One-side forward-backward asymmetry at the LHC You-kai Wang1 ∗, Bo Xiao1 †, and Shou-hua Zhu1,2 ‡ 1 Institute of Theoretical Physics & State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, China 1 2 Center for High Energy Physics, Peking University, Beijing 100871, China 1 0 (Dated: February 1, 2011) 2 n a Forward-backwardasymmetryAFB isanessentialobservabletostudythenatureof J coupling in the standard modeland physics beyondthe standard model, as shown at 9 2 LEPandTevatron. Asaproton-protoncollider,theLHCdoesnothavethepreferred ] h direction contrary to her counterpart, namely, LEP and Tevatron. Therefore AFB p - is not applicable at the LHC. However for the proton the momentum of valence p e h quark is usually larger than that of the sea quark. Utilizing this feature we have [ 2 defined a so-called one-side forward-backward asymmetry AOFB for the top quark v pair production at LHC in the previous work. In this paper we extend our studies 8 2 4 to the charged leptons and bottom quarks as the final states. Our numerical results 1 1. show that at the LHC AOFB can be utilized to study the nature of the couplings 1 once enough events are collected. 0 1 : v PACS numbers: 14.60.-z,14.65.Fy, 12.15.-y, 12.38.Bx i X r a I. INTRODUCTION At high energy colliders discovering a new particle is not enough, one of the most im- portant subsequent tasks is how to pin down its properties, for example, spin, nature of the coupling, and so on. Based on this information the internal quantum structure can be scrutinized and the possible subtle deviation may be found. In practice once enough data sample is collected, the forward-backward asymmetry (A ) for a specific final state can be FB measured and compared with theoretical prediction. ∗ E-mail:[email protected] † E-mail:[email protected] ‡ E-mail:[email protected] 2 A , or sometimes called the charge asymmetry if CP conservation is assumed, is an FB interesting experimental observable. The primary definition of the A is FB N(cosθ > 0) N(cosθ < 0) A − , (1) FB ≡ N(cosθ > 0)+N(cosθ < 0) where θ is thepolar anglebetween thefinal stateparticle and thebeam line. The polarangle in Eq.(1) can be defined in different frames, such as Collins-Soper frame for the lepton pair production in the Drell-Yan processes, lab frame, and tt¯rest frame for top pair production process at Tevatron. In the tt¯rest frame, Eq.(1) can be transformed as σ(∆Y > 0) σ(∆Y < 0) A = − , (2) FB σ(∆Y > 0)+σ(∆Y < 0) where ∆Y Yt Yt¯ is the difference of rapidity of the top and antitop quark, which is ≡ − invariant under tt¯or pp¯rest frame. Here the use of anti-top quark information implies that CP conservation of the top and antitop quark is assumed. In some sense A is a measure to study the angular distributions of the specific final FB particle. The distribution is determined by the nature of the couplings among the initial and final particles with the intermediate particle in a certain theory. Currently the successful theory which can describe the data is the standard model (SM). There are good reasons to expect physics beyond the SM (BSM), which usually predict new particles and/or new cou- plings. Such new particles and/or couplings can be firstly detected via A measurements, FB namely, the deviation from the SM prediction. Therefore A is a useful tool to test SM FB and even to discover BSM. Up to now, A for many final particles, e.g., charged leptons, bottom quark, and top FB quark have been measured at different colliders, say SLD, LEP and Tevatron. Generally speaking, the measurements are in excellent agreement with SM predictions. However there are some anomaly for the bottom quark at LEP and for the top quark at Tevatron. The measurements and theoretical predictions are listed in Table I. Both A measurements have a deviation about 2 σ from SM predictions. It is obvious FB that only less than 3σ deviation is inadequate to conclude the failure of the SM. However it is interesting to explore the implications of the deviations both in the SM and the BSM [4–21]. The present experimental results still have too large uncertainties to make a clear judgement. So the cross-check of these measurements in the more powerful collider are extremely necessary. 3 TABLE I:Measurements andtheoretical predictions (inbracket) ofAFB forbottom andtop quark. Here pp¯and tt¯represent measurements in the lab and the center-of-mass frame of the top quark pair respectively. Bottom Top LEP 0.0992 0.0016 (0.10324 0.00088) [1] ± ± ··· CDF tt¯ 0.158 0.072 0.017 (0.058 0.009) [2] ± ± ± Tevatron CDF pp¯0.150 0.050 0.024 (0.038 0.006) [2] ··· ± ± ± D0 tt¯ 0.08 0.04 0.01 (1+2%) [3] ± ± −1 The large hadron collider (LHC) is the most hopeful machine to make this cross-check and even discovery, because it has the larger production rate and most importantly, the more powerful reconstruction capacity of both the bottom and top quark. Unfortunately, unlike the e+e− collider, LEP, or pp¯collider, Tevatron, the pp collider, LHC, does not have preferred direction in the laboratory frame. The definition of A in Eqs.(1) and (2) are not FB applicable here. Forward-backward asymmetry at pp collider has already been discussed in the literature[22–27]. A in these papers are mostly used for exploiting a possible massive FB Z′ boson. For example, A can be defined as[26, 27] FB R[F(y) B(y)]dy A = − (3) FB R[F(y)+B(y)]dy where F(y) is the number of forward events with pseudorapidity |ηf| > |ηf¯| and B(y) is the number of backward events with pseudorapidity |ηf| < |ηf¯| for a given Z′ rapidity, y. In a previous paper, we proposed a new definition of forward-backward asymmetry, namely, the one-side forward-backward asymmetry A , to study the forward-backward asymmetry at OFB the LHC[28]. The basic idea is that valence quark momentum is averagely larger than that of sea quark in the proton. Once the z direction momentum of the final states is required to be larger than a specific value, the partonic forward-backward asymmetry will be kept. A is defined as OFB F +B σA − − A = (4) OFB F +B ≡ σ + + with F = (σ(∆Y > 0) σ(∆Y < 0)) (5) ± ± |Pfz+f−>Pczut,Mf+f−>Mcut 4 B = (σ(∆Y < 0) σ(∆Y > 0)) (6) ± ± |Pfz+f−<−Pczut,Mf+f−>Mcut where Pfz+f− is the final particle pair’s z direction momentum and Mf+f− is the invariant mass of the final particle pair. By adopting some kinematic cuts, especially cuts on Pz , the forward-backward asym- f+f− metry generated at the partonic level can be kept even after the convolution with parton dis- tribution functions. The A can be an efficient tool in investigating the forward-backward OFB asymmetry at the LHC. In principle, all the forward backward asymmetry measured in the left right asymmetric beam collides, eg., e+e− or pp¯, can now be cross-checked at the left right symmetric pp beam collider, LHC. In this paper, we will extend our previous study to various final state cases[28]. As shown in Eq.(4), the precise momentum measurement at z direction is essential for A . At the LHC, the momentum of charged leptons are the most precisely measured OFB quantities. Thus it is quite natural to study first the A for charged leptons at the LHC. OFB In the SM, the charged lepton pair can be generated via s channel Z and/or γ∗ electroweak (EW) diagrams, and these tree-level diagrams can contribute to A because the couplings OFB of left- and right-handed fermions with gauge boson Z are different. At the LHC, besides the s channel Z and/or γ∗ induced EW diagrams, bottom quarks are also produced via the strong interaction. The contributions to Ab in QCD starts fromthe next-to-leading order, OFB namely, at O(α3) [29, 30]. The situation is similar to that of top quark pair production [28]. S Away from Z-pole, the EW contributions to Ab is much less than that of QCD ones. In OFB order to study Ab arising from the EW source, we have to select events around the Z-pole. OFB The paper is organized as following. In Sec. II, the charged lepton one-side forward backward asymmetry Aℓ at the LHC is calculated. As the charged lepton momentum can OFB be precisely measured, Aℓ can be a test ground of the newly proposed one-side forward- OFB backward asymmetry. In Sec. III, Ab is calculated at the NLO in QCD. In section OFB IV, Ab is calculated in the vicinity of the Z pole in order to study the EW origin of OFB forward-backward asymmetry. Section V contains our conclusions and discussions. 5 II. CHARGED LEPTON ONE-SIDE FORWARD-BACKWARD ASYMMETRY Aℓ OFB At the LHC, the main production mechanisms of the charged leptons (elec- tron/muon/tau) at partonic level are qq¯ Z/γ∗ l+l−, similar to those at LEP and → → Tevatron. Because the couplings among Z boson and left- or right-handed fermions are different, even at leading order O(α2), forward-backward asymmetry is non-zero 1. The measurements of Aℓ (cf. Eq. 1) at LEP and Tevatron are in good agreement with the FB SM predictions. At the LHC there is no preferred direction in lab frame. The one-side forward-backward asymmetry for l+l− production process is defined as Eq.(4), where F = (σ(∆Y > 0) σ(∆Y < 0)) (7) ± ± |Plz+l−>Pczut B = (σ(∆Y < 0) σ(∆Y > 0)) . (8) ± ± |Plz+l−<−Pczut Here ∆Y = Yl+ Yl− is the difference of rapidity of the charged leptons, which is invariant − along the boost in beam directions. Pz is the z direction momentum of the lepton pair in l+l− the laboratory frame. At the pp collider LHC, for the subprocess qq¯ l+l−, the momentum of the valence → quark q is usually larger than that of the sea quark q¯. If taking the momentum of q as the positive z direction, we will get Pz > 0. However there is the possibility that momentum l+l− of valence quark is less than that of sea quark. In this case, Pz < 0. This will induce l+l− the opposite contribution to asymmetric cross section. Moreover, the valence quark can symmetrically come from the other proton. The usual A is strictly equal to zero. The FB asymmetric cross section of the partonic processes can survive only if we just observe one- side l+l− events, for example Pz > 0 or Pz > Pz . The usual forward cross section l+l− l+l− cut σ(∆Y > 0) and backward cross section σ(∆Y < 0) can be calculated after imposing the Pz cut. So the forward-backward asymmetry in this side is F /F . If we evaluate the l+l− − + opposite side events, namely, Pz < Pz , the forward-backward asymmetry in this side is l+l− − cut B /B . At the LHC the consistence between these two forward-backward asymmetries can − + be checked. Moreover if we define A in Eq.(4), the statistics will be doubled. Besides OFB keeping the forward-backward asymmetry at partonic level, Pz has other advantages for cut example increasing the significance to observe the forward-backward asymmetry. 1 Fore+e− e+e− the AFB =0arisesalsofromthe interferencebetweens- andt-channelQEDdiagrams. → 6 6 In our calculations here, F and B are calculated at the leading order O(α2). Because ± ± of the small mass compared with the collider beam energy, three charged leptons will have similar signatures although they will be measured (reconstructed) by different methods. Limitedbythecoverageoftherealdetector, thechargedleptonisrequiredtosatisfy η < 2.4 | | [31]. In massless limit, η = Y. Figures 1 and 2 show the differential spectrum of the asymmetric cross section σA, total cross section σ, AOFB as a function of the lepton pair invariant mass Me+e− (taking electron as the example), and the significance sig = √ σA/√σ ( with = 10fb−1) as a function of L L Pz at the LHC for √s = 7 TeV and 14 TeV respectively. No η cuts are applied for the left cut column plots, and η < 2.4 is applied for the right column plots. The significance plots are | | used to select the optimal Pczut. In these plots we take the typical value Me+e− = 100.5GeV as an example. The optimal Pczut are not sensitive to Me+e−. Thus, we take Pczut = 150GeV in the left upper three plots and Pz = 50GeV in the right upper three plots. From the cut curves with and without η cut we can see that the asymmetric cross section is sensitive to η. This behavior indicates that asymmetric cross section is mostly located in large η region due to the large boost along the longitudinal direction. From figures we can also see clearly the resonance around Z in dσ/dMe+e− and dσA/dMe+e−. Moreover, the AOFB varies with Me+e− and the distribution is similar to that of usual A at e+e− and pp¯ colliders. The reason is FB simply because both A and A arise mainly from the same subprocesses uu¯ e+e− OFB FB → and dd¯ e+e−. → For our purpose we only study the A at leading order, namely, at O(α2). In practice OFB [32] higher-order effects must be included. Such higher-order effects, especially the contri- butions from the high P l+l− events which arise from the extra hard photon radiation, T can be treated by adopting Collins-Soper frame [32–34]. The advantage of adopting the Collins-Soper frame is that A is free from the impact of the 2 3 process with initial γ FB → radiation which will cause a nonzero P of the lepton pair. A can also be extended to T OFB Collins-Soper frame with extra cut on z-direction momentum of lepton pair. We will study this issue in detail elsewhere. One-side forward-backward asymmetry can be tested in the charged lepton production processes. Theoretically A can also be utilized to study the more complicated bottom OFB quark production at the LHC, though in practice the channel is not as clean as that of charged leptons. 7 A/d M-+ee105000000 d σA/d Mee σA/d M-+ee11240000 d σA/d Mee σd 0 d 1000 800 -5000 600 -10000 400 -15000 200 0 -20000 0 20 40 60 80 100 120 140 160 180 200 0 20 40 60 80 100 120 140 160 180 200 Me+e- Me+e- d M-+ee108 d σ/d Mee d M-+ee105 d σ/d Mee σ/ σ/ d 107 d 104 106 105 103 104 102 103 10 102 0 20 40 60 80 100 120 140 160 180 200 10 20 40 60 80 100 120 140 160 180 200 Me+e- Me+e- B 0.5 B 0.3 AOF 0.4 AOF0.25 0.3 0.2 0.2 0.15 0.1 0.1 0 0.05 -0.1 0 -0.2 -0.05 -0.3 AOFB -0.1 AOFB -0.4 -0.15 -0.5 -0.2 0 20 40 60 80 100 120 140 160 180 200 0 20 40 60 80 100 120 140 160 180 200 Me+e- Me+e- -1)b 50 -1)b 14 0 f 45 0 f g (1 40 g (1 12 si 35 si 10 30 8 25 20 6 15 4 10 Mee= 100.5 GeV Mee= 100.5 GeV 2 5 0 0 0 100 200 300 400 500 600 700 800 0 100 200 300 400 500 600 700 800 Pz Pz cut cut FIG. 1: dσA/dMe+e−, dσ/dMe+e−, AOFB as a function of Me+e− and sig as a function of Pczut at the LHC for √s = 7 TeV. The left plots have no η cut, and the right plots have η < 2.4 cut. | | Optimal Pz are determined by the sig plots. The left upper three plots have Pz =150GeV and cut cut the right upper three plots have Pz = 50GeV. cut 8 A/d M-+ee1105000000 d σA/d Mee σA/d M-+ee11020000 d σA/d Mee σd 5000 d 800 0 600 -5000 400 -10000 200 -15000 0 -20000 0 20 40 60 80 100 120 140 160 180 200 0 20 40 60 80 100 120 140 160 180 200 Me+e- Me+e- d M-+ee108 d σ/d Mee d M-+ee105 d σ/d Mee σ/ σ/ d 107 d 104 106 105 103 104 102 103 10 102 0 20 40 60 80 100 120 140 160 180 200 10 20 40 60 80 100 120 140 160 180 200 Me+e- Me+e- B 0.5 B 0.2 AOF 0.4 AOF 0.15 0.3 0.2 0.1 0.1 0.05 0 -0.1 0 -0.2 -0.05 -0.3 AOFB AOFB -0.1 -0.4 -0.5 -0.15 0 20 40 60 80 100 120 140 160 180 200 0 20 40 60 80 100 120 140 160 180 200 Me+e- Me+e- -1)b 50 -1)b 10 0 f 45 0 f 9 g (1 40 g (1 8 si 35 si 7 30 6 25 5 20 4 15 3 10 Mee= 100.5 GeV 2 Mee= 100.5 GeV 5 1 0 0 0 100 200 300 400 500 600 700 800 0 100 200 300 400 500 600 700 800 Pz Pz cut cut FIG. 2: Same as Fig. 1 except √s = 14TeV. Optimal Pz = 300GeV for left upper three plots cut and optimal Pz = 100GeV for right upper three plots. cut 9 III. BOTTOM QUARK ONE-SIDE FORWARD-BACKWARD ASYMMETRY Ab IN QCD OFB Unlike the top quark, the bottom quark life time is longer than the hadronization scale, which meansbottomquarkwill appearasbjetinthedetector. Forsimplicity inouranalysis, we treat the b quark as b jet in the calculation. As mentioned above, at the LHC, the bottom quark forward backward asymmetry arises from two sources, namely, the QCD and EW processes. The dominant bottom quark pro- ¯ duction processes are gg(qq¯) bb via strong interaction. However at the leading order in → QCD i.e. O(α2), the forward backward asymmetry is zero. The QCD induced asymmetric S cross section starts from O(α3). Same as top pair production, the contributions can be s classified into three categories: (1) Interference among diagrams for the initial and final ¯ state radiation processes qq¯ bbg; (2) Interference among the born diagrams and virtual → ¯ box diagrams for the process qq¯ bb; (3) Contribution from diagrams of the real processes → ¯ qg bbq. The calculation has been carried out in Ref. [29, 30]. For the EW interaction → ¯ contribution, the leading contribution comes from the born cross section qq¯ bb via a Z → and/or γ∗ boson, similar with the case of charged lepton. At the LHC the EW contribution is mostly from the vicinity of the Z pole, while the QCD contribution extends in the wider energy regime. Moreover except at Z pole the QCD contribution is much larger than that of the EW one. In this section we will focus on the QCD contribution to Ab . OFB At the Tevatron the theoretical calculation of heavy quark forward backward asymmetry arising from the QCD contributions has been studied in previous literature [29, 30]. Even at the LHC, the so-called central charge asymmetry A has been constructed to study the C forward backward asymmetry of the top quark [29, 30, 35–38]. Some comparison have been made between the central charge asymmetry and the one-side forward backward asymmetry in Ref. [28]. At the LHC A is much larger than A because Pz can suppress the huge OFB C cut symmetric gg fusion efficiently. One-side forward-backward asymmetry for b quark at the LHC can be defined in the pp rest frame as in Eq. 4, F = (σ(∆Y > 0) σ(∆Y < 0)) (9) ± ± |Pbz¯b>Pczut,Mb¯b>Mcut B = (σ(∆Y < 0) σ(∆Y > 0)) . (10) ± ± |Pbz¯b<−Pczut,Mb¯b>Mcut 10 Here we only consider QCD contributions and ignore the electroweak contributions. The purpose to apply constraints on Ptzt¯ and Mtt¯ is to suppress the symmetric gg → tt¯events, which will be illustrated in the following figures. To measure A at the LHC, the charge of the b jet should be identified to distinguish OFB the bottom or anti-bottom jet. So one bottom/antibottom quark is required to decay into a charged lepton, and the other antibottom/bottom can decay hadronically. For the b tagging, there are two selecting criteria [39]: P > 40GeV and η < 1.5 without second T | | vertex reconstruction, and P > 10 GeV and η < 2.4 with second vertex reconstruction. T | | We find that our signal b jets locate mostly in large η regions due to the high longitudinal boost. So we take the second cut criteria in the following analysis. Note that the definition in Eq.(4) is based on the CMS or ATLAS detector at the LHC. For the LHCb, one can take real “one-side” definition, namely F − A = . (11) OFB F + In this case b tagging requirements should also be adjusted accordingly. The obvious differ- ¯ ence is thatthere will bea lower boundonη, e.g. 2.0 < η < 5.5 [40]. As most ofbb events are boosted in the z-direction, LHCb has the unique advantage to collect more bottom events to reach higher precision measurement of forward-backward asymmetry. Figure 3 shows the asymmetric cross section σA, symmetric cross section σ, A and OFB significance sig ( with = fb−∞) as a function of Pz without and with b jet cut for cut L ∞′ √s = 7 TeV. From the left column plots, we see that both σA and σ drop with the increase of Pz . σ decreases even faster so A rises with the increase of Pz . This is due to cut OFB cut two reasons. First, as mentioned in above sections, A will be polluted by the negative OFB contributions to asymmetric cross section in the case that the sea quark’s momentum is larger than the valence quark’s momentum. These events locates mostly in small Pz region. ¯ bb Alargercut ofPz canincrease theportionofpositive signasymmetric crosssection. Second, ¯ bb ¯ due to the properties of the parton distribution function, the symmetric gg bb events are → mostly distributed in the small Pz region and the asymmetric events are likely to be highly ¯ bb boosted along the z direction. The Pz can remove more symmetric backgrounds. cut The right column plots indicate that b jet cut can change the above distributions signif- icantly. Most of the events are lost. Low M ¯ events are more sensitive to b jet cuts than bb the large Mb¯b events, which indicates that they tends to have lager η and small PT. The σA