LHCPhysics Web>LHCHXSWG2>LHCHWG2KAPPA (2017-02-10, ReiTanaka)

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

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

Use the same SM input parameters for Higgs XS&BR calculations for CERN Yellow Report 4
Update for Ecm=[7,8,13,14]TeV and for MH=[124.5,125.0,125.09,125.5]GeV
Inclusive cross section
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).
Cross section or partial decay width in significant digits
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. α_s etc.) but not for quark-mass.
Provide information if public tool is available so that EXP can calculate themselves with experimental cuts later on

1. gluon-gluon Fusion Process

Cross sections are calculated in N3LO QCD by Zürich group (Note by Zürich group).
QCD scales: μ=μ_F=μ_R=M_h/2
PDF set: PDF4LHC15_nnlo_100
References: [Anastasiou:2014vaa,Anastasiou:2014lda,Anastasiou:2016cez,Anastasiou:2016hlm]

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 M_h=125 GeV at √s=8 TeV,
- CERN Yellow Report 3: κ_g² = 1.058κ_t² + 0.007κ_b² - 0.065κ_tκ_b
- CERN Yellow Report 4: κ_g² = 1.042κ_t² + 0.002κ_b² - 0.040κ_tκ_b - 0.005κ_tκ_c + 0.0005κ_bκ_c + 0.00002κ_c²
The main origins of these differences are:
1. Due to change in central QCD scale from M_h (CERN Yellow Report 3) to M_h/2 (CERN Yellow Report 4). This affects σ_tt but doesn’t affect much σ_tb or σ_bb.
2. Due to inclusion of charm quark.
3. Due to change in quark-mass definition from on-shell mass in CERN Yellow Report 3 (M_t=172.5 GeV, M_b=4.84131 GeV) to MSbar mass in CERN Yellow Report 4 (M_t((M_t)=162.7 GeV, M_b(M_b)=4.18 GeV and M_c(3 GeV)=0.986 GeV).
  - In the MSbar scheme the light quark masses run to a significantly lower value (at scale of μ ~ M_h/2 or M_h) 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 σ_EW nor σ_tot are used for calculations on κ as we use QCD corrections (σ_QCD=Σσ_qq) only and no NLO EW correction.

7 TeV
M_h [GeV]	σ_EW [pb]	σ_tt [pb]	σ_tb [pb]	σ_bb [pb]	σ_tc [pb]	σ_bc [pb]	σ_cc [pb]	σ_tot [pb]	σ_QCD [pb]	κ_t²	κ_tκ_b	κ_b²	κ_tκ_c	κ_bκ_c	κ_c²
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
M_h [GeV]	σ_EW [pb]	σ_tt [pb]	σ_tb [pb]	σ_bb [pb]	σ_tc [pb]	σ_bc [pb]	σ_cc [pb]	σ_tot [pb]	σ_QCD [pb]	κ_t²	κ_tκ_b	κ_b²	κ_tκ_c	κ_bκ_c	κ_c²
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
M_h [GeV]	σ_EW [pb]	σ_tt [pb]	σ_tb [pb]	σ_bb [pb]	σ_tc [pb]	σ_bc [pb]	σ_cc [pb]	σ_tot [pb]	σ_QCD [pb]	κ_t²	κ_tκ_b	κ_b²	κ_tκ_c	κ_bκ_c	κ_c²
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
M_h [GeV]	σ_EW [pb]	σ_tt [pb]	σ_tb [pb]	σ_bb [pb]	σ_tc [pb]	σ_bc [pb]	σ_cc [pb]	σ_tot [pb]	σ_QCD [pb]	κ_t²	κ_tκ_b	κ_b²	κ_tκ_c	κ_bκ_c	κ_c²
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

Cross sections are calculated in NNLO QCD with VBF@NNLO program (CERN Yellow Report 4, Appendix).
QCD scales: μ=μ_F=μ_R=M_W
PDF set: PDF4LHC15_nnlo_30_pdfas
References: [Bolzoni:2010xr,Bolzoni:2011cu]

	7 TeV				8 TeV				13 TeV				14 TeV
M_h [GeV]	σ_WW [pb]	σ_ZZ [pb]	κ_W²	κ_Z²	σ_WW [pb]	σ_ZZ [pb]	κ_W²	κ_Z²	σ_WW	σ_ZZ	κ_W²	κ_Z²	σ_WW [pb]	σ_ZZ [pb]	κ_W²	κ_Z²
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: σ_WW = 0.938 (1.210) pb and σ_ZZ = 0.321 (0.417) pb for √s = 7(8) TeV for M_h = 125 GeV, which corresponds to coupling modifiers of κ_W²; 0.745 (0.744) and κ_Z²; 0.255 (0.256) for √s = 7(8) TeV.

3. gg→ZH Process

Cross sections are calculated in LO QCD with VH@NNLO program.
QCD scales: μ=μ_F=μ_R=M_ZH
PDF set: PDF4LHC15_nnlo_mc
References: [Brein:2012ne,Harlander:2013mla] for VH@NNLO. [Han:1991ia,Kniehl:1990iv,Kniehl:2011aa] for original calculations for gg→ZH process

7 TeV
M_h [GeV]	σ_t² [fb]	σ_b² [fb]	σ_Z² [fb]	σ_tσ_b [fb]	σ_tσ_Z [fb]	σ_bσ_Z [fb]	σ(ZZ→ZH) [fb]	κ_t²	κ_b²	κ_Z²	κ_tκ_b	κ_tκ_Z	κ_bκ_Z
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
M_h [GeV]	σ_t² [fb]	σ_b² [fb]	σ_Z² [fb]	σ_tσ_b [fb]	σ_tσ_Z [fb]	σ_bσ_Z [fb]	σ(ZZ→ZH) [fb]	κ_t²	κ_b²	κ_Z²	κ_tκ_b	κ_tκ_Z	κ_bκ_Z
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
M_h [GeV]	σ_t² [fb]	σ_b² [fb]	σ_Z² [fb]	σ_tσ_b [fb]	σ_tσ_Z [fb]	σ_bσ_Z [fb]	σ(ZZ→ZH) [fb]	κ_t²	κ_b²	κ_Z²	κ_tκ_b	κ_tκ_Z	κ_bκ_Z
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
M_h [GeV]	σ_t² [fb]	σ_b² [fb]	σ_Z² [fb]	σ_tσ_b [fb]	σ_tσ_Z [fb]	σ_bσ_Z [fb]	σ(ZZ→ZH) [fb]	κ_t²	κ_b²	κ_Z²	κ_tκ_b	κ_tκ_Z	κ_bκ_Z
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

ATLAS and CMS 7&8TeV coupling paper (CERN-EP-2016-100) Table 4: 2.27κ_Z² + 0.37κ_t² - 1.64 κ_tκ_Z for √s = 8 TeV and M_h = 125.09 GeV.

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=μ_F=μ_R=(m_H+m_t)/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
M_h [GeV]	σ_t² [fb]	σ_W² [fb]	σ_tσ_W [fb]	σ(t-ch) [fb]	κ_t²	κ_W²	κ_tκ_W
125.00	37.99	48.79	-74.52	12.26	3.099	3.980	-6.078
8 TeV
M_h [GeV]	σ_t² [fb]	σ_W² [fb]	σ_tσ_W [fb]	σ(t-ch) [fb]	κ_t²	κ_W²	κ_tκ_W
125.00	55.78	72.62	-109.7	18.69	2.984	3.886	-5.870
13 TeV
M_h [GeV]	σ_t² [fb]	σ_W² [fb]	σ_tσ_W [fb]	σ(t-ch) [fb]	κ_t²	κ_W²	κ_tκ_W
125.00	195.5	265.7	-387.0	74.25	2.633	3.578	-5.211
14 TeV
M_h [GeV]	σ_t² [fb]	σ_W² [fb]	σ_tσ_W [fb]	σ(t-ch) [fb]	κ_t²	κ_W²	κ_tκ_W
125.00	232.6	318.8	-461.3	90.10	2.582	3.538	-5.120

ATLAS and CMS 7&8TeV coupling paper (CERN-EP-2016-100) Table 4: 3.40κ_t² + 3.56κ_W² - 5.96 κ_tκ_W for √s = 8 TeV and M_h = 125.09 GeV.

W-associated (gb→HW)

Cross sections are calculated in NLO QCD with MG5_aMC@NLO
QCD scales: μ=μ_F=μ_R=(m_H+m_t+m_W)/2
PDF set: PDF4LHC15_nlo_30_pdfas
References: [Demartin:2016axk] for tHW process, employing the DR2 technique.

7 TeV
M_h [GeV]	σ_t² [fb]	σ_W² [fb]	σ_tσ_W [fb]	σ(tHW) [fb]	κ_t²	κ_W²	κ_tκ_W
125.00	5.143	3.784	-6.697	2.23	2.306	1.697	-3.003
8 TeV
M_h [GeV]	σ_t² [fb]	σ_W² [fb]	σ_tσ_W [fb]	σ(tHW) [fb]	κ_t²	κ_W²	κ_tκ_W
125.00	8.515	6.381	-11.39	3.51	2.426	1.818	-3.244
13 TeV
M_h [GeV]	σ_t² [fb]	σ_W² [fb]	σ_tσ_W [fb]	σ(tHW) [fb]	κ_t²	κ_W²	κ_tκ_W
125.00	44.13	35.05	-64.01	15.17	2.909	2.310	-4.220
14 TeV
M_h [GeV]	σ_t² [fb]	σ_W² [fb]	σ_tσ_W [fb]	σ(tHW) [fb]	κ_t²	κ_W²	κ_tκ_W
125.00	55.46	44.49	-81.39	18.56	2.988	2.397	-4.385

ATLAS and CMS 7&8TeV coupling paper (CERN-EP-2016-100) Table 4: 1.84κ_t² + 1.57κ_W² - 2.41 κ_tκ_W for √s = 8 TeV and M_h = 125.09 GeV.

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

Attachments

Topic attachments
I	Attachment	History	Action	Size	Date	Who	Comment
pdf	inclusive_higgs_n3lo_ichep.pdf	r1	manage	161.9 K	2016-06-23 - 15:58	ReiTanaka	ggF cross section in N3LO QCD (Zürich group)
pdf	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)

Topic revision: r18 - 2017-02-10 - ReiTanaka

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