Mass Varying Neutrinos (MaVaN’s) mechanisms were proposed to link the neutrino mass scale with the dark energy density, addressing the coincidence problem. In some scenarios, this mass can present a dependence on the baryonic density felt by neutrinos, creating an effective neutrino mass that depends both on the neutrino and baryonic densities. In this work, we study the phenomenological consequence of MaVaN’s scenarios in which the matter density dependence is induced by Yukawa interactions of a light neutral scalar particle which couples to neutrinos and matter. Under the assumption of one mass scale dominance, we perform an analysis of KamLAND neutrino data which depends on 4 parameters: the two standard oscillation parameters,

In cosmology, dark energy is a hypothetical form of energy which permeates all space and leads to the accelerated expansion of the universe [

The need for a new mysterious dark energy component can be interpreted as an indication for physics beyond the standard model. In the present time, the density of dark matter and dark energy is similar,

Relying on the similarity of scales,

The potential

This would explain not only the origin of dark energy but can also significantly modify the limits of cosmological neutrino mass [

It can be shown that interactions of subgravitational force can occur naturally between ordinary matter and the field

In this work, we investigate the phenomenology of MaVaN’s effects in neutrino oscillation, focusing in reactor neutrino data. By applying a parametrization of the effect already used in another context and with a detailed Earth’s crust description, we intend to analyze experimental data with this hypothetical matter-neutrino interaction.

In Section

Previous works found limits for the product of the effective neutrino-scalar and matter-scalar Yukawa coupling described in [

The aim of this work is to find at least one combination of parameters for the new physics that could lead to an acceptable solution to the neutrino oscillation data where such new physics is more than a sub-leading effect. This implies a nonhomogeneity effect of the Earth’s crust in the neutrino evolution.

We consider an effective low energy model containing the standard model particles plus a light scalar

The Lagrangian takes the form

It has been argued in [

For solar neutrinos of hierarchical masses, the dominant contribution to the neutrino mass is due to the matter background density. Correspondingly, we neglect the contribution to the neutrino mass from the background neutrino density, and we concentrate on the matter density dependence.

With the additional freedom that the new matter density dependence provides, there is no reason to believe that the three neutrino oscillation dynamics factorize into the dynamics of two neutrino subsystems. However, we will assume that this is still the case and study their effect on solar and KamLAND oscillations under the hypothesis of one mass-scale dominance. Under this assumption, we parametrize the evolution equation as

The environment effect is introduced as a dependence of the mass terms with the baryonic matter density with the following parametrization:

The KamLAND collaboration uses the constant density crust approximation of

The

The KamLAND experiment uses as a source of antineutrinos several different reactors. With the geographic location of each reactor and considering a linear path to the detector, this path will describe a density map specific for each source. The neutrino cross specific values of depth as shown in Figure

Simplified representation of the creation-detection neutrino path, different cases generate different density maps.

Real density maps used for specific sources, presented in intervals of constant density. Path between the Korean reactors and the detector.

As we can see in the specific density maps, it is clear that the description leads to a completely nonadiabatic evolution of the neutrino. So the effective angle variation relative to the local density change causes the nondiagonal terms in the evolution equation of the mass eigenstates to become relevant. So one cannot use here the analytic survival probability.

We use the analysis of the probability amplitudes, which allows local calculation for each region of constant density. Using what is called slab approximation in [

The transition amplitude

In the case of choice, we consider a pure electronic initial neutrino so

We could have a smooth description of the density profiles based on the stepped profiles generated by the model. However, this would result in a calculation much more expensive computationally since integration would be numerical outside the approximation of (

The results of the simulation, that is, the expected number of events for each energy range are analyzed by the method of maximum likelihood. Particularly, the Poisson statistics where the

We developed a code to simulate the KamLAND neutrino events and, based on the presented parametrization and phenomenology of MaVaN’s models, we tested the new physics. We implemented the model with normal hierarchy and a lighter neutrino with zero mass, to avoid the instability already mentioned:

Therefore, the probability amplitude for each interval of constant density can be written as

The effective KamLAND mass split is given by

As we can see in (

To cover then the parameter space, we let the values run between

We find the best fit point

Figures

We can see that there is a statistically significant improvement of the fit with the inclusion of terms MaVaN; however, we must be careful when interpreting this result, since we choose a specific parametrization on the behaviour of the MaVaN effects that is expected to at least reproduce the quality of the fit from the standard oscillation mechanism.

The value of

Correlation between the effective value of mass after the inclusion of the effect MaVaN and the same term with only the parameters of the standard model.

Result of the test for MaVaN model (color curves) compared with simulation data for the standard model (dotted line).

Ratio curve of the survival probability of survival with the case of no oscillation. We compared the experimental data (red) with the description of the standard model (black) and the obtained for the MaVaN model (green).

Such effect is observed only in a small island in parameter space, as seen in Figure

Exclusion curves in the parameter space MaVaN to

In order to quantify the features of this effect inside such island on MaVaN’s parameters, we display the global dependence of

Dependence of

Dependence of

The results and analysis presented here must be viewed as a specific choice of a particular model. We have three sources of arbitrariness in the model, the choice of

We studied the phenomenological effects of a specific dependence of the effective neutrino mass with the local density of the propagation medium, considering a model that included the standard model plus a light scalar (

Assuming that neutrinos masses follow the hierarchy

We observed that the new physics is more then a sub-leading effect and clearly dependent on the specific density description used. Such effect appears due to a strong variation of neutrino parameters at lower densities than the value usually used as constant for Earth crust in the literature, impliyng a nonhomogeneity effect of the Earth’s crust in the neutrino evolution.

To write specific limits including the null value for the new physics parameters is not possible due to a parameter degeneracy. The standard model is reproduced when any of the parameters that describes the MaVaN effects goes to zero. We believe that a joint analysis with solar neutrinos may clarify this point. These limits will be tested in the future for an analysis with solar neutrinos.

The authors would like to thank Daniel Boriero for his valuable and constructive suggestions during the planning and development of this paper. They also thank CNPq and CAPES for several financial supports.