arXiv subjects

Christian Y. Cardall

Publications and source records attributed to Christian Y. Cardall.

53 records · Page 3Linked to original sources

arXiv2001

Theory of Neutrino Flavor Mixing

The depth of our theoretical understanding of neutrino flavor mixing should match the importance of this phenomenon as a herald of long-awaited empirical challenges to the standard model of particle physics. After reviewing the familiar, simplified quantum mechanical model and its flaws, I sketch the deeper understanding of both vacuum and matter-enhanced flavor mixing that is found in the framework of scattering theory. While the simplified model gives the ``correct answer'' for atmospheric, solar, and accelerator/reactor neutrino phenomena, I argue that a key insight from the deeper picture will simplify the treatment of neutrino transport in astrophysical environments---supernovae, for example---in which neutrinos play a dynamically important role.

hep-ph↗

arXiv2001

NewtonPlus: Approximating Relativistic Effects in Supernova Simulations

We propose an approximation to full relativity that captures the main gravitational effects of dynamical importance in supernovae. The conceptual link between this formalism and the Newtonian limit is such that it could likely be implemented relatively easily in existing multidimensional Newtonian gravitational hydrodynamics codes employing a Poisson solver. As a test of the formalism's utility, we display results for rapidly rotating (and therefore highly deformed) neutron stars.

astro-ph↗

arXiv2001

NewtonPlus: Approximate Relativity for Supernova Simulations

We propose an approximation to general relativity that captures the main gravitational effects of dynamical importance in supernovae. The conceptual link between this formalism and the Newtonian limit is such that it could likely be implemented in existing multidimensional Newtonian gravitational hydrodynamics codes employing a Poisson solver. As a test of the formalism's utility, we display results for rapidly rotating (and therefore highly deformed) neutron stars.

astro-ph↗

arXiv2001

On Steady State Neutrino Heated Ultra-Relativistic Winds from Compact Objects

We study steady state winds from compact objects in the regime where the wind velocity at infinity is ultra-relativistic. This may have relevance to some models of Gamma-Ray-Bursts (GRB's). Particular attention is paid to the case where neutrinos provide the heating. Unless the neutrino luminosity is very large, L>10^{54} erg/s, the only allowed steady state solutions are those where energy deposition is dominated by neutrino-antineutrino annihilation at the sonic point. In this case, the matter temperature near the neutron star surface is low, less than 1MeV for typical neutrino luminosities. This is in contrast to the case for sub-relativistic winds discussed in the context of supernovae where the matter temperature near the neutron star approximates the temperature characterizing the neutrinos. We also investigate the setting of the neutron to proton ratio (n/p) in these winds and find that only for large (>10 MeV) electron neutrino or electron anti-neutrino temperatures is n/p entirely determined by neutrino capture. Otherwise, n/p retains an imprint of conditions in the neutron star.

astro-ph↗

arXiv2000

Effects of Strong Magnetic Fields on Neutron Star Structure

We study static neutron stars with poloidal magnetic fields and a simple class of electric current distributions consistent with the requirement of stationarity. For this class of electric current distributions, we find that magnetic fields are too large for static configurations to exist when the magnetic force pushes a sufficient amount of mass off-center that the gravitational force points outward near the origin in the equatorial plane. (In our coordinates an outward gravitational force corresponds to $\partial\ln g_{tt}/\partial r>0$, where $t$ and $r$ are respectively time and radial coordinates and $g_{tt}$ is coefficient of $dt^2$ in the line element.) For the equations of state (EOSs) employed in previous work, we obtain configurations of higher mass than had been reported; we also present results with more recent EOSs. For all EOSs studied, we find that the maximum mass among these static configurations with magnetic fields is noticeably larger than the maximum mass attainable by uniform rotation, and that for fixed values of baryon number the maximum mass configurations are all characterized by an off-center density maximum.

astro-ph↗

arXiv1999

Coherence of neutrino flavor mixing in quantum field theory

In the simplistic quantum mechanical picture of flavor mixing, conditions on the maximum size and minimum coherence time of the source and detector regions for the observation of interference---as well as the very viability of the approach---can only be argued in an ad hoc way from principles external to the formalism itself. To examine these conditions in a more fundamental way, the quantum field theoretical $S$-matrix approach is employed in this paper, without the unrealistic assumption of microscopic stationarity. The fully normalized, time-dependent neutrino flavor mixing event rates presented here automatically reveal the coherence conditions in a natural, self-contained, and physically unambiguous way, while quantitatively describing the transition to their failure.

hep-ph↗

arXiv1999

The MSW Effect in Quantum Field Theory

We show in detail the general relationship between the Schrödinger equation approach to calculating the MSW effect and the quantum field theoretical S-matrix approach. We show the precise form a generic neutrino propagator must have to allow a physically meaningful ``oscillation probability'' to be decoupled from neutrino production fluxes and detection cross-sections, and explicitly list the conditions---not realized in cases of current experimental interest---in which the field theory approach would be useful.

hep-ph↗

arXiv1998

Semianalytic Analysis of Primordial Black Hole Formation During a First-order QCD Phase Transition

It has recently been suggested that cosmologically significant numbers of black holes could form during a first-order QCD phase transition. Further, it has been asserted that these black holes would have masses corresponding naturally to the inferred mass ($\sim 1 M_{\odot}$) of the MACHOs responsible for the observed gravitational microlensing events. In this model, the underlying spectrum of primordial density perturbations provides the fluctuations that give rise to black holes at the epoch of the QCD transition. We employ a simplified model to estimate the reduction in the critical overdensity of a horizon-sized primordial perturbation required for collapse to a black hole. We find that a first-order QCD transition does indeed produce a sharp peak in the black hole mass spectrum, but that this peak corresponds to the horizon mass at an epoch somewhat earlier than the cosmological transition itself. Assuming a COBE normalized primordial density perturbation spectrum with constant spectral index, for the black holes so produced to be cosmologically significant would require an extremely finely tuned ``blue'' primordial density perturbation spectrum. Specifically, in the context of our simplified model, a spectral index in the range $n=1.37-1.42$ corresponds to the range $Ω\sim 10^{-5}-10^3$ of the black hole contribution to the present-day density parameter.

astro-ph↗

arXiv1997

Intermediate baseline appearance experiments and three-neutrino mixing schemes

Three-neutrino mixing schemes suggested by Cardall & Fuller and Acker & Pakvasa are compared and contrasted. Both of these schemes seek to solve the solar and atmospheric neutrino problems and to account for the possible neutrino oscillation signal in the LSND experiment. These neutrino oscillation schemes have different atmospheric and solar neutrino signatures that will be discriminated by Super-Kamiokande and SNO. They will also have different signatures in proposed long-baseline accelerator and reactor experiments. In particular, both of these schemes would give dramatic (and dramatically different) signals in an ``intermediate baseline'' experiment, such as the proposed ICARUS detector in the Jura mountains 17 km from CERN.

hep-ph↗

arXiv1997

Neutrino Physics and the Primordial Elemental Abundances

Limits can be placed on nonstandard neutrino physics when big bang nucleosynthesis (BBN) calculations employing standard neutrino physics agree with the observationally inferred primordial abundances of deuterium (D), $^3$He, $^4$He, and $^7$Li. These constraints depend most sensitively on the abundances of D and $^4$He. New observational determinations of the primordial D and/or $^4$He abundances could force revisions in BBN constraints on nonstandard neutrino physics.

astro-ph↗

arXiv1997

General relativistic effects in the neutrino-driven wind and r-process nucleosynthesis

We discuss general relativistic effects in the steady-state neutrino-driven ``wind'' which may arise from nascent neutron stars. In particular, we generalize previous analytic estimates of the entropy per baryon $S$, the mass outflow rate $\dot M$, and the dynamical expansion time scale $τ_{dyn}$. We show that $S$ increases and $τ_{dyn}$ decreases with increasing values of the mass-to-radius ratio describing the supernova core. Both of these trends indicate that a more compact core will lead to a higher number of neutrons per iron peak seed nucleus. Such an enhancement in the neutron-to-seed ratio may be required for successful r-process nucleosynthesis in neutrino-heated supernova ejecta.

astro-ph↗

arXiv1996

Neutrino oscillations in curved spacetime: an heuristic treatment

We discuss neutrino oscillations in curved spacetime. Our heuristic approach can accomodate matter effects and gravitational contributions to neutrino spin precession in the presence of a magnetic field. By way of illustration, we perform explicit calculations in the Schwarzschild geometry. In this case, gravitational effects on neutrino oscillations are intimately related to the redshift. We discuss how spacetime curvature could affect the resonance position and adiabaticity of matter-enhanced neutrino flavor conversion.

hep-ph↗

arXiv1996

The Deuteron Confronts Big Bang Nucleosynthesis

Recent determinations of the deuterium abundance, $^2$H/H, in high redshift Lyman limit hydrogen clouds challenge the usual picture of primordial nucleosynthesis based on \lq\lq concordance\rq\rq\ of the calculated light element ($^2$H, $^3$He, $^4$He, $^7$Li) nucleosynthesis yields with the observationally-inferred abundances of these species. Concordance implies that all light element yields can be made to agree with the observationally-inferred abundances (within errors) for single global specifications of the baryon-to-photon ratio, $η$; lepton number; neutron lifetime; and expansion rate (or equivalently, effective number of light neutrino degrees of freedom $N_ν $). Though one group studying Lyman limit systems obtains a high value of $^2$H/H ($\sim 2\times {10}^{-4}$), another group finds consistently low values ($\sim 2\times {10}^{-5}$). In the former case, concordance for $N_ν =3$ is readily attained for the current observationally-inferred abundances of $^4$He and $^7$Li. But if the latter case represents the primordial deuterium abundance, then concordance for {\it any} $N_ν$ is impossible unless the primordial value of $^7$Li/H is considerably larger than the abundance of lithium as measured in old, hot Pop II halo stars. Furthermore, concordance with $N_ν=3$ is possible for low $^2$H/H only if either (1) the primordial $^4$He abundance has been significantly underestimated, or (2) new neutrino sector physics is invoked. We argue that systematic underestimation of both the $^7$Li and $^4$He primordial abundances is the likely resolution of this problem, a conclusion which is strengthened by new results on $^4$He.

astro-ph↗

arXiv1996

Three-generation neutrino mixing and LSND dark matter neutrinos

The reported signal at the LSND experiment, when interpreted as neutrino mixing with $δm^2 = 6 \;\rm{eV}^2$, provides evidence for neutrinos with a cosmologically significant mass. However, attempts to reconcile this interpretation of the experiment with other hints about neutrino properties require a (sterile) fourth neutrino and/or an ``inverted'' neutrino mass hierarchy. An interpretation of the LSND experiment employing $δm^2 = 0.3\; \rm{eV}^2$, with three-generation mixing and a ``normal'' neutrino mass hierarchy, can just barely be reconciled with the negative results of other laboratory neutrino oscillation experiments and the positive hints of neutrino oscillation from the solar and atmospheric neutrino problems. Though subject to test by by future experiments, such a solution allows (but does not demand) neutrino masses relevant for dark matter.

astro-ph↗

arXiv1996

Limits on Active-Sterile Neutrino Mixing and the Primordial Deuterium Abundance

Studies of limits on active-sterile neutrino mixing derived from big bang nucleosynthesis considerations are extended to consider the dependance of these constraints on the primordial deuterium abundance. This study is motivated by recent measurements of D/H in quasar absorption systems, which at present yield discordant results. Limits on active-sterile mixing are somewhat relaxed for high D/H. For low D/H ($\approx 2 \times 10^{-5}$), no active-sterile neutrino mixing is allowed by currently popular upper limits on the primordial $^4$He abundance $Y$. For such low primordial D/H values, the observational inference of active-sterile neutrino mixing by upcoming solar neutrino experiments would imply that $Y$ has been systematically underestimated, unless there is new physics not included in standard BBN.

astro-ph↗

arXiv1996

Big-Bang Nucleosynthesis in Light of Discordant Deuterium Measurements

Two dimensional concordance plots involving the baryon-to-photon ratio, $η$, and an effective number of light neutrinos, $N_ν$, are used to discuss the overall consistency of standard big-bang nucleosynthesis in light of recent determinations of the primordial deuterium ($^2$H) abundance. Observations of high-redshift Ly-$α$ clouds have provided discordant $^2$H/H determinations: one cloud with $^2$H/H high compared with the previously accepted upper limit on ($^2$H + $^3$He)/H; and one system with a significantly lower upper bound on $^2$H/H than those previously obtained. The high value of $^2$H/H agrees well with the current observationally-inferred primordial abundances of $^4$He and $^7$Li for $N_ν=3$. The low value of $^2$H/H does not fit well with the current observationally-inferred primordial abundance of $^4$He for $N_ν=3$. In addition, if the low value of $^2$H/H is indicative of the primordial deuterium abundance, then significant depletion of $^7$Li in old, hot Pop II halo stars is probably required to obtain a concordant range of $η$, for {\em any} effective number of neutrino flavors. The use of conservative ranges for the primordial abundances of $^2$H, $^4$He, and $^7$Li allow success of the standard picture for $N_ν=3$.

astro-ph↗

arXiv1996

Can a ``natural'' three-generation neutrino mixing scheme satisfy everything?

We examine the potential for a ``natural'' three-neutrino mixing scheme to satisfy available data and astrophysical arguments. By ``natural'' we mean no sterile neutrinos, and a neutrino mass hierarchy similar to that of the charged leptons. We seek to satisfy (or solve): 1. Accelerator and reactor neutrino oscillation constraints, including LSND; 2. The atmospheric muon neutrino deficit problem; 3. The solar neutrino problem; 4. Supernova $r$-process nucleosynthesis in neutrino-heated supernova ejecta; 5. Cold+hot dark matter models. We argue that putative supernova $r$-process nucleosynthesis bounds on two-neutrino flavor mixing can be applied directly to three-neutrino mixing in the case where one vacuum neutrino mass eigenvalue difference dominates the others. We show that in this ``one mass scale dominance'' limit, a natural three-neutrino oscillation solution meeting all the above constraints exists only if the atmospheric neutrino data {\em and} the LSND data can be explained with one neutrino mass difference. In this model, an explanation for the solar neutrino data can be effected by employing the {\em other} independent neutrino mass difference. Such a solution is only marginally allowed by the current data, and proposed long-baseline neutrino oscillation experiments can definitively rule it out. If it were ruled out, the simultaneous solution of the above constraints by neutrino oscillations would then require sterile neutrinos and/or a neutrino mass hierarchy of a different nature than that of the charged leptons.

astro-ph↗