Competition between triplet, singlet, and FFLO states in organic superconductors (TMTSF) 2 X under magnetic field H Aizawa, K Kuroki, T Yokoyama et al. Abstract. We study the competition between triplet f -wave, singlet d-wave, and the FFLO state in a model for (TMTSF)2X using random phase approximation. The result suggests the possibility of the singlet→FFLO→triplet transition upon increasing the magnetic field. We also show that the triplet component mixing increases in the FFLO state with increasing the magnetic field, and the off-site repulsions increase the mixing rate. The results seem to suggest that the large triplet mixing results in an enhanced tendency toward the FFLO state over the usual pairing state. Experiments for the quasi one dimensional (Q1D) organic superconductors (TMTSF) 2 X (X=PF 6 , ClO 4 , etc.), suggest the possibility of spin triplet pairing and/or the FFLO state in the large magnetic field regime. [6,7,8,9] We have previously shown that spin triplet fwave pairing can compete with spin singlet d-wave pairing, where d-wave and f -wave in this study are shown in Figure 1 (b). [10,11,12] This is because (i) the f -wave and the d-wave gap has the same number of nodes intersecting the Fermi surface, and (ii) competing 2k F spin and 2k F charge fluctuations results in a nearly similar magnitude of the singlet and triplet pairing interactions. Recently, we have further found that the triplet pairing mediated by 2k F spin+2k F charge fluctuations is strongly enhanced by the field, which supports the possibility of singlet-triplet transition in (TMTSF) 2 X under magnetic field. [13] In the present study, we investigate the possibility of the FFLO state from the microscopic point of view by applying random phase approximation(RPA) to a model for (TMTSF) 2 X. We investigate the competition between triplet, singlet and the FFLO state, and propose the