Revisiting Q-ball Interactions with Matters

TL;DR

This work investigates how Q-ball dark matter interacts with ordinary matter by incorporating the chemical-potential cost $\omega$ and the possibility of electromagnetic charge-up after baryon absorption. It develops a colorless toy model for quark scattering in a time-dependent Q-ball background, analyzing both infinite-wall and spherical-Wave geometries to derive reflection and transmission amplitudes and the corresponding S-matrix structure. A key result is that a left-handed quark incident on a large Q-ball wall is reflected as a right-handed anti-quark with unit probability when $E>2\omega$, while Milky Way–class nucleons cannot reflect as anti-nucleons due to the energy constraint, though partial quark-to-anti-quark conversions can occur inside nucleons. The study further shows that charge-up of the Q-ball leads to Coulomb-barrier–suppressed proton scattering and discusses implications for paleo-detectors and macroscopic-DM searches, including bound-state formation channels and the dependence on flat-direction–determined charge fractions $Z_Q$.

Abstract

Q-ball dark matter is one of the candidates for the macroscopic dark matter: Q-ball is a non-topological solitonic configuration, whose stability can be ensured by global charge and energy conservation. One of the crucial factors for discovering signatures from the Q-ball dark matter, is the interactions of the Q-ball dark matter with ordinary matter. In particular, the scattering of ordinary matter off the Q-ball dark matter is important for the direct detection searches, such as paleo-detectors. It was conjectured that quarks incident on the Q-ball were reflected as anti-quarks with a probability of order unity, but it costs the energy of the squark in the Q-ball, which cannot be paid in the scattering of ordinary matter off the Q-ball dark matter. In addition, once a proton is reflected as an anti-proton, the Q-ball obtains the electromagnetic charge. In this study, we revisit the scattering process of quarks with the Q-ball with taking into account the energy cost of the scattering and the electromagnetic charge-up of the Q-ball.

Figures (4)

• Figure 1: Scattering on the infinitely large Q-ball wall with the left-handed quark coming in: the shaded area corresponds to the Q-ball. The black solid lines depict the incoming, reflected, and transmitted quarks with the energy of $E$, while the colored lines depict the reflected and transmitted quarks with the energy of $E-2\omega$. Since the energy $E$ is much less than the masses of the fermions inside the Q-ball, the massive fermions are assumed to run on the $z$-axis and the transmitted fermions are emitted from the $z$-axis.
• Figure 2: The $ER$-dependence of the absolute values of the coefficients $\overline B_{\pm}$ for fixed parameters: fixed $\varkappa = 10$ in the right panel, while fixed $\omega/E = 0.3$ in the left panel. $\overline B_{-}$ is depicted as the solid lines, while $\overline B_{+}$ is depicted as the dashed lines.
• Figure 3: The relative phase of the coefficients $B_{\pm}$ with fixed $\varkappa = 10$. $B_{-}$ is depicted as the solid lines with the same color code as \ref{['fig:reflectedquark']}, while $B_{+}$ is depicted as the dashed lines with light colors.
• Figure 4: The proton--charged Q-ball scattering cross section. The relative velocity of the Q-ball and the proton is assumed to be $v \simeq 10^{-3}$. The electromagnetic charge of the Q-ball $Z_Q$ is fixed for each solid lines: $Z_Q = 1$ (blue) and $Z_Q = 2$ (red). The thin-dashed vertical lines show the point where $R = R_2$ for each $Z_Q$ with the same color code as the solid lines. The geometric cross section $\sigma_\mathrm{geo} = \pi R^2$ is depicted as the black dashed line. The radius $R$ of our interest is $10\,\mathrm{fm} \lesssim R \lesssim \mathcal{O}(1) \, \mathrm{nm}$Kasuya:2015uka.