## 1 Introduction  
Quantum key distribution (QKD) promises to share the secret key bits with its security guaranteed by the laws of quantum physics [1; 2; 3]. Combined with the one-time pad, [PERSON] and [PERSON] can achieve unconditionally secure private communication. However, there are inevitable imperfections in the practical QKD systems which can be exploited by [PERSON] and compromise the practical security. With the development of QKD, the proposal of the measurement-device-independent (MDI) QKD [4] and the decoy-state method [5; 6; 7] have greatly improved the practicality, performance, and practical security. However, the secret key rate and distance are two implementation bottlenecks of point-to-point QKD. For example, the TGW bound [8] and PLOB bound [9] determine the repeaterless secret key capacity. To overcome this limit of repeaterless QKD, [PERSON] et al. [10] proposed the twin-field QKD (TF-QKD) protocol whose secret key rate scales with the square root of the channel transmittance by using the single-photon interference. However, the security is not completed as a security loophole is caused by the later announcement of the phase information [11]. Then, many variants of TF-QKD [11; 12; 13; 14; 15; 16; 17] have been proposed to deal with this security loophole and each has its own advantages. To accelerate the application of the TF-QKD protocols, many effects have been considered and analyzed, including the finite-keyeffects [18; 19; 20; 21], the asymmetric effects [22; 23; 24], the discrete phase randomization [25; 26], the optimization of the protocol [27; 28; 29], and the practical issues [30; 31]. Meanwhile, several experiments of the TF-QKD have been carried out in the laboratory and field, demonstrating its ability to break the limit of repeaterless QKD [32; 33; 34; 35; 36; 37; 38; 39]. However, the physical implementations of the TF-QKD protocols with the side channels remain to be further researched at present. Ideally, it is assumed that the sending devices are placed in a protected laboratory, and can prepare and encode quantum states correctly without information leakage. Unfortunately, these conditions may be not satisfied in the practical systems due to the imperfect devices [40; 41; 42; 43] or [PERSON]'s disturbance [44; 45; 46; 47; 48; 49; 50]. In those QKD protocols with the practical light source, the decoy-state method is vital and used to monitor the channel eavesdropping [51] in which the security is based on the fact that [PERSON] cannot distinguish between the signal and decoy states. However, the indistinguishability of the signal and decoy states may be violated due to the imperfections of the real apparatuses or [PERSON]'s disturbance. For instance, the probability distributions of the signal and decoy states do not overlap in the time domain completely with the pump-current modulation [42]. In the frequency domain, [PERSON] could apply the wavelength-selected photon-number-splitting attack [52] or the frequency shift attack [53] actively to distinguish the signal and decoy states in the \"plug-and-play\" systems. However, the frequency shift attack needs to perform time shift on the signal pulses actively which is only applicable to the \"plug-and-play\" systems. In addition, it only analyzes the frequency shift in the ideal case. Therefore, to exploit the negative effects of the frequency side channels clearly, we consider the most general case of side channels caused only by the imperfect devices and test it experimentally. As the decoy-state method is used in the TF-QKD protocols, it is of significance to analyze its practical security in this aspect. More specifically, we concentrate on the sending or not-sending (SNS) TF-QKD protocol [11] with the actively odd-parity pairing (AOPP) method [29] and propose a side-channel attack, named the passive frequency-shift attack, which could take advantage of the most general side channels in the frequency domain. The paper is arranged as follows.