Color confinement mechanism and the type of the QCD vacuum Tsuneo Suzuki (Kanazawa Univ.)...
-
Upload
dominick-hunter -
Category
Documents
-
view
216 -
download
2
Transcript of Color confinement mechanism and the type of the QCD vacuum Tsuneo Suzuki (Kanazawa Univ.)...
![Page 1: Color confinement mechanism and the type of the QCD vacuum Tsuneo Suzuki (Kanazawa Univ.) Collaborators: K.Ishiguro, Y.Mori, Y.Nakamura, T.Sekido ( M.Polikarpov,](https://reader037.fdocuments.us/reader037/viewer/2022110208/56649de55503460f94adca02/html5/thumbnails/1.jpg)
Color confinement mechanism and
the type of the QCD vacuum
Tsuneo Suzuki (Kanazawa Univ.)
Collaborators: K.Ishiguro, Y.Mori, Y.Nakamura, T.Sekido( M.Polikarpov, M.Chernodub, V.Zakharov)
![Page 2: Color confinement mechanism and the type of the QCD vacuum Tsuneo Suzuki (Kanazawa Univ.) Collaborators: K.Ishiguro, Y.Mori, Y.Nakamura, T.Sekido ( M.Polikarpov,](https://reader037.fdocuments.us/reader037/viewer/2022110208/56649de55503460f94adca02/html5/thumbnails/2.jpg)
1. Color confinement mechanism
Color confinement could be understood as the dual Meissner effect. (’75 ‘tHooft & Mandelstam)
How to find a magnetically charged particle from QCD?
Perform a partial gauge-fixing called abelian projection.QCD is reduced to U(1)2 theory with magnetic monopoles. If the monopoles condense, the dual Meissner effect occurs.(’80 ‘tHooft)
![Page 3: Color confinement mechanism and the type of the QCD vacuum Tsuneo Suzuki (Kanazawa Univ.) Collaborators: K.Ishiguro, Y.Mori, Y.Nakamura, T.Sekido ( M.Polikarpov,](https://reader037.fdocuments.us/reader037/viewer/2022110208/56649de55503460f94adca02/html5/thumbnails/3.jpg)
2. Lattice QCD study of abelian projection
When we perform a partial gauge-fixing called Maximally abelian (MA) gauge (’87 Kronfeld et al.), the ‘tHooft-Mandelstam conjecture seems to be correct.
1.Abelian dominance, monopole dominance
2. Monopole condensation occurs. Entropy dominates over energy.
3.The dual Meissner effect is observed clearly.
(M.Chernodub and M.Polikarpov, hep-th/9710205; T.Suzuki,P.T.P.Suppl.131(‘98)633;
R.W. Haymaker, P.R.315, 153 (‘99), H.Shiba and T.Suzuki, P.L. B 351, 519 (‘95), Y.Koma et al, KI & PRD68 (2003) 114504 and references therein)
![Page 4: Color confinement mechanism and the type of the QCD vacuum Tsuneo Suzuki (Kanazawa Univ.) Collaborators: K.Ishiguro, Y.Mori, Y.Nakamura, T.Sekido ( M.Polikarpov,](https://reader037.fdocuments.us/reader037/viewer/2022110208/56649de55503460f94adca02/html5/thumbnails/4.jpg)
Dual Meissner effect:
Electric field flux tube
Monopole current distribution
Dual Meissner picture is seen very beautifully.
![Page 5: Color confinement mechanism and the type of the QCD vacuum Tsuneo Suzuki (Kanazawa Univ.) Collaborators: K.Ishiguro, Y.Mori, Y.Nakamura, T.Sekido ( M.Polikarpov,](https://reader037.fdocuments.us/reader037/viewer/2022110208/56649de55503460f94adca02/html5/thumbnails/5.jpg)
3. gauge-independent?
Is the dual Meissner effect in the infrared region gauge-independent?
(1)Polyakov gauge where Polyakov loops are diagonalized. Monopoles are always static. Do not contribute to the usual abelian Wilson loop. Monopole dominance is broken.(M.Chernodub ’00)
(2)Landau gauge: Configurations are so smooth. No DeGrand-Toussaint monopoles.
No?
![Page 6: Color confinement mechanism and the type of the QCD vacuum Tsuneo Suzuki (Kanazawa Univ.) Collaborators: K.Ishiguro, Y.Mori, Y.Nakamura, T.Sekido ( M.Polikarpov,](https://reader037.fdocuments.us/reader037/viewer/2022110208/56649de55503460f94adca02/html5/thumbnails/6.jpg)
Existence of the linear potential indicates the flux-squeezing occurs generally in QCD.
Is it understood as the dual Meissner effect?What squeezes the electric field?
![Page 7: Color confinement mechanism and the type of the QCD vacuum Tsuneo Suzuki (Kanazawa Univ.) Collaborators: K.Ishiguro, Y.Mori, Y.Nakamura, T.Sekido ( M.Polikarpov,](https://reader037.fdocuments.us/reader037/viewer/2022110208/56649de55503460f94adca02/html5/thumbnails/7.jpg)
1)Imroved Iwasaki gauge action: Nearer to the continuum limit
2) (Landau) Gauge fixing: study of electric and magnetic field flux directly
3) Comparison with MA gauge + U1 Landau
4.Study of flux in Landau gauge(T.Suzuki et al, Phys. Rev. Lett. 94, 132001 (2005))
![Page 8: Color confinement mechanism and the type of the QCD vacuum Tsuneo Suzuki (Kanazawa Univ.) Collaborators: K.Ishiguro, Y.Mori, Y.Nakamura, T.Sekido ( M.Polikarpov,](https://reader037.fdocuments.us/reader037/viewer/2022110208/56649de55503460f94adca02/html5/thumbnails/8.jpg)
Define abelian field strength
MA
![Page 9: Color confinement mechanism and the type of the QCD vacuum Tsuneo Suzuki (Kanazawa Univ.) Collaborators: K.Ishiguro, Y.Mori, Y.Nakamura, T.Sekido ( M.Polikarpov,](https://reader037.fdocuments.us/reader037/viewer/2022110208/56649de55503460f94adca02/html5/thumbnails/9.jpg)
Non-abelian Wilson loops (a source of a Q-Qbar pair)
Electric field
Magnetic field
![Page 10: Color confinement mechanism and the type of the QCD vacuum Tsuneo Suzuki (Kanazawa Univ.) Collaborators: K.Ishiguro, Y.Mori, Y.Nakamura, T.Sekido ( M.Polikarpov,](https://reader037.fdocuments.us/reader037/viewer/2022110208/56649de55503460f94adca02/html5/thumbnails/10.jpg)
Results 1
Abelian electric field is squeezed also as in non-abelian one. Other components are almost zero. Quark-antiquark are located in z direction.
R
r
![Page 11: Color confinement mechanism and the type of the QCD vacuum Tsuneo Suzuki (Kanazawa Univ.) Collaborators: K.Ishiguro, Y.Mori, Y.Nakamura, T.Sekido ( M.Polikarpov,](https://reader037.fdocuments.us/reader037/viewer/2022110208/56649de55503460f94adca02/html5/thumbnails/11.jpg)
Results 2: Electric field is squeezed by abelian magnetic displacement current
Magnetic solenoidal current
![Page 12: Color confinement mechanism and the type of the QCD vacuum Tsuneo Suzuki (Kanazawa Univ.) Collaborators: K.Ishiguro, Y.Mori, Y.Nakamura, T.Sekido ( M.Polikarpov,](https://reader037.fdocuments.us/reader037/viewer/2022110208/56649de55503460f94adca02/html5/thumbnails/12.jpg)
Solenoidal current observed !!!
Landau gauge perpendicular plane
![Page 13: Color confinement mechanism and the type of the QCD vacuum Tsuneo Suzuki (Kanazawa Univ.) Collaborators: K.Ishiguro, Y.Mori, Y.Nakamura, T.Sekido ( M.Polikarpov,](https://reader037.fdocuments.us/reader037/viewer/2022110208/56649de55503460f94adca02/html5/thumbnails/13.jpg)
Landau gauge MA gauge
Landau gauge
MA Gauge
( Bali (’98))
![Page 14: Color confinement mechanism and the type of the QCD vacuum Tsuneo Suzuki (Kanazawa Univ.) Collaborators: K.Ishiguro, Y.Mori, Y.Nakamura, T.Sekido ( M.Polikarpov,](https://reader037.fdocuments.us/reader037/viewer/2022110208/56649de55503460f94adca02/html5/thumbnails/14.jpg)
Comments1.The positions of the peak of the solenoidal current distribution in Landau and in MA are almost the same.
2. The dual Meissner effect is observed also in Landau gauge, where naive DT lattice monopoles do not exist. New monopole or essentially non-static?
The dual Meissner effect must be a universalconfinement mechanism.
![Page 15: Color confinement mechanism and the type of the QCD vacuum Tsuneo Suzuki (Kanazawa Univ.) Collaborators: K.Ishiguro, Y.Mori, Y.Nakamura, T.Sekido ( M.Polikarpov,](https://reader037.fdocuments.us/reader037/viewer/2022110208/56649de55503460f94adca02/html5/thumbnails/15.jpg)
5. Type of the QCD vacuum in MA(Kanazawa + M.Chernodub, M.Polikarpov, V.Zakharo
v)The penetration length ( inverse of the dual photon mass)is fixed from the electric field flux.
R=Distnce between Q and Qbar
![Page 16: Color confinement mechanism and the type of the QCD vacuum Tsuneo Suzuki (Kanazawa Univ.) Collaborators: K.Ishiguro, Y.Mori, Y.Nakamura, T.Sekido ( M.Polikarpov,](https://reader037.fdocuments.us/reader037/viewer/2022110208/56649de55503460f94adca02/html5/thumbnails/16.jpg)
How to determine the coherence length(inverse of the dual Higgs mass)Study monopole around QCD string in dual Ginzburg-Landau theory: (Suzuki 1988)
![Page 17: Color confinement mechanism and the type of the QCD vacuum Tsuneo Suzuki (Kanazawa Univ.) Collaborators: K.Ishiguro, Y.Mori, Y.Nakamura, T.Sekido ( M.Polikarpov,](https://reader037.fdocuments.us/reader037/viewer/2022110208/56649de55503460f94adca02/html5/thumbnails/17.jpg)
Behaviors of classical solutions
![Page 18: Color confinement mechanism and the type of the QCD vacuum Tsuneo Suzuki (Kanazawa Univ.) Collaborators: K.Ishiguro, Y.Mori, Y.Nakamura, T.Sekido ( M.Polikarpov,](https://reader037.fdocuments.us/reader037/viewer/2022110208/56649de55503460f94adca02/html5/thumbnails/18.jpg)
place the static quarks at the (spatial) infinities of the z axis in London limit
![Page 19: Color confinement mechanism and the type of the QCD vacuum Tsuneo Suzuki (Kanazawa Univ.) Collaborators: K.Ishiguro, Y.Mori, Y.Nakamura, T.Sekido ( M.Polikarpov,](https://reader037.fdocuments.us/reader037/viewer/2022110208/56649de55503460f94adca02/html5/thumbnails/19.jpg)
Real world: dominant
![Page 20: Color confinement mechanism and the type of the QCD vacuum Tsuneo Suzuki (Kanazawa Univ.) Collaborators: K.Ishiguro, Y.Mori, Y.Nakamura, T.Sekido ( M.Polikarpov,](https://reader037.fdocuments.us/reader037/viewer/2022110208/56649de55503460f94adca02/html5/thumbnails/20.jpg)
Expected behavior of monopole density around QCD string
The coherence length can be derived from this behavior !!
![Page 21: Color confinement mechanism and the type of the QCD vacuum Tsuneo Suzuki (Kanazawa Univ.) Collaborators: K.Ishiguro, Y.Mori, Y.Nakamura, T.Sekido ( M.Polikarpov,](https://reader037.fdocuments.us/reader037/viewer/2022110208/56649de55503460f94adca02/html5/thumbnails/21.jpg)
Numerical data of the coherence length
![Page 22: Color confinement mechanism and the type of the QCD vacuum Tsuneo Suzuki (Kanazawa Univ.) Collaborators: K.Ishiguro, Y.Mori, Y.Nakamura, T.Sekido ( M.Polikarpov,](https://reader037.fdocuments.us/reader037/viewer/2022110208/56649de55503460f94adca02/html5/thumbnails/22.jpg)
Correlation of monopole density and D=2 gluon operator
![Page 23: Color confinement mechanism and the type of the QCD vacuum Tsuneo Suzuki (Kanazawa Univ.) Collaborators: K.Ishiguro, Y.Mori, Y.Nakamura, T.Sekido ( M.Polikarpov,](https://reader037.fdocuments.us/reader037/viewer/2022110208/56649de55503460f94adca02/html5/thumbnails/23.jpg)
Is minimized in MA
![Page 24: Color confinement mechanism and the type of the QCD vacuum Tsuneo Suzuki (Kanazawa Univ.) Collaborators: K.Ishiguro, Y.Mori, Y.Nakamura, T.Sekido ( M.Polikarpov,](https://reader037.fdocuments.us/reader037/viewer/2022110208/56649de55503460f94adca02/html5/thumbnails/24.jpg)
Various D=2 gluon operators in MA+U(1) LA
![Page 25: Color confinement mechanism and the type of the QCD vacuum Tsuneo Suzuki (Kanazawa Univ.) Collaborators: K.Ishiguro, Y.Mori, Y.Nakamura, T.Sekido ( M.Polikarpov,](https://reader037.fdocuments.us/reader037/viewer/2022110208/56649de55503460f94adca02/html5/thumbnails/25.jpg)
Border between the type 1 and the type 2(Cea et al,1995, Singh et al.1993, Matsubara et al.,1994, kato et al.,1998,Bali 1998, Koma 2003)
![Page 26: Color confinement mechanism and the type of the QCD vacuum Tsuneo Suzuki (Kanazawa Univ.) Collaborators: K.Ishiguro, Y.Mori, Y.Nakamura, T.Sekido ( M.Polikarpov,](https://reader037.fdocuments.us/reader037/viewer/2022110208/56649de55503460f94adca02/html5/thumbnails/26.jpg)
6. The type of the QCD vacuum in Landau gauge
![Page 27: Color confinement mechanism and the type of the QCD vacuum Tsuneo Suzuki (Kanazawa Univ.) Collaborators: K.Ishiguro, Y.Mori, Y.Nakamura, T.Sekido ( M.Polikarpov,](https://reader037.fdocuments.us/reader037/viewer/2022110208/56649de55503460f94adca02/html5/thumbnails/27.jpg)
Border between type 1 and 2 ?
Landau gauge
![Page 28: Color confinement mechanism and the type of the QCD vacuum Tsuneo Suzuki (Kanazawa Univ.) Collaborators: K.Ishiguro, Y.Mori, Y.Nakamura, T.Sekido ( M.Polikarpov,](https://reader037.fdocuments.us/reader037/viewer/2022110208/56649de55503460f94adca02/html5/thumbnails/28.jpg)
7. Study of gauge dependence
Penetration length Coherence length
![Page 29: Color confinement mechanism and the type of the QCD vacuum Tsuneo Suzuki (Kanazawa Univ.) Collaborators: K.Ishiguro, Y.Mori, Y.Nakamura, T.Sekido ( M.Polikarpov,](https://reader037.fdocuments.us/reader037/viewer/2022110208/56649de55503460f94adca02/html5/thumbnails/29.jpg)
8. Summary and outlook
• The dual Meissner effect works good also in Landau gauge. How about in other general gauges? Expectation: It must work in general.
• Magnetic displacement current plays a role of monopole currents if we see naive abelian components.
• The vacuum is near the border of the type 1 and the type 2.
![Page 30: Color confinement mechanism and the type of the QCD vacuum Tsuneo Suzuki (Kanazawa Univ.) Collaborators: K.Ishiguro, Y.Mori, Y.Nakamura, T.Sekido ( M.Polikarpov,](https://reader037.fdocuments.us/reader037/viewer/2022110208/56649de55503460f94adca02/html5/thumbnails/30.jpg)
• Existence of the dual Meissner effect suggests that something magnetic condenses in the vacuum. Gauge-invariant monopoles are working? Extraction of monopole need not always abelian projection. Or essentially non-static?
1. Gubarev’s monopoles may be important and should be studied extensively.(Gubarev, hep-lat/0204018, Gubarev-Zakharov hep-lat/0204017)
2. Violation of non-abelian Bianchi identity may be important?(Gubarev & Morozov, hep-lat/0503023)
![Page 31: Color confinement mechanism and the type of the QCD vacuum Tsuneo Suzuki (Kanazawa Univ.) Collaborators: K.Ishiguro, Y.Mori, Y.Nakamura, T.Sekido ( M.Polikarpov,](https://reader037.fdocuments.us/reader037/viewer/2022110208/56649de55503460f94adca02/html5/thumbnails/31.jpg)
• D=2 gluon condensate operator important?
(1) Consider A+ A- in MA gauge:
The effect of the off-diagonal gluons appears
only in the screening of adjoint charged particles. Fundamental quark confinement is not affected.
(T.Suzuki and M.Chernodub, P.L. B563 (2003) 183)
(2)A3A3: non-perturbative part is given by monopoles
(3) In LA gauge, both effects are included in