In the following we propose preliminary guidelines (including some open issues) for the calculation of official inclusive cross section for ttH and tH production. They should be adopted for the calculations only once discussed and approved by the ttH and WG1 conveners (mid November at the latest).
## ttV cross sections at NLO QCD+EW

**Collider energy** **Other input parameters and PDFs** **(N)LO EW ingredients**
**Presentation of the results** ## General aspects applicable to ttH and tH

**Higgs Mass scan for ttH and tH (as communicated by WG1 conveners on Nov 18 2015)**

**An additional collider energy scan should be provided with sqrt(s) between 6-15TeV in 0.5TeV steps for MH=125.0 and 125.09.**
**Presentation of the results** ## ttH specific aspects

**Scale choice and variations** **QCD and EW corrections** ## tH specific aspects

**Top-antitop splitting of results**

**Final state bosons**

- V=W+,W-,Z without decays

- 13 and 14 TeV

- Mt=172.5 GeV according to https://cds.cern.ch/record/2047636
- the G_mu input scheme should be used for EW couplings (and EW corrections) with G_mu, MW and MZ as defined in https://cds.cern.ch/record/2047636
- PDFs and alphaS=0.118+0.0015 according to PDF4LHC15 recommendation 2015 http://arxiv.org/abs/1510.03865 (see below for QED PDF effects)
- two central-scale choices should be compared: (a) mu=m_t+m_V/2 and (b) mu=HT/2, where HT=sum of t,T,V transverse energies (ignoring extra jet emissions)

(a) Similarly as for the ttH calculation the following LO and NLO EW ingredients should be included:

- LO EW contributions of O(alpha^3)
- LO mixed EW-QCD contributions of O(alpha^2*alphaS)
- Complete O(alpha^2*alphaS^2) corrections

(c) QED-PDF effects should be included as follows (approach adopted for ttH)

- all quark/gluon induced channels with PDF4LHC15
- reconstruct effects due to QED-evolution of PDFs evaluating the LO QCD ttV cross section with NNPDF.2.3 QED (at NLO QCD) and subtracting the corresponding results with NNPDF2.3 NLO QCD without QED effects
- all gamma-induced channels using NNPDF2.3 QED PDFs

- absolute NLO QCD prediction at the central scale in femtobarn (not the midpoint of the uncertainty band)
- positive and negative scale variation in percent. Here the usual 6-point variation should be applied, including independent factor 0.5 and 2 variations of muR and muF apart from uncorrelated ones.
- positive and negative PDF+alphaS variations in percent (see PDF4LHC recommendation 2015)
- also the NLO QCD K factor (K=NLO/LO both with the same NLO PDFs and input parameters) should be provided
- absolute NLO QCD+EW prediction at the central scale. No scale variation should be applied to the NLO EW correction
- EW K factor defined as (NLO QCD+EW)/(NLO QCD)

See general HXSWG guidelines https://twiki.cern.ch/twiki/bin/view/LHCPhysics/LHCHXSWGCrossSectionsCalc#Gauge_Boson_Masses_and_Widths_PD

**Collider energy**

- 7,8,13 and 14 TeV

mH[GeV] | 10-115 | 120-123.5 | 124-126 | 125.09 | 126.5-130 | 135-150 | 160-500 | 550-3000 |

Delta mH [GeV] | 5 | 0.5 (instead of 1) |
0.1 | 0.5 (instead of 1) |
5 | 10 | 50 | |

# points | 22 | 8 | 21 | 1 | 8 | 4 | 35 | 50 |

- 38 points in 120-130 GeV range are for SM Higgs. We propose to start the generation in this range.
- the additional 111 mass points between 10-3000 GeV are supposed to provide a reference for BSM es.
- the desired statistical accuracy is 0.1%

**Other input parameters and PDFs**

- Mt=172.5 GeV according to https://cds.cern.ch/record/2047636
- On-shell top mass (and the tree-level relation lambda_t=Sqrt(2*Sqrt(2)*G_F)*Mt) for the top-Yukawa coupling
- PDFs and alphaS=0.118+0.0015 according to PDF4LHC recommendation 2015 http://arxiv.org/abs/1510.03865

- absolute NLO prediction at the central scale in picobarn (not the midpoint of the uncertainty band)
- positive and negative scale variation in percent. Here the usual 6-point variation should be applied, including independent factor 0.5 and 2 variations of muR and muF apart from uncorrelated ones.
- positive and negative PDF+alphaS variations in percent (see PDF4LHC recommendation 2015)
- also the K factor (K=NLO/LO both with the same NLO PDFs and input parameters) should be provided

**Production of cross sections**

- Marco Zaro has volunteered to take care of the calculations
- other groups might want to cross check the results (?)

- the conventional scale choice mu_R=mu_F=m_t+m_H/2 should be used for the inclusive ttH cross section.
- note that for differential distributions at scales well above Mt a dynamical scale should be used. This is however not relevant for the total cross section.

- Both NLO QCD and NLO QCD+EW predictions should be prepared.
- (N)LO EW effects should be computed using nominal input parameters and PDFs, without any variation. For EW contributions the latest NNPDF QED set (NLO QCD+LO QED) should be used.
- the G_mu input scheme should be used for EW corrections with G_mu, MW and MZ as defined in https://cds.cern.ch/record/2047636
- separate K-factors K_QCD=(NLO QCD)/(LO QCD) and K_EW=(NLO QCD+EW)/(NLO QCD) should be provided; Optionally, also additional numerical results for an alternative EW K-factor defined as (NLO QCD+EW)/(LO QCD)=K_EW*K_QCD can be presented
- At 13 TeV with Mh=125 GeV NLO EW and LO EW contributions, as well as photon- and q/g-induced contributions are of similar size (see numbers below by M.Zaro) and add up to 0.0%:.

QCD induced gamma-induced Sum NLO EW -1.4% +0.2% -1.2% LO EW-QCD -0.4% +1.6% +1.2% Sum - 1.8% +1.8% 0.0% - we plan to discuss and decide with the WG1 conveners whether EW corrections will be included in the official predictions or presented in the dedicated YR4 section in the form of a relative correction (K_EW). The same applies to other suppressed effects of order 1% (e.g. off-shell effects, resummation effects)

Recommended singl-top+Higgs cross sections will presented only for the t-channel and s-channel processes. Results for WtH production (to date still unpublished) will be presented in a dedicated section of YR4.

**Production of cross sections**

- Federico Demartin has volunteered to ake care of the calculations
- other groups might want to cross check the results (?)

**t-channel**

- scale=(Mt+MH)/4
- nominal prediction in the 5F scheme
- scale uncertainty from full envelope of 6-point scale variations in the 5F and 4F scheme
- standard PDF and alphaS variations (PDF4LHC15)
- no Mb-variations (can be discussed in tH YR4 subsection)
**s-channel** - scale=(Mt+MH)/2
- nominal prediction in the 5F scheme
- standard 6-point scale variation in the 5F scheme

* standard PDF and alphaS variations (PDF4LHC15)

**Mass scan strategy: priorities for precision SM range**

MH | 13 TeV | 14 TeV | 7 TeV | 8 TeV |

120 | x | |||

120.5 | ||||

121 | x | |||

121.5 | ||||

122 | x | |||

122.5 | ||||

123 | x | |||

123.5 | ||||

124.0 | x | |||

124.1 | ||||

124.2 | ||||

124.3 | ||||

124.4 | ||||

124.5 | ||||

124.6 | ||||

124.7 | ||||

124.8 | ||||

124.9 | ||||

125.0 | x | |||

125.1 | ||||

125.2 | ||||

125.3 | ||||

125.4 | ||||

125.5 | ||||

125.6 | ||||

125.7 | ||||

125.8 | ||||

125.9 | ||||

126.0 | x | |||

126.5 | ||||

127 | x | |||

127.5 | ||||

128 | x | |||

128.5 | ||||

129 | x | |||

129.5 | ||||

130 | x |

- results and uncertainties should be presented for the combined (anti)top+H cross section
- in addition also central-value predictions for the individual top+H and antitop+H contributions should be presented (similarly as for WH production https://twiki.cern.ch/twiki/bin/view/LHCPhysics/CERNYellowReportPageAt7TeV2014#WH_Production)

-- StefanoPozzorini - 2015-10-30

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