Test lepton (cid:13)avor universality with (semi)leptonic D decays at BESIII

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Introduction
In the standard model (SM), the strong and weak interactions in leptonic and semileptonic D decays can be well separated, as shown in Fig. 1. The decay amplitude is described as the vector product of the hadronic current and the leptonic current. As a result, we have [1] for pure leptonic decays, and for semileptonic decays to pseudoscalar mesons, where f D and f + (q 2 ) are the D meson decay constant and hadronic from factor parametrizing the hadronic current, V cs(d) is the Cabbibo-Kobayashi-Maskawa (CKM) matrix element describing the mixing between quark weak eigenstates and flavor eigenstates, G F is the Fermi coupling constant, m D and m ℓ are the masses of D meson and lepton [2], and p P is the momentum of the pseudoscalar meson. Thus, if we calculate the ratio of the decay rates of (semi)leptonic decays involving different generations of leptons, the hadronic currents which are not well calculated in theory are almost canceled out. This gives a very strict constraint on the SM, which can be used to test the lepton flavor universality (LFU).
If there is a new physics (NP) mechanism that couples with different generations of leptons with different strengths, such as NP models involving a charged Higgs boson, or a NP mechanism that allows the lepton to change its flavor, such as the leptoquark mechanism, then the LFU in the SM may be violated [3][4][5][6][7][8]. Evidence of LFU violation has been found in B meson decays in the measurements of R D ( * ) = Γ(B→D ( * ) τ + ντ ) Γ(B→D ( * ) µ + νµ) and [9][10][11][12][13]. While in the charm sector, no significant deviation from the SM prediction has been found [14]. With the world's largest DD samples near threshold, test of the LFU using (semi)leptonic D decays with better precision at BESIII provides a chance to further test the SM and understand the anamolies in B meson decays.
Besides, study of (semi)leptonic D decays allow us to measure the corresponding D meson decay constants, hadronic from factors, and the CKM matrix elements. These measurements can help to validate the theoretical calculations and test the unitarity of the CKM matrix.

The BESIII detector
The BESIII detector is a magnitic spectrometer [15] located at the Beijing Electorn Positron Collider [16]. The cylindrical core of the BESIII detector consists of a heliumbased multilayer drift chamber, a plastic scintillator time-of-flight system (TOF), and a CsI(Tl) electromagnetic calorimeter (EMC), which are all enclosed in superconducting solenoidal magnet providing a 1.0 T magnetic field. The solenoid is supported by an octagonal flux-return yoke with resistive plate counter muon identifier modules interleaved with steel. The acceptance of charged particles and photons is 93% over 4π solid angle. The charged-particle momentum resolution at 1 GeV/c is 0.5%, and the dE/dx resolution is 6% for the electrons from Bhabha scattering. The EMC measures photon energies with a resolution of 2.5% (5%) at 1 GeV in the barrel (end cap) region. The time resolution of the TOF barrel part is 68 ps, while that of the end cap part is 110 ps. The end cap TOF system is upgraded in 2015 with multi-gap resistive plate chamber technology, providing a time resolution of 60 ps [17,18].

The analysis method
For data taken at the center mass energy near DD threshold in e + e − collider, the D mesons are produced in pair. If we fully reconstruct a D meson via hadronic decays (called the single tagged D meson), the other D meson is guaranteed to exist. By searching for the (semi)leptonic decay in the recoiling system of the single tagged D meson, we can then measure its branching fraction (BF) via where N ST and N sig are the number of single tagged D mesons and the number of reconstructed (semi)leptonic events, respectively. ε sig is the efficiency of reconstructing the (semi)leptonic decay in the present of the single tagged D meson. Here the number of reconstructed (semi)leptonic events is determined by examining the kinematic variables of the missing neutrio U miss = E miss − |⃗ p miss | M 2 miss = E 2 miss − |⃗ p miss | 2 where E miss and p miss are the missing energy and missing momentum of the system. For correctly reconstructed (semi)leptonic decays, there variables should peak at zero.

Leptonic D + s decays
In 2014, BESIII collected 482 pb −1 data at the center mass energy of 4.009 GeV (near D + s D − s threshold. Using this data sample, the BFs of leptonic D + s decays are measured with a total number of 15127 ± 321 single tagged D s mesons reconstruced [19]. By constraining the ratio of the decay rates of D + s → τ + ν τ and D + s → µ + ν µ to the SM prediction 9.74, the BFs of these two decays are determined to be (See Fig. 2) MeV. The BFs are also determined without the SM constraint to be In 2016, BESIII collected another 3.19 fb −1 data at the center mass energy of 4.178 GeV. Taking advantage of the much higher e + e − → D + s D * − s cross section here, more precise measurements are perfromed with a total number of about 3.9 × 10 5 single tagged D s mesons reconstructed. The preliminary result of the BF of D + s → µ + ν µ is (See Fig. 3) which is consistent with the SM prediction. The measurement of the BF of D + s → τ + ν τ using this larger data sample is also ongoing.

Leptonic D + decays
Measurements of the BFs of leptonic D + decays are perfromed using 2.93 fb − 1 data at the center mass energy of 3.773 GeV collected in 2010 and 2011. With a total number of about 1.7 × 10 6 single tagged D mesons reconstructed, the BF of D + → µ + ν µ is measured to be (3.71 ± 0.19 ± 0.06) × 10 −4 (See Fig. 4) [20], which gives Meanwhile, preliminary result of the measurement of the BF of D + → τ + ν τ find the evidence of D + → τ + ν τ signal for the first time with a statistical significance of 4 σ (See Fig. 5). The BF is measured to be (1.20±0.24)×10 −3 . Combining these two measurements we have which is consistent with the SM prediction 2.66.  distributions of the muon-like sample (with deposited energy in the EMC less than 300 MeV) and the pion-like sample (with deposited energy in the EMC larger than 300 MeV).

Conclusion
In summary, with the world's largest DD samples near threshold, precision measurements of the BFs of D + (s) → ℓ + ν ℓ , D →Kµ + ν µ and D → πµ + ν µ are performed at BESIII. Besides, CKM matrix elements |V cs(d) |, D meson decay constants f D + Meanwhile, LFU test using (semi)leptonic D decays is perfromed at BESIII, and no significant deviation from the SM prediction is found at current statistics, as summarized in Table 1.