Chinese Physics C > 2025, Vol. 49 > Issue(8): 083101 DOI: 10.1088/1674-1137/add5c7

Asymmetry ${{\boldsymbol A}_{\boldsymbol{LL}}^{\bf\cos2\boldsymbol\phi}} $ in the polarized proton-proton Drell-Yan process within TMD factorization

1.
School of Physics and Electronic Engineering, Shanxi Normal University, Taiyuan 030031, China
2.
School of Physics, Zhengzhou University, Zhengzhou 450001, China
3.
School of Physics, Southeast University, Nanjing 211189, China

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Abstract：
We study $ \cos2\phi $ azimuthal asymmetry in doubly longitudinally polarized proton-proton Drell-Yan collisions within the transverse momentum dependent factorization framework. The asymmetry arises from the convolution of the longitudinal transversity distribution $ h_{1L}^{\perp} $ for both protons. Using the Bacchetta-Delcarro-Pisano-Radici-Signori parameterization for the nonperturbative Sudakov form factor and the Wandzura-Wilczek approximation for collinear $ h_{1L}^{\perp} $ , we predict the double spin asymmetry $ A_{LL}^{\cos2\phi} $ at RHIC and NICA kinematics. Our results demonstrate sensitivity to sea quark distributions, with the asymmetry reaching up to 25% for maximal sea quark contributions. These predictions highlight the potential of polarized Drell-Yan measurements to probe sea quark dynamics and advance our understanding of nucleon structures.

References

[1]	V. Barone, A. Drago, and P. G. Ratcliffe, Phys. Rept.359, 1 (2002) doi:10.1016/S0370-1573(01)00051-5
[2]	V. Barone, F. Bradamante, and A. Martin, Prog. Part. Nucl. Phys.65, 267 (2010) doi:10.1016/j.ppnp.2010.07.003
[3]	A. Bacchetta, M. Diehl, K. Goekeet al., JHEP02, 093 (2007) doi:10.1088/1126-6708/2007/02/093
[4]	P. J. Mulders and R. D. Tangerman, Nucl. Phys. B461, 197 (1996) doi:10.1016/0550-3213(95)00632-X
[5]	D. Boer and P. J. Mulders, Phys. Rev. D57, 5780 (1998) doi:10.1103/PhysRevD.57.5780
[6]	A. Kotzinian, Nucl. Phys. B441, 234 (1995) doi:10.1016/0550-3213(95)00098-D
[7]	A. M. Kotzinian and P. J. Mulders, Phys. Lett. B406, 373 (1997) doi:10.1016/S0370-2693(97)00708-9
[8]	A. Airapetianet al. (HERMES Collaboration), Phys. Rev. Lett.84, 4047 (2000) doi:10.1103/PhysRevLett.84.4047
[9]	A. Airapetianet al. (HERMES Collaboration), Phys. Lett. B562, 182 (2003) doi:10.1016/S0370-2693(03)00566-5
[10]	H. Avakianet al. (CLAS Collaboration), Phys. Rev. Lett.105, 262002 (2010) doi:10.1103/PhysRevLett.105.262002
[11]	Z. Lu, B. Q. Ma, and J. She, Phys. Rev. D84, 034010 (2011) doi:10.1103/PhysRevD.84.034010
[12]	J. Zhu and B. Q. Ma, Phys. Lett. B696, 246 (2011) doi:10.1016/j.physletb.2010.12.036
[13]	S. Boffi, A. V. Efremov, B. Pasquiniet al., Phys. Rev. D79, 094012 (2009) doi:10.1103/PhysRevD.79.094012
[14]	B. Q. Ma, I. Schmidt, and J. J. Yang, Phys. Rev. D63, 037501 (2001) doi:10.1103/PhysRevD.63.037501
[15]	B. Q. Ma, I. Schmidt, and J. J. Yang, Phys. Rev. D65, 034010 (2002) doi:10.1103/PhysRevD.65.034010
[16]	H. Li and Z. Lu, Eur. Phys. J. C82, 668 (2022) doi:10.1140/epjc/s10052-022-10562-z
[17]	J. Zhu and B. Q. Ma, Eur. Phys. J. C71, 1807 (2011) doi:10.1140/epjc/s10052-011-1807-y
[18]	S. Arnold, A. Metz, and M. Schlegel, Phys. Rev. D79, 034005 (2009) doi:10.1103/PhysRevD.79.034005
[19]	S. M. Aybat and T. C. Rogers, Phys. Rev. D83, 114042 (2011) doi:10.1103/PhysRevD.83.114042
[20]	J. C. Collins and T. C. Rogers, Phys. Rev. D87, 034018 (2013) doi:10.1103/PhysRevD.87.034018
[21]	M. G. Echevarría, A. Idilbi, and I. Scimemi, Phys. Lett. B726, 795 (2013) doi:10.1016/j.physletb.2013.09.003
[22]	D. Pitonyak, M. Schlegel, and A. Metz, Phys. Rev. D89, 054032 (2014) doi:10.1103/PhysRevD.89.054032
[23]	M. G. Echevarria, A. Idilbi, Z. B. Kanget al., Phys. Rev. D89, 074013 (2014) doi:10.1103/PhysRevD.89.074013
[24]	A. Bacchetta, F. Delcarro, C. Pisanoet al., JHEP06, 051 (2019) doi:10.1007/JHEP06(2017)081
[25]	X. Y. Wang, Z. Lu, and I. Schmidt, JHEP08, 137 (2017) doi:10.1007/JHEP08(2017)137
[26]	X. Wang and Z. Lu, Phys. Rev. D97, 054005 (2018) doi:10.1103/PhysRevD.97.054005
[27]	H. Li, X. Wang, and Z. Lu, Phys. Rev. D101, 054013 (2020) doi:10.1103/PhysRevD.101.054013
[28]	Z. B. Kang, A. Prokudin, P. Sunet al., Phys. Rev. D93, 014009 (2016) doi:10.1103/PhysRevD.93.014009
[29]	J. C. Collins and D. E. Soper, Nucl. Phys. B193, 381 (1981) doi:10.1016/0550-3213(81)90339-4
[30]	J. C. Collins, D. E. Soper, and G. F. Sterman, Nucl. Phys. B250, 1 (1985) doi:10.1016/0550-3213(85)90473-0
[31]	J. Collins, Camb. Monogr. Part. Phys. Nucl. Phys. Cosmol.32, 1 (2011) doi:10.1017/9781009401845
[32]	Z. Lu, B. Q. Ma, and J. Zhu, Phys. Rev. D84, 074036 (2011) doi:10.1103/PhysRevD.84.074036
[33]	A. Idilbi, X. d. Ji, J. P. Maet al., Phys. Rev. D70, 074021 (2004) doi:10.1103/PhysRevD.70.074021
[34]	J. C. Collins and F. Hautmann, Phys. Lett. B472, 129 (2000) doi:10.1016/S0370-2693(99)01384-2
[35]	Z. B. Kang, B. W. Xiao, and F. Yuan, Phys. Rev. Lett.107, 152002 (2011) doi:10.1103/PhysRevLett.107.152002
[36]	M. G. Echevarria, A. Idilbi, and I. Scimemi, Phys. Rev. D90, 014003 (2014) doi:10.1103/PhysRevD.90.014003
[37]	F. Landry, R. Brock, P. M. Nadolskyet al., Phys. Rev. D67, 073016 (2003) doi:10.1103/PhysRevD.67.073016
[38]	C. T. H. Davies, B. R. Webber, and W. J. Stirling, Nucl.Phys.B256, 413 (1985) doi:10.1016/0550-3213(85)90402-X
[39]	R. K. Ellis, D. A. Ross, and S. Veseli, Nucl. Phys. B503, 309 (1997) doi:10.1016/S0550-3213(97)00403-3
[40]	S. M. Aybat, J. C. Collins, J. W. Qiuet al., Phys. Rev. D85, 034043 (2012) doi:10.1103/PhysRevD.85.034043
[41]	P. Sun, J. Isaacson, C. P. Yuanet al., Int. J. Mod. Phys. A33, 1841006 (2018) doi:10.1142/S0217751X18410063
[42]	J. Collins and T. Rogers, Phys. Rev. D91, 074020 (2015) doi:10.1103/PhysRevD.91.074020
[43]	P. M. Nadolsky, D. R. Stump, and C. P. Yuan, Phys. Rev. D61, 014003 (2000) doi:10.1103/PhysRevD.64.059903
[44]	C. A. Aidala, B. Field, L. P. Gamberget al., Phys. Rev. D89, 094002 (2014) doi:10.1103/PhysRevD.89.094002
[45]	A. V. Konychev and P. M. Nadolsky, Phys. Lett. B633, 710 (2006) doi:10.1016/j.physletb.2005.12.063
[46]	A. Bacchettaet al. (MAP Collaboration), JHEP10, 127 (2022) doi:10.1007/JHEP10(2022)127
[47]	A. Bacchettaet al. (MAP Collaboration), JHEP08, 232 (2024) doi:10.1007/JHEP08(2024)232
[48]	A. Bacchettaet al. (MAP Collaboration), Phys. Rev. Lett.135(2), 021904 (2025) doi:10.1103/csc2-bj91
[49]	D. Boer, Phys. Rev. D60, 014012 (1999) doi:10.1103/PhysRevD.60.014012
[50]	X. D. Ji, J. P. Ma, and F. Yuan, Phys. Rev. D71, 034005 (2005) doi:10.1103/PhysRevD.71.034005
[51]	X. D. Ji, J. P. Ma, and F. Yuan, Phys. Lett. B597, 299 (2004) doi:10.1016/j.physletb.2004.07.026
[52]	H. Li, X. Wang, and Z. Lu, Phys. Rev. D104, 034020 (2021) doi:10.1103/PhysRevD.104.034020
[53]	J. Collins, L. Gamberg, A. Prokudinet al., Phys. Rev. D94, 034014 (2016) doi:10.1103/PhysRevD.94.034014
[54]	M. G. Echevarria, A. Idilbi, A. Schäferet al., Eur. Phys. J. C73, 2636 (2013) doi:10.1140/epjc/s10052-013-2636-y
[55]	J. W. Qiu and X. f. Zhang, Phys. Rev. Lett.86, 2724 (2001) doi:10.1103/PhysRevLett.86.2724
[56]	A. Bacchetta and A. Prokudin, Nucl. Phys. B875, 536 (2013) doi:10.1016/j.nuclphysb.2013.07.013
[57]	A. Prokudin, P. Sun, and F. Yuan, Phys. Lett. B750, 533 (2015) doi:10.1016/j.physletb.2015.09.064
[58]	J. Zhou, F. Yuan, and Z. T. Liang, Phys. Rev. D81, 054008 (2010) doi:10.1103/PhysRevD.81.054008
[59]	S. Bastami, H. Avakian, A. V. Efremovet al., JHEP06, 007 (2019) doi:10.1007/JHEP06(2019)007
[60]	D. Boer, L. Gamberg, B. Muschet al., JHEP10, 021 (2011) doi:10.1007/JHEP10(2011)021
[61]	H. L. Lai, M. Guzzi, J. Hustonet al., Phys. Rev. D82, 074024 (2010) doi:10.1103/PhysRevD.82.074024
[62]	R. L. Jaffe and X. D. Ji, Nucl. Phys. B375, 527 (1992) doi:10.1016/0550-3213(92)90110-W
[63]	D. de Florian, R. Sassot, M. Stratmannet al., Phys. Rev. D80, 034030 (2009) doi:10.1103/PhysRevD.80.034030
[64]	M. Botje, Comput. Phys. Commun.182, 490 (2011) doi:10.1016/j.cpc.2010.10.020
[65]	J. Zhou, F. Yuan, and Z. T. Liang, Phys. Rev. D79, 114022 (2009) doi:10.1103/PhysRevD.79.114022
[66]	Z. B. Kang and J. W. Qiu, Phys. Rev. D79, 016003 (2009) doi:10.1103/PhysRevD.79.016003
[67]	G. Bunce, N. Saito, J. Sofferet al., Ann. Rev. Nucl. Part. Sci.50, 525 (2000) doi:10.1146/annurev.nucl.50.1.525
[68]	V. M. Abazovet al.(SPD proto Collaboration), arXiv: 2102.00442

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Asymmetry ${{\boldsymbol A}_{\boldsymbol{LL}}^{\bf\cos2\boldsymbol\phi}} $ in the polarized proton-proton Drell-Yan process within TMD factorization

Abstract：

References

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