10 Jet-vetoed cross sections

Chapter 10
Jet-vetoed cross sections

The jet veto scale

p_{T}^{veto}

can induce large logarithms if it is smaller than the hard process scale

Q

, which then mandates resummation. We consider processes where jets have been defined using sequential recombination jet algorithms [64] with distance measure

d_{ij} = min (k_{Ti}^{2 n}, k_{Tj}^{2 n}) \frac{Δ y_{ij}^{2} + Δ ϕ_{ij}^{2}}{R^{2}}, d_{iB} = k_{Ti}^{2 n},

(10.1)

where the choice $n = - 1$ is the anti- $k_{T}$ algorithm [59], $n = 0$ is the Cambridge-Aachen algorithm [65, 66], and $n = 1$ is the $k_{T}$ algorithm [67, 68]. $k_{Ti}$ denotes the transverse momentum of (pseudo-)particle $i$ with respect to the beam direction, and $Δ y_{ij}$ and $Δ ϕ_{ij}$ are the rapidity and azimuthal angle differences of (pseudo-)particles $i$ and $j$ .

10.1 Benchmark results for jet-vetoed cross sections

Results for benchmark cross sections for a variety of single-boson processes taken from ref. [10] are shown in Tables 10.1–10.3 and for diboson processes in Tables 10.4–10.6. The input files are linked in the tables. The uncertainties indicated in these tables represent the numerical integration (Monte Carlo) uncertainty.


Final state	input file	contribution	cross section

$H$	`H/veto30nlo.ini`	NLO	$26.23 \pm 0.01$ pb
	`H/veto30nnlo.ini`	NNLO	$28.97 \pm 0.09$ pb
	`H/veto30nnll.ini`	NNLL	$24.89 \pm 0.01$ pb
	`H/veto30n3ll.ini`	N $^{3}$ LL $_{p}$	$24.29 \pm 0.01$ pb
	`H/veto30nlomc.ini`	NLO+NNLL MC	$2.25 \pm 0.01$ pb
	`H/veto30nnlomc.ini`	NNLO+N $^{3}$ LL $_{p}$ MC	$3.89 \pm 0.19$ pb

Table 10.1: Benchmark results for jet-vetoed Higgs cross sections.


Final state	input file	contribution	cross section

$W^{+}$	`W/vetowp30nlo.ini`	NLO	$3.048 \pm 0.001$ nb
	`W/vetowp30nnlo.ini`	NNLO	$2.81 \pm 0.003$ nb
	`W/vetowp30nnll.ini`	NNLL	$2.517 \pm 0.002$ nb
	`W/vetowp30n3ll.ini`	N $^{3}$ LL $_{p}$	$2.250 \pm 0.002$ nb
	`W/vetowp30nlomc.ini`	NLO+NNLL MC	$0.561 \pm 0.006$ nb
	`W/vetowp30nnlomc.ini`	NNLO+N $^{3}$ LL $_{p}$ MC	$0.57 \pm 0.02$ nb


$W^{−}$	`W/vetowm30nlo.ini`	NLO	$2.101 \pm 0.001$ nb
	`W/vetowm30nnlo.ini`	NNLO	$1.979 \pm 0.002$ nb
	`W/vetowm30nnll.ini`	NNLL	$1.796 \pm 0.002$ nb
	`W/vetowm30n3ll.ini`	N $^{3}$ LL $_{p}$	$1.600 \pm 0.001$ nb
	`W/vetowm30nlomc.ini`	NLO+NNLL MC	$0.327 \pm 0.003$ nb
	`W/vetowm30nnlomc.ini`	NNLO+N $^{3}$ LL $_{p}$ MC	$0.33 \pm 0.01$ nb

Table 10.2: Benchmark results for jet-vetoed

W^{±}

cross sections.


Final state	input file	contribution	cross section

$Z$	`Z/veto30nlo.ini`	NLO	$668 \pm 1$ pb
	`Z/veto30nnlo.ini`	NNLO	$628 \pm 2$ pb
	`Z/veto30nnll.ini`	NNLL	$676 \pm 2$ pb
	`Z/veto30n3ll.ini`	N $^{3}$ LL $_{p}$	$596 \pm 2$ pb
	`Z/veto30nlomc.ini`	NLO+NNLL MC	$- 11 \pm 1$ pb
	`Z/veto30nnlomc.ini`	NNLO+N $^{3}$ LL $_{p}$ MC	$- 7.7 \pm 0.7$ pb

Table 10.3: Benchmark results for jet-vetoed

Z

cross sections.


Final state	input file	contribution	cross section

$WW$	`WW/veto30nlo.ini`	NLO	$234.0 \pm 0.2$ fb
	`WW/veto30nnlo.ini`	NNLO	$242.7 \pm 0.4$ fb
	`WW/veto30nnll.ini`	NNLL	$204.7 \pm 0.2$ fb
	`WW/veto30n3ll.ini`	N $^{3}$ LL $_{p}$	$205.2 \pm 0.2$ fb
	`WW/veto30nlomc.ini`	NLO+NNLL MC	$25.8 \pm 0.9$ fb
	`WW/veto30nnlomc.ini`	NNLO+N $^{3}$ LL $_{p}$ MC	$19.8 \pm 0.6$ fb

Table 10.4: Benchmark results for jet-vetoed

W^{+} W^{−}

cross sections.


Final state	input file	contribution	cross section


$W^{+} Z$	`WZ-atlas/vetowp25nlo.ini`	NLO	$20.11 \pm 0.01$ fb
	`WZ-atlas/vetowp25nnlo.ini`	NNLO	$19.14 \pm 0.02$ fb
	`WZ-atlas/vetowp25nnll.ini`	NNLL	$18.87 \pm 0.01$ fb
	`WZ-atlas/vetowp25n3ll.ini`	N $^{3}$ LL $_{p}$	$17.72 \pm 0.01$ fb
	`WZ-atlas/vetowp25nlomc.ini`	NLO+NNLL MC	$0.17 \pm 0.06$ fb
	`WZ-atlas/vetowp25nnlomc.ini`	NNLO+N $^{3}$ LL $_{p}$ MC	$0.07 \pm 0.01$ fb


$W^{−} Z$	`WZ-atlas/vetowm25nlo.ini`	NLO	$13.54 \pm 0.01$ fb
	`WZ-atlas/vetowm25nnlo.ini`	NNLO	$12.82 \pm 0.01$ fb
	`WZ-atlas/vetowm25nnll.ini`	NNLL	$12.66 \pm 0.01$ fb
	`WZ-atlas/vetowm25n3ll.ini`	N $^{3}$ LL $_{p}$	$11.77 \pm 0.01$ fb
	`WZ-atlas/vetowm25nlomc.ini`	NLO+NNLL MC	$0.21 \pm 0.04$ fb
	`WZ-atlas/vetowm25nnlomc.ini`	NNLO+N $^{3}$ LL $_{p}$ MC	$0.12 \pm 0.01$ fb

Table 10.5: Benchmark results for jet-vetoed

WZ

cross sections.


Final state	input file	contribution	cross section

$ZZ$	`ZZ/veto30nlo.ini`	NLO	$12.17 \pm 0.01$ fb
	`ZZ/veto30nnlo.ini`	NNLO	$12.88 \pm 0.01$ fb
	`ZZ/veto30nnll.ini`	NNLL	$11.90 \pm 0.01$ fb
	`ZZ/veto30n3ll.ini`	N $^{3}$ LL $_{p}$	$11.85 \pm 0.01$ fb
	`ZZ/veto30nlomc.ini`	NLO+NNLL MC	$- 0.22 \pm 0.01$ fb
	`ZZ/veto30nnlomc.ini`	NNLO+N $^{3}$ LL $_{p}$ MC	$- 0.17 \pm 0.01$ fb

Table 10.6: Benchmark results for jet-vetoed

ZZ

cross sections.

Chapter 10Jet-vetoed cross sections

10.1 Benchmark results for jet-vetoed cross sections

Chapter 10
Jet-vetoed cross sections