Title: Geoneutrino sources and fluxes: A systematic approach to
their uncertainties and correlations
(E. Lisi, work in collaboration with G.L. Fogli, A. Palazzo,
and A.M. Rotunno - Univ. of Bari and INFN, Bari).
Abstract: Models and observables related to geoneutrinos involve,
in general, highly
(anti)correlated quantities. Examples of covariant quantities include the
U, Th, and K abundances in any Earth reservoir, the radiogenic heat versus
the neutrino luminosity, and the estimated geoneutrino fluxes in different
detectors. Negative correlations arise instead among geoneutrino source
abundances in complementary reservoirs (due to mass balance constraints in
the Bulk Silicate Earth model) and between the U and Th event rates in a
typical geoneutrino experiment (due to a prevailing sensitivity to the sum
of U+Th events).
We propose a simple and systematic approach to the covariance matrices
arising in the context of geoneutrino analyses, based on the fact that all
the relevant observables and constraints can be expressed as linear
of the U, Th and K abundances through relatively well-known coefficients.
We construct first a "zeroth-order" GeoNeutrino Source Model (GNSM),
reasonable errors and correlations for the U, Th, and K abundances in
relevant Earth reservoirs. The construction of such a GNSM, based on
geophysical and geochemical data+models (when available), on plausible
hypotheses (when possible) and, admittedly, on arbitrary assumptions (when
unavoidable), shed light on some critical issues in the evaluation of
geophysical and geochemical uncertainties and covariances.
We then show how the central values and the error matrix of such
GNSM can be easily "updated" whenever new geoneutrino and geological data,
as well as more refined mass-balance and heat-flow constraints, will
available in the future. Subsequent updates might either converge towards
a more accurate "concordance GNRM," or diverge if some "tension" emerges
different inputs - possibly suggesting a GNSM revision. Alternative GNSMs
(based, e.g., on "unorthodox" assumptions) could be similarly tested. In
context, our approach can provide a well-defined statistical framework for
evaluating the global consistency of (future or prospective) geoneutrino
data and models.