Parity violation of primordial magnetic fields in the CMB bispectrum

We study the parity violation in the cosmic microwave background (CMB) bispectrum induced by primordial magnetic fields (PMFs). Deriving a general formula for the CMB bispectrum generated from not only non-helical but also helical PMFs, we find that helical PMFs produce characteristic signals, which disappear in parity-conserving cases, such as the intensity-intensity-intensity bispectra arising from ∑ₙ₌₁³ ₙ = odd. For fast numerical calculation of the CMB bispectrum, we reduce the one-loop formula to the tree-level one by using the so-called pole approximation. Then, we show that the magnetic anisotropic stress, which depends quadratically on non-helical and helical PMFs and acts as a source of the CMB fluctuation, produces the local-type non-Gaussianity. Comparing the CMB bispectra composed of the scalar and tensor modes with the noise spectra, we find that assuming the generation of the nearly scale-invariant non-helical and helical PMFs from the grand unification energy scale (10¹⁴ GeV) to the electroweak one (10³ GeV), the intensity-intensity-intensity bispectrum for ∑ₙ₌₁³ ₙ = odd can be observed by the WMAP experiment under the condition that B1 Mpc2/3 B1 Mpc1/3 > 2.7 - 4.5 nG with B1 Mpc and B1 Mpc being the non-helical and helical PMF strengths smoothed on 1 Mpc, respectively.