-
FCN interaction of the top quark is highly suppressed by the GIM mechanism. The branching ratios for two-body top FCN decays in SM are of the order of
$ 10^{-12} $ –$ 10^{-15} $ [61–63]. Any hint for such processes would thus immediately point to physics beyond SM. A wide variety of limits have been set on these couplings. For example, flavor changing decay modes$ t\to qZ $ and$ t\to q\gamma $ were searched for at the Tevatron by CDF [11–13] and D0 [14], and at the LHC by ATLAS [15–19] and CMS [20–22]. At the LHC,$ t\to qH $ was also searched for [23–32]. Direct top production,$ pp\to t $ , was considered at the Tevatron by CDF [33], and at the LHC by ATLAS [34–36], while a similar production with an additional jet in the final state was considered by D0 [37, 38] and CMS [39]. Single top production in association with a photon and a Z were searched for by CMS [40] and ATLAS [41]. At LEP2,$ e^+e^-\to tj $ was investigated by all four collaborations [42–47], while at HERA, the single-top$ e^-p\to e^-t $ production was considered by ZEUS [48, 49] and H1 [50–52]. The most constraining limits were recently collected and summarized in Table 33 of Ref. [57]. The sensitivities in terms of the two-body branching ratios are roughly of the order$ 10^{-4} $ to$ 10^{-3} $ , approaching the expected values from typical new physics models [64].A complete and systematic description of the top quark FCN couplings based on the Standard Model Effective Field Theory (SMEFT) [65–67] was discussed and documented in the LHC TOP Working Group note [68]. The idea is that starting from the Warsaw basis operators [69], one defines linear combinations of Wilson coefficients that give independent contributions in a given measurement. For the
$ e^+e^-\to tj $ process, the relevant basis operators are the following two-fermion operators:$ O_{\varphi q}^{1(ij)} = (\varphi^\dagger i\!\!\overleftrightarrow{D}_\mu\varphi) \left( \bar q_i \gamma^\mu q_j \right), $
(1) $ O_{\varphi q}^{3(ij)} = (\varphi^\dagger i\!\!\overleftrightarrow{D}^I_\mu\varphi) \left( \bar q_i \gamma^\mu \tau^I q_j \right), $
(2) $ O_{\varphi u}^{(ij)} = (\varphi^\dagger i\!\!\overleftrightarrow{D}_\mu\varphi) \left( \bar u_i \gamma^\mu u_j \right), $
(3) $ O_{uW}^{(ij)} = \left( \bar q_i\sigma^{\mu\nu}\tau^I u_j \right)\tilde \varphi W_{\mu\nu}^I, $
(4) $ O_{uB}^{(ij)} = \left( \bar q_i\sigma^{\mu\nu} u_j \right)\tilde \varphi B_{\mu\nu}, $
(5) where
$ \varphi $ is the Higgs doublet,$ \tilde\varphi = i\sigma_2\varphi $ ,$ \tau^I $ is the Pauli matrix,$ B_{\mu\nu} $ and$ W_{\mu\nu}^I $ are the$ U(1)_Y $ and$ SU(2)_L $ gauge field strength tensors,$ (\varphi^\dagger i\!\!\overleftrightarrow{D}_\mu\varphi)\!\equiv\! i\varphi^\dagger\left( D_\mu\!\!-\!\!\overleftarrow{D}_\mu \right)\varphi $ , and$ (\varphi^\dagger i\!\!\overleftrightarrow{D}_\mu\varphi)\!\equiv\! $ $ i\varphi^\dagger\left( \tau^ID_\mu-\overleftarrow{D}_\mu \tau^I\right)\varphi $ . The following four-fermion basis operators are also relevant:$ O_{lq}^{1(ijkl)} = \left( \bar l_i \gamma_\mu l_j \right) \left( \bar q_k \gamma^\mu q_l \right), $
(6) $ O_{lq}^{3(ijkl)} = \left( \bar l_i \gamma_\mu \tau^I l_j \right) \left( \bar q_k \gamma^\mu \tau^I q_l \right), $
(7) $ O_{lu}^{(ijkl)} = \left( \bar l_i \gamma_\mu l_j \right) \left( \bar u_k \gamma^\mu u_l \right), $
(8) $ O_{eq}^{(ijkl)} = \left( \bar e_i \gamma_\mu e_j \right) \left( \bar q_k \gamma^\mu q_l \right), $
(9) $ O_{eu}^{(ijkl)} = \left( \bar e_i \gamma_\mu e_j \right) \left( \bar u_k \gamma^\mu u_l \right), $
(10) $ O_{lequ}^{1(ijkl)} = \left( \bar l_i e_j \right)\varepsilon \left( \bar q_k u_l \right), $
(11) $ O_{lequ}^{3(ijkl)} = \left( \bar l_i \sigma_{\mu\nu} e_j \right)\varepsilon \left( \bar q_k \sigma^{\mu\nu} u_l \right), $
(12) where
$ i,j,k,l $ are flavor indices. For the four-fermion operators, only the$ i = j = 1 $ components are relevant for the$ e^+e^-\to t(\bar t)j $ process. Other operators such as$O_{u\varphi}^{(ij)}\equiv $ $ \left( \varphi^\dagger\varphi \right)\left( \bar q_iu_j\tilde\varphi \right) $ and$ O_{uG}^{(ij)} \equiv \left( \bar q_i\sigma^{\mu\nu} T^a u_j \right)\tilde \varphi G_{\mu\nu}^a $ could lead to FCN couplings$ tqH $ and$ tqg $ , but they cannot be probed in the single top channel. The following linear combinations of Wilson coefficients can be defined as independent degrees of freedom that enter this process:Two-fermion degrees of freedom:
$ c_{\varphi q}^{-[I](3+a)}\equiv {}_{\Re}^{[\Im]}\! \left\{ C_{\varphi q}^{1(3a)} - C_{\varphi q}^{3(3a)} \right\}, $
(13) $ c_{\varphi u}^{[I](3+a)}\equiv {}_{\Re}^{[\Im]}\! \left\{ C_{\varphi u}^{1(3a)} \right\}, $
(14) $ c_{uA}^{[I](3a)}\equiv \left\{ c_WC_{uB}^{(3a)}+s_WC_{uW}^{(3a)} \right\}, $
(15) $ c_{uA}^{[I](a3)}\equiv \left\{ c_WC_{uB}^{(a3)}+s_WC_{uW}^{(a3)} \right\}, $
(16) $ c_{uZ}^{[I](3a)}\equiv \left\{ -s_WC_{uB}^{(3a)}+c_WC_{uW}^{(3a)} \right\}, $
(17) $ c_{uZ}^{[I](a3)}\equiv \left\{ -s_WC_{uB}^{(a3)}+c_WC_{uW}^{(a3)} \right\}. $
(18) Four-fermion eetq degrees of freedom:
$ c_{lq}^{-[I](1,3+a)}\equiv {}_{\Re}^{[\Im]}\!\left\{ C_{lq}^{1(113a)}-C_{lq}^{3(113a)} \right\}, $
(19) $ c_{eq}^{[I](1,3+a)}\equiv {}_{\Re}^{[\Im]}\!\left\{ C_{eq}^{(113a)} \right\}, $
(20) $ c_{lu}^{[I](1,3+a)}\equiv {}_{\Re}^{[\Im]}\!\left\{ C_{lu}^{(113a)} \right\}, $
(21) $ c_{eu}^{[I](1,3+a)}\equiv {}_{\Re}^{[\Im]}\!\left\{ C_{eu}^{(113a)} \right\}, $
(22) $ c_{lequ}^{S[I](1,3a)}\equiv {}_{\Re}^{[\Im]}\!\left\{ C_{lequ}^{1(113a)} \right\}, $
(23) $ c_{lequ}^{S[I](1,a3)}\equiv {}_{\Re}^{[\Im]}\!\left\{ C_{lequ}^{1(11a3)} \right\}, $
(24) $ c_{lequ}^{T[I](1,3a)}\equiv {}_{\Re}^{[\Im]}\!\left\{ C_{lequ}^{3(113a)} \right\}, $
(25) $ c_{lequ}^{T[I](1,a3)}\equiv {}_{\Re}^{[\Im]}\!\left\{ C_{lequ}^{3(11a3)} \right\}, $
(26) where quark generation indices (
$ a = 1,2 $ ) and lepton generation indices are enclosed in parentheses. An I in the superscript represents the imaginary part of the coefficient, denoted by$ \Im $ on the right hand side, while without I only the real part is taken, represented by$ \Re $ on the right hand side. In total, one collects the following 28 real and independent degrees of freedom for each a (and thus 56 in total):$ \begin{array}{*{20}{c}} c_{\varphi q}^{-(3+a)} \!\!&\!\! c_{uZ}^{(a3)} \!\!& \!\!c_{uA}^{(a3)} \!\!& \!\! c_{lq}^{-(1,3+a)} \!\!&\!\! c_{eq}^{(1,3+a)}\!\! & \!\! c_{lequ}^{S(1,a3)} \!\!&\!\! c_{lequ}^{T(1,a3)} \\ c_{\varphi u}^{(3+a)} \!\!&\!\!c_{uZ}^{(3a)} \!\!& \!\!c_{uA}^{(3a)} \!\!& \!\! c_{lu}^{(1,3+a)} \!\!&\!\! c_{eu}^{(1,3+a)}\!\! & \!\! c_{lequ}^{S(1,3a)} \!\!&\!\! c_{lequ}^{T(1,3a)} \\ c_{\varphi q}^{-I(3+a)} \!\!& \!\!c_{uZ}^{I(a3)}\!\! &\!\! c_{uA}^{I(a3)} \!\!& \!\! c_{lq}^{-I(1,3+a)}\!\!& \!\!c_{eq}^{I(1,3+a)} \!\!& \!\! c_{lequ}^{SI(1,a3)} \!\!& \!\!c_{lequ}^{TI(1,a3)} \\ c_{\varphi u}^{I(3+a)} \!\!&\!\! c_{uZ}^{I(3a)} \!\!&\!\! c_{uA}^{I(3a)} \!\!& \!\! c_{lu}^{I(1,3+a)} \!\!&\!\! c_{eu}^{I(1,3+a)}\!\! & \!\! c_{lequ}^{SI(1,3a)} \!\!&\!\! c_{lequ}^{TI(1,3a)} \end{array} $
(27) Among the seven columns, the first three come from the two-fermion operators.
$ c^-_{\varphi q} $ and$ c_{\varphi u} $ give rise to$ tqZ $ coupling with a vector-like Lorentz structure, while$ c_{uA} $ and$ c_{uZ} $ give rise to the$ tq\gamma $ and$ tqZ $ dipole interactions. The last four come from the$ eetq $ four-fermion operators.$ c^-_{lq} $ ,$ c_{lu} $ ,$ c_{eq} $ , and$ c_{eu} $ coefficients give rise to interactions between two vector currents, while$ c^S_{lequ} $ and$ c^T_{lequ} $ to interactions between two scalar and two tensor currents, respectively. We note that the first two rows are CP-even while the last two rows are CP-odd. The first and the third rows involve a left-handed light quark, while the second and the fourth rows involve a right-handed light quark. The interference between coefficients from different rows in the limit of massless quarks vanishes for this reason. Furthermore, the signatures of the degrees of freedom in the first row are identical to those in the third row, and similarly the second row is identical to the fourth row. This is due to the absence of an SM amplitude that interferes with the FCN coefficients, which leads to cross-sections that are invariant under a change of phase:$ c_i+c^I_ii\to {\rm e}^{{\rm i}\delta} (c_i+c^I_ii) $ . It is therefore sufficient to focus on the degrees of freedom in the first two rows, and in the rest of the paper we will refer to them simply as coefficients. We also note that the$ e^+e^-\to tj $ signal of the coefficients from the first two rows are similar, up to a$ \theta\to \pi-\theta $ transformation of the scattering angle in the$ tj $ production. The decay of the top quark, however, breaks this similarity. This is because the two coefficients produce left-handed and right-handed top quarks respectively, while the lepton momentum from the top decay is correlated with the top helicity. This leads to a difference in signal efficiencies between the first two rows.Two-fermion FCN interactions in the first three columns are considered in almost all experimental searches. Four-fermion FCN interactions, on the other hand, have unduly been neglected. They were proposed in Ref. [70], and searched for at LEP2 by the L3 and DELPHI collaborations [45, 47], but the three-body decays through four-fermion FCN interactions have never been searched for at the Tevatron or LHC, except for the lepton-flavor violating case. As for the prospects at future
$ e^+e^- $ colliders, four-fermion couplings were also neglected in the studies of single top at TESLA and FCC-ee [58, 59], although the recent CLIC yellow report has included them [60]. However, the four-fermion operators are indispensable for a complete characterization of the top quark flavor properties. They could arise, for example, in the presence of a heavy mediator coupling to one top quark and one light quark, or in the cases where the equation of motion (EOM) is used to remove redundant two-fermion operators in terms of the basis operators. Their existence also guarantees the correctness of the effective description when particles go off-shell or in loops, see [53] for a detailed discussion. The three-body decay$ t\to cf\bar f $ was calculated in several explicit models [54–56], giving a further motivation for considering the$ tcll $ contact operators. Ref. [71] recast the LHC constraints of$ t\to qZ $ to provide bounds. Finally, the lepton-and-quark-flavor violating top decay through contact interactions was studied in [72], and recently searched for by the ATLAS collaboration [73].An interesting fact about the
$ eetq $ four-fermion FCN interaction is that the most stringent limits are still coming from the LEP2 experiments. In Ref. [57], a global analysis based on the current bounds was performed within the SMEFT framework. The result clearly showed that the LHC is more sensitive to the two-fermion operator coefficients, while LEP2 is more sensitive to the four-fermion ones. Hence, their results are currently complementary in the full parameter space, as demonstrated in Fig. 59 in Section 8.1 of Ref. [57]. The complementarity persists even with HL-LHC (see Fig. 59 right of Ref. [57]), despite an order of magnitude difference between the LEP2 and HL-LHC luminosities. Clearly, this implies that an$ e^+e^- $ collider with higher luminosity could continue to provide valuable information about the top FCN interactions, and explore the parameter space which will not be covered by the HL-LHC.The difference in sensitivities between the two types of colliders can be understood as follows. The two-fermion operators can be searched for at the LHC by the flavor-changing decay of the top quark, but the same decay through a four-fermion operator is a three-body decay and will be suppressed by an additional phase space factor. As an illustration, the decay rates of
$ t\to ce^+e^- $ through$ c_{\varphi u} $ ,$ c_{uZ} $ and$ c_{eu} $ are$ 8.1\times 10^{-5} $ ,$ 2.4\times10^{-4} $ GeV and$ 3.2\times10^{-6} $ GeV , respectively, for$ c/\Lambda^2 = 1 $ TeV−2. Furthermore, the$ e^+e^- $ mass spectrum is a continuum, and thus the best sensitivity requires a dedicated search without a mass window cut (see discussions in Refs. [53, 71]). Searching for four-fermion operators in single top channels at a hadron collider suffers from the same phase-space suppression. The situation in an$ e^+e^- $ collider is, however, different. The two-fermion operators can be searched for through single top$ e^+e^-\to Z^*/\gamma^* \to tj $ (or through top decay if the center-of-mass energy allows for top quark pair production, though typically the former has a better sensitivity [58]). In the case of a four-fermion operator, instead of a suppression effect, the production rate is actually enhanced due to the fact that there is one less propagator than in the two-fermion case. As an illustration, the single top production cross-section at$ E_{\rm cm} = 240 $ GeV for$ c_{\varphi u} $ ,$ c_{uZ} $ and$ c_{eu} $ are 0.0018 pb, 0.020 pb and 0.12 pb, respectively, for$ c/\Lambda^2 = 1 $ TeV−2, and this enhancement effect increases with energy. The comparison of the two cases is illustrated in Fig. 1. Another advantage of a lepton collider is that one can reconstruct the missing momentum. This is not relevant for the problem at hand, but could be important for setting bounds on four-fermion operator with neutrinos, see Ref. [74].Figure 1. (color online) (top) The flavor-changing decay at the LHC. The four-fermion operator contribution is suppressed by an additional phase space factor compared with the two-fermion contribution. (bottom) The flavor-changing single top at a
$e^+e^-$ collider. The four-fermion operator contribution is enhanced due to one less s-channel propagator than in the two-fermion case. Green dots and blue squares represent two- and four-fermion operator insertions. -
To study the prospects of top FCN couplings, we consider the scenario of CEPC running with a center-of-mass energy
$ E_{\rm cm} = 240 $ GeV and an integrated luminosity of 5.6 ab−1. We simulate the signal and background at leading order with parton shower by MADGRAPH5_AMC@NLO [75] and PYTHIA8 [76, 77]. The signal is generated with the UFO model [78, 79], DIM6TOP, which follows the LHC TopWG EFT recommendation [68] and is available at https://feynrules.irmp.ucl.ac.be/wiki/dim6top. The detector level simulation is performed with DELPHES with the default CEPC card [80]. Jets are reconstructed using the FASTJET package [81] with the anti-$ k_t $ algorithm [82] with a radius parameter of 0.5. Automatic calculation for QCD corrections of processes involving only two-fermion FCN operators were developed in Ref. [83] (see also Refs. [84–92] where the results for the other top flavor-changing channels have been presented). The corrections for four-fermion operators were given in the appendix of Ref. [53]. The sizes are below 20%, corresponding to less than 10% change in the coefficients, and therefore we neglect these corrections in this work. The dominant background comes from the W-pair and Z-pair production, and we do not expect a significant change at the next-to-leading order in QCD.We consider the semi-leptonical top quark decays. The signal final state is
$ bjl\nu $ , where j is an up or charm quark jet. The dominant background is$ qq'l\nu $ , with one light or charm quark jet misidentified as a b-jet. A large fraction comes from the W pair production with one W decaying hadronically and the other leptonically, while the diagrams with only one W resonance decaying leptonically also make an important contribution. We thus take into account the full contribution from the$ e^+e^-\to Wq\bar q' $ process with W decaying leptonically. Adding all the diagrams from$ e^+e^-\to l\nu q\bar q' $ does not make a sizable change to the background [58], and so they are not taken into account. Another source of background comes from$ b\bar bll $ and$ c\bar cll $ , where one of the jets is mistagged and one of the leptons is missed by the detector. This is included in our simulation, but the contribution is subdominant. Selected diagrams for the signal and background are shown in Fig. 2.Figure 2. (color online) Selected Feynman diagrams for the signal (top) and background (bottom). Green dots and blue squares represent two- and four-fermion operator insertions. Red double lines represent top quark propagators.
Based on the expected signature of the signal process, we select events with exactly one charged lepton (electron or muon) and at least two jets. The charged lepton must have
$ p_{\rm{T}}>10 $ GeV and$ |\eta|<3.0 $ . All jets are required to have$ p_{\rm{T}}>20 $ GeV and$ |\eta|<3.0 $ . Exactly one jet should be b-tagged. If more than one non-b-tagged jet is present, the one with the highest$ p_{\rm{T}} $ is selected as the up or charm quark jet candidate. We have chosen a b-tagging working point with 80% efficiency for b-jets and a mistagging rate of 10% (0.1%) from c-jets (light jets) [93]. A missing energy greater than 30 GeV is also required due to the presence of a neutrino. The W boson candidate is reconstructed from the charged lepton and the missing energy. The top quark candidate is reconstructed by combining the W boson candidate with the b-jet.At the parton level, we expect the non-b-tagged jet from the signal to have
$ E_j = \dfrac{s-m_{\rm top}^2}{2\sqrt{s}}\approx 58\ {\rm{GeV}} $ . For the background, if the contribution comes from the diboson production (e.g. Fig. 2 down left), we expect the dijet mass to peak at$ m_W = 80.4 $ GeV. The contribution from the non-resonant diagrams (e.g. Fig. 2 down right) cannot, however, be neglected and gives rise to a continuum spectrum in the dijet mass distribution. At the reconstruction level, it turns out that the energy of the non-b-tagged jet$ E_j $ , the invariant mass of the b-jet and the non-b-tagged jet$ m_{jj} $ , and the invariant mass of the top quark candidate$ m_{\rm top} $ are the most useful variables to discriminate the signal from background. In Fig. 3, we plot these variables at the reconstruction level, for the background as well as for the signals from the two typical operator coefficients,$ c_{uZ} $ and$ c_{eq} $ , for illustration.Figure 3. (color online) Signal and background at the reconstruction level. Distributions of
$m_{\rm top}$ ,$E_j$ , and$m_{jj}$ are shown for signals from$c_{uZ}^{(23)}$ and$c_{eq}^{(1,3+2)}$ .As our baseline analysis, we impose the following kinematic cuts at the reconstruction level
$ E_j< 60\ {\rm{GeV}}\,, $
(28) $ m_{jj}>100 \ {\rm{GeV}}\,, $
(29) $ m_{\rm top}<180 \ {\rm{GeV}}\,. $
(30) These cuts are motivated by Fig. 3. The expected number of background events after event selection is about 1400 with an integrated luminosity of 5.6 ab−1, corresponding to a statistical uncertainty of about 2.7%. We assume that the systematic uncertainty will be under control below this level. The impact of the systematic uncertainty can be easily estimated, e.g. a 3% systematic uncertainty will weaken the bound of the cross-section by a factor of about 1.5, which corresponds to a factor of 1.2 on the value of the coefficients. In the rest of the paper we simply ignore the systematic effects. We will see that this simple baseline scenario already allows to obtain reasonable sensitivities.
In the absence of any FCN signal, the 95% confidence level (CL) upper bound of the fiducial cross-section is
$ 0.0134 $ fb. Alternatively, the 5$ \sigma $ discovery limit of the signal cross-section, determined by$ S/\sqrt{B} = 5 $ , is a function of the integrated luminosity$ L_{\rm{int}} $ :$ \sigma = \frac{5\sqrt{\sigma_{B}}}{\sqrt{L_{\rm{int}}}} = \frac{2.51\ {\rm{fb}}}{\sqrt{L_{\rm{int}}/{\rm{fb}}^{-1}}}. $
(31) The cross-section is a quadratic function of the operator coefficients. Including the interference effects, such a function has 28 independent terms for the 7 coefficients in each row of Eq. (27). These terms for the first two rows are the same as those for the last two rows, because they only differ by a CP phase which would never show up in the cross-section (without any possible interference with SM). Thus, only 56 independent terms need to be determined for the first two rows for each a. We sample the parameter space by 56 points and simulate the fiducial cross-section for each of them. The results are fitted by the following form:
$ \sigma = \sum\limits_{a = 1,2} {\frac{{{{(1\;{\rm{TeV}})}^4}}}{{{\Lambda ^4}}}} \left( {\overrightarrow {C_1^a} \cdot {{M}}_{\bf{1}}^{{a}} \cdot {{\overrightarrow {C_1^a} }^T} + \overrightarrow {C_2^a} \cdot {{M}}_{\bf{2}}^{{a}} \cdot {{\overrightarrow {C_2^a} }^T}} \right), $
(32) where
$ \vec{C}_{1,2} $ denote the vectors formed by the coefficients in the first and second rows of Eq. (27). a is the light quark generation.$ {{M}}_{1,2}^a $ are$ 7\times7 $ matrices. The above result allows to convert the upper bound and discovery limit of the cross-section into a 56-dimensional coefficient space.We have verified the relations between signatures from different rows in Eq. (27): the 1st (2nd) and the 3rd (4th) rows always give the same signatures; the 1st (3rd) and the 2nd (4th) rows at the production level are identical up to a
$ \theta\to \pi-\theta $ transformation in the production angle, but differ if the top decays. In Appendix A, a comparison between the signals from$ c_{uZ}^{(23)} $ ,$ c_{uZ}^{(32)} $ and$ c_{uZ}^{I(23)} $ are shown in Fig. A1. A comparison between the signals from$ c_{eq}^{(1,3+2)} $ ,$ c_{eu}^{(1,3+2)} $ and$ c_{eq}^{I(1,3+2)} $ are shown in Fig. A2.Figure A1. (color online) Signals from
$c_{uZ}^{(23)}$ ,$c_{uZ}^{(32)}$ and$c_{uZ}^{I(23)}$ at the parton level. Distributions of the scattering angle, the lepton energy, and the lepton pseudorapidity are compared.Figure A2. (color online) Signals from
$c_{eq}^{(1,3+2)}$ ,$c_{eu}^{(1,3+2)}$ and$c_{eq}^{I(1,3+2)}$ at the parton level. Distributions of the scattering angle, the lepton energy, and the lepton pseudorapidity are compared.Our baseline analysis could be improved by exploiting additional features of the signal with a template fit. One possibility is to make use of heavy flavor tagging. The operators with
$ a = 2 $ , requiring a tagged c-jet in the signal definition, could largely suppress the background, as most background comes from events with one charm quark and one strange quark in the final state, with the charm mistagged as a b. The clean environment of CEPC allows a precise determination of the displaced vertices and excellent capability of c-jet tagging [5]. We assume a working point with a 70% tagging efficiency for c-jets and 20% (12%) mistagging rate from b-jets (light jets) [93]. To constrain the coefficients with$ a = 2 $ , we require a c-jet in the signal definition, while to constrain the$ a = 1 $ coefficients we veto the events with a c-jet, although the latter is not expected to significantly change the sensitivity as most background events do not have an extra c-jet except the one that fakes the b-jet. Another useful information is the angular distribution of the single top, which is determined by the specific Lorentz structure of the operator. In Fig. 4 , we show the distribution of the top scattering angle from all 7 coefficients in the first row at the parton level and the reconstruction level. The scattering angle$ \theta $ is defined as the angle between the momentum of the$ e^+ $ beam and t or$ \bar t $ . The distributions for the top and anti-top are related by$ \theta\to\pi-\theta $ , and this is illustrated by comparing the first two plots in Fig. 4. Furthermore, this holds even for the reconstructed top and anti-top candidates from the background due to the CP symmetry. For this reason, we consider the observable$ c = Q_l\times\cos\theta $ , i.e. the lepton charge times the cosine of the scattering angle. The discrimination power of this observable is illustrated in the right plot of Fig. 4, at the reconstruction level. We perform a template fit by further dividing the signal region into 4 bins, defined as$ c\in(-1,-0.5) $ ,$ [-0.5,0) $ ,$ [0,0.5) $ , and$ [0.5,1) $ . To construct a$ \chi^2 $ fit, we take$ \sqrt{B} $ in each bin as the experimental uncertainty. The smallest number of events in one bin is 24 even after requiring a c-jet, and so the Gaussian distribution is a good approximation. We simulate the Gaussian fluctuation in all bins by generating a large number of pseudo-measurement samples and compute the average$ \chi^2 $ for each point in the coefficient space. Our 95% CL bound is determined by$ \left<\chi^2\right><9.49 $ .Figure 4. (color online) Scattering angle from the signals of the seven coefficients in the first row of Eq. (27).
$\theta_{\rm top}$ is defined as the angle between the momentum of the$e^+$ beam and t or$\bar t$ . (left) parton level, for top production. (middle) parton level, for anti-top production. (right) reconstruction level, for top production, including the background.
Probing the top quark flavor-changing couplings at CEPC
- Received Date: 2019-06-20
- Accepted Date: 2019-09-06
- Available Online: 2019-11-01
Abstract: We propose to study the flavor properties of the top quark at the future Circular Electron Positron Collider (CEPC) in China. We systematically consider the full set of 56 real parameters that characterize the flavor-changing neutral interactions of the top quark, which can be tested at CEPC in the single top production channel. Compared with the current bounds from the LEP2 data and the projected limits at the high-luminosity LHC, we find that CEPC could improve the limits of the four-fermion flavor-changing coefficients by one to two orders of magnitude, and would also provide similar sensitivity for the two-fermion flavor-changing coefficients. Overall, CEPC could explore a large fraction of currently allowed parameter space that will not be covered by the LHC upgrade. We show that the c-jet tagging capacity at CEPC could further improve its sensitivity to top-charm flavor-changing couplings. If a signal is observed, the kinematic distribution as well as the c-jet tagging could be exploited to pinpoint the various flavor-changing couplings, providing valuable information about the flavor properties of the top quark.