1,720,984 research outputs found
Status of the Standard Solar Model and the Importance of New Tests of the Model
No full textHaxton, Wick. (2009). Status of the Standard Solar Model and the Importance of New Tests of the Model. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/52762
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Harmonic Oscillator Based Effective Theory, Connecting LQCD to Nuclear Structure
Full text linkThis work focuses on construction of a bridge from QCD (quantum chromodynamics), the theory of quarks, gluons, and their interactions, to nuclear structure, an obvious but unattained objective ever since the introduction of QCD in 1973. The bridge footing on one side of the chasm is QCD in the non-perturbative regime, only now beginning to yield to massively parallel computation in a Monte-Carlo space-time lattice formulation of QCD called LQCD (lattice quantum chromodynamics) that is our only tool for such problems. The resulting trickle of information about the nucleon interaction comes in the form of a fuzzy spectrum for two nucleons in a periodic box. It can be expected that the spectrum will sharpen and even eventually include a spectrum for three nucleons in a box with the introduction of larger and faster supercomputers as well as more clever algorithms. Fundamentally though, limits on what can be accomplished in LQCD are set by the famous fermion sign problem. Results in LQCD are produced as a small residual of the sum of large positive and negative contributions from the Monte-Carlo trials and accuracy only improves slowly with the number of expensive trials.The bridge footing on the other side of the chasm is the configuration interaction shell model, which is commonly used for nuclear structure calculations from a microscopic Hamiltonian expressed in the colorless degrees of freedom of QCD we call nucleons. As currently executed, this method is a model, the two- and possibly three-body interaction in use lacking a rigorous connection to QCD or direct accounting for contributions from scattering outside the model space. Nucleons, like quarks, are fermions and a fermion sign like problem exists in these calculations as well. The configuration interaction shell model is formulated in an antisymmetrized harmonic oscillator basis that grows with the number of permutations of identical nucleons in the model space. However, fantastically e cient parallel sparse matrix techniques for finding low lying eigenstates exist, allowing quite large problems to be solved.One footing of the bridge is solid and the other is nearing completion. Construction of the bridge itself then faces three major problems addressed in this dissertation, construction of the effective nuclear interaction from observables, finite volume effects associated with the periodic volume in which LQCD results are calculated, and the construction of the A-body effective Hamiltonian from the two body effective interaction.An effective theory is a organized and complete parameterized approximation limited to and preserving the known symmetries of an underlying theory (QCD in this case), constrained to some regime (energies below the mass of the pion in this case), and expressed in degrees of freedom suitable for solving the problem at hand (nucleons in a harmonic oscillator basis below an energy cutoff for the nuclear structure problem). An effective theory has a formal relationship to the underlying theory that a model does not. Unlike a model, a small number of observables may be used to fix the lowest order expansion parameters of the effective theory approximation with the expectation that the approximation remains valid in other situations for which observables are not available.The first portion of this work focuses on the construction of a harmonic oscillator based effective theory (HOBET) from observables in a spherical harmonic oscillator basis. It builds on the prior work of Haxton, Song, and Luu in demonstrating the construction of an convergent effective theory from a known potential, establishing the form of the required effective theory expansion. The new work required the extension of HOBET to a theory no longer limited to bound states and with continuity in energy, enabling uniform treatment of bound and continuum states. Here the expansion parameters are instead derived from phase shift observables at continuum energies. A key insight developed during this work was the way in which the effective theory constructed at an energy is connected to the boundary constraints of the wave function. Using known techniques, Lu ̈scher’s method and the HAL QCD potential method, to transform the LQCD spectrum in periodic box to infinite volume phase shifts produces a successful mechanism for fitting the effective interaction without knowledge of the details of the potential.The techniques for converting LQCD results to phase shifts have issues such as uncontrolled systematics related to the volume size and range of the interaction as well as suspect perturbative expansions. These issues motivated an investigation into the possibility of directly constructing the effective theory in a periodic volume. This new construction relies heavily on the previous insight about the connection of the effective theory to the wave function boundary constraints. A key result is that the kernel of the effective theory, which captures scattering through the excluded degrees of freedom, is in fact independent of the boundary conditions. It can be fit in the periodic volume context and then transplanted into an infinite volume spherical formulation of the effective theory by a straightforward basis transformation. Finite volume effects are automatically handled in the process. Of immediate interest to the LQCD community is that accurate phase shifts can be easily extracted from the effective theory, avoiding systematic and finite volume errors in existing methods.With a two body effective interaction in hand the last step to a usable bridge is the construction of an A-body interaction in terms of the two body one. The exact form this construction is not settled yet, but one promising structure with leading contributions that can be calculated is explored.The assembly of these three pieces completes the bridge, producing a way to perform nuclear structure calculations that is formally connected to the underlying theory of QCD
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Nuclear Structure Dependent Radiative Corrections to Gamow-Teller Transitions and Proton-Proton Fusion
Full text linkPrecision in semileptonic weak nuclear interactions has become an important topic, with applications to both high-energy and solar physics. We can search for physics beyond the standard model by checking CKM unitarity using superallowed Fermi beta decay. This is one of the most precise tests of the standard model. With better measurements of the axial form factor , the neutron lifetime can also become a competitive test of CKM unitarity. In solar physics, the rate of pp-fusion can be used in the luminosity constraint to test for new physics in the sun.The radiative correction to superallowed Fermi beta decay comes from a box diagram involving the axial-vector weak current. It is known that the spin-flip transitions generated by the magnetic moment and Gamow-Teller operators are modified by the nuclear environment. Nuclear shell model calculations of these transitions consistently give larger results than what is seen in experiments. This is corrected by phenomenological ``quenching factors" which suppress the rates to match experiment. In the analysis done by Towner and Hardy, they accounted for this effect by modifying the free-nucleon Born correction by a product of these quenching factors.Their analysis was challenged in a 2019 paper by Seng Gorchtein and Ramsey-Musolf, who claim that this analysis is flawed due to the fact that the quasi-elastic contribution has been shown not to require this quenching correction. They provide a formula for the quasi-elastic part of the box diagram, which involves nuclear structure corrections due to Pauli blocking and the nucleon removal energy.The goal of this thesis is to focus on a smaller nuclear system, in which the calculation does not suffer from these issues. Instead of focusing on Fermi decay, which has been the focus of much of the field, we analyze the case of -fusion which is mediated by a Gamow-Teller interaction. We also are able to confirm the approximation claimed in a 2003 analysis done by Kurylov Ramsey-Musolf and Vogel. In particular, we will be able to directly calculate the two-body contribution, Figure 1b in their paper.Since much of the focus has been on Fermi decays, and much less has been written about Gamow-Teller transitions, we go through the analysis for both the one-body Born contribution and the two-body nuclear structure correction. We give a new analysis of the Born correction for Gamow-Teller transitions, which is slightly different from that of Hayen 2021. This contribution is important for comparing the measured value of in neutron decay to the one calculated in lattice QCD. We also derive new formulas for the two-body nuclear structure correction, in analogy with the analysis of Fermi decays by Towner 1992. Using the standard two-body density matrix technique, these formulas can be used to calculate the nuclear structure correction to Gamow-Teller transitions in larger nuclear systems.We calculate the nuclear structure correction in -fusion in three different ways. First, we apply our new formulas for the two-body nuclear structure correction. This result depends on the approximation scheme outlined in Jaus and Rasche 1990 and Towner 1992, where we ignore the nuclear environment effects on the Green's function. Our result is slightly smaller than the estimate given by Kurylov and collaborators, due to a partial cancellation between the spin and the tensor terms and the narrow momentum space wavefunction of the initial -state.We then give a new method which does not rely on approximating the nuclear Green's function. This involves expanding the box diagram in terms of all possible intermediate states. We are able to check that this works by verifying the completeness relation, which must be exactly satisfied if all intermediate states are included. This is the main reason we are limited to small nuclear systems, such as the two and three body system.Once we expand the box diagram in terms of intermediate states, we are then able to directly calculate the effect of the nuclear environment through the nuclear Green's function. We find a significant enhancement over the previous calculation - much larger than one would expect from the non-relativistic power counting. This effect is due to a persistent energy gap at low momentum transfer, coming from the binding energy of the deuteron.Using our detailed knowledge of the system, we are then able to derive an approximate form of the result - the ``modified normal ordering" scheme. We pick an average value of the nuclear energy, which is allowed to depend on the loop momentum. This approximation scheme allows us to remove the intermediate states and normal order the currents, thus allowing us to separate out the one-body and two-body parts.In addition to narrowing the uncertainty in the -fusion cross section, the analysis done here is one concrete demonstration of the method outlined in Seng Gorchtein and Ramsey-Musolf's 2019 paper. While we were not able to resolve the issue of how to handle the phenomenological quenching factors in larger systems, the work done here can provide some insight into what an alternative method might look like
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Use of Effective Theories in Nuclear Physics
Full text linkApproximations are inevitable in solving realistic physics problems, and reliability of calculations depends on evaluation of how much error is associated with the approximations. One method to quantify errors is building effective theories, which organize successive approximations as a power series in some small parameter. We apply effective theories to two problems in nuclear physics.One is the calculation of atomic electric dipole moments (EDMs). EDMs are of interest as a probe of CP-violating physics. For atoms, EDM signals can be thought of as departures from Schiff theorem, which states that a neutral system of point-like, nonrelativistic charges that interact only electrostatically has no net EDM. We show how each of the conditions for Schiff theorem are violated in actual atoms by expanding the Breit interaction between the electrons and the nucleus in spherical multipoles. We see that EDM signals arising from violations of the Schiff limit can be organized as a power series in RN/RA, the ratio between the spatial sizes of the nucleus and the atom. This ratio is of order 10-5, and the power series in this parameter would have quantifiable errors. We identify the contributions to atomic EDM that correspond to the so-called Schiff moment, and give the general considerations for other contributions that may be of the same order as the Schiff moment in powers of RN/RA.The other problem is nucleon-nucleon (NN) interaction. The difficulty in describing this basic interaction is the fine tuning that exists between the long-range attraction and short-range repulsion in the NN potential. An effective theory of NN interaction must separate these two length scales. In order to achieve this separation, we introduce a harmonic oscillator (HO) basis, and restrict the calculation to a finite Hilbert space (P-space) of states with energies below some cutoff Λℏω. HO eigenstates contains a length scale, the oscillator length b, which we choose to be 1.7fm, as an intermediate scale. We show that, despite the short range nature of HO states, restricted wavefunctions contain enough information to reconstruct phase shifts. Projecting wavefunctions into this space throws away both the long-range physics due to the kinetic energy, and the short-range physics due to the strong interactions. We derive an equation in the P-space whose solution is the P-space restriction of the full-space scattering wavefunction, and identify the components of the equation that treat the long-range and short-range physics, respectively. The long-range information is encoded in what we call the tilde states, which are modification to the HO wavefunction with slower decay as r → ∞. The short-range information is modeled by a contact-gradient expansion, which is essentially a power series in a/b, where a is the length scale associated with the repulsive core in the NN potential. The behavior of the theory is investigated using a toy model of a spherical square well with a repulsive core
Is there an Ay problem in low-energy neutron–proton scattering?
Full text linkWe calculate Ay in neutron–proton scattering for the interactions models WJC-1 and WJC-2 in the Covariant Spectator Theory. We find that the recent 12 MeV measurements performed at TUNL are in better agreement with our results than with the Nijmegen Phase Shift Analysis of 1993, and after reviewing the low-energy data, conclude that there is no Ay problem in low-energy np scattering
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Nuclear Effective Theory of Conversion
Full text linkThe coming decade promises exceptional experimental progress in searches for charged lepton flavor-violating (CLFV) conversion due to efforts at Fermilab (Mu2e) and J-PARC (COMET). Branching ratio sensitivities for this process are expected to advance by four orders of magnitude, potentially extending the reach of these probes up to energies of TeV. A pressing challenge for theorists is to extract the maximum amount of information about possible sources of CLFV from these measurements, whether or not a signal of new physics is detected. Efforts to observe conversion share many similarities with other experimental programs where the nucleus is treated as a laboratory in which to search for beyond-standard-model (BSM) physics. These approaches are utilized because they present certain practical advantages: In searches for CLFV, the act of trapping a muon into the Coulomb field of a nucleus allows one to control the energy of the final state electron, ensuring that it is maximal compared to the energy of background electrons originating in standard-model free muon decays. The downside of employing the nucleus as part of the apparatus is that a host of complex nuclear physics consequently intervenes between the experimentalist and the desired observable. To extract meaningful constraints, one must have a method for disentangling the nuclear physics from the underlying BSM physics.Another experimental setting in which the nucleus is treated as a laboratory is in direct detection searches for weakly-interacting massive particle (WIMP) dark matter, where one aims to discern the mass, spin, and fundamental interactions of WIMP dark matter through scattering off of atomic nuclei. Again, to access the sought-after information about BSM physics, one must be able to separate it cleanly from the nuclear physics. In the case of dark matter direct detection, this separation has been achieved through the development of an effective theory formulated at the nuclear scale, which factorizes the nuclear physics from the BSM dark matter physics, sequestering the latter quantity into unknown low-energy constants (LECs) that are probed directly by experiment. As the effective theory describes the most general coupling between the WIMPs and the nucleus, the LECs that specify the effective theory represent the maximum information about the nature of dark matter that can be obtained from scattering off of nuclei. In this thesis, we introduce an analogous effective theory for the problem of conversion. In order to adapt the existing framework to the problem at hand, several significant modifications are required, primarily stemming from the differing nature of the particles that couple to the nucleus in each scenario: non-relativistic plane-wave dark matter must be replaced by a bound muon in the initial state and an ultra-relativistic electron in the final state. We focus primarily on the case of elastic conversion, wherein the nucleus remains in its ground state (as this ensures that the energy of the outgoing electron is maximal). The three-momentum transferred from the leptons to the nucleus is comparable to the inverse nuclear size, allowing significant angular momentum to be transferred between the leptons and the nucleus. As a result, the nuclear multipole expansion cannot be truncated at any order. This decomposition is complicated by the fact that the outgoing electron interacts with the nuclear charge through the Coulomb potential. Nonetheless, the nuclear multipole expansion can be performed in a straightforward manner by replacing the Coulomb-distorted electron wave function with a plane-wave form parameterized by a suitable local momentum.The effective theory is then specified by a controlled expansion in terms of the relevant velocity operators for the nucleons and the bound muon . (The electron velocity is, in essence, ``integrated out'' of the theory by the assumption that it is ultra-relativistic.) The construction of the nucleon-scale effective theory proceeds in two steps: First, we specify a complete set (through a given order in power-counting) of CLFV operators that couple the leptons to single-nucleon charges and currents. Next, after performing the nuclear multipole decomposition, the resulting nucleon-level theory is embedded into the target nucleus, where the approximate parity and time-reversal symmetries of the nuclear ground state restrict the operators that can contribute to elastic conversion. A valid effective theory can be constructed at three distinct degrees of complexity: The most basic theory is generated by including neither nor . Relativistic corrections to the muon wave function and effects stemming from nuclear compositeness are completed ignored, and the CLFV amplitude depends on just three nuclear response functions, those of a point-like nucleus. Next, we extend the theory by considering to first order, and consequently the set of nuclear responses is enlarged by the addition of three velocity-dependent response functions. Finally, we formulate the most complete effective theory, including both velocity operators, and , to first order. This corresponds to the inclusion of relativistic muon effects, in the form of the muon's lower Dirac component, and introduces six additional nuclear responses. The muon's lower component always appears as a correction to the upper-component contribution, and therefore we consider the second of these constructions---containing but not ---to be the prototypical effective theory, complete through leading order in the nuclear response. The various nuclear responses can be understood as the ``nuclear dials'' that an experimentalist can tune through nuclear target selection in order to access different regions of CLFV parameter space. The nucleus Al, the target of the Mu2e and COMET experiments, has ground-state angular momentum and provides good sensitivity across a range of responses that are spin- and velocity-dependent/independent. On the other hand, a target such as Ca, whose natural abundance consists (almost) entirely of isotopes with ground-state angular momentum , will not couple to non-scalar operators. A detailed understanding of the interplay between the various nuclear responses is prerequisite to carrying out an experimental program---across a multitude of targets---in order to fully constrain the unknown CLFV parameters of the nuclear-scale effective theory.Much of the previous literature has focused on a narrow special case in which the leading operator that mediates conversion couples equally to protons and neutrons and is spin- and velocity-independent. Such an operator sums coherently in the conversion amplitude and receives an enhancement by the atomic mass number relative to incoherent operators, thereby dominating the CLFV response in cases where it is present. The primary advantage of working in this limited case is that the nuclear physics, which is a source of significant complication in general, becomes exceedingly simple. In fact, the coherent nuclear response is governed entirely by the scalar nucleon density, a quantity that is accurately determined by experiments. When considering specific extensions of the standard model that yield a leading coherent response, the branching ratio can be predicted with a well-understood uncertainty. However, in the initial discovery phase of CLFV searches, one should not assume anything about the underlying nature of flavor-violating operators. The proper approach, which we pursue in this thesis, is to constrain the most general interaction as specified by the effective theory
Fast-time Variations of Supernova Neutrino Fluxes and Detection Perspectives
Full text linkAbstractIn the delayed explosion scenario of a core-collapse supernova, the accretion phase shows pronounced convective over-turns and a low-multipole hydrodynamic instability, the so-called standing accretion shock instability (SASI). Neutrino signal variations from the first full-scale three-dimensional core-collapse supernova simulations with sophisticated neutrino transport are presented as well as their detection perspectives in IceCube and Hyper-Kamiokande
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Effective Theories in Few-Body Physics
Full text linkEffective theories are a controlled approach to making approximations in physics. We describe here work on two applications of effective theory techniques in few-body physics, specifically to nuclear and atomic systems.First, we analytically reduce the chiral three-nucleon interaction at NNLO to a density-dependent effective two-body potential by summing the third particle over the states of a spin-symmetric Fermi gas. Results are given for the potential in momentum space and in coordinate space, where the potential is seen to be nonlocal. An expansion of the potential in the difference of the nonlocal coordinates is made in order to arrive at a fully local effective two-body potential. We then explore the two-body spectra of spin-1/2 fermions in isotropic harmonic traps with external spin-orbit potentials and short range two-body interactions. Using a truncated basis of total angular momentum eigenstates, which is known to be equivalent to an effective theory when the atomic gas is harmonically confined, nonperturbative results are presented for experimentally realistic forms of the spin-orbit coupling: a pure Rashba coupling, Rashba and Dresselhaus couplings in equal parts, and a Weyl-type coupling. The technique is easily adapted to bosonic systems and other forms of spin-orbit coupling
SHEDDING NEW LIGHT ON EXPLODING STARS: TERASCALE SIMULATIONS OF NEUTRINO-DRIVEN SUPERNOVAE AND THEIR NUCLEOSYNTHESIS
Full text linkThis project was focused on simulations of core-collapse supernovae on parallel platforms. The intent was to address a number of linked issues: the treatment of hydrodynamics and neutrino diffusion in two and three dimensions; the treatment of the underlying nuclear microphysics that governs neutrino transport and neutrino energy deposition; the understanding of the associated nucleosynthesis, including the r-process and neutrino process; the investigation of the consequences of new neutrino phenomena, such as oscillations; and the characterization of the neutrino signal that might be recorded in terrestrial detectors. This was a collaborative effort with Oak Ridge National Laboratory, State University of New York at Stony Brook, University of Illinois at Urbana-Champaign, University of California at San Diego, University of Tennessee at Knoxville, Florida Atlantic University, North Carolina State University, and Clemson. The collaborations tie together experts in hydrodynamics, nuclear physics, computer science, and neutrino physics. The University of Washington contributions to this effort include the further development of techniques to solve the Bloch-Horowitz equation for effective interactions and operators; collaborative efforts on developing a parallel Lanczos code; investigating the nuclear and neutrino physics governing the r-process and neutrino physics; and exploring the effects of new neutrino physics on the explosion mechanism, nucleosynthesis, and terrestrial supernova neutrino detection
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