-N(c) limit reduces the number of independent few-body parity-violating low-energy constants in pionless effective field theory

The symmetries of the Standard Model dictate that for very low energies, where nucleon dynamics can be described in terms of a pionless effective field theory, the leading-order parity-violating nucleon-nucleon Lagrangian contains five independent unknown low-energy constants (LECs). We find that imposing the approximate symmetry of QCD that appears when the number of colors N(c) becomes large reduces the number of independent LECs to two at leading order in the combined pionless effective field theory and large-N(c) expansions. We also find a relation between the two isoscalar LECs in the large-N(c) limit. This has important implications for the number of experiments and/or lattice calculations necessary to confirm this description of physics.

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arXiv2017

The Triton Charge Radius to Next-to-next-to-leading order in Pionless Effective Field Theory

The triton point charge radius is calculated to next-to-next-to-leading order (NNLO) in pionless effective field theory ($\mathrm{EFT}(\not{\!π})$), yielding a prediction of $1.14\pm0.19$ fm (leading order), $1.59\pm0.08$ fm (next-to leading order), and $1.62\pm0.03$ fm (NNLO) in agreement with the current experimental extraction of $1.5978\pm0.040$ fm [Angeli and Marinova, At. Data Nucl. Data Tables 99, 69 (2013)]. The error at NNLO is due to cutoff variation ($\sim$ 1%) within a reasonable range of calculated cutoffs and from a $\mathrm{EFT}(\not{\!π})$ error estimate ($\sim$ 1.5%). In addition new techniques are introduced to add perturbative corrections to bound and scattering state calculations for short range effective field theories, but with a focus on their use in $\mathrm{EFT}(\not{\!π})$

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arXiv2017

Charge and Magnetic Properties of Three-Nucleon Systems in Pionless Effective Field Theory

A method to calculate the form factor for an external current with non-derivative coupling for the three-body system in an effective field theory (EFT) of short-range interactions is shown. Using this method the point charge radius of ${}^3\mathrm{He}$ is calculated to next-to-next-to-leading order (NNLO) in pionless EFT ($\mathrm{EFT}(\not{\!π})$), and the magnetic moment and magnetic radius of ${}^3\mathrm{H}$ and ${}^3\mathrm{He}$ are calculated to next-to-leading order (NLO). For the ${}^3\mathrm{He}$ charge and magnetic form factors Coulomb interactions are ignored. The ${}^3\mathrm{He}$ point charge radius is given by 1.74(4) fm at NNLO. This agrees well with the experimental ${}^3\mathrm{He}$ point charge radius of 1.7753(54) fm [Angeli and Marinova, At. Data Nucl. Data Tables 99, 69 (2013)]. The ${}^3\mathrm{H}$ (${}^3\mathrm{He}$) magnetic moment in units of nuclear magnetons is found to be 2.92(35) (-2.08(25)) at NLO in agreement with the experimental value of 2.979 (-2.127). For ${}^3\mathrm{H}$ (${}^3\mathrm{He}$) the NLO magnetic radius is 1.78(11) fm (1.85(11) fm) which agrees with the experimental value of 1.840(182) fm (1.965(154) fm) [I. Sick, Prog. Part. Nucl. Phys. 47, 245 (2001)]. The fitting of the low-energy constant $L_{1}$ of the isovector two-body magnetic current and the consequences of Wigner-SU(4) symmetry for the three-nucleon magnetic moments are also discussed.

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arXiv2017

Three-nucleon bound states and the Wigner-SU(4) limit

We examine the extent to which the properties of three-nucleon bound states are well-reproduced in the limit that nuclear forces satisfy Wigner's SU(4) (spin-isospin) symmetry. To do this we compute the charge radii up to next-to-leading order (NLO) in an effective field theory (EFT) that is an expansion in powers of $R/a$, with $R$ the range of the nuclear force and $a$ the nucleon-nucleon ($N\!N$) scattering lengths. In the Wigner-SU(4) limit, the triton and Helium-3 point charge radii are equal. At NLO in the range expansion both are $1.66$ fm. Adding the first-order corrections due to the breaking of Wigner symmetry in the $N\!N$ scattering lengths gives a ${}^3\mathrm{H}$ point charge radius of $1.58$ fm, which is remarkably close to the experimental number, $1.5978\pm0.040$ fm (Angeli and Marinova in At Data Nucl Data Tables 99:69-95, 2013). For the ${}^3\mathrm{He}$ point charge radius we find $1.70$ fm, about 4% away from the experimental value of $1.77527\pm0.0054$ fm (Angeli and Marinova 2013). We also examine the Faddeev components that enter the tri-nucleon wave function and find that an expansion of them in powers of the symmetry-breaking parameter converges rapidly. Wigner's SU(4) symmetry is thus a useful starting point for understanding tri-nucleon bound-state properties.

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arXiv2016

Charge and Matter Form Factors of Two-Neutron Halo Nuclei in Halo Effective Field Theory at Next-to-leading-order

Using halo effective field theory (EFT), an expansion in $R_{core}/R_{halo}$, where $R_{core}$ is the radius of the core and $R_{halo}$ the radius of the halo nucleus, we calculate the charge and neutron form factors of the two-neutron halo nuclei $^{11}$Li, $^{14}$Be, and $^{22}$C to next-to-leading-order (NLO) by treating them as an effective three-body system. From the form factors we extract the point charge and point matter radii, inter-neutron distance, and neutron opening angle. Agreement is found with existing experimental extractions. Results are given for the point charge and point matter radii for arbitrary neutron core scattering effective range, $ρ_{cn}$, that can be used for predictions once $ρ_{cn}$ is measured. Estimates for $ρ_{cn}$ are also used to make NLO predictions. Finally, our point charge radii are compared to other halo-EFT predictions, and setting the core mass equal to the neutron mass our point charge radius is found to agree with an analytical prediction in the unitary limit.

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arXiv2016

Three-body systems in pionless effective field theory

Investigations of three-body nuclear systems using pionless effective field theory ($\mathrm{EFT}_{\notπ}$) are reviewed. The history of $\mathrm{EFT}_{\notπ}$ in $nd$ and $pd$ scattering is briefly discussed and emphasis put on the use of strict perturbative techniques. In addition renormalization issues appearing in $pd$ scattering are also presented. Bound state calculations are addressed and new perturbative techniques for describing them are highlighted. Three-body breakup observables in $nd$ scattering are also considered and the utility of $\mathrm{EFT}_{\notπ}$ for addressing them.

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arXiv2016

$nd$ Scattering and the $A_y$ Puzzle to Next-to-next-to-next-to-leading Order

Polarization observables in neutron-deuteron scattering are calculated to next-to-next-to-next-to-leading order ($\mathrm{N}^{3}\mathrm{LO}$) in pionless effective field theory ($\mathrm{EFT}_{\notπ}$). At $\mathrm{N}^{3}\mathrm{LO}$ the two-body $P$-wave contact interactions are found to be important contributions to the neutron vector analyzing power, $A_{y}(θ)$, and the deuteron vector analyzing power, $iT_{11}(θ)$. Extracting the two-body $P$-wave $\mathrm{EFT}_{\notπ}$ coefficients from two-body scattering data and varying them within the expected $\mathrm{EFT}_{\notπ}$ theoretical errors provides results that are consistent (at the $\mathrm{N}^{3}\mathrm{LO}$ level) with $A_y$ experimental data at low energies. Cutoff dependence of the $\mathrm{N}^{3}\mathrm{LO}$ correction of the doublet $S$-wave $nd$ scattering amplitude suggests the need for a new three-body force at $\mathrm{N}^{3}\mathrm{LO}$, which is likely one that mixes Wigner- symmetric and Wigner-antisymmetric three-body channels.

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arXiv2014

Energy dependence of the parity-violating asymmetry of circularly polarized photons in $d\vecγ \to np$ in pionless effective field theory

We calculate the energy dependence of the asymmetry in the cross sections for circularly polarized photons on an unpolarized deuteron target in $d\vecγ \to np$ in pionless effective field theory. By matching the parity-violating low-energy constants to different sets of corresponding model parameters we obtain estimates for the asymmetry. In addition we calculate two possible figures of merit for the asymmetry in order to assess the preferred photon energy at which to perform a possible future experiment at a high-intensity photon source.

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arXiv2014

${}^{3}\mathrm{He}$ and $pd$ Scattering to Next-to-Leading Order in Pionless Effective Field Theory

We study the three-body systems of ${}^{3}\mathrm{He}$ and $pd$ scattering and demonstrate, both analytically and numerically, that a new $pd$ three-body force is needed at next-to-leading order in pionless effective field theory. We also show that at leading order these observables require no new three-body force beyond what is necessary to describe $nd$ scattering. We include electromagnetic effects by iterating only diagrams that involve a single photon exchange in the three-body sector.

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