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In the era of Large Language Models (LLMs), efficient retrieval is crucial for integration with modern retrieval-augmented LLM systems, making sparse retrieval modules a popular choice due to their efficiency and robustness in low-resource settings. To enhance sparse retrieval performance, LLM-based Query Expansion (QE) has emerged as a solution to bridge the lexical gap between queries and documents. However, existing QE methods face a fundamental trade-off between efficiency and effectiveness, driven by the length of generated tokens. To address this, we propose Discarded candidate Tokens Query Expansion (DTQE), a novel query expansion method that leverages conventionally unselected tokens from the LLM’s decoding process by indexing them separately. Experimental results demonstrate that DTQE maintains high efficiency compared to more resource-intensive baselines while significantly outperforming keyword-based expansion ones.