Abstract
We study the production of polarized Λ-hyperons in electron-positron annihilation. We are particularly interested in the transverse-spin dependence of the cross section for unpolarized incident electron-positron pairs. At high energies this process may be described in the collinear twist-3 framework, where the hadronization transition of partons into a transversely polarized Λ-hyperon can be written in terms of collinear twist-3 fragmentation matrix elements. We calculate the hard partonic cross sections and interference terms in perturbative QCD to next-to-leading order accuracy. We find that the QCD equation of motion plays a crucial role in our analysis. As a byproduct, assuming the validity of QCD factorization for twist-3 observables at next-to-leading order, we derive the evolution equation for the relevant twist-3 fragmentation matrix element.
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References
G. Bunce et al., Λ0 hyperon polarization in inclusive production by 300 GeV protons on beryllium, Phys. Rev. Lett. 36 (1976) 1113 [INSPIRE].
L. Schachinger et al., A precise measurement of the Λ0 magnetic moment, Phys. Rev. Lett. 41 (1978) 1348 [INSPIRE].
K.J. Heller et al., Polarization of Ξ0 and Λ hyperons produced by 400 GeV/c protons, Phys. Rev. Lett. 51 (1983) 2025 [INSPIRE].
B. Lundberg et al., Polarization in inclusive Λ and \( \overline{\Lambda} \) production at large p T, Phys. Rev. D 40 (1989) 3557 [INSPIRE].
B.S. Yuldashev et al., Neutral strange particle production in p Ne-20 and pN interactions at 300 GeV/c, Phys. Rev. D 43 (1991) 2792 [INSPIRE].
E.J. Ramberg et al., Polarization of Λ and \( \overline{\Lambda} \) produced by 800 GeV protons, Phys. Lett. B 338 (1994) 403 [INSPIRE].
V. Fanti et al., A measurement of the transverse polarization of Λ hyperons produced in inelastic pN reactions at 450 GeV proton energy, Eur. Phys. J. C 6 (1999) 265 [INSPIRE].
HERA-B collaboration, Polarization of Λ and \( \overline{\Lambda} \) in 920 GeV fixed-target proton-nucleus collisions, Phys. Lett. B 638 (2006) 415 [hep-ex/0603047] [INSPIRE].
S. Erhan et al., Λ0 polarization in proton proton interactions at \( \sqrt{s}=53 \) GeV and 62 GeV, Phys. Lett. B 82 (1979) 301.
ATLAS collaboration, Measurement of the transverse polarization of Λ and \( \overline{\Lambda} \) hyperons produced in proton-proton collisions at \( \sqrt{s}=7 \) TeV using the ATLAS detector, Phys. Rev. D 91 (2015) 032004 [arXiv:1412.1692] [INSPIRE].
HERMES collaboration, Longitudinal Spin Transfer to the Lambda Hyperon in Semi-Inclusive Deep-Inelastic Scattering, Phys. Rev. D 74 (2006) 072004 [hep-ex/0607004] [INSPIRE].
HERMES collaboration, Transverse Polarization of Lambda and anti-Lambda Hyperons in Quasireal Photoproduction, Phys. Rev. D 76 (2007) 092008 [arXiv:0704.3133] [INSPIRE].
HERMES collaboration, Transverse polarization of Λ hyperons from quasireal photoproduction on nuclei, Phys. Rev. D 90 (2014) 072007 [arXiv:1406.3236] [INSPIRE].
NOMAD collaboration, Measurement of the Lambda polarization in ν μ charged current interactions in the NOMAD experiment, Nucl. Phys. B 588 (2000) 3 [INSPIRE].
NOMAD collaboration, Measurement of the \( \overline{\Lambda} \) polarization in muon-neutrino charged current interactions in the NOMAD experiment, Nucl. Phys. B 605 (2001) 3 [hep-ex/0103047] [INSPIRE].
M. Anselmino, D. Boer, U. D’Alesio and F. Murgia, Λ polarization from unpolarized quark fragmentation, Phys. Rev. D 63 (2001) 054029 [hep-ph/0008186] [INSPIRE].
M. Anselmino, D. Boer, U. D’Alesio and F. Murgia, Transverse Λ polarization in semiinclusive DIS, Phys. Rev. D 65 (2002) 114014 [hep-ph/0109186] [INSPIRE].
D. Boer, Z.-B. Kang, W. Vogelsang and F. Yuan, Test of the universality of naive-time-reversal-odd fragmentation functions, Phys. Rev. Lett. 105 (2010) 202001 [arXiv:1008.3543] [INSPIRE].
A. Metz and A. Vossen, Parton fragmentation functions, Prog. Part. Nucl. Phys. 91 (2016) 136 [arXiv:1607.02521] [INSPIRE].
OPAL collaboration, Polarization and forward-backward asymmetry of Λ baryons in hadronic Z 0 decays, Eur. Phys. J. C 2 (1998) 49 [hep-ex/9708027] [INSPIRE].
Belle collaboration, Production cross sections of hyperons and charmed baryons from e + e − annihilation near \( \sqrt{s}=10.52 \) GeV, Phys. Rev. D 97 (2018) 072005 [arXiv:1706.06791] [INSPIRE].
Belle collaboration, Observation of transverse \( \Lambda /\overline{\Lambda} \) hyperon polarization in e + e − annihilation at Belle, arXiv:1611.06648 [INSPIRE].
Belle collaboration, Observation of transverse \( \Lambda /\overline{\Lambda} \) hyperon polarization in e + e − annihilation at Belle, arXiv:1808.05000 [INSPIRE].
J.-w. Qiu and G.F. Sterman, Single transverse spin asymmetries in direct photon production, Nucl. Phys. B 378 (1992) 52 [INSPIRE].
J.-w. Qiu and G.F. Sterman, Single transverse spin asymmetries in hadronic pion production, Phys. Rev. D 59 (1999) 014004 [hep-ph/9806356] [INSPIRE].
C. Kouvaris, J.-W. Qiu, W. Vogelsang and F. Yuan, Single transverse-spin asymmetry in high transverse momentum pion production in pp collisions, Phys. Rev. D 74 (2006) 114013 [hep-ph/0609238] [INSPIRE].
H. Eguchi, Y. Koike and K. Tanaka, Single transverse spin asymmetry for large-p T pion production in semi-inclusive deep inelastic scattering, Nucl. Phys. B 752 (2006) 1 [hep-ph/0604003] [INSPIRE].
H. Eguchi, Y. Koike and K. Tanaka, Twist-3 formalism for single transverse spin asymmetry reexamined: semi-inclusive deep inelastic scattering, Nucl. Phys. B 763 (2007) 198 [hep-ph/0610314] [INSPIRE].
Y. Koike and T. Tomita, Soft-fermion-pole contribution to single-spin asymmetry for pion production in pp collisions, Phys. Lett. B 675 (2009) 181 [arXiv:0903.1923] [INSPIRE].
H. Beppu, Y. Koike, K. Tanaka and S. Yoshida, Contribution of twist-3 multi-gluon correlation functions to single spin asymmetry in semi-inclusive deep inelastic scattering, Phys. Rev. D 82 (2010) 054005 [arXiv:1007.2034] [INSPIRE].
Y. Koike and S. Yoshida, Three-gluon contribution to the single spin asymmetry in Drell-Yan and direct-photon processes, Phys. Rev. D 85 (2012) 034030 [arXiv:1112.1161] [INSPIRE].
Z.-B. Kang, F. Yuan and J. Zhou, Twist-three fragmentation function contribution to the single spin asymmetry in pp collisions, Phys. Lett. B 691 (2010) 243 [arXiv:1002.0399] [INSPIRE].
A. Metz and D. Pitonyak, Fragmentation contribution to the transverse single-spin asymmetry in proton-proton collisions, Phys. Lett. B 723 (2013) 365 [Erratum ibid. B 762 (2016) 549] [arXiv:1212.5037] [INSPIRE].
K. Kanazawa and Y. Koike, Contribution of twist-3 fragmentation function to single transverse-spin asymmetry in semi-inclusive deep inelastic scattering, Phys. Rev. D 88 (2013) 074022 [arXiv:1309.1215] [INSPIRE].
H. Beppu, K. Kanazawa, Y. Koike and S. Yoshida, Three-gluon contribution to the single spin asymmetry for light hadron production in pp collision, Phys. Rev. D 89 (2014) 034029 [arXiv:1312.6862] [INSPIRE].
D. Pitonyak, Transverse spin observables in hard-scattering hadronic processes within collinear factorization, Int. J. Mod. Phys. A 31 (2016) 1630049 [arXiv:1608.05353] [INSPIRE].
Y. Kanazawa and Y. Koike, Polarization in hadronic Lambda hyperon production and chiral odd twist-three quark distribution, Phys. Rev. D 64 (2001) 034019 [hep-ph/0012225] [INSPIRE].
J. Zhou, F. Yuan and Z.-T. Liang, Hyperon polarization in unpolarized scattering processes, Phys. Rev. D 78 (2008) 114008 [arXiv:0808.3629] [INSPIRE].
K. Kanazawa, A. Metz, D. Pitonyak and M. Schlegel, Single-spin asymmetries in the leptoproduction of transversely polarized Λ hyperons, Phys. Lett. B 744 (2015) 385 [arXiv:1503.02003] [INSPIRE].
Y. Koike, K. Yabe and S. Yoshida, Hyperon polarization from the twist-3 distribution in unpolarized proton-proton collision, Phys. Rev. D 92 (2015) 094011 [arXiv:1509.06830] [INSPIRE].
Y. Koike, A. Metz, D. Pitonyak, K. Yabe and S. Yoshida, Twist-3 fragmentation contribution to polarized hyperon production in unpolarized hadronic collisions, Phys. Rev. D 95 (2017) 114013 [arXiv:1703.09399] [INSPIRE].
W. Vogelsang and F. Yuan, Next-to-leading order calculation of the single transverse spin asymmetry in the Drell-Yan process, Phys. Rev. D 79 (2009) 094010 [arXiv:0904.0410] [INSPIRE].
Z.-B. Kang, I. Vitev and H. Xing, Transverse momentum-weighted Sivers asymmetry in semi-inclusive deep inelastic scattering at next-to-leading order, Phys. Rev. D 87 (2013) 034024 [arXiv:1212.1221] [INSPIRE].
L.-Y. Dai, Z.-B. Kang, A. Prokudin and I. Vitev, Next-to-leading order transverse momentum-weighted Sivers asymmetry in semi-inclusive deep inelastic scattering: the role of the three-gluon correlator, Phys. Rev. D 92 (2015) 114024 [arXiv:1409.5851] [INSPIRE].
S. Yoshida, New pole contribution to P h⊥ -weighted single-transverse spin asymmetry in semi-inclusive deep inelastic scattering, Phys. Rev. D 93 (2016) 054048 [arXiv:1601.07737] [INSPIRE].
A.P. Chen, J.P. Ma and G.P. Zhang, One-loop corrections to single spin asymmetries at twist-3 in Drell-Yan processes, Phys. Rev. D 95 (2017) 074005 [arXiv:1607.08676] [INSPIRE].
A.P. Chen, J.P. Ma and G.P. Zhang, One-loop corrections of single spin asymmetries in semi-inclusive DIS, Phys. Rev. D 97 (2018) 054003 [arXiv:1708.09091] [INSPIRE].
S. Meissner and A. Metz, Partonic pole matrix elements for fragmentation, Phys. Rev. Lett. 102 (2009) 172003 [arXiv:0812.3783] [INSPIRE].
L.P. Gamberg, A. Mukherjee and P.J. Mulders, A model independent analysis of gluonic pole matrix elements and universality of TMD fragmentation functions, Phys. Rev. D 83 (2011) 071503 [arXiv:1010.4556] [INSPIRE].
Y. Koike, K. Tanaka and S. Yoshida, Drell-Yan double-spin asymmetry A(LT) in polarized \( p\overline{p} \) collisions: Wandzura-Wilczek contribution, Phys. Lett. B 668 (2008) 286 [arXiv:0805.2289] [INSPIRE].
J. Zhou, F. Yuan and Z.-T. Liang, Transverse momentum dependent quark distributions and polarized Drell-Yan processes, Phys. Rev. D 81 (2010) 054008 [arXiv:0909.2238] [INSPIRE].
Z.T. Liang et al., Double spin asymmetry A LT in direct photon production, Phys. Lett. B 712 (2012) 235 [arXiv:1203.3956] [INSPIRE].
A. Metz, D. Pitonyak, A. Schaefer and J. Zhou, Analysis of the double-spin asymmetry A LT in inelastic nucleon-nucleon collisions, Phys. Rev. D 86 (2012) 114020 [arXiv:1210.6555] [INSPIRE].
K. Kanazawa, A. Metz, D. Pitonyak and M. Schlegel, Longitudinal-transverse double-spin asymmetries in single-inclusive leptoproduction of hadrons, Phys. Lett. B 742 (2015) 340 [arXiv:1411.6459] [INSPIRE].
Y. Koike, D. Pitonyak and S. Yoshida, Twist-3 effect from the longitudinally polarized proton for A LT in hadron production from pp collisions, Phys. Lett. B 759 (2016) 75 [arXiv:1603.07908] [INSPIRE].
K. Kanazawa et al., Operator constraints for twist-3 functions and Lorentz invariance properties of twist-3 observables, Phys. Rev. D 93 (2016) 054024 [arXiv:1512.07233] [INSPIRE].
X.-D. Ji, Chiral odd and spin dependent quark fragmentation functions and their applications, Phys. Rev. D 49 (1994) 114 [hep-ph/9307235] [INSPIRE].
K. Chen, G.R. Goldstein, R.L. Jaffe and X.-D. Ji, Probing quark fragmentation functions for spin 1/2 baryon production in unpolarized e + e − annihilation, Nucl. Phys. B 445 (1995) 380 [hep-ph/9410337] [INSPIRE].
P.J. Mulders and R.D. Tangerman, The complete tree level result up to order 1/Q for polarized deep inelastic leptoproduction, Nucl. Phys. B 461 (1996) 197 [Erratum ibid. B 484 (1997) 538] [hep-ph/9510301] [INSPIRE].
D. Boer, R. Jakob and P.J. Mulders, Asymmetries in polarized hadron production in e + e − annihilation up to order 1/Q, Nucl. Phys. B 504 (1997) 345 [hep-ph/9702281] [INSPIRE].
J.C. Collins and D.E. Soper, Parton distribution and decay functions, Nucl. Phys. B 194 (1982) 445 [INSPIRE].
J. Collins, Foundations of perturbative QCD, Camb. Monogr. Part. Phys. Nucl. Phys. Cosmol. 32 (2011) 1 [INSPIRE].
J.C. Collins, Leading twist single transverse-spin asymmetries: Drell-Yan and deep inelastic scattering, Phys. Lett. B 536 (2002) 43 [hep-ph/0204004] [INSPIRE].
X.-d. Ji and F. Yuan, Parton distributions in light cone gauge: where are the final state interactions?, Phys. Lett. B 543 (2002) 66 [hep-ph/0206057] [INSPIRE].
A.V. Belitsky, X. Ji and F. Yuan, Final state interactions and gauge invariant parton distributions, Nucl. Phys. B 656 (2003) 165 [hep-ph/0208038] [INSPIRE].
D. Boer, P.J. Mulders and F. Pijlman, Universality of T odd effects in single spin and azimuthal asymmetries, Nucl. Phys. B 667 (2003) 201 [hep-ph/0303034] [INSPIRE].
J.C. Collins and A. Metz, Universality of soft and collinear factors in hard-scattering factorization, Phys. Rev. Lett. 93 (2004) 252001 [hep-ph/0408249] [INSPIRE].
A. Bacchetta et al., Semi-inclusive deep inelastic scattering at small transverse momentum, JHEP 02 (2007) 093 [hep-ph/0611265] [INSPIRE].
Y. Koike and S. Yoshida, Probing the three-gluon correlation functions by the single spin asymmetry in p ↑ p → DX, Phys. Rev. D 84 (2011) 014026 [arXiv:1104.3943] [INSPIRE].
R.L. Jaffe, Parton distribution functions for twist four, Nucl. Phys. B 229 (1983) 205 [INSPIRE].
N. Christ and T.D. Lee, Possible tests of Cst and Tst invariances in l ± + N → l ± + Γ and A → B + e + +e −, Phys. Rev. 143 (1966) 1310 [INSPIRE].
A. Metz, M. Schlegel and K. Goeke, Transverse single spin asymmetries in inclusive deep-inelastic scattering, Phys. Lett. B 643 (2006) 319 [hep-ph/0610112] [INSPIRE].
A. Afanasev, M. Strikman and C. Weiss, Transverse target spin asymmetry in inclusive DIS with two-photon exchange, Phys. Rev. D 77 (2008) 014028 [arXiv:0709.0901] [INSPIRE].
A. Metz et al., Single-spin asymmetries in inclusive deep inelastic scattering and multiparton correlations in the nucleon, Phys. Rev. D 86 (2012) 094039 [arXiv:1209.3138] [INSPIRE].
M. Schlegel, Partonic description of the transverse target single-spin asymmetry in inclusive deep-inelastic scattering, Phys. Rev. D 87 (2013) 034006 [arXiv:1211.3579] [INSPIRE].
K. Goeke, A. Metz and M. Schlegel, Parameterization of the quark-quark correlator of a spin-1/2 hadron, Phys. Lett. B 618 (2005) 90 [hep-ph/0504130] [INSPIRE].
G. Leibbrandt, Noncovariant gauges: quantization of Yang-Mills and Chern-Simons theory in axial type gauges, World Scientific, Singapore (1994).
D. de Florian, M. Stratmann and W. Vogelsang, QCD analysis of unpolarized and polarized Λ baryon production in leading and next-to-leading order, Phys. Rev. D 57 (1998) 5811 [hep-ph/9711387] [INSPIRE].
D. de Florian, M. Stratmann and W. Vogelsang, Polarized Λ baryon production in pp collisions, Phys. Rev. Lett. 81 (1998) 530 [hep-ph/9802432] [INSPIRE].
G. ’t Hooft and M.J.G. Veltman, Regularization and renormalization of gauge fields, Nucl. Phys. B 44 (1972) 189 [INSPIRE].
P. Breitenlohner and D. Maison, Dimensional renormalization and the action principle, Commun. Math. Phys. 52 (1977) 11 [INSPIRE].
J.C. Collins and J.-w. Qiu, A new derivation of the Altarelli-Parisi equations, Phys. Rev. D 39 (1989) 1398 [INSPIRE].
A.V. Belitsky and E.A. Kuraev, Evolution of chiral odd spin independent fracture functions in quantum chromodynamics, Nucl. Phys. B 499 (1997) 301 [hep-ph/9612256] [INSPIRE].
Z.-B. Kang, QCD evolution of naive-time-reversal-odd fragmentation functions, Phys. Rev. D 83 (2011) 036006 [arXiv:1012.3419] [INSPIRE].
J.P. Ma and G.P. Zhang, Evolution of chirality-odd twist-3 fragmentation functions, Phys. Lett. B 772 (2017) 559 [arXiv:1701.04141] [INSPIRE].
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Gamberg, L., Kang, ZB., Pitonyak, D. et al. Polarized hyperon production in single-inclusive electron-positron annihilation at next-to-leading order. J. High Energ. Phys. 2019, 111 (2019). https://doi.org/10.1007/JHEP01(2019)111
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DOI: https://doi.org/10.1007/JHEP01(2019)111