Electroweak measurements in the forward region at LHCb

The electroweak theory is an essential component of the Standard Model of particle physics. Precision measurements of electroweak physics observable, through different decay modes and approaches, could not only provide stringent tests on the Standard Model, but also be used to search for new physics indirectly. The LHCb detector is a forward spectrometer in the Large Hadron Collider. Compared to general-purpose detectors, such as the ATLAS and CMS detectors, it covers a unique acceptance region, and provides comprehensive and complementary information. Therefore, the data collected by the LHCb detector could provide stringent constraint on the parton distribution functions of the proton, which is also an important input for the global fit of parton distribution functions. For many important measurements, the LHCb results combined with those from ATLAS and CMS experiments could significantly reduce the systematic uncertainty. This paper introduces the importance of the electroweak physics of the Standard Model and reviews the most recent electroweak results from the LHCb experiment. In the Standard Model, the W mass and weak mixing angle are the fundamental parameters of the electroweak theory. However, tensions between results from different experiments are seen. In 2022, the CDF collaboration published its result on the W mass, which has a large tension between measured results and the electroweak global fit expectation, indicating the existence of new physics. However, tensions between the CDF result and results from other experiments are also seen. Therefore, it is important to have more experimental results to either confirm or exclude the CDF result. As a proof-of-principle, the LHCb collaboration performed the W mass measurement with part of its Run-2 dataset. The measured result is consistent with the electroweak global fit expectation, while an update with more data in the future is expected to have higher precision. The LHCb collaboration also performed the first measurement of the weak mixing angle in the forward region using the Run-1 dataset. A good agreement between the measured value and the global fit expectation is seen. The LHCb collaboration has conducted measurements related to the parton distribution functions of the proton, including the mechanism of Z boson production and the polarization of Z boson. The production cross-sections are measured in different center-of-mass energies, as 13 and 5.02 TeV. The measured results are compared with different theoretical predictions and provide unique information for the global fit of parton distribution functions. Reasonable agreements between measured results and predictions are seen. The measurement of Z + c is performed, and a significant deviation between the measured result and predictions is seen, which could be a hint for the existing of an intrinsic charm component inside the proton. The LHCb collaboration also performed a search for rare decays of the W and Z boson, using a dataset collected in 2018. The branching fraction of radiative decays of electroweak bosons is highly suppressed in the Standard Model, which can be enhanced in some new physics modes. These measurements demonstrate that the LHCb experiment has a large potential in electroweak physics. With more data collected in the future, the LHCb measurements could deepen our understanding on the electroweak physics and parton distribution functions of proton in the forward region.