LO and NLO PDFs in Monte Carlo Event Generators

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1 LO and NLO PDFs in Monte Carlo Event Generators Juan Rojo CERN, PH Division, TH Unit CMS Affiliate Scientist CMS Physics Comparisons and Generator Tunes CERN,

2 LO/NLO PDFs in Event Generators The problem of which is the correct PDF set/order to use in different theoretical calculations has been recently emphasized by a wide range of tools available: multileg LO, PS, multileg LO matched to PS, NLO, NLO matched to PS, multileg NLO, matched to PS, NNLO... A crucial point is that, in Event Generators, PDFs are required to describe not only the perturbative physics but also the non-perturbative one from UE, MB etc Event Generators such as Pythia, Herwing and Sherpa derive tunes of non-perturbative physics that are based on specific PDF sets Now, we see the first issue (there are many!): are (say) Pythia tunes (that have been obtained with Pythia stand-alone) still valid when Pythia is used as PS module for amcatnlo/powheg? To which extent this has been checked? Who is responsible for that? Second issue: surely I want to use NLO PDFs in the hard-scattering calculation of a NLO+PS code, but then for the PS part, should I use a LO PDF? Is this inconsistent? Does this matter at all? To be really kosher, should we derive PDFs based on exactly the same theory info that in NLO+PS calculations? This is the ultimate consistency, but is relevant for LHC pheno? In this talk, I ll try to set up the discussion and open problems, but not a comprehensive review!

3 LO PDFs in Event Generators Already in the simplest case, LO generators, we encounter some conundrums. Some MCs, like Pythia8, only recommend tunes based on LO PDFs. NLO PDFs tunes give also a good description to the data, but leading to some unphysical NP parameters like the QCD cross-section cut-off p T 0 Other MCs, like Sherpa, provide as default tunes based on NLO PDFs (like NNPDF.3 NLO) Ideally one would like to use NLO PDFs everywhere, since these lead to an improved description of collider data. Pythia8 allows to use different PDFs in hard-scattering and in the UE/MB parts LO PDFs lead to a very poor description of experimental data and are affected by very large (and uncontrolled) theory uncertainties: substantial differences between LO PDFs. Which one is better? It is necessarily the one that leads to a better tune?

4 Negative PDFs N(N)LO PDFs do not have probabilistic interpretation, and thus in principle negative values are allowed On the other hand, positivity of physical observables should be enforced (done in NNPDF, not in MSTW -> negative FL at small-x) Data prefer small or even negative gluon at small-x, and large-x antiquarks can be also very small This is a major problem for LO generators, since the Sudakovs blow up if PDFs are zero or negative So a first requirement, if NLO PDFs are to be used in MCs, they need to be positive definite NNPDF.3 NLO MC is a positive-definite version of NNPDF.3 NLO, which maintains the excellent description of all available data, including LHC data

5 LO and LO* PDFs Several improved LO sets have been produced to i) improve the description of hard-scattering data while ii) still leading to a steeply rising small-x gluon as required in some UE/MB tunes These improved sets, MRST LO*, CT09MC, NNPDF.1 LO*, different from standard LO in the running of the strong coupling (NLO in some cases) and relaxing the momentum sum rule However, once a flexible enough functional form is used (NNPDF.1 LO analysis), fit quality for various types of LO PDF sets is essentially identical From the point of view of experimental data, the use of LO* sets is nor required nor justified: better to use vanilla LO PDFs.

6 LO/NLO PDFs and MB/UE physics A completely different topic (from the physics point of view) is which PDFs should be used to describe MB/UE in event generators Recall that UE physics requires PDFs at low scales and down to x= -7, far from any experimental constraints However, a steep rise of the small-x gluon is expected both from HERA F data and from the pp cross section. This is naturally achieved in LO PDFs to DIS data, but is also consistent with NLO PDFs Could we obtain reasonable tunes with NLO PDFs? Yes, one can use, instead of the central value for the gluon (at small-x it is small or negative), one of the 0 replicas of NNPDF, with a strong rise at small-x (within the PDF uncertainty band) 0 QCD+QED PDFs, Q = GeV NNPDF.3 QCD+QED NLO Rep3 ) [new] g ( x, Q NNPDF.3 QCD+QED LO Steeply rising gluon (for MB/UE) and good description of all hard scattering data with a single PDF possible x

7 NNPDF.3 LO QCD+QED NNPDF.3 QED is the first ever PDF set obtained at (N)NLO accuracy in QCD and LO accuracy in QED, where the photon PDF has been determined from LHC W,Z production data Upon Tobjorn s request, we have produced a LO QCD+QED set, which will be added to the Pythia8 stand-alone PDFs. This will allow to derive consistent predictions including both QCD and QED showers Validation of the NNPDF LO QCD+QED wrt MB/UE etc will begin soon, might become Pythia8 default if reasonable tune is obtained Differences in gluon between commonly used LO sets can be as large as LO/NLO differences ) [ref] ) [new] / g ( x, Q g ( x, Q QCD+QED PDFs, Q = GeV -3 x - NNPDF.3 QCD+QED NLO =0.119 S NNPDF.3 QCD+QED LO =0.130 S -1 ) [ref] ) [new] / g ( x, Q g ( x, Q QCD+QED PDFs, Q = GeV -5-4 x -3 NNPDF.3 QCD+QED LO =0.130 S MRST007LOmod CTEQ6L CT09 MC1 - -1

8 Outlook The problem of the optimal PDF set to be used in Event Generators is still open, and more work is required by theorists Ideally, one should use the same PDF set in all the computation (hard+soft). When this is not possible, use NLO PDFs for hard part and LO PDFs for the soft part It should be possible to have reasonable tunes with NLO PDFs - If anything because the steep rise of the gluon at small-x is compatible with available hard scattering data within uncertainties. Instead of deriving LO* updated sets, better to think of improved strategies to derive NLO PDFs that agree better with soft and semi-hard data (if generic, generator independent ) Recently, LO PDFs sets with both QCD and QED effects have become available, with allow consistent inclusion of both QCD and EW/QED showers in MCs Many open questions: do tunes for LO MCs still hold when used in NLO+PS calculations? Do we need PDFs based on NLO+PS theory? Can we include UE/MB data directly into PDF analysis (at least the semi-hard data)? Lots of work to do!!