Replot the differences between p+p and d+Au correlation width as the function $\sqrt{\sigma_{dAu}^{2}-\sigma_{pp}^{2}}$.

Fig1, with different EEMC tower threshold

Fig2, with different mass lower limit cut for the EEMC jet-like cluster

Conclusion:

The new defination of the difference between p+p and d+Au width does not change too much with different underlying event contribution. This is consistent with what we see in the width difference between p+p and d+Au collisions.