We present PBFormer, an efficient yet powerful scene text detector that unifies the transformer with a novel text shape representation Polynomial Band (PB). The representation has four polynomial curves to fit a text's top, bottom, left, and right sides, which can capture a text with a complex shape by varying polynomial coefficients. PB has appealing features compared with conventional representations: 1) It can model different curvatures with a fixed number of parameters, while polygon-points-based methods need to utilize a different number of points. 2) It can distinguish adjacent or overlapping texts as they have apparent different curve coefficients, while segmentation-based or points-based methods suffer from adhesive spatial positions. PBFormer combines the PB with the transformer, which can directly generate smooth text contours sampled from predicted curves without interpolation. A parameter-free cross-scale pixel attention (CPA) module is employed to highlight the feature map of a suitable scale while suppressing the other feature maps. The simple operation can help detect small-scale texts and is compatible with the one-stage DETR framework, where no postprocessing exists for NMS. Furthermore, PBFormer is trained with a shape-contained loss, which not only enforces the piecewise alignment between the ground truth and the predicted curves but also makes curves' positions and shapes consistent with each other. Without bells and whistles about text pre-training, our method is superior to the previous state-of-the-art text detectors on the arbitrary-shaped text datasets.