1 / 18

Chaos in the Color Glass Condensate

Explore the implications of chaos theory on high-energy evolution in Color Glass Condensate through intricate equations and bifurcation diagrams. Understand the profound effects of non-linear phenomena in perturbative QCD.

lindsayp
Download Presentation

Chaos in the Color Glass Condensate

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chaos in the Color Glass Condensate Kirill Tuchin

  2. DIS in the Breit frame P • Interaction time int~1/qz=1/Q • Life-time of a parton part~k+/mt2. • Since kz=xpz, part~Q/mt2. • Thus, part>> int : photon is a “microscope” of resolution ~1/Q q  e

  3. How many gluons are resolved • Proton’s radius R~ln1/2(s) • Density of gluons: • Number of gluons • resolved by a photon: ~1: High parton density Qs2 (Gribov,Levin,Ryskin,82)

  4. Target rest frame  • Life-time of a dipole is • Total cross section is a forward scattering amplitude • Quasi-classical regime: (McLerran,Venugopalan,94)

  5. Linear evolution • High energy linear evolution regime (Fadin,Kuraev,Lipatov,Balitsky,75,78) • Evolution equation:

  6. Operator form of BFKL • Fourier image of the forward amplitude • The BFKL equation: where

  7. Evolution in a dense system • Evolution in a Color Glass Condensate:  (Balitski,Kovchegov,96,00) • Equivalently: (Kovchegov,01)

  8. Discretization of BK equation (Kharzeev, K.T., 05) • At small x emission of a gluon into a wave function of a high energy hadron happens when sln(1/x)~1 • Let’s impose the boundary condition by putting a system in • a box of size L~ • We can think of evolution as a discrete process of gluon • emission when parameter n=sln(1/x)changes by unity. • Evolution equation can be written as

  9. Diffusion approximation • Diffusion approximation: • Let’s keep only the first term • Rescale • Discrete equation: • For fixed kT this is the ‘logistic map’. • It is used to describe • population growth in the ecological systems. • It’s properties are very different from those of the continuous equation. (von Neumann,47)

  10. n n=1 n=4 n=8 n=11 kT 1<<3 continuous • Stable fixed point: discrete • Unstable fixed point: 

  11.  • is a bifurcation point: fixed point condition admits two • new solutions (period doubling). • Unstable fixed points • Stable fixed points:

  12. n n=4 n=7 n=1 n=10 kT Period doubling continuous discrete 

  13. n n=1 n=5 n=7 n=9 kT  

  14. n n=1 n=5 n=8 n=11 kT Onset of chaos FFeigenbaum’s number) • In pertubative QCD: • min=1+4ln2=3.77>F 

  15. Chaos in ecology Canadian Lynx population (Hudson Bay Company’s archives)

  16. Bifurcation diagram Note large fluctuations Fixed points  High energy evolution starts here.

  17. Implication to diffraction • Diffraction cross section is the statistical dispersion in the • absorption probabilities of different eigenstates. diff=<2>-<>2 • Large fluctuations in the scattering amplitude imply large • target independent diffractive cross sections at highest • energies.

  18. Summary • Optimistic/pessimistic point of view: there are an interesting non-linear effects in the Color Glass Condensate beyond the continuum limit. • Pessimistic/optimistic point of view: appearance of chaos in the high energy evolution signals breakdown of a perturbation theory in vacuum.

More Related