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Energy Independence of the Collins Asymmetry in $p^{\uparrow}p$ Collisions

STAR Collaboration, B. E. Aboona, J. Adam, L. Adamczyk, I. Aggarwal, M. M. Aggarwal, Z. Ahammed, A. K. Alshammri, E. C. Aschenauer, S. Aslam, J. Atchison, V. Bairathi, X. Bao, P. Barik, K. Barish, S. Behera, R. Bellwied, P. Bhagat, A. Bhasin, S. Bhatta, S. R. Bhosale, J. Bielcik, J. Bielcikova, J. D. Brandenburg, C. Broodo, X. Z. Cai, H. Caines, M. Calderón de la Barca Sánchez, D. Cebra, J. Ceska, I. Chakaberia, P. Chaloupka, Y. S. Chang, Z. Chang, A. Chatterjee, D. Chen, J. H. Chen, Q. Chen, W. Chen, Z. Chen, J. Cheng, Y. Cheng, W. Christie, X. Chu, S. Corey, H. J. Crawford, M. Csanád, G. Dale-Gau, A. Das, D. De Souza Lemos, I. M. Deppner, A. Deshpande, A. Dhamija, A. Dimri, P. Dixit, X. Dong, J. L. Drachenberg, E. Duckworth, J. C. Dunlop, Y. S. El-Feky, J. Engelage, G. Eppley, S. Esumi, O. Evdokimov, O. Eyser, B. Fan, R. Fatemi, S. Fazio, H. Feng, Y. Feng, E. Finch, Y. Fisyak, F. A. Flor, C. Fu, T. Fu, C. A. Gagliardi, T. Galatyuk, T. Gao, Y. Gao, G. Garcia, F. Geurts, A. Gibson, A. Giri, K. Gopal, X. Gou, D. Grosnick, A. Gu, J. Gu, A. Gupta, W. Guryn, A. Hamed, R. J. Hamilton, J. Han, X. Han, S. Harabasz, M. D. Harasty, J. W. Harris, H. Harrison-Smith, L. B. Havener, X. H. He, Y. He, N. Herrmann, L. Holub, C. Hu, Q. Hu, Y. Hu, H. Huang, H. Z. Huang, S. L. Huang, T. Huang, Y. Huang, Y. Huang, Y. Huang, M. Isshiki, W. W. Jacobs, A. Jalotra, C. Jena, A. Jentsch, Y. Ji, J. Jia, X. Jiang, C. Jin, Y. Jin, N. Jindal, X. Ju, E. G. Judd, S. Kabana, D. Kalinkin, J. Kang, K. Kang, A. R. Kanuganti, D. Kapukchyan, K. Kauder, D. Keane, M. Kesler, A. Khanal, Y. V. Khyzhniak, D. P. Kikoła, J. Kim, D. Kincses, I. Kisel, A. Kiselev, A. G. Knospe, J. Kołaś, B. Korodi, L. K. Kosarzewski, L. Kumar, M. C. Labonte, R. Lacey, J. M. Landgraf, C. Larson, J. Lauret, A. Lebedev, J. H. Lee, Y. H. Leung, C. Li, D. Li, H-S. Li, H. Li, H. Li, H. Li, W. Li, X. Li, X. Li, Y. Li, Z. Li, Z. Li, X. Liang, R. Licenik, T. Lin, Y. Lin, M. A. Lisa, C. Liu, G. Liu, H. Liu, L. Liu, L. Liu, Z. Liu, Z. Liu, T. Ljubicic, O. Lomicky, E. M. Loyd, T. Lu, J. Luo, X. F. Luo, L. Ma, R. Ma, Y. G. Ma, N. Magdy, D. Mallick, R. Manikandhan, C. Markert, O. Matonoha, K. Mi, S. Mioduszewski, B. Mohanty, B. Mondal, M. M. Mondal, I. Mooney, J. Mrazkova, M. I. Nagy, C. J. Naim, A. S. Nain, J. D. Nam, M. Nasim, H. Nasrulloh, J. M. Nelson, M. Nie, G. Nigmatkulov, T. Niida, T. Nonaka, G. Odyniec, A. Ogawa, S. Oh, K. Okubo, B. S. Page, S. Pal, A. Pandav, A. Panday, A. K. Pandey, T. Pani, A. Paul, S. Paul, D. Pawlowska, C. Perkins, S. Ping, J. Pluta, B. R. Pokhrel, I. D. Ponce Pinto, M. Posik, E. Pottebaum, S. Prodhan, T. L. Protzman, A. Prozorov, V. Prozorova, N. K. Pruthi, M. Przybycien, J. Putschke, Y. Qi, Z. Qin, H. Qiu, C. Racz, S. K. Radhakrishnan, A. Rana, R. L. Ray, R. Reed, C. W. Robertson, M. Robotkova, M. A. Rosales Aguilar, D. Roy, P. Roy Chowdhury, L. Ruan, A. K. Sahoo, N. R. Sahoo, H. Sako, S. Salur, S. S. Sambyal, J. K. Sandhu, S. Sato, B. C. Schaefer, N. Schmitz, F-J. Seck, J. Seger, R. Seto, P. Seyboth, N. Shah, P. V. Shanmuganathan, T. Shao, M. Sharma, N. Sharma, R. Sharma, S. R. Sharma, A. I. Sheikh, D. Shen, D. Y. Shen, K. Shen, S. Shi, Y. Shi, E. Shulga, F. Si, J. Singh, S. Singha, P. Sinha, M. J. Skoby, N. Smirnov, Y. Söhngen, Y. Song, T. D. S. Stanislaus, M. Stefaniak, Y. Su, M. Sumbera, X. Sun, Y. Sun, B. Surrow, M. Svoboda, Z. W. Sweger, A. C. Tamis, A. H. Tang, Z. Tang, T. Tarnowsky, J. H. Thomas, A. R. Timmins, D. Tlusty, D. Torres Valladares, S. Trentalange, P. Tribedy, S. K. Tripathy, T. Truhlar, B. A. Trzeciak, O. D. Tsai, C. Y. Tsang, Z. Tu, J. E. Tyler, T. Ullrich, D. G. Underwood, G. Van Buren, J. Vanek, I. Vassiliev, F. Videbæk, S. A. Voloshin, F. Wang, G. Wang, G. Wang, J. S. Wang, J. Wang, K. Wang, X. Wang, Y. Wang, Y. Wang, Y. Wang, Z. Wang, Z. Wang, Z. Y. Wang, A. J. Watroba, J. C. Webb, P. C. Weidenkaff, G. D. Westfall, D. Wielanek, H. Wieman, G. Wilks, S. W. Wissink, R. Witt, C. P. Wong, J. Wu, X. Wu, X. Wu, X. Wu, B. Xi, Y. Xiao, Z. G. Xiao, G. Xie, W. Xie, H. Xu, N. Xu, Q. H. Xu, Y. Xu, Y. Xu, Y. Xu, Y. Xu, Z. Xu, Z. Xu, G. Yan, Z. Yan, C. Yang, Q. Yang, S. Yang, Y. Yang, Z. Ye, Z. Ye, L. Yi, Y. Yu, H. Zbroszczyk, W. Zha, C. Zhang, D. Zhang, J. Zhang, L. Zhang, S. Zhang, W. Zhang, X. Zhang, Y. Zhang, Y. Zhang, Y. Zhang, Y. Zhang, Z. Zhang, Z. Zhang, F. Zhao, J. Zhao, S. Zhou, Y. Zhou, X. Zhu, M. Zurek, M. Zyzak

Abstract

The STAR experiment reports new, high-precision measurements of the transverse single-spin asymmetries for $π^{\pm}$ within jets, namely the Collins asymmetries, from transversely polarized ${p^{\uparrow}p}$ collisions at $\sqrt{s}$ = 510 GeV. The energy-scaled distribution of jet transverse momentum, $x_{\mathrm{T}} = 2p_{\mathrm{T,jet}}/\sqrt s$, shows a remarkable consistency for Collins asymmetries of $π^{\pm}$ in jets between $\sqrt{s}$ = 200 GeV and 510 GeV. This indicates that the Collins asymmetries are nearly energy independent with, at most, a very weak scale dependence in $p^{\uparrow}p$ collisions. These results extend to high-momentum scales ($Q^2 \leq 3400$ GeV$^2$) and enable unique tests of evolution and universality in the transverse-momentum-dependent formalism, thus providing important constraints for the Collins fragmentation functions.

Energy Independence of the Collins Asymmetry in $p^{\uparrow}p$ Collisions

Abstract

The STAR experiment reports new, high-precision measurements of the transverse single-spin asymmetries for within jets, namely the Collins asymmetries, from transversely polarized collisions at = 510 GeV. The energy-scaled distribution of jet transverse momentum, , shows a remarkable consistency for Collins asymmetries of in jets between = 200 GeV and 510 GeV. This indicates that the Collins asymmetries are nearly energy independent with, at most, a very weak scale dependence in collisions. These results extend to high-momentum scales ( GeV) and enable unique tests of evolution and universality in the transverse-momentum-dependent formalism, thus providing important constraints for the Collins fragmentation functions.

Paper Structure

This paper contains 4 equations, 4 figures.

Figures (4)

  • Figure 1: The representation of the jet scattering plane along with the definitions of the azimuthal angles $\phi_S$ and $\phi_H$STARCollins2018.
  • Figure 2: Collins asymmetries, $A_{\mathrm{UT}}^{\sin(\phi_S - \phi_H)}$, as a function of jet $x_{\mathrm{T}}$ ($\equiv \frac{2p_{\mathrm{T,jet}}}{\sqrt{s}}$) for $\pi^{\pm}$ in $p^{\uparrow}p$ collisions at $\sqrt{s} = 510$ GeV (solid points), compared with previous results at $\sqrt{s} = 200$ GeV (open points). Vertical bars show the statistical uncertainties; boxes show the systematic uncertainties in $x_{\mathrm{T}}$ and $A_{\mathrm{UT}}$.
  • Figure 3: Collins asymmetries, $A_{\mathrm{UT}}^{\sin(\phi_S - \phi_H)}$ as a function of $\pi^{\pm}$ longitudinal momentum fraction $z$ in $p^{\uparrow}p$ collisions at $\sqrt{s} = 510$ GeV and 200 GeV. Vertical bars show the statistical uncertainties; boxes show the systematic uncertainties. Model uncertainties can be found in supply.
  • Figure 4: Collins asymmetries, $A_{\mathrm{UT}}^{\sin(\phi_S - \phi_H)}$, as a function of the $\pi^{\pm}$ momentum transverse to the jet axis, $j_{\mathrm{T}}$, in four longitudinal momentum fraction $z$ bins. The solid points show the results from this analysis of $\sqrt{s} = 510$ GeV $p^{\uparrow}p$ collisions with an average $\langle p_{\mathrm{T,jet}} \rangle = 32.3$ GeV/c, while the open points show the results from $\sqrt{s} = 200$ GeV $p^{\uparrow}p$ collisions with an average $\langle p_{\mathrm{T,jet}} \rangle = 13.3$ GeV/c STAR:2022hqg. Vertical bars show the statistical uncertainties and boxes show the systematic uncertainties in $j_{\mathrm{T}}$ and $A_{\mathrm{UT}}$.