VISCOUS CORRECTIONNS TO SPECTRA, ELLIPTIC FLOW, AND HBT RADII. Page: 3 of 4
This article is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided to UNT Digital Library by the UNT Libraries Government Documents Department.
Extracted Text
The following text was automatically extracted from the image on this page using optical character recognition software:
3
.)jz 2 -
- : o .14- rg/t =1/3
1.5-
F5/to = 1/3
0.12
1
0.50.
Ideal
-0.5 to 0 6.5 Fm 0.06 b ~ 6 fm
.i= 10.0 Fm o.o4
To =160 MeV ....-
-1.5 U = 0.50 C 0.02 -
_....--- Viscous
0 0.5 1 1.5 2 2.5 00.2 0.4 0.6 0.8 1 1.2 1.4
pT (GeV) PT(GeV)
Figure 1. Viscousity corrected spec- Figure 2. Elliptic flow as a function trans-
trum relative to uncorrected spectrum. verse momentum. The blast wave param-
The band indicates where hydrodynamics eters (see text) are chosen to approximate
breaks down. a AuAu collision at b = 6 Fm.
To understand this figure qualitatively, consider a Bjorken expansion of infinitely large
nuclei. The longitudinal pressure is reduced [4}, pL = p - s . Because the shear tensor is
traceless, the transverse pressure is increased, pT = p+ . Thus, the matter distribution
is pushed out to larger pT by the shear in the longitudinal direction. More mathematically,
the ratio of the corrected spectrum to the uncorrected spectrum is given by,
S dN F r (pT l2 mz l2a1 K3t ( )-1(7
dNo 4T \T J \ T 2 K1U(T) J
For large pr we find, d 4 (~ . Eq. 7 reproduces the shape and dependence of the
full viscous blast wave calculation shown in Fig. 1.
Viscous corrections become of order one when the pT of the particle approaches 1.4 GeV.
This signals the breakdown of the hydrodynamic approach. In fact, ideal hydrodynamics
generally fails to reproduce the single particle spectra above pT of 1.5 GeV. Viscosity
provides a ready explanation for this breakdown.
In non-central collisions elliptic flow is calculated using the spectrum indicated in Eq.
5. In non-central collisions, the matter is assumed to have a cylindrical distribution but
the flow velocity has an elliptic component, ur(r, q) = uo(1 + 2u2 cos(q)). For non-
central collisions the parameters are: uo = 0.5, u2 = 0.1, Ro = 6 Fm and To = 4.0 Fm. As
illustrated in Fig. 2, viscosity reduces elliptic flow by a factor of three.
Next consider viscous corrections to HBT radii. The HBT radii are calculated with the
method of variances. First the ideal radii parameters are displayed in Fig. 3. The results
are typical of the blast wave parametrization. Next the viscous correction to the blast
wave results are illustrated in Fig. 4.,
Upcoming Pages
Here’s what’s next.
Search Inside
This article can be searched. Note: Results may vary based on the legibility of text within the document.
Tools / Downloads
Get a copy of this page or view the extracted text.
Citing and Sharing
Basic information for referencing this web page. We also provide extended guidance on usage rights, references, copying or embedding.
Reference the current page of this Article.
Teaney, D. VISCOUS CORRECTIONNS TO SPECTRA, ELLIPTIC FLOW, AND HBT RADII., article, July 18, 2002; Upton, New York. (https://digital.library.unt.edu/ark:/67531/metadc741878/m1/3/: accessed April 19, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.