Abstract
We perform a re-analysis of Belle data for the transverse Λ and \( \overline{\Lambda} \) polarization in e+e− annihilation processes within a transverse momentum dependent (TMD) factorization approach. We consider two data sets, one referring to the associated production of Λ’s with a light unpolarized hadron in an almost back-to-back configuration, and one for the inclusive Λ production, with the reconstruction of the thrust axis. We adopt the Collins-Soper-Sterman framework and employ the recent formulation on the factorization of single-inclusive hadron production. This extends a previous phenomenological study carried out in a more simplified TMD approach, leading to a new extraction of the polarizing fragmentation function (FF). While confirming several features of the previous analysis, here we include the proper QCD scale dependence of this TMD FF and carefully exploit the role of its nonperturbative component. The compatibility, within a unique TMD factorization scheme, of double and single-inclusive hadron production is discussed in detail. Moreover, we consider another data set for inclusive Λ production, at much larger energies, from the OPAL Collaboration, in order to test the consistency of the entire approach. Finally, we elaborate on some fundamental issues like the role of SU(2) isospin symmetry and the heavy quark contributions.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
L. Dick et al., Spin Effects in the Inclusive Reactions π± p(↑) π± + Anything at 8 GeV/c, Phys. Lett. B 57 (1975) 93 [INSPIRE].
R.D. Klem et al., Measurement of Asymmetries of Inclusive Pion Production in Proton Proton Interactions at 6 GeV/c and 11.8 GeV/c, Phys. Rev. Lett. 36 (1976) 929 [INSPIRE].
W.H. Dragoset et al., Asymmetries in Inclusive Proton-Nucleon Scattering at 11.75 GeV/c, Phys. Rev. D 18 (1978) 3939 [INSPIRE].
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 Λ’s and \( \overline{\Lambda} \)’s Produced by 400 GeV Protons, Phys. Rev. Lett. 41 (1978) 607 [INSPIRE].
D.L. Adams et al., Analyzing power in inclusive π+ and π− production at high xF with a 200 GeV polarized proton beam, Phys. Lett. B 264 (1991) 462 [INSPIRE].
FNAL-E704 collaborations, Large xF spin asymmetry in π0 production by 200 GeV polarized protons, Z. Phys. C 56 (1992) 181 [INSPIRE].
FNAL, E581 and E704 collaborations, First results for the two spin parameter ALL in π0 production by 200 GeV polarized protons and anti-protons, Phys. Lett. B 261 (1991) 197 [INSPIRE].
Fermilab E704 collaboration, Single spin asymmetries in inclusive charged pion production by transversely polarized anti-protons, Phys. Rev. Lett. 77 (1996) 2626 [INSPIRE].
STAR collaboration, Cross sections and transverse single-spin asymmetries in forward neutral pion production from proton collisions at \( \sqrt{s} \) = 200 GeV, Phys. Rev. Lett. 92 (2004) 171801 [hep-ex/0310058] [INSPIRE].
STAR collaboration, Forward neutral pion production in p + p and d + Au collisions at \( \sqrt{s_{\textrm{NN}}} \) = 200 GeV, Phys. Rev. Lett. 97 (2006) 152302 [nucl-ex/0602011] [INSPIRE].
PHENIX collaboration, Absence of suppression in particle production at large transverse momentum in \( \sqrt{s_{\textrm{NN}}} \) = 200 GeV d + Au collisions, Phys. Rev. Lett. 91 (2003) 072303 [nucl-ex/0306021] [INSPIRE].
PHENIX collaboration, Measurement of transverse single-spin asymmetries for mid-rapidity production of neutral pions and charged hadrons in polarized p + p collisions at \( \sqrt{s} \) = 200 GeV, Phys. Rev. Lett. 95 (2005) 202001 [hep-ex/0507073] [INSPIRE].
BRAHMS collaboration, Single Transverse Spin Asymmetries of Identified Charged Hadrons in Polarized p + p Collisions at \( \sqrt{s} \) = 62.4 GeV, Phys. Rev. Lett. 101 (2008) 042001 [arXiv:0801.1078] [INSPIRE].
BRAHMS collaboration, Production of mesons and baryons at high rapidity and high pT in proton-proton collisions at \( \sqrt{s} \) = 200 GeV, Phys. Rev. Lett. 98 (2007) 252001 [hep-ex/0701041] [INSPIRE].
B. Lundberg et al., Polarization in Inclusive Λ and \( \overline{\Lambda} \) Production at Large pT, Phys. Rev. D 40 (1989) 3557 [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 [INSPIRE].
G.L. Kane, J. Pumplin and W. Repko, Transverse Quark Polarization in Large pT Reactions, e+e− Jets, and Leptoproduction: A Test of QCD, Phys. Rev. Lett. 41 (1978) 1689 [INSPIRE].
HERMES collaboration, Longitudinal Spin Transfer to the Λ Hyperon in Semi-Inclusive Deep-Inelastic Scattering, Phys. Rev. D 74 (2006) 072004 [hep-ex/0607004] [INSPIRE].
HERMES collaboration, Transverse Polarization of Λ and \( \overline{\Lambda} \) 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 Λ polarization in νμ charged current interactions in the NOMAD experiment, Nucl. Phys. B 588 (2000) 3 [INSPIRE].
NOMAD collaboration, Measurement of the \( \overline{\Lambda} \) polarization in νμ charged current interactions in the NOMAD experiment, Nucl. Phys. B 605 (2001) 3 [hep-ex/0103047] [INSPIRE].
Belle collaboration, Observation of Transverse Λ/\( \overline{\Lambda} \) Hyperon Polarization in e+e− Annihilation at Belle, Phys. Rev. Lett. 122 (2019) 042001 [arXiv:1808.05000] [INSPIRE].
OPAL collaboration, Polarization and forward-backward asymmetry of Λ baryons in hadronic Z0 decays, Eur. Phys. J. C 2 (1998) 49 [hep-ex/9708027] [INSPIRE].
Z.-B. Kang, D.Y. Shao and F. Zhao, QCD resummation on single hadron transverse momentum distribution with the thrust axis, JHEP 12 (2020) 127 [arXiv:2007.14425] [INSPIRE].
L. Gamberg, Z.-B. Kang, D.Y. Shao, J. Terry and F. Zhao, Transverse Λ polarization in e+e− collisions, Phys. Lett. B 818 (2021) 136371 [arXiv:2102.05553] [INSPIRE].
U. D’Alesio, F. Murgia and M. Zaccheddu, First extraction of the Λ polarizing fragmentation function from Belle e+e− data, Phys. Rev. D 102 (2020) 054001 [arXiv:2003.01128] [INSPIRE].
D. Callos, Z.-B. Kang and J. Terry, Extracting the transverse momentum dependent polarizing fragmentation functions, Phys. Rev. D 102 (2020) 096007 [arXiv:2003.04828] [INSPIRE].
M. Anselmino, D. Boer, U. D’Alesio and F. Murgia, Lambda polarization from unpolarized quark fragmentation, Phys. Rev. D 63 (2001) 054029 [hep-ph/0008186] [INSPIRE].
Y. Makris, F. Ringer and W.J. Waalewijn, Joint thrust and TMD resummation in electron-positron and electron-proton collisions, JHEP 02 (2021) 070 [arXiv:2009.11871] [INSPIRE].
M. Boglione and A. Simonelli, Factorization of e+e− → H X cross section, differential in zh, PT and thrust, in the 2-jet limit, JHEP 02 (2021) 076 [arXiv:2011.07366] [INSPIRE].
M. Boglione and A. Simonelli, Universality-breaking effects in e+e− hadronic production processes, Eur. Phys. J. C 81 (2021) 96 [arXiv:2007.13674] [INSPIRE].
M. Boglione and A. Simonelli, Kinematic regions in the e+e− → h X factorized cross section in a 2-jet topology with thrust, JHEP 02 (2022) [arXiv:2109.11497] [INSPIRE].
U. D’Alesio, F. Murgia and M. Zaccheddu, General helicity formalism for two-hadron production in e+e− annihilation within a TMD approach, JHEP 10 (2021) 078 [arXiv:2108.05632] [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].
D. Pitonyak, M. Schlegel and A. Metz, Polarized hadron pair production from electron-positron annihilation, Phys. Rev. D 89 (2014) 054032 [arXiv:1310.6240] [INSPIRE].
A. Bacchetta, U. D’Alesio, M. Diehl and C.A. Miller, Single-spin asymmetries: The Trento conventions, Phys. Rev. D 70 (2004) 117504 [hep-ph/0410050] [INSPIRE].
J. Collins, L. Gamberg, A. Prokudin, T.C. Rogers, N. Sato and B. Wang, Relating Transverse Momentum Dependent and Collinear Factorization Theorems in a Generalized Formalism, Phys. Rev. D 94 (2016) 034014 [arXiv:1605.00671] [INSPIRE].
J. Collins, Foundations of Perturbative QCD, Cambridge University Press (2011) [DOI].
J. Collins and T. Rogers, Understanding the large-distance behavior of transverse-momentum-dependent parton densities and the Collins-Soper evolution kernel, Phys. Rev. D 91 (2015) 074020 [arXiv:1412.3820] [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].
J.-w. Qiu and G.F. Sterman, Single transverse spin asymmetries, Phys. Rev. Lett. 67 (1991) 2264 [INSPIRE].
J.-w. Qiu and G.F. Sterman, Single transverse spin asymmetries in direct photon production, Nucl. Phys. B 378 (1992) 52 [INSPIRE].
J.C. Collins, D.E. Soper and G.F. Sterman, Transverse Momentum Distribution in Drell-Yan Pair and W and Z Boson Production, Nucl. Phys. B 250 (1985) 199 [INSPIRE].
C.A. Aidala, B. Field, L.P. Gamberg and T.C. Rogers, Limits on transverse momentum dependent evolution from semi-inclusive deep inelastic scattering at moderate Q, Phys. Rev. D 89 (2014) 094002 [arXiv:1401.2654] [INSPIRE].
P. Sun, J. Isaacson, C.P. Yuan and F. Yuan, Nonperturbative functions for SIDIS and Drell-Yan processes, Int. J. Mod. Phys. A 33 (2018) 1841006 [arXiv:1406.3073] [INSPIRE].
F. Landry, R. Brock, P.M. Nadolsky and C.P. Yuan, Tevatron Run-1 Z boson data and Collins-Soper-Sterman resummation formalism, Phys. Rev. D 67 (2003) 073016 [hep-ph/0212159] [INSPIRE].
A.V. Konychev and P.M. Nadolsky, Universality of the Collins-Soper-Sterman nonperturbative function in gauge boson production, Phys. Lett. B 633 (2006) 710 [hep-ph/0506225] [INSPIRE].
A. Bacchetta, F. Delcarro, C. Pisano, M. Radici and A. Signori, Extraction of partonic transverse momentum distributions from semi-inclusive deep-inelastic scattering, Drell-Yan and Z-boson production, JHEP 06 (2017) 081 [arXiv:1703.10157] [INSPIRE].
MAP collaboration, Unpolarized transverse momentum distributions from a global fit of Drell-Yan and semi-inclusive deep-inelastic scattering data, JHEP 10 (2022) 127 [arXiv:2206.07598] [INSPIRE].
M. Boglione, J.O. Gonzalez-Hernandez and R. Taghavi, Transverse parton momenta in single inclusive hadron production in e+e− annihilation processes, Phys. Lett. B 772 (2017) 78 [arXiv:1704.08882] [INSPIRE].
M. Boglione, J.O. Gonzalez-Hernandez and A. Simonelli, Transverse momentum dependent fragmentation functions from recent BELLE data, Phys. Rev. D 106 (2022) 074024 [arXiv:2206.08876] [INSPIRE].
T. Becher, M. Neubert, L. Rothen and D.Y. Shao, Effective Field Theory for Jet Processes, Phys. Rev. Lett. 116 (2016) 192001 [arXiv:1508.06645] [INSPIRE].
T. Becher, M. Neubert, L. Rothen and D.Y. Shao, Factorization and Resummation for Jet Processes, JHEP 11 (2016) 019 [arXiv:1605.02737] [INSPIRE].
T. Becher, B.D. Pecjak and D.Y. Shao, Factorization for the light-jet mass and hemisphere soft function, JHEP 12 (2016) 018 [arXiv:1610.01608] [INSPIRE].
T. Becher, R. Rahn and D.Y. Shao, Non-global and rapidity logarithms in narrow jet broadening, JHEP 10 (2017) 030 [arXiv:1708.04516] [INSPIRE].
S. Caron-Huot, Resummation of non-global logarithms and the BFKL equation, JHEP 03 (2018) 036 [arXiv:1501.03754] [INSPIRE].
Z. Nagy and D.E. Soper, Summing threshold logs in a parton shower, JHEP 10 (2016) 019 [arXiv:1605.05845] [INSPIRE].
Z. Nagy and D.E. Soper, What is a parton shower?, Phys. Rev. D 98 (2018) 014034 [arXiv:1705.08093] [INSPIRE].
M. Dasgupta and G.P. Salam, Resummation of nonglobal QCD observables, Phys. Lett. B 512 (2001) 323 [hep-ph/0104277] [INSPIRE].
S. Albino, B.A. Kniehl and G. Kramer, AKK Update: Improvements from New Theoretical Input and Experimental Data, Nucl. Phys. B 803 (2008) 42 [arXiv:0803.2768] [INSPIRE].
D. de Florian, R. Sassot and M. Stratmann, Global analysis of fragmentation functions for pions and kaons and their uncertainties, Phys. Rev. D 75 (2007) 114010 [hep-ph/0703242] [INSPIRE].
M. Anselmino, M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia and A. Prokudin, The Role of Cahn and Sivers effects in deep inelastic scattering, Phys. Rev. D 71 (2005) 074006 [hep-ph/0501196] [INSPIRE].
H. Dembinski et al., scikit-hep/iminuit: v2.17.0, 2022 [ZENODO].
Z.-B. Kang, A. Prokudin, N. Sato and J. Terry, Efficient Fourier Transforms for Transverse Momentum Dependent Distributions, Comput. Phys. Commun. 258 (2021) 107611 [arXiv:1906.05949] [INSPIRE].
M. Anselmino et al., Sivers Effect for Pion and Kaon Production in Semi-Inclusive Deep Inelastic Scattering, Eur. Phys. J. A 39 (2009) 89 [arXiv:0805.2677] [INSPIRE].
K.-B. Chen, Z.-T. Liang, Y.-L. Pan, Y.-K. Song and S.-Y. Wei, Isospin Symmetry of Fragmentation Functions, Phys. Lett. B 816 (2021) 136217 [arXiv:2102.00658] [INSPIRE].
K.-b. Chen, Z.-t. Liang, Y.-k. Song and S.-y. Wei, Longitudinal and transverse polarizations of Λ hyperon in unpolarized SIDIS and e+e− annihilation, Phys. Rev. D 105 (2022) 034027 [arXiv:2108.07740] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2209.11670
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
D’Alesio, U., Gamberg, L., Murgia, F. et al. Transverse Λ polarization in e+e− processes within a TMD factorization approach and the polarizing fragmentation function. J. High Energ. Phys. 2022, 74 (2022). https://doi.org/10.1007/JHEP12(2022)074
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2022)074