過去，我們已經精確測量了頂夸克質量。然而，借助機器學習的幫助，我們可以通過考慮更多標記精確度更高的噴流來提升測量的準確性。在這篇論文中，我們使用了二維形象圖法並比較了三種不同的方法，Kinematic Likelihood Fitter (KLFitter)，Permutation Dense Neural Network (PDNN)，和Symmetry Preserving Attention Network (SPANet)。此外，我們也使用真卻標記來計算頂夸克質量最佳的不確定度，以了解改進的空間有多大。我們同時確定了頂夸克質量和噴流能量刻度因子，以降低不確定度。結果，KLFitter、PDNN、SPANet和Perfect在一維擬合中的頂夸克質量不確定度分別為0.118、0.107、0.100和0.072 GeV。對於二維形象圖法，分別為0.189、0.177、0.168和110 GeV。總之，SPANet改進了噴流標記的準確性，並在二維擬合中進一步改進了頂夸克質量的測量，比KLFitter提高了0.2 GeV。

In the past, we already measured top mass accurately. However, with the help of machine learning, we can extend the measurement's accuracy by considering more jets with tagging of higher accuracy. In this thesis, we use the 2D ideogram method and compare three different methods, Kinematic Likelihood Fitter (KLFitter), Permutation Dense Neural Network (PDNN), and Symmetry Preserving Attention Network (SPANet). Also, we use the ground truth to calculate the Perfect uncertainty for top mass to see how much room for improvement. We determined the top-quark mass and jet energy scale factor simultaneously to reduce uncertainty. As a result, the uncertainties of top mass for KLFitter, PDNN, SPAnet, and Perfect are 0.118, 0.107, 0.100, and 0.072 GeV respectively on 1D fit. For 2D fit, we have 0.189, 0.177, 0.168, and 110 GeV respectively. In conclusion, SPAnet improved the correctness of jet tagging and further improved the top mass measurement over KLFitter 0.2 GeV in 2D fit.

[1]Michael James Fenton, Alexander Shmakov, Ta-Wei Ho, Shih-Chieh Hsu,
Daniel Whiteson, and Pierre Baldi. Permutationless many-jet event re-
construction with symmetry preserving attention networks. Phys. Rev. D,
105(11):112008, 2022.
[2] Alexander Shmakov, Michael James Fenton, Ta-Wei Ho, Shih-Chieh Hsu,
Daniel Whiteson, and Pierre Baldi. SPANet: Generalized permutationless set assignment for particle physics using symmetry preserving attention. SciPost Phys., 12:178, 2022.
[3] Michael Fenton, Alexander Shmakov, Hideki Okawa, Yuji Li, Ko-Yang Hsiao, Shih-Chieh Hsu, Daniel Whiteson, and Pierre Baldi. Extended symmetry pre- serving attention networks for lhc analysis. page 30, 09 2023.
[4] Johannes Erdmann, Stefan Guindon, Kevin Kroeninger, Boris Lemmer, Olaf Nackenhorst, Arnulf Quadt, and Philipp Stolte. A likelihood-based reconstruction algorithm for top-quark pairs and the KLFitter framework. Nucl. Instrum. Meth. A, 748:18–25, 2014.
[5] Johannes Erdmann, Tim Kallage, Kevin Kröninger, and Olaf Nackenhorst. From the bottom to the top—reconstruction of t ̄t events with deep learning.47 JINST, 14(11):P11015, 2019.
[6] Albert M Sirunyan et al. Measurement of the top quark mass using a profile likelihood approach with the lepton+jets final states in proton-proton collisions at √s = 13 TeV. JHEP, 04:23, 2023.