Axial anomaly effect on the chiral-partner structure of diquarks at high temperature

Masses of positive-parity and negative-parity diquarks are investigated at finite temperature with a quark chemical potential. We employ the three-flavor Nambu-Jona-Lasinio model, in order to delineate chiral properties of the diquarks, in particular, the mass degeneracy of chiral partners under extreme conditions. We focus on the effects of $U(1{)}_A$ axial anomaly on manifestation of the chiral-partner structures. We find that, in the absence of anomaly effects to the diquarks, the mass degeneracies in all $[ud]$, $[su]$, and $[sd]$ diquark sectors take place prominently above the pseudocritical temperature of the chiral restoration. On the other hand, the anomaly effects are found to hinder the $[ud]$ diquark from exhibiting the mass degeneracy, accompanied by a slow reduction of the $\overline{s}s$ condensate, while the $[su]$ and $[sd]$ diquarks are not much affected. Our present investigation will provide useful information on the chiral-partner structure with the anomaly effects of diquarks for heavy-ion collision experiments of singly heavy baryons and doubly heavy tetraquarks, and for future lattice simulations of the diquarks.

Figure 1

Temperature dependences of the chiral condensates $⟨\overline{q}q⟩$ and $⟨\overline{s}s⟩$ normalized by their vacuum values (top), and those of the dynamical quark masses $M_q$ and $M_s$ (bottom), at vanishing quark chemical potential $\mu =0$.

Figure 2

Temperature dependence of the diquark masses for the parameter Set (I) (left) with no anomaly effects and Set (II) (right) with significant anomaly effects at $\mu =0$. The mass differences are defined by $\mathrm{\Delta }{m}_{[qq]}=m_{[qq{]}_{-}}-m_{[qq{]}_{+}}$ and $\mathrm{\Delta }{m}_{[sq]}=m_{[sq{]}_{-}}-m_{[sq{]}_{+}}$.

Figure 3

Temperature dependence of the diquark masses and mass differences for the Set (I) (left) and Set (II) (right) at $\mu =0.2\mathrm{GeV}$.

Figure 4

Temperature dependence of the antidiquark masses and mass differences for the Set (I) (left) and Set (II) (right) at $\mu =0.2\mathrm{GeV}$. The mass differences are defined by $\mathrm{\Delta }{m}_{[\overline{q}\overline{q}]}=m_{[\overline{q}\overline{q}{]}_{-}}-m_{[\overline{q}\overline{q}{]}_{+}}$ and $\mathrm{\Delta }{m}_{[\overline{s}\overline{q}]}=m_{[\overline{s}\overline{q}{]}_{-}}-m_{[\overline{s}\overline{q}{]}_{+}}$.

Figure 5

Quark chemical potential dependence of the diquark masses for the Set (I) (top) and Set (II) (bottom) at $T=0$. The dotted vertical line corresponds to the critical chemical potential ${\mu }^{*}$ at which $m_{[qq{]}_{+}}=0$ is satisfied.

Figure 6

Temperature dependence of the masses of ${\mathrm{\Lambda }}_c(1/2^{+})$ and ${\mathrm{\Lambda }}_c(1/2^{-})$ for $\mu =0$ with the Set (II).

Figure 7

Temperature dependence of the decay width of ${\mathrm{\Lambda }}_c(1/2^{-})\to {\mathrm{\Lambda }}_c(1/2^{+})\eta$ for $\mu =0$ with the Set (II).