Lepton flavour violating top decays at the LHC.

We consider lepton-flavour violating decays of the top quark, mediated by 4-fermion operators. We compile constraints on a complete set of SU(3) [Formula: see text] U(1)-invariant operators, arising from their loop contributions to rare decays and from HERA's single-top search. The bounds on e-[Formula: see text] flavour change are more restrictive than on [Formula: see text]-[Formula: see text]; nonetheless the top could decay to a jet [Formula: see text] with a branching ratio of order [Formula: see text]. We estimate that the currently available LHC data (20 fb[Formula: see text] at 8 TeV) could be sensitive to [Formula: see text]+ jet) [Formula: see text], and we extrapolate that 100 fb[Formula: see text] at 13 TeV could reach a sensitivity of [Formula: see text].

Introduction

Lepton Flavour Violation (LFV) [1-3], meaning local interactions that change the flavour of charged leptons, should occur because neutrinos have mass and mix. This motivates sensitive searches for processes such as [4] and [5, 6]. However, the mechanism responsible for neutrino masses is unknown, so it is interesting to parametrise LFV with contact interactions, and to look for it everywhere. In this context, the LHC could have the best sensitivity to LFV processes involving a heavy leg, such as the Z [7-31], the Higgs [31-62], or a top [63, 64]. In this paper, we study the LFV top decays , where .

We suppose that these decays are mediated by a 4-fermion interaction, and outline in Sect. 2 the current bounds on LFV branching ratios of the top. The bounds arise from rare decays and HERA’s single-top search, and they are discussed in more detail in the appendices. We find that, while these bounds place strong constraints on some specific Lorentz structures for the 4-fermion interactions, they still allow for decays with rates within the LHC reach. In Sect. 3, we estimate the LHC sensitivity to , with 20 fb of LHC data at 8 TeV. This estimate relies on simulations of the background and signal and is inspired by the CMS search for [65]. The extrapolation to higher energies and luminosities is discussed in Sect. 4.

Quark-flavour-changing top decays, such as and , have been studied in the context of explicit models [62, 66–79] or described by contact interaction parametrisations [80-87], and they have been searched for at the LHC [65, 88–90]. Quark-flavour-changing (but lepton-flavour-conserving) three-body decays of the top, , where f is a lepton or quark, have also been calculated in explicit models [91-94]. Top interactions that change quark and lepton flavour, and, in addition, baryon and lepton number, have been explored in [95, 96] and searched for by CMS [97]. In models with weak-scale neutrinos N [98], there can be lepton number- and flavour-changing W decays: , which could appear in the final state of top decays. In the presence of this decay, production could give a final state with 3 leptons, missing energy and jets, as in the decay we study (see Fig. 2). However, a different combination of leptons and jets should reconstruct to the top mass. Finally, Fernandez et al. [63] studied almost the same process as us, , but mediated by a (pseudo)-scalar boson. They obtained separately the low-energy bounds on the quark- and lepton-flavour-changing couplings of their boson, and they show that LFV top branching ratios can be if the boson mass is . Heng et al. [64] calculated LFV top decay rates in R-parity non-conserving supersymmetry, finding rates comparable to our leptoquark estimates.

Fig. 2

Feynman diagram for the considered signal where or (the conjugate diagram is also considered)

Current bounds

We are interested in the decays of a top (or anti-top) to a jet and a pair of oppositely charged leptons of different flavour. In this work, we focus on the processes , where , because the e and are easy to identify at the LHC, and flavour violation is the most strictly constrained at low energy. We leave the decays to and for a later analysis.

We suppose that these decays are mediated by 4-fermion contact interactions. A complete list of the invariant operators that we study is given in Appendix A. We do not impose SU(2) on our operators, because the scale we will probe is not far from the electroweak scale. We refer to these LFV operators as “top operators”. Here, as an example, consider the exchange of a heavy SU(2) singlet leptoquark with couplings and , which (after Fierz rearrangement) generates the dimension-six contact interactionAlternatively, we could define the operator coefficient as , in which case because (we take  GeV). We will quote low-energy bounds on such interactions as limits on the dimensionless s. In the case of our leptoquark example, to satisfy current bounds on second generation leptoquarks from the LHC [99-101], and thus, for , one expects .

Notice that and are mediated by different operators. Most of the bounds we quote will apply to , and we will study the LHC sensitivity assuming equal rates for and .

Decay of the top

In the Standard Model, the top decays almost always to , at a tree-level rate given byIn the presence of the operator of Eq. (1), the three-body decay rate isso the branching ratio, allowing for all the operators listed in Appendix A, and neglecting fermion masses other than the top (to remove interferences), isHere , and we approximated . This is small (), due to the three-body phase space. For the leptoquark example discussed above, for .

The phase space distribution of the and q depends on the Lorentz and spinor structure of the contact interaction and could affect the efficiency of experimental searches for this decay. The squared matrix elements for the individual contact interactions have the form , where and is the invariant mass-squared of a pair of final state fermions a and b. Our study will not take this into account, since we found, in some explicit examples, only a small relative effect on the selection efficiency (of the order of 5 %).

Bounds from flavour physics and HERA

Low-energy constraints on 4-fermion operators involving 2 leptons and 2 quarks have been estimated and compiled for many operators taken one at a time [102-104], and carefully studied for selected flavour combinations (see e.g. [105], or global fits to operators [106-109]). However, even in the more recent compilations [103, 104], bounds on LFV operators involving a single top are not quoted. In Appendices B and C, we estimate bounds on such operators from their possible contributions, inside a loop, to rare , B and K decays. In Appendix D, we estimate bounds from single-top searches at HERA. Here, we summarise the resulting bounds, and we list in Tables 1 and 2 the best limits on the coefficients of the various operators. We will find that only the coefficients of some operators are stringently constrained, while others could mediate LFV top decays within the sensitivity of the LHC.

Table 1

Constraints on the dimensionless coefficient of the 4-fermion operator (see the operator list in Appendix A), where XY are given in the top row, and generation indices ijqt are given in the first column. The bounds are on the first line of each box, their origin on the second. They can arise from the HERA single-top search, or from the loop contribution to the operator involving lighter fermions whose coefficient is given in parentheses below the bound (see Appendix C.1 for current experimental bounds on the lighter-fermion operator coefficients). The bounds are discussed in Appendix D.4. We expect that , so in boldface are the bounds that impose an upper limit smaller than 1

ijqt	LL	RL	LR	RR
eμut	0.0037	0.0037	0.33	0.22
	(ϵLLeμds)	(ϵLLeμds)	(HERA)	(HERA)
eμct	0.015	0.015	1	1
	(ϵLLeμds)	(ϵLLeμds)	(ϵLLeμds)	(ϵLLeμds)
eτut	1.2	1.2	∼1.3	∼0.85
	(ϵLLeτdb)	(ϵLLeτdb)	(HERA)	(HERA)
eτct	1	1	60	60
	(ϵLLeτsb)	(ϵLLeτsb)	(ϵLLeτsb)	(ϵLLeτsb)
μτut	0.8	0.8	-	-
	(ϵLLμτdb)	(ϵLLμτdb)
μτct	1.5	1.5	100	100
	(ϵLLμτsb)	(ϵLLμτsb)	(ϵLLμτsb)	(ϵLLμτsb)

Table 2

Constraints on the dimensionless coefficient , of the scalar and tensor 4-fermion interactions. See Appendix A for operator definitions corresponding to the subscript of . The generation indices ijqt are given in the first column. Beneath each bound is given its origin in parentheses; are the limits of Table 7, and are from Table 8. See the caption of Table 1 for additional details

ijqt	ϵ_S-P,R	ϵ_S+P,R	ϵ_T,R	ϵ_S-P,L	ϵ_S+P,L	ϵ_T,L
eμut	O(10^-2)	O(10^-2)	O(10^-2)	0.66	0.03
	(μ→eγ)	(μ→eγ)	(μ→eγ)	HERA	(ϵCCeνub)
eμct	O(10^-3)	O(10^-3)	O(10^-3)		22
	(μ→eγ)	(μ→eγ)	(μ→eγ)		(ϵCCeνcs)
eτut	23	23			0.03
	(ϵS±P,Xeτdb)	(ϵS±P,Xeτdb)			(ϵCCeνub)
eτct	100	100			22
	(ϵS±P,Xeτdb)	(ϵS±P,Xeτdb)			(ϵCCeνcs)
μτut	21	21			0.03
	(ϵS±P,Xμτdb)	(ϵS±P,Xμτdb)			(ϵCCμνub)
μτct	100	100			100
	(ϵS±P,Xμτdb)	(ϵS±P,Xμτdb)			(ϵCCμνcs)

The current upper limit [4] severely restricts flavour change. For our top operators to contribute, the quark lines must be closed, which requires at least two loops and a CKM factor, see the second diagram of Fig. 5. Nonetheless, in the case of scalar or tensor operators involving this diagram can overcontribute to by several orders of magnitude, because the lepton chirality flip is provided by the operator (rather than ), so the diagram is enhanced by a factor . We make order-of-magnitude estimates in Appendix B, and we quote the resulting bounds in Table 2.

Fig. 5

Left Example three-loop diagram by which a the neutral current vector operator of Eq. (24) could induce . “x” is a mass insertion, the grey blob is the operator, and the photon could be attached to any quark line. On the right is an example two-loop diagram by which a tensor/scalar operator could induce without GIM suppression and with enhancement

Table 7

Constraints on , for the index combination given in the first column, where the s are coefficients of the operators , in a basis containing also tensor operators. The second column is the constraint, which arises from the observable given in column 3. The experimental value used is the last column. These bounds are also valid under lepton and/or quark index permutation

ijαβ	Constraint on ϵ^ijαβ	Observable	Experimental value
μeds	9.0×10^-9	BR(KL0¯→μ¯e)	<4.7×10^-12
eμbd	8.1×10^-6	BR(B^0→e¯μ)	<9.2×10^-8
eμbs	2.9×10^-5	BR(Bs0→e¯μ)	<1.1×10^-6
eτds	2.9×10^-4	BR(τ→KS0e)	<2.6×10^-8
eτdb	5.6×10^-4	BR(B^0¯→e¯τ)	<2.8×10^-5
eτsb
μτbd	5.0×10^-4	BR(B^0→μ¯τ)	<2.2×10^-5
μτds	2.6×10^-4	BR(τ→KS0e)	<2.3×10^-8
μτsb

Table 8

Constraints from “charged-current” processes on operators. This bound applies to , in a basis using tensor operators. The first column is the index combination , the second is the constraints, which arise from the observable given in column 3. The experimental value used is the last column. is any flavour of neutrino

(ν¯_ie_j)(d¯_βu_q)	Constraint on ϵ^ijβq	Observable	Experimental value
ν_iedu	1.6×10^-5	R_π	(1.230±0.004)×10^-4
ν_iedc	1.4×10^-3	Γ(D^+→e¯ν_i)	<8.8×10^-6
ν_iesu	1.5×10^-5	BR(K^+→e¯ν_i)	(1.55±0.07)×10^-5
ν_iesc	3.9×10^-3	BR(Ds+→e¯ν_i)	<8.3×10^-5
ν_iebu	7.8×10^-5	BR(B^+→e¯ν)	<9.8×10^-7
ν_iebc
ν_iμdu	3.2×10^-3	R_π	(1.230±0.004)×10^-4
ν_iμdc	3.7×10^-3	BR(D^+→μ¯ν)	(3.82±0.33)×10^-4
ν_iμsu	3.0×10^-3	R_K	(2.44±0.11)×10^-5
ν_iμsc	1.5×10^-2	BR(Ds+→μ¯ν)	5.56×10^-3
ν_iμbu	7.7×10^-5	BR(B^+→μ¯ν)	<1.0×10^-6
ν_iμbc
ν_iτdu	8.0×10^-2	BR(τ→π^+ν)	(1.083±0.006)×10^-1
ν_iτdc	5.2×10^-2	BR(D^+→τ¯ν)	<1.2×10^-3
ν_iτsu	2.6×10^-2	BR(τ→K^+ν)	(7.0±0.1)×10^-3
ν_iτsc	4.9×10^-2	BR(Ds+→τ¯ν)	5.54×10^-2
ν_iτbu	7.2×10^-4	BR(B^+→τ¯ν_τ)	(1.1±0.3)×10^-4
ν_iτbc

Exchanging a W between the t and q quark legs of the top operator will generate an operator with down-type external quark legs, see the left diagram of Fig. 1. The coefficient of this light quark operator will be suppressed by a loop, CKM factors, and various masses. Numerical values for these suppression factors are given in Table 9 of the appendix; however, their approximate magnitude is simple to estimate. If the top is singlet (), then the loop is finite; in the case of interactions, this is because mass insertions are required on both internal quark lines to flip chirality. In the case of scalar operators, one internal quark mass for chirality flip is still required; then terms linear in the loop momentum vanish, so the diagram is also proportional to an external quark mass. For scalar operators involving (which require an insertion to connect the W to the q line), the best limit can arise from exchanging a W between the t and a charged lepton leg, which generates a charged-current operator as represented in the second diagram of Fig. 1. In the appendix are also given current bounds on the coefficients of the various light quark operators that the top operators can induce. Comparing these bounds to the induced coefficients, gives the limits of Tables 1 and 2 that are labelled with ()s.

Fig. 1

Diagrams for generating an LFV operator with light external quark legs, by dressing a top operator with a W loop. To reduce index confusion, down-type quarks have Greek indices

Table 9

The last two columns give the numerical value of the coefficient given in the second column, generated by loop containing the top LFV operator given in the first column, of coefficient . The top LFV operator involves the top and the quark ; the two choices of q identify the last two columns. The operators also induce FCNC operators (involving 2 down-type quarks), but the coefficients are not listed because they are suppressed by two light quark masses

Top op.	Down coeff.	q=u	q=c
	ϵXLijdb	8.0×10^-8	7.7×10^-6
OijqtXR	ϵXLijsb	1.8×10^-8	3.4×10^-5
	ϵXLijds	3.2×10^-9	3.1×10^-7
	ϵXLijdb	2.0×10^-3	4.6×10^-4
OijqtXL	ϵXLijsb	4.6×10^-4	2.0×10^-3
	ϵXLijds	8.2×10^-5	1.9×10^-5
	ϵS±P,Rijdb	2.4×10^-5	5.3×10^-6
OijqtS±P,R	ϵS±P,Rijsb	5.3×10^-6	2.4×10^-5
	ϵS±P,Rijds	4.1×10^-9	1.8×10^-8
	ϵCCijqb	2.5×10^-3	2.5×10^-3
OijqtS+P,L	ϵCCijqs	1.0×10^-4	1.0×10^-4
	ϵCCijqd	2.0×10^-5	2.0×10^-5

HERA collided protons with positrons (or electrons) at a centre-of-mass energy of 319 GeV, and searched for single tops in the final state. The H1 collaboration had a few events with energetic isolated leptons and missing energy, consistent with followed by leptonic decay of the top [110, 111]. However, this signal was not confirmed by the ZEUS experiment [112], and neither collaboration had a signal consistent with hadronic top decays. Both collaborations set bounds on ; we follow H1, since they had some events and a weaker bound:Contact interactions of the form and could, respectively, mediate and . As discussed in Appendix D, the limit of Eq. (5) translates to for the various operators, as given in Tables 1 and 2.

It can be seen from Tables 1 and 2, that rare decays give very weak bounds on some contact interactions of the form and . Such interactions might have contributed a signal at HERA via leptonic decays, so we make some approximate estimates in Appendix D.4, and we include the bounds in the tables with a .

Implications

The current bounds on LFV branching ratios of the top can be obtained from Tables 1 and 2, and from and Eq. (4). In these tables, the bound on appears on the first row of each box, where the flavour indices ijqt are given in the left column, and the operator label XYZ is given in the first row (see Appendix A for the operator definitions). In parentheses below the bound is a clue to where it comes from: HERA means the single-top searches at HERA that are discussed in Appendix D, and the ()s mean the bound comes from dressing the top operator with a W loop. For instance, the bound 0.0037 in the second row and third column of Table 1 arises by exchanging a W between the t and u legs of the top operator, which gives the operator . This would mediate the unobserved decay , so its coefficient is bounded above, as indicated in Table 6. (The bounds on lighter-quark operators relevant to constraining top operators are given in Tables 6, 7 and 8, and Table 9 gives the loop suppression factors with which the top operators generate the lighter-quark operators.) Translated back to the top operator, the upper limit on gives the quoted limit on the top-operator coefficient.

Table 6

Constraints on the dimensionless coefficient of 4-fermion interactions . can be or . The generation indices are given in the first column, and the best bound in column 3. It arises from the observable of column 4, and the experimental value we used is given in column 5. In column 2 is given the linear combination of s to which the bound applies. All bounds apply under permutation of the lepton and/or quark indices

ijαβ		Constraint on ϵ^ijαβ	Observable	Experimental value
eμds	(ϵ_LL-ϵ_LR),(ϵ_RR-ϵ_RL)	3.0×10^-7	BR(KL0→e¯μ)	<4.7×10^-12
eμdb	(ϵ_LL-ϵ_LR),(ϵ_RR-ϵ_RL)	3.0×10^-4	BR(B^0→e¯μ)	<2.8×10^-9
	ϵ_LL+ϵ_LR,ϵ_RR+ϵ_RL	1.3×10^-4	BR(B^+→π^+e¯μ)BR(B^0→π^-e¯ν)	<1.3×10^-3
eμsb	ϵ_LL+ϵ_LR,ϵ_RR+ϵ_RL	1.0×10^-4	BR(B^+→K^+e¯μ)BR(B^+→D^0e¯ν_e)	<9.1×10^-82.2×10^-2
eτds	(ϵ_LL-ϵ_LR),(ϵ_RR-ϵ_RL)	4.1×10^-4	BR(τ→eK)BR(τ→ν¯K)	<2.6×10^-87.0×10^-3
eτdb	(ϵ_LL-ϵ_LR),(ϵ_RR-ϵ_RL)	2.1×10^-3	BR(B^0→e¯τ)	<2.8×10^-5
eτsb	ϵ_LL+ϵ_LR,ϵ_RR+ϵ_RL	2.0×10^-3	BR(B^+→K^+τ¯e)BR(B^+→D^0τ¯ν)	<3.0×10^-57.7×10^-3
μτds	(ϵ_LL-ϵ_LR),(ϵ_RR-ϵ_RL)	4.3×10^-4	BR(τ→μK)BR(τ→ν¯K)	<2.3×10^-87.0×10^-3
μτdb	(ϵ_LL-ϵ_LR),(ϵ_RR-ϵ_RL)	1.6×10^-3	BR(B^0→μ¯τ)	<2.2×10^-5
μτsb	ϵ_LL+ϵ_LR,ϵ_RR+ϵ_RL	3.1×10^-3	BR(B^+→K^+τ¯μ)BR(B^+→D^0τ¯ν)	<4.8×10^-57.7×10^-3

In this paper, we are interested in top decays to , the bounds on which are given in the second and third rows of the tables. For many1 of the operators involving the doublet component of the top (; recall that the last index in the operator label is the top chirality), the rare decay bounds are restrictive, implying that these operators could only induce . Scalar and tensor operators involving e, and would overcontribute to . However, there remain operators which are weakly or not constrained, allowing for a branching ratio . It is therefore interesting to explore the sensitivity of the LHC to decays.

Finally, it is interesting to consider how large the coefficient of the top operators can be. Some of the upper bounds quoted in Tables 1 and 2 are 1, and should not be interpreted as relevant constraints.2 Indeed, the width of the top is given by D0 [113] as GeV (the theoretical decay rate to bW is 1.3 GeV), which constrains . Furthermore, phenomenological prejudice and the leptoquark example of Eq. (1), suggest that , because the three-body decay should be mediated by sufficiently heavy ( particles, with sufficiently small couplings to have not yet been detected. We therefore quote in boldface the “relevant” bounds that impose .

at the 8 TeV LHC

In this section, we estimate the sensitivity of current LHC data to the LFV top decays , where . We consider strong production of a pair, because this is the most abundant source of tops at the LHC, followed by the leptonic decay on one top, and the LFV decay of the other. This is illustrated in Fig. 2 and gives a final state containing 3 isolated muons or electrons,3 which has small Standard Model backgrounds.

Simulation setup

This study is performed for proton–proton collisions at the LHC, with a centre-of-mass energy of 8 TeV and an integrated luminosity of 20 , corresponding to the LHC Run1. The details of the signal and background generation are given in Sect. 3.2. The detector simulation is carried out by Delphes [114] using a CMS setup parametrisation.

Delphes uses a particle-flow-like reconstruction. The relative isolation of leptons is calculated from the total of the particles inside a cone of around the lepton direction ( for electrons and 0.4 for muons), divided by the of the lepton. Jets are clustered using the fastjet package [115] with the Anti-kt [116] algorithm with distance parameter . The b-tagging performances are tuned on the typical efficiency and fake rate obtained in CMS.

For this study, no additional interactions in the same or neighbouring bunch crossing (pileup) are simulated.

Signal and SM backgrounds generation

The signal is generated with PYTHIA 8.205 [117] using tune 4C. Top quarks are pair produced, then one top is forced to decay to charm, , and , with equal probability between and . The decay products are distributed according to the available phase space. 100k events have been generated both for LFV top and anti-top decays.

The backgrounds for this search, listed in Table 3, are processes that can give rise to 3 isolated leptons and at least 2 jets in the final state. Most of them are related to the production of real isolated leptons, e.g. from a top pair or vector bosons in the final state. In the table, are also shown the details as regards the number of generated events and production cross section for 8 and 13 TeV proton–proton collisions. The number of generated events refers to the generation at 8 TeV. The cross section is calculated with the Top++2.0 program to next-to-next-to-leading order in perturbative QCD, including soft-gluon resummation to next-to-next-to-leading-log order (see [118] and references therein), and assuming a top-quark mass of  GeV. When an explicit calculation was not available, the cross sections have been calculated with the MCFM package [119], version 7.0. The kinematic cuts used for the calculation are also shown in the table.

Table 3

Number of events generated, and cross sections at NLO (except for jets), for each background category. Here

Process	Events	σ [pb] (8 TeV)	σ [pb] (13 TeV)	Source
tt¯ (2l2ν2b)	12M	26.19	86.26	Top++2.0 (NNLO) [118]
WW+jets (2l2ν, m_ll>10GeV/c^2)	1M	5.84	11.57	MCFM [120, 121]
ZZ+jets (2l2q, m_ll>10GeV/c^2)	2.5M	2.71	5.35	MCFM [120, 121]
ZZ+jets (2l2ν, m_ll>10GeV/c^2)	1M	0.774	1.53	MCFM [120, 121]
ZZ+jets (4l, m_ll>10GeV/c^2)	2.5M	0.390	0.738	MCFM [120, 121]
WZ+jets (2l2q, m_ll>10GeV/c^2)	1M	2.37	4.60	MCFM [120, 121]
WZ+jets (3lν, m_ll>10GeV/c^2)	1M	1.15	2.23	MCFM [120, 121]
tt¯W+jets	1M	0.212	0.612	MCFM [120, 121]
tt¯Z+jets	1M	0.192	0.798	aMC@NLO [122]
tbZ+jets	2M	0.014	0.047	aMC@NLO [122]

The leading order (LO) matrix element generator, MADGRAPH 5 [123], with CTEQ6 parton distribution functions, is used to generate top pair production, and associated production of a top pair and a vector boson (ttW, ttZ). MADGRAPH, interfaced with tauola for decays, is used to generate vector–vector production (WW, WZ and ZZ) and the contribution of weak processes giving rise to final states with one top quark, one b quark and a Z boson (decaying to leptons). For the vector–vector production, we only consider final states with at least 2 real charged leptons. This means that for the WW system, the considered final states are 2 charged leptons and 2 neutrinos; for WZ, they are 3 charged leptons and one neutrino or 2 charged leptons and 2 quarks; and for ZZ, they are 2 charged leptons and 2 neutrinos, 2 charged leptons and 2 quarks, or 4 charged leptons. In all cases, MADGRAPH accounts for the presence of up to 2 additional jets at matrix-element level, and the hadronisation is carried out by PYTHIA 8.205. The details of the SM background simulation and cross sections are shown in Table 3.

Event selection

The signal for this search is production, followed by the lepton-flavour violating decay of one top (which will be denoted as LFV top in the following), and the leptonic decay of the other (standard top, in the following). The number of expected signal events is given bywhere , the integrated luminosity, the selection efficiency on the signal, and pb (see [118] and references therein).

The considered signature is 3 isolated leptons (with one pair of opposite sign and opposite flavour from the LFV decay), 2 jets (one of which is a b-jet), and missing transverse energy. For the event selection, we consider only muons of  GeV and , electrons of  GeV and , and jets of  GeV and . These criteria are comparable to those used in real analyses by the CMS or ATLAS collaborations. A muon is considered isolated if its relative isolation value is less that 0.12, and an electron is considered isolated if its relative isolation value is less that 0.1. We select events containing:The efficiency of the final selection on signal events iswhere the uncertainty is statistical only. The signal efficiency is calculated on events where one top decays through , and the other one decays to a b quark and a W, which subsequently decays to a charged lepton (e, or ) and a neutrino, and is defined as the fraction of such events passing the selection criteria.

exactly 3 isolated charged leptons (electrons or muons), 2 of which must be of opposite sign and opposite flavour.

Events are requested to contain at least 2 jets, and

exactly one b-tagged jet, and

the missing transverse energy has to be higher than 20 GeV.

In order to exclude events where 2 of the isolated leptons come from a real Z boson, we reject events containing any pair of opposite sign isolated muons or electrons with invariant mass between 78 and 102 GeV/c. This cut is particularly helpful in rejecting background arising from associated production with a Z.

The charged lepton that does not belong to the pair of opposite sign and opposite flavour leptons is assigned to the standard top in the event, and assumed to come from the W decay (bachelor lepton). Following a common procedure in reconstruction of semi-leptonic events, the x and y components of the missing transverse energy are taken as a measurement of the neutrino and , and the longitudinal component of the neutrino momentum is calculated imposing the requirement that the invariant mass of the system composed of the bachelor lepton and the neutrino must equal the mass of the W boson. The bachelor lepton and the neutrino 4-momenta are then combined with that of the b-tagged jet, to build a candidate standard top. When more choices of the bachelor lepton are possible (there can be up to two possible pairs of opposite sign opposite flavour charged leptons in one event), all are considered and the one giving the best standard top mass is chosen. We reject events in which the invariant mass of the standard top candidate is more than 45 GeV away from the nominal top mass. After the choice of the bachelor lepton, there is only one possible pair of opposite sign and opposite flavour leptons in each event. This is combined with all good (non b-tagged) jets present in the event to build a list of candidates for the LFV top. Events are required to have at least one combination giving a LFV top mass within 25 GeV of the nominal value.

The number of expected events, for the signal and for each background category, on 20 fb of proton–proton data at 8 TeV is shown in Table 4, for different subsequent selection requirements.

Table 4

Number of expected events for a luminosity of 20 fb, at various steps of the selection, for the signal process normalised to a branching ratio , and the various backgrounds considered in this study normalised to their NLO cross sections. All uncertainties are statistical only. The considered backgrounds are the same as in Table 3, grouped in wider categories. In particular, the numbers in the “no selection” column are relative only to the final states detailed in Table 3. The steps in the selection are as follows; step 1: 3 leptons with 2 opposite sign opposite flavour, step 2: at least 2 jets, step 3: exactly one b-tag, step 4: missing greater than 20 GeV, step 5: Z boson veto, step 6: invariant masses cuts (see Sect. 3.3 and Fig. 3). Uncertainties are statistical only

Process	No selection	Step 1	Step 2	Step 3	Step 4	Step 5	Step 6
Signal	202.57	32.98±0.17	22.66±0.14	9.12±0.09	8.20±0.09	7.50±0.09	3.75±0.06
tt¯	542806	14.78±0.81	10.51±0.69	4.36±0.44	4.36±0.44	3.55±0.40	0.63±0.17
WW+jets	116760	0.93±0.33	0.35±0.20	<0.35	<0.35	<0.35	<0.35
ZZ+jets	72900	353.74±0.95	82.50±0.47	3.74±0.10	1.60±0.07	0.25±0.03	0.03±0.01
WZ+jets	63360	852.21±4.04	182.96±1.90	8.70±0.42	7.62±0.39	0.74±0.12	0.04±0.03
tt¯W	4240	9.36±0.24	7.67±0.22	3.59±0.15	3.45±0.14	3.10±0.14	0.27±0.04
tt¯Z	3840	17.25±0.33	16.44±0.32	7.72±0.22	7.16±0.21	1.85±0.11	0.22±0.04
tbZ	282	5.75±0.03	3.59±0.02	1.51±0.01	1.37±0.01	0.13±0.01	0.01±0.01

Fig. 3

Invariant mass of the LFV top candidates (left) and standard top candidate (right) in events passing all the selection, apart from the cut on the masses themselves. The different background contributions are shown in filled histograms and stacked, normalised to the number of events expected in 20 fb. For comparison, the distribution for signal events is also shown as a dashed line, normalised to the number of events expected in 20 fb, for an example signal branching ratio , equal to the expected limit extracted in Sect. 3.4

Results and expected limits on the branching ratio

The selection and its efficiency, on signal and background, are discussed in Sect. 3.3, and summarised in Table 4. Assuming a branching ratio of for the signal, an uncertainty of 2.5 % on the luminosity, and 20 fb of data, we would expect signal events, to compare to the expected events from known backgrounds.

In Fig. 3, we show the invariant mass of the LFV top candidate (left) and the standard top candidate (right), in events passing all the cuts except those on the masses themselves.

In order to evaluate the sensitivity of this search for , we calculate the expected upper limit that could be set, in the case of absence of the signal. The calculation is based on the number of expected background events surviving the final selection, in 20 fb of 8 TeV LHC data, so the result can be interpreted as the possible upper limit the CMS or ATLAS collaborations (alone) could expect to set with Run1 data, if the signal were not there.

A 95  confidence level (CL) upper limit on the branching fraction of is calculated using the modified frequentist approach (CL method [124, 125]), as it is implemented in the RooStats framework [126]. Based on the number of expected background events, summarised in Table 4, and on Eq. (6), the obtained limit isAlternative techniques for limit calculations, as implemented in RooStats, have been tried, leading to compatible results. An eventual variation of 100  in the number of expected background events would lead, in the worst case, to an expected limit of at 95 % CL.

As explained in Appendix E, we emulate in our framework the published CMS search for [65]. The reason for this exercise is twofold: on one hand it allows one to validate our procedure on simulated samples, by comparing with the CMS background expectations. On the other hand, it provides an estimate of the constraint set on from this previous analysis, which is found to be , on the verge of probing LFV top decays mediated by a 4-fermion operator. As proven in the present study, a dedicated analysis would set a limit 50 times stronger (of the order of ), showing that the existing LHC data from Run1 can still be used to obtain interesting constraints on lepton-flavour violation.

Discussion

Perspectives at 13 and 14 TeV

To estimate the reach of the described search at a centre-of-mass energy of 13 TeV, we extrapolate the 8 TeV results, rather than performing a full simulation of signal and background processes at 13 TeV. The increase of the production cross sections for SM processes, from 8 to 13 TeV (see Table 3), is taken into account. The selection requirements and efficiencies are kept the same as for the 8 TeV analysis. For the signal, we have checked on simulated events that the efficiencies at 8 and 13 TeV are consistent within 5 %.

The sensitivity is estimated by calculating the expected upper limits on , in the absence of signal, for two scenarios: the case of 20 and 100 fb proton–proton data collected by the LHC at 13 TeV centre-of-mass energy. We also extrapolate the sensitivity to the case of 3000 fb of integrated luminosity at 14 TeV. In this last case, we simply rescale signal and background rates from 13 to 14 TeV, and use the square root of the number of expected background events as an estimate of their uncertainty. The obtained values are summarised in Table 5. The upper limits presented here are derived using statistical uncertainties only, so do not take into account the possibility for such analyses to become systematically dominated in the future. In order to have an accurate evaluation of the systematics evolution, a deeper study from the LHC experiments would be needed. On the other hand, for an analysis on 13 or 14 TeV data, the selection would have to be re-optimised, possibly leading to an increase in sensitivity.

Table 5

Expected upper limits on , under the hypothesis of the absence of signal, for 8, 13 TeV (in two scenarios: the case of 20 and 100 fb collected luminosity) and 14 TeV for 3000 fb collected luminosity

	8 TeV (20 fb^-1)	13 TeV (20 fb^-1)	13 TeV (100 fb^-1)	14 TeV (3000 fb^-1)
BR(t→qμ^±e^∓)	<6.3×10^-5	<2.9×10^-5	<1.2×10^-5	≲2×10^-6

Single top

In addition to mediating LFV top decays, the top operators listed in Appendix A could lead to single-top production with an pair, as illustrated in Fig. 4. The objects in the final state would be the same as for the process we studied: 3 leptons, missing energy, and jets, of which one is a b. We estimate that at 8 TeV, the cross section for is of similar order to the cross section for , for operators involving a u quark and slightly less for a c quark.

Fig. 4

Single-top production via the LFV contact interaction, which produces a final state similar to the considered signal

We neglect this process for two reasons. First, the contact interaction approximation (the |4-momentum in the process ) is more difficult to justify than in top decay, because the energy scale in the process can be . Second, finding such events in the backgrounds could be more challenging because the cannot be required to participate in the reconstruction of a top (step 6 of Sect. 3.3).

We envisage that it makes sense to neglect the LFV single top process in a first search for LFV top decays. This is conservative, because LFV single-top production could contribute events that pass our selection. In the absence of a signal, such a search could sufficiently constrain the contact interaction scale , to justify including the single top process in subsequent analyses.

Summary

The aim of this paper was to explore the LHC sensitivity to the decay , which is lepton and quark flavour-changing, but baryon and lepton number conserving. We parametrise this decay as occurring via a contact interaction, and list a complete set of invariant dimension-six operators in Appendix A. We parametrise the coefficient of these interactions, which we refer to as “top operators”, as or equivalently , withModel-building prejudice (see Sect. 2.3) suggests that . The top branching ratio is thenThese contact interactions are currently constrained from their contribution in loops to rare decays, and from single top searches at HERA. These bounds are discussed in the appendices, and summarised in Sect. 2. For interactions involving e and , rare decay bounds impose for some operators, but others can have .

In Sect. 3, we evaluate the sensitivity reach of a dedicated search for lepton-flavour violation in top decays, at the 8 TeV LHC. The search targets events, where one top decays to an up-type quark (u or c) and a pair of leptons of opposite sign and opposite flavour, and the other one decays to a b quark and a W, which subsequently decays to a charged lepton and a neutrino. This is illustrated in Fig. 2.

The relevant signal and SM background processes are simulated for LHC Run1-like conditions: proton–proton collisions at 8 TeV centre-of-mass energy, for an integrated luminosity of about 20 fb. The detector simulation is based on Delphes, with parameters tuned on the CMS detector reconstruction and performances, but it does not include pileup. The analysis setup is validated by emulating an existing CMS search for rare top decays to Zq in events, showing reasonable results.

We find that a dedicated search by a single experiment using 20 fb of 8 TeV data could be sensitive toand we extrapolate that a sensitivity of () could be reached with 100 fb at 13 TeV (3000 fb at 14 TeV). From Eq. (4), we see that the 100 fb data could impose for the operators, and for the and LQ operators. This analysis shows that the existing LHC data from Run1 can still be used to obtain interesting constraints on lepton-flavour violation. Although this is understandably not the priority focus in the times of the Run2 startup, let’s not to leave unchecked this possible path to New Physics.