Probing triaxial deformation of atomic nuclei in high-energy heavy ion collisions

Most atomic nuclei are deformed with a quadrupole shape described by its overall strength $\beta_2$ and triaxiality $\gamma$. The deformation can be accessed in high-energy heavy-ion collisions by measuring the collective flow response of the produced quark-gluon plasma to the eccentricity $\varepsilon_2$ and the density gradient $d_{\perp}$ in the initial state. Using analytical estimate and a Glauber model, I show that the variances, $\langle\varepsilon_2^2\rangle$ or $\langle(\delta d_{\perp}/d_{\perp})^2\rangle$, and skewnesses, $\langle\varepsilon_2^2\delta d_{\perp}/d_{\perp}\rangle$ or $\langle(\delta d_{\perp}/d_{\perp})^3\rangle$, have a simple analytical form of $a'+b'\beta_2^2$ and $a'+(b'+c'\cos(3\gamma))\beta_2^3$, respectively. From these, I constructed several normalized skewnesses to isolate the $\gamma$ dependence from that of $\beta_2$, and show that the correlations between any normalized skewness and any variance can constrain simultaneously the $\beta_2$ and $\gamma$. Assuming a linear relation with elliptic flow $v_2$ and mean-transverse momentum $[p_{\mathrm{T}}]$ of final state particles, similar conclusions are also expected for the variances and skewnesses of $v_2$ and $[p_{\mathrm{T}}]$. Our findings motivate a dedicated system scan of high-energy heavy ion collisions to measure triaxiality of atomic nuclei. This is better done by collisions of prolate, $\cos(3\gamma)=1$, and oblate nuclei, $\cos(3\gamma)=-1$, with well known $\beta_2$ values to calibrate the coefficients $b'$ and $c'$, followed by collisions of species of interest especially those with known $\beta_2$ but unknown $\gamma$. The results demonstrate the unique opportunities offered by high-energy collisions as a tool to perform interdisciplinary nuclear physics studies.