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Despite notable advancements achieved on Hyperspectral (HS) pansharpening tasks through deep learning techniques, previous methods are inherently constrained by convolution or self-attention intrinsic defects, leading to limited performance. In this paper, we proposed an Attention-Interactive Dual-Branch Convolutional Neural Network (AIDB-Net) for HS pansharpening. Our model purely consists of convolutional layers and simultaneously inherits the strengths of both convolution and self-attention, especially the modeling of short- and long-range dependencies. Specially, we first extract, tokenize, and align the hyperspectral image (HSI) and panchromatic image (PAN) by Overlapping Patch Embedding Blocks. Then, we specialize a novel Spectral-Spatial Interactive Attention which is able to globally interact and fuse the cross-modality features. The resultant token-global similarity scores can guide the refinement and renewal of the textural details and spectral characteristics within HSI features. By deeply combined these two paradigms, our AIDB-Net significantly improve the pansharpening performance. Moreover, with the acceleration by the convolution inductive bias, our interactive attention can be trained without large scale dataset and achieves competitive time cost with its counterparts. Compared with the state-of-the-art methods, our AIDB-Net makes 5.2%, 3.1%, and 2.2% improvement on PSNR metric on three public datasets, respectively. Comprehensive experiments quantitatively and qualitatively demonstrate the effectiveness and superiority of our AIDB-Net. [ABSTRACT FROM AUTHOR]