QCD cross sections at high energies

In order to gain some intuition about the kind of known physics that will be encoun-tered at such a machine, representative cross sections for the production of relevant high-multiplicity final states are compiled inFig. 5.1. As in all studies in this chapter, the anti-kT

algorithm [107] is used to cluster jets with a radius parameter ofR=0.4. The first thing to notice is the inelastic cross section at theFCC, being around 105 mb [175], which consti-tutes a 45 % raise compared to theLHC(∼72 mb). To contrast that, we calculatedLOcross sections for a multitude of processes, with cross sections ranging from a few attobarn up to hundreds of microbarn, across 15 orders of magnitude.QCD-only processes come with the largest cross sections when a jet cut ofpT,min=50 GeV is used, with dijet production at 315 µb. Also higher jet multiplicities have very high cross sections, and only inclusive 7-jet production is less probable than any other hard process: The inclusive single vector boson production cross sections come with 350 nb–600 nb and are thus slightly enhanced compared to 7-jet production. The least probable cross sections included inFig. 5.1are those of triple Higgs production in association with a vector boson or from vector-boson fusion with at least two jets. These cross sections are between 3 and 20 ab. Thus at least the H³j²cross section would still correspond to several events at a luminosity of 1–10 ab⁻¹.

The total inclusive cross sections are compared to those at 14 TeV in Fig. 5.2a where one clearly sees the increasing multiplicity of events at the higher centre-of-mass energy.

Turning our attention to thepTspectra, inFig. 5.2bwe show cumulative distributions for a democratic cut of 1 TeV on all jets for the first 6 jets ordered inpT. This sample now has been generated using Sherpa with aMEPS@LOset-up with matrix elements for up to two

QCD &ttH W Z Photons Higgs mixedV Leading-order cross sections at a100 TeVppcollider 1 b

pp!Xat LO,p

s= 100 TeV anti-kTjetsR= 0.4

pT,j/ >50 GeV,Rj, >0.4

Figure 5.1.:A compilation of LO cross sections at the 100 TeV future proton-proton collider.

The Higgs cross sections labelled with “GF” refer to Higgs production via gluon fusion, whereas “VBF” stands for vector-boson fusion production. For gluon-fusion Higgs production the top-mass effects have been included.

additional jets on top of the dijet core process merged together and dressed with parton showers. Though the energy distribution for the highest multiplicity jets fall quickly, many events will be observed where the 6th jet has still more than 400–500 GeV. The leading jets are accessible at energies much greater than 3 TeV.

InFig. 5.3jet rates atNLO QCDdifferential in jet transverse momentum and additionally binned in jet rapidity y are presented. These results have been obtained with Black-Hat+Sherpa [77]. The renormalisation and factorisation scale have been set toµR=µF = HT/2. For the definition ofHT, cf.Eq. (3.54). Comparing rates for 14 and 100 TeV centre-of-mass energy an increase of about one order of magnitude for central jets with low and moderatepT is observed. Considering largerpTvalues the differences get more extreme, atpT =3.5 TeV theFCCrates are more than three orders of magnitude larger than at the LHC. In fact, theFCCprovides substantial jet rates even for very large rapidities: 200 GeV jets with 5< ∣y∣ <6 come with rates about two orders of magnitude larger than those for 200 GeV jets in the 4< ∣y∣ <5 bin at theLHC. From these rate estimates it can be concluded

2 3 4 5 6 7 8

(a)A comparison for inclusive jet multiplicitiesNjet

between collisions at√s=14 TeV and√s=100 TeV,

(b)Cumulative MEPS@LOpTdistributions for the first six highestpTjets, ordered inpT, at√s=100 TeV. The labels for the 4th through 6th jet are omitted.

Figure 5.2.:Jet cross sections for dijet production in proton-proton collisions.

10² 10³

Figure 5.3.:NLO QCD inclusive jet cross sections for√s=14 TeV (left) and√s=100 TeV (right), differential inpTfor different bins in jet rapidityy. Note that for illustrative purposes the results have been multiplied by variable scaling factors (SF), as indicated in the legend.

that one can expect at least ten times more jets at theFCCcompared to theLHC, and this factor gets larger when looking into highpT and/or high∣y∣regions or demanding large jet multiplicities. Accordingly, the rapidity coverage of general-purpose detectors at theFCC should increase with respect toATLASorCMS.

AtNLO, we can study the reduction of the scale uncertainties in jetpTspectra compared toLO. InFig. 5.4, we show NJet+Sherpa [80] predictions for the first and second leading jets ordered inpT. Variations in the factorisation and renormalisation scale choices atNLO leads to the expected reduction in theoretical uncertainty—in this case around 10 % atNLO, compared with 20 % atLO.

To summarise theLOresults in this section we collect a number of multi-jetQCD pro-cesses inFig. 5.5. For four different values of the minimumpTwe show pure jet productions with up to 8 jets and single photon with up to 7 jets. As a comparison we also show top pair

10⁻⁵

Figure 5.4.:The first and second leading jetpTfor dijet production. LO and NLO scale varia-tions in the range[1/2, 2]are shown around the central scale ofµR=µF =HT/2. The top row shows a linear scale from 50 GeV to 10 TeV while the bottom row shows the same plot using a logarithmic scale over the range 250 GeV to 10 TeV in order to avoid the singularity which affects the first bin.

10 ²

Figure 5.5.:A comparison of inclusive jet rates between various QCD processes calculated at LO for differentp_T,min. For pure jets production, an additional comparison is made between jets with radiiR=0.2 andR=0.4.

production with up to 6 jets, two quark pairs with up to 4 jets and three top pairs with up to two jets. The fact that the latter processes are accessible with relatively high-pTjets impres-sively demonstrates the degree to whichQCDcan be studied in the 100 TeV environment, opening up huge amounts of phase space for new physics searches.