For searching beyond Standard Model physics, stars are laboratories which complement terrestrial experiments. Massless neutrinos in the Standard Model of particle physics cannot have a magnetic moment, but massive neutrinos have a finite magnetic moment in the minimal extension of the Standard Model. Large extra dimensions are a possible solution of the hierarchy problem. Both of these provide additional energy loss channels in stellar interiors via the electromagnetic interaction and radiation into extra dimensions, respectively, and thus affect stellar evolution. We perform simulations of stellar evolution with such additional energy losses and find that they eliminate the blue loops in the evolution of intermediate-mass stars. The existence of Cepheid stars can be used to constrain the neutrino magnetic moment and large extra dimensions. In order for Cepheids to exist, the neutrino magnetic moment should be smaller than the range ~2×10^{-10} to 4×10^{-11}mu_B, where mu_B is the Bohr magneton, and the fundamental scale in the (4+2)-spacetime should be larger than ~2 to 5 TeV, depending on the rate of the ^{12}C(alpha, gamma)^{16}O reaction. The fundamental scale also has strong dependence on the metallicity. This value of the magnetic moment is in the range explored in the reactor experiments, but higher than the limit inferred from globular clusters. Similarly the fundamental scale value we constrain corresponds to a size of the compactified dimensions comparable to those explored in the torsion balance experiments, but is smaller than the limits inferred from collider experiments and low-mass stars.