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Bottom-up approach to texture zeros in the neutrino mass matrix

Iffat Ara Mazumder, Rupak Dutta

TL;DR

This work performs a bottom-up, data-driven exploration of texture zeros in the Majorana neutrino mass matrix by scanning the lightest neutrino mass, CP-violating phases, and oscillation parameters within current experimental uncertainties. It determines which individual matrix elements can vanish (one texture zero) and which pairs can vanish simultaneously (two texture zeros) for normal and inverted mass ordering, revealing tight correlations with Majorana phases and the mass scale. The study finds that M_ee can vanish only for normal ordering, while several other elements can vanish in both orderings; for two zeros, only (ee, eμ) and (ee, eτ) survive NO, whereas IO allows five patterns. The results underscore the critical role of CP phases and mass ordering and provide concrete phase- and mass-range predictions that can guide future neutrinoless double beta decay and oscillation experiments toward testing these texture-zero scenarios.

Abstract

We investigate one and two texture zeros in the neutrino mass matrix using the latest oscillation data through a bottom-up approach. In this context, we begin by estimating the detailed features of each matrix element by varying the CP violating phases within $(0,\,2π)$, the lowest neutrino mass within $(0,\,1)\,{\rm eV}$ and the neutrino oscillation parameters such as three mixing angles and the two mass squared differences within $3σ$ of their central values. We find that for normal ordering, only $ee$, $eμ$ and $eτ$ elements of the mass matrix can vanish, whereas, for inverted ordering, five elements -- $eμ$, $eτ$, $μμ$, $μτ$ and $ττ$ -- can vanish. For two texture zeros, only $(ee,\, eμ= 0)$ and $(ee,\, eτ=0)$ are allowed in case of normal ordering. For a particular vanishing element, we also estimate the range of the lowest neutrino mass and the CP violating phases. In particular, very interesting correlation among the CP violating phases and the lowest neutrino mass is obtained for each vanishing cases.

Bottom-up approach to texture zeros in the neutrino mass matrix

TL;DR

This work performs a bottom-up, data-driven exploration of texture zeros in the Majorana neutrino mass matrix by scanning the lightest neutrino mass, CP-violating phases, and oscillation parameters within current experimental uncertainties. It determines which individual matrix elements can vanish (one texture zero) and which pairs can vanish simultaneously (two texture zeros) for normal and inverted mass ordering, revealing tight correlations with Majorana phases and the mass scale. The study finds that M_ee can vanish only for normal ordering, while several other elements can vanish in both orderings; for two zeros, only (ee, eμ) and (ee, eτ) survive NO, whereas IO allows five patterns. The results underscore the critical role of CP phases and mass ordering and provide concrete phase- and mass-range predictions that can guide future neutrinoless double beta decay and oscillation experiments toward testing these texture-zero scenarios.

Abstract

We investigate one and two texture zeros in the neutrino mass matrix using the latest oscillation data through a bottom-up approach. In this context, we begin by estimating the detailed features of each matrix element by varying the CP violating phases within , the lowest neutrino mass within and the neutrino oscillation parameters such as three mixing angles and the two mass squared differences within of their central values. We find that for normal ordering, only , and elements of the mass matrix can vanish, whereas, for inverted ordering, five elements -- , , , and -- can vanish. For two texture zeros, only and are allowed in case of normal ordering. For a particular vanishing element, we also estimate the range of the lowest neutrino mass and the CP violating phases. In particular, very interesting correlation among the CP violating phases and the lowest neutrino mass is obtained for each vanishing cases.
Paper Structure (33 sections, 17 equations, 61 figures, 1 table)

This paper contains 33 sections, 17 equations, 61 figures, 1 table.

Table of Contents

  1. Introduction
  2. Formalism
  3. One Texture Zero
  4. $M_{ee}$: the $ee$ element of the mass matrix
  5. Normal ordering:
  6. Inverted Ordering:
  7. $M_{e\mu}$: the $e\mu$ element of the mass matrix
  8. Normal Ordering:
  9. Inverted Ordering
  10. $M_{e\tau}$: the $e\tau$ element of the mass matrix
  11. $M_{\mu\mu}$: the $\mu\mu$ element of the mass matrix
  12. Normal Ordering:
  13. Inverted Ordering
  14. $M_{\mu\tau}$: the $\mu\tau$ element of the mass matrix
  15. Normal Ordering:
  16. ...and 18 more sections

Figures (61)

  • Figure 1: Variation of $|M_{ee}|$ with the lightest neutrino mass $m_1$ in case of normal ordering. The red and the magenta lines represent total neutrino mass $\sum m_{i} = 0.12\,{\rm eV}$Zhang:2020mox and $\sum m_{i} = 0.072\,{\rm eV}$DESI:2024mwx, respectively. The yellow line represents $|M_{ee}|= 0.06\,{\rm eV}$KamLAND-Zen:2016pfg.
  • Figure 2: Variation of $|M_{ee}|$ with the three CP violating phases $\alpha$, $\beta$ and $\delta$ in case of normal ordering.
  • Figure 3: Correlation between $\beta$ and $\alpha$, and between $\alpha$ and $m_{1}$ for $\delta=0^{\circ}$ (Left panel) and $\delta=90^{\circ}$ (Right panel) with vanishing $|M_{ee}|$ in case of normal ordering. The red and magenta lines represent $\sum m_i = 0.12\,{\rm eV}$Zhang:2020mox and $\sum m_i = 0.072\,{\rm eV}$DESI:2024mwx, respectively.
  • Figure 4: Variation of $|M_{ee}|$ with the lightest neutrino mass $m_{3}$ in case of inverted ordering. Total neutrino mass $\sum m_{i} = 0.12\,{\rm eV}$Zhang:2020mox is shown with the red vertical line. The yellow line represents $|M_{ee}| = 0.06\,{\rm eV}$KamLAND-Zen:2016pfg.
  • Figure 5: Variation of $|M_{ee}|$ with the CP violating phases $\alpha$, $\beta$ and $\delta$ in case of inverted ordering.
  • ...and 56 more figures