Analysis of B c →τ ν τ at CEPC
Taifan Zheng, Ji Xu, Lu Cao, Dan Yu, Wei Wang, Soeren Prell, Yeuk-Kwan E. Cheung, Manqi Ruan
EEPJ manuscript No. (will be inserted by the editor)
Analysis of B c → τ ν τ at CEPC Taifan Zheng , Ji Xu , Lu Cao , Dan Yu , Wei Wang , Soeren Prell , Yeuk-Kwan E. Cheung , and Manqi Ruan School of Physics, Nanjing University, Nanjing, China INPAC, SKLPPC, MOE KLPPC, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China Physikalisches Institut der Rheinischen Friedrich-Wilhelms-Universit¨at Bonn, 53115 Bonn, Germany Institute of High Energy Physics, Beijing, China Department of Physics and Astronomy, Iowa State University, Ames, IA, USAReceived: date / Revised version: date
Abstract.
The precise determination of the B c → τν τ branching ratio provides an advantageous opportunity for un-derstanding the electroweak structure of the Standard Model, measuring the CKM matrix element | V cb | and probingnew physics models. In this paper, we discuss the potential of measuring the processes of B c → τν τ with τ decayingleptonically at the proposed Circular Electron Positron Collider (CEPC). We conclude that during the Z pole operation,the channel signal can achieve five σ significance with ∼ Z decays, and the signal strength accuracies for B c → τν τ can reach around 1% level at the nominal CEPC Z pole statistics of one trillion Z decays assuming the total B c → τν τ yield is 1 . × . Our theoretical analysis indicates the accuracy could provide a strong constraint on the general ef-fective Hamiltonian for the b → c τν transition. If the total B c yield can be determined to 1% level of accuracy in thefuture, these results also imply | V cb | could also be measured up to 1% level of accuracy. PACS.
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Weak decays of heavy mesons not only provide a unique plat-form to test the electroweak structures of the Standard Model(SM) but can also shed light on new physics (NP) beyond theSM. Among different species of heavy mesons, the B + c meson,discovered in 1998 by the CDF collaboration [1, 2], is of partic-ular interest in this regard. The B + c meson has specific produc-tion and decay mechanisms, and accordingly the measurementof its mass, lifetime and decay branching ratios would help toprobe the underlining quark dynamics and determine SM pa-rameters.Consisting of two heavy quarks of different types, the B + c meson has three decay categories: 1) b -quark decay with spec-tator c -quark; 2) c -quark decay with spectator b -quark; 3) an-nihilation process (e.g. B + c → τ + ν τ , cs ). The purely leptonicdecay through the annihilation process is sensitive to the de-cay constant f B c and the CKM matrix element | V cb | . Such ascheme has been used for the determination of | V cd | and | V cs | in D + / D + s → τ + ν τ , µ + ν µ [3]. For | V cb | , since the B + c → τ + ν τ channel has not been discovered, it is measured using inclu-sive semileptonic b → c transitions and the exclusive channelof B → D ∗ l ν l . However, even if B + c → τ + ν τ had been discov-ered, the decay B → D ∗ l ν l would still provide a more precise | V cb | measurement. Send offprint requests to : a Email: [email protected] The charge conjugate state is implied throughout the paper.
In recent years a few discrepancies have been found be-tween the SM predictions and different experimental measure-ments in the bottom sector, especially in tauonic decay modesof B mesons [4–6]. In view of no clear signal in the directsearches of NP to date, the implications in low-energy pro-cesses are of great importance. The study of tauonic decaymodes of B mesons, mostly B → D ( ∗ ) τν decays, have indi-cated some hints for lepton flavor universality violation. Whilethese decay modes are very sensitive to vector/axial-vector typeinteractions, the (pseudo)scalar type interactions which can beinduced in many popular NP models, e.g., the two-Higgs dou-blet and leptoquark models are less constrained by them. Dueto the mass hierarchy m τ (cid:28) m B c that results in helicity sup-pression for B + c → τ + ν τ with V − A interactions in the SM, B c → τν has a better sensitivity to the (pseudo)scalar NP inter-actions [7, 8]. Therefore, measurement of the branching ratio B ( B + c → τ + ν τ ) can be a key in the search for NP. As we willshow in Section II, based on the current knowledge, NP canaffect B ( B + c → τ + ν τ ) significantly, which highlights the studyof this quantity in the future.The recently proposed CEPC (Circular Electron PositronCollider) [9] provides an excellent opportunity to measure B ( B + c → τ + ν τ ) . It has a circumference of 100 km and two interac-tion points. Its primary objective is the precision Higgs studyat a center-of-mass-energy ( √ s ) of 240 GeV. Around 10 Higgsbosons will be produced during seven years of operation, im-proving most of the Higgs measurements by around 1 order ofmagnitude compared to the HL-LHC. In addition, a dedicated WW threshold scan ( √ s = −
172 GeV) and the Z factory a r X i v : . [ h e p - e x ] J u l Taifan Zheng et al.: Analysis of B c → τν τ at CEPC mode ( √ s = . Z factory will produce up to one tril-lion Z bosons (Tera- Z ) in two years, far exceeding LEP’s pro-duction [10]. Such a huge data sample will enable high preci-sion tests of the SM and allow to study many previously unob-servable processes. Furthermore, the clean e + e − collision envi-ronment and the well-defined initial state compared to hadroncolliders are advantages for this analysis at the CEPC. (Super)B factories operating at the ϒ (4S) center-of-mass-energy arebelow the energy threshold for B + c production. A detailed dis-cussion on the various advantages and prospects on flavor stud-ies at CEPC can be found in [9].In this paper, we discuss the potential of measuring the pro-cesses of B + c → τ + ν τ , τ + → e + ν e ν τ and τ + → µ + ν µ ν τ atthe CEPC. Important backgrounds are Z → cc and Z → bb ,especially the decay of B + → τ + ν τ in Z → bb events. Both B + c and B + have similar masses and event topologies [3]. Themain difference is the lifetime (the B + c lifetime is around onethird of the B + lifetime). The L3 experiment at LEP had orig-inally searched for B + → τ + ν τ in 1996 with 1 . × Z → qq events [11], and determined B ( B + → τ + ν τ ) < . × − at 90% CL. The study did not consider the contribution from B + c → τ + ν τ . However, [12, 13] later argued the B + c → τ + ν τ contribution could be comparable to the B + → τ + ν τ contribu-tion, and that a similar analysis method could be used to mea-sure B + c → τ + ν τ . Understanding the B + → τ + ν τ backgroundis crucial in this analysis.We estimate the B + c / B + → τ + ν τ event yield at the CEPC Z pole as follows. The number of B + → τ + ν τ events producedis given by: N ( B ± → τ ± ν τ ) = N Z × B ( Z → bb ) × × f ( b → B + X ) × B ( B + → τ + ν τ ) , (1)where N Z is the total number of Z bosons produced. The factortwo accounts for the quark anti-quark pair. The branching ratios B ( Z → bb ) = . ± . f ( b → B + X ) = . ± . B ( B + → τ + ν τ ) = ( . ± . ) × − are taken from [3].For the B c production, the theoretical result at next-to-leadingorder in α s gives B ( Z → B ± c X ) = . × − [24], and ourestimate of B ( B + c → τ + ν τ ) (see the next section) is ( . ± . ) %. These numbers give R B c / B = N ( B ± c → τ ± ν τ ) N ( B ± → τ ± ν τ ) = . ± . , (2)where we use R B c / B to denote the ratio. Note that the actualuncertainty for R B c / B is larger since we lack the uncertainty for B ( Z → B ± c X ) . We conduct our analysis with 10 simulated Z boson decays including ( . ± . ) × B ± → τ ± ν τ events.For simplicity and a larger signal dataset for analysis, we as-sume both N ( B ± c / B ± → τν τ ) are equal to 1 . × and discussother scenarios at the end, since the results are easily scalablefor different values of R B c / B .The rest of this paper is organized as follows. Sect. 2 givesthe decay width of B + c → τ + ν τ in the SM and estimates theeffects in NP scenarios. Sect. 3 introduces the detector, soft-ware and the MC-simulated event samples. Sect. 4 presents theanalysis method and results. The conclusion is given in Sect. 5. W + ¯bc τ + ν τ H + ¯bc τ + ν τ ¯bc τ + ν τ Y − / Fig. 1: Feynman diagrams for tauonic B c decays in the SM,2HDM and LQ models. B + c → τ + ν τ in the SM and in NP models In the SM, the decay width of the purely leptonic decay B + c → l + ν l is given by: Γ SM ( B + c → l + ν l ) = G F π | V cb | f B c m B c m l (cid:32) − m l m B c (cid:33) , (3)where G F is the Fermi coupling constant, V cb is the CKM ma-trix element, f B c is the decay constant, and m B c , m l are themasses of the meson and the charged lepton, respectively. Dueto helicity suppression, the τ final state has the largest branch-ing fraction. The measurement of B + c → τ + ν τ would help todetermine the fundamental parameter | V cb | , once the decay con-stant is known from first-principle calculations, i.e. lattice QCD.Feynman diagram for B + c → τ + ν τ in the SM is shown in the leftpanel of Fig. 1.With the decay constant f B c = ( . ± . ) GeV [14], τ ( B c ) = ( . ± . ) × − s and | V cb | = ( . ± . ) × − [3], we obtain B ( B + c → τ + ν τ ) = ( . ± . ) % , (4)where the errors from the decay constant and lifetime of the B + c have been added in quadrature. The uncertainty in the B + c branching fraction is dominated by the decay constant that mightbe further reduced in a more accurate Lattice QCD calculationin the future.Since the tau lepton has the largest mass compared to theother two species of leptons, the NP coupling might have amore evident effect in tauonic decays of heavy mesons. Twopopular NP models include the two Higgs doublet model (2HDM)with a charged Higgs boson propagator similar to the W bosonpropagator, and the leptoquark (LQ) models that couple lep-tons with quarks. The charged Higgs boson in 2HDM can havea significant coupling with the tau, and thereby its contributionsto decay widths could be sizable [15].Theoretical studies of NP contributions can be conducted intwo distinct ways. One is to confront the explicit model predic-tions one by one with available experimental constraints, whilethe other is to employ an effective field theory (EFT) approach.Integrating out the massive particles, e.g. charged Higgs parti-cle or the LQ in Fig. 1, the NP contributions are incorporatedinto a few effective operators, with the interaction strengths em-bedded in Wilson coefficients. A general effective Hamiltonianfor the b → c τν transition can be written as H eff = G F √ V cb [( + C V ) O V + C V O V + C S O S + C S O S ] + h . c . , (5) aifan Zheng et al.: Analysis of B c → τν τ at CEPC 3 - - - - - - [ C V ] I m [ C V ] - Fig. 2: Sensitivities of ( Γ total − Γ SM ) / Γ SM ( % ) to C V . The SMlies at the origin with Re [ C V ] = Im [ C V ] =
0. Labels (in unitsof %) on contours denote the modification of branching ratios(decay widths) with respect to the SM values. The red shadedarea corresponds to the global fitted results of available dataon b → c τν decays, as shown in Eq. (9). These areas deviatefrom the SM predictions by about a few σ .where O i are four-fermion operators and C i are the correspond-ing Wilson coefficients. The four-fermion operators are definedas O V = ( ¯ c L γ µ b L ) (cid:0) ¯ τ L γ µ ν L (cid:1) , O V = ( ¯ c R γ µ b R ) (cid:0) ¯ τ L γ µ ν L (cid:1) , O S = ( ¯ c L b R ) ( ¯ τ R ν L ) , O S = ( ¯ c R b L ) ( ¯ τ R ν L ) . (6)where O V is the only operator present in the SM. The 2HDMcan contribute to O S , while the LQs can have more versa-tile contributions depending on their spin and chirality in cou-plings.Having Eq.(5) and Eq.(6) at hand, one arrives at Γ total ( B + c → τ + ν τ ) Γ SM ( B + c → τ + ν τ ) = (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) + C V − C V + C S m B c m (cid:96) − C S m B c m (cid:96) (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) , (7)where m B c ≡ m B c / ( m b + m c ) . This expression shows the devi-ation of decay width of B + c → τ + ν τ compared with the SM.Inspired by the experimental measurements of B → D ( ∗ ) τν and other decays induced by b → c τν , quite a few theoreticalanalyses of NP contributions have been made in recent years.In this work, we will make use of the results for the Wilsoncoefficients from Refs.[16, 17]: | + Re [ C V ] | + | Im [ C V ] | = . ± . , (8) C V = ( − . ± . ) ± ( . ± . ) i , (9) C S = ( . ± . ) + ( . ± . ) i , (10) C S = ( − . ± . ) ± ( . ± . ) i , (11) - - - - - - [ C S ] I m [ C S ] Fig. 3: Sensitivities of ( Γ total − Γ SM ) / Γ SM ( % ) to C S . The SMlies at the origin with Re [ C S ] = Im [ C S ] =
0. Labels (in unitsof %) on contours denote the modification of branching ratios(decay widths) with respect to the SM values. The red shadedarea corresponds to the global fitted results of available dataon b → c τν decays, as shown in Eq. (10). - - - - - [ C S ] I m [ C S ] Fig. 4: Similar to Fig. 3 with red shaded area as parameterspace of C S given in Eq. (11).and the masses: m B c = . , m b = .
18 GeV , m c = .
27 GeV , m τ = . . (12)Eq. (8) directly implies that the branching fraction of B + c → τ + ν τ can be affected by ( . ± . ) % if only the SM-like V − A operator O V is included. If O V is considered, the con-tributions to ( Γ total − Γ SM ) / Γ SM are shown in Fig. 2. The redshaded area in this figure corresponds to the global fitted re-sults of data on B meson decays induced by b → c τν , as shown Taifan Zheng et al.: Analysis of B c → τν τ at CEPC in Eq. (9). In this figure and the following ones, we do not con-sider the correlation between the real and imaginary part in theWilson coefficients. Two branches are found due to the ambigu-ous sign in the imaginary part of C V . From this figure, one caninfer that the NP contributions range from about 10% to 30%.In these two scenarios, branching fractions of B + c → τ + ν τ aremildly affected due to helicity suppression.If we switch to O S , the results are shown in Fig. 3, andagain the red shaded area corresponds to the global fitted resultsshown in Eq. (10). Similar results are shown in Fig. 4 for O S .In these two figures, one can clearly see that Γ ( B + c → τ + ν τ ) is dramatically affected by NP contributions. At this stage theerrors do not allow a very conclusive result on the existenceof NP, and accordingly measurements of this width at CEPCwould help to confirm or rule out these NP scenarios.Next let’s consider the | V cb | measurement in the SM sce-nario. Its uncertainty can be derived from the relative uncer-tainty of the signal strength σ ( µ ) / µ . The signal strength µ is the ratio between the measured effective cross section andthe corresponding SM prediction, and σ ( µ ) is its uncertainty.Therefore it is straightforward that: σ ( µ ) µ = σ ( N ( B ± c → τν τ )) N ( B ± c → τν τ ) = σ ( B ( Z → B ± c X ) B ( B + c → τ + ν τ )) B ( Z → B ± c X ) B ( B + c → τ + ν τ )= σ ( B ( Z → B ± c ) Γ SM ( B + c → τ + ν τ ) / Γ ( B + c )) B ( Z → B ± c ) Γ SM ( B + c → τ + ν τ ) / Γ ( B + c ) , (13)where Γ ( B + c ) is the total width of the B + c . Substituting Eq. (3)into the above equation and we have: (cid:18) σ ( µ ) µ (cid:19) = (cid:18) σ ( B ( Z → B ± c X )) B ( Z → B ± c X ) (cid:19) + (cid:18) σ ( | V cb | ) | V cb | (cid:19) + (cid:18) σ ( f B c ) f B c (cid:19) + (cid:18) σ ( Γ ( B + c )) Γ ( B + c ) (cid:19) + Cov. + O ( − ) , (14)where Cov. refers to the covariances between variables. The σ ( f B c ) / f B c and σ ( Γ ( B + c )) / Γ ( B + c ) are both at 1% level. Sect. 4shows that σ ( µ ) / µ is also likely at 1% level at Tera- Z . Thisleaves the error terms to be dominated by the B + c productionterm, which has a much bigger uncertainty, and will determinethe uncertainty of | V cb | . If the B + c production term can be de-termined to 1% level in the future and the covariances are alsoaround the same level or less, the | V cb | could be determined to1% level as well. The CEPC CDR (conceptual design report) [9] provides a de-tailed description of the detector setup and the software infras-tructure. Both of them are inspired by the International LargeDetector (ILD) of the International Linear Collider (ILC) andoffer comparable performances. The general flow of softwareis as follows: 1) create simulated event samples using Pythia[18] and Whizard [19], 2) the MokkaPlus [20], a GEANT4[21] based simulation tool, simulates the interaction with thedetector, 3) the reconstruction framework mimics the electron-ics’ responses and creates physics objects. Upon completing the standard procedures, two more softwares are used for fur-ther analysis. One is the LCFIPlus [22], an ILC software whichcan perform jet clustering and flavor tagging operations to sep-arate different quark flavors in Z → qq . The other one is theTMVA [23], a multi-variable analysis tool for BDT (boosteddecision tree) training. Electron energy/GeV0 10 20 30 E n t r i e s Fig. 5: Signal electron energy distribution
Electron energy/GeV0 10 20 30 F r ac ti on EfficiencyPurityEfficiencyPurity
Fig. 6: Signal electron reconstruction efficiency and purityversus energy.The simulated sample consists of Z → qq , B + → τ + ν τ and B + c → τ + ν τ . The latter two are additional Z → qq events thatcontain the corresponding processes. In order to save time, only aifan Zheng et al.: Analysis of B c → τν τ at CEPC 5 a fraction of the qq (do not include B + c / B + → τ + ν τ ) events thatare sufficient for analysis are actually simulated. The data arethen scaled to reach the sample size corresponds to 10 Z bosondecays.Since we are looking for leptonic final states, it is eluci-dating to demonstrate the lepton reconstruction performanceof CEPC. Figure 5 shows the generated energy spectrum ofthe signal electrons of 1.76 × B + c → τ + ν τ , τ + → e + ν e ν τ events. We define the efficiency as the fraction of correctlyidentified electrons with respect to the total number of gener-ated electrons. The purity is defined as the fraction of correctlyidentified electrons among all of the reconstructed particles thatare associated with electrons. The dependence of the electronefficiency and purity on the electron energy in signal events isshown in Fig. 6. The relative high energy of the signal electronand the clean environment enables a high efficiency and purity.The muon final state has a similar performance. The characteristic event topology of B + c / B + → τ + ν τ , τ + → e + / µ + νν is shown in Fig. 7. The entire space can be dividedinto two hemispheres by the plane normal to the thrust axis.The thrust axis is the unit vector ˆ n which maximizes T = Σ i | p i · ˆ n | Σ i | p i | , (15)where p i is the momentum of the i th final state particle. Thedirection points towards the hemisphere with less total energy.The hemisphere in which the B + c / B + → τ + ν τ , τ + → e + / µ + νν decay occurs is the signal hemisphere and the other one is thetag hemisphere. The main event topology features are: 1) a b-jet in the tag hemisphere, 2) a single energetic e or µ with rel-atively large impact parameter along the thrust axis, 3) largeenergy imbalance between the signal and the tag hemispheredue to missing neutrinos in the signal hemisphere, 4) some softfragmentation tracks are also present. Based on the above def-initions and features, it is clear that the thrust axis will mostlypoint towards the signal hemisphere. And the impact parame-ter is defined as follows: find the point on the thrust axis thatis closest to the track, the impact parameter is the signed dis-tance from the point to the interaction point. If the point liesin the signal hemisphere, then the impact parameter is positive,otherwise it is negative. Therefore, the signal lepton’s impactparameter characterizes the total decay length of the B mesonand the τ . The main difference between B + and B + c events is theimpact parameter due to the difference between their lifetimes.The general analysis strategy is:1. Employ a cut chain which exploits the main features ofthe event topology to reduce most of the backgrounds from Z decays to light flavor jets.2. Use a BDT to separate B + c / B + → τ + ν τ , τ + → e + / µ + νν from heavy flavor jets. In this case both the B c and B events areconsidered as signal.3. Use another BDT to separate between B + c and B + events. Fig. 7: B c / B → τν , τ → e / µνν event topology. Be remindedthat the extension of the lepton track passes close by the thrustaxis, but does not need to intersect it.Using two BDTs allows us to maximize the separation powerof the final state lepton’s impact parameter in the second BDTwhere it will be used as an additional parameter. However, lim-ited by the amount of simulated events, we do not have suffi-cient MC data left after a cut on the output of the first BDT isapplied to conduct a meaningful analysis of the second BDTcut. The solution is to apply the second BDT to a larger set ofdata and scale the results down to our original assumption. Thedetails will be explained later. We begin with the electron finalstate and apply the same method to the muon final state as theyare highly similar. The first stage cut chain is described in thefollowing:1. The b-tagging score (ranging from zero to unity) hasto be greater than 0.6. This reduces most of non- bb qq back-grounds.2. The energy asymmetry, defined as the total energy inthe tag hemisphere subtracted by the total energy in the sig-nal hemisphere, has to be larger than 10 GeV. This step signif-icantly reduces all of qq events again while preserving most ofthe B + / B + c events.3. The signal hemisphere needs to have at least one elec-tron. In case of multiple electrons, the most energetic one isselected for analysis. Most of the signal electrons have suffi-cient momenta to hit the electromagnetic calorimeter and meetthe requirement.4. The electron is the most energetic particle in the signalhemisphere.5. The nominal B meson energy is greater than 20 GeV. Thequantity is defined as: E B = . − all visible energy except the signal electron . Table 1 shows the number of events during the cut chain.We have eliminated most of the light flavor backgrounds. Al-though their total number is comparable to the signal, consid-
Taifan Zheng et al.: Analysis of B c → τν τ at CEPC Table 1: The cut chain for the electron final state. The numbers in the parentheses are corresponding scale factors. B ± c → τν τ B ± → τν τ dd ( ) + uu ( ) + ss ( ) cc ( . ) bb ( . ) τ → e νν excl. τ → e νν τ → e νν excl. τ → e νν All events 2352 10584 2289 10647 409929226 119954033 150563659b-tag > >
10 GeV 1520 6249 1381 5883 476126 1609771 29919812Has electron insignal hemisphere 1352 1334 1231 1161 140300 625670 15828883Electron is the mostenergetic particle 996 126 876 108 8270 79190 4565454 E B >
20 GeV 987 120 873 105 953 34147 31876351 st BDT score > st BDT score > nd BDT score > nd BDT score > ering the corresponding scale factors, and they are likely to beeliminated by the following process, we ignore the events on-wards.After the first stage cut chain, we choose several variablesfor the BDT to eliminate bb and cc backgrounds. Some of thevariables have been used in the L3 analysis [11]. They are listedas following: – Nominal B meson energy. – Maximum neutral cluster energy inside a 30 degree conearound the thrust axis in the signal hemisphere. – Electron’s impact parameter along the thrust axis. – The largest impact parameter along the thrust axis in thesignal hemisphere besides the selected electron. After thecut chain, in most events the signal electron has the largestimpact parameter in the signal hemisphere. – Energy asymmetry. – Second largest track momentum in the signal hemisphere. – Electron’s energy.We then apply cuts on the outputs of two BDTs as describedbefore. In the first BDT, we use all but the electron’s impact pa-rameter along the thrust axis. The parameter will then be addedin the second BDT. Our solution for the aforementioned prob-lem of insufficient data for second training is as follows:1. use the first training result to evaluate 1 . × B + c / B + → τ + ν τ , τ + → e + ν e ν τ events each . Other τ decay channels andthe qq events are ignored.2. cut at the same BDT score in Table 1.3. perform the second BDT training using electron’s impactparameter as additional variable.4. scale down the results to match the original statistics.The extreme values in the BDT variable distrbutions are cutbefore training and the entire data are randomly split in equalamounts for training and test, respectively. Corresponds to one million B + c / B + → τ + ν τ events each, basedon the B ( τ + → e + ν e ν τ ) . BDT score st E n t r i e s nn e fi t , nt fi /B c B b b fi Z c c fi Z ) nn e fi t (excl. nt fi /B c B(Test data) nn e fi t , nt fi /B c B nn e fi t , nt fi /B c B b b fi Z c c fi Z ) nn e fi t (excl. nt fi /B c B(Test data) nn e fi t , nt fi /B c B Fig. 8: The first BDT score for the training data and the testsignal data. Here the notation B c / B means the combination ofthe two data.The first BDT score for the training data and the test signaldata are shown in Fig. 8. The presence of the signal is apparentat large BDT scores and we have a good matching between thetraining and test signal data. We apply a cut on the BDT score atzero. The second BDT score is shown in Fig. 9. The histogramsare already scaled to match 10 Z boson decays and we cut onthe second BDT score also at zero. Numbers from both resultsare shown in Table 1. aifan Zheng et al.: Analysis of B c → τν τ at CEPC 7 BDT score nd E n t r i e s (Training data) nn e fi t , nt fi c B(Test data) nn e fi t , nt fi c B(Training data) nn e fi t , nt fi B (Test data) nn e fi t , nt fi B (Training data) nn e fi t , nt fi c B(Test data) nn e fi t , nt fi c B(Training data) nn e fi t , nt fi B (Test data) nn e fi t , nt fi B Fig. 9: The second BDT score.Now we can compute the relative accuracy of the signalstrength: σ ( µ ) / µ = (cid:112) N S + N B / N S , (16)where N S and N B denote the number of signal and backgroundevents that pass all selection cuts, respectively. We computethe quantity using the test data results multiplied by 2 . Herewe assume that all of the other backgrounds from the test dataof the first BDT cut survive the second BDT cut, which means N B = ( + + + + ) × = σ ( µ e ) / µ e = . e indicates the electron final state. This is worse than the σ ( µ e ) / µ e from the first BDT training, which is 8.5%. The totalnumber of non- B + → τ + ν τ , τ + → e + ν e ν τ backgrounds in thetest data after the second BDT cut has to be below 24 to achievethe same accuracy. This can be reliably verified with a larger setof data. We can repeat the entire process for the muon final stateand the cut chain is shown in Table 2, and σ ( µ µ ) / µ µ = . σ ( µ ) / µ = . . × Z decays toachieve 5 σ significance. It is now straightforward to calculatethe σ ( µ ) / µ for both B + c / B + → τ + ν τ at Tera- Z at various sig-nal luminosities. Figure 10 shows their relationship with R B c / B .Here, the yield N ( B ± → τ + ν τ ) is fixed at 1 . × per one bil-lion Z . The projected σ ( µ ) / µ s at Tera- Z are around 1% levelfor both B + c → τ + ν τ and B + → τ + ν τ . In Sect. 2 we have dis-cussed the | V cb | measurement and with current results we arguethat the accuracy could reach up to 1% level with certain im-provements. Which means we are extrapolating the test data, which representshalf of our analysis sample, to all of the sample. /B c B R -2 -1
10 1 10 / % f o r T e r a - Z m ) / m ( s -2 -1 nt fi c B nt fi B nt fi c B nt fi B Fig. 10: σ ( µ ) / µ at Tera- Z versus R B c / B . The estimated rangeof R B c / B in Eq. (2) is shown in red band. Be reminded that theactual uncertainty is larger since we lack uncertainty for B ( Z → B ± c X ) . As we have shown in Sec. 2, based on the current results on NPin b → c τν , the Γ ( B + c → τ + ν τ ) tends to deviate from SM pre-dictions, but the statistical importance is not significant. FromFig. 10, one can see that at CEPC the σ ( µ ) / µ for B + c → τ + ν τ can reach about 1% level. This includes the constraint in boththe production of B + c and the decay into τ + ν τ . If the productionmechanism is well understood, the result on σ ( µ ) / µ wouldalso imply that the uncertainties in Γ ( B + c → τ + ν τ ) are reducedto the percent level. On the other side, in the future one can alsouse the B ( B + c → J / ψπ + ) as a calibration mode. In theory theLattice QCD can calculate the B c → J / ψ transition form fac-tors while the perturbative contributions are well under controlin perturbation theory.One can use such results on Γ ( B + c → τ + ν τ ) to probe NP toa high precision. In Fig. 11, we show the constraints on Re [ C V ] and Im [ C V ] . If the central values in Eq. (9) remain the samewhile the uncertainty in Γ ( B + c → τ + ν τ ) is reduced to 1%, theallowed region for C V shrinks as the dark-blue region, wherethe deviation from the SM is greatly enhanced.Similar results can be obtained for NP coefficients C S and C S , but as we have demonstrated in Sec. 2, both scenarios willinduce dramatic changes to Γ ( B + c → τ + ν τ ) . These NP effectsare so large that they would already be verified or ruled outbefore entering into the very precision era of the CEPC. Thusit is less meaningful to present the constraints for these twocoefficients. Nowadays hunting for new physics beyond the Standard Modelis a primary objective in particle physics. In this paper, we have
Taifan Zheng et al.: Analysis of B c → τν τ at CEPC Table 2: The cut chain for the muon final state. The qq data is scaled in the same way as in Table 1. B ± c → τν τ B ± → τν τ dd ( ) + uu ( ) + ss ( ) cc ( . ) bb ( . ) τ → µνν excl. τ → µνν τ → µνν excl. τ → µνν All events 2256 10680 2279 10657 409929226 119954033 150563659b-tag > >
10 GeV 1428 6341 1428 5832 476126 1609771 29919812Has Muon insignal hemisphere 1224 2304 1232 2282 239356 813083 19476244Muon is the mostenergetic particle 936 231 903 180 9541 89290 4920088 E B >
20 GeV 932 223 892 174 1674 39583 34999931 st BDT score > st BDT score > nd BDT score > nd BDT score > - - - - [ C V ] I m [ C V ] Fig. 11: Constraints on the real and imaginary parts of C V .The red shaded area corresponds to the current constraintsusing available data on b → c τν decays. If the central valuesin Eq. (9) remain while the uncertainty in Γ ( B + c → τ + ν τ ) isreduced to 1%, the allowed region for C V shrinks to thedark-blue region.first demonstrated that the decay B + c → τ + ν τ provides a uniqueopportunity to probe new physics contributions especially tothe (pseudo)scalar interactions that exist in many popular mod-els like the two Higgs doublet model and the leptoquark mod-els. We then analyzed the decay B + c → τ + ν τ , τ + → e + / µ + νν at the CEPC Z pole. We took references of the methods used in the L3 analysis [11] on the search of B + → τ + ν τ , which sharesa similar event topology. The backgrounds under considerationare Z → qq , B + → τ + ν τ as well as other τ decay channels of B + c → τ + ν τ . We used a first stage cut chain to suppress mostof the light-flavor backgrounds, and subsequently used 2-stageBDT method to perform a fine-tuned multi-variable analysis.The first BDT separates heavy flavor backgrounds and the sec-ond BDT separates B + → τ + ν τ events. The current detectordesign and reconstruction algorithms provide excellent signallepton reconstruction efficiency and purity, and do not pose sig-nificant constraints on the analysis. We have demonstrated thatunder current estimates for N ( B ± c → τ ± ν τ ) , we need around ∼ Z decays to achieve five σ significance. The relative ac-curacy of signal strength could reach around 1% level at Tera- Z . If the total B + c yield can be determined to 1% level accu-racy in the future the | V cb | can also be expected to be mea-sured to 1% level of accuracy. Our theoretical analysis showsthe channel has a good potential for NP search and could pro-vide a significant constraint on the NP related to the Wilsoncoefficient C V in Eq. (5). We also showed the projected sig-nal strength accuracy for various signal event numbers for both B + c / B + → τ + ν τ . The results could be improved with a moreexhaustive analysis, especially the inclusion of hadronic τ de-cays and a larger sample of MC-simulated events.To summarize, we have demonstrated the CEPC’s bench-mark capability on the B + c → τ + ν τ study. The results show theCEPC could provide a new opportunity to search for the NPsuch as the 2HDM and LQ models, measure | V cb | and test ourunderstanding of QCD. Acknowledgement
We thank Yiming Li, Haibo Li and Jianchun Wang for use-ful discussions, and Chengdong Fu and Gang Li for providingsome of the samples and tools. We give special thank to Fen-fen An for some preliminary studies and useful discussions. aifan Zheng et al.: Analysis of B c → τν τ at CEPC 9 This work is supported by the Beijing Municipal Science &Technology Commission, project No. Z181100004218003 andZ191100007219010, the Natural Science Foundation of Chinaunder grant No. 11735010, 11911530088, 11775110, and 11690034, the Natural Science Foundation of Shanghai under grantNo. 15DZ2272100, the DFG Emmy-Noether Grant No. BE6075/1-1. We also acknowledge the Priority Academic Pro-gram Development for Jiangsu Higher Education Institutions(PAPD).
References
1. F. Abe et al. [CDF], Phys. Rev. Lett. , 2432-2437 (1998) doi:10.1103/PhysRevLett.81.2432 [arXiv:hep-ex/9805034 [hep-ex]].2. F. Abe et al. [CDF], Phys. Rev. D , 112004 (1998)doi:10.1103/PhysRevD.58.112004 [arXiv:hep-ex/9804014[hep-ex]].3. P.A. Zyla et al. (Particle Data Group), to be published inProg. Theor. Exp. Phys. 2020, 083C01 (2020).4. J. Lees et al. [BaBar], Phys. Rev. Lett. (2012), 101802doi:10.1103/PhysRevLett.109.101802 [arXiv:1205.5442[hep-ex]].5. A. Abdesselam et al. [Belle], [arXiv:1904.08794 [hep-ex]].6. R. Aaij et al. [LHCb], Phys. Rev. Lett. (2018), 171802doi:10.1103/PhysRevLett.120.171802 [arXiv:1708.08856[hep-ex]].7. X. Q. Li, Y. D. Yang and X. Zhang, JHEP , 054(2016) doi:10.1007/JHEP08(2016)054 [arXiv:1605.09308[hep-ph]].8. R. Alonso, B. Grinstein and J. M. Camalich, Phys. Rev. Lett. , 081802 (2017) doi:10.1103/PhysRevLett.118.081802[arXiv:1611.06676 [hep-ph]].9. CEPC Study Group, [arXiv:1811.10545 [hep-ex]].10. Line Shape Sub-Group of the LEP Electroweak Work-ing Group, DELPHI, LEP, ALEPH, OPAL, L3 Collabora-tion, Combination procedure for the precise determinationof Z boson parameters from results of the LEP experiments,[arXiv:hep-ex/0101027]. 11. M. Acciarri et al. [L3], Phys. Lett. B , 327-337 (1997)doi:10.1016/S0370-2693(97)00138-X12. M. L. Mangano and S. Slabospitsky, Phys. Lett. B , 299-303 (1997) doi:10.1016/S0370-2693(97)00953-2[arXiv:hep-ph/9707248 [hep-ph]].13. A. Akeroyd, C. H. Chen and S. Recksiegel, Phys.Rev. D , 115018 (2008) doi:10.1103/PhysRevD.77.115018[arXiv:0803.3517 [hep-ph]].14. B. Colquhoun et al. [HPQCD], Phys. Rev. D (2015), 114509 doi:10.1103/PhysRevD.91.114509[arXiv:1503.05762 [hep-lat]].15. W. S. Hou, Phys. Rev. D , 2342 (1993).doi:10.1103/PhysRevD.48.234216. Z. R. Huang, Y. Li, C. D. Lu, M. A. Parachaand C. Wang, Phys. Rev. D (2018), 095018doi:10.1103/PhysRevD.98.095018 [arXiv:1808.03565[hep-ph]].17. K. Cheung, Z. R. Huang, H. D. Li, C. D. L, Y. N. Mao andR. Y. Tang, [arXiv:2002.07272 [hep-ph]].18. The Pythia Group, An Introduction to PYTHIA 8.2, Com-put. Phys. Commun. (2015).19. W. Kilian, T. Ohl, J. Reuter, WHIZARD: simulating multi-particle processes at LHC and ILC , Eur. Phys. J. C , 1742(2011).20. C.D. Fu, Full simulation software at CEPC, http://cepcdoc.ihep.ac.cn/DocDB/0001/000167/001 , Ac-cessed 23 Oct 2017.21. S. Agostinelli et al. , Geant4-a simulation toolkit. Nucl. In-strum. Methods Phys. Res. Sect. A Accel. Spectrom. Detect.Assoc. Equip. , 250303 (2003)22. T. Suehara, T. Tanabe, LCFIPlus: A framework for jet anal-ysis in linear collider studies, Nuclear Instruments and Meth-ods in Physics Research Section A: Accelerators, Spectrom-eters, Detectors and Associated Equipment, Feburary, 2016.23. A. Hocker et al ., TMVA-toolkit for multivariate data anal-ysis, physics/0703039, CERN-OPEN-2007-00724. J. Jiang, L. B. Chen and C. F. Qiao, Phys. Rev.D91