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Nucleon Structure Physics by Proton-Proton Collisions

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Nucleon Structure Physics by Proton-Proton Collisions Nucleon Structure Physics by Proton-Proton Collisions Ming Xiong Liu Physics Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA E-mail: [email protected] (Received April 23, 2019) Today, the nucleons (protons and neutrons) make up most of the visible matter in the universe, from the nucleus to the galaxy. Understanding the fundamental constituents of the nucleon and the internal parton dynamics is of great interest of modern physics. However, describing the nucleon structure with the fundamental degree of freedom of quarks and gluons in the QCD framework remains as one of the most outstanding challenges in modern high energy nuclear and particle physics. In the last decades, largely due to the worldwide collaborative effort and advances in beam acceleration and target polarization technologies, tremendous progress has been made in the study of nucleon structures with polarized high energy leptons and hadron beams. The complementarity of lepton scattering and pure hadronic interaction is critical in the study of nucleon structure and QCD. In this presentation, I highlight a few recent achievements in the study of the nucleon structures with high energy (polarized) hadronic scatterings at the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory, at COMPASS at CERN as well as the SeaQuest experiments at Fermilab. Future prospects of new opportunities at above and other facilities worldwide are also discussed briefly. KEYWORDS: Proton, neutron, spin, QCD 1. Introduction Understanding the structure of the nucleon at the fundamental level with quark and gluon’s degree of freedom is one of the goals of modern physics. In the high-energy nucleon reactions, the nucleon can be described as a collection of partons, whose distributions inside the nucleon are generally universal and process independent, the so called parton distribution functions (PDFs). The reaction rate can be calculated in the perturbative QCD (pQCD) framework as a sum of the factorized individual parton-parton interactions. PDFs are fundamental properties of the nucleon. At the leading twist in the collinear factorization framework, there are three kinds of parton f(x, Q2) distribution functions: 1) the unpolarized parton distribution functions, <latexit sha1_base64="pl9OnI3LCgd5Oo69EqJYEEN/9Lw=">AAAB8XicbVBNS8NAEJ3Ur1q/qh69LBahgpSkCnosevHYgv3ANpbNdtMu3WzC7kYsof/CiwdFvPpvvPlv3LQ5aOuDgcd7M8zM8yLOlLbtbyu3srq2vpHfLGxt7+zuFfcPWiqMJaFNEvJQdjysKGeCNjXTnHYiSXHgcdr2xjep336kUrFQ3OlJRN0ADwXzGcHaSPd++ekMNR6qp4V+sWRX7BnQMnEyUoIM9X7xqzcISRxQoQnHSnUdO9JugqVmhNNpoRcrGmEyxkPaNVTggCo3mV08RSdGGSA/lKaERjP190SCA6UmgWc6A6xHatFLxf+8bqz9KzdhIoo1FWS+yI850iFK30cDJinRfGIIJpKZWxEZYYmJNiGlITiLLy+TVrXinFeqjYtS7TqLIw9HcAxlcOASanALdWgCAQHP8ApvlrJerHfrY96as7KZQ/gD6/MHLYePSA==</latexit> ; 2) the parton 2 h (x, Q2) ∆f(x, Q ) <latexit sha1_base64="v3CKPK6oF/iljfbyihoax6Mad3w=">AAAB83icbVBNS8NAEJ3Ur1q/qh69LBahgpSkFfRY9OKxBfsBbSyb7aZdutmE3Y1YQv+GFw+KePXPePPfuGlz0NYHA4/3ZpiZ50WcKW3b31ZubX1jcyu/XdjZ3ds/KB4etVUYS0JbJOSh7HpYUc4EbWmmOe1GkuLA47TjTW5Tv/NIpWKhuNfTiLoBHgnmM4K1kfrjgVN+ukDNh+p5YVAs2RV7DrRKnIyUIENjUPzqD0MSB1RowrFSPceOtJtgqRnhdFbox4pGmEzwiPYMFTigyk3mN8/QmVGGyA+lKaHRXP09keBAqWngmc4A67Fa9lLxP68Xa//aTZiIYk0FWSzyY450iNIA0JBJSjSfGoKJZOZWRMZYYqJNTGkIzvLLq6RdrTi1SrV5WarfZHHk4QROoQwOXEEd7qABLSAQwTO8wpsVWy/Wu/WxaM1Z2cwx/IH1+QNbHY/u</latexit> helicity distribution functions, <latexit sha1_base64="nBgmVrPeYwo+DKZwyBfwCKBCb/k=">AAAB+nicbVBNS8NAEN34WetXqkcvi0WoICWpgh6LevDYgv2ANpbNdtIu3WzC7kYtsT/FiwdFvPpLvPlvTNoctPXBwOO9GWbmuSFnSlvWt7G0vLK6tp7byG9ube/smoW9pgoiSaFBAx7ItksUcCagoZnm0A4lEN/l0HJHV6nfugepWCBu9TgExycDwTxGiU6knlnoXgPXBHulxxNcv6sc53tm0SpbU+BFYmekiDLUeuZXtx/QyAehKSdKdWwr1E5MpGaUwyTfjRSEhI7IADoJFcQH5cTT0yf4KFH62AtkUkLjqfp7Iia+UmPfTTp9oodq3kvF/7xOpL0LJ2YijDQIOlvkRRzrAKc54D6TQDUfJ4RQyZJbMR0SSahO0kpDsOdfXiTNStk+LVfqZ8XqZRZHDh2gQ1RCNjpHVXSDaqiBKHpAz+gVvRlPxovxbnzMWpeMbGYf/YHx+QNq2pIl</latexit> ; and 3) the transversity functions, 1 . Here x represents the parton light-cone momentum fraction, and Q2 denotes the momentum transfer under the reaction. In the three-dimensional partonic picture of the nucleon, one can go one step further beyond the above one-dimensional PDFs, describing the parton distribution functions in the (2+1) dimension, including the parton’s transverse momentum kT, in addition to the longitudinal momentum fraction x, thus they are Transverse-Momentum-Dependent (TMD) functions. At leading twist, there are eight TMD PDFs describing the partons’ longitudinal and transverse motion distributions and their correlations with the nucleon spin and momentum directions. All these functions can be probed in high-energy hadron-hadron or hadron-lepton scattering experiments, for recent reviews and some early work, see [1] and references therein. With the advance of accelerator technology, the world’s first high energy polarized proton collider was built at the Brookhaven National Laboratory in New York, USA, in late 1990s, and has been in operation since 2001. Since then, tremendous progress has been made in studying the proton internal structures and QCD dynamics using longitudinally and transversely polarized proton-proton collisions at high energies at the Relativistic Heavy Ion Collider (RHIC). Fig. 1 shows the layout of the world’s first high-energy polarized proton accelerator complex at RHIC. Figure 1. LH: The layout of the world’s first high energy polarized proton + proton collider at the Brookhaven National LaBoratory in New York. The proton Beam has been polarized up to about 60% either in longitudinal or transverse direction relative to the Beam momentum direction, at center of mass energies from 62 to 510GeV. RH: High energy particles are produced in the polarized proton + proton collisions at RHIC. The polarized PDFs have be derived from the measured spin- dependent cross-sections in the pQCD framework. QCD is the theory of strong interactions. Particle production in the high energy polarized proton + proton collisions can be calculated as a sum of the product of the universal PDFs, f(x1) and f(x2) of the incoming partons and the partonic scattering cross sections that can be calculated in the perturbative QCD framework: x +x h +h +X σ f(x ) f(x )ˆσ 1 2! 1 2 <latexit sha1_base64="SULX0HJ+N/cFDHdlNeTP18Yzv/s=">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</latexit> 1 2 ⇠ ⌦ Using above theoretical tool, one can derive the universal parton distribution function f(x) with the experimentally measured cross section, σ<latexit sha1_base64="qaWP98Kf7fcq0FfPj92xonE0duU=">AAAB7nicbVBNSwMxEJ34WetX1aOXYBE8ld0q6LHoxWMF+wHtUrJptg1NskuSFcrSH+HFgyJe/T3e/Ddm2z1o64OBx3szzMwLE8GN9bxvtLa+sbm1Xdop7+7tHxxWjo7bJk41ZS0ai1h3Q2KY4Iq1LLeCdRPNiAwF64STu9zvPDFteKwe7TRhgSQjxSNOiXVSp2/4SJLyoFL1at4ceJX4BalCgeag8tUfxjSVTFkqiDE930tskBFtORVsVu6nhiWETsiI9RxVRDITZPNzZ/jcKUMcxdqVsniu/p7IiDRmKkPXKYkdm2UvF//zeqmNboKMqyS1TNHFoigV2MY4/x0PuWbUiqkjhGrubsV0TDSh1iWUh+Avv7xK2vWaf1mrP1xVG7dFHCU4hTO4AB+uoQH30IQWUJjAM7zCG0rQC3pHH4vWNVTMnMAfoM8f1DCPOw==</latexit> , and the theoretically calculated partonic cross- section, σ<latexit sha1_base64="XflvfPp4jmbgLHjuompi9W/uHyU=">AAAB9HicbVBNS8NAEN34WetX1aOXxSJ4KkkV9Fj04rGC/YAmlM120y7d3cTdSaGE/g4vHhTx6o/x5r9x0+agrQ8GHu/NMDMvTAQ34Lrfztr6xubWdmmnvLu3f3BYOTpumzjVlLVoLGLdDYlhgivWAg6CdRPNiAwF64Tju9zvTJg2PFaPME1YIMlQ8YhTAlYK/BGBzDd8KMms3K9U3Zo7B14lXkGqqECzX/nyBzFNJVNABTGm57kJBBnRwKlgs7KfGpYQOiZD1rNUEclMkM2PnuFzqwxwFGtbCvBc/T2REWnMVIa2UxIYmWUvF//zeilEN0HGVZICU3SxKEoFhhjnCeAB14yCmFpCqOb2VkxHRBMKNqc8BG/55VXSrte8y1r94arauC3iKKFTdIYukIeuUQPdoyZqIYqe0DN6RW/OxHlx3p2PReuaU8ycoD9wPn8ArWWSCA==</latexit> ˆ. In the following, I present a few highlights selected from recent experimental and theoretical studies of the (polarized) nucleon structures using high energy (polarized) hadronic scatterings at BNL, CERN and Fermilab. 2. The proton spin puzzle and the polarized parton distribution functions The nucleon’s quark and gluon helicity distributions, Df(x, Q2), are universal property of the nucleon. They are derived from high-energy polarized nucleon-nucleon or polarized nucleon- lepton scattering data. Before 1987, it was believed through some naïve nucleon quark models that the proton’s spin is mostly coming from the sum of quarks’ spin. When EMC collaboration at CERN carried out the first measurement of quark’s spin contribution to the proton spin in the deep- inelastic polarized muon-proton scattering in 1987, the results socked the world – the sum of the quark’s spin can only account for about 30% of the total proton spin, known as the “spin crisis”, see [2] and references therein. Several new polarized DIS experiments were conducted following the EMC’s discovery and further confirmed the surprising results. Where does the rest of the proton spin come from? In QCD, the proton helicity sum rule is given by [1], <latexit sha1_base64="1gO7w4X5Nx/xB4uuTsXm3aa6JEI=">AAAB8HicbVBNSwMxEM3Wr1q/qh69BIvgqexWQY9FBT1WsB/SLiWbZtvQJLsks0JZ+iu8eFDEqz/Hm//GbLsHbX0w8Hhvhpl5QSy4Adf9dgorq2vrG8XN0tb2zu5eef+gZaJEU9akkYh0JyCGCa5YEzgI1ok1IzIQrB2MrzO//cS04ZF6gEnMfEmGioecErDSY++GCSD4ttQvV9yqOwNeJl5OKihHo1/+6g0imkimgApiTNdzY/BTooFTwaalXmJYTOiYDFnXUkUkM346O3iKT6wywGGkbSnAM/X3REqkMRMZ2E5JYGQWvUz8z+smEF76KVdxAkzR+aIwERginH2PB1wzCmJiCaGa21sxHRFNKNiMshC8xZeXSatW9c6qtfvzSv0qj6OIjtAxOkUeukB1dIcaqIkokugZvaI3RzsvzrvzMW8tOPnMIfoD5/MHg1aPjw==</latexit>
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