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1. Determining the helicity structure of the nucleon at the Electron Ion Collider in China

   https://doi.org/10.1007/JHEP08(2021)034  

   Anderle, Daniele Paolo ; Hou, Tie-Jiun ; Xing, Hongxi ; Yan, Mengshi ; Yuan, C.-P. ; Zhao, Yuxiang ( August 2021 , Journal of High Energy Physics)

   A bstract Understanding how sea quarks behave inside a nucleon is one of the most important physics goals of the proposed Electron-Ion Collider in China (EicC), which is designed to have a 3.5 GeV polarized electron beam (80% polarization) colliding with a 20 GeV polarized proton beam (70% polarization) at instantaneous luminosity of 2 × 10 33 cm − 2 s − 1 . A specific topic at EicC is to understand the polarization of individual quarks inside a longitudinally polarized nucleon. The potential of various future EicC data, including the inclusive and semi-inclusive deep inelastic scattering data from both doubly polarized electron-proton and electron- 3 He collisions, to reduce the uncertainties of parton helicity distributions is explored at the next-to-leading order in QCD, using the Error PDF Updating Method Package ( e P ump ) which is based on the Hessian profiling method. We show that the semi-inclusive data are well able to provide good separation between flavour distributions, and to constrain their uncertainties in the x > 0 . 005 region, especially when electron- 3 He collisions, acting as effective electron-neutron collisions, are taken into account. To enable this study, we have generated a Hessian representation of the DSSV14 set of PDF replicas, named DSSV14H PDFs. 

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2. Measurement of the axial vector form factor from antineutrino–proton scattering

   https://doi.org/10.1038/s41586-022-05478-3  

   Cai, T. ; Moore, M. L. ; Olivier, A. ; Akhter, S. ; Dar, Z. Ahmad ; Ansari, V. ; Ascencio, M. V. ; Bashyal, A. ; Bercellie, A. ; Betancourt, M. ; et al ( February 2023 , Nature)

   Abstract Scattering of high energy particles from nucleons probes their structure, as was done in the experiments that established the non-zero size of the proton using electron beams 1 . The use of charged leptons as scattering probes enables measuring the distribution of electric charges, which is encoded in the vector form factors of the nucleon 2 . Scattering weakly interacting neutrinos gives the opportunity to measure both vector and axial vector form factors of the nucleon, providing an additional, complementary probe of their structure. The nucleon transition axial form factor, F A , can be measured from neutrino scattering from free nucleons, ν μ n  →  μ − p and $${\bar{\nu }}_{\mu }p\to {\mu }^{+}n$$ ν ¯ μ p → μ + n , as a function of the negative four-momentum transfer squared ( Q 2 ). Up to now, F A ( Q 2 ) has been extracted from the bound nucleons in neutrino–deuterium scattering 3–9 , which requires uncertain nuclear corrections 10 . Here we report the first high-statistics measurement, to our knowledge, of the $${\bar{\nu }}_{\mu }\,p\to {\mu }^{+}n$$ ν ¯ μ p → μ + n cross-section from the hydrogen atom, using the plastic scintillator target of the MINERvA 11 experiment, extracting F A from free proton targets and measuring the nucleon axial charge radius, r A , to be 0.73 ± 0.17 fm. The antineutrino–hydrogen scattering presented here can access the axial form factor without the need for nuclear theory corrections, and enables direct comparisons with the increasingly precise lattice quantum chromodynamics computations 12–15 . Finally, the tools developed for this analysis and the result presented are substantial advancements in our capabilities to understand the nucleon structure in the weak sector, and also help the current and future neutrino oscillation experiments 16–20 to better constrain neutrino interaction models. 

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3. Measurement and QCD analysis of double-differential inclusive jet cross sections in proton-proton collisions at $$ \sqrt{s} $$ = 13 TeV

   https://doi.org/10.1007/JHEP02(2022)142  

   Tumasyan, A. ; Adam, W. ; Andrejkovic, J. W. ; Bergauer, T. ; Chatterjee, S. ; Damanakis, K. ; Dragicevic, M. ; Escalante Del Valle, A. ; Frühwirth, R. ; Jeitler, M. ; et al ( February 2022 , Journal of High Energy Physics)

   A bstract A measurement of the inclusive jet production in proton-proton collisions at the LHC at $$ \sqrt{s} $$ s = 13 TeV is presented. The double-differential cross sections are measured as a function of the jet transverse momentum p T and the absolute jet rapidity |y| . The anti- k T clustering algorithm is used with distance parameter of 0.4 (0.7) in a phase space region with jet p T from 97 GeV up to 3.1 TeV and |y| < 2 . 0. Data collected with the CMS detector are used, corresponding to an integrated luminosity of 36.3 fb − 1 (33.5 fb − 1 ). The measurement is used in a comprehensive QCD analysis at next-to-next-to-leading order, which results in significant improvement in the accuracy of the parton distributions in the proton. Simultaneously, the value of the strong coupling constant at the Z boson mass is extracted as α S ( m Z ) = 0 . 1170 ± 0 . 0019. For the first time, these data are used in a standard model effective field theory analysis at next-to-leading order, where parton distributions and the QCD parameters are extracted simultaneously with imposed constraints on the Wilson coefficient c 1 of 4-quark contact interactions. 

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4. Parton Distribution Functions and Lattice QCD

   https://doi.org/10.1051/epjconf/201920601003  

   Lin, Huey-Wen ; Yang, A. ; Wang, W.Y. ; Ng, S.C.C. ; Chan, A.H. ; Oh, C.H. ; Phua, K.K. ( January 2019 , EPJ Web of Conferences)

   Recently, there have been rapid developments in lattice-QCD calculations of proton structure, especially in the parton distribution functions (PDFs). We overcame a longstanding obstacle and for the first time in lattice-QCD are able to directly calculate the Bjorken- x dependence of the quark, helicity and transversity distributions. The PDFs are obtained using the large-momentum effective field theory (LaMET) framework where the full Bjorken- x dependence of finite-momentum PDFs, called “quasi-PDFs”, can be calculated on the lattice. The quasi-PDF nucleon matrix elements are renormalized non-perturbatively in RI/MOM-scheme. Following a nonperturbative renormalization of the parton quasi-distribution in a regularization-independent momentum-subtraction scheme, we establish its matching to the $ \overline {{\rm{MS}}} $ PDF and calculate the non-singlet matching coefficient at next-to-leading order in perturbation theory. In this proceeding, I will show the progress that has been made in recent years, highlighting the latest state-of-the art PDF calculations at the physical pion mass. Future impacts on the large- x global PDF fits are also discussed. 

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5. Isovector and flavor diagonal charges of the nucleon from 2+1+1 flavor QCD

   https://doi.org/10.22323/1.334.0131  

   Gupta, Rajan ; Bhattacharya, Tanmoy ; Cirigliano, Vincenzo ; Yoon, Boram ; Jang, Yong-Chull ; Lin, Huey-Wen ( May 2019 , The 36th Annual International Symposium on Lattice Field Theory (LATTICE2018))

   We present high-statistics results for the isovector and flavor diagonal charges of the proton using 11 ensembles of 2+1+1 flavor HISQ fermions. In the isospin symmetric limit, results for the neutron are given by the $u \leftrightarrow d$ interchange. A chiral-continuum fit with leading order corrections was made to extract the connected and disconnected contributions in the continuum limit and at $M_\pi=135$~MeV. All results are given in the $\overline{MS}$ scheme at 2~GeV. The isovector charges, $g_A^{u-d} = 1.218(25)(30)$, $g_S^{u-d} = 1.022(80)(60) $ and $g_T^{u-d} = 0.989(32)(10)$, are used to obtain low-energy constraints on novel scalar and tensor interactions, $\epsilon_{S}$ and $\epsilon_{T}$, at the TeV scale. The flavor diagonal axial charges are: $g_A^u \equiv \Delta u \equiv \langle 1 \rangle_{\Delta u^+} = 0.777(25)(30)$, $g_A^d \equiv \Delta d \equiv \langle 1 \rangle_{\Delta d^+} = -0.438(18)(30)$, and $g_A^s \equiv \Delta s \equiv \langle 1 \rangle_{\Delta s^+} = -0.053(8)$. Their sum gives the total quark contribution to the proton spin, $\sum_{q=u,d,s} (\frac{1}{2} \Delta q) = 0.143(31)(36)$. This result is in good agreement with the recent COMPASS analysis $0.13 < \frac{1}{2} \Delta \Sigma < 0.18$. Implications of results for the flavor diagonal tensor charges, $g_T^u = 0.784(28)(10)$, $g_T^d = -0.204(11)(10)$ and $g_T^s = -0.0027(16)$ for constraining the quark electric dipole moments and their contributions to the neutron electric dipole moment are discussed. These flavor diagonal charges also give the strength of the interaction of dark matter with nucleons via axial and tensor mediators. 

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