First Measurement of the Absolute Branching Fraction of $\Lambda \to p \mu^- \bar{\nu}_{\mu}$

The absolute branching fraction of $\Lambda \to p \mu^- \bar{\nu}_{\mu}$ is reported for the first time based on an $e^+e^-$ annihilation sample of ten billion $J/\psi$ events collected with the BESIII detector at $\sqrt{s}=3.097$ GeV. The branching fraction is determined to be ${\mathcal B}(\Lambda \to p\mu^- \bar{\nu}_{\mu}) = [1.48\pm0.21(\rm stat) \pm 0.08(\rm syst)]\times 10^{-4}$, which is a significant improvement in precision over the previous indirect measurements. Combining this result with the world average of ${\mathcal B}(\Lambda \to p e^- \bar{\nu}_{e})$, we obtain the ratio, $\frac{\Gamma(\Lambda \to p \mu^- \bar{\nu}_{\mu})}{\Gamma(\Lambda \to p e^- \bar{\nu}_{e})}$, to be $0.178 \pm 0.028$, which agrees with the standard model prediction assuming lepton flavor universality. The asymmetry of the branching fractions of $\Lambda \to p \mu^- \bar{\nu}_{\mu}$ and $\bar{\Lambda} \to \bar{p} \mu^+ \nu_{\mu}$ is also determined, and no evidence for $CP$ violation is found.

The absolute branching fraction of Λ → pµ −ν µ is reported for the first time based on an e + e − annihilation sample of ten billion J/ψ events collected with the BESIII detector at √ s = 3.097 GeV.
The branching fraction is determined to be B(Λ → pµ −ν µ) = [1.48 ± 0.21(stat) ± 0.08(syst)] × 10 −4 , which is a significant improvement in precision over the previous indirect measurements. Combining this result with the world average of B(Λ → pe −ν e), we obtain the ratio, Γ(Λ→pe −ν e) , to be 0.178 ± 0.028, which agrees with the standard model prediction assuming lepton flavor universality. The asymmetry of the branching fractions of Λ → pµ −ν µ andΛ →pµ + νµ is also determined, and no evidence for CP violation is found.
The Standard Model (SM) of particle physics provides precise predictions for the properties and interactions of fundamental particles, which have been confirmed by numerous experimental results (e.g. the discovery of the Higgs boson [1,2]). However, recently there have been indications of tensions between theory and experiment, in particular in the lepton sector [3].
Semileptonic (SL) hyperon decays provide a benchmark to test the SM and complement direct searches for physics beyond the SM, especially for muonic modes which are very sensitive to non-standard scalar and tensor contributions [4]. In the SM, the SL hyperon decays are described by SU (3) flavor symmetry, which enables systematic expansions and accurate predictions with a simplified dependence on hadronic form factors [4]. Therefore, a comparison of the branching fraction (BF) B(Λ → pµ −ν µ ) between its experimental measurement and its SM expectation provides an important probe of physics beyond the SM.
Lepton flavor universality (LFU), which is an acci-dental feature of the SM [5], has been tested in recent years using a variety of different probes, and there are hits for a possible violation of LFU in semileptonic bquark decays. The measurements are obtained from experiments at the B-factories (BaBar [6,7] and Belle [8][9][10][11]), as well as at the LHC (LHCb) [12][13][14][15]. According to the results from the Heavy Flavor Averaging Group, a combined discrepancy at the level of three standard deviations is observed in b → cℓν ℓ decays [16]. A similar comprehensive analysis of exotic effects in s → u transitions has not yet been done, especially for SL hyperon decays, which can be denoted as B 1 → B 2 ℓ −ν ℓ . For the SL hyperon decays, the LFU test observable is the ratio between decay rates of the semimuonic decay and the semielectronic decay, R µe ≡ which is not only sensitive to LFU violation but is also linearly sensitive to the contributions of (pseudo-)scalar and tensor operators [4].
In theory, working at next-to-leading order, the LFU test observable R µe of Λ → p decay is predicted to be 0.153 ± 0.008 [4], while the current experimental measurement is 0.189 ± 0.041 [3]. The large experimental uncertainty is dominated by the BF B(Λ → pµ −ν µ ). So far, experimental information for B(Λ → pµ −ν µ ) has only come from fixed-target experiments [17][18][19][20], which were performed about fifty years ago. The most precise measurement was performed in 1972 [20] and was reported as a relative BF = (1.4 ± 0.5) × 10 −4 based on fourteen signal events which were selected from about 0.6 million bubble chamber pictures. With the current level of precision, the experimental R µe result agrees with the SM prediction. A more accurate measurement of B(Λ → pµ −ν µ ) will provide a more stringent test of LFU.
In addition, it is possible to test for CP violation, which has been observed in K [21] and B meson decays [22,23] and in 2019 in neutral charm meson decays [24]. However, all effects observed so far of CP violation in particle decays cannot explain the observed matter-antimatter asymmetry in the Universe. This motivates further searches for new sources of CP violation, which has not yet been observed in the decays of any baryon. Within the SM, CP violation for downtype quarks (s or b) is expected to be larger than for up-type quark (c) [25], which motivates us to search for CP violation in hyperon decays. In 2019, the BESIII collaboration reported the most precise direct test of CP violation in Λ hyperon nonleptonic decays Λ → pπ − and Λ →pπ + ,nπ 0 [26]. In comparison, no search for CP violation in SL hyperon decays has yet been reported. Hence, a search for CP violation in SL hyperon decays offers complementary information in the hyperon sector.
In this Letter, we report the first measurement of the absolute BF B(Λ → pµ −ν µ ), by analyzing ΛΛ hyperon pairs in ten billion J/ψ meson decay events collected with the BESIII detector at √ s = 3.097 GeV. We use the double-tag (DT) technique [27], which provides a clean and straightforward BF measurement without requiring knowledge of the total number of ΛΛ events produced. Based on the measured absolute branching fraction, B(Λ → pµ −ν µ ), R µe for Λ semileptonic decays is determined. In addition, the CP asymmetry of Λ → pµ −ν µ andΛ →pµ + ν µ is also presented for the first time.
Details about the design and performance of the BESIII detector are given in Refs. [28,29]. Simulated data samples produced with a Geant4-based [30] Monte Carlo (MC) software, which includes the geometric description of the BESIII detector and the detector response, are used to determine the detection efficiencies and to estimate backgrounds. The simulation includes the beam energy spread and initial state radiation in the e + e − annihilations modeled with the generator kkmc [31]. For the simulations of both of the decays Λ → pµ −ν µ and Λ → pe −ν e , we use the form factors of Λ → pe −ν e obtained from experimental measurements, which are summarized in Ref. [32]. The generator constructed in Ref. [26] is used to simulate the dominant background Λ → pπ − decay. An 'inclusive' MC sample of generic events includes both the production of the J/ψ resonance and the continuum processes incorporated in kkmc [31]. The known decay modes are modeled with evtgen [33] using BFs taken from the Particle Data Group [3], and the remaining unknown charmonium decays are modeled with lundcharm [34]. Final state radiation from charged final state particles is incorporated with photos [35].
Using the DT technique, we obtain the BF by reconstructing signal Λ → pµ −ν µ decays in events with Λ decays reconstructed in its dominant hadronic decay mode,Λ →pπ + . If aΛ hyperon is found, it is referred to as a single-tag (ST) candidate. An event in which a signal Λ decay and an STΛ are simultaneously found is referred as a DT event. The BF of the signal decay is given by where N DT is the DT yield, ǫ DT is the DT selection efficiency, and N ST and ǫ ST are the ST yield and the ST selection efficiency. Throughout this paper, chargeconjugated channels are always implied. Good charged tracks detected in the main drift chamber (MDC) must satisfy | cos θ| < 0.93, where θ is the polar angle with respect to the z axis, which is the axis of the MDC. Events with at least two good charged tracks are selected. Combinations of any pair of oppositely-charged tracks are assigned as STΛ candidates without imposing further particle identification (PID) criteria. The pairs are constrained to originate from a common vertex by requiring the χ 2 of the vertex fit to be less than 100. The decay length of theΛ candidate is required to be greater than twice the vertex resolution away from the interaction point. At least oneΛ hyperon is required to be reconstructed successfully via the vertex fits. The taggedΛ hyperons are selected using two variables, the energy difference and the beam-constrained mass where E beam is the beam energy, and pΛ and EΛ are the momentum and the energy of theΛ candidate in the e + e − rest frame. If there are multiple combinations, the one giving the minimum |∆E tag | is retained for further analysis. The taggedΛ are required to satisfy ∆E tag ∈ [−17, 13] MeV. The yield of STΛ hyperons is obtained from a maximum likelihood fit to the M tag BC distribution of the accepted ST candidates, where we use the MCsimulated signal shape convolved with a double-Gaussian resolution function to represent the signal shape and a third order Chebyshev function to describe the backgrounds. The signal yield is estimated in the mass region [1.089, 1.143] GeV/c 2 . The fit result is shown in Fig. 1, and the total STΛ + c.c. yield is N ST = 14, 609, 800 ± 7, 117(stat). Candidate events for Λ → pµ −ν µ decays are selected from the remaining tracks recoiling against the STΛ candidates. We require the total number of all good charged tracks to be four (N Track = 4) with the criteria for additional good charged tracks the same as those used in the ST selection. We further identify a charged track as a µ − by requiring the PID likelihoods calculated by combining the MDC ionization energy loss, time-offlight and electromagnetic calorimeter information satisfy L µ > 0.001 and L µ > L e , where the L µ and L e are likelihoods for the muon and electron hypotheses, respectively. The other track is assumed to be a proton. As the neutrino is not detected, we employ the kinematic variable to obtain information on the neutrino, where E miss and p miss are the missing energy and momentum carried by the neutrino, respectively. E miss is calculated by where E p and E µ − are the measured energies of p and µ − , respectively. We use the magnitude of the constrained Λ momentum to calculate p miss where p Λ , p p and p µ − are the momenta of Λ, p and µ − , respectively, in which p Λ is given by where m Λ is the nominal Λ mass. For signal events, U miss is expected to peak around zero. For the accepted signal candidates of Λ → pµ −ν µ decay, there is still background from the dominant hadronic decay Λ → pπ − , because of misidentification between µ − and π − and π − decay which leads to Λ → pπ − → pµ −ν µ background. To suppress this background, we first impose a four-constraint energy momentum conservation (4C-fit) kinematic fit with the J/ψ → ΛΛ hypothesis. Before the 4C-fit, a Λ is reconstructed based on the pπ − hypothesis to obtain the momentum vector of the Λ. The χ 2 of the 4C-fit is required to be larger than twenty. Second, for this background, the mass recoiling againstΛp, i.e. M recoil Λp , is expected to be the π − mass. Therefore, we require the signal candidates satisfy M recoil Λp > 0.170 GeV/c 2 . This requirement can effectively suppress the Λ → pπ − background, resulting in the relative signal efficiency being 34 times larger than that of the background. Third, after the 4Cfit, if we assign the π − mass to µ − candidates when calculating the invariant mass of pµ − , i.e. M sig pµ(4C) , we can eliminate background by only retaining the events with M sig pµ(4C) ∈ [1.075, 1.100] GeV/c 2 . To verify the reliability of these requirements, ten cross checks varying the criteria above and below the nominal requirements have been performed using the method reported in Ref. [36].
The inclusive MC sample is analyzed using TopoAna [37] to study potential backgrounds. After imposing the above selection criteria, there is no peaking background in the signal region, and the dominant backgrounds are Λ → pπ − and Λ → pe −ν e decays that are included in the determination of the signal yield. For the potential backgrounds that include an extra photon, J/ψ → γΛΛ and Λ → pπ − γ decays, which are studied with corresponding exclusive MC simulation, the J/ψ → γΛΛ decay background is negligible. The Λ → pπ − γ decay background is small but will be taken into consideration as a systematic uncertainty.
To determine the signal yield, an unbinned extended maximum likelihood fit is performed to the U miss distribution. The signal is modeled by the MC-simulated signal shape convolved with a Gaussian resolution function to account for imperfect simulation of the detector resolution. The main backgrounds are modeled  by the MC-simulated shapes obtained from the exclusive MC samples. Other backgrounds are described by a firstorder polynomial. The parameters of the Gaussian, the first-order polynomial, and all yields are left free in the fit. The fit to the data is shown in Fig. 2. The numbers of N ST , ǫ ST , N DT , ǫ DT and the BF of Λ → pµ −ν µ + c.c. are summarized in the first row of Table 1. .100] GeV/c 2 (1.04%) are studied with the control sample J/ψ → Λ(→ pπ − )Λ(→pπ + ) using the method reported in Ref. [26]. For the simulation of the signal MC model (2.80%), it is estimated by varying the input values of form factors [32] by one standard deviation. Other sources of systematic uncertainty include the following items: the MC statistics (0.01%); the proton tracking (1.00%), muon tracking (1.00%) and the muon PID (2.00%), which are cited from Refs. [38,39]; the fits to the U miss (1.87%) and M tag BC (2.17%) distributions estimated by using alternative fit procedures, i.e. changing the signal and background shapes for both of these fits and changing the bin size for the fit to the M tag BC distribution. For the fit to U miss , the signal shape is changed by removing the Gaussian resolution function, and the background shapes are changed in three ways. First, we convolve the background shapes with the Gaussian resolution function which is the same as the one for the signal shape. Then, the Λ → pπ − γ MC-simulated shape is added. Finally, we change the input parameters [26] by one standard deviation to determine the Λ → pπ − MC-simulated shape. The total systematic uncertainty is estimated to be 5.55% by adding all these uncertainties in quadrature. Finally, we obtain the BF, B(Λ → pµ −ν µ ) = (1.48 ± 0.21 ± 0.08) × 10 −4 , where the first uncertainty is statistical and the second is systematic. Combining with the well-measured BF of the decay Λ → pe −ν e , B(Λ → pe −ν e ) = (8.32 ± 0.14) × 10 −4 [3], we determine the ratio R µe ≡ Γ(Λ→pµ −ν µ ) Γ(Λ→pe −ν e) to be R µe = 0.178 ± 0.028. This result is consistent within uncertainties with the value 0.153 ± 0.008 that is expected from LFU in the SM [4].

Decay mode
The BFs of the charge-conjugated decays Λ → pµ −ν µ andΛ →pµ + ν µ , B Λ→pµ −ν µ and BΛ →pµ + νµ , are measured separately. The asymmetry of these two BFs is determined as The corresponding N ST , N DT , ǫ ST , ǫ DT and the BFs are summarized in the last two rows of Table 1.
The asymmetry is determined to be A CP = 0.02 ± 0.14(stat)±0.02(syst), where the systematic uncertainties of N Track = 4, Λ reconstruction through the vertex fit, the 4C-fit, the M recoil Λp > 0.170 GeV/c 2 , the M sig pµ(4C) ∈ [1.075, 1.100] GeV/c 2 and the signal MC model cancel. Other systematic uncertainties are estimated separately as above. No evidence for CP violation is found.
In summary, using ten billion J/ψ decay events collected with the BESIII detector at √ s = 3.097 GeV, the semileptonic hyperon decay Λ → pµ −ν µ is studied at a collider experiment for the first time. Based on the double-tag method, we report the first measurement of the absolute BF of Λ → pµ −ν µ as B(Λ → pµ −ν µ ) = [1.48 ± 0.21(stat) ± 0.08(syst)] × 10 −4 which improves the precision of the world average value significantly. The BF is consistent with theoretical predictions that incorporate quark SU(3) flavor symmetry without symmetry breaking [40], and predictions based on the factorization of the contribution of valence quarks and chiral effects [41].
Using the well-measured branching fraction of the decay Λ → pe −ν e , we determine the ratio R µe ≡ Γ(Λ→pµ −ν µ ) Γ(Λ→pe −ν e ) to be R µe = 0.178 ± 0.028 which is in agreement with the previous results but is the most precise to date. The R µe result agrees with LFU, and the higher precision can aid in the study of the (pseudo-)scalar and tensor operator contributions in theory [4]. The asymmetry of the BFs of charge-conjugated decays Λ → pµ −ν µ andΛ →pµ + ν µ is also determined. No evidence for CP violation is found.