Up to this point, we have discussed the interactions included in the SM. The SM has been extensively tested over the past several decades, showing a remarkable agreement across a huge range of different processes. The predictive power of SM is illustrated in Fig.1.3, which shows the comparison of ATLAS measurements and SM predictions of production cross-sections of processes spanning twelve orders of magnitude. There are, however, several limitations of the SM that prevent it from being a fundamental “theory of everything”. Some of the most important omissions include:
• No description of gravity. SM does not include gravitational interaction, as quantization of general theory of relativity yields a non-renormalisable QFT.
• No explanation of the mass range of the fermions. The range of masses of fundamental particles in the SM spans twelve orders of magnitude. The SM gives no clues as to why this is
(19)There may be dependence on other properties of the partons if relevant, such as spin. It is implicitly assumed that sum over all relevant initial parton states is performed in the factorization theorem.
1.6. Limitations of the Standard Model
the case.
• Properties of neutrinos in the SM.The neutrinos in the SM are massless, effectively predicting existence of sterile right-handed neutrinos. However, experimental observations of neutrino flavour oscillations prove that at least two neutrino flavours must have non-zero mass to allow for the mixing of mass and weak eigenstates. It is possible to extend the SM by adding mass terms for neutrinos. However, due to the zero electric charge of neutrinos, it is not clear whether neutrinos are Dirac particles (distinct particle and anti-particle), or Majorana particles (particle is its own anti-particle).
• Insufficient explanation of the baryon asymmetry in the universe. It is generally accepted, that at the Big Bang, matter and anti-matter was created in equal amounts, however the visible universe appears to lack anti-matter. CP violation is necessary to introduce the asymmetry after the Big Bang, however the sources of CP violation in the SM are not sufficiently strong to explain this phenomenon.
• No explanation of dark matter and dark energy. The SM only describes about 5 % of the content of the universe, the visible matter. There are beyond-SM (BSM) theories, such assupersymmetrythat predict neutral weakly interacting particles that could be dark matter candidates. However, no explanation of the dark energy is provided by SM or its extensions.
pp
500µb−1 80µb−1
W Z t¯t t
t-chan
WW H
total
t¯tH VBF VH
Wt
2.0 fb−1
WZ ZZ t
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t¯tW t¯tZ tZj 10−1
1 101 102 103 104 105 106 1011
σ
[pb]Status: July 2018
ATLAS Preliminary Run 1,2 √s= 7,8,13TeV
Theory
LHC pp√s= 7TeV Data4.5−4.6fb−1
LHC pp√s= 8TeV Data20.2−20.3fb−1
LHC pp√s= 13TeV Data3.2−79.8fb−1
Standard Model Total Production Cross Section Measurements
Fig. 1.3: Summary of several total cross-section measurements compared to the corresponding SM theoretical predictions [30]. The coloured bands show the uncertainties on the measurements while the grey bands show the uncertainties on the theoretical predictions. All of the theoretical predictions were calculated with NLO precision or higher.
2
Top quark and the charge asymmetry
The top quark is the third-generation up-type quark. It was discovered in 1995 at the Tevatron accelerator by the CDF [31] and D0 [32] experiments, completing the three generations of quarks predicted by the SM. It is the heaviest known elementary particle with a mass of approximately 173 GeV [33]. Because of the large mass, the top quark has a very large predicted decay widthΓ=1.32 GeV [34], resulting in an extremely short mean life-time(1)of≈10−25s. It is in fact order of magnitude less than the mean hadronisation time(2)≈10−23s. This means that the properties of the top quark are passed directly onto its decay products, allowing for precise measurements of properties of a “pseudo-bare” quark.
The top quark has the largest Yukawa coupling to Higgs boson yt ∼ 1 of all SM fermions, suggesting that it plays an important role in the EW sector. Studies of the top-Higgs Yukawa coupling are investigated in measurements of the associated production of thett¯pair and the Higgs boson (ttH)¯ which can probe the consistency of the SM as well as search for anomalous Yukawa coupling. Bothtt¯ and single top production and top-quark decays are sensitive to various BSM physics, ranging fromt¯t resonances, flavour changing neutral currents in top-quark decays, to anomalous couplings of top-quark to Higgs boson and to EW vector bosons. In addition, the top-quark production processes are an important background in many BSM searches involving top quarks as well as processes involving the Higgs boson production.
At hadron colliders, top quarks are most abundantly produced viatt¯pair production which is driven by strong interactions, though other production channels are also investigated, such as the single top quark production via weak interaction.
2.1 Top quark pair production
The pair production at hadron colliders occurs primarily through two initial states, either a quark-antiquark annihilation (qq¯ → tt), or a gluon fusion (gg¯ → tt). The leading-order (LO) Feynman¯ diagrams depicting these production channels are shown in Fig.2.1. The relative contribution of qq¯ →tt¯andgg →tt¯depends on the PDFs, and more specifically on the collision energy as well as on the collided hadrons. The top quark was discovered at the Tevatron collider, which was a proton-antiproton (pp) collider operating at centre-of-mass energy¯ √s = 1.96 TeV. At this energy regime and due to thepp¯collisions, theqq¯→tt¯is the dominant production channel (≈85 %), where the initial-state quark originates from proton and initial-state anti-quark from anti-proton. At the LHC, which is a proton-proton (pp) collider, the situation is dramatically different. Forqq¯ → tt¯
(1)The mean life time of a particle isτ=Γ−1, whereΓis the decay width of the particle.
(2)The mean hadronisation time is estimated asΛ−1QCD.
2.1. Top quark pair production
production channel at least one of the quarks must come from the proton sea. The sea-quark PDFs at the LHC energies are more suppressed than the valence-quark or gluon PDFs. Additionally, due to the increase in√s, morett¯pairs are produced via partons with low momentum fractionx. The gluon PDF dominates for small values of x. Due to these factors, the dominanttt¯production channel at the LHC isgg→tt. At¯ √s=13 TeV, the contribution is≈90 %.
q
q
t
t g
g
t
t g
g
t
t g
g
t
t
+ +
Fig. 2.1: Leading-order Feynman diagrams oft¯tpair production: qq¯annihilation (top), andggfusion (bottom) [35].
The latest inclusive cross-section predictions [36–39] are calculated up to next-to-next-to-leading order (NNLO) accuracy in QCD with soft-gluon resummations up to next-to-next-to-leading logarithmic (NNLL) accuracy. These calculations are implemented in theTop++v2.0 [40] software. The predictions for Tevatron and for LHC at various energies are shown in Table2.1. The predictions are calculated assuming a top-quark mass of 172.5 GeV and use MSTW2008 NNLO PDF set [41]. A comparison of the predictions with latest cross-section measurements is shown in Fig.2.2, showing good agreement between measurements and the SM.
Table 2.1: Predicted inclusivet¯t cross-sections based on NNLO QCD calculations [36–40] for the Tevatronpp¯collider and LHCppcollider at various centre-of-mass energies. The uncertainties include an envelope obtained from the renormalisation and factorisation scale variations of factor 0.5 and 2.0 with respect to the nominal value ofmtop=172.5 GeV as well as envelope from the PDF andαS variations. The total uncertainty is the sum in quadrature of the scale uncertainties and the PDF +αS uncertainty.
Accelerator (√s) σtt¯[pb]
Tevatron (1.96 TeV) 7.35+0.20−0.24 LHC (7 TeV) 172+−6.47.5 LHC (8 TeV) 253+15−16 LHC (13 TeV) 832+40−46
2. Top quark and the charge asymmetry
cross section [pb]t Inclusive t
topWG Tevatron combined 1.96 TeV (L
-1) CMS dilepton,l+jets 5.02 TeV (L = 27.4 pb
-1)
Czakon, Fiedler, Mitov, PRL 110 (2013) 252004 0.001
Fig. 2.2: The prediction of dependence of the inclusivett¯production cross-section [36–40] vs√s forpp(green line) andpp¯(cyan line) collisions. The points show a comparison with various recent Tevatron, ATLAS and CMS measurements. The summary is compiled by the LHC Top Working Group [42].