
MSTW PDFs : PDF sets for different m_{c} and m_{b} values and 3 and 4flavour PDFs
Here we provide additional PDF grid files associated with the paper:
A. D. Martin, W. J. Stirling, R. S. Thorne and G. Watt,
“Heavyquark mass dependence in global PDF analyses and 3 and 4flavour parton distributions”,
Eur. Phys. J. C 70 (2010) 5172
[arXiv:1007.2624 [hepph]].
Please reference this paper if you use these PDF grids for a publication.
We provide NLO and NNLO grids with the heavyquark pole masses m_{c} 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 m_{b} 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 m_{c} = 1.40 GeV and m_{b} = 4.75 GeV. For each value of m_{c} and m_{b} the strong coupling α_{S}(M_{Z}) is treated as a free parameter in the fits. We also provide grids with varying m_{c} and α_{S}(M_{Z}) held fixed at the MSTW 2008 values. The correlation between m_{b} and α_{S}(M_{Z}) is negligible, so fits with varying m_{b} and fixed α_{S}(M_{Z}) are not explicitly provided.
For the default quark masses, m_{c} = 1.40 GeV and m_{b} = 4.75 GeV, 3 and 4flavour PDFs are generated by evolving the fitted input PDFs and α_{S}(Q_{0}) determined from the 5flavour MSTW 2008 fits at Q_{0} = 1 GeV. This is also done for the 40 associated eigenvector PDF sets at both 68% and 90% confidencelevel (C.L.) to allow the calculation of PDF uncertainties in a 3 or 4flavour scheme. For all fits with varying m_{c}, both with free and fixed α_{S}(M_{Z}), 3flavour PDF grids are provided. Similarly, for all fits with varying m_{b}, with free α_{S}(M_{Z}), 4flavour PDF grids are provided. These additional grids will allow the m_{c} or m_{b} dependence to be consistently studied in a 3 or 4flavour scheme calculation, respectively.
To assess the uncertainty due to m_{c} and m_{b} on an observable such as a hadronic cross section, our recommendation is to calculate the central value with m_{c} = 1.40 GeV and m_{b} = 4.75 GeV using the default MSTW 2008 PDFs. The crosssection variation should then be calculated by separately varying m_{c} = 1.40±0.15 GeV at 68% C.L. (or ±0.25 GeV at 90% C.L.) and m_{b} = 4.75±0.25 GeV at 68% C.L. (or ±0.50 GeV at 90% C.L.), with α_{S}(M_{Z}) held fixed in the case of m_{c}. The resulting crosssection variation can then be added in quadrature with the other uncertainties.
Below we provide plots documenting the charmquark mass dependence of the NLO and NNLO global fits; see Section 3.1 of arXiv:1007.2624 for more explanation.
 Change in global chisquared versus charmquark mass:
NLO, NNLO.
 Change in chisquared for each data set versus charmquark mass:
NLO, NNLO.
 Range of charmquark 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.
 First make sure you have the standalone code and grids for the default m_{c} and m_{b} values in the 5flavour scheme, provided with the earlier MSTW 2008 paper. Note that minor changes were needed to the interpolation code to support the full range of heavyquark 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 ≤ m_{c} ≤ 1.55 GeV and m_{b} ≤ 5.00 GeV, but it will terminate with an error message if m_{c} or m_{b} are outside these ranges.)
 Download the following additional files into the “Grids/” directory.
 mstw2008lo_nf3.00.dat (322 KB) : LO, 3flavours, central set.
 mstw2008lo_nf4.00.dat (322 KB) : LO, 4flavours, central set.
 mstw2008nlo_nf3.00.dat (322 KB) : NLO, 3flavours, central set.
 mstw2008nlo_nf4.00.dat (322 KB) : NLO, 4flavours, central set.
 mstw2008nnlo_nf3.00.dat (393 KB) : NNLO, 3flavours, central set.
 mstw2008nnlo_nf4.00.dat (393 KB) : NNLO, 4flavours, central set.
 mstw2008lo_nf3eig.tar.gz (6.0 MB) : LO, 3flavours, 40 eigenvector sets at both 68% and 90% C.L.
 mstw2008lo_nf4eig.tar.gz (6.8 MB) : LO, 4flavours, 40 eigenvector sets at both 68% and 90% C.L.
 mstw2008nlo_nf3eig.tar.gz (6.0 MB) : NLO, 3flavours, 40 eigenvector sets at both 68% and 90% C.L.
 mstw2008nlo_nf4eig.tar.gz (6.8 MB) : NLO, 4flavours, 40 eigenvector sets at both 68% and 90% C.L.
 mstw2008nnlo_nf3eig.tar.gz (6.3 MB) : NNLO, 3flavours, 40 eigenvector sets at both 68% and 90% C.L.
 mstw2008nnlo_nf4eig.tar.gz (8.0 MB) : NNLO, 4flavours, 40 eigenvector sets at both 68% and 90% C.L.
 mstw2008nlo_mc.tar.gz (4.7 MB) : NLO grids for a range of m_{c} 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 m_{c} value, with free α_{S}(M_{Z}) (default) or fixed α_{S}(M_{Z}), and with 5flavour (default) or 3flavour evolution.
 mstw2008nnlo_mc.tar.gz (5.4 MB) : NNLO grids for a range of m_{c} 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 m_{c} value, with free α_{S}(M_{Z}) (default) or fixed α_{S}(M_{Z}), and with 5flavour (default) or 3flavour evolution.
 mstw2008nlo_mb.tar.gz (1.1 MB) : NLO grids for a range of m_{b} 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 m_{b} value, with free α_{S}(M_{Z}) (but the correlation with m_{b} is negligible), and with 5flavour (default) or 4flavour evolution.
 mstw2008nnlo_mb.tar.gz (1.3 MB) : NNLO grids for a range of m_{b} 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 m_{b} value, with free α_{S}(M_{Z}) (but the correlation with m_{b} is negligible), and with 5flavour (default) or 4flavour evolution.
 Unpack each file into the “Grids/” directory with e.g. tar zxvf filename.tar.gz.
 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:
 Replace wrapmstw.f and wrapmstwlite.f in the src/ directory, then rebuild with make; make install.
 Download MSTW2008hqLHgrids.tar.gz (54 MB) into the “share/lhapdf/PDFsets/” directory.
 Unpack with e.g. tar zxvf MSTW2008hqLHgrids.tar.gz.
 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:
 MSTW2008lo68cl_nf3.LHgrid (13 MB) : LO, 3flavours, central set and 40 eigenvector sets at 68% C.L.
 MSTW2008lo90cl_nf3.LHgrid (13 MB) : LO, 3flavours, central set and 40 eigenvector sets at 90% C.L.
 MSTW2008lo68cl_nf4.LHgrid (13 MB) : LO, 4flavours, central set and 40 eigenvector sets at 68% C.L.
 MSTW2008lo90cl_nf4.LHgrid (13 MB) : LO, 4flavours, central set and 40 eigenvector sets at 90% C.L.
 MSTW2008nlo68cl_nf3.LHgrid (13 MB) : NLO, 3flavours, central set and 40 eigenvector sets at 68% C.L.
 MSTW2008nlo90cl_nf3.LHgrid (13 MB) : NLO, 3flavours, central set and 40 eigenvector sets at 90% C.L.
 MSTW2008nlo68cl_nf4.LHgrid (13 MB) : NLO, 4flavours, central set and 40 eigenvector sets at 68% C.L.
 MSTW2008nlo90cl_nf4.LHgrid (13 MB) : NLO, 4flavours, central set and 40 eigenvector sets at 90% C.L.
 MSTW2008nnlo68cl_nf3.LHgrid (16 MB) : NNLO, 3flavours, central set and 40 eigenvector sets at 68% C.L.
 MSTW2008nnlo90cl_nf3.LHgrid (16 MB) : NNLO, 3flavours, central set and 40 eigenvector sets at 90% C.L.
 MSTW2008nnlo68cl_nf4.LHgrid (16 MB) : NNLO, 4flavours, central set and 40 eigenvector sets at 68% C.L.
 MSTW2008nnlo90cl_nf4.LHgrid (16 MB) : NNLO, 4flavours, central set and 40 eigenvector sets at 90% C.L.
 MSTW2008nlo_mcrange.LHgrid (4.7 MB) : NLO, 5flavours, range of m_{c} values, free α_{S}(M_{Z}).
 MSTW2008nlo_mcrange_nf3.LHgrid (4.7 MB) : NLO, 3flavours, range of m_{c} values, free α_{S}(M_{Z}).
 MSTW2008nlo_mcrange_fixasmz.LHgrid (4.7 MB) : NLO, 5flavours, range of m_{c} values, fixed α_{S}(M_{Z}).
 MSTW2008nlo_mcrange_fixasmz_nf3.LHgrid (4.7 MB) : NLO, 3flavours, range of m_{c} values, fixed α_{S}(M_{Z}).
 MSTW2008nlo_mbrange.LHgrid (2.2 MB) : NLO, 5flavours, range of m_{b} values, free α_{S}(M_{Z}).
 MSTW2008nlo_mbrange_nf4.LHgrid (2.2 MB) : NLO, 4flavours, range of m_{b} values, free α_{S}(M_{Z}).
 MSTW2008nnlo_mcrange.LHgrid (5.8 MB) : NNLO, 5flavours, range of m_{c} values, free α_{S}(M_{Z}).
 MSTW2008nnlo_mcrange_nf3.LHgrid (5.8 MB) : NNLO, 3flavours, range of m_{c} values, free α_{S}(M_{Z}).
 MSTW2008nnlo_mcrange_fixasmz.LHgrid (5.8 MB) : NNLO, 5flavours, range of m_{c} values, fixed α_{S}(M_{Z}).
 MSTW2008nnlo_mcrange_fixasmz_nf3.LHgrid (5.8 MB) : NNLO, 3flavours, range of m_{c} values, fixed α_{S}(M_{Z}).
 MSTW2008nnlo_mbrange.LHgrid (2.7 MB) : NNLO, 5flavours, range of m_{b} values, free α_{S}(M_{Z}).
 MSTW2008nnlo_mbrange_nf4.LHgrid (2.7 MB) : NNLO, 4flavours, range of m_{b} values, free α_{S}(M_{Z}).
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 α_{S} running, whereas the original 4flavour PDFs given above were evolved with a 4flavour α_{S} running. Some plots showing the change in the NLO PDFs relative to the usual 4flavour and 5flavour PDFs can be found here.
Here are additional grids for the standalone code, all using 4flavour PDF evolution but 5flavour α_{S} running, only for the default quark masses of m_{c} = 1.40 GeV and m_{b} = 4.75 GeV:
Here are the corresponding additional grids for the LHAPDF interface:
Comments to Graeme Watt <gwatt(at)physik.uzh.ch>.
