===== Gluon Fusion Background to VBF =====

== Topic Ideas ==
  * Study top mass dependence at [[https://arxiv.org/abs/2110.06953|NLO_FTapprox]]
  * Compare to impact of [[https://indico.ph.ed.ac.uk/event/118/contributions/2401/attachments/1273/1802/RADCOR23_Jaskiewicz_talk.pdf|HEJ]] (see slide 6)
  * in HH, the effects were more sizeable [https://arxiv.org/pdf/1803.02463.pdf]; can we understand what differs for H+2j?
  * A possible simple prescription for Powheg: use LO ratio (exact/HTL) evaluated on Born-projected kinematics as a first approximation.

== Setup ==

Input parameters and settings
  * $\sqrt{s} = 13.6\,\mathrm{TeV}$
  * PDF set:  ''PDF4LHC21_40''
  * $M_\mathrm{H} = 125.09\,\mathrm{GeV}$
  * $m_\mathrm{t} = 172.5\,\mathrm{GeV}$
  * $M_\mathrm{Z} = 91.1876\,\mathrm{GeV}$,  $\Gamma_\mathrm{Z} = 2.4952\,\mathrm{GeV}$
  * $M_\mathrm{W} = 80.379\,\mathrm{GeV}$,  $\Gamma_\mathrm{W} = 2.085\,\mathrm{GeV}$
  * G-mu scheme with $\alpha_{G_\mu} = 0.75652103079904\ldots \times 10^{-2}$ (from $G_\mu = 1.16638 \times 10^{-5}\,\mathrm{GeV}^{-2}$)
  * central scale choice:  $\mu_0^2 = (M_\mathrm{H}/2) \, \sqrt{ (M_\mathrm{H}/2)^2 + p_\mathrm{T,H}^2 }$ (Eq.(2) of 1506.02660)

== Cuts/Binning ==

Event definition/selection:
  * jets: anti-kT with $R=0.4$
  * $p_{\mathrm{T},j} > 30\,\mathrm{GeV}$
  * $|\eta_j| < 4.7$
  * $m_{jj} > 300\,\mathrm{GeV}$
  * $|\Delta y_{jj}| > 2$ 
  * no rapidity selection on Higgs

Histograms and binning:
  * double-differential ($m_{jj} \times p_\mathrm{T,H}$):  ''[300, 500, 700, 900, 1100, ∞] × [0, 80, 120 ,260, 500, 850, ∞]''
  * double-differential ($m_{jj} \times \Delta\phi_{jj}$):  ''[300, 500, 700, 900, 1100, ∞] × [0, π/4, π/2, 3π/4, π]''
  * double-differential ($m_{jj} \times \Delta y_{jj}$):  ''[300, 500, 700, 900, 1100, ∞] × [2, 4, 5, 6, 7, ∞]''
  * double-differential ($p_\mathrm{T,H} \times \Delta y_{jj}$):  ''[0, 80, 120 ,260, 500, 850, ∞] × [2, 4, 5, 6, 7, ∞]''


Underlying event tunes in CMS:

  *'Tune:preferLHAPDF = 2',
  *'Main:timesAllowErrors = 10000',
  *'Check:epTolErr = 0.01',
  *'Beams:setProductionScalesFromLHEF = off',
  *'SLHA:minMassSM = 1000.',
  *'ParticleDecays:limitTau0 = on',
  *'ParticleDecays:tau0Max = 10',
  *'ParticleDecays:allowPhotonRadiation = on',

  *'Tune:pp 14',
  *'MultipartonInteractions:ecmPow=0.03344',
  *'MultipartonInteractions:bProfile=2',
  *'MultipartonInteractions:pT0Ref=1.41',
  *'MultipartonInteractions:coreRadius=0.7634',
  *'MultipartonInteractions:coreFraction=0.63',
  *'ColourReconnection:range=5.176',
  *'SigmaTotal:zeroAXB=off',
  *'SpaceShower:alphaSorder=2',
  *'SpaceShower:alphaSvalue=0.118',
  *'SigmaProcess:alphaSvalue=0.118',
  *'SigmaProcess:alphaSorder=2',
  *'MultipartonInteractions:alphaSvalue=0.118',
  *'MultipartonInteractions:alphaSorder=2',
  *'TimeShower:alphaSorder=2',
  *'TimeShower:alphaSvalue=0.118',
  *'SigmaTotal:mode = 0',
  *'SigmaTotal:sigmaEl = 22.08',
  *'SigmaTotal:sigmaTot = 101.037',  
  *'PDF:pSet=LHAPDF6:NNPDF31_nnlo_as_0118',