Distorted quarkonia and spin alignment

Abstract

It is well-known that atoms can change their shape when subject to external electromagnetic fields. Analogous phenomenon is expected for particles, which are much smaller in size with the corresponding shape change much harder to observe. We point out that shape change of particles can be accessed by measurements of their spin alignment. Motivated by recent measurements of spin alignment in relativistic heavy ion collisions, we consider quarkonia in electromagnetic fields as an example. We show that the quarkonia spin alignment receives both spin contribution from spin states mixing and orbital contribution from shape change. By a proper choice of quantization axis, it is possible to switch off the spin contribution, leaving only the orbital contribution. This makes spin alignment measurement a valuable probe of quarkonium structure.

Figures (4)

• Figure 1: Magnetic field distorts wave function of quarkonium, leading to anisotropic distribution of its decay product. Magnetic field direction is chosen as quantization axis.
• Figure 2: Heatmap for the transition coefficient $c_{nm}=\frac{\langle n20|\Delta H|m10\rangle\langle m10|\Delta H|100\rangle}{(E_{n20}-E_{m10})(E_{m10}-E_{100})}$ for Stark effect, all in units of $(e|\mathbf{E}|)^2/\text{GeV}^4$. The row labels the intermediate P wave state $|m10\rangle$. The column labels the end point D wave state $|n20\rangle$. The color intensity, mapped on a logarithmic scale in the color bar, corresponding to the absolute value of the coefficient. Parameters for $J/\psi$ have been used. One should see the translations to higher energy levels are excessively suppressed.
• Figure 3: Contributions to quarkonia spin alignment from different sources at their maxima reached at $\theta_{Bl}=0$ or $\theta_{El}=0$. Stark effect and diamagnetic effect are scaled by 10 and 100 times separately to be compared with the Zeeman effect. $m=1.84\text{GeV}$ is used corresponding to ${J/\psi}$Eichten:1979ms.
• Figure 4: Comparison of spin alignment from Stark effect from Cornell potential and power potential. A significant difference of about $43\%$ is seen, as compared to less than $1\%$ difference in mass spectrum, making the spin alignment a sensitive probe of the quarkonium potential.