WHDG @ TECHQM
William Horowitz
The Ohio State University
Columbia University
December 16, 2008
DGLV: M. Djordjevic and M. Gyulassy, Nucl.Phys.A733, 265 (2004) [nucl-th/0310076]
WHDG: S. Wicks, W. Horowitz, M. Djordjevic, and M. Gyulassy,
Nucl.Phys.A784, 426 (2007) [arXiv:nucl-th/0512076]
WHDG@TECHQM: https://wiki.bnl.gov/TECHQM/index.php/WHDG
With many thanks to Ulrich Heinz, Abhijit Mujumder,
Guangyou Qin, Simon Wicks,
Magdalena Djordjevic and Miklos Gyulassy
12/16/08
TECHQM 2nd Workshop, LBNL
William Horowitz
1
WHDG Overview
• Convolved rad+elastic:
– Radiative energy loss
• dNg/dx kernel: no support as x , 1
• Poisson convolution => Prad(e)
– Any Poisson conv. leads to P(e > 1) > 0
– Collisional energy loss
• B-T mean loss (for light quarks)
• Pel(e): Gaussian, width from F-D thm
12/16/08
TECHQM 2nd Workshop, LBNL
William Horowitz
2
Radiative Notation
• WHDG rad: First Order in Opacity
• Diagrams
– Gluon momentum k
– Exchange momentum q
12/16/08
TECHQM 2nd Workshop, LBNL
William Horowitz
3
dNg/dx Kernel
– Use DGLV
• see also Appendix B of WHDG
M. Djordjevic and M. Gyulassy, Nucl.Phys.A733, 265 (2004) [nucl-th/0310076]
– NB: x << 1 assumed, 1 – x  1, etc. here
– Kinematics:
• 0 < kT < kmax
• 0 < qT < qmax
12/16/08
TECHQM 2nd Workshop, LBNL
William Horowitz
4
dNg/dx Kinematics
• kmax
– Assume eikonality: k+ >> k- and p+ >> p=> kmax ~ 2 E Min(x,1-x)
• Equivalent to keeping virtuality finite
• GLV: (4E2 Min[x2,(1-x)2] – m2); PLB538, 282 (2002)
• WHDG: 2 x (1-x) E
• qmax
• WHDG: 3mE
• Really: ET
• Let’s artificially vary
this by factor of 2
12/16/08
TECHQM 2nd Workshop, LBNL
William Horowitz
5
Kinematics Plots: dNg/dx
kmax
qmax
– Note that dNg/dx  naturally as x  0, 1
– Dependence on kinematics is small
• k phase space 50% larger for second (dashed) case
• especially so for qmax (100% larger)
12/16/08
TECHQM 2nd Workshop, LBNL
William Horowitz
6
Kinematics Plots: P(e)
– kmax
– qmax
– Differences further washed out by convolutions
12/16/08
TECHQM 2nd Workshop, LBNL
William Horowitz
7
Poisson Convolution
– GLV Multigluons
r = dNg/dx
M. Gyulassy, P. Levai and I. Vitev, PLB538, 282 (2002) [nucl-th/0112071]
– Always leads to probability leakage:
P(e > 1)  0
– Neglects correlations of non-Abelian gluons
12/16/08
TECHQM 2nd Workshop, LBNL
William Horowitz
8
To Reweigh or Not to Reweigh
– Reweigh Pn(e)
– Reweigh P(e)
– For moderate loss, not a large difference
12/16/08
TECHQM 2nd Workshop, LBNL
William Horowitz
9
Collisional Loss
– Gaussian distribution
• Mean loss for light quarks:
– Braaten-Thoma, PRD44, 2625 (1991)
– Width given by Fluctuation-Dissipation theorem
– Poisson conv. not well approx
by Gaussian for realistic,
small num of scatterings
• See Simon Wicks’ thesis
12/16/08
TECHQM 2nd Workshop, LBNL
William Horowitz
10
Running as?
– as = .2, .3
– as = .3, .4
– Not surprisingly, changes in as make huge
difference to P(e)
12/16/08
TECHQM 2nd Workshop, LBNL
William Horowitz
11
WHDG thru KKP
– Facilitate comparison between WHDG and HT
– Elastic gain => D(z > 1) > 0
12/16/08
TECHQM 2nd Workshop, LBNL
William Horowitz
12
WHDG Pros/Cons
• Advantages:
– Includes finite kinematics
• E, p conserved at level of dNg/dx
– Interference with production radiation
– Includes elastic loss
• Disadvantages:
Djordjevic and Heinz, PRC77:024905 (2008);
– Static scattering centers See
PRL101:022302 (2008)
– Simplistic rad Poisson conv.
– Simplistic el Gaussian
– Fixed as
12/16/08
TECHQM 2nd Workshop, LBNL
William Horowitz
13
Conclusions
• Within WHDG:
– rad kinematics under control
– rad Poisson approx. seems OK
– Pressing issues:
• Effect of running as not yet explored (should be
much easier to address in brick problem)
– Weak coupling comp. under control?
– Hope for quantitative understanding of QGP?
• Elastic loss, dynamic medium
• Ease of comparison:
– Results fragmented through KKP
– Temperature scans; standard output
12/16/08
TECHQM 2nd Workshop, LBNL
William Horowitz
14
Backup Slides
12/16/08
TECHQM 2nd Workshop, LBNL
William Horowitz
15
WHDG T and L Dependence
– Decreasing T, L decreases loss
12/16/08
TECHQM 2nd Workshop, LBNL
William Horowitz
16
qmax Detail
• Inconsequential difference
12/16/08
TECHQM 2nd Workshop, LBNL
William Horowitz
17
WHDG thru KKP
12/16/08
TECHQM 2nd Workshop, LBNL
William Horowitz
18
WHDG thru KKP
12/16/08
TECHQM 2nd Workshop, LBNL
William Horowitz
19
WHDG T and L Dependence
• Decreasing T, L decreases loss
12/16/08
TECHQM 2nd Workshop, LBNL
William Horowitz
20
Error from QFT Ward Violation
• Identical expressions are not a surprise
• QFT Calculation
– Gluon momentum carried away crucial for
cancellation of gluon mass
• Classical case neglects both; effects cancel
12/16/08
TECHQM 2nd Workshop, LBNL
William Horowitz
21
Resulting Expression
– To lowest order in 1/E+
– New:
• (1-x)2 prefactor: naturally kills hard gluons
• mg2 in numerator: fills in the dead cone!?!
– What are the sizes of these effects?
12/16/08
TECHQM 2nd Workshop, LBNL
William Horowitz
22