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The Circular Electron Positron Collider (CEPC) [1] is a particle physics research program of great scientific significance and has great potential. The concept of the CEPC is developed in the context of many international large colliders, such as the Large Hadron Collider (LHC) at the European Center for Nuclear Research (CERN). In contrast to previous colliders with high energy consumption and costs as well as the pressure of data processing and storage, the CEPC has unique features and advantages. Firstly, the CEPC is an electron collider in which positrons and electrons collide with each other to produce high-energy particle events. Unlike hadron collisions, electron collisions produce particle events that are much clearer and more controllable, facilitating precise measurements and particle identification. Secondly, the CEPC plans to build a highly detailed detector that will be able to capture and record all the important information in particle collisions, providing physicists with a large amount of data to study the behavior of elementary particles. In addition, the CEPC will invest significant effort in improving data processing and storage techniques to cope with the high density of collision data. Finally, the CEPC has a much brighter and cleaner experimental environment. The standard model (SM) observables can be studied with unprecedented precision, and the precision of many electroweak observables can be improved by an order of magnitude or more. Therefore, the CEPC offers an unmatched opportunity for precision measurements and searches far beyond the standard model (BSM) physics.
Among the many new physics (NP) scenarios, a class of models can predict the existence of leptophilic gauge boson
Zx ; this kind of new neutral gauge boson arises due to the extension of a group in the standard model (SM) with theU(1)Lx−Ly forx,y∈{e,μ,τ} [2−4]. The global symmetryU(1)Lx−Ly can be introduced to the SM, which is anomaly-free, without any additional particles [5, 6]. When theU(1)Lx−Ly gauge symmetry is spontaneously broken, the leptophilic gauge bosonZx gains mass. This class of models can be a good solution to solve some problems in the SM, such as the neutrino mass and mixing problem [7−9], the dark matter dark energy problem [9−12], and the muon anomalous magnetic moment problem [13−15]. In our paper, we discuss the possibility of probing this class of the leptophilic gauge bosonZx at the CEPC.The study of the leptophilic gauge boson
Zx is an important step in exploring NP. TheZx boson can be produced at current collider experiments. For example, at the LHC, the leptophilic gauge bosonZx is mainly produced via the Drell-Yan process, where theZx is radiated from the final-state leptons; the constraints on theZx boson can be given via the processespp→4ℓ,3ℓ+EmissT,2ℓ+EmissT , or1ℓ+EmissT [16−19]. At the KEKB collider, the leptophilic gauge bosonZx is produced via the processe+e−→μ+μ−Zx(Zx→μ+μ−) in the framework of theU(1)Lμ−Lτ model in the small mass rangeMZx<10 GeV [20]. The processese+e−→Zx→ℓ+ℓ− orqˉq [21] ande+e−→γZx(→ℓ+ℓ−,μ+μ−) [22] can also be used to search for theZx boson at the LEP and BABAR. Most of the LHC (and Tevatron) bounds coming from resonance searches do not directly apply to such a neutral leptophilic sector. The relevant collider constraints of theU(1)Le−Lμ model mainly come from the LEP and are generally much weaker than the direct LHC constraints applicable for hadrophilic resonances [23]. Therefore, the futuree+e− colliders are uniquely capable of probing the leptophilic gauge bosonZx to unprecedented mass and coupling values. Previous studies [24, 25] have investigated the sensitivity of the processe+e−→Zxγ to explore the leptophilic gauge bosonZx in futuree+e− colliders. In general, properties of any new particle can be studied via different processes, even for the same collider experiments. Furthermore, we find that there are few studies that search for the gauge bosonZx predicted by theU(1)Le−Lμ model via four-lepton final state processes at futuree+e− colliders; hence, we propose searching for this kind of leptophilic gauge bosonZx via the processese+e−→ℓ+ℓ−Zx(Zx→ℓ+ℓ−) ande+e−→ℓ+ℓ−Zx(Zx→νℓ¯νℓ) at the 240 GeV CEPC. We expect these processes to give better sensitivities in the certain mass range.The remainder of the paper is organized as follows. Section II briefly introduces the
U(1)Le−Lμ model and summarizes the constraints of existing experiments on the model. Based on the details of the analysis of theZx signal processese+e−→ℓ+ℓ−Zx(Zx→ℓ+ℓ−) ande+e−→ℓ+ℓ−Zx(Zx→νℓ¯νℓ) and the relevant SM backgrounds, the sensitivity projections of the CEPC to theU(1)Le−Lμ model parameter space are presented and compared with other experimental results in Section III. Finally, the conclusion and discussion are given in Section IV. -
The
U(1)Lx−Ly model [2−4] comprises the SM gauge groupSU(3)C⊗SU(2)L⊗U(1)Y expanding aU(1)Lx−Ly group without introducing an anomaly. This surprising feature is the main motivation considered here. For convenience, in Table 1, we list the lepton charges for theU(1)Lx−Ly models. Here, e, μ, and τ are three generations of charged leptons;νe ,νμ , andντ represent the corresponding left-handed neutrinos, respectively.Model Charge e,νe μ,νμ τ,ντ Le−Lμ 1 −1 0 Le−Lτ 1 0 −1 Lμ−Lτ 0 Le−12(Lμ+Lτ) −1 Le−12(Lμ+Lτ) 1 −12 12 Le+2(Lμ+Lτ) 1 2 2 Table 1. Lepton charges corresponding to the
U(1)Lx−Ly models.The Lagrangian part of the
U(1)Le−Lμ model can be written asL(Zx)=−g′Zxα[Qe(ˉeγαe+¯νeγαPLνe)+Qμ(ˉμγαμ+¯νμγαPLνμ)+Qτ(ˉτγατ+¯ντγαPLντ)]−14ZxμνZxμν+12m2ZxZxμZxμ,
(1) where the gauge coupling constant is denoted as
g′ ;PL=12(1−γ5) is the left chirality projector; andQe ,Qμ , andQτ correspond to the charges of leptons of three generations in theU(1)Le−Lμ model. TheZx− field strength tensor can be written asZxμν=∂μZxν−∂νZxμ.
(2) Before we discuss the experimental constraints on the gauge boson
Zx , we present the decays of theZx boson. The partial decay width ofZx→ℓ+ℓ−(νℓ¯νℓ) for a single flavor lepton is given byΓ(Zx→ℓ+ℓ−)=(g′Qℓ)2MZx12π(1+2m2ℓM2Zx)√1−4m2ℓM2Zx,
(3) Γ(Zx→νℓ¯νℓ)=(g′Qℓ)2MZx24π.
(4) In the
U(1)Le−Lμ model, the gauge bosonZx can only couple to two flavor leptons; therefore, the decay channels of theZx boson are as follows:Zx→e+e−, Zx→μ+μ−, Zx→νe¯νe, Zx→νμ¯νμ.
(5) Since
MZx≫Mℓ , we can neglect the mass of the lepton in Eq. (3), which gives the total width of the gauge bosonZx asΓZx≃g′24πMZx.
(6) There are two possible ways to discover the
Zx boson. On the one hand, theZx boson is heavy at the current energy, and we would need a higher energy to find it. On the other hand, it may be that theZx mass is very small, and the coupling to the particles in the SM is weak (similar to the search for the Higgs boson); hence, researchers search for it by directly or indirectly producing it at future colliders. In our work, we prefer the latter .When the bosonZx has a small mass, the τ mass is heavy and unstable, and we mainly consider that theZx boson couples only to the e and μ subsets and their corresponding neutrinos in theU(1)Le−Lμ model. Some existing constraints on the leptophilic gauge boson massMZx and couplingg′ in theU(1)Le−Lμ model are summarized in Ref. [26]. The LEP bounds give the most stringent bounds in the larger mass rangeMZx≤103 GeV at1σ(2σ) viae+e−→ℓ+ℓ− processes. CMS investigated the final state4μ for the case that all muons originate from the decay of an (almost) on-shell Z boson, offering good sensitivity for10 GeV<MZx<60 GeV. The strongest constraints on the couplingg′ with the10−60 GeV mass range come from the LHC at a 95% confidence level (CL). Theg′ can be as low as2×10−2 [19, 23]. The production of a muon-antimuon pair in the scattering of muon neutrinos in the Coulomb field of a target nucleus gives a strong bound, e.g., neutrino trident production [27, 28]. A combination of measurements of the trident cross section from CHARM-II [29], CCFR [30], and NuTeV [31] imposes a bound ofg′≲1.9×10−3MZx/GeV on theU(1)Le−Lμ model [23]. The sensitivities from(g−2)e and(g−2)μ ong′ in theU(1)Le−Lμ model are also considered; their results are in the range0.2−1 and4×10−2−1 , respectively [23, 32−40]. Hence, we propose the processe+e−→ℓ+ℓ−Zx(Zx→ℓ+ℓ− orνℓ¯νℓ) in theU(1)Le−Lμ model with10 GeV≤MZx≤60 GeV to progress further in the search for expected sensitivities of theZx boson at the√s=240 GeV CEPC. -
The main Feynman diagrams of the signal process
e+e−→ℓ+ℓ−Zx(Zx→ℓ+ℓ− orνℓ¯νℓ) are shown in Fig. 1, which can be expanded into the following four processes:e+e−→e+e−Zx(Zx→e+e−)→e+e−e+e− ,e+e−→μ+μ−Zx(Zx→μ+μ−)→μ+μ−μ+μ− ,e+e−→e+e−Zx(Zx→νe¯νe)→e+e−νe¯νe , ande+e−→μ+μ−Zx(Zx→νμ¯νμ)→μ+μ−νμ¯νμ . In Fig. 2, we present the cross sections of four signaling processes and the corresponding backgrounds. The numerical results for the cross sections are imposed on the basic cuts. We make the transverse momenta of the leptonsPT(ℓ) greater than 10 GeV, and the absolute value of the lepton pseudorapidityηℓ needs to be less than 2.5. These basic cuts are then summed up asFigure 2. (color online) Cross sections of the signal and background processes as functions of the mass
Zx when the coupling limitsg′=0.01GeV−1 .PT(ℓ)>10GeV,∣ηℓ∣<2.5.
(7) When the leptophilic gauge boson
Zx decays to a pair of neutrinos, the beam polarizations can help further suppress the SM backgrounds to enhance the signals [41]. Therefore, in the right panel of Fig. 2, we show the polarized cross sections of thee+e−→ℓ+ℓ−νℓ¯νℓ processes with the beam polarization configurations(Pe+,Pe−)=(−30%,+80%) . The solid lines represent the signal cross sections, and the dashed lines represent the SM background cross sections. The cross section ranges of signal processese+e−→e+e−νe¯νe ande+e−→μ+μ−νμ¯νμ for10 GeV≤ MZx≤60 GeV are3.24×10−4−1.6×10−3 pb and1.7×10−4−2.24×10−4 pb , respectively, withg′=0.01GeV−1 . For the above two processes, the background cross sections are 0.04823 pb and 0.03663 pb, respectively.The left panel shows the
Zx boson decaying to a pair of leptons. We consider the effect of polarization on the processZx→ℓ+ℓ− , but the variations in the cross sections are not significant; hence, we do not impose beam polarizations on the cross sections. The solid-red and solid-black lines represent the cross sections of the signal processese+e−→e+e−e+e− ande+e−→μ+μ−μ+μ− , respectively. The numerical results are2.31×10−4−4.24×10−4 pb and2.49×10−5−8.91×10−5 pb, respectively, in the mass range10 GeV≤MZx≤60 GeV when the coupling constantg′=0.01GeV−1 . The dashed-red and dashed-black lines represent the cross sections of the background processese+e−→e+e−e+e− (0.01477 pb) ande+e−→μ+μ−μ+μ− (0.001899 pb), respectively. The cross sections of signals in the parameter region are smaller than the cross sections of corresponding SM backgrounds.Next, we used FeynRules [42] to simulate the signals to produce a model file output in the UFO format. Then, all signal and background events were simulated using MadGraph5 [43]; the parton shower and hadronization were carried out with Pythia8 [44], while the detector simulation was performed using MadAnalysis5 [45] and Delphes3 [46]. In our analysis, we generate, in each case, 10k signal events in an interval where the mass of
Zx increases in order from 10 GeV to 60 GeV, with 500k events for backgrounds. -
To further improve event selection, the signal and background distributions of the angular separation
△R between two muons, which is defined as△R=√(△ϕ)2+(△η)2 , and invariant massesM(μ+,μ−) are shown in Fig. 3. We can see that the background and signal have very distinctive characteristics. In particular, for the distribution of invariant massesM(μ+,μ−) , the peaks inM(μ+,μ−) still denounce the presence of signals, making the distinction against the smooth background easy. We selectM(μ+,μ−)−MZx≤5 .△R is greater than0.5 forZx mass from 10 GeV to 30 GeV and greater than 0.7 when theZx mass is in the mass range30−60 GeV for the processe+e−→μ+μ−μ+μ− . Based on the characteristics of the kinematic distributions, the selected cuts are listed in Table 2. After these improved cuts are applied, the SM background is significantly depressed. We take a signal benchmark point every 10 GeV in the10−60 GeV mass interval and display the cross sections of the signal and background after applying the above selection cuts for these benchmark points forg′=0.01GeV−1 at the 240 GeV CEPC withL=5.6ab−1 in Table 3. We also show the statistical significance (SS) in the last column of Table 3, which is defined asSS=S/√S+B , whereS represents the number of signal events, andB represents the number of background events. The1σ ,2σ ,3σ , and5σ regions in theg′ -MZx plane are plotted in Fig. 4. The expected bounds ong′ can reach6.2×10−3 (8.1×10−3 )GeV−1 at3σ(5σ) levels. For the same signal process for the massMZx<10 GeV, Ref. [20] provides the upper limit ong′ at SS=1σ level; however, we can provide the SS at3σ(5σ) levels for the mass range10−60 GeV. Thus, the CEPC has the potential to discover theZx boson in the considered mass range.Figure 3. (color online) Normalized distributions of
△R (a) andM(μ+,μ−) (b) from the signal and background events for differentMZx benchmark points for the processe+e−→μ+μ−μ+μ− at the CEPC with√s=240 GeV andL=5.6ab−1 .Cut Mass 10GeV≤MZx≤30GeV 30GeV<MZx≤60GeV Cut1 △R>0.5 △R>0.7 Cut2 M(μ+,μ−)−MZx≤5 M(μ+,μ−)−MZx≤5 Table 2. Improved cuts for the process
e+e−→ μ+μ−μ+μ− .Cross sections for signal (background)/fb MZx /GeVBasic cuts Cut1 Cut2 SS 10 2.4852×10−2 2.4804×10−2 2.3443×10−2 4.7640 (1.899) (1.894) (0.112) 20 6.7516×10−2 6.7369×10−2 6.3763×10−2 7.4520 (1.899) (1.894) (0.346) 30 8.2532×10−2 8.2393×10−2 7.8353×10−2 7.1090 (1.899) (1.894) (0.601) 40 8.7872×10−2 8.7711×10−2 8.3870×10−2 6.4464 (1.899) (1.894) (0.864) 50 8.8983×10−2 8.8865×10−2 8.5551×10−2 5.8548 (1.899) (1.894) (1.109) 60 8.8160×10−2 8.8096×10−2 8.5297×10−2 5.3669 (1.899) (1.894) (1.325) Table 3. Cross sections of the signal and background after imposing the improved cuts for
g′=0.01GeV−1 at the CEPC with√s=240 GeV andL=5.6ab−1 for the processe+e−→ μ+μ−μ+μ− .Figure 4. (color online)
1σ ,2σ ,3σ , and5σ regions for the processe+e−→μ+μ−μ+μ− at the CEPC with√s=240 GeV andL=5.6ab−1 in theg′ -MZx plane.For the case where the gauge boson
Zx decays into a pair of electrons, the kinematic distributions of the signal processe+e−→e+e−e+e− ,△R ,ηe− ,ηe+ , andM(e+,e−) are shown in Fig. 5. The mass ofZx is greater than 40 GeV, and the distributions of the peaks ofηe− andηe+ are shifted. Therefore, we divide the mass range into two segments of10−40 GeV and40−60 GeV when we select the effective cuts. Ultimately, we summarize the specific cuts in Table 4. After applying improved cuts, the cross sections of the signal and the background are shown in Table 5. We also present the regions of SS at1σ ,2σ ,3σ , and5σ levels in Fig. 6. As can be seen from the figure, the sensitivity projections ofZx become weaker with increasing mass, and there is a significant dip atMZx=30 GeV with g′=5×10−3GeV−1 . By comparing the above two processes, the four-electron final state is more sensitive to discovering theZx boson.Figure 5. (color online) Normalized distributions of
△R (a),ηe− (b),ηe+ (c), andM(e+,e−) (d) from the signal and background events for differentMZx benchmark points for the processe+e−→e+e−e+e− at the CEPC with√s=240 GeV andL=5.6ab−1 .Cut Mass 10GeV≤MZx≤40GeV 40GeV<MZx≤60GeV Cut1 △R>0.7 △R>1 Cut2 ηe−>−1.4 ηe−>−1.1 Cut3 ηe+<1.4 ηe+<1.1 Cut4 M(e+,e−)−MZx≤5 M(e+,e−)−MZx≤5 Table 4. Improved cuts for the process
e+e−→ e+e−e+e− .Cross sections for signal (background)/fb MZx /GeVBasic cuts Cut1 Cut2 Cut3 Cut4 SS 10 0.2317 0.2178 0.1965 0.1784 0.1533 10.7950 (14.77) (14.18) (12.30) (10.77) (0.9745) 20 0.3526 0.3360 0.3124 0.2905 0.2465 10.9270 (14.77) (14.18) (12.30) (10.77) (2.602) 30 0.4241 0.4061 0.3765 0.3495 0.3027 10.2330 (14.77) (14.18) (12.30) (10.77) (4.596) 40 0.3876 0.3698 0.3323 0.2984 0.2674 8.3090 (14.77) (14.11) (11.27) (9.133) (5.532) 50 0.3261 0.3108 0.2839 0.2588 0.2357 6.6985 (14.77) (14.11) (11.27) (9.133) (6.696) 60 0.2672 0.2544 0.2338 0.2148 0.1984 5.3463 (14.77) (14.11) (11.27) (9.133) (7.508) Table 5. Cross sections of the signal and background after imposing the improved cuts for
g′=0.01GeV−1 at the CEPC with√s=240 GeV andL=5.6ab−1 for the processe+e−→ e+e−e+e− . -
If the
Zx boson decays to a pair of neutrinos, the processese+e−→e+e−νe¯νe ande+e−→μ+μ−νμ¯νμ have larger cross sections compared to those for the case when theZx boson decays to a pair of leptons. For the processe+e−→μ+μ−νμ¯νμ , according to the kinetic distributions in Fig. 7, the transverse momentumPT(ℓ) , invariant massM(μ+,μ−) , angular separation△R between two muons, and transverse energyET are improved cuts, as presented in Table 6 for the entire mass rangeMZx=10−60 GeV. Optimized cuts might preserve as many signal events as possible. Then, we provide the signal and background cross sections after imposing the optimized cuts for the process in Table 7. We can see that, when the background is suppressed by two orders of magnitude, the signal is substantially preserved. Figure 8 shows the SS =1σ,2σ,3σ,5σ ranges in theg′ -MZx plane; the constraints on theZx boson are very strict with the coupling constantg′ reaching6.7×10−3GeV−1 at SS=5σ .Figure 7. (color online) Normalized distributions of
PT(ℓ) (a),M(e+,e−) (b),△R (c), andET (d) from the signal and background events for differentMZx benchmark points for the processe+e−→μ+μ−νμ¯νμ at the CEPC with√s=240 GeV andL=5.6ab−1 .Cut Mass 10GeV≤MZx≤60GeV Cut1 PT(ℓ)>5 Cut2 ∣M(μ+,μ−)−MZx∣≤5 Cut3 △R<4 Cut4 ET<150 Table 6. Improved cuts for the process
e+e−→ μ+μ−νμ¯νμ .Cross sections for signal (background)/fb MZx /GeVBasic cuts Cut1 Cut2 Cut3 Cut4 SS 10 0.1708 0.1706 0.03665 0.03665 0.03665 5.4300 (36.63) (36.59) (0.2205) (0.2205) (0.2200) 20 0.2122 0.2215 0.1054 0.1054 0.1054 10.1420 (36.63) (36.59) (0.4993) (0.4993) (0.4985) 30 0.2216 0.2215 0.1317 0.1317 0.1317 11.0030 (36.63) (36.59) (0.6723) (0.6721) (0.6711) 40 0.2229 0.2215 0.1317 0.1317 0.1414 10.8980 (36.63) (36.59) (0.8064) (0.8056) (0.8046) 50 0.2205 0.2204 0.1467 0.1467 0.1467 10.5890 (36.63) (36.59) (0.9205) (0.9195) (0.9195) 60 0.2153 0.2153 0.1443 0.1443 0.1443 9.9480 (36.63) (36.59) (1.037) (1.036) (1.034) Table 7. Cross sections of the signal and background after imposing the improved cuts for
g′=0.01GeV−1 at the CEPC with√s=240 GeV andL=5.6ab−1 for the processe+e−→ μ+μ−νμ¯νμ .Figure 8. (color online)
1σ ,2σ ,3σ and5σ regions for the processe+e−→μ+μ−νμ¯νμ at the CEPC with√s=240 GeV andL=5.6ab−1 in theg′ -MZx plane.When
Zx decays toνe¯νe , the peak distribution of thee+ energy for the signal processe+e−→e+e−νe¯νe is clearly demarcated from the background in Fig. 9. For the low mass rangeMZx=10−40 GeV, thee+ energy retains more signals after applying the cuts. On the contrary, for the large mass rangeMZx=40−60 GeV, the signal events of the invariant massM(e+,e−) outnumber the signal events ofE(e+) after improving cuts; therefore, we add to the effective cuts atMZx=40 GeV, as shown in Table 8. Finally, Table 9 presents the cross sections of the signal and background after the improved cuts are imposed on thee+e−→e+e−νe¯νe process, and we plot1σ ,2σ ,3σ and5σ ranges in Fig. 10. The sensitivity projections of theZx boson that we obtain are very strict for the process, especially in the region of massMZx=10−40 GeV. In contrast to the three processes mentioned above, this process is more sensitive to theZx boson.Figure 9. (color online) Normalized distributions of
PT(ℓ) (a),E(e+) (b), andM(e+,e−) (c) from the signal and background events for differentMZx benchmark points for the processe+e−→e+e−νe¯νe at the CEPC with√s=240 GeV andL=5.6ab−1 .Cut Mass 10GeV≤MZx≤40GeV 40GeV<MZx≤60GeV Cut1 PT(ℓ)>5 PT(ℓ)>5 Cut2 E(e+)>110 ∣M(e+,e−)−MZx∣≤5 Table 8. The improved cuts for the process
e+e−→ e+e−νe¯νe .Cross sections for signal (background)/fb MZx /GeVBasic cuts Cut1 Cut2 SS 10 1.6011 1.5658 0.49924 51.6830 (48.23) (46.75) (0.02334) 20 0.8491 0.8312 0.1709 28.9830 (48.23) (46.75) (0.02334) 30 0.5879 0.5761 0.06803 16.7940 (48.23) (46.75) (0.02334) 40 0.4583 0.4491 0.02810 9.2220 (48.23) (46.75) (0.02334) 50 0.3755 0.3677 0.1192 7.3630 (48.233) (46.75) (1.522) 60 0.3247 0.3172 0.1187 6.6180 (48.23) (46.75) (0.1187) Table 9. Cross sections of the signal and background after imposing the improved cuts for
g′=0.01GeV−1 at the CEPC with√s=240 GeV andL=5.6ab−1 for the processe+e−→ e+e−νe¯νe . -
Recently, there have been many studies related to the leptophilic gauge boson
Zx . The search for the mass range of10−500 GeVZx in theU(1)Lμ−Lτ model is widely studied at the LHC. However, the search for a small mass ofZx is very limited in theU(1)Le−Lμ model at the futuree+e− colliders. It is evident that there is still a large parameter space around the electroweak scale for us to explore theZx boson [23]. Thus, we can search for theZx predicted by theU(1)Le−Lμ model at the CEPC to facilitate the extension of the sensitivity ofZx or stricter couplings. In our study, we investigate the prospects of the CEPC to unravel the NP associated with a new weak interaction, and the gauge bosonZx only couples to the e and μ subsets in theU(1)Le−Lμ model.We investigated the sensitivity of the CEPC with
√s=240 GeV andL=5.6ab−1 to the coupling parameterg′ forMZx=10−60 GeV. As can be seen from the four processes explored in the previous sections, the expected bounds of the processe+e−→e+e−νe¯νe ong′ can reach1.0×10−3 (1.6×10−3 )GeV−1 forMZx=10−40 GeV at3σ (5σ ); these are the strictest constraints on theU(1)Le−Lμ model. However, in theZx mass range of40−60 GeV, the strictest constraints come from the processe+e−→μ+μ−νμ¯νμ , and the expected bounds ong′ can reach5.1×10−3 (6.7×10−3 )GeV−1 at3σ (5σ ). Compared to the other three processes, the processe+e−→μ+μ−μ+μ− is less constrained.In conclusion, the expected sensitivities of the four processes to the parameter space of the
U(1)Le−Lμ models are different. However, when we compare our numerical results in Fig. 2 with those in Ref. [23], they are not experimentally excluded except from the processe+e−→μ+μ−μ+μ− . At the same time, Ref. [24] indicates that the sensitivity tog′ for the processe+e−→Zxγ can be as low as5×10−3 in the mass range of10−60 GeV at the2σ level. Our results can reach1×10−3 forMZx=10 GeV via the processe+e−→e+e−νe¯νe , and the constraints from the processe+e−→μ+μ−νμ¯νμ can reach4.2×10−3 at the2σ level in the entire mass range of10−60 GeV. Our numerical results align with those of Ref. [24], as the same conclusions are applicable to the processe+e−→e+e−e+e− . Hence, searching for theZx boson predicted by theU(1)Le−Lμ model at the 240 GeV CEPC via processese+e−→ℓ+ℓ−Zx(Zx→νℓ¯νℓ orℓℓ) can enhance the sensitivity projections to the parameter space and promote further exploration of futuree+e− colliders for theU(1)Le−Lμ model, providing more opportunities for further discoveries regarding the leptophilic gauge bosonZx . -
Yan-Yu Li would like to thank Han Wang for very useful discussions.
Searching for the light leptophilic gauge boson Zx via four-lepton final states at the CEPC
- Received Date: 2023-12-05
- Available Online: 2024-04-15
Abstract: We investigate the possibility of detecting the leptophilic gauge boson