The effect of weak magnetic photon emission from quark-gluon plasma

We propose a novel effect that accounts for the photon emission from a quark-gluon plasma in the presence of a weak external magnetic field. Although the weak magnetic photon emission from quark-gluon plasma only leads to a small correction to the photon production rate, the induced photon spectrum can be highly azimuthally anisotropic, as a consequence of the coupled effect of the magnetic field and the longitudinal dynamics in the background medium. With respect to a realistic medium evolution containing a tilted fireball configuration, the direct photon elliptic flow from experiments is reproduced. In comparison to the experimental data of direct photon elliptic flow, the strength of the magnetic field during the evolution of quark-gluon plasma can be extracted. For the top energy of RHIC collisions, $\left|eB\right|$ is found no larger than a few percent of the pion mass square.