  In this note, we study a class of indefinite stochastic McKean-Vlasov
linear-quadratic (LQ in short) control problem under the control taking
nonnegative values. In contrast to the conventional issue, both the classical
dynamic programming principle (DPP in short) and the usual Riccati equation
approach fail. We tackle these difficulties by extending the state space from
$\mathbb{R}$ to probability measure space, afterward derive the the
corresponding the infinite dimensional Hamilton--Jacobi--Bellman (HJB in short)
equation. The optimal control and value function can be obtained basing on two
functions constructed via two groups of novelty ordinary differential equations
satisfying the HJB equation mentioned before. As an application, we revisit the
mean-variance portfolio selection problems in continuous time under the
constraint that short-selling of stocks is prohibited. The investment risk and
the capital market line can be captured simultaneously.
