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A correlation between the intrinsic energy and the burst duration ofnon-repeating fast radio bursts (FRBs) has been reported. If it exists, thecorrelation can be used to estimate intrinsic energy from the duration, andthus can provide us with a new distance measure for cosmology. However, thecorrelation suffered from small number statistics (68 FRBs) and was not freefrom contamination by latent repeating populations, which might not have such acorrelation. How to separate/exclude the repeating bursts from the mixture ofall different types of FRBs is essential to see this property. Using a muchlarger sample from the new FRB catalogue (containing 536 FRBs) recentlyreleased by the CHIME/FRB project, combined with a new classification methoddeveloped based on unsupervised machine learning, we carried out furtherscrutiny of the relation. We found that there is a weak correlation between theintrinsic energy and duration for non-repeating FRBs at z < 0.3 with Kendall'stau correlation coefficient of 0.239 and significance of 0.001 (statisticallysignificant), whose slope looks similar to that of gamma-ray bursts. Thiscorrelation becomes weaker and insignificant at higher redshifts (z > 0.3),possibly due to the lack of the faint FRBs at high-z and/or the redshiftevolution of the correlation. The scattering time in the CHIME/FRB catalogueshows an intriguing trend: it varies along the line obtained from linear fit onthe energy versus duration plane between these two parameters. A possiblecosmological application of the relation must wait for faint FRBs at high-z.

On the relation between duration and energy of non-repeating fast radio bursts: census with the CHIME data