# Edge Charge Asymmetry in Top Pair Production at the LHC

Abstract

In this brief report, we propose a new definition of charge asymmetry in top pair production at the LHC, namely the edge charge asymmetry (ECA). ECA utilizes the information of drifting direction only for single top (or anti-top) with hadronically decay. Therefore ECA can be free from the uncertainty arising from the missing neutrino in the event reconstruction. Moreover rapidity of top (or anti-top) is required to be greater than a critical value in order to suppress the symmetric events mainly due to the gluon-gluon fusion process. In this paper ECA is calculated up to next-to-leading order QCD in the standard model and the choice of the optimal is investigated.## I Introduction

Being the heaviest fermion ever known, the top quark has many unique features and it is thought to be closely related with the new physics beyond the standard model (BSM). After top quark was discovered in 1994, the measurement of its angular distribution is the critical issue because it reflects the coupling structure of the interactions. As such forward-backward asymmetry in top pair production is one of the most interesting quantities. Sometimes is also called the charge asymmetry when CP conservation in top sector is assumed. Tevatron has already observed some experimental and theoretical inconsistency in measurements CDFAfbnote ; D0Afbnote ; Abazov:2008xq ; Aaltonen:2008hc ; Aaltonen:2011kc ; Kuhn:1998jr ; Kuhn:1998kw ; Antunano:2007da ; Bernreuther:2010ny ; Almeida:2008ug ; Ahrens:2010zv . It stirred up immediately many investigations in the BSM Frampton:2009rk ; Shu:2009xf ; Chivukula:2010fk ; Jung:2009jz ; Cheung:2009ch ; Cao:2010zb ; Djouadi:2009nb ; Jung:2009pi ; Cao:2009uz ; Barger:2010mw ; Arhrib:2009hu ; Xiao:2010hm ; Bauer:2010iq ; Xiao:2010ph ; Dorsner:2009mq ; Chen:2010hm ; Cheung:2011qa . However, so far the precision of is limited by the small sample collected at the Tevatron and it is hard to make a clear judgement. In order to confirm/exclude the inconsistence, it is natural to expect that top quark will be measured with higher precision at the LHC, which is the top factory. If the top quark inconsistence with the SM prediction can be confirmed at the LHC, it will be a sign of the BSM.

However LHC is a forward-backward symmetric proton-proton collider, so there is no straightforward definition of as that at the Tevatron which is a forward-backward asymmetric proton-anti-proton collider. New observable that can reveal the top-antitop forward-backward asymmetry, which is generated at partonic level for example , is needed at the LHC. There are some existing observables in literatures that can fulfill this need Langacker:1984dc ; Dittmar:1996my ; Petriello:2008zr ; Li:2009xh ; Diener:2009ee ; Diener:2010sy ; Wang:2010du ; Wang:2010tg ; Dvergsnes:2004tw ; Kuhn:1998jr ; Kuhn:1998kw ; Antunano:2007da ; Ferrario:2008wm . However, each of them poses some advantages and disadvantages. Generally speaking, the favorite decay chain to tag the top quark pair is , which implies that the top (or anti-top) decays semi-leptonically in order to label the mother particle charge. Although some techniques can be adopted, such as requiring the invariant mass of the lepton and the neutrino should be just equal to the mass, the undetected by-product neutrino may still cause the non-negligible uncertainty during the event reconstruction. The precision of forward-backward asymmetry will be limited by this uncertainty. As such it is better not to use the momentum information of semi-leptonically decaying top (anti-top) quark. In this paper only hadronically decaying top (anti-top) quark momentum information is utilized.

In order to isolate the asymmetric events from the symmetric ones which is mainly due to the symmetric gluon-gluon fusion processes, some kinematic region should be chosen. The requirement that the rapidity of top is larger than a critical value can greatly suppress the symmetric cross section. In this paper, we define a new charge asymmetry observable in production at the LHC, namely the edge charge asymmetry (cf. Eq. 1). In some sense is an optimized version of the central charge asymmetry Kuhn:1998jr ; Kuhn:1998kw ; Antunano:2007da ; Ferrario:2008wm . is free from the uncertainty of neutrino momentum reconstruction and much larger than since is much less polluted by the symmetric contributions.

## Ii The edge charge asymmetry in top pair production at the LHC

As mentioned in above section, the new edge charge asymmetry satisfies: (a) utilizing single top (anti-top) kinematical information rather than the top pair information to avoid the uncertainty in neutrino reconstruction; (b) suppressing symmetric background events as much as possible. The edge charge asymmetry is defined as

(1) |

where rapidity is the border between the edge and the central regions, and is the maximum value that the detector can cover. An ideal detector has . is the ratio of the difference and sum of the number of and events that fall in the edge region of the detector. Here and are unnecessarily from the same quark pair.

depends on the choice of and . is determined by the geometry of the detector and should be taken at its optimal value to obtain the most significant . We will investigate the optimal at LHC in section III.

As a comparison, the so called central charge asymmetry is defined as Kuhn:1998jr ; Kuhn:1998kw ; Antunano:2007da ; Ferrario:2008wm

(2) |

It can be seen that the difference between and is that they are defined in different regions. As symmetric events are mostly located in the central regions, the expected value of should be larger than that of the . For the events at the LHC, in the edge region , the number of events will be a bit larger than the number of the events. Oppositely, in the central region , the number of events will be a bit larger than the number of the events. If we cover the total kinematical region, the asymmetric and events in central and edge region will be canceled completely out.

In the SM, the leading order QCD producing cross section is symmetric, and the asymmetric cross section arise from the next-to-leading order (NLO) QCD at the partonic level, which has already been well studied in many literatures. In the calculation of , the asymmetric cross section in the numerator is up to NLO QCD, the total cross section in the denominator is taken as the LO QCD symmetric cross section Fig.1, so as is up to . Other higher order correction such as electro-weak contribution is ignored here. The calculation are carried out with the help of FeynCalc, FormCalc, and QCDLoop Mertig:1990an ; Hahn:1998yk ; Ellis:2007qk .

Up to NLO QCD, gets contributions from: (1) the interference among virtual box in Fig. 2 and the leading diagrams for the process in Fig. 1; (2) the interference among initial and final gluon radiation diagrams of in Fig. 3; and (3) contributions from diagrams of and in Fig. 4. Pay attention that the above mentioned processes does not contain ultra-violet divergence so renormalization is unnecessary in the calculation. Moreover, and contain collinear divergence respectively, but the divergences cancel completely out when calculating the asymmetric cross section. Soft divergences are contained in the former (1)virtual box and (2)real radiation contributions, but are canceled after adding the two. Technically a soft cut is introduced after the soft divergence cancelationHarris:2001sx . The final results are -independent, which is carefully checked in our calculation.

## Iii Numerical Results

In the numerical calculations, the SM parameters are chosen to be and . We choose cteq6l for leading order calculation and cteq6m for NLO calculations. The scales are chosen as .

Fig. 5 shows the numerical estimations for the LHC with . The left-up plot is the symmetric and asymmetric differential distribution as a function of the rapidity of or . Notice that they are labeled in different scales. Also shown are the separate contributions to symmetric cross section from and fusion processes. As can be seen the symmetric events dominantly come from the gg fusion processes and lie mainly in the small Y region. On the contrary the asymmetric cross section changes sign around . Namely in the central region, the number of events is larger than that of the events. Oppositely, in the edge region, the number of events is larger than that of the events. This feature can be easily understood as following. The asymmetric cross section will be completely canceled out after integrating over the whole region. Therefore there should be a turning point where asymmetric cross section turns into the opposite sign. These behaviors can also be extracted from the right-up plot, which show the symmetric and asymmetric cross sections (cf. Eq. 2) as a function of . As a cross check, our result of the total leading order cross section is , which is consistent with the LO QCD prediction in Ref. Cacciari:2008zb . In the left(right)-down plot in Fig. 5 we shown (significance ) as a function of for several respectively. Significance is defined as . Here () is the number of asymmetric (symmetric) events, and the integrated luminosity is chosen to be as an example. In the numerical estimations we take three values according to the coverage of the real detectors. is a conservative choice and is an optimal one. () is also shown here. From the plots, we can see clearly the central asymmetry is negative and the edge charge asymmetry is positive. Moreover is much larger than that of . From curves is usually several percentages while is only percentage. Significance is also a measure to determine the optimal choice of . The maximal significance for and with is almost the same. This is not strange because for the event numbers for both symmetric and asymmetric are reduced greatly. Therefore the precision to measure and is similar. For the bigger rapidity coverage, the significance for is much larger than that of for the optimal . Based on the numerical studies, we can conclude that the detection for larger rapidity top quark is essential to measure significantly.

Fig. 6 shows the same distributions as those in Fig. 5 except for . Due to the lower energy, the produced top pair events have smaller longitudinal boosts(). Thus curves with and have small difference. The values of the asymmetries are larger than those of the . They are mainly caused by two effects. First, at the parton level, a lower energy can generate higher asymmetry. The parton level asymmetry distribution with can be found in ref.Kuhn:1998kw . This can be kept at the hadron level after the convolution of parton distribution function. Second, the portion of the symmetric process become smaller for a lower . Thus the value of the charge asymmetry can be larger with a lower than that with a higher at the LHC.

From the figures we can also see that the significance of at 7TeV is larger than that of at 14TeV in the case . The reason is that for the higher energy LHC, the top quarks tend to be highly boosted, which shifts the distribution of to the higher rapidity. After imposing cut, the positive asymmetric cross section in the high rapidity region losts much. Thus with the same integrated luminosity the lower energy LHC has certain advantage to measure the top quark edge charge asymmetry in low case.

## Iv Conclusions and discussions

In this paper, we propose a new observable namely edge charge asymmetry in top pair production at the LHC. has two advantages: (1) free from the uncertainty arising from the missing neutrino in the event reconstruction because in the definition only single hadronically decaying top (or anti-top) kinematical information is needed; (2) suppressing greatly the symmetric events mainly due to the gluon-gluon fusion process. Our numerical estimation showed that is much larger than that of central charge asymmetry Kuhn:1998jr ; Kuhn:1998kw ; Antunano:2007da ; Ferrario:2008wm . Moreover the significance to measure the is usually greater than that of , provided that the capacity to identify high rapidity top quark is efficient.

## Acknowledgment

This work was supported in part by the Natural Sciences Foundation of China (No 11075003).

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