Tau leptons have a mass of
mτ=1776.86±0.12 MeV, (2.51)
making them the most massive leptons in the SM [6]. Like its older sister, the muon, the tau lepton only decays weakly to other less massive leptons, but due to its relatively large mass also to hadrons. An example of a Feynman diagram of the decay is shown in Fig. 2.14. In the figure`stands for electron or
9“The Top Quark” review
2.6 Tau lepton physics
muon. The tau neutrino conserves the tau lepton number and is not directly observable. Considering that the two quarks can appear in three colour combinations, there are five diagrams that contribute to the decay process. Naively, one would expect a decay toeandµin a fraction of 2/5 of times and a decay to hadrons in 3/5 of times [52]. This intuition matches well with the measured branching fractions shown in Fig. 2.15. When recognising that the decay diagrams are justWboson decays with the additional neutrino, the naive expectation also matches the knownWbranching ratios when corrected for the kinematically allowed decay products.
τ− ντ
ν¯`,u¯
`−,d W−
Figure 2.14: Example of Feynman diagram of tau lepton decay.
There are several different hadronic10decay modes of a tau lepton. The most common ones are listed in Tab. 2.4. The two broad characteristic categories are the decays to only one charged hadron or three charged hadrons through intermediate light scalar or vector mesons (η, ρ, ω,...). Decays to more than three exist but are rare. As an example for a tau decay Fig. 2.16 is showing the decay to three charged and one neutral pion. A description of how the occurrence of a tau decay is inferred from the hadron signatures is given in Sec. 3.4.7. With an average proper decay length ofcτ=87.03µm [6], tau leptons can travel measurable fractions of millimetres in detectors which is one of the experimental signatures used to identify its decays.
Decays to strange mesons (kaons) are rare because the transition amplitude in the corresponding W →usdecay is proportional to the CKM matrix element [53]
|Vus|=0.22508+−0.000280.00030, (2.52) and the probability for it to occur is suppressed by the square of its value. Inversely, measuring the branching ratios of decay modes involving kaons allows to infer knowledge about the strange quark.
Measurements of the hadronic spectra allow for precision measurements in perturbative QCD [54].
One example is the determination of the strong coupling constant at the scale of the tau lepton mass αs(mτ) as already seen in Fig. 2.2. The relevant measurements were performed at lepton colliders where there are little to no hadronic backgrounds.
At a hadron collider such as the LHC, precision QCD measurements of and with hadronic tau lepton decays are hindered by the necessity to distinguish them from quark/gluon jets. At such machines, the main merit of the tau lepton is its large mass. It is used mainly in searches for processes with couplings proportional to mass. Indeed the first evidence for the existence of a Higgs interaction of Yukawa type, i.e. with fermions, was found with tau leptons [55, 56].
Furthermore, tau leptons provide a third lepton flavour that opens search channels for processes that might violate the conservation of the lepton quantum numbers which is not foreseen in the SM. Or, as is the case in thet¯tHanalysis, it simply increases the acceptance to a rare process.
The fact that the tau lepton is so much heavier than the other leptons which were originally named after the greek word for small or light, often leads to the use of the oxymoron heavy lepton to signify the tau lepton and the tautology light lepton to signify electrons and muons. Nevertheless, the latter phrase is
10Semileptonic decay would be more accurate as there is also the tau neutrino among the daughter particles. However, the neutrino is always present. Thus hadronic decay is used to refer to a decay to hadrons.
used in this thesis as it is useful to refer to electrons and muons with a single word when the difference is irrelevant.
50%
15%
18%
17%
one charged hadron three charged hadrons electron
muon
Figure 2.15: Dominant tau lepton decay modes [6].
Relative uncertainties are less than 1 % in all cases and omitted for readability.
Decay mode Branching fraction in %
h− 11.51±0.05
h−π0 25.93±0.09
h−≥2π0 10.81±0.09
h−h−h+ 9.80±0.05
h−h−h+≥1π0 5.29±0.05 Table 2.4: Branching fractions of major hadronic decay modes of the tau lepton [6]. h±signifies a charged hadron which is a pion in most cases. Tau neutrinos are present in all decays and omitted from the table.
Figure 2.16: Drawing of a tau decay to three charged and one additional neutral pion [57]. The cones are instrumental in its reconstruction. All pions and the neutrino originate from the displaced vertex where the tau decayed. The neutral pion is observable by the two photons it decays to. Other tracks not related to the tau decay are background.
C H A P T E R 3
ATLAS detector at the LHC
3.1 LHC
The large hadron collider (LHC) is a particle accelerator and storage ring for protons and heavier ions (Xe, Au, Pb) [58]. It is located at CERN near Geneva, Switzerland, in a tunnel about 100 m underground and has a circumference of 27 km, making it the largest machine in the world. Protons are accelerated in bunches by a chain of smaller accelerators at CERN. In the LHC they are further accelerated by RF cavities up to an energy of 6.5 TeV. Several hundred bunches with spacings of at least 25 ns make up beams of protons that circulate around LHC in both directions. The beams are kept on the circular path by superconducting dipole magnets and are made to cross in four points around the ring where the resulting proton-proton collision can have a centre-of-mass energy of √
s=13 TeV1. There was a period of data taking from 2010–2012 with a lower energy of 7–8 TeV and there are plans for raising it to 14 TeV.
The four detectors that measure the collisions in each interaction point are: ATLAS [59], CMS [60], LHCb [61] and ALICE [62]. The two general purpose detectors, ATLAS and CMS, are designed to discover and measure the Higgs boson and search for new physics. The delivered luminosity to these experiments is as high as possible. LHCb is specialised in measuring B-hadron decays, while ALICE is focused on measuring the heavy ion collision data. Figure 3.1 shows a drawing of the LHC, the chain of injecting accelerators and the four interaction points with the corresponding detectors.
The beam intensities are expressed as a luminosityLwhich acts as a proportionality factor between the cross section of a processσand its corresponding interaction rate ˙N,
N˙ =L·σ. (3.1)
To summarise a period of data taking one can quote the time-integrated luminosity which can be interpreted as a total amount of interactions. To achieve the highest possible luminosities the proton beams are focused by multi-pole magnets when they are made to cross inside ATLAS. A consequence of it, is that in each bunch crossing more than one proton–proton collision occurs. One makes a distinction between collisions with large momenta transfers which likely include physical processes of interest and other collisions called “pileup”. The number of interactions follows a Poisson distribution with mean
hµi= L·σinelastic
fLHC , (3.2)
where fLHCis the revolution frequency of the beams in the LHC. Figure 3.2 shows that during 2015–2016
1s=(p1+p2)2,pare the 4-momenta of the incoming protons,sis known as a Mandelstam variable.
Figure 3.1: Drawing of the LHC, its four interaction points with detectors, and its injection chain. [63]
the mean number of interactions per bunch crossing in ATLAS was 24. Additionally, even collisions from preceding and subsequent crossings can contribute to pileup in sub-detectors that have signal lengths and readout times longer than the 25 ns between bunches.
Beams that are not made to cross in any interaction point, can circulate within the LHC almost indefinitely. However, when they do cross the colliding protons are removed from the beams and their intensities decay exponentially. In the years 2015–2016, the half life of crossing beams was about 10 h, which in ideal conditions lead to a useful time of roughly 15 h of collisions before the LHC had to be refilled with replenished beams.