κ coupling modifiers (update in 2017 for CERN Yellow Report 4)


This is the update of κ coupling modifiers (see CERN Yellow Report 3, Section 10.2) for Higgs-boson production and decay.

Calculation Instructions

  1. Use the same SM input parameters for Higgs XS&BR calculations for CERN Yellow Report 4
  2. Update for Ecm=[7,8,13,14]TeV and for MH=[124.5,125.0,125.09,125.5]GeV
  3. Inclusive cross section
  4. Purely N3LO/NNLO/NLO/LO QCD and no NLO EW correction
    • In LO κ-framework we assume that QCD corrections factorize for κ’s (but not for EW corrections).
  5. Cross section or partial decay width in significant digits
  6. Also provide uncertainties in sigma and coefficients in kappa for THU and PU if possible
    • Certain THU and PU should cancel out for coefficients in kappa (ex. αs etc.) but not for quark-mass.
  7. Provide information if public tool is available so that EXP can calculate themselves with experimental cuts later on


1. gluon-gluon Fusion Process

  • Numbers in bottom-quark related cross sections and corresponding κ coupling modifiers have changed with respect to CERN Yellow Report 3 (see Eq. (111) and Table 38).
  • For Mh=125 GeV at √s=8 TeV,
  • The main origins of these differences are:
    1. Due to change in central QCD scale from Mh (CERN Yellow Report 3) to Mh/2 (CERN Yellow Report 4). This affects σtt but doesn’t affect much σtb or σbb.
    2. Due to inclusion of charm quark.
    3. Due to change in quark-mass definition from on-shell mass in CERN Yellow Report 3 (Mt=172.5 GeV, Mb=4.84131 GeV) to MSbar mass in CERN Yellow Report 4 (Mt((Mt)=162.7 GeV, Mb(Mb)=4.18 GeV and Mc(3 GeV)=0.986 GeV).
      • In the MSbar scheme the light quark masses run to a significantly lower value (at scale of μ ~ Mh/2 or Mh) than their pole masses.
      • Hence there is an effect on the top-bottom interference and the bottom-bottom part (also for charm).
  • It has been checked that HIGLU (M. Spira) and Zürich calculations agree perfectly with the same input condition in on-shell mass scheme.
  • In the table below σEW nor σtot are used for calculations on κ as we use QCD corrections (σQCD=Σσqq) only and no NLO EW correction.

7 TeV
Mh [GeV] σEW [pb] σtt [pb] σtb [pb] σbb [pb] σtc [pb] σbc [pb] σcc [pb] σtot [pb] σQCD [pb] κt2 κtκb κb2 κtκc κbκc κc2
124.50 0.84 16.86 -0.67 0.04 -0.08 0.01 0.0003 17.00 16.16 1.043 -0.041 0.002 -0.005 0.0006 0.00002
125.00 0.83 16.71 -0.66 0.04 -0.08 0.01 0.0003 16.85 16.02 1.043 -0.041 0.002 -0.005 0.0006 0.00002
125.09 0.83 16.69 -0.66 0.04 -0.08 0.01 0.0003 16.83 16.00 1.043 -0.041 0.002 -0.005 0.0006 0.00002
125.50 0.83 16.57 -0.65 0.04 -0.08 0.01 0.0003 16.72 15.89 1.043 -0.041 0.003 -0.005 0.0006 0.00002
8 TeV
Mh [GeV] σEW [pb] σtt [pb] σtb [pb] σbb [pb] σtc [pb] σbc [pb] σcc [pb] σtot [pb] σQCD [pb] κt2 κtκb κb2 κtκc κbκc κc2
124.50 1.06 21.41 -0.83 0.05 -0.10 0.01 0.0004 21.60 20.54 1.042 -0.040 0.002 -0.005 0.0005 0.00002
125.00 1.06 21.23 -0.82 0.05 -0.10 0.01 0.0004 21.43 20.37 1.042 -0.040 0.002 -0.005 0.0005 0.00002
125.09 1.06 21.20 -0.82 0.05 -0.10 0.01 0.0004 21.40 20.34 1.042 -0.040 0.002 -0.005 0.0005 0.00002
125.50 1.05 21.06 -0.81 0.05 -0.10 0.01 0.0004 21.26 20.21 1.042 -0.040 0.002 -0.005 0.0005 0.00002
13 TeV
Mh [GeV] σEW [pb] σtt [pb] σtb [pb] σbb [pb] σtc [pb] σbc [pb] σcc [pb] σtot [pb] σQCD [pb] κt2 κtκb κb2 κtκc κbκc κc2
124.50 2.40 48.35 -1.76 0.10 -0.22 0.02 0.0009 48.89 46.49 1.040 -0.038 0.002 -0.005 0.0004 0.00002
125.00 2.39 48.00 -1.74 0.10 -0.22 0.02 0.0009 48.55 46.16 1.040 -0.038 0.002 -0.005 0.0004 0.00002
125.09 2.39 47.94 -1.73 0.10 -0.22 0.02 0.0009 48.50 46.11 1.040 -0.038 0.002 -0.005 0.0004 0.00002
125.50 2.39 47.65 -1.72 0.10 -0.22 0.02 0.0009 48.22 45.83 1.040 -0.038 0.002 -0.005 0.0004 0.00002
14 TeV
Mh [GeV] σEW [pb] σtt [pb] σtb [pb] σbb [pb] σtc [pb] σbc [pb] σcc [pb] σtot [pb] σQCD [pb] κt2 κtκb κb2 κtκc κbκc κc2
124.50 2.70 54.39 -1.95 0.12 -0.25 0.02 0.0010 55.03 52.33 1.039 -0.037 0.002 -0.005 0.0004 0.00002
125.00 2.69 54.00 -1.93 0.11 -0.24 0.02 0.0010 54.65 51.96 1.039 -0.037 0.002 -0.005 0.0004 0.00002
125.09 2.69 53.93 -1.92 0.11 -0.24 0.02 0.0010 54.59 51.90 1.039 -0.037 0.002 -0.005 0.0004 0.00002
125.50 2.69 53.61 -1.91 0.11 -0.24 0.02 0.0010 54.28 51.59 1.039 -0.037 0.002 -0.005 0.0004 0.00002


2. VBF Process

  7 TeV   8 TeV   13 TeV   14 TeV
Mh [GeV] σWW [pb] σZZ [pb] κW2 κZ2   σWW [pb] σZZ [pb] κW2 κZ2   σWW σZZ κW2 κZ2   σWW [pb] σZZ [pb] κW2 κZ2
120.0 0.993 0.349 0.740 0.260   1.278 0.452 0.739 0.261   3.001 1.091 0.733 0.267   3.392 1.238 0.733 0.267
125.0 0.946 0.333 0.740 0.260   1.220 0.432 0.738 0.262   2.882 1.049 0.733 0.267   3.260 1.191 0.732 0.268
130.0 0.902 0.318 0.740 0.260   1.166 0.413 0.738 0.262   2.770 1.009 0.733 0.267   3.135 1.146 0.732 0.268
  • CERN Yellow Report 3: σWW = 0.938 (1.210) pb and σZZ = 0.321 (0.417) pb for √s = 7(8) TeV for Mh = 125 GeV, which corresponds to coupling modifiers of κW2; 0.745 (0.744) and κZ2; 0.255 (0.256) for √s = 7(8) TeV.


3. gg→ZH Process

7 TeV
Mh [GeV] σt2 [fb] σb2 [fb] σZ2 [fb] σtσb [fb] σtσZ [fb] σbσZ [fb] σ(ZZ→ZH) [fb] κt2 κb2 κZ2 κtκb κtκZ κbκZ
124.50 3.87 0.005 25.07 0.04 -17.69 -0.16 11.13 0.347 0.0005 2.252 0.004 -1.589 -0.015
125.00 3.86 0.005 24.96 0.04 -17.64 -0.16 11.06 0.349 0.0005 2.256 0.004 -1.595 -0.015
125.09 3.86 0.005 24.94 0.04 -17.63 -0.16 11.05 0.349 0.0005 2.257 0.004 -1.595 -0.015
125.50 3.85 0.005 24.86 0.04 -17.60 -0.16 11.00 0.350 0.0005 2.260 0.004 -1.600 -0.014
8 TeV
Mh [GeV] σt2 [fb] σb2 [fb] σZ2 [fb] σtσb [fb] σtσZ [fb] σbσZ [fb] σ(ZZ→ZH) [fb] κt2 κb2 κZ2 κtκb κtκZ κbκZ
124.50 5.89 0.007 36.55 0.05 -26.37 -0.22 15.91 0.370 0.0004 2.298 0.003 -1.658 -0.014
125.00 5.88 0.007 36.41 0.05 -26.31 -0.21 15.82 0.372 0.0004 2.302 0.003 -1.663 -0.013
125.09 5.88 0.007 36.38 0.05 -26.30 -0.21 15.80 0.372 0.0004 2.303 0.003 -1.665 -0.014
125.50 5.87 0.007 36.26 0.05 -26.25 -0.22 15.73 0.373 0.0004 2.306 0.003 -1.669 -0.014
13 TeV
Mh [GeV] σt2 [fb] σb2 [fb] σZ2 [fb] σtσb [fb] σtσZ [fb] σbσZ [fb] σ(ZZ→ZH) [fb] κt2 κb2 κZ2 κtκb κtκZ κbκZ
124.50 23.47 0.021 126.80 0.14 -98.07 -0.58 51.75 0.454 0.0004 2.450 0.003 -1.895 -0.011
125.00 23.45 0.021 126.34 0.14 -97.87 -0.58 51.47 0.456 0.0004 2.455 0.003 -1.902 -0.011
125.09 23.44 0.021 126.26 0.14 -97.83 -0.58 51.42 0.456 0.0004 2.456 0.003 -1.903 -0.011
125.50 23.42 0.020 125.88 0.14 -97.66 -0.57 51.19 0.457 0.0004 2.459 0.003 -1.908 -0.011
14 TeV
Mh [GeV] σt2 [fb] σb2 [fb] σZ2 [fb] σtσb [fb] σtσZ [fb] σbσZ [fb] σ(ZZ→ZH) [fb] κt2 κb2 κZ2 κtκb κtκZ κbκZ
124.50 28.49 0.024 151.02 0.16 -117.89 -0.62 61.12 0.466 0.0004 2.471 0.003 -1.929 -0.010
125.00 28.46 0.024 150.48 0.16 -117.65 -0.61 60.79 0.468 0.0004 2.475 0.003 -1.935 -0.010
125.09 28.45 0.024 150.45 0.16 -117.67 -0.67 60.73 0.468 0.0004 2.477 0.003 -1.937 -0.011
125.50 28.43 0.024 149.98 0.16 -117.46 -0.64 60.45 0.470 0.0004 2.481 0.003 -1.943 -0.011


4. tH Process

  • Single-top associated Higgs production in s-ch (qqbar→tHb), t-ch (qb→tHq) and W-associated (gb→tHW) production modes.
  • s-ch cross section is small (about 4% of t-ch) and neglected.
  • All the results are obtained with MG5_aMC@NLO (Note by MG5 group)
    • Standard Model results are generated with the default distribution of MG5.
    • kappa-framework results are generated using the HC_NLO_X0 model.

t-ch (qb→tHq)

  • Cross sections are calculated in NLO QCD with MG5_aMC@NLO
  • QCD scales: μ=μFR=(mH+mt)/4
  • PDF set: PDF4LHC15_nlo_30_pdfas
  • References: [Demartin:2015uha] for tH process, CERN Yellow Report 4, Section I.6.6.1.1

7 TeV
Mh [GeV] σt2 [fb] σW2 [fb] σtσW [fb] σ(t-ch) [fb] κt2 κW2 κtκW
125.00 37.99 48.79 -74.52 12.26 3.099 3.980 -6.078
8 TeV
Mh [GeV] σt2 [fb] σW2 [fb] σtσW [fb] σ(t-ch) [fb] κt2 κW2 κtκW
125.00 55.78 72.62 -109.7 18.69 2.984 3.886 -5.870
13 TeV
Mh [GeV] σt2 [fb] σW2 [fb] σtσW [fb] σ(t-ch) [fb] κt2 κW2 κtκW
125.00 195.5 265.7 -387.0 74.25 2.633 3.578 -5.211
14 TeV
Mh [GeV] σt2 [fb] σW2 [fb] σtσW [fb] σ(t-ch) [fb] κt2 κW2 κtκW
125.00 232.6 318.8 -461.3 90.10 2.582 3.538 -5.120

W-associated (gb→HW)

  • Cross sections are calculated in NLO QCD with MG5_aMC@NLO
  • QCD scales: μ=μFR=(mH+mt+mW)/2
  • PDF set: PDF4LHC15_nlo_30_pdfas
  • References: [Demartin:2016axk] for tHW process, employing the DR2 technique.

7 TeV
Mh [GeV] σt2 [fb] σW2 [fb] σtσW [fb] σ(tHW) [fb] κt2 κW2 κtκW
125.00 5.143 3.784 -6.697 2.23 2.306 1.697 -3.003
8 TeV
Mh [GeV] σt2 [fb] σW2 [fb] σtσW [fb] σ(tHW) [fb] κt2 κW2 κtκW
125.00 8.515 6.381 -11.39 3.51 2.426 1.818 -3.244
13 TeV
Mh [GeV] σt2 [fb] σW2 [fb] σtσW [fb] σ(tHW) [fb] κt2 κW2 κtκW
125.00 44.13 35.05 -64.01 15.17 2.909 2.310 -4.220
14 TeV
Mh [GeV] σt2 [fb] σW2 [fb] σtσW [fb] σ(tHW) [fb] κt2 κW2 κtκW
125.00 55.46 44.49 -81.39 18.56 2.988 2.397 -4.385


5. HH Process

  • See CERN Yellow Report 4 HH section on the dependence on the EFT coefficients. For HH, it doesn't make sense to have the top Yukawa varied without varying the HHH coupling. The bottom-quark loop is fairly irrelevant for HH production.


6. Higgs boson decay width

  • The Higgs-boson decay branching ratios in CERN Yellow Report 4 have changed only below O(1%) with respect to those in CERN Yellow Report 3, hence one can use partial decay width for h→gg (Table 39), h→γγ (Table 40) and h→Zγ (Table 41) in CERN Report 3.
  • Inclusion of charm quark is under investigation with HDECAY.


-- ReiTanaka - 2016-06-23

Topic attachments
I Attachment History Action Size Date Who Comment
PDFpdf inclusive_higgs_n3lo_ichep.pdf r1 manage 161.9 K 2016-06-23 - 15:58 ReiTanaka ggF cross section in N3LO QCD (Zürich group)
PDFpdf tables_tH_tWH_kappas.pdf r1 manage 167.4 K 2017-01-26 - 19:28 ReiTanaka tH (t-ch and tHW) cross sections (by F. Demartin)
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Topic revision: r18 - 2017-02-10 - ReiTanaka
 
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