Precise $^{136}$Xe Double Beta Decay Measurement in PandaX-4T with Implications on the Nuclear Matrix Elements and Majorons

Abstract

The continuous spectrum of double beta decay ($\beta\beta$) provides a sensitive probe to test the predictions of the standard model and to search for signatures of new physics beyond it. We present a comprehensive analysis of the $^{136}$Xe $\beta\beta$ spectrum utilizing $39.1 \pm 0.7~\textrm{kg}\cdot\textrm{yr}$ of $^{136}$Xe exposure from the PandaX-4T experiment. The analysis yields the most precise measurement to date of the $^{136}$Xe two-neutrino double beta decay ($2\nu\beta\beta$) half-life, $(2.14 \pm 0.05) \times 10^{21}$ years, the uncertainty of which is reduced by a factor of 2 compared to our previous result. We measure the parameter $\xi_{31}^{2\nu}$, defined as the ratio between the subleading and leading components of the $^{136}$Xe $2\nu\beta\beta$ nuclear matrix element, to be $0.59^{+0.41}_{-0.38}$, which is consistent with theoretical predictions. We also search for Majoron-emitting modes of $^{136}$Xe $\beta\beta$, establishing the most stringent limit for the spectral index $n=7$.