2.4 Top Quark
2.4.4 Asymmetry
An important quantity that can be analysed in the top quark sector at the LHC is the distribution in pseudorapidityk of the top quark versus its anti-matter partner. The
asymmetry causes a difference in these distributions, which themselves relate to parton level differences between the two collding partons. As such, no asymmetry exists in a gg initial state, but is instead manifested in qq¯collisions andqg, andqg, initial states.
The asymmetry can be written as [41] AF B =
Nt(cosθ ≥0)−Nt(cosθ ≥0)
Nt(cosθ≥0) +Nt(cosθ ≥0)
which can be qualitatively described as the number of top quarks in the forward region compared to the number of anti-top quarks.
The physical asymmetry originates from NLO and higher order diagrams. In a lead- ing order diagram, the exchange oftandtquarks is an entirely symmetric mechanism. In the process of a leading orderqq diagram, as well as gluon fusion diagrams, no asymme- try is calculated. The NLO manifestation has two different origins, the first is radiative corrections toqq annihilation diagrams, and the second is interference between different amplitudes in the qg→ttq and qg→ttq processes [42]. Contributing diagrams towards the charge asymmetry can be found in Figure 2.10, where for example, final state and initial state gluon radiation interfere.
A rapidity-dependent asymmetry analysis from CDF yields results of [41]: AF B(|∆y|>1.0) = 0.611±0.256
AF B(|∆y|<1.0) = 0.026±0.104±0.0506
in comparison to SM predictions of:
AF B(|∆y|>1.0) = 0.123±0.018
AF B(|∆y|<1.0) = 0.039±0.006.
kPseudorapidity is an experimental observable which can be considered to be a measure of the particle’s
direction of travel with respect to the beam axis. It is η = −ln¡
tanθ 2 ¢
and can be shown to be equivalent to y=1 2ln ³ E+pz E−pz ´
in the limit ofm→0 using the identitytan2θ=1−cos(2θ) 1+cos(2θ).
Figure 2.10: The diagrams which contribute towards the QCD charge asymmetry. Interfer- ence between diagrams (a) (final-state) and (b) (initial-state) gluon radiation,
and interference of double virtual gluon exchange (c) with the leading orderqq
diagram (d). Reproduced from [42].
A summary plot of the Tevatron asymmetry results is presented in Figure 2.11. Two potential Beyond Standard Model explanations for anomalous asymmetry measurements are elaborated upon in[43, 44], where aZ′ boson could contribute marginally to the cross-
section, but provides a significant change in the distribution of the top quarks.
Further observations from the Tevatron include a mass-dependent forward-backward asymmetry, with a result of Att
F B(Mtt > 450 GeV/c2) = 0.475 ± 0.112 in comparison
to a SM prediction of 0.088 ± 0.013, or a 3.5σ deviation [41]. It is also possible to perform a measurement based on the charge of the lepton, in which D0 observe a re- sult of Al
F B = (15.2 ± 4.0)% in comparison to an MC@NLO generator prediction of
(2.1 ± 0.1)% [45].
The top asymmetry measurement at the LHC is a difficult measurement to make, despite the significantly larger cross-section. At the LHC, the direction of the colliding quark is harder to determine due to the symmetry of the proton-proton collisions com- pared to the Tevatron with proton-antiproton collisions, in which the colliding quark direction is taken to be a valence quark from the proton. This coupled with the signifi- cantly increased proportion of events produced by gluon fusion generally make the LHC a challenging environment for a top asymmetry study, in contrast to the Tevatron where proton-antiproton collisions result in qq annihilation providing the dominant process.
Figure 2.11: Tevatron top asymmetry results. Reproduced from [46].
However, for the LHCb experiment the high pseudorapidity coverage yields an in- creased purity of qq events with respect to the symmetric gg fusion events, as can be seen in Figure 2.12 and Figure 2.13.
Figure 2.12: The two dominant production mechanisms of top quark pairs as a function of pseudorapidity. Reproduced from [47].
At the LHC, the incident quark direction is tagged from the outgoing top quark direction, with the top quark preferentially being in the same direction as the incoming
Figure 2.13: The ratio of top quark pairs produced byqqannihilation versus gluon fusion as a function of pseudorapidity. Reproduced from [48].
quark [49]. Together with the fraction of the momentum carried by the colliding valence quarks being on average larger when compared to the sea antiquarks, this results in top quarks being produced at higher η than anti-top quarks [50]. This is illustrated in Figure 2.14, in contrast to the Tevatron distribution which is illustrated in Figure 2.15.
Figure 2.14: The rapidity distributions for top (blue) and anti-top (red) quarks at the LHC. Reproduced from [51].
Figure 2.15: The rapidity distributions for top (blue) and anti-top (red) quarks at the Teva- tron. Reproduced from [51].
ATLAS have performed a measurement [52] of
AC = 0.029 ± 0.018 (stat.) ± 0.014(syst.)
which is consistent with the SM expectations at the LHC, and has systematic uncertain- ties comparable to the statistical ones, where AC is defined as [53, 54]:
AC =
N(∆|y|>0)−N(∆|y|<0) N(∆|y|>0) +N(∆|y|<0) where
∆|y|=|yt| − |yt|.
At LHCb, the top asymmetry is a unique measurement, given the forward region coverage of the detector, in contrast to ATLAS and CMS which typically go up to
∼ |η| < 2.5. The geometry of the detector yields a higher probability of assigning the correct colliding parton charge to the outgoing top, and thus offers a potential advantage over the General Purpose Detectors (GPDs) for this measurement [55].