Removed long analytic results from validation.py and f-and-g.py

michel-decay/arbuzov.py

@@ -17,8 +17,10 @@ try:
 except ImportError:
     pass
 
+sys.dont_write_bytecode = True
 dilog = pymule.maths.Li2
 trilog = pymule.maths.Li3
+sqrt = np.sqrt
 
 
 def zeta(n):

michel-decay/f-and-g/arbuzov.py

+../arbuzov.py
\ No newline at end of file

michel-decay/f-and-g/f-and-g.py

@@ -2,7 +2,7 @@
 ## Init{{{
 from pymule import *
 from pymule.plot import twopanel
-from arbuzov import f1, g1, f2LL, g2LL
+import arbuzov
 
 gamma0 = Mmu**5/192/pi**3
 
@@ -159,7 +159,7 @@ G = addplots(glo, addplots(gnlo, gnnlo))
 ###########################################################}}}
 ##########################################################################}}}
 ## Compare at LO and NLO{{{
-# Here we compare the results with Arbuzov [??]
+# Here we compare the results with Arbuzov [hep-ph/0110047]
 Ee = flo[:, 0]
 xe = 2*Ee/Mmu
 beta = sqrt(1-Mel**2/Ee**2)
@@ -189,8 +189,8 @@ twopanel(
 ylim(-5e-2, 5e-2)
 ###########################################################}}}
 ### Compare at NLO{{{
-fNLOref = alpha/(2*pi) * 2/Mmu * xe**2*beta * f1(xe, Mel/Mmu)
-gNLOref = alpha/(2*pi) * 2/Mmu * xe**2*beta * g1(xe, Mel/Mmu)
+fNLOref = alpha/(2*pi) * 2/Mmu * xe**2*beta * arbuzov.fnlo(xe, Mel/Mmu)
+gNLOref = alpha/(2*pi) * 2/Mmu * xe**2*beta * arbuzov.gnlo(xe, Mel/Mmu)
 fNLOref[Ee < Mel] = 0.
 gNLOref[Ee < Mel] = 0.
 fNLOref[Ee > Mmu/2 + Mel**2/Mmu**2] = 0.
@@ -210,8 +210,8 @@ twopanel(
 ylim(-2e-3, 2e-3)
 ###########################################################}}}
 ### Compare at NNLO{{{
-fNNLOref = (alpha/(2*pi))**2 * 2/Mmu * (np.log(Mmu**2/Mel**2)-1)**2/2 * f2LL(xe, Mel/Mmu)  # nopep8
-gNNLOref = (alpha/(2*pi))**2 * 2/Mmu * (np.log(Mmu**2/Mel**2)-1)**2/2 * g2LL(xe, Mel/Mmu)  # nopep8
+fNNLOref = (alpha/(2*pi))**2 * 2/Mmu * (np.log(Mmu**2/Mel**2)-1)**2/2 * arbuzov.f2LL(xe)  # nopep8
+gNNLOref = (alpha/(2*pi))**2 * 2/Mmu * (np.log(Mmu**2/Mel**2)-1)**2/2 * arbuzov.g2LL(xe)  # nopep8
 fNNLOref[Ee < Mel] = 0.
 gNNLOref[Ee < Mel] = 0.
 fNNLOref[Ee > Mmu/2 + Mel**2/Mmu**2] = 0.

michel-decay/validation/arbuzov.py

+../arbuzov.py
\ No newline at end of file

michel-decay/validation/validation.py

@@ -2,6 +2,7 @@
 from pymule import *
 from pymule.maths import Li2, Li3, zeta2, zeta3
 import pymule.compress
+import arbuzov
 
 gamma0 = Mmu**5/192/pi**3
 
@@ -24,91 +25,17 @@ xev = np.array([1, 1 / gamma0, 1 / gamma0])*addplots(nnlo['xe'], openLeptons)
 
 ##########################################}}}
 ## Load logarithms from [hep-ph/0205172] (Arbuzov et al.){{{
-# see also meg2d/arbuzov.py
-def fLL(xe):
-    gam = (
-        -32*xe**3/9
-        + 4*xe**2*(3 - 2*xe)*(
-            -Li2(1 - xe) - zeta2 + np.log(xe)**2/2
-            - 2*np.log(xe)*np.log(1 - xe) + np.log(1 - xe)**2
-        )
-        + 8*xe**2/3 + 17*xe/6
-        + (-32*xe**3/3 + 8*xe**2 - 2*xe - 5./6)*np.log(xe)
-        + (32*xe**3/3 - 16*xe**2 + 8*xe + 10./3)*np.log(1 - xe) + 11./36
-    )
-    NS = (
-        8*xe**3/3 + 2*xe**2*(3 - 2*xe)*np.log((1 - xe)/xe)
-        - 4*xe**2 + 2*xe + 5./6
-    )
-    S = (
-        -8*xe**3/9 - 14*xe**2/3 + 3*xe
-        + (4*xe**2 + 4*xe + 5./3)*np.log(xe) + 17./9 + 2/(3*xe)
-    )
-    return gam/2 + NS/3 + S/2
-
-
-def fNLL(xe):
-    def Sot(z):
-        return (
-            0.5*np.log(1-z)**2*np.log(z)
-            + np.log(1-z)*Li2(1-z) - Li3(1-z) + zeta3
-        )
-
-    gam = (
-        -559*xe**3/54
-        + 2*xe**2*(3 - 2*xe)*(
-            -2*Sot(xe) + 2*Li2(xe)*np.log(xe) + 2*Li2(xe)*np.log(1 - xe)
-            - 2*Li3(xe) - 2*zeta2*np.log(xe) - 2*zeta2*np.log(1 - xe)
-            + 7*zeta3 + 2*np.log(xe)**3 - 5*np.log(xe)**2*np.log(1 - xe)
-            + 5*np.log(xe)*np.log(1 - xe)**2
-        )
-        + 83*xe**2/3 - 287*xe/12
-        + (8*xe**3 - 4*xe**2 - 12*xe)*np.log(1 - xe)**2
-        + (-98*xe**3/3 + 35*xe**2 - 2*xe - 10./3)*zeta2
-        + (-70*xe**3/3 + 22*xe**2 - 5*xe - 25./12)*np.log(xe)**2
-        + (-12*xe**3 + 64*xe**2/3 - 53*xe/3 - 17./3)*np.log(1 - xe)
-        + (44*xe**3/9 + 4*xe**2/3 + 37*xe/6 - 3./4)*np.log(xe)
-        + (92*xe**3/3 - 54*xe**2 + 32*xe + 25./3)*np.log(xe)*np.log(1 - xe)
-        + (92*xe**3/3 - 40*xe**2 + 14*xe + 10./3)*Li2(xe) + 211./216
-    )
-    NS = (
-        -64*xe**3/9
-        + 2*xe**2*(3 - 2*xe)*(
-            -2*Li2(1 - xe) - 2*zeta2/3 - np.log(xe)**2
-            - 2*np.log(xe)*np.log(1 - xe)/3 + 2*np.log(1 - xe)**2/3
-        )
-        + 100*xe**2/9 - 19*xe/3
-        + (-76*xe**3/9 + 8*xe**2 + 4*xe/3 + 5./9)*np.log(xe)
-        + (12*xe**3 - 46*xe**2/3 - 4*xe/3 + 10./9)*np.log(1 - xe)
-        - 11./6
-    )
-    S = (
-        10*xe**3/9 + 77*xe**2/18 + 43*xe/18 +
-        (Li2(1 - xe) + np.log(xe)*np.log(1 - xe))*(4*xe**2 + 4*xe + 5./3)
-        + (4*xe**2 + 6*xe + 5./2)*np.log(xe)**2
-        + (-19*xe**2/3 - 5*xe/6 + 8./9 + 4/(3*xe))*np.log(xe)
-        + (-8*xe**3/9 - 14*xe**2/3 + 3*xe + 17./9 + 2/(3*xe))*np.log(1 - xe)
-        - 67./9 - 1/(3*xe)
-    )
-    int = (
-        104*xe**3/9
-        + 2*xe**2*(3 - 2*xe)*(
-            -4*Sot(1 - xe) - 2*Li2(1 - xe)*np.log(xe)
-            + 2*Li3(1 - xe)
-        )
-        - 55*xe**2/3 + 41*xe/3 + (26*xe**3/3 - 9*xe**2)*np.log(xe)**2
-        + (-28*xe**2/3 - 5*xe/3 - 5./3)*np.log(xe)
-        + (52*xe**3/3 - 26*xe**2 + 4*xe + 5./3)*Li2(1 - xe) - 62./9
-    )
-    return gam+NS+S+int
-
-
 def f2loop(xe):
+    fLL = arbuzov.f2LLns(xe)/3 + arbuzov.f2LLs(xe)/2 + arbuzov.f2LL(xe)/2
+    fNLL = (
+        arbuzov.f2NLLns(xe) + arbuzov.f2NLLs(xe)
+        + arbuzov.f2NLL(xe) + arbuzov.f2NLLint(xe)
+    )
     z = Mel / Mmu
     f0 = -np.sqrt(xe**2 - 4*z**2)*(2*xe**2 + 4*z**2 - 3*xe*(1 + z**2))
     f00 = -xe**2*(-3 + 2*xe)
     L = np.log(Mmu**2/Mel**2)
-    return f0 / f00 * (L**2 * fLL(xe) + L * fNLL(xe)) / 2 / pi / pi
+    return f0 / f00 * (L**2 * fLL + L * fNLL) / 2 / pi / pi
 
 
 ###########################################################}}}