Solve the BK equation in coordinate space with running coupling

Questions and comments: Heikki Mäntysaari [email protected]

License: CC-BY

Reference: T. Lappi, H. Mäntysaari, Phys.Rev.D 88 (2013) 114020, arXiv:1309.6963

Parallerized using OpenMP

Compile (requires GSL and CMake)

mkdir build
cd build
cmake ..
make

The datafiles containing the solution (evolved dipole amplitude) can be read using the code rcbkdipole

Examples

Solve up to $y=10$, save data to datafile, use the Balitsky running coupling prescription, set $C^2=10$, initial condition at $x_0=0.01$ is the MV model with $Q_{s,0}^2=1$ GeV$^2$, $\gamma=1.2$, $e_c=2$.

./build/bin/rcbk -ic MV 1 1.2 0.01 2 -alphas_scaling 10 -rc BALITSKY -output datafile -maxy 10 -minr 1e-6 -fast 2>/dev/null

Notes

• Without the -fast flag the code is very slow, and the effect at the level of the dipole amplitude is negligible, except maybe if you want to compute the Fourier transform
• Lower limit of the dipole size grid is here set to $r_\mathrm{min}=10^{-6}$ $\mathrm{GeV}^{-1}$. Especially at small $r$ the required numerical precision may not be reached
• and the code may print a lot of warnings, thus in the example above these warnings are directed to /dev/null (=hidden)

Same example, but read the initial condition at $x_0=0.01$ from a datafile where the structure is

r1 N(r1)
r2 N(r2)
...
rN N(rN)

(here ri is in GeV $^{-1}$ )

./build/bin/rcbk -ic FILE initial_condition_file 0.01 -alphas_scaling 10 -rc BALITSKY -output datafile -maxy 10 -fast 2>/dev/null

Read the main.cpp to see all other parameters