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Relativistic Collective Coordinate System of Solitons and Spinning Skyrmion

Relativistic Collective Coordinate System of Solitons and Spinning Skyrmion. Toru KIKUCHI (Kyoto Univ.). Based on arXiv:1002.2464 ( Phys. Rev. D 82, 025017 ) arXiv:1008.3605. with Hiroyuki HATA (Kyoto Univ.) . Introduction. We consider Skyrme theory (2-flavors),. ,.

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Relativistic Collective Coordinate System of Solitons and Spinning Skyrmion

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  1. Relativistic Collective Coordinate System of Solitons and Spinning Skyrmion Toru KIKUCHI (Kyoto Univ.) Based on arXiv:1002.2464 (Phys. Rev. D 82, 025017) arXiv:1008.3605 with Hiroyuki HATA (Kyoto Univ.)

  2. Introduction We consider Skyrme theory (2-flavors), , and its soliton solution(Skyrmion) . The Skyrmion is not rotationally symmetric, and has free parameter ; collective coordinate

  3. Skyrmions represent baryons. The collective coordinate describes the d.o.f. of spins and isospins. How do we extract its dynamics? Rigid body approximation [Adkins-Nappi-Witten, 83] . Substitute this into the action:

  4. The necessity of the relativistic corrections Large contribution of the rotational energy ① 939MeV 1232MeV 8% 30% Energy 0 Ω nucleon delta High frequency ② 23 -1 velocity at r=1fm ～ light velocity Ω ～ 10 s The relativistic corrections seem to be important. How do Skyrmions deform due to spinning motion?

  5. Deformation of spinning Skyrmions . . . labframe body-fixed frame static Skyrmion spinning deformed Skyrmion

  6. Deformation of spinning Skyrmions . . . C (３) 2B Particular combinations of A,B,C correspond to three modes of deformation. (1) (２) -A+2B+C

  7. Deformation of spinning Skyrmions . . . These are the most general terms that share several properties with the rigid body approximation. ex.) left and right constant SO(3) transformations on rotations of field in real and iso space

  8. Requiring this to satisfy field theory EOM for constant , we get three differential equations for A,B,C. For example, for ,

  9. Energy and isospin with corrections To fix the parameters of the theory, take the data of nucleon: , delta: as inputs. We are now ready to obtain the numerical results.

  10. Result 1. the shape of the baryons delta nucleon original static Skyrmion (at r=1 fm)

  11. Result 2. relativistic corrections to physical quantities ours rigid body experiment 125MeV 108MeV 186MeV 0.59fm 0.68fm 0.81fm 1.04fm 0.94fm 1.17fm 0.85fm 0.95fm 0.82fm 2.79 1.65 1.97 ・・・ ・・・ ・・・ ・・・ The fundamental parameter of the theory becomes better. However, most of the static properties of nucleon become worse.

  12. A comment on the numerical results Looking at the numerical ratio of each term of the energy, ： ： nucleon 89 7 4 (%) ： ： delta 14 18 68 it does not seem that these are good convergent series. Conclusion Relativistic corrections are important. In fact, they are so large that our Ω-expansion is not a good one.

  13. Summary ・ We calculated the leading relativistic corrections to the spinning Skyrmions. ⇒ The shape of the baryons ⇒ Relativistic corrections to various physical quantities ・ We found that the relativistic corrections are numerically important. ・ For more appropriate analysis of the spinning Skyrmion, a method beyond Ω-expansion is needed.

  14. Back up Slides

  15. numerical results for nucleon properties win: ○ lose: × ○ × × ○ × × × × × Exp. Ours Rigid 10%-20% relativistic corrections . Generally, the numerical values get worse.

  16. 1fm

  17. C 2B (３) (1) (２) -A+2B+C

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