1 Introduction

WSU–HEP–XXYY May 6, 2018

leptonic and semileptonic decays

Hailong Ma (For BESIII Collaboration)

Institute of High Energy Physics, Chinese Academy of Sciences

Based on 2.92 fb data taken at the center-of-mass energy GeV with the BESIII detector, we report recent results on the decay constant , the hadronic form factors, as well as the quark mixing matrix elements , which are extracted from analyses of the leptonic decay and the semileptonic decays , , and at BESIII.

PRESENTED AT

The 7th International Workshop on Charm Physics (CHARM 2015)

Detroit, MI, 18-22 May, 2015

## 1 Introduction

In the Standard Model, the mesons decay into via a virtual boson. The decay rate of the leptonic decays can be parameterized by the decay constant via

 Γ(D+→ℓ+νℓ)=G2F8π|Vcd|2fD+m2ℓmD+(1−m2ℓm2D+), (1)

where is the Fermi coupling constant, is the quark mixing matrix element between the two quarks , and are the lepton and masses.

On the other hand, the semileptonic decays can be parameterized by the quark mixing matrix element and the form factor of hadronic weak current simply, thus providing an ideal window to probe for the weak and strong effects. For example, the differential decay rates of can be simply written as

 dΓdq2=G2F24π3|Vcs(d)|2p3K(π)|fK(π)+(q2)|2, (2)

where is the Fermi coupling constant, is the quark mixing matrix element between the two quarks , is the kaon(pion) momentum in the rest frame, is the form factor of hadronic weak current depending on the square of the four momentum transfer .

In 2010 and 2011, BESIII [1] accumulated 2.92 fb data at = 3.773 GeV [2], where or is produced predominantly. Based on the studies of the leptonic and semileptonic decays of and mesons, the decay constant, the hadronic form factors or the quark mixing matrix elements can be extracted accurately. These will validate the LQCD calculations of the decay constant and the hadronic form factors or test the unitarity of the quark mixing matrix at higher accuracies. They are also helpful to improve the measurement precisions in the experimental studies of the leptonic and semileptonic decays of mesons indirectly. Herein, we report recent results on the studies of the leptonic decay and the semileptonic decays , , and at BESIII. Throughout the proceeding, charge conjugate is implied.

## 2 Leptonic decay [3]

To investigate the leptonic decay , we reconstruct the singly tagged mesons using 9 hadronic decays. Figure 1 (left side) shows the fits to the beam-energy-constrained mass () spectra of the (a) , (b) , (c) , (d) , (e) , (f) , (g) , (h) and (i) combinations, which yield singly tagged mesons.

Figure 1 (right side) shows the distribution of the candidates for , which are selected in the systems against the singly tagged mesons. We obtain signals of , which yields the branching fraction

 B(D+→μ+νμ)=(3.71±0.19stat.±0.06sys.)×10−4.

Using the measured and the quark mixing matrix element from a global Standard Model fit [4], we determine the decay constant

 fD+=203.2±5.3stat.±1.8sys. MeV.

The and measured at BESIII are consistent within errors with those measured at BESI [5], BESII [6] and CLEO-c [7], but with the best precision. Figure 2 compares the measured at BESIII and CLEO-c as well as those calculated by recent theories.

So far, the quark mixing matrix element has been measured though experimental studies of the semileptonic decay or measurement of charm production cross section of interaction, among which the best measurement precision is 4.8% [4]. By using the measured and the Lattice QCD calculation on [8], we determine

 |Vcd|=0.2210±0.058stat.±0.047sys.,

which has the best precision in the world to date.

## 3 Semileptonic decays

### 3.1 D0 semileptonic decays [9]

To investigate the semileptonic decays , we reconstruct the singly tagged mesons using 5 hadronic decays. Figure 3 (left side) shows the fits to the spectra of the (a) , (b) , (c) , (d) and (e) combinations. singly tagged mesons are accumulated.

Figure 3 (right side) shows the fits to the distributions of the candidates for and , which are selected in the systems against the singly tagged mesons. From the fits, we obtain and signals of and . Based on these, we determine the branching fractions

 B(D0→K−e+νe)=(3.505±0.014stat.±0.033sys.)%

and

 B(D0→π−e+νe)=(0.2950±0.0041stat.±0.0026sys.)%,

respectively. The and measured at BESIII are consistent within errors with those measured at BESII [10], CLEO-c [11], BELLE [12] and BABAR [13, 14], but with the best precision.

Figure 4 shows the fits to the partial widths and the projections on the form factors of and using the Simple Pole model [15], the Modified Pole model [15], the ISGW2 model [16], the two-parameter series expansion (Series.2.Par.) [17] and the three-parameter series expansion (Series.3.Par.) [17]. From the fits, we obtain the extracted parameters of different models, which are summarized in Table 1.

With the extracted and the expected by LQCD [18], we determine the quark mixing matrix element . Figure 5 compares the extracted at BESIII with the ones from other experiments.

### 3.2 D+ Semileptonic decays

To study the semileptonic decays , and , we reconstruct the singly tagged mesons using 6 hadronic decays of , , , , and . About 1.6 millions of singly tagged mesons are accumulated [19]. Based on these, we study the semileptonic decays , and .

#### Analysis of D+→K0Le+νe

Although flights long distance, it interacts with the Electron Magnetic Cluster of BESIII and deposits a portion of energy, thus leaving some position information. So, after reconstructing all other particles in the final states, the mesons can be inferred with the position information and constraining the of the candidates to zero. We obtain about 24 thousands of signals of , based on which we determine the branching fraction

 B(D+→K0Le+νe)=(4.482±0.027stat.±0.103sys.)%

and the CP asymmetry

supporting that there is no CP asymmetry in this decay. In addition, simultaneous fit to the event density for different tag modes with the two-parameter series expansion is performed, as shown in Fig. 6, which yields the product of . These are made for the first time.

#### D+→K−π+e+νe

Based on 18262 signals of , we determine the branching fraction

 B(D+→K−π+e+νe)=(3.71±0.03±0.08)%.

A partial wave analysis (PWA) is performed on the selected candidates, with results shown in Fig. 7. The PWA results show that the dominant component is accompanied by an -wave contribution accounting for of the total rate, and other components can be negligible. We obtain the mass and width of MeV/ and MeV/, the Blatt-Weisskopf parameter , as well as the parameters of the hadronic form factors , , MeV/, MeV/, . Here, the first errors are statistical and the second systematic.

In the above PWA process, the phase of the non-resonant background is factorized by the LASS parameterizations, and the helicity form factors , and are parameterized by the spectroscopic pole dominance (SPD) model. We also make model-independent measurements of the , and the helicity form factors, respectively. The results are consistent with the expectations of the corresponding models and previous measurements.

#### D+→ω(ϕ)e+νe[19]

Based on signals of , we determine the branching fraction

 B(D+→ωe+νe)=(1.63±0.11stat.±0.08sys.)×10−3,

which is consistent with previous measurements but with better precision. We perform amplitude analysis of the selected candidates, with results shown in Fig. 8. We obtain the ratios of the hadronic form factors to be and .

Also, we search for , but do not find obvious signal. So, we set the upper limit on the branching fraction for to be at 90% Confidence Level, which is significantly better than previous searches.

## 4 Summary

By analyses of the leptonic decay and the semileptonic decays , , and from 2.92 fb data taken at 3.773 GeV with the BESIII detector, we extract the decay constant, the hadronic form factors and the quark mixing matrix elements . These provide key experimental data to validate the LQCD calculations of the decay constant and the hadronic form factors and to test the unitarity of the quark mixing matrix at higher accuracies.

ACKNOWLEDGEMENTS

I would like to thank for the support of the National Natural Science Foundation of China (NSFC) under Contracts No. 10935007 and No. 11305180, and the Ministry of Science and Technology of China (973 by MOST) under Contracts No. 2009CB825200 and No. 2015CB856700.

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