Signals from R-parity violating top quark decays at LHC

We evaluate the potential of the CERN LHC collider to observe rare decays of the top quark in channels involving R-parity violating ( ) interactions. We stress the importance of calculating top quark production and decay simultaneously as a true 2→4 process. The process of t pair production followed by decay of one of the top quarks is analyzed with fast detector simulation. We show that intermediate supersymmetric particles can be observed as resonances even if they are heavier than the top quark due to the significant off-shell top quark mass effects. The approach where the top quark is produced on-mass-shell and then decays into 2- or 3-body final state would in general lead to incorrect kinematical distributions and rates. The rates of the 2→4 process with top quark production and 3-body decay depend on the total width of the heavy intermediate sfermion which could, therefore, be measured indirectly. We find that the LHC collider offers a unique potential to study rare top quark decays in the framework of supersymmetry with broken R-parity for branching fractions of top decays as low as 10−6.


Introduction
Processes involving the top quark, the heaviest known fermion with a mass close to the scale of the electroweak symmetry breaking, offer a unique possibility to search for physics beyond the Standard Model(SM). It is well known that the SM suffers from fundamental problems such as hierarchy, fine-tuning, and absence of dark matter candidates. It is therefore believed that there must exist a more fundamental underlying theory. One of the most promising alternative models which resolves these problems is supersymmetry. The Minimal Supersymmetric extension of the Standard Model(MSSM), with the gauge group SU(3) c × SU(2) L × U(1) Y contains SM particles, their superpartners and an additional Higgs doublet. The MSSM possesses an additional discrete symmetry, called R-parity (R p ), which conserves lepton and baryon number: where B, L and S are the baryon number, lepton number and spin, respectively. However, there is no clear theoretical preference for the status of R p -to be conserved or violated -in the supersymmetric theories. Therefore the answer whether the parity is realized in nature or not should be given by experiment. It is important to notice that / R p is much less constrained in general for the 3-rd fermion-sfermion generation compared to the first two generations. Therefore the CERN LHC collider, which can be considered as a top quark factory, plays a special role as a the perfect tool for testing the conservation of R p in the top-stop sector. With tt production cross section of the order of 800 pb [1], ∼ 10 8 top quarks will be produced per year, assuming an integrated luminosity of 100 f b −1 . These high statistics will allow for precision measurements of top quark physics and in particular, for high sensitivity to rare top quark decays in a / R p scenario.
Rare top-decays with / R p have been intensively studied for the last decade, and even before the discovery of the top quark [2]. If sfermions are light enough, the 2-body decay of top quark into fermion-sfermion pair will take place [3, 4, 5, 6, 7, 8, ?, ?], otherwise the decay with a single neutralino (χ 0 ) (hereafter we are using χ 0 notation for the lightest neutralino) in the final state proceeds with the kinematics of a 3-body decay [8,9].
The aim of the present paper is to take a closer look at / R p 3-body top quark decay expanding on previous studies in the following way: • we treat top quark production and decay coherently (i.e. calculate diagrams with off-mass-shell top quark) and show the crucial role of this approach for the predictions of kinematical distributions and production rates; • we perform a simulation of the processes at detector level, thus obtaining realistic predictions for the reach at the LHC.
The outline of the paper is as follows: In Sect. 2, we evaluate production rates for the process pp → tχ 0 qℓ. We show that only by calculating together top quark production and decay do we obtain the correct cross section. We scan the µ − M 2 plane and present parton-level kinematical distributions. Sect. 3 gives details of the fast Monte-Carlo simulation, including the effect of initial and final state radiation, as well as hadronization effects, followed by the fast detector simulation. In Sect. 4, we describe the analysis procedure for extracting the signal from backgrounds and reconstructing the top quark and the slepton. In Sect. 5, we estimate the sensitivity of the LHC for observing of / R p top quark decays and we draw our conclusions in Sect. 6.
2. Top quark production and decay: / R p scenario The / R p superpotential of the MSSM can be written as [10,11,12] where L i (Q i ) and E i (U i , D i ) are the left-handed lepton (quark) doublet and right-handed lepton (quark) singlet chiral superfields; H 2 is the second Higgs doublet field; µ i are bilinear / R p couplings; i, j, k are generation indices. Terms with λ and λ ′ coefficients violate lepton number while the term with coefficient λ ′′ violates baryon number. Lepton-and baryon-number violating operators together would lead to fast proton decay. It has been shown [13,14,15] that there exist symmetries that allow the / R p for the subset of these operators consistent with the limits on proton decay. Therefore, here we assume hereafter that the baryon-number violating operator is vanishing. The alternative case, with non-vanishing baryon-number violating operator but no lepton-number violating operator, leads to hadronic top quark decay, which is very difficult to observe due to the huge QCD background.
The last bi-linear R-parity violating (BRPV) term in the superpotential (2) is responsible for spontaneous / R p violation. In general, it cannot be rotated away from the superpotential together with the SUSY soft breaking term by a suitable choice of the basis [16]. If one tried to do this, then / R p terms would be reintroduced via two trilinear terms given by LLĒ and LQD in equation (2). Since our specific study of / R p involves only the top quark decay, the LQD / R p operator (precisely, LQ 3D ) is given by the second term of (2), which also can effectively arise from BRPV term. It leads to the following Lagrangian in four-component Dirac notation: Since we study / R p in the third family, only λ ′ i3k couplings are relevant. They give rise to top quark decay into a single neutralino via the Feynman diagrams shown in Fig. 1. Three kinds of virtual fermions can be present in the diagrams for non-vanishing λ ′ i3k : a slepton, a squark of the first or second generation and a stop-quark. The decay width for this process of top-quark decay depends on: Figure 1. Tree-level diagrams for three-body top quark decay into neutralino (χ 0 ), lepton (l) and quark (q) via / R p operators.
• The magnitudes of the neutralino and chargino masses and couplings, which are functions of the MSSM parameters. Assuming gaugino-mass unification, the U(1) and SU(2) gaugino masses M 1 and M 2 are related by M 1 = 5 3 tan θ 2 W M 2 , in which case the gaugino and higgsino masses and couplings are determined by M 2 -SU(2) gaugino mass, µ -superpotential Higgs mass parameter and tan β.
• The masses of the intermediate sfermion -squarks and sleptons -which could be either lighter or heavier than the top-quark.
We assume here for simplicity the case where one sfermion, for example, a slepton, is lighter than any other intermediate sfermions, i.e. it gives the leading contribution to the / R p decay of the top quark. For our calculations we have used CompHEP v33.23 [17] together with a fully implemented model of / R p (Eq.2) interactions [18]. Contours of the partial width, Γ top , for top decay by the channel t →χ 0 ℓq in the (µ − M 2 ) plane are shown in Fig. 2. The partial width was calculated as in [9].    The decay width decreases as M 2 increases since the neutralino mass increases with this parameter. The cross section of the complete 2 → 4 process gg → tχ 0 ℓq describing tt production and / R p decay of one of top quarks can now be evaluated. The corresponding diagrams are shown in Fig. 3.  For the parton-level calculations, we used the CTEQ5L [19] parton density function with the top quark mass as the QCD scale. In order to avoid soft and collinear divergences when massless quarks are present in the final state, we applied a quark transverse momentum cut, p q T > 10 GeV. Diagrams (1-3) in Fig. 3 form a gauge-invariant subset which does not require the p q T cut. However, the total set of subprocesses leading to tχ 0 ℓq state consists of 8 Feynman diagrams which should be calculated together.
One can see that the cross section evaluated in approach (i) agrees within 30-50% with those of (ii) or (iii) when ml < m top . On the other hand, when ml > m top approach (i) underestimates the true cross section of approach (iii) by about an order of magnitude! Rates predicted by approach (ii) are about a factor of 2.5 smaller compared with those of approach (iii). To understand the origin of the difference between approaches (i) and (iii), we studied kinematical distributions. Fig. 5 shows theχ 0 ℓ (top) andχ 0 ℓq (bottom) invariant mass distributions for the complete calculation of (iii).
Even for a quite heavy slepton ( ml = 200 GeV ), the resonant peak from the slepton inχ 0 ℓ distribution is clearly seen. This means that the slepton forces the top m slep ,GeV  quark to be off-shell and becomes the resonance itself. The contribution from the onshell heavy slepton is significant. In approach ii.) theχ 0 ℓ distribution is similar, but the slepton resonance peak is slightly suppressed. The qχ 0 ℓ invariant mass distribution (bottom of Fig. 5) in the top quark decay is sensitive to the mass of the intermediate slepton. For a heavy slepton ml ≥ m top , the top quark resonance peak is strongly suppressed and a right shoulder appears in the ℓχ 0 q invariant mass spectrum. This happens because the heavy slepton "pushes" the top quark to be off-shell and becomes itself on-shell. In this case, the experimental reconstruction of the top quark mass is more difficult due to this shoulder. On the contrary, if the slepton mass is less than the top quark mass, two-body top quark decay takes place and one can observe a pronounced peak in the ℓχ 0 q invariant mass distribution.
We have explicitly checked that total cross sections for approaches (i), (ii) and (iii) agree fairly well (at about 20% level) after the application of a 20 GeV mass window cut on ℓχ 0 invariant mass to remove the contribution from the slepton. Another difference between the predictions of approaches (i) and (iii) must be pointed out. In Fig. 2, one can see that the / R p top decay width decreases with an increase of the M 2 parameter. Therefore, in approach (i), the cross section for the gg → tχ 0 ℓq process also decreases as M 2 increases. The situation is just the opposite in approach (iii), because the cross section of the true 2 → 3 process also depends on the slepton width. In Fig. 6, one can see that the cross section increases with M 2 due a decrease of the slepton width.
For the rest of the analysis, we use approach (iii) which gives the correct cross section and kinematical distributions.
One should also note that we treated neutralino as an on-shell particle. It decays through the intermediate sparticle, which could also, in principle, "push" a neutralino to be off-shell and invalidate the on-shell approach for the neutralino. However one should recall that neutralino width is at least several orders of magnitude smaller than the width of the intermediate scalar (∼ 10 −6 − 10 −8 GeV for λ ∼ 0.1 − 0.2 and mq ,l ∼ 100 − 200 GeV). ♯ This fact eliminates the probability for the intermediate sparticle to be on-shell for theχ 0 → ℓ + (l − * ) → dq chain. The asteriks here denotes an off-shell intermediate sparticle. We have checked this qualitative argument numerically and have calculated the width and mass distributions for the t → d(l + ) → ℓ + (χ 0 ) → ℓ + (l − * ) → dq process for true 1 → 5 top quark decay. We have chosen ml=150 GeV and have found that, indeed, the invariant mass distribution of the ldq system fromχ 0 → ℓ + (l − * ) → dq process, has a delta-function-like shape and the exact width for the 1 → 5 top quark decay can be accurately (within numerical errors of 1%) reproduced by product of the 1 → 3 top quark decay width and the neutralino branching ratio. This validates the treating of neutralino as on-shell particle and suffices dealing with 3-body top decay.
In the next section, we perform a fast Monte Carlo simulation of the gg → tχ 0 ℓq process in order to estimate a realistic experimental sensitivity to / R p top quark decay. ♯ In principle, the neutralino width could be comparable with the width of a slepton, when the χ 0 1 →tt 2-body decay channel becomes open if ml > m 0 χ > m t . But such case is not relevant to our study since in this scenario the RPV top-quark decay branching ratio will be several orders (∼ 3 − 4) of magnitude below the sensitivity of the LHC.

Signatures and details of simulation
We have used the CompHEP package to generate tt events with / R p decay of one of the top-quarks -t →χ 0 qℓ and SM decay of the other onet → W b. We have studied the cases of hadronic and leptonic decay modes of the W -boson from the top-quark undergoing the SM decay. In case of the leptonic decay of W , we studied W → µν decay channel in order to enhance the separation between the top / R p SUSY and SM decay chains.
In the present study we assume that only one λ ′ i3k parameter in Eq. (3) is nonvanishing. A value of 0.5 for λ ′ 131 was chosen for a reference. The following values of supersymmetric parameters were used: a gaugino mass M 2 = 120 GeV, a higgsino mass parameter µ = −300 GeV, tanβ = 10, and a slepton mass either ml = 150 GeV (ml < m top ) or 200 GeV (ml > m top ). Under these conditions, the total cross-sections obtained with CompHEP for the 2 → 4 signal process (see Fig. 3, p q T > 10 GeV) are 8 pb for a slepton mass ml = 150 GeV and 480 fb for ml = 200 GeV. This is to be compared with the total cross section of 833 pb [1] for the tt background.
With this set of parameters, the mass of the neutralino is m χ 0 = 58 GeV. If λ ′ i3k is non-zero only for i = k = 1, the neutralino will decay intoν eb d or ν e bd (BDN) (Fig. 7).
We also consider the possibility of stop-scharm mixing leading to neutralino decay into ℓ − cd or ℓ +c d (Fig. 8). It must be pointed out that such mixing, leading to flavor changing neutral currents (FCNC), is practically not constrained by experimental data [20,21]. We assume maximum stop-scharm mixing here, but the results can be easily rescaled for any arbitrary value of the mixing. If the stop-scharm mixing is significant, and if one of the stop quarks is lighter than other sfermions appearing in the Feynman diagrams, then theχ 0 →cdē(cde) (CDE) channel could be dominant. In this case, one would be able to obtain with much higher efficiency ( in comparison to BDN case ) a narrow peak for the reconstructed top quark mass.
An additional advantage of this decay mode is that the neutralino, by virtue of its Majorana nature, decays equally to positively and negatively charged leptons. This means that half of all events would contain two like-sign leptons. This clean signal signature allows the application of an effective cut to suppress possible backgrounds. The study of the / R p rare top decays at the LHC would also allow the direct measurement of, or the establishment of a limit on stop-scharm mixing. Below, we perform an analysis under both assumptions for neutralino decay: with and without stop-scharm mixing. PYTHIA 6.2 [22] was used to account for initial and final state radiation and to perform hadronization and decay of resonances. The Lund symmetric fragmentation function has been used for light flavors, but charm and heavier ones -according to the Peterson/SLAC function. The simulation of the signal and background was performed with ATLFAST [23] to take into account the experimental conditions prevailing at LHC for the ATLAS detector [24].
φ is the azimuthal angle. The hadronic energy resolution of the ATLAS detector is parametrized as 0.5/ E(GeV )⊕0.03 over this η region. Hadronic showers are regarded as jets if its deposited transverse energy E T is greater than 10 GeV within a cone of radius ∆R = 0.4. Electromagnetic calorimeters cells of dimensions ∆η × ∆φ = 0.025 × 0.025 within the same pseudorapidity range −2.5 < η < 2.5 are used to measure the lepton energy. The electromagnetic energy resolution is given by 0.1/ E(GeV )⊕0.007 over this η region. Electromagnetic showers are identified as electron candidates if their E T > 5 GeV within a cone of radius ∆R = 0.15. Default ATLFAST electron isolation criteria were applied: separation by ∆R > 0.4 from other clusters and E T < 10 GeV deposition in ∆R = 0.2 cone around the electron). Default selection criteria for muons ( P T > 6 GeV and |η| < 2.5 ) and isolation criteria, the same as for in the case of electron, were also applied. ATLFAST labels a jet as a b-jet if a b-quark is present in a cone ∆R = 0.2 around the reconstructed jet for jets with η < 2.5. Efficiencies for b-jet tagging have been parametrized by P T -dependent functions, with maximal saturated efficiency ǫ b = 0.7 at high P T . We have checked that for slepton mass within the range 100 − 1000 GeV and λ ′ > 0.005, the lifetime of the neutralino is shorter than the lifetime of a B-meson. Therefore displacements of the B-meson vertex due to the neutralino decay will not affect the b-tagging efficiency.
The analysis transverse momentum cuts used for electrons, muons and jets were 10 GeV, 10 GeV and 20 GeV, respectively.

Signal and background analysis forχ 0 → cde channel
In this section we study CDE neutralino decay channel:χ 0 → cde. First we analyze kinematical characteristics of jets for this channel. The partonic distributions of the transverse momentum and pseudorapidity of quarks and leptons for the process pp → tχ 0 qℓ(χ 0 → cde) are shown in Figs. 9, 10, 11 and 12. For completeness, we also show distributions for jets originating from W → jets decay from top-quark undergoing SM decay mode. The transverse momentum spectra of quarks in the process involving a light slepton (ml = 150 GeV) ( Fig. 9(left)) indicate that the highest P T jet in the event, with P T > 50 GeV is a b-jet from the top quark SM decay. Using b-jet tagging technique this jet can be effectively separated from the analysis. Among jets of P T < 50 GeV, a d-quark from the / R p top quark decay dominates, as well as in the very high P T region. For the case of a heavy slepton (ml = 200 GeV) , a d-quark from / R p decay tends to be with the highest P T in the P T > 150 GeV region and to be emitted in the forward direction (see Fig. 10(right)). The two jets with smallest P T in the events, originate from a neutralino decay.
The transverse momentum for a lepton from / R p top quark decay is the largest in the region P T > 50 GeV and P T > 75 GeV for the light and heavy slepton set of events, respectively (see Fig. 11). In terms of the pseudorapidity variable, leptons are mainly emitted in the central region (Fig. 12).  The effect of initial (ISR) and final state (FSR) QCD radiation approximately doubles the number of jets with P T > 10 GeV produced in the event. Fig. 13 shows the jet multiplicity distribution.
The only non-negligible background for the CDE channel is tW W (q) processes. This process would be a background for the case whereχ 0 → cde when both W 's decay leptonically and the W from the top quark decays hadronically. The Feynman diagrams for tW W q background are shown in Fig. 14. The total cross-section for this process, obtained from CompHEP is 1.1 pb.

Results forχ 0 → cde channel
The following cuts have been worked out for the top quark reconstruction: • At least 4 ( or 6 for t → bjj final state ) jets with P T > 20 GeV and one electron with P T > 10 GeV within |η| < 2.5 pseudorapidity.
• one jet tagged as a b-jet: required to get rid of a b-jet from a top quark which Figure 14. Tree-level diagrams for the tW W q process decayed in the framework of the SM.
• cut on invariant mass of (jjee), M(jjee) < 150 GeV (for the light slepton case) or < 200 GeV (for the heavy slepton case), to suppress the influence of the on-shell slepton on the top quark signal, especially effective in the ml < m top case.
For the mass reconstruction we combine two electrons with the three jets in the event. If the number of jets in the event was larger than three (but less than seven), the three jets with the smallest P T in the event were combined with both electrons.
The resulting mass distributions of the (jjjee) system are shown in Fig. 15 for the two different W decay modes studied and the light slepton case , ml = 150 GeV (left), and the heavy one, ml = 200 GeV (right), respectively. The data are presented for an integrated luminosity of 100 fb −1 (one year of running at high luminosity at LHC) for the light slepton case, and 300 fb −1 for the heavy slepton case. After the fiducial cuts given above, the tW W q background for the events withχ 0 → cde is appears to be very small and practically is not seen on the Fig. 15.
The events for the heavy slepton case show the shift of the mass value of the top quark signature because of a heavy on-shell slepton mass dominance and big combinatorial jet pairs background.
Based on the kinematical distributions shown above, we define procedures to select and reconstruct the neutralino and the slepton in the events of interest.
For the case of a light slepton, in order to reconstruct the neutralino (Fig. 16, left), we combine the electron with smallest P T with the two jets with smallest P T . The figure shows the invariant mass distribution for an integrated luminosity of 100f b −1 , with the contributions from events where W → µν and where W → jets explicitly indicated.
For the heavy slepton case (Fig. 16, right) we use the same procedure, but due to a lower production cross-section, we present the mass reconstruction for an integrated luminosity of 300f b −1 .
For the reconstruction of the slepton, we combine both electrons in the event with the same two soft jets (Fig. 17). Light slepton case presented in Fig. 17 (left). For the heavy slepton case (Fig. 17, right) we use the same procedure, but again due to a lower production cross-section, we present the mass reconstruction of sleptons for an integrated luminosity of 300f b −1 .

Results forχ 0 → bdν channel
In the case whereχ 0 → bdν, we considered only the scenario where W decays into jets, since the decay mode W → νℓ leads to two neutrinos in the final state, making the event reconstruction difficult. Fig. 18 shows the partonic distributions of the transverse momentum of quarks for events where the neutralino decaysχ 0 → bdν(right). Thus, we are led to event topologies with 6 quarks, one electron and a neutrino at the parton level. Although the large combinatorial background in jet pair selection makes it difficult to reconstruct the signal for the event under study, one can observe certain correlations in these distributions. For example, the two softest light jets are originating from a neutralino.
The natural background for the case whereχ 0 → bdν is tt and, possibly, ttbb production. These backgrounds have the topology of the signal when one W -boson decays into jets and the other W decays leptonically to eν.
We applied the following selection cuts for reconstructing events where one top quark decays via the / R p SUSY mechanism, and its decay product, a neutralino, decays to bdν, while the other top quark in the event, decays in the SM to a b quark and two jets.
• at least two jets tagged as b-jets with P T > 20 GeV: one for the top quark with the SM decay and another from the decay of the neutralino.
• No two-jet combination should have the invariant mass of a W , in a window ±20 GeV.
• cut on the mass of the system (ebν) < 140 GeV (see Fig.19), to suppress the tt background, since no such decays of the top quark should occur in the / R p top decay scenario.
• cut on the transverse mass of (jjeν): M(jje E T ) < 150 GeV (for the light slepton case ) to suppress the influence of the on-shell slepton on the top quark signal, especially effective in the ml < m top case.
The mass reconstruction was performed for one electron, E T and three jets in the event. When the number of jets in the event was larger than three (but less than seven), the three jets with the smallest P T in the event were taken into the reconstruction system.
The resulting mass distributions are shown for the (jjjeν) system in Fig. 20(left) forχ 0 → bdν decay channel and the light slepton case(ml = 150 GeV). The data are presented for an integrated luminosity of 100 fb −1 . The distributions for signal and background are shown with separate contributions from tt and ttbb events. The generation of the ttbb background has been performed with CompHEP and the crosssection obtained was 5.44 pb. As one can see below, this background brings contribution of about 2% to the total background for all signal signatures considered.
For the heavy slepton case (ml = 200 GeV) we present our results in Fig. 20(right)for the signal events only for an integrated luminosity of 300f b −1 . Bearing in mind the large tt background forχ 0 → bdν, it is clear that no signal can be extracted for the BDN channel and the heavy slepton case. We do not show for this case the distributions for backgrounds due to their overwhelming dominance.  For these events to reconstruct the neutralino, we combine the E T with the two jets with smallest P T , and for the slepton, we combine the same two jets with the softest electron and the E T . The shift from nominal simulated values for the neutralino ( 60 GeV ) and the slepton ( 150 GeV ) is due to the difficulties to calculate the energy of neutrino. The relative strengths of signal (χ 0 → bdν) and the tt background are compared in Figs. 20(left) and 21.
For the heavy slepton case we use the same procedure, but due to a lower production cross-section the signal cannot be seen due to the tt background dominance.
It is worth to mention that the accuracy of the tt background measurement for the BDN decay channel would be very important. An error of 1% on the top quark mass measurements corresponds to an error of 5% on the total ttbar cross-section, or vice versa. Systematic uncertainties of the measurements of the top quark mass are dominated by the jet energy scale and FSR effects. Assuming a 1% scale uncertainty, which is feasible in ATLAS, and varying the jet cone size, should reduce the total systematic uncertainties [?]. The precision of the measurements of the total tt crosssection is expected also to be dominated by the knowledge of the absolute scale of the luminosity. In any case, the significant amount of data will be required before the tt background contribution can be estimated accurately.

LHC reach
Our final results are presented in Tables 1, 2 and 3 and Fig. 22.
Tables 1 and 2 present signal and background cut efficiencies (ǫ CDE and ǫ BDN ) ) for the channelsχ 0 → cde andχ 0 → bdν channels, respectively, for the light slepton case.  Table 3 gives the number of expected events, calculated for an integrated luminosity of L = 100f b −1 , for the channels CDE and BDN and for the light slepton mass ml = 150 GeV. For the heavy slepton case, i.e. ml = 200 GeV we only present in parentheses the numbers only for the CDE case, since the BDN case is hopeless in view of the dominant tt background.
As can be seen from this table, the CDE signature has negligible background for both hadronic and leptonic W decay channels. The BDN channel, on the contrary, has much larger background coming from SM tt events. Nevertheless, the tt is effectively suppressed by the fiducial cuts, and the S/ √ B ∼ 50 for the case of a light slepton.  Table 3. Number of expected signal events for CDE(χ 0 → cde) and BDN (χ 0 → bdν channels for an integrated luminosity of L = 100f b −1 . Background(BG) presented are: tW W q events forχ 0 → cde case and tt +ttbb production forχ 0 → bdν sample of signal events. Heavy slepton case for the CDE channel is given in parenthesis.  The sensitivity of the LHC to λ ′ mainly depends on the slepton mass, µ, M 2 and tan β which define the top / R p decay branching ratio. For our particular choice of these parameters, we estimate the potential of the LHC to measure λ ′ coupling by studying the significance S/ √ B versus λ ′ for both cases of neutralino decay presented in Fig. 22. fraction BF t / R p of the R-parity violating top quark decay in the range of ≃ 10 −6 − 10 −7 for the CDE channel and ≃ 10 −3 for the BDN channel. We have shown that the CDE channel is not only very sensitive to the λ ′ coupling, but will also allow the measurement (or the setting of a limit ) on thec −t mixing which is practically unconstrained, at present. The BDN channel can provide an independent limit on the λ ′ coupling, irrespective of the squark-mixing parameter.