Les Houches

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====== Fixed-Order vs ME+PS for inclusive jets ======
People: Kostas Theofilatos, Joey Huston, Silvan Kuttimalai, Suman Chatterjee, Simone Alioli, Emanuele Re (I can't guarantee, but I'll try), Valentin Hirschi, Joao Pires, Efe Yazgan (for NP effects), Andy Buckley , Johannes Bellm... (**add your name** if you are interested)
 

===== Motivation =====
This is a followup to the Higgs+jets comparisons that occurred in Les Houches 2015. The inclusive jet cross section has the widest dynamic range of any process at the LHC, and has served as one of the key benchmark cross sections in global PDF fits. Til now, jet production has been included at NLO, even in NNLO fits due to its importance. Now, for the first time, the fits can be performed with NNLO jets. The Tevatron jet data all had a jet radius of 0.7. At the LHC, data with jet radii of 0.4, 0.5, 0.6 and 0.7 are available. The perturbative jet cross sections are corrected for effects from the underlying event and fragmentation. These corrections are determined by Monte Carlo parton shower programs and the assumption made is that corrections determined from parton showers apply equally well to fixed order, i.e. the jet shapes for the two are similar enough for this connection to be valid. 

This study will test:

(1)    if there are significant resummation (parton shower) effects on top of the fixed order core prediction
(2)    if the NLO results are incorrect because of the inability of the NLO matrix elements to correctly describe the jet shape; this will be more serious for the smaller jet sizes than the larger ones
(3)    if the impact from either of the above effects is reduced at NNLO, and if residual corrections are needed in global PDF fits to account for these effects

The study will be undertaken with both fixed order (NLO and NNLO) and ME+PS programs. Results will be quoted both at the parton (parton shower) level and at the hadron level (for ME+PS).  The same PDF will be used, and the same core scale (as much as possible) will also be used. A Rivet routine will be provided based on CMS measurements at 13 TeV for R=0.4 and 0.7. It will be supplemented with jet sizes of 0.3, 0.6, and 1.0. 

Note that this will also lead to an effective prediction of the jet shape at the various orders. 

===== Addendum 1 =====

Following the quark/gluon meeting on Saturday morning, we would like to add to the Rivet routine variables measuring the jet mass, the jet width and the Les Houches angularity for each kinematic bin and each R value. Jesse will provide the exact code. These variables, of course, are not measured by CMS, but such a comprehensive study should prove useful for multiple reasons. 

These three observables are defined in section 3.1 of:

https://arxiv.org/abs/1704.03878

and have been included in the RIVET routine for the quark/gluon study:

https://github.com/gsoyez/lh2015-qg/blob/master/MC_LHQG_dijet.cc

The key functions are ca_wta_recluster() and compute_and_record().

===== Addendum 2 =====

This study can also be used as a testbed for the impact of scale choices on the inclusive jet cross section calculation. In the inclusive cross section, both in data and in theory, each jet contributes to its respective pT and y bin in the histograms. For fixed order calculations, it has been traditional for the matrix element to be evaluated with the scale of the jet pT being considered, i.e. pTjet. If there are 4 jets in the event (for a NNLO calculation), then there are 4 entries corresponding to each event, with each entry being calculated with a different scale. An alternative is to use as a scale for all entries the maximum jet pT in the event (pTmax), and/or a global scale of HT/2 (where HT is the sum of the jet pT's). As an add-on to this study, we would like to calculate the:

-leading jet pT cross section

-2nd leading jet pT cross section

-3rd leading jet pT cross section

-4th leading jet pT cross section

using either the individual jet pT values, or the maximum pT of any jet in the event. It is easier to adjust the core scale in ME+PS programs than the scale for the 3rd and 4th jet, so an exact correspondence to the fixed order test may not be possible, but we can try to be as close as possible. There is a matching coffee bet from Daniel Maitre on the resulting comparisons. 

These comparisons should be done inclusively and exclusively. For the exclusive study, it would be, for example, the 3rd leading jet for events in which there are exactly 3 jets, etc. 

===== Addendum 3 =====

This study also serves as a good testbed for non-perturbative corrections for inclusive jet cross sections, as a function of R, since the ME+PS calculations will be carried out for both parton shower level and full hadron level. As the non-perturbative corrections seem to differ between CMS and ATLAS, the results may serve as a useful benchmarks. 

===== Files ======
  * Slides from the discussion session at Les Houches {{:2017:working_groups:sm:lh2017_jets.pdf}}  
  * CMS rivet routine (SMP-15-007) {{:2017:working_groups:cms_2016_i1459051.tar}}  ; extra R values, distributions will be added
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