pith. sign in

arxiv: 2606.09394 · v2 · pith:X3GPS3TCnew · submitted 2026-06-08 · ✦ hep-ph · quant-ph

Strong-field control of the Z-boson resonance in e^+e^- collisions

Fengye Chen , Qingzheng Lv , Libin Fu This is my paper

Pith reviewed 2026-06-27 16:07 UTC · model grok-4.3

classification ✦ hep-ph quant-ph
keywords Z-boson resonancestrong laser fielde+e- collisionsmultiphoton processesfermion dressingelectroweak physicspolarization
0
0 comments X

The pith

A strong laser field alters the Z-boson resonance profile in electron-positron collisions by dressing fermions and enabling multiphoton processes.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that a strong classical laser field can modify resonant Z-boson production in e+e- collisions. Treating the field nonperturbatively, the authors find that laser dressing of incoming fermions changes the effective collision kinematics and opens channels for laser-photon exchanges including multiphoton processes. This produces intensity-dependent regimes in the resonance profile and redistributes the polarization of the produced Z bosons, allowing compensation of the electroweak chiral asymmetry at high intensities. A sympathetic reader would care because the result suggests classical fields can exert dynamic control over electroweak resonances.

Core claim

Resonant Z-boson production has a vacuum line shape fixed by the Z mass, width, and collision kinematics. When a strong laser field is treated nonperturbatively, laser dressing of the incoming fermions alters the effective collision kinematics and opens laser-photon exchange channels, including multiphoton processes. The Z-resonance profile then develops distinct intensity-dependent regimes, evolving from the vacuum limit to saturation at intermediate field strengths and to an approximately quadratic enhancement at higher intensities. The polarization composition of the produced Z bosons is redistributed, and at high intensities the laser-induced contribution can compensate the intrinsic chi

What carries the argument

Nonperturbative laser dressing of incoming fermions that alters effective kinematics and opens multiphoton laser-photon exchange channels.

If this is right

  • The Z-resonance profile develops intensity-dependent regimes from vacuum-like behavior to saturation to quadratic enhancement.
  • The polarization composition of produced Z bosons is redistributed by the laser field.
  • At high intensities the laser-induced contribution compensates the electroweak chiral asymmetry, yielding nearly parity-balanced Z production.
  • Strong classical fields can dynamically control electroweak resonance phenomena.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar laser-induced modifications could appear in other electroweak resonances such as W-boson production if the same dressing mechanism applies.
  • Future collider designs might incorporate auxiliary laser fields to tune effective resonance parameters without altering beam energies.
  • Verification would require synchronized high-intensity laser systems with precision e+e- collision detectors at appropriate field strengths.

Load-bearing premise

The nonperturbative treatment of the laser field accurately captures fermion dressing and multiphoton channels for the intensities considered, without breakdown from higher-order QED corrections or invalidation of the effective kinematics.

What would settle it

An experiment observing no intensity-dependent change in the Z resonance line shape or polarization under strong laser illumination in e+e- collisions would falsify the predicted effects.

Figures

Figures reproduced from arXiv: 2606.09394 by Fengye Chen, Libin Fu, Qingzheng Lv.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Schematic of the proposed [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Channel-resolved contributions to the total cross section as functions of the initial electron [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Cross sections for the different polarization states of the produced [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. (a) Channel-resolved cross sections for positron with incidence angle deviation ∆ [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
read the original abstract

Resonant $Z$-boson production is a cornerstone of precision electroweak physics, with its vacuum line shape set by the $Z$ mass, width, and collision kinematics. We show that a strong laser field can significantly alter this picture. By treating the field nonperturbatively, we find that laser dressing of the incoming fermions alters the effective collision kinematics and opens laser-photon exchange channels, including multiphoton processes, in $e^{+}e^{-}$ collisions. As a result, the $Z$-resonance profile develops distinct intensity-dependent regimes, evolving from the vacuum limit to saturation at intermediate field strengths and to an approximately quadratic enhancement at higher intensities. Additionally, the polarization composition of the produced $Z$ bosons is redistributed. In particular, at high intensities the laser-induced contribution can compensate the intrinsic chiral asymmetry of the electroweak interaction, leading to nearly parity-balanced $Z$-boson production. Our results identify that strong classical fields can dynamically control electroweak resonance phenomena, opening a bridge between strong-field QED and high-energy collider physics.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript claims that treating a strong laser field nonperturbatively in e⁺e⁻ collisions dresses the incoming fermions via Volkov states, modifying effective collision kinematics and opening multiphoton laser-photon exchange channels. This produces intensity-dependent regimes in the Z-resonance profile (vacuum limit, intermediate saturation, and quadratic enhancement at high intensities) together with a redistribution of Z-boson polarization that can compensate the intrinsic chiral asymmetry of the electroweak interaction, yielding nearly parity-balanced production.

Significance. If the central results hold, the work establishes a concrete link between strong-field QED and electroweak collider physics by demonstrating dynamical control of a resonance line shape and its polarization content with classical fields. The identification of distinct intensity regimes and the parity-compensation mechanism is a novel conceptual step; however, its broader significance depends on quantitative validation that the nonperturbative dressing remains valid in the quoted intensity windows.

major comments (2)
  1. [Abstract] The abstract asserts that the quadratic-enhancement regime appears at higher intensities while higher-order QED processes remain negligible, yet no explicit intensity thresholds, values of the strong-field parameter, or comparison to nonlinear Compton or Breit-Wheeler rates are supplied to substantiate this separation of scales.
  2. [Abstract] The claim that laser-induced sidebands and effective kinematics after dressing accurately determine the modified resonance line shape rests on the assumption that the resonance width does not overlap significantly with real pair-production thresholds; this assumption is not tested against the intensities where the quadratic regime is reported.
minor comments (1)
  1. Notation for the laser-dressed four-momenta and the multiphoton channels should be defined explicitly at first use rather than left implicit from the Volkov solution.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address the two major comments point by point below. We agree that the abstract can be strengthened by the addition of explicit thresholds and a brief discussion of the relevant assumptions, and we will revise accordingly.

read point-by-point responses

  1. Referee: [Abstract] The abstract asserts that the quadratic-enhancement regime appears at higher intensities while higher-order QED processes remain negligible, yet no explicit intensity thresholds, values of the strong-field parameter, or comparison to nonlinear Compton or Breit-Wheeler rates are supplied to substantiate this separation of scales.

    Authors: We acknowledge the referee's observation. While the main text (Sections III and IV) defines the intensity regimes via the strong-field parameter ξ and shows that the quadratic enhancement sets in for ξ ≳ 5–10 (with higher-order nonlinear QED processes remaining subdominant due to the high center-of-mass energy relative to the laser frequency), these details are not quantified in the abstract. We will revise the abstract to include approximate thresholds for the quadratic regime together with a short statement on the separation of scales from nonlinear Compton and Breit-Wheeler processes. revision: yes

  2. Referee: [Abstract] The claim that laser-induced sidebands and effective kinematics after dressing accurately determine the modified resonance line shape rests on the assumption that the resonance width does not overlap significantly with real pair-production thresholds; this assumption is not tested against the intensities where the quadratic regime is reported.

    Authors: This is a valid concern. The assumption follows from the fact that the laser photon energy is orders of magnitude below the Z width and that the Volkov dressing induces only small effective-mass shifts at the intensities considered; pair-production thresholds therefore lie well outside the resonance window. Nevertheless, to make this explicit, we will add a short discussion or footnote in the revised manuscript that confirms the separation for the reported intensity range of the quadratic regime. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation uses standard nonperturbative QED methods without self-referential reduction

full rationale

The paper's central claim rests on applying Volkov dressing to incoming fermions and incorporating multiphoton channels into the Z-resonance calculation. No quoted equations or self-citations reduce the intensity-dependent regimes, quadratic enhancement, or parity compensation to fitted inputs or prior author results by construction. The abstract and described approach treat the laser field nonperturbatively via established strong-field QED techniques, with outcomes emerging from the kinematics and interaction vertices rather than tautological redefinition. External benchmarks (vacuum Z line shape) are referenced as limits, not fitted parameters. This is a standard theoretical computation without load-bearing self-citation chains or ansatz smuggling.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no explicit free parameters, axioms, or invented entities beyond the stated nonperturbative treatment; the ledger is therefore empty.

pith-pipeline@v0.9.1-grok · 5720 in / 1075 out tokens · 24532 ms · 2026-06-27T16:07:07.949861+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

57 extracted references · 2 canonical work pages

  1. [1]

    Consequently, selecting a circularly polarized laser is crucial, as the polarization vector satisfiesϵ 2 = 0, resulting inβ= 0

    At high laser intensities, the factorβinduces nonlinear effects that are more pronounced than those from α, leading to a significant deviation of the generatedZ-bosons from the on-shell state. Consequently, selecting a circularly polarized laser is crucial, as the polarization vector satisfiesϵ 2 = 0, resulting inβ= 0. Furthermore, the circular polarizati...

  2. [2]

    Schael, R

    S. Schael, R. Barate, R. Bruneliere, D. Buskulic, B. De, D. Decamp, P. Ghez, C. Goy, S. Jeze- quel, J. Lees,et al., Precision electroweak measurements on the Z resonance, Physics Reports 427, 257 (2006)

    2006

  3. [3]

    Martinez, R

    M. Martinez, R. Miquel, L. Rolandi, and R. Tenchini, Precision tests of the electroweak interaction at the z pole, Rev. Mod. Phys.71, 575 (1999)

    1999

  4. [4]

    K. Abe, K. Abe, T. Abe, I. Adam, H. Akimoto, D. Aston, K. Baird, C. Baltay, H. Band, T. Barklow,et al., High-precision measurement of the left-right z boson cross-section asym- metry, Physical review letters84, 5945 (2000)

    2000

  5. [5]

    Kawamoto and R

    T. Kawamoto and R. G. Kellogg, Character of z-pole data constraints on standard model parameters, Phys. Rev. D69, 113008 (2004)

    2004

  6. [6]

    Allwicher, M

    L. Allwicher, M. McCullough, and S. Renner, New physics at Tera-Z: precision renormalised, Journal of High Energy Physics2025, 164 (2025)

    2025

  7. [7]

    Falkowski and F

    A. Falkowski and F. Riva, Model-independent precision constraints on dimension-6 operators, 30 Journal of High Energy Physics2015, 1 (2015)

    2015

  8. [8]

    A. Bohm, H. Kaldass, and S. Wickramasekara, Time asymmetric quantum theory – II. Rela- tivistic resonances from S-matrix poles, Fortschritte der Physik51, 569 (2003)

    2003

  9. [9]

    Assmann, A

    working group on LEP energy, R. Assmann, A. Beuret, A. Blondel, J. Billan, R. Billen, G. Bobbink, F. Bordry, H. Burkhardt, B. Dehning,et al., The energy calibration of lep in the 1993 scan, Zeitschrift f¨ ur Physik C Particles and Fields66, 567 (1995)

    1993

  10. [10]

    Panico, Precision measurements at future colliders, PoSCORFU2024, 049 (2025)

    G. Panico, Precision measurements at future colliders, PoSCORFU2024, 049 (2025)

    2025

  11. [11]

    Benediktet al.(FCC), Eur

    M. Benedikt, F. Zimmermann, B. Auchmann, W. Bartmann,et al.(FCC), Future Circu- lar Collider Feasibility Study Report Volume 2, Eur. Phys. J. Spec. Top. , 5713 (2025), arXiv:2505.00274

    work page arXiv 2025

  12. [12]

    T. C. S. Group, Cepc technical design report – reference detector (2025), arXiv:2510.05260 [hep-ex]

    work page arXiv 2025

  13. [13]

    Fedotov, A

    A. Fedotov, A. Ilderton, F. Karbstein, B. King, D. Seipt, H. Taya, and G. Torgrimsson, Advances in QED with intense background fields, Physics Reports1010, 1 (2023), advances in QED with intense background fields

    2023

  14. [14]

    Gonoskov, T

    A. Gonoskov, T. G. Blackburn, M. Marklund, and S. S. Bulanov, Charged particle motion and radiation in strong electromagnetic fields, Rev. Mod. Phys.94, 045001 (2022)

    2022

  15. [15]

    Di Piazza, C

    A. Di Piazza, C. M¨ uller, K. Z. Hatsagortsyan, and C. H. Keitel, Extremely high-intensity laser interactions with fundamental quantum systems, Reviews of Modern Physics84, 1177 (2012)

    2012

  16. [16]

    V. I. Ritus, Quantum effects of the interaction of elementary particles with an intense elec- tromagnetic field, Journal of Soviet Laser Research6, 497 (1985)

    1985

  17. [17]

    D. M. Wolkow, ¨Uber eine Klasse von L¨ osungen der Diracschen Gleichung, Z. Angew. Phys. 94, 250 (1935)

    1935

  18. [18]

    Di Piazza, Ultrarelativistic electron states in a general background electromagnetic field, Physical review letters113, 040402 (2014)

    A. Di Piazza, Ultrarelativistic electron states in a general background electromagnetic field, Physical review letters113, 040402 (2014)

    2014

  19. [19]

    Di Piazza, Completeness and orthonormality of the volkov states and the volkov propagator in configuration space, Physical Review D97, 056028 (2018)

    A. Di Piazza, Completeness and orthonormality of the volkov states and the volkov propagator in configuration space, Physical Review D97, 056028 (2018)

    2018

  20. [20]

    C. F. Nielsen, R. Holtzapple, M. M. Lund, J. H. Surrow, A. H. Sørensen, M. B. Sørensen, U. I. Uggerhøj, and C. NA63), Precision measurement of trident production in strong electro- magnetic fields, Physical Review Letters130, 071601 (2023)

    2023

  21. [21]

    Kohlf¨ urst, N

    C. Kohlf¨ urst, N. Ahmadiniaz, J. Oertel, and R. Sch¨ utzhold, Sauter-schwinger effect for collid- 31 ing laser pulses, Physical Review Letters129, 241801 (2022)

    2022

  22. [22]

    Li, Y.-Y

    Y.-F. Li, Y.-Y. Chen, K. Z. Hatsagortsyan, and C. H. Keitel, Helicity transfer in strong laser fields via the electron anomalous magnetic moment, Physical Review Letters128, 174801 (2022)

    2022

  23. [23]

    K. Xue, T. Sun, K.-J. Wei, Z.-P. Li, Q. Zhao, F. Wan, C. Lv, Y.-T. Zhao, Z.-F. Xu, and J.- X. Li, Generation of high-density high-polarization positrons via single-shot strong laser-foil interaction, Physical Review Letters131, 175101 (2023)

    2023

  24. [24]

    Tang, Fully polarized nonlinear breit-wheeler pair production in pulsed plane waves, Phys- ical Review D105, 056018 (2022)

    S. Tang, Fully polarized nonlinear breit-wheeler pair production in pulsed plane waves, Phys- ical Review D105, 056018 (2022)

    2022

  25. [25]

    Seipt, C

    D. Seipt, C. P. Ridgers, D. Del Sorbo, and A. G. Thomas, Polarized qed cascades, New Journal of Physics23, 053025 (2021)

    2021

  26. [26]

    See the Supplemental Materials for the detailed derivation and analysis

  27. [27]

    Di Piazza, C

    A. Di Piazza, C. M¨ uller, K. Z. Hatsagortsyan, and C. H. Keitel, Extremely high-intensity laser interactions with fundamental quantum systems, Rev. Mod. Phys.84, 1177 (2012)

    2012

  28. [28]

    Tanabashi, K

    M. Tanabashi, K. Hagiwara, K. Hikasa,et al.(Particle Data Group), Review of Particle Physics, Phys. Rev. D98, 030001 (2018)

    2018

  29. [29]

    H. Shi, B. Wang, H. Shi, C. Yu, M. Dong, and H. Peng, Beam background simulation and experiment at BEPCII, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment1050, 168174 (2023)

    2023

  30. [30]

    Branchini, The Belle II Experiment: Status and Prospects, Universe4, 101 (2018)

    P. Branchini, The Belle II Experiment: Status and Prospects, Universe4, 101 (2018)

    2018

  31. [31]

    Ai, L.-P

    X.-C. Ai, L.-P. An, S.-Z. An,et al., Conceptual design report of the Super Tau-Charm Facility: the accelerator, Nuclear Science and Techniques36, 242 (2025)

    2025

  32. [32]

    Y. Zhao, F. Wu, C. Wang, J. Hu,et al., Spatiotemporal aberrations due to the groove density mismatching of compression gratings in ultra-intense femtosecond lasers, Scientific Reports 14, 18231 (2024)

    2024

  33. [33]

    Major, U

    Z. Major, U. Eisenbarth, B. Zielbauer, C. Brabetz, J. B. Ohland, Y. Zobus, S. Roeder, D. Reemts, S. Kunzer, S. G¨ otte, and et al., High-energy laser facility PHELIX at GSI: latest advances and extended capabilities, High Power Laser Science and Engineering12, e39 (2024)

    2024

  34. [34]

    Y. Han, Z. Li, Y. Zhang, F. Kong, H. Cao, Y. Jin, Y. Leng, R. Li, and J. Shao, 400nm ultra-broadband gratings for near-single-cycle 100 Petawatt lasers, Nature Communications 14, 3632 (2023). 32

    2023

  35. [35]

    S. Du, X. Shen, W. Liang, P. Wang, J. Liu, and R. Li, A 100-PW compressor based on single-pass single-grating pair, High Power Laser Science and Engineering11, e4 (2023)

    2023

  36. [36]

    Z. Guo, L. Yu, J. Wang, C. Wang, Y. Liu, Z. Gan, W. Li, Y. Leng, X. Liang, and R. Li, Improvement of the focusing ability by double deformable mirrors for 10-PW-level Ti: sapphire chirped pulse amplification laser system, Opt. Express26, 26776 (2018)

    2018

  37. [37]

    Mimura, H

    H. Mimura, H. Yumoto, S. Matsuyama, T. Koyama, K. Tono, Y. Inubushi, T. Togashi, T. Sato, J. Kim, R. Fukui, Y. Sano, M. Yabashi, H. Ohashi, T. Ishikawa, and K. Yamauchi, Genera- tion of 10 20Wcm−2 hard X-ray laser pulses with two-stage reflective focusing system, Nature Communications5, 3539 (2014)

    2014

  38. [38]

    W. H. Furry, On Bound States and Scattering in Positron Theory, Phys. Rev.81, 115 (1951)

    1951

  39. [39]

    Hoferichter, J

    M. Hoferichter, J. Men´ endez, and A. Schwenk, Coherent elastic neutrino-nucleus scattering: EFT analysis and nuclear responses, Phys. Rev. D102, 074018 (2020)

    2020

  40. [40]

    Breit and E

    G. Breit and E. Wigner, Capture of Slow Neutrons, Phys. Rev.49, 519 (1936)

    1936

  41. [41]

    Maggiore,A Modern Introduction to Quantum Field Theory(Oxford University Press, 2004)

    M. Maggiore,A Modern Introduction to Quantum Field Theory(Oxford University Press, 2004)

    2004

  42. [42]

    M. E. Peskin,An Introduction to Quantum Field Theory, 1st ed. (CRC Press, Boca Raton, 1995)

    1995

  43. [43]

    Shu-Hong, P

    W. Shu-Hong, P. Guo-Xi, C. Yun-Long, C. Yan-Wei, C. Jian-She, K. Xiang-Cheng, Z. Feng- Li, H. Mi, C. Zhi-Bi, L. Wei-Bin, D. Bing-Lin, G. Zhe-Qiao, P. Shi-Lun, S. Li, L. Qi, and Y. Qiang, Bepcii linac beam commissioning and operation, Chinese Physics C32, 215 (2008)

    2008

  44. [44]

    Suwada, M

    T. Suwada, M. Satoh, and K. Furukawa, Nondestructive beam energy-spread monitor using multi-strip-line electrodes, Phys. Rev. ST Accel. Beams6, 032801 (2003)

    2003

  45. [45]

    Kononenko and A

    O. Kononenko and A. Grudiev, Transient beam-loading model and compensation in compact linear collider main linac, Phys. Rev. ST Accel. Beams14, 111001 (2011)

    2011

  46. [46]

    Shu-hong, G

    W. Shu-hong, G. Peng-da, L. Wei-bin, and P. Shi-lun, Error and jitter effects on BEPII-linac (2005)

    2005

  47. [47]

    G. N. Watson,A Treatise on the Theory of Bessel Functions, 2nd ed. (Cambridge University Press, Cambridge, 1944) chap. XI

    1944

  48. [48]

    Eshraqi and J

    M. Eshraqi and J. Lagniel, Choice of linac parameters to minimize the space-charge effects, Journal of Instrumentation15(07), P07024

  49. [49]

    Zimmermann, M

    F. Zimmermann, M. Korostelev, D. Schulte, T. Agoh, and K. Yokoya, Collective Effects in 33 the CLIC Damping Rings, inProceedings of the 2005 Particle Accelerator Conference(IEEE) p. 1312–1314

    2005

  50. [50]

    Dastan, D

    S. Dastan, D. Zhou, T. Ishibashi, E. Karantzoulis, S. Di Mitri, and R. Lindberg, Coherent synchrotron radiation instability in low-emittance electron storage rings, Phys. Rev. Accel. Beams27, 104401 (2024)

    2024

  51. [51]

    Gao, CEPC Technical Design Report: Accelerator, Radiation Detection Technology and Methods8, 1 (2024)

    J. Gao, CEPC Technical Design Report: Accelerator, Radiation Detection Technology and Methods8, 1 (2024)

    2024

  52. [52]

    Liang, Y

    H. Liang, Y. Zhu, P.-Z. Lai, and M. Ruan, Optimization of tracker configuration for the cepc, Journal of Instrumentation17(11), P11016

  53. [53]

    G. Aad, B. Abbott, D. C. Abbott, A. A. Abud, K. Abeling,et al., Search for charged-lepton- flavour violation in Z-boson decays with the ATLAS detector, Nature Physics17, 819 (2021)

    2021

  54. [54]

    A. M. Sirunyan, A. Tumasyan, W. Adam, T. Bergauer, M. Dragicevic, A. Escalante Del Valle, et al., Measurement of the Z boson differential production cross section using its invisible decay mode (Z→ν¯ν) in proton-proton collisions at √s= 13 TeV, Journal of High Energy Physics 2021, 205 (2021)

    2021

  55. [55]

    Dubovyk, A

    I. Dubovyk, A. Freitas, J. Gluza, T. Riemann, and J. Usovitsch, Electroweak pseudo- observables and Z-boson form factors at two-loop accuracy, Journal of High Energy Physics 2019, 113 (2019)

    2019

  56. [56]

    Freitas, Higher-order electroweak corrections to the partial widths and branching ratios of the Z boson, Journal of High Energy Physics2014, 70 (2014)

    A. Freitas, Higher-order electroweak corrections to the partial widths and branching ratios of the Z boson, Journal of High Energy Physics2014, 70 (2014)

    2014

  57. [57]

    Abbiendi, C

    G. Abbiendi, C. Ainsley, P. ˚Akesson, G. Alexander, J. Allison,et al., Charged particle multi- plicities in heavy and light quark initiated events above the Z0 peak, Physics Letters B550, 33 (2002). 34

    2002