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High-pT Ψ(2S) studies#3

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Radonirinaunimi wants to merge 7 commits intomasterfrom
psi
Open

High-pT Ψ(2S) studies#3
Radonirinaunimi wants to merge 7 commits intomasterfrom
psi

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@Radonirinaunimi
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@Radonirinaunimi Radonirinaunimi commented Jan 30, 2026

The following PR records the following changes:

  • fix the mismatch in starting evolution scale
  • fine-tune the Talbot contour integration to accurately resolve the inverse Mellin transform for functions with steep rise near z=1
  • increase the number of $x$ and $Q$ nodes for the LHAPDF grid
  • check values of MELA moments for various $Q$ points and dump the results into ./build/run/mela_Nscan.dat
  • add a python script ./scripts/compare_Nscan.py to compare the moments with the Mellin-transformed LHAPDF FF
  • remove the Circle CI tests in favor of a simple GitHub action

Using fc27084, we get the following results:

         Q         MELA_g       LHAPDF_g   diff_g %    ratio_g         MELA_c       LHAPDF_c   diff_c %    ratio_c
------------------------------------------------------------------------------------------------------------------------
      4.92  2.4234414e-03 -1.0965417e-02    -552.47    -4.5247  4.2442417e-05  4.1393988e-05      -2.47     0.9753
      6.84  1.9268109e-03 -1.3503619e-03    -170.08    -0.7008  5.6289292e-05  5.5140178e-05      -2.04     0.9796
      8.76  1.6423880e-03  6.1808378e-04     -62.37     0.3763  6.2577170e-05  6.1516038e-05      -1.70     0.9830
     10.68  1.4549454e-03  1.1147007e-03     -23.39     0.7661  6.5905881e-05  6.4937981e-05      -1.47     0.9853
     12.60  1.3205316e-03  1.2244367e-03      -7.28     0.9272  6.7822057e-05  6.6965538e-05      -1.26     0.9874
     14.52  1.2185527e-03  1.2195809e-03       0.08     1.0008  6.8976136e-05  6.8210373e-05      -1.11     0.9889
     16.44  1.1380000e-03  1.1767331e-03       3.40     1.0340  6.9683533e-05  6.8966439e-05      -1.03     0.9897
     18.36  1.0724197e-03  1.1239249e-03       4.80     1.0480  7.0113140e-05  6.9452549e-05      -0.94     0.9906
     20.28  1.0177601e-03  1.0717952e-03       5.31     1.0531  7.0362247e-05  6.9739626e-05      -0.88     0.9912
     22.20  9.7133976e-04  1.0242471e-03       5.45     1.0545  7.0490128e-05  6.9911120e-05      -0.82     0.9918
     24.12  9.3130785e-04  9.8090015e-04       5.33     1.0533  7.0534524e-05  6.9973557e-05      -0.80     0.9920
     26.04  8.9634211e-04  9.4106291e-04       4.99     1.0499  7.0520340e-05  6.9992316e-05      -0.75     0.9925
     27.96  8.6547068e-04  9.0568204e-04       4.65     1.0465  7.0464495e-05  6.9963747e-05      -0.71     0.9929
     29.88  8.3796181e-04  8.7409787e-04       4.31     1.0431  7.0378765e-05  6.9898047e-05      -0.68     0.9932
     31.80  8.1325307e-04  8.4568247e-04       3.99     1.0399  7.0271512e-05  6.9812362e-05      -0.65     0.9935
     33.72  7.9090439e-04  8.1964900e-04       3.63     1.0363  7.0148777e-05  6.9700167e-05      -0.64     0.9936
     35.64  7.7056603e-04  7.9611100e-04       3.32     1.0332  7.0014986e-05  6.9599924e-05      -0.59     0.9941
     37.56  7.5195619e-04  7.7497543e-04       3.06     1.0306  6.9873419e-05  6.9455658e-05      -0.60     0.9940
     39.48  7.3484504e-04  7.5539834e-04       2.80     1.0280  6.9726534e-05  6.9326933e-05      -0.57     0.9943
     41.40  7.1904307e-04  7.3703070e-04       2.50     1.0250  6.9576185e-05  6.9185220e-05      -0.56     0.9944
     43.32  7.0439246e-04  7.2043630e-04       2.28     1.0228  6.9423779e-05  6.9042443e-05      -0.55     0.9945
     45.24  6.9076064e-04  7.0459735e-04       2.00     1.0200  6.9270390e-05  6.8902059e-05      -0.53     0.9947
     47.16  6.7803533e-04  6.9078229e-04       1.88     1.0188  6.9116839e-05  6.8762519e-05      -0.51     0.9949
     49.08  6.6612075e-04  6.7728060e-04       1.68     1.0168  6.8963755e-05  6.8615935e-05      -0.50     0.9950
     51.00  6.5493461e-04  6.6507689e-04       1.55     1.0155  6.8811619e-05  6.8464954e-05      -0.50     0.9950
     52.92  6.4440581e-04  6.5323604e-04       1.37     1.0137  6.8660795e-05  6.8331729e-05      -0.48     0.9952
     54.84  6.3447256e-04  6.4206992e-04       1.20     1.0120  6.8511561e-05  6.8186591e-05      -0.47     0.9953
     56.76  6.2508083e-04  6.3220784e-04       1.14     1.0114  6.8364124e-05  6.8036430e-05      -0.48     0.9952
     58.68  6.1618321e-04  6.2191387e-04       0.93     1.0093  6.8218636e-05  6.7906044e-05      -0.46     0.9954
     60.60  6.0773788e-04  6.1290292e-04       0.85     1.0085  6.8075206e-05  6.7765395e-05      -0.46     0.9954
     62.52  5.9970777e-04  6.0422970e-04       0.75     1.0075  6.7933910e-05  6.7638075e-05      -0.44     0.9956
     64.44  5.9205992e-04  5.9560694e-04       0.60     1.0060  6.7794795e-05  6.7497157e-05      -0.44     0.9956
     66.36  5.8476491e-04  5.8817880e-04       0.58     1.0058  6.7657890e-05  6.7369166e-05      -0.43     0.9957
     68.28  5.7779639e-04  5.8087203e-04       0.53     1.0053  6.7523203e-05  6.7245374e-05      -0.41     0.9959
     70.20  5.7113066e-04  5.7349741e-04       0.41     1.0041  6.7390733e-05  6.7112620e-05      -0.41     0.9959
     72.12  5.6474636e-04  5.6666363e-04       0.34     1.0034  6.7260465e-05  6.6979890e-05      -0.42     0.9958
     74.04  5.5862417e-04  5.6020347e-04       0.28     1.0028  6.7132378e-05  6.6852614e-05      -0.42     0.9958
     75.96  5.5274658e-04  5.5389115e-04       0.21     1.0021  6.7006445e-05  6.6727372e-05      -0.42     0.9958
     77.88  5.4709767e-04  5.4766459e-04       0.10     1.0010  6.6882632e-05  6.6610117e-05      -0.41     0.9959
     79.80  5.4166292e-04  5.4194116e-04       0.05     1.0005  6.6760903e-05  6.6495269e-05      -0.40     0.9960
     81.72  5.3642908e-04  5.3666243e-04       0.04     1.0004  6.6641219e-05  6.6381760e-05      -0.39     0.9961
     83.64  5.3138400e-04  5.3144461e-04       0.01     1.0001  6.6523539e-05  6.6269897e-05      -0.38     0.9962
     85.56  5.2651655e-04  5.2623277e-04      -0.05     0.9995  6.6407820e-05  6.6150496e-05      -0.39     0.9961
     87.48  5.2181649e-04  5.2121185e-04      -0.12     0.9988  6.6294020e-05  6.6045095e-05      -0.38     0.9962
     89.40  5.1727438e-04  5.1656311e-04      -0.14     0.9986  6.6182095e-05  6.5936978e-05      -0.37     0.9963
     91.32  5.1288150e-04  5.1206851e-04      -0.16     0.9984  6.6072002e-05  6.5831495e-05      -0.36     0.9964
     93.24  5.0862982e-04  5.0755868e-04      -0.21     0.9979  6.5963696e-05  6.5731850e-05      -0.35     0.9965
     95.16  5.0451187e-04  5.0320003e-04      -0.26     0.9974  6.5857136e-05  6.5619919e-05      -0.36     0.9964
     97.08  5.0052074e-04  4.9901036e-04      -0.30     0.9970  6.5752278e-05  6.5514854e-05      -0.36     0.9964
     99.00  4.9664999e-04  4.9500455e-04      -0.33     0.9967  6.5649080e-05  6.5415965e-05      -0.36     0.9964

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