{
  "id": "2109.00604",
  "version": "v1",
  "published": "2021-09-01T20:27:20.000Z",
  "updated": "2021-09-01T20:27:20.000Z",
  "title": "Probing triaxial deformation of atomic nuclei in high-energy heavy ion collisions",
  "authors": [
    "Jiangyong Jia"
  ],
  "comment": "23 pages, 17 figures, plus 2 appendix",
  "categories": [
    "nucl-th",
    "hep-ph",
    "nucl-ex"
  ],
  "abstract": "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, we 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, we 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, $v_2\\propto \\varepsilon_2$ and $\\delta d_{\\perp}/d_{\\perp} \\propto \\delta[p_{\\mathrm{T}}]/[p_{\\mathrm{T}}]$, similar conclusions are also expected for the variances and skewnesses of $v_2$ and $[p_{\\mathrm{T}}]$, which can be measured precisely in top RHIC and LHC energies. 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 $\\gamma$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-01T20:27:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "high-energy heavy ion collisions",
      "atomic nuclei",
      "probing triaxial deformation",
      "high-energy heavy-ion collisions",
      "normalized skewness"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}