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

The continuous spectrum of double beta decay (ββ) 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 ββ spectrum utilizing 39.1±0.7 kg·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 (2νββ) half-life, (2.14±0.05)×10^{21} years, the uncertainty of which is reduced by a factor of 2 compared to our previous result. We measure the parameter ξ_{31}^{2ν}, defined as the ratio between the subleading and leading components of the ^{136}Xe 2νββ nuclear matrix element, to be 0.59_{-0.38}^{+0.41}, which is consistent with theoretical predictions. We also search for Majoron-emitting modes of ^{136}Xe ββ, establishing the most stringent limit for the spectral index n=7.