2.5.1 Observables sensitive to charge asymmetry at the LHC
Measurements of charge asymmetry at the LHC are significantly more challenging compared to Tevatron due to theppcollisions as well as the energy regime. The asymmetry is strongly diluted due to the dominant, charge-symmetricgg →t¯tproduction channel. In addition, in theppcollisions, there is no apparent significant direction in the initial state and the asymmetry definition in Eq.2.5cannot be used. However, in case ofqq¯ →tt¯events inppcollisions, typically a valence quarkqfrom one proton interacts with a sea anti-quark ¯qfrom the other proton(5). Valence quarks tend to have, on average, higher momentum compared to sea quarks, therefore the centre-of-mass of theqq¯interaction will be on average boosted in the direction ofq. This effectively means, that if the top quark is produced in the direction ofq, its rapidity magnitude|yt|will be larger compared to|yt¯|(Fig.2.12a). On the other hand, if anti-top quark is produced in the direction ofq, then |yt¯| > |yt| (Fig.2.12b). It follows, that one can use absolute difference of rapidities of top and anti-top quark∆|y| =|yt| − |yt¯|as an observable that is sensitive to the direction of the top quark with respect toqin theqq¯rest frame. The impact of a positive charge asymmetry on the rapidity distributions of top and anti-top quark is visualized in Fig.2.12c. The charge asymmetry definition usable at LHC can be then defined as follows:
AtCt¯= N(∆|y| >0)−N(∆|y|< 0)
N(∆|y| >0)+N(∆|y|< 0) (2.9)
q q¯
t
t¯ (a)tproduced in direction ofq:
|yt|>|y¯t| ⇒∆|y|>0
q q¯
t¯
t (b) ¯tproduced in direction ofq:
|yt|<|y¯t| ⇒∆|y|<0
proton Lab frame
y top anti-top
proton (c)
Fig. 2.12: Illustration of the effect ofqq¯longitudinal boost inqq¯ →tt¯on the rapidity magnitudes oft (a) and ¯t(b) quarks and their rapidity distributions in the laboratory frame at the LHC under positive asymmetry assumption (c). If the asymmetry was zero, the rapidity distributions oftand ¯twould coincide.
(5)It is also possible that a sea quark interacts with sea antiquark, however such initial state is heavily suppressed by sea-quark PDFs.
2.5. Charge asymmetry measurements at the LHC
In the case of dileptonictt¯decays, it is also possible to measure so-called leptonic charge asymmetry, which is defined using pseudorapidities of the two final-state leptons:
A``C = N(∆|η| >0)−N(∆|η| <0)
N(∆|η| >0)+N(∆|η| <0) (2.10) where∆|η| =|η`+| − |η`−|is the difference of absolute pseudorapidities of the leptons from top and anti-top quark, respectively. In contrast to AtCt¯, this observable does not require full reconstruction oftt¯ system, and is less sensitive to detector-related systematic uncertainties, because in general leptons are more well-measured objects than jets from quarks, however the observable is more diluted due to the three-body top-quark decay.
While the observables in Eq.2.9and2.10are commonly referred to as charge asymmetries, it should be noted that they are rather “forward-central” asymmetries, and only have an indirect connection to the asymmetry defined in Eq. 2.1. In addition, the predicted magnitudes for these observables are suppressed by more than an order of magnitude compared to the Tevatron predictions. On the other hand, the increase in collision energy at the LHC allows to probe for evidence of BSM theories that predict seizable contribution to the charge asymmetry at energies previously inaccessible at the Tevatron. In addition, it is possible to impose additional kinematic criteria to select regions of phase where the charge asymmetry is enhanced. One such option is probing higher invariant masses of the tt¯pair (mtt¯). This is because higher-mt¯ttt¯pairs are produced by incoming partons carrying higher momentum fraction x of the colliding protons. The probability that the interacting partons areqq¯ rather thanggincreases with x as was shown in Fig.1.2. Another option to enhance theqq¯ → tt¯ contribution is to cut on the longitudinal boost of thett¯pair βz,tt¯(6). Finally, an option to directly impact the underlying asymmetry in qq¯ →t¯tis to impose a cut on the maximum pT of thet¯t pair (pT,tt¯). This constraints the amount of ISR/FSR in thett¯production, reducing the negative contribution to the asymmetry from the interference term of the ISR/FSR amplitudes.
2.5.2 Measurements at the LHC
At the LHC, both ATLAS and CMS performed inclusive and differential measurements of the charge asymmetry, using Run-I collision data at√s=7 TeV and√s=8 TeV.
The observables investigated were very similar between ATLAS and CMS, measuring inclusive AtCt¯ and A``C as well as differential AtCt¯ as a function of mt¯t, pT,tt¯ and |ytt¯| or βz,tt¯. The 7 TeV measurements [67–70] were largely statistically dominated due to the relatively small integrated luminosity of approximately 5 fb−1. The 8 TeV measurements [71–75] achieved a significantly better precision thanks to the much larger dataset with integrated luminosity of approximately 20 fb−1, allowing for differential measurements of A``C as well. Further precision was gained by a combination of the 7 TeV as well as the 8 TeV ATLAS and CMS measurements [76]. The combination results as well as comparisons with the individual inclusive asymmetry measurements are shown in Fig.2.13 and 2.15. A comparison of the SM predictions with the combined ATLAS and CMS differential measurement of ACvsmtt¯is shown in Fig.2.14. None of the measurements reported any significant excess with respect to the SM predictions.
(6)The longitudinal boost of at¯tpair is defined asβz,t¯t= pz,t¯t
Ett¯, wherepz,t¯tandEtt¯are the longitudinal momentum and energy of thet¯tpair, respectively.
2. Top quark and the charge asymmetry
Finally, ATLAS has also performedACmeasurement in the single-lepton channel using boosted top-quark pairs [77], using dedicated techniques we will discuss in Ch.5. The measurement was focused on the region ofmt¯t > 750 GeV, but suffered from both low statistics and non-negligible systematic uncertainties, as can be seen in Fig.2.15.
−0.1 −0.05 0 0.05 0.1 0.15
Fig. 2.13: Summary of the inclusive AtCt¯ and A``C measurements at the LHC [76] using Run-I dataset at√s=7 TeV. Both standalone ATLAS [67,68] and CMS [69,70] measurements and their combination [76] is shown. The inner bars on the measurement points indicate the statistical uncertainty and the outer bars the total uncertainty. The theoretical prediction [60] with its uncertainty is shown by the grey bar.
(GeV)
t
mt
400 600 800 1000 1200
C A
Fig. 2.14: Combination of the ATLAS and CMS results of the differential AtCt¯ measurement as a function of mtt¯ using Run-I data at√s = 8 TeV [76]. The measurement is compared to the SM predictions [60,62] and to the example predictions for light and heavy colour-octet models [78]. The bands around the BSM predictions show the statistical uncertainty of the simulations. The bands around the SM predictions are uncertainties dominated by scale variations.