From 2cc494390386d8a2f90e7e71ac9936587925c1d3 Mon Sep 17 00:00:00 2001 From: hiro98 Date: Thu, 2 Apr 2020 09:16:33 +0200 Subject: [PATCH] some more discussion around pseudo rapidity --- ...de667c0ccb1d17fef74918e3f462a1340df113.png | Bin 0 -> 11425 bytes ...7a2432093426a961983767c2f23e1cd8b105a5.png | Bin 0 -> 16055 bytes ...1912645d2fc9da47c8880435b9ee4e622c722f.png | Bin 0 -> 9659 bytes ...547bdeaa79bb956057b552090b4ab6305a20e6.png | Bin 13508 -> 0 bytes prog/python/qqgg/analytical_xs.org | 24 +- prog/python/qqgg/figs/xs/xs_integrand.pdf | Bin 17858 -> 23152 bytes prog/python/qqgg/figs/xs/xs_integrand.pgf | 26 +- prog/python/qqgg/figs/xs/xs_integrand_η.pdf | Bin 0 -> 12973 bytes prog/python/qqgg/figs/xs/xs_integrand_η.pgf | 4040 +++++++++++++++++ 9 files changed, 4073 insertions(+), 17 deletions(-) create mode 100644 prog/python/qqgg/.ob-jupyter/09de667c0ccb1d17fef74918e3f462a1340df113.png create mode 100644 prog/python/qqgg/.ob-jupyter/377a2432093426a961983767c2f23e1cd8b105a5.png 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y&E42K-M=?VqXe)@gKf~W_Wc09{QrA#?=wo_C*$f~bOoF^0)2wYLP|gCef?kGf;4gf diff --git a/prog/python/qqgg/analytical_xs.org b/prog/python/qqgg/analytical_xs.org index 0ce72ed..cc88d57 100644 --- a/prog/python/qqgg/analytical_xs.org +++ b/prog/python/qqgg/analytical_xs.org @@ -210,6 +210,9 @@ Define the integrand. #+begin_src jupyter-python :exports both :results raw drawer def xs_pb_int(θ): return 2*np.pi*gev_to_pb(np.sin(θ)*diff_xs(θ, charge=charge, esp=esp)) + + def xs_pb_int_η(η): + return 2*np.pi*gev_to_pb(diff_xs_eta(η, charge, esp)) #+end_src #+RESULTS: @@ -219,7 +222,7 @@ Plot the integrand. # TODO: remove duplication fig, ax = set_up_plot() ax.plot(plot_points, xs_pb_int(plot_points)) ax.set_xlabel(r'$\theta$') -ax.set_ylabel(r'$\sin(\theta)\cdot\frac{d\sigma}{d\theta}$ [pb]') +ax.set_ylabel(r'$\sin(\theta)\cdot\frac{d\sigma}{d\Omega}$ [pb]') ax.axvline(interval[0], color='gray', linestyle='--') ax.axvline(interval[1], color='gray', linestyle='--', label=rf'$|\eta|={η}$') ax.legend() @@ -227,7 +230,7 @@ save_fig(fig, 'xs_integrand', 'xs', size=[4, 4]) #+end_src #+RESULTS: -[[file:./.ob-jupyter/9e547bdeaa79bb956057b552090b4ab6305a20e6.png]] +[[file:./.ob-jupyter/377a2432093426a961983767c2f23e1cd8b105a5.png]] Intergrate σ with the mc method. #+begin_src jupyter-python :exports both :results raw drawer @@ -248,16 +251,29 @@ tex_value(xs_pb_mc, unit=r'\pico\barn', prefix=r'\sigma = ', err=xs_pb_mc_err, s : \(\sigma = \SI{0.05389\pm 0.00005}{\pico\barn}\) +Plot the intgrand of the pseudo rap. +#+begin_src jupyter-python :exports both :results raw drawer +fig, ax = set_up_plot() +points = np.linspace(*interval_η, 1000) +ax.plot(points, xs_pb_int_η(points)) +ax.set_xlabel(r'$\eta$') +ax.set_ylabel(r'$\frac{d\sigma}{d\theta}$ [pb]') +save_fig(fig, 'xs_integrand_η', 'xs', size=[4, 4]) +#+end_src + +#+RESULTS: +[[file:./.ob-jupyter/09de667c0ccb1d17fef74918e3f462a1340df113.png]] + As we see, the result is much better if we use pseudo rapidity, because the differential cross section does not difverge anymore. #+begin_src jupyter-python :exports both :results raw drawer - xs_pb_η = monte_carlo.integrate(lambda x: 2*np.pi*gev_to_pb(diff_xs_eta(x, charge, esp)), + xs_pb_η = monte_carlo.integrate(xs_pb_int_η, interval_η, 1000) xs_pb_η #+end_src #+RESULTS: -| 0.05359070224781967 | 7.127342563203912e-05 | +| 0.053758763260352345 | 7.109470263473152e-05 | And yet again export that as tex. #+begin_src jupyter-python :exports both :results raw drawer diff --git a/prog/python/qqgg/figs/xs/xs_integrand.pdf b/prog/python/qqgg/figs/xs/xs_integrand.pdf index beb2714beb8c800a041458cbf51f772cfce72cf0..62c50fbef8c22b05a36dbdb654a320f274dcccc6 100644 GIT binary patch delta 10225 zcmZu#cOcbo7w=l(+B?LxN5p686uInO!g`8I_EepLWU>j2pHlCLkB(=(rUb)89`*#T6L@=gJ~ z4fr9$ig9-*ueg~D-B^I1otmsg3dEW9$-ajGdPDu6zbvTSF!c+I_lYvKyxO;diEVe? z-SOWF*rJ!u6nEKTKd`jqj~X@ij`)2$3ENXI{jMrg{;GteM6{fG_buV&^=4P=AhTkY z*b*RC?cTz;hy37v{W;Qh>z3QKzuGGenw*#*2D#JnpOUcR^@pClep)0wa+n<@Ua{u&ZMnRicx!0o 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