LLM-based query expansion improves retrieval by generating document-like passages. In hybrid retrieval, however, most evaluations fuse fixed top-$L$ dense and sparse rankings.

Because the cutoff controls both which cross-channel contributions enter fusion and how much of each ranking is accessed, gains measured at one $L$ can change or reverse at another. We separate these effects by evaluating retrieval effectiveness under complete-list fusion and recording the policy-specific per-channel replay stopping depths at which its ordered top-$K$ is certified.

We then introduce DESA (Dense Expansion and Sparse Anchoring), a channel-asymmetric query expansion method. An LLM generates complementary reference passages; orthogonal residual expansion adds their new semantic directions to the dense query, while score-product anchoring incorporates their lexical cues into sparse retrieval without broadening the original query's lexical support.

Across seven BEIR datasets, DESA improves nDCG@10 and Recall@20 over the unexpanded query by 3.82% and 2.38%, while reducing dense and sparse access depths by 36.90% and 36.56%. With equal dataset weighting, 63.31% of queries become shallower in both channels.

However, both depths increase with Contriever on Touché-2020. These results support channel-specific integration of generated passages and joint evaluation of retrieval effectiveness and access depth.