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 Σ3n=1ln = 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 (1014GeV) to the electroweak one (103GeV), the intensity-intensity-intensity bispectrum for Σ3n=1ln = odd can be observed by the WMAP experiment under the condition that B1Mpc;2/3B1Mpc;1/3 > 2.7−4.5nG with B1Mpc; and B1Mpc; being the non-helical and helical PMF strengths smoothed on 1 Mpc, respectively