Color Sextet Vector Bosons and Same-Sign Top Quark Pairs at the LHC

We investigate the production of beyond-the-standard-model color-sextet vector bosons at the Large Hadron Collider and their decay into a pair of same-sign top quarks. We demonstrate that the energy of the charged lepton from the top quark semi-leptonic decay serves as a good measure of the top-quark polarization, which, in turn determines the quantum numbers of the boson and distinguishes vector bosons from scalars.


Introduction -
The cross section for production of top quarks is relatively high at the energies of the Large Hadron Collider (LHC). While conventional mechanisms produce either a single top-quark or a top-antitop pair, it is important to be alert to the observation of a pair of same-sign top quarks. One consequence would be the appearance of a pair of same-sign leptons with large transverse momentum. In a recent paper, we explore the potential for discovery of an exotic color-sextet scalar in the production of a pair of same-sign top-quarks in early runs of the LHC at 7 TeV [1]. The standard model (SM) backgrounds are small. We demonstrate that one can measure the scalar mass and the top-quark polarization, and confirm the scalar nature of the resonance with 1 fb −1 of integrated luminosity. Moreover, the top-quark polarization distinguishes gauge triplet-and singlet-scalars. In the present manuscript, we address color sextet vector production in same-sign top-quark pair-production, and we show that its discovery, and the determination of its properties, could also be accomplished with early LHC data. Important in our analysis is the recognition that among the products of semi-leptonic top-quark decay, the direction of the charged-lepton is highly correlated with the top-quark spin. The top-quark polarization can be measured from the distribution in cos θ [2], the cosine of helicity angle between the charged-lepton momentum in the top-quark rest frame and the top-quark momentum in the center-of-mass frame of the production process (i.e. the rest frame of the parent scalar or vector). Gauge triplet scalars decay to t L t L , and gauge singlet scalars to t R t R . Here, t L and t R denotes top quarks with lefthanded and right-handed polarization. In either case, both top quarks produce the same angular distribution, either (1 − cos θ)/2 (t L t L )or (1 + cos θ)/2 (t R t R ), allowing unambiguous identification of the scalar [1]. A color sextet vector decays into a t L t R pair. In this case, the observed inclusive angular distribution in the final state would be a flat, a sum of the shapes from the t L and the t R decays. The flat profile would distinguish a vector from a scalar, but it also would admit a mechanism that yields unpolarized top quarks.
In this paper we establish that one can separate the angular distributions corresponding to t L and t R from the color sextet vector decay into a t L t R pair. The solution relies of the introduction of asymmetric cuts on the momenta of the leptons from the top-quark decays.
The Model -The most general SU (3) C × SU (2) L × U (1) Y effective invariant Lagrangian for color sextet scalars Φ and vectors V µ has the form [3][4][5] where q L = (u L , d L ) denotes the left-handed quark doublet, u R and d R are the corresponding right-handed gauge singlet fields, and q c ≡ Cq T is the charge conjugated quark field. For the sake of simplicity, color and generation indices are omitted. The subscripts on the Φ and V fields denote the standard model gauge quantum We are interested in same-sign top-quark pair production via a sextet vector decay. Only the axial-vector part of the coupling contributes while the pure vector coupling vanishes due to the identical quarks. The effective coupling of the color sextet vector to a pair of identical quarks (qq) is where the K M ab are Clebsch-Gordan coefficients; a and b are the color indices in the fundamental representation; M is the color index in the sextet representation; and g is the coupling strength. Without loss of generality, we concentrate on real and flavor-conserving couplings in this work.
The coupling of the vector to two up-type quarks is largely constrained by the measurement of D 0 −D 0 mix-ing which is affected by the vector at the tree level. The |∆C = 2| Hamiltonian induced by V is The four-fermion operators Q 2 and Q 3 are and the Wilson coefficients are The vector's contribution to ∆m D ≡ |m D 0 − mD0 | is where the hadron matrix elements are [7] with f D = 222.6 ± 16.7 +2.3 −2.4 MeV, m D = 1865 MeV, and B D = 0.82 [8]. To be consistent with the measured ∆m D [9], the coupling g qq is stringently constrained: for m V ≃ 1 TeV, after an enhancement factor ∼ 2.1 is included from the QCD running of the Wilson coefficients from the scale m V to m c . This strong constraint on the product g uu g cc allows freedom for the production of V at the LHC if the coupling g cc to the second generation quarks is minimized. Alternatively, the first generation may be suppressed while the second generation is not, but such sea-quark initiated processes are relatively suppressed.
For the choice g = 1, we show the cross section for V production via the process uu → V at the LHC in Fig. 1(a) and the tt cross section via the process uu → tt in Fig. 1(b). The large cross sections arise from the large parton distribution functions for valence u quarks in the initial state. If the LHC energy is raised from 7 TeV to 14 TeV the cross section is increased by roughly a factor of 3 to 4.
Discovery Potential -We focus on the same sign dilepton decay mode in which the W bosons from both t → W b decays lead to a final state containing an electron or muon, W → lν, accounting for about 5% of all tt decays. We concentrate on the clean µ + µ + final state because muon reconstruction has a large average efficiency of 95 − 99% within the pseudorapidity range |η| < 2.4 and transverse momentum range 5 GeV ≤ p T ≤ 1 TeV, while the charge mis-assigned fraction for muons with p T = 100 GeV is less than 0.1% [11].
These events are characterized by two high-energy same-sign leptons, two jets from the hadronization of the b-quarks, and large missing energy ( E T ) from two unobserved neutrinos. We generate the dominant backgrounds with ALPGEN [12]: I: Signal and background cross sections (pb) before and after cuts, with g = 1, for six values of mV (GeV). The decay branching ratios of the signal Br(tt) are given in the second column. The "no cut" rates correspond to all lepton and quark decay modes of W -bosons, whereas those "with cut" are obtained after all cuts, the restriction to 2 µ + 's and with tagging efficiencies included.
mV The first process (W W jj) is the SM irreducible background while the second (tt) is a reducible background as it contributes when some tagged particles escape detection, carrying small p T or falling out of the detector rapidity coverage. For example, one of the b-quarks decays into an isolated charged lepton while one of the two jets from the W − boson decay is mis-tagged as a b-jet.
Other SM backgrounds, e.g. triple gauge boson production (W W W , ZW W , and W Zg(→ bb)), occur at a negligible rate after kinematic cuts, and are not shown here. At the analysis level, all signal and background events are required to pass the following acceptance cuts: where we order the two charged leptons in the final state by their energies and label the more energetic lepton as "greater" and the other one as "lesser". Owing to spin correlations, the charged lepton from right-handed top quark decay is more energetic than the one from the left-handed top quark decay. This difference motivates our asymmetric cut on the p T of the two charged leptons. The separation ∆R in the azimuthal angle (φ)pseudorapidity (η) plane between the objects k and l is We model detector resolution effects by smearing the final state energy according to where we take A = 10(50)% and B = 0.7(3)% for leptons(jets). To account for b-jet tagging efficiencies, we demand two b-tagged jets, each with a tagging efficiency of 60%. We also apply a mistagging rate for charm-quarks ǫ c→b = 10% for p T (c) > 50 GeV. The mistag rate for a light jet is ǫ u,d,s,g→b = 0.67% for p T (j) < 100 GeV and 2% for p T (j) > 250 GeV. For 100 GeV < p T (j) < 250 GeV, we linearly interpolate the fake rates given above. After lepton and jet reconstruction, we demand that the two hard leptons are of the same sign, a requirement which greatly reduces the SM background, giving a rejection of order 10 −4 and 10 −3 for the tt and W W jj processes, respectively. After the cuts are imposed, we find a total of 1.0 background event, 0.4 from tt and 0.6 from W W jj for 1 fb −1 of integrated luminosity.
After b-tagging and restriction to the µ + µ + mode, 15-30% the signal events survive the analysis cuts depending on the vector mass. Signal and background cross sections are shown in Table I, before and after cuts, for 6 values of m V .
Because the decay width of V is narrow, one can factor the process uu → tt into vector production and decay terms, The decay branching ratio Br(tt) ≡ Br(V → tt) is Subscript "0" denotes the reference value g = 1. We choose to work with the following two parameters in the rest of this paper: the vector mass m V and the product g 2 Br(V → tt). The kinematics of the final state particles are determined by the vector mass, whereas the couplings of the vector to the light and heavy fermions change the overall normalization. In Fig. 2, we show the expected numbers of signal events as a function of m V for a range of values of the coupling g 2 Br(V → tt). We obtain the event rate lines by converting the required cross section into g 2 Br(V → tt) via Eq. 15. Based on Poisson statistics, one needs 8 signal events in order to claim a 5σ discovery significance (equivalent to a 99.999943% confidence level) on top of 1 background event. We plot the 5σ discovery line (solid) in the figure. Rates for other values of g uu and g tt can be obtained from Eq. 15.
The search for same-sign top quark pair production in the dilepton mode at the Tevatron imposes an upper limit σ(tt +tt) ≤ 0.7 pb [13][14][15]. The constraint is plotted in the orange shaded region. The CDF collaboration measured the tt invariant mass spectrum in the semi-leptonic decay mode [16]. Since b andb jets from t → W b are not distinguished well, tt pairs lead to the same signature as tt in the semi-leptonic mode. Hence, the m tt spectrum provides an upper limit on σ(tt +tt), shown in the cyan shaded region in Fig. 2. The lower gray shaded region is the region in which V would hadronize before decay, washing out the spin correlation effects we utilize to probe the coupling and spin of the sextet state.
Top Quark Polarization -We use the observation of a pair of same sign dileptons as indicative of a same sign top quark pair and to suppress SM backgrounds efficiently. The two missing neutrinos in the final state complicate event reconstruction. Following Ref. [1], we use the MT2 method to select the correct b-µ combinations and to verify whether the final state is consistent with t → W b parentage. Then we make use of the onshell conditions of the two W bosons and two top quarks to solve for the neutrino momenta [17,18]. Once the neutrino momenta are known, the kinematics of the entire final state is fixed, and the vector boson mass is computed from the invariant mass of the two reconstructed top quarks. The next step is to verify that the top-quarks exhibit opposite polarization, accomplished here by making use of the difference in the momentum spectra of decay leptons from left-handed and right-handed top quarks [19]. The energy of a charged lepton in a right-handed topquark decay is harder than the one in a left-handed topquark decay. The differential distribution in the energy of the charged lepton energy is lepton, and z = cos θ where θ is the helicity angle defined in the Introduction. The variables x ′ and z ′ are defined in the top-quark rest frame and are linked to x and z in the laboratory frame through the top quark boost: where γ = E t /m t and β = 1 − 1/γ 2 . The lower and upper limits of integration are The differential cross section dΓ/dx ′ dz ′ in the rest frame of the top quark is [20] dΓ ArcTan(x) = arctan(x), for x ≥ 0, π + arctan(x), for x < 0, andŝ t labels the top quark spin direction. Here, m W and Γ W denote the mass and width of the W boson, respectively.
In this work we choose the helicity basis to measure the top quark polarization. In this basis, the top quark spin is chosen to be along (against) the direction of motion of the top quark in the center of mass frame of the system. After a boost from the top-quark rest frame to the laboratory frame, we obtain the energy distributions of the charged leptons from left-handed and right-handed topquark decays shown in Fig. 3. The solid curves denote the t L decay while the dashed curves the t R decay. As the charged lepton follows the top quark spin, the lepton from  -1 -0.8-0.6 -0.4-0.2 -0 0.2 0.4 0.6  t R decay tends to follow the direction of motion of the top-quark, and is more energetic. The lepton from the t L decay tends to move against the direction of motion of its top quark, and it is therefore less energetic. The difference in the energy spectra becomes more evident with increasing m V . For example, for a 1000 GeV vector, the charged lepton from t R decay peaks near x = 0.5 while the one from t L decay peaks below x = 0.1. We note that both solid and dashed curves have a kink feature. For the left-handed top-quark decay, the kink arises largely from the boost, which generates the lower integration limit z min . The limit yields a scale of x ≃ 1 − β for a heavy vector. On the other hand, the kink in the distribution for right-handed top-quark decays comes mainly from the non-continuity of the ArcTan function in the matrix element, which yields a scale of x ≃ B (1 + β) after the boost.
In sextet vector boson decay into a t L t R pair, the charged leptons exhibit a mixture of the energetic and soft spectra. To utilize this feature, we order the energy of the leptons and define the top quark containing the greater energy lepton as t greater and the other top quark as t lesser . The cos θ distributions of the reconstructed t lesser and t greater are displayed in Fig. 4. These results show that one can differentiate the (1 + cos θ) (t R ) and (1 − cos θ) (t L ) shapes. The reconstruction is not perfect, however, owing to imperfect assignment of the charged lepton. As shown in Fig. 3, charged leptons from t L decay can be more energetic than those from t R decay with small probability. With increasing vector mass, the probability of wrong assignment becomes smaller.
As a consistency check on this method for determining polarizations, we apply the same reconstruction to  -1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1   FIG. 5: Distribution of cos θ of the reconstructed t lesser and tgreater of a singlet scalar decay into tRtR. For illustration we choose mV = 600 GeV. singlet scalar decay into two right-handed top-quarks. The reconstructed t lesser and t greater distributions for singlet scalar decay are shown in Fig. 5. Both distributions maintain the expected (1 + cos θ) trend, but the shapes are distorted by event reconstruction. Hence, we gain added confidence that the top-quark polarization can be determined and used to discriminate vector bosons from scalar bosons.
Summary -We present a study of the search for exotic charge 4/3 color-sextet vector bosons in the production of same-sign top-quark pairs at the LHC at 7 TeV. We examine the final states in which both top-quarks decay semi-leptonically. We show that vector bosons can be distinguished from scalars. The top quarks from vector decay exhibit opposite polarization, one left-handed and one right-handed. The inclusive distribution in the helicity angle cos θ of a charged lepton is flat since it receives contributions from both top quarks. However, we show that an energy selection on the charged leptons can re-store the characteristic shapes that distinguish left-and right-handed top quarks. Correspondingly, we show that LHC data should allow one to observe V → t R t L and distinguish vector from scalar decay.