Highlight of Charm Physics at BESIII

In this talk, we present the recent results of charm physics from the BESIII collaboration. This talk covers the studies of the leptonic and semi-leptonic decays of D mesons, and the measurement of the strong phase difference based on the quantum correlation.


Introduction
The BESIII [1] experiment at the BEPCII collider started data taking since 2008.For the study of charm meson decays, about 2.9 fb −1 data on the ψ(3770) peak has been accumulated.ψ(3770) dominantly decays into D D, which provides an ideal place for studying the decays of D 0 and D + mesons.
2 Determination of B(D + → μ + ν) and the decay constant f D + In the Standard Model of particle physics, the D + meson can decay into l + ν l via a virtual W + boson.The decay rate depends on the D + decay constant f D + , in which all of the strong interaction effects between the two initial-state quarks are absorbed.The decay width of D + → l + ν l is given by [2] where G F is the Fermi coupling constant.So by measuring the branching ratio of D + → l + ν l , the decay constant f D + can be determined to test the calculations from lattice QCD.In addition, |V cd | can be directly accessed.f D + is also helpful to constrain the CKM matrix element |V td | through its relation to the mixing parameter x B and the ratio f D / f B [3,4].
To determine the branching ratio of D + → μ + ν μ , the D tagging method is used.Firstly, D − mesons are reconstructed with 9 hadronic decay modes ( ), and then μ + is sought out in the remaining tracks.around 0. Finally, with 2.9 fb −1 ψ(3770) data, the branching fraction of With combination of G F , the mass of μ + and D + , the lifetime of D + and |V cd | from the global fit in the SM [6], the decay constant f D + is obtained with the best precision in the world [5] The differential decay rate of D 0 → K − (π − )e + ν is written as With the precisely determined V cs(d) from the unitarity of the CKM matrix, we can obtain the formfactor f + (q 2 ) to check the lattice QCD calculations.This analysis has been done using one-third of the 2.9 fb −1 ψ(3770) data, with a partialblind method.Firstly, the singly tagged D0 is reconstructed with four hadronic modes ( D0 → These two results are consistent with the world averages [6]. To measure the form factor, the partial decay rates are measured in different q 2 bins, where q 2 is the squared invariant mass of e + ν system.The f + (q 2 ) distributions are shown in figure 1 with theoretical curves overlaid [7].

Measurement of the strong phase difference δ Kπ
Studying the D 0 -D0 mixing is important for identifying the size of the long distance effect and searching for new physics [8], and also helpful for studying CP violation in charm physics.Charm mixing is described by two dimensionless parameters x and y.The measurement of the strong phase difference δ between the doubly Cabibbo-suppressed (DCS) decay D0 → K − π + and the corresponding Cabibbo-favored (CF) D 0 → K − π + , allows x and y to be extracted from x ≡ x cos δ + y sin δ and y ≡ y cos δ − x sin δ [9].Furthermore, finer precision of δ helps the γ/φ 3 angle measurement in CKM matrix according to the so-called ADS method [6].
5 Measurement of the Relative Strong-phase Difference between D 0 and D0 decay to The CKM angle γ/φ3 can be measured from the decay B + → D(K 0 S π + π − )K ± through the GGSZ method [12,13].The Dalitz plot can be separated into 2N bins as shown in figure 2(a).The N bins lying below the symmetry axis are denoted by the index i, while the remaining bins are indexed with ī, and these square bins are symmetric under exchange of x and y (x ≡ m 2 The two parameters c i and s i denote the weighted average of cos(Δδ D ) and sin(Δδ D ) in the i th bin, respectively.And Δδ D is the strong phase difference between the DCS decay D0 → K 0 S π + π − and the corresponding CF decay D 0 → K 0 S π + π − .The number of events in the i th bin of a Dalitz plot originating from the B ± decay is The normalization factors, r B and δ B could be determined at B factories.Using ψ(3770), K i can be obtained by flavor tagged D → K 0 S π + π − decays, c i can be obtained from CP tagged D → K 0 S π + π − decays, and s i is obtained from double Dalitz decays D 0 → K 0 S π + π − and D0 → K 0 S π + π − .The Dalitz plot is split into 8 bins as shown in figure 2(b), which have been optimized, to get the highest sensitivity of γ.The results of c i and s i in each bin are given in figure 2(c).Our results will allow for increased precision in the measurement of γ/φ3.

Summary
Based on the 2.9 fb −1 data taken at the ψ(3770) peak, the recent results on the study of charm physics are presented.The BESIII experiment aims at getting 20 fb −1 ψ(3770), and more promising results are expected.

Figure 1 .
Figure 1.f + (q 2 ) distributions for the decay of D 0 → K − e + ν (left) and D 0 → π − e + ν (right).Points are measured from data, curves are the theoretical predictions varying within one statistical standard sigma.

MESON 2014 13 th
International Workshop on Production, Properties and Interaction of Mesons -04009-p.3

Figure 2 .
Figure 2. (a): Squared binned Dalitz plot with symmetric bins over an exchange of x and y. (b): Modified optimal binning.(c): Red squares mark the model predicted value of c i and s i [14], and the blue dot mark fitted value from data with statistical error.