The main method for calibrating the luminosity at Large Hadron Collider (LHC) is van der Meer scan where the beams are swept transversely across each other. This beautiful method was invented in 1968. Despite the honourable age, it remains the preferable tool at hadron colliders. It delivers the lowest calibration systematics, which still often dominates the overall luminosity uncertainty at LHC experiments. Various details of the method are discussed in the paper. One of the main factors limiting proton–proton van der Meer scan accuracy is the beam–beam electromagnetic interaction. It modifies the shapes of the colliding bunches and biases the measured luminosity. In the first years of operation, four main LHC experiments did not attempt to correct the bias because of its complexity. In 2012 a correction method was proposed and then subsequently used by all experiments. It was based, however, on a simplified linear approximation of the beam–beam force and, therefore, had limited accuracy. In this paper, a new simulation is presented, which takes into account the exact non-linear force. Depending on the beam parameters, the results of the new and old methods differ by \(\sim 1\%\). This needs to be propagated to all LHC cross-section measurements after 2012. The new simulation is going to be used at LHC in future luminosity calibrations.

校准大型强子对撞机（LHC）的亮度的主要方法是van der Meer扫描，其中光束横向横扫。这种漂亮的方法是1968年发明的。尽管年代久远，但它仍然是强子对撞机的首选工具。它提供了最低的校准系统，这在LHC实验中仍经常在总体亮度不确定性中占主导地位。本文讨论了该方法的各种细节。限制质子-质子范德米尔扫描精度的主要因素之一是束-束电磁相互作用。它修改了碰撞束的形状并偏斜了测得的光度。在运行的最初几年中，四个大型大型强子对撞机实验由于其复杂性而未尝试纠正偏差。在2012年，提出了一种校正方法，随后在所有实验中使用。但是，它基于对束力的简化线性近似，因此精度有限。在本文中，提出了一种新的模拟，其中考虑了确切的非线性力。根据光束参数的不同，新方法和旧方法的结果有所不同\（\ SIM 1 \％\） 。这需要在2012年之后传播到所有LHC横截面测量中。新的模拟将在LHC中用于未来的光度校准。