Summary of the discussions in the VH-VBF working subgroup 
This is a list of deliverables that we would like to discuss during the January general assembly, in order to foster the necessary work to have them attained. For each of the final states, we address a list of features that we'd like to have available in the final simulation we will use for the 13 TeV data taking.  Those features are the following: 
	•	NNLO QCD precision
	•	NNLO QCD calculation uncertainty
	•	NLO EWK precision
	•	NLO EWK calculation uncertainty
	•	uncertainty related to the matching to parton shower 
	•	uncertainty related to the merging in the calculation with additional jets
	•	backgrounds specifically relevant for the final state in study 
	•	BSM in the specific final states 
The general framework is that experiments will start the first run of event generation very soon, and this will be dedicated to the analyses addressing the first dataset with 5/fb luminosity. New rounds of production are probable for the analyses using an extended dataset of about 10/fb; therefore, the timeframe for developments should ideally meet the start date of this second round (possibly Spring 2015). 
Besides the avaiability of tools to produce the various calculations, we recognise as an important feature the usability of those tools as well, from a community which is in general wider than the authors of the code. Therefore, the tools should be easily operated, possibly easily integrated in the experiments’ software frameworks, and should not require an undue amount of resources. 
To start with, we assume that the work for the implementation of BSM in the VBF and VH final state has to be discussed with the responsible conveners of the proper WG in the XSWG organisation; therefore, this point will not be addressed in the following discussion.  We will be in contact with the relevant subgroups from WG3. 
Several tools are present, and some of them have even been already used in the past LHC data analyses. 
	•	Signal event generation: typically NLO precision, matching with shower, merging when necessary because of the presence of additional jets. POWHEG, Madgraph5/aMC@NLO are the most used ones. They allow for NLO QCD generation and provide reweighting capabilities to calculate QCD uncertainties. VBFHJJJ exists as well, both in POWHEG and aMC@NLO. 
	•	Signal differential cross-section calculations are available to address NLO EWK and approximate NNLO QCD corrections (as well as BSM models). HAWK, VBFNLO, VBFNNLO are the most used ones. Tools for events reweighting (REPOLO) are also available on the market. 
	•	Background events generation: tools are available to calculate HJ, HJJ and to generate events with them, even merged if necessary (POWHEG, Madgraph5/aMC@NLO). HJJJ calculations are being develped (GoSam). 
In the following, the points are discussed in detail for VH and VBF. 
The VH associated production 
	•	The NNLO QCD precision for the VH production process can be attained, as in the past, through a bread-and-butter differential reweighting of some relevant variables, or through a NNLOPS-like procedure implemented within the POWHEG-MINLO framework. This second implementation requires the generation of huge samples (possibly on the order of a billion events) to properly calculate the NNLO/NLO reweighting that can then be used on top of NLO generated events. The timescale of this procedure to be put in place might be Spring 2015. The fully differential NNLO QCD corrections for H decay into a b-bbar pair has been worked out by two completely independent groups who find perfect agreement between them. A parton-level code that will merge both NNLO QCD corrections for the production and the decay in the narrow-width approximation could be constructed and might be available beginning in Spring 2015.
	•	The NNLO QCD calculation uncertainty will be addressed on top of these tools, both the parton level one and, if/when available, the NNLOPS one. Furthermore, MG5_aMC has also been proposed to produce a merged sample for VH plus jets with the aim of performing a tuned comparison with the NNLO code.
	•	The NLO EWK precision corrections will be derived with HAWK and applied to generated samples through reweighting, as done in the past for data taking. The aMC@NLO generator is including the EWK corrections following basically this same recipe. 
	•	The NLO EWK calculation uncertainty will come from the same procedure, using some estimates based on previous experience with higher-order effects in related production processes.
	•	The uncertainty related to the matching to parton shower will be calculated through variations of the generated sample, after the reweighting described in the first point. In fact, the MINLO-based procedure will already account for removing double countings between NNLO calculation and NLO+PS. 
	•	For processes with colorless final state at the Born level, like VH production, the uncertainty related to the merging with the calculation with an extra jet radiation appears to be under control within the Minlo scheme, but comparisons with other schemes might also be useful.
	•	The backgrounds specifically relevant for the final state in study are the components of the very large V+jets background. Historically, ATLAS and CMS use different generators for the main production, plus several other generators for comparison studies. Such comparisons are crucial for the analysis understanding, and yet very experiment-dependent. Therefore, even if we do not see a clear way to perform a unequivocal study at generator level, and even if we think that the data-driven techniques will absorb part of possible differences between generators, we would find it interesting to perform some comparisons in the working group, provided manpower is found for the task.  The gluon-induced di-boson production with two additional jets will be studied as well, starting from the PHANTOM generator. 
The vector boson fusion production 
	•	The NNLO QCD precision does not seem to pose a major problem for the analysis, as the k-factors are expected to be generically small and flat. Therefore, we plan to calculate them and reweight NLO events, to improve the uncertainty associated to the cross-section. Besides these, the POWHEG VBF HJJJ calculation (Higgs plus three jets at born level, where two of them are the tag jets) is of relevance, since it addresses the real third additional jet radiation (while the NLO corrections to VBFH are NLO accurate for the HJJ final state, but only LO accurate for the third jet). Such a calculation also exists in MadGraph5_aMC@NLO, but we do not know whether the merging to lower jet multiplicities has ever been implemented or tested.
	•	The NNLO QCD calculation uncertainty will be addressed from the calculations mentioned in the previous point.
	•	The NLO EWK precision corrections will be derived from HAWK and applied to generated samples through reweighting, as done in the past data taking.
	•	The uncertainty related to the matching to parton shower will be calculated through variations of the generated sample, after the reweighting described in the first point. 
	•	The uncertainty related to the merging in the calculation with additional jets still needs to be studied.
	•	A background relevant for the final state under study is the gluon-fusion Higgs produced in association with jets. The GF-induced Higgs plus jets production is one major background in the VBF signal region and needs to be addressed with care in close collaboration with the WG1 gluon-fusion subgroup.   Our belief is that the POWHEG HJ and HJJ generations, each of them coupled to a shower, and after applying selections which prevent problems of merging between the two, will be usable during the future data taking. The HJJJ generation is also being developed with GoSam. 
	•	Another interesting issue is related to the continuum diboson + two jets production (VVjj). The VVjj background will be relevant in the case of off-shell studies; therefore, we think that a discussion should happen between us and the relevant working group in the XS WG. For this, LO (PHANTOM, VBNLO) and for some processes NLO (POWHEG) tools exist and can generate events. 
In summary, the work dedicated to the VH final state will have to focus first on QCD NNLO corrections, and second on the peculiarities of the backgrounds. For the VBF case, the activity will be in the line of what has been done in the past, adapting to the new data taking conditions. 
From past experience, we find it important to provide recipes to be followed by all the experiments to get at the events characterised by the best precison attainable, with a proper estimate of the uncertainties. In some aspects, this can be obtained by adapting the procedures already suggested for the past data taking and working to obtain some consensus.