# PDF¶

## Using a built-in PDF¶

A built-in PDF like the MRST PDF can be used in the following way as a default PDF:

cd /Herwig/Partons
cp /Herwig/Partons/MRST PDFSet
set /Herwig/Particles/p+:PDF PDFSet
set /Herwig/Particles/pbar-:PDF PDFSet
cd /


## Using a PDF from the LHAPDF interface¶

A PDF from the LHAPDF interface like the CT10 PDF can be used in the following way as a default PDF:

cd /Herwig/Partons
create ThePEG::LHAPDF PDFSet ThePEGLHAPDF.so
set PDFSet:PDFName CT10.LHgrid
set /Herwig/Particles/p+:PDF PDFSet
set /Herwig/Particles/pbar-:PDF PDFSet
cd /


Note: Up to now the alphaS value, the Z reference mass, and the quark masses among other parameters defined in the corresponding LHAPDF info file of the chosen PDF are not automatically considered. It is the responsibility of the Herwig user to set these parameters accordingly if required.

## Set default PDF¶

The default PDF can be set by the following command:

set /Herwig/Particles/p+:PDF    DefaultPDF
set /Herwig/Particles/pbar-:PDF DefaultPDF


This PDF is then used for the hard subprocess, the LHEReader, the parton shower and the underlying event / multi-parton interactions.

## Set PDF of the hard subprocess¶

The PDF of the hard subprocess can be set by the following command:

set /Herwig/Partons/QCDExtractor:FirstPDF  HardPDF
set /Herwig/Partons/QCDExtractor:SecondPDF HardPDF


## Set PDF of the LHEReader¶

In case of reading in a LHE file and changing the PDF of the hard subprocess, it is not enough to only set the PDF of the hard subprocess. Additionally, the PDF of the LHEReader must also be set to the PDF of the hard subprocess:

set /Herwig/Partons/QCDExtractor:FirstPDF  HardPDF
set /Herwig/Partons/QCDExtractor:SecondPDF HardPDF


## Set PDF of the parton shower¶

The PDF of the parton shower can be set by the following command:

set /Herwig/Shower/ShowerHandler:PDFA ShowerPDF
set /Herwig/Shower/ShowerHandler:PDFB ShowerPDF


## Set PDF of the underlying event and the multi-parton interactions¶

The PDF of the underlying event and the multi-parton interactions can be set by the following command:

set /Herwig/Partons/MPIExtractor:FirstPDF  MPIPDF
set /Herwig/Partons/MPIExtractor:SecondPDF MPIPDF


Beware: In general, the PDF of the underlying event and the multi-parton interactions should be a LO PDF. These LO PDFs are strictly tied to the tune you have selected. So please do not swap the PDF if a tune is explicitly branded with a particular PDF set. Changing them in the shower, though, should only have mild impact on the results.

## Choosing of PDFs in NLO matching¶

A few more considerations apply to choosing of PDFs if considering NLO matched samples:

• POWHEG matching

For POWHEG matching, there is basically no cross talk between the hard subprocess PDFs and the shower PDFs, so choosing a LO shower PDF different from whatever (NLO) PDF has been used with Powheg should not be a problem.

• MC@NLO matching

Things are different with MC@NLO matching as there are explicit matching subtractions present in the hard subprocess, which are linked to the shower and so naively using two different PDFs in the hard subprocess and the parton shower could result in unreasonable results.

## How do I switch off ISR in e+e- collisions?¶

ISR in $$e^+e^-$$ collisions is handled slightly differently from that in hadronic collisions. You need to remove the PDF for the electron which allows the ISR to be generated by replacing the PDF with the NoPDF PDF, by adding

set /Herwig/Particles/e-:PDF /Herwig/Partons/NoPDF
set /Herwig/Particles/e+:PDF /Herwig/Partons/NoPDF


to your input file.

## How to I include saturation?¶

We introduced the class SatPDF to be able to mimic parton saturation on whatever used PDF set. With that class it is possible to force the PDF set to be modified in the following way, below $$x_0$$, $$xf(x)$$ will be replaced by

$x f(x) = \left(\frac{x}{x_0}\right)^{\rm exp} x_0f(x_0),$

where $$x_0$$ and $$\rm exp$$ are parameters, which can be modified from the .in files. Example

After copying an appropriate input file to your local directory, adding the following lines before any run or saverun statement will enable the PDF modifications described above.

##################################################
# saturation modifications
##################################################
cd /Herwig/Partons
create Herwig::SatPDF SaturationMod HwSatPDF.so

## Assign the pdf that should be modified:
## use internal pdf
set SaturationMod:PDF MRST
## use lhapdf. This depends on the name YOU have chosen for the LHAPDF PDF set
#set SaturationMod:PDF foo

## may change X0: default is 1E-4
#set SaturationMod:X0 1E-3

## may change Exp: default is 0
#set SaturationMod:Exp 1

## Assign the modified pdf to the beam particles,
## without this step the original pdf's will be used
set /Herwig/Particles/p+:PDF SaturationMod
set /Herwig/Particles/pbar-:PDF SaturationMod
cd /Herwig/Generators