relativistic collective coordinate system of solitons and spinning skyrmion
DESCRIPTION
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),. ,. - PowerPoint PPT PresentationTRANSCRIPT
Relativistic Collective Coordinate System of Solitons and Spinning Skyrmion
Toru KIKUCHI(Kyoto Univ.)
Based on arXiv:1002.2464 (Phys. Rev. D 82, 025017 )
arXiv:1008.3605with Hiroyuki HATA
(Kyoto Univ.)
Introduction
and its soliton solution (Skyrmion)
We consider Skyrme theory (2-flavors),
,
.
The Skyrmion is not rotationally symmetric, and has free parameter ;
collective coordinate
Substitute this into the action:
Skyrmions represent baryons.The collective coordinate describes the d.o.f. of spins and isospins.
Rigid body approximation [Adkins-Nappi-Witten, 83]
.
How do we extract its dynamics?
Ω ~ 10 s23 -1 velocity at r=1fm ~ light velocity
The necessity of the relativistic corrections
Large contribution of the rotational energy
②
Energy
0 Ωnucleon delta
939MeV 1232MeV
8% 30%
①
High frequency
The relativistic corrections seem to be important. How do Skyrmions deform due to spinning motion?
Deformation of spinning Skyrmions
lab frame body-fixed frame
spinning deformed Skyrmion static Skyrmion
. ..
(1)
( 2 )
( 3)
. ..
Deformation of spinning Skyrmions
Particular combinations of A,B,C correspond to three modes of deformation.
C
2B
-A+2B+C
. ..
left and right constant SO(3) transformations on
Deformation of spinning Skyrmions
rotations of field in real and iso space
These are the most general terms that share several properties with the rigid body approximation.ex.)
Requiring this to satisfy field theory EOM for constant , we get three differential equations for A,B,C.
For example, for ,
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.
Result 1. the shape of the baryons
original static Skyrmion
(at r=1 fm)
nucleondelta
Result 2. relativistic corrections to physical quantities
The fundamental parameter of the theory becomes better.
rigid body ours experiment
125MeV 108MeV 186MeV
However, most of the static properties of nucleon become worse.
0.68fm0.59fm 0.81fm
1.04fm1.17fm 0.94fm
1.971.65 2.79
・・・
0.95fm0.85fm・・・・・・ ・・・
0.82fm
A comment on the numerical results
delta 68 14 18: :nucleon 89 7 4: : (%)
Relativistic corrections are important. In fact, they are so large that our Ω-expansion is not a good one.
Conclusion
Looking at the numerical ratio of each term of the energy,
it does not seem that these are good convergent series.
Summary
We calculated the leading relativistic corrections to the spinning Skyrmions.
We found that the relativistic corrections are numerically important.
For more appropriate analysis of the spinning Skyrmion, a method beyond Ω-expansion is needed.
・
・
・
⇒ The shape of the baryons ⇒ Relativistic corrections to various physical quantities
Back up Slides
Exp. OursRigid
○
×
×
×
×
××
○
×
win: ○lose: ×
10%-20% relativistic corrections . Generally, the numerical values get worse.
numerical results for nucleon properties
1fm
(1)
( 2 )
( 3)
C
2B
-A+2B+C