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MSTW PDFs : PDF sets for different mc and mb values and 3- and 4-flavour PDFs

Here we provide additional PDF grid files associated with the paper:

A. D. Martin, W. J. Stirling, R. S. Thorne and G. Watt,
“Heavy-quark mass dependence in global PDF analyses and 3- and 4-flavour parton distributions”,
Eur. Phys. J. C 70 (2010) 51-72 [arXiv:1007.2624 [hep-ph]].
Please reference this paper if you use these PDF grids for a publication.

We provide NLO and NNLO grids with the heavy-quark pole masses mc in the range 1.05 GeV to 1.75 GeV (in steps of 0.05 GeV excluding 1.40 GeV, i.e. 14 different values) and mb in the range 4.00 GeV to 5.50 GeV (in steps of 0.25 GeV excluding 4.75 GeV, i.e. 6 different values). The default MSTW 2008 fits took mc = 1.40 GeV and mb = 4.75 GeV. For each value of mc and mb the strong coupling αS(MZ) is treated as a free parameter in the fits. We also provide grids with varying mc and αS(MZ) held fixed at the MSTW 2008 values. The correlation between mb and αS(MZ) is negligible, so fits with varying mb and fixed αS(MZ) are not explicitly provided.

For the default quark masses, mc = 1.40 GeV and mb = 4.75 GeV, 3- and 4-flavour PDFs are generated by evolving the fitted input PDFs and αS(Q0) determined from the 5-flavour MSTW 2008 fits at Q0 = 1 GeV. This is also done for the 40 associated eigenvector PDF sets at both 68% and 90% confidence-level (C.L.) to allow the calculation of PDF uncertainties in a 3- or 4-flavour scheme. For all fits with varying mc, both with free and fixed αS(MZ), 3-flavour PDF grids are provided. Similarly, for all fits with varying mb, with free αS(MZ), 4-flavour PDF grids are provided. These additional grids will allow the mc or mb dependence to be consistently studied in a 3- or 4-flavour scheme calculation, respectively.

To assess the uncertainty due to mc and mb on an observable such as a hadronic cross section, our recommendation is to calculate the central value with mc = 1.40 GeV and mb = 4.75 GeV using the default MSTW 2008 PDFs. The cross-section variation should then be calculated by separately varying mc = 1.40±0.15 GeV at 68% C.L. (or ±0.25 GeV at 90% C.L.) and mb = 4.75±0.25 GeV at 68% C.L. (or ±0.50 GeV at 90% C.L.), with αS(MZ) held fixed in the case of mc. The resulting cross-section variation can then be added in quadrature with the other uncertainties.

Below we provide plots documenting the charm-quark mass dependence of the NLO and NNLO global fits; see Section 3.1 of arXiv:1007.2624 for more explanation.

  • Change in global chi-squared versus charm-quark mass: NLO, NNLO.
  • Change in chi-squared for each data set versus charm-quark mass: NLO, NNLO.
  • Range of charm-quark masses for which data sets are described within their 90% C.L. limit (outer error bars) or 68% C.L. limit (inner error bars): NLO, NNLO.

Additional grids for standalone code

  1. First make sure you have the standalone code and grids for the default mc and mb values in the 5-flavour scheme, provided with the earlier MSTW 2008 paper. Note that minor changes were needed to the interpolation code to support the full range of heavy-quark masses, therefore it is recommended to use the modified version updated on 14th July 2010. (The previous version of the code is still sufficient if using the grid files with 1.25 GeV ≤ mc ≤ 1.55 GeV and mb ≤ 5.00 GeV, but it will terminate with an error message if mc or mb are outside these ranges.)
  2. Download the following additional files into the “Grids/” directory.
    • mstw2008lo_nf3.00.dat (322 KB) : LO, 3-flavours, central set.
    • mstw2008lo_nf4.00.dat (322 KB) : LO, 4-flavours, central set.
    • mstw2008nlo_nf3.00.dat (322 KB) : NLO, 3-flavours, central set.
    • mstw2008nlo_nf4.00.dat (322 KB) : NLO, 4-flavours, central set.
    • mstw2008nnlo_nf3.00.dat (393 KB) : NNLO, 3-flavours, central set.
    • mstw2008nnlo_nf4.00.dat (393 KB) : NNLO, 4-flavours, central set.
    • mstw2008lo_nf3eig.tar.gz (6.0 MB) : LO, 3-flavours, 40 eigenvector sets at both 68% and 90% C.L.
    • mstw2008lo_nf4eig.tar.gz (6.8 MB) : LO, 4-flavours, 40 eigenvector sets at both 68% and 90% C.L.
    • mstw2008nlo_nf3eig.tar.gz (6.0 MB) : NLO, 3-flavours, 40 eigenvector sets at both 68% and 90% C.L.
    • mstw2008nlo_nf4eig.tar.gz (6.8 MB) : NLO, 4-flavours, 40 eigenvector sets at both 68% and 90% C.L.
    • mstw2008nnlo_nf3eig.tar.gz (6.3 MB) : NNLO, 3-flavours, 40 eigenvector sets at both 68% and 90% C.L.
    • mstw2008nnlo_nf4eig.tar.gz (8.0 MB) : NNLO, 4-flavours, 40 eigenvector sets at both 68% and 90% C.L.
    • mstw2008nlo_mc.tar.gz (4.7 MB) : NLO grids for a range of mc values between 1.05 GeV and 1.75 GeV in steps of 0.05 GeV (excluding 1.40 GeV). Four grids are provided for each mc value, with free αS(MZ) (default) or fixed αS(MZ), and with 5-flavour (default) or 3-flavour evolution.
    • mstw2008nnlo_mc.tar.gz (5.4 MB) : NNLO grids for a range of mc values between 1.05 GeV and 1.75 GeV in steps of 0.05 GeV (excluding 1.40 GeV). Four grids are provided for each mc value, with free αS(MZ) (default) or fixed αS(MZ), and with 5-flavour (default) or 3-flavour evolution.
    • mstw2008nlo_mb.tar.gz (1.1 MB) : NLO grids for a range of mb values between 4.00 GeV and 5.50 GeV in steps of 0.25 GeV (excluding 4.75 GeV). Two grids are provided for each mb value, with free αS(MZ) (but the correlation with mb is negligible), and with 5-flavour (default) or 4-flavour evolution.
    • mstw2008nnlo_mb.tar.gz (1.3 MB) : NNLO grids for a range of mb values between 4.00 GeV and 5.50 GeV in steps of 0.25 GeV (excluding 4.75 GeV). Two grids are provided for each mb value, with free αS(MZ) (but the correlation with mb is negligible), and with 5-flavour (default) or 4-flavour evolution.
  3. Unpack each file into the “Grids/” directory with e.g. tar zxvf filename.tar.gz.
  4. An example program ggh_hq_mstwpdf.f illustrates the use of the additional grids. Compile by linking to mstwpdf.f and alphaS.f. It should give output as in ggh_hq_mstwpdf.output. The example program is only provided in Fortran. However, the additional grids can be used just as well with either the Fortran, C++ or Mathematica interpolation code.

Additional grids for LHAPDF

The updated source code and grids will very soon be available in LHAPDF V5.8.4. To use the new grids immediately with older versions of LHAPDF (V5.8.0 to V5.8.3), follow these instructions:

  1. Replace wrapmstw.f and wrapmstw-lite.f in the src/ directory, then rebuild with make; make install.
  2. Download MSTW2008hqLHgrids.tar.gz (54 MB) into the “share/lhapdf/PDFsets/” directory.
  3. Unpack with e.g. tar zxvf MSTW2008hqLHgrids.tar.gz.
  4. An example program ggh_hq_lhapdf.f illustrates the use of the additional grids. Compile by linking to the LHAPDF library in the usual way. It should give output as in ggh_hq_lhapdf.output.
The provided grid files obtained after unpacking MSTW2008hqLHgrids.tar.gz (54 MB) are as follows: Enough information should be given in the description of each .LHgrid file stored in the header to be able to identify each PDF member.

Update (2nd August 2010): The updated code and additional grids are now included in LHAPDF V5.8.4.

Update (17th September 2013): For certain processes it is useful to have PDFs evolved with a maximum of 4 flavours, but allowing for up to 5 flavours in the αS running, whereas the original 4-flavour PDFs given above were evolved with a 4-flavour αS running. Some plots showing the change in the NLO PDFs relative to the usual 4-flavour and 5-flavour PDFs can be found here.

Here are additional grids for the standalone code, all using 4-flavour PDF evolution but 5-flavour αS running, only for the default quark masses of mc = 1.40 GeV and mb = 4.75 GeV:

Here are the corresponding additional grids for the LHAPDF interface:

Comments to Graeme Watt <gwatt(at)physik.uzh.ch>.