Asymmetric dark matter and the hadronic spectra of hidden QCD

The idea that dark matter may be a composite state of a hidden non-Abelian gauge sector has received great attention in recent years. Frameworks such as asymmetric dark matter motivate the idea that dark matter may have similar mass to the proton, while mirror matter and $G\times G$ grand unified theories provide rationales for additional gauge sectors which may have minimal interactions with standard model particles. In this work we explore the hadronic spectra that these dark QCD models can allow. The effects of the number of light colored particles and the value of the confinement scale on the lightest stable state, the dark matter candidate, are examined in the hyperspherical constituent quark model for baryonic and mesonic states.

Figure 1

The variation of an example hypercentral potential $V(x)$ with $\xi$ (left) and the value of $r_c$, an estimate of the radius of confinement, as a function of $\xi$ (right). By scaling the dimensionful parameters of the interaction potential with the confinement scale, we are directly scaling the range at which the interaction transitions from perturbative to nonperturbative.

Figure 2

The resonances of the $N$ and ${\mathrm{\Delta }}^0$ states compared to PDG. The spin $1/2$ ground state of the neutron and spin $3/2$ ground state of the ${\mathrm{\Delta }}^0$ are fitted to match the experimental ground states exactly in each case. These values serve as the reference for dark QCD calculations.

Figure 3

Spin $1/2$ and spin $3/2$ for a confinement scale ratio $\xi =5$ and three light quarks. Dimensional parameters scale with $\xi$ displayed in the upper left. The PDG values for the experimental spectra are shown for reference to the scale of the $\xi =1$ case. Each of the results (P1, P2, P3) corresponds to a choice of parameters for the $\xi =1$ potential given in Table 1.

Figure 4

Spin $1/2$ and spin $3/2$ states as a function of the parameter $\xi$, the ratio of confinement scales. The direct scaling with the confinement scale becomes more significant at large $\xi$ as one expects from dimensional analysis. This uses an average of the three parameter regimes P1, P2, and P3. Using this plot we can see at each value of $\xi$ the lowest lying baryon in a dark QCD spectrum for models of one flavor (uuu, orange curve), or with two or more flavors (udd, blue curve).

Figure 5

Baryon states in our model for visible QCD compared to PDG values [59]. Parameters for the Gürsey-Radicati formula are fitted from the baryon mass results of the hypercentral Schrodinger equation.

Figure 6

The top two plots show the masses of the dark sector ${\mathrm{\Lambda }}^0$ and $\mathrm{\Sigma }$ and states for a range of values of the semilight mass splitting $\delta m_s$ and $\xi$. The lower plots display the mass differences for the $\mathrm{\Sigma }$ and ${\mathrm{\Sigma }}^{*}$ baryons as well as the mass splitting of the two different three-quark spin-flavor wave functions ($\mathrm{\Lambda }$, $\mathrm{\Sigma }$) for a range of $\delta m_s$ and $\xi$.

Figure 7

Gürsey-Radicati states for a hidden QCD with two flavors, $\xi =5$, and degenerate light quark masses in increasing mass values in four flavor combination cases.

Figure 8

Spin $1/2$ and spin $3/2$ baryon ground states for a factor of $\xi =5$ in the case of three light quarks where one quark may have additional mass. The more massive state is then labeled as the c or s dark quark depending on its quantum charges.

Figure 9

Meson states from Eq. (17) compared to PDG values in QCD. As with the baryon model, these fits will act as the starting point for the scaling of dark meson masses.

Figure 10

Three flavor (uds) meson spectra for $\xi =3$, 5 and semilight state values given by $\delta m_s$.

Figure 11

Scaling of the meson spectra with $\xi$ for a given value of $\delta m_s$ shown in the upper left. The value of the pion decay constant, and thus the strength of chiral symmetry breaking, is taken to remain constant.