Charge asymmetry measurements at the Tevatron

A substantial investigation of the charge asymmetry in heavy quark production was induced by measurements at the Tevatron accelerator by CDF and D0 experiments. Tevatron was a very suitable collider for studyingtt¯charge asymmetry due to the dominant qq¯ → tt¯production channel, thus suffering from only a smallgg→t¯tdilution.

2.4.1 Observables sensitive to charge asymmetry at the Tevatron

Several observables were studied intt¯final states with one or two leptons (electrons and muons). All of the observables discussed in this section make use of the assumption that in theqq¯→t¯tprocess, the initial quark is from the proton and the anti-quark from anti-proton. Combining this fact with the assumption about CP conservation, it follows from Eq.2.4, that at Tevatron it is possible to measure a forward-backward asymmetry. The most common definition of this observable uses kinematics of both quarks from thett¯pair:

A_FB= N(∆y >0)−N(∆y < 0)

N(∆y >0)+N(∆y < 0), (2.5) where∆y = y_t −y_t_¯is the rapidity difference of top and antitop quark. The rapidity of a particle is defined as follows:

y = 1

2lnE+p_z

E−p_z, (2.6)

where E is the energy and p_z the longitudinal momentum of the particle. This variable gives us information about the direction of motion of the particle with respect to thez-axis, which is identical to the direction of the proton beam. If the particle is moving forward with respect to proton beam, y > 0, and vice-versa. For y = 0 case, the particle is moving exactly perpendicular to the proton beam. In theqq¯ rest frame, thet and ¯t are produced back-to-back so it follows that∆y > 0 when y_t >0 and vice-versa. The∆yis used because it is Lorentz-invariant with respect to boosts along the z-axis. This is a useful property since in hadron-hadron collisions, the longitudinal momenta of the interacting partons are random, and so theqq¯system is in general boosted along thez-axis direction.

Using a non-invariant definition would lead to additional dilution of the observed asymmetry. Finally, measuringA_FBrequires full reconstruction of thett¯kinematics. The charge of the lepton from the leptonically-decaying (anti)top quark is used to distinguish the reconstructed top quark from antitop quark candidate.

Additionally, observables sensitive to the asymmetry using only the final-state leptons can be constructed. In the single-lepton channel, using rapidity distribution of the single lepton, it is possible to measure:

A^`_FB= N(q_`y_` >0)−N(q_`y_` <0)

N(q_`y_` >0)+N(q_`y_` <0), (2.7) whereq_`y_`is the product of lepton charge and its rapidity. This definition makes the assumption that if top quark is produced more abundantly in one direction with respect to the proton beam, then this property transfers to the lepton from the leptonic top decay.

Finally, in the dilepton channel, it is also possible to measure leptonic asymmetry using the rapidity difference of the two leptons fromtt¯decay analogously to A^t_FB^t^¯ definition, since kinematics of each of

2.4. Charge asymmetry measurements at the Tevatron

the leptons is correlated with thett¯kinematics:

A^``_FB= N(∆y_``> 0)−N(∆y_`` < 0)

N(∆y_``> 0)+N(∆y_`` < 0), (2.8) where∆y_`` = y_`⁺ − y_`− is the rapidity difference of the lepton from top and lepton from antitop, respectively. Both A^`_FBandA^``_FBasymmetries are affected by dilution due to neglecting other decay products from the top-quark decays. The limited coverage of the tracking system also further reduces the sensitivity to asymmetry which is pronounced more in the forward region.

2.4.2 Measurements at the Tevatron

The firsttt¯forward-backward asymmetry measurements by CDF and D0 experiments performed in Run-II period of data-taking using dataset with integrated luminosity (L) of approximately 5 fb⁻¹ showed an unexpected tension in comparison to the SM prediction calculated up to NLO accuracy in QCD [47–50]. In particular, the CDF measurement [51] of A_FB as a function of the invariant mass of thet¯tsystem (m_t_t_¯)⁽⁴⁾, showed a much stronger dependence than predicted (Fig.2.8), reaching significance of more than three standard deviations for high-m_t¯_tregion of the phase space. The D0 experiment also reported inconsistency with the SM prediction for the inclusive A_FBmeasurement [52], though no significant dependence with respect tom_t¯_t was observed.

QCD tNLO t t

A

GeV/c2

450 M^t^t

0 . 0

2 . 0

4 . 0

2 .

−0

fb-1

5.3 data CDF

level -parton t t

Fig. 2.8: Comparison of A_FB^t¯^t NLO QCD prediction [47–50] with measurement by the CDF experi-ment [51] intt¯events with single lepton. The comparison is performed in bins ofmt¯t <450 GeV and m_t¯_t >450 GeV. The shaded blue area on the measurement points shows the total uncertainty while the purple area shows the uncertainty on the theoretical prediction.

The initial partial-dataset measurements were followed up by full Run-II datasets measurements of A^t_FB^t^¯ [53–55],A^`_FB[56,57] andA^``_FB[58,59], which benefit from the almost factor of two increase in integrated luminosity. These measurements also improved the precision by combining single-lepton and dilepton channels and combining both CDF and D0 measurements.

(4)The invariant mass oft¯tsystem is defined asq

(E_t+E_t_¯)²− |~p_t+p~_t_¯|², whereE_t(E_t_¯) is the energy of thet(¯t) quark, and~p_t(~p_t_¯) is the momentum vector of thet(¯t) quark.

2. Top quark and the charge asymmetry

The results also motivated theory efforts to provide more precise SM predictions, which resulted in NLO EW and NNLO QCD calculations [60–62]. These predictions showed a sizeable increase in the asymmetry, reducing the tension between theory and experiment. A summary comparison of all the inclusive measurements with the SM predictions is shown in Fig.2.9. The improved predictions also reduced the tension in the differentialA^t_FB^t^¯ vsm_tt¯measurements, as is shown in Fig.2.10. Additionally, the A_FB measurements prompted BSM interpretations, that are discussed in Sec.2.6for both the Tevatron and the LHC.

−15 0 15 30

Asymmetry [%]

t¯t∆yAsymmetry A^t¯_FB^t CDF`+jets, 9.4 fb⁻¹

PRD 87, 092002 (2013)

16.4± 4.7 CDF``, 9.1 fb⁻¹

PRD 93, 112005 (2016)

12 ±13 D0`+jets, 9.7 fb⁻¹

PRD 90, 072011 (2014)

10.6± 3.0 D0``, 9.7 fb⁻¹

PRD 92, 052007 (2015)

17.5± 6.3

Tevatron combination 12.8± 2.5

LeptonqηAsymmetry A^`_FB CDF`+jets, 9.4 fb⁻¹

PRD 88, 072003 (2013)

10.5± ^3.22.9

CDF``, 9.1 fb⁻¹

PRL 113, 042001 (2014)

7.2± 6.0 D0`+jets, 9.7 fb⁻¹

PRD 90, 072001 (2014) 5.0± ^3.43.7

D0``, 9.7 fb⁻¹

PRD 88, 112002 (2013) 4.4± 3.9

Tevatron combination 7.3± 2.0

Lepton∆ηAsymmetry A^``_FB CDF``, 9.1 fb⁻¹

PRL 113, 042001 (2014)

7.6± 8.2 D0``, 9.7 fb⁻¹

PRD 88, 112002 (2013)

12.3± 5.6

Tevatron combination 10.8± 4.6

NNLO QCD + NLO EW [Czakonet al.]

NLO SM [Bernreuther and Si]

Fig. 2.9: Summary comparison of all inclusiveA_FBmeasurements [55] by CDF and D0 experiments with NLO QCD+EW [60] and NNLO QCD + NLO EW [61,62] SM predictions. The summary includes measurements usingtt¯reconstruction (A^t¯_FB^t ) [53–55] as well as using only observables related to the lepton(s) fromtt¯decays (A^`_FB, A^``_FB) [56–59]. The hash bands show the theoretical prediction and its uncertainty, while the points and the bars show the measurements and their total uncertainty.

In addition to theA_FBmeasurements intt¯production, measurements ofA_FBinbb¯production were also performed with the aim to investigate a different region of phase space, given the large difference between the top and bottom quark mass. The reconstruction of thebb¯pairs involves identifying events with two jets originating fromB-hadrons. In addition, it is necessary to distinguish the charge of theb and ¯bquark. One option is to consider only semileptonicB-hadron decays with a soft muon in the final state and using the soft muon charge as a proxy to the charge of theB-hadron. This approach has been used in the measurement ofA^b_FB^b^¯ in events with low-m_bb¯ [63] (Fig.2.11a). This approach suffers

2.4. Charge asymmetry measurements at the Tevatron

0.0 0.4 0.8 1.2 1.6 2.0

|∆yt¯t|

−0.4−0.20.00.20.40.60.8At

¯t FB

Tevatron combination:α∆yt¯t=0.187±0.038 NNLO QCD + NLO EW [Czakonet al.]

D0`+jets, 9.7 fb⁻¹ CDF`+jets, 9.4 fb⁻¹ CDF``, 9.1 fb⁻¹

Fig. 2.10: Comparison of A^t¯_FB^t as a function of m_t¯_t, of CDF and D0 measurements [53,54,58] and their combination [55] with the NNLO QCD + NLO EW SM prediction [61,62]. The inner error bars on data points show the statistical uncertainty while the outer bars show the total uncertainty. A one-parameter linear fit is performed to all the data points, shown by the black line, where the grey area shows the uncertainty on the fitted parameter. A similar band is shown for the theoretical prediction.

from the low branching ratio of theB-hadron decays to soft muons (approximately 11 % [33]), but at the same time the identification of the charge of the muon is very precise. A different approach was used in the CDF measurement of theA^b_FB^b^¯ in high-m_bb¯ events [64] (Fig.2.11b), where theb-quark charge was inferred from the tracks matched to the calorimeter jet [65].

Neither of the measurements of A_FB^b^b^¯ report any significant deviation with respect to SM prediction in Ref. [66]. In contrast tott¯production, in the case ofbb¯production the asymmetry is strongly diluted by the dominant, charge-symmetric gluon fusion production mechanism.

CDF Run II Preliminary, Data

NLO SM (PRL 111, 062003)

(a) CDF Run II PreliminaryR

L= 9.5 fb⁻¹

(b)

Fig. 2.11: Measurements of the A^b_FB^b^¯ as a function ofm_bb¯ in low-m_bb¯ [63] (a) and high-m_bb¯ [64] (b) region of phase space. Predictions for axigluon contributions with two different masses are shown in (b). The error-bars on data points show the total uncertainty on the measurement, while the bands show the theoretical predictions from Ref. [66] and their uncertainties.

2. Top quark and the charge asymmetry

Dans le document Charge Asymmetry in Boosted Top Quark Pair Production in pp Collisions at the ATLAS Experiment (Page 38-42)