Measurements of strong phase in D 0 →Kπ decay and y CP at BESIII
aa r X i v : . [ h e p - e x ] N ov September 10, 2018
Measurements of strong phase in D → K π decay and y CP atBESIII Xiao-Rui Lu on behalf of the BESIII Collaboration School of PhysicsUniversity of Chinese Academy of Sciences, 100049, Beijing, China
In this paper, I report the preliminary results of the strong phasedifference cos δ Kπ between the doubly Cabibbo-suppressed process D → K − π + and Cabibbo-favored D → K − π + at BESIII. In addition, thepreliminary results of the D - D mixing parameter y CP by analyzing CP -tagged semileptonic D decays are presented. These measurements werecarried out based on the quantum-correlated technique in studying theprocess of D D pair productions of 2.92 fb − e + e − collision data collectedwith the BESIII detector at √ s = 3.773 GeV.PRESENTED AT The 6 th International Workshop on Charm Physics(CHARM 2013)Manchester, UK, 31 August – 4 September, 2013 E-mail: [email protected]
Introduction D - D mixing originated from the short distance effect is highly suppressed by thethe GIM mechanism [1] and by the CKM matrix elements [2] within standard model.However, long distance effect, which is not calculated reliable, can manifest size of themixing. Thus, to probe the D - D mixing constitutes identifying the size of the longdistance effect and searching for new physics [3]. In addition, improving constraintson charm mixing is important for studying CP violation ( CP V ) in charm physics.Charm mixing is described by two dimensionless parameters x = 2 M − M Γ + Γ y = Γ − Γ Γ + Γ , where M , and Γ , are the masses and widths of two mass eigenstates. Because CP V in D decays is quite small compared with the mixing parameters, it is reasonable toassume no direct CP V . The parameter y CP is defined as follows [4] y CP ≡
12 [ y cos φ ( | qp | + | pq | ) − x sin φ ( | qp | − | pq | )] , where | pq | and φ correspond to the CP V in mixing and in interference between mixingand decay, respectively [5]. So far, y CP is measured mainly from the time-dependentanalysis of D → K + K − and D → π + π − . At BESIII, y CP can be measured bycomparing decay rates of D semileptonic decays in different CP -eigenstates. BESIIIresults provide further constrains to the world measurements of the mixing parametersin D sector. In case no CP V , we have | pq | = 1 and sin φ = 0. Hence, y CP = y .In the context of CP conservation, the mass eigenstates D and D can be writtenas | D i ≡ | D i + | D i√ , | D i ≡ | D i − | D i√ . If we take the phase convention CP | D i = + | D i [5], D and D are also CP eigen-states of CP -even and CP -odd, respectively. The strong phase difference δ Kπ betweenthe doubly Cabibbo-suppressed (DCS) decay D → K + π − and the correspondingCabibbo-favored (CF) D → K − π + is denoted as h K − π + | D ih K − π + | D i = − re − iδ Kπ , which plays an important role in precise determinations of D - D mixing parameters.Here r = (cid:12)(cid:12)(cid:12)(cid:12) h K − π + | D ih K − π + | D i (cid:12)(cid:12)(cid:12)(cid:12) .
1n the limit of CP conservation, we have h K − π + | D i = h K + π − | D i , h K − π + | D i = h K + π − | D i . Hence, δ Kπ is the same in the final states of K − π + and K + π − . In this paper, weuse the notation of K − π + , and its charge conjugation mode is always implied to beincluded.The most precise determination of the size of the mixing comes from the measure-ment of the time dependence of the decay rate of the wrong-sign process D → K + π − .These analyses are sensitive to y ′ ≡ y cos δ Kπ − x sin δ Kπ and x ′ ≡ x cos δ Kπ + y sin δ Kπ [6]. The measurement of δ Kπ can allow x and y to be extracted from x ′ and y ′ . An improved determination of δ Kπ is important for this extraction. Fur-thermore, finer precision of δ Kπ helps the γ/φ angle measurement in CKM matrixaccording to the so-called ADS method [5].Using the quantum-correlated technique, δ Kπ and y CP can be measured in themass-threshold production process e + e − → D D [7]. In this process, the initialsystem has J P C = 1 −− ; as a result, the D and D are in a CP -odd quantum-coherent state. At any time, the D and D mesons are in opposite CP -eigenstates,until one of them decays [3]. This provides an unique way to probe D - D mixingas well as the strong phases difference between D and D decay amplitudes, takingadvantage of the quantum coherence of D - D pairs.In this paper, we present the preliminary results of δ Kπ and y CP that uses thequantum correlated productions of D - D mesons at √ s = 3 .
773 GeV in e + e − colli-sions with an integrated luminosity of 2.92 fb − collected with the BESIII detector [8].Details of the BESIII detector can be found in Ref. [8]. δ Kπ The strong phase difference δ Kπ can be accessed using the following formula2 r cos δ Kπ + y = (1 + R WS ) · A CP → Kπ , (1)where R WS is the decay rate ratio of the wrong sign process D → K − π + and theright sign process D → K − π + [9] and A CP → Kπ is the asymmetry between CP -oddand CP -even states decaying to K − π + A CP → Kπ = B D → K − π + − B D → K − π + B D → K − π + + B D → K − π + . (2)Using D tagging method in the quantum-coherent D pair production, we can calcu-late the branching fractions with B D CP ± → Kπ = n Kπ,CP ± n CP ± · ε CP ± ε Kπ,CP ± . (3)2ype ModeFlavored K − π + , K + π − CP + K + K − , π + π − , K S π π , π π , ρ π CP − K S π , K S η, K S ω Table 1: D decay modes reconstructed in the analysis of δ Kπ .Here, n CP ± ( n Kπ,CP ± ) and ε CP ± ( ε Kπ,CP ± ) are yields and detection efficiencies of sin-gle tags (ST) of D → CP ± (double tags (DT) of D → CP ± , D → Kπ ), respectively.With external inputs of the parameters of r , y and R WS , we can extract δ Kπ from A CP → Kπ . Based on a dataset of 818 pb − of collision data collected with the CLEO-cdetector at the center of mass √ s = 3 .
77 GeV, the CLEO collaboration measuredcos δ Kπ = 0 . +0 . . − . − . [10]. Using a global fit method with inclusion of the externalmixing parameters, CLEO obtained cos δ Kπ = 1 . +0 . . − . − . [10].We choose 5 CP -even D decay modes and 3 CP -odd modes, as listed in Tab. 1,with π → γγ , η → γγ , K S → π + π − and ω → π + π − π . Variable M BC ≡ q E /c − | ~p D | /c is plotted in Fig. 1 to identify the CP ST signals, where ~p D is the total momentumof the D candidate and E is the beam energy. Yields of the CP ST signals areestimated by maximum likelihood fits to data, in which signal shapes are derivedfrom MC simulation convoluted with a smearing Gaussian function, and backgroundfunctions are modeled with the ARGUS function [11]. In the events of the CP STmodes, we reconstruct the Kπ combinations using the remaining charged tracks withrespect to the ST D candidates. Similar fits are implemented to the distributions of M BC ( D → CP ± ) in the survived DT events to estimate yields of DT signals. Thefits are shown in Fig. 2.We get the asymmetry to be A CP → Kπ = (12 . ± . +0 . − . )% , where the first uncertainty is statistical and the second is systematic. To measure thestrong phase δ Kπ in Eq. (1), we quote the external inputs of R D = r = 3 . ± . ‰ , y = 6 . ± . ‰ , and R WS = 3 . ± . ‰ from HFAG 2013 [12] and PDG [5]. Hence,we obtain cos δ Kπ = 1 . ± . ± . ± . , where the first uncertainty is statistical, the second uncertainty is systematic, and thethird uncertainty is due to the errors introduced by the external input parameters.This result is more precise than CLEO’s measurement and provides the world bestconstrain to δ Kπ . 3 (GeV/c BC M ) E v en t s / ( M e V / c ) (GeV/c BC M ) E v en t s / ( M e V / c - K + K ) (GeV/c BC M ) E v en t s / ( M e V / c ) (GeV/c BC M ) E v en t s / ( M e V / c p p ) (GeV/c BC M ) E v en t s / ( M e V / c ) (GeV/c BC M ) E v en t s / ( M e V / c p S0 K ) (GeV/c BC M ) E v en t s / ( M e V / c ) (GeV/c BC M ) E v en t s / ( M e V / c - p + p ) (GeV/c BC M ) E v en t s / ( M e V / c ) (GeV/c BC M ) E v en t s / ( M e V / c pr ) (GeV/c BC M ) E v en t s / ( M e V / c ) (GeV/c BC M ) E v en t s / ( M e V / c h S0 K ) (GeV/c BC M ) E v en t s / ( M e V / c ) (GeV/c BC M ) E v en t s / ( M e V / c p p S0 K ) (GeV/c BC M ) E v en t s / ( M e V / c ) (GeV/c BC M ) E v en t s / ( M e V / c w S0 K Figure 1: ST M BC distributions of the D → CP ± decays and fits to data. Data areshown in points with error bars. The solid lines show the total fits and the dashedlines show the background shapes. 4 (GeV/c BC M ) E v en t s / ( M e V / c ) (GeV/c BC M ) E v en t s / ( M e V / c - K + , K p K ) (GeV/c BC M ) E v en t s / ( M e V / c ) (GeV/c BC M ) E v en t s / ( M e V / c p p , p K ) (GeV/c BC M ) E v en t s / ( M e V / c ) (GeV/c BC M ) E v en t s / ( M e V / c p S0 , K p K ) (GeV/c BC M ) E v en t s / ( M e V / c ) (GeV/c BC M ) E v en t s / ( M e V / c - p + p , p K ) (GeV/c BC M ) E v en t s / ( M e V / c ) (GeV/c BC M ) E v en t s / ( M e V / c pr , p K ) (GeV/c BC M ) E v en t s / ( M e V / c ) (GeV/c BC M ) E v en t s / ( M e V / c h S0 , K p K ) (GeV/c BC M ) E v en t s / ( M e V / c ) (GeV/c BC M ) E v en t s / ( M e V / c p p S0 , K p K ) (GeV/c BC M ) E v en t s / ( M e V / c ) (GeV/c BC M ) E v en t s / ( M e V / c w S0 , K p K Figure 2: DT M BC distributions and the corresponding fits. Data are shown inpoints with error bars. The solid lines show the total fits and the dashed lines showthe background shapes. 5ype Modes CP + K + K − , π + π − , K S π π CP − K S π , K S ω , K S ηl ± Keν , Kµν
Table 2: CP -tag modes and D semileptonic decay modes. y CPFor D decays to any CP -eigenstate final states, their decay rates can be formulatedto be R ( D /D → CP ± ) ∝ | A CP ± | (1 ∓ y CP ) . When the partner D decays semileptonically in the DD pair production at threshold,double decay rates will be R l ; CP ± = | A l | | A CP ± | . If we take the ratio of the single decay rate and the double decay rate and neglecthigher order of y , we can extract y CP using the following equation [4] y CP = 14 ( R l ; CP + R CP − R l ; CP − R CP + − R l ; CP − R CP + R l ; CP + R CP − ) . Similar to the notations in Eq. (3), experimentally we denote the decay rate ratios of R l ; CP ± R CP ± to be B ± and determine it with the D tagging method B ± = n l ; CP ± n CP ± · ε CP ± ε l ; CP ± . Hence, y CP = [ ˜ B + ˜ B − − ˜ B − ˜ B + ], where ˜ B ± is combinations of different CP -tag mode α using the least square method χ = X α ( ˜ B ± − B α ± ) ( σ α ± ) . CP -tag modes in Tab. 2 are used in this analysis. Similar to the analysis of δ Kπ , ST yields are estimated by fits to the M BC distributions, as shown in Fig. 3.Semileptonic decays of D → Keν and D → Kµν are selected with respect to the CP -tagged D candidates in ST events. Due to the undetectable neutrino in the finalstates, variable U miss is used to distinguish the signals of semileptonic decays frombackgrounds. The definition is given as U miss ≡ E miss − | ~p miss | , (GeV/c BC M E ve n t s / . M e V / c ) (GeV/c BC M E ve n t s / . M e V / c - K + K ) (GeV/c BC M E ve n t s / . M e V / c ) (GeV/c BC M E ve n t s / . M e V / c - p + p ) (GeV/c BC M E ve n t s / . M e V / c ) (GeV/c BC M E ve n t s / . M e V / c ) (GeV/c BC M E ve n t s / . M e V / c ) (GeV/c BC M E ve n t s / . M e V / c p K ) (GeV/c BC M E ve n t s / . M e V / c ) (GeV/c BC M E ve n t s / . M e V / c w K ) (GeV/c BC M E ve n t s / . M e V / c ) (GeV/c BC M E ve n t s / . M e V / c h K Figure 3: M BC distributions and fits to data. E miss ≡ E − E K − E l , ~p miss ≡ − [ ~p K + ~p l + ˆ p ST q E − m D ] . Here, E K/l ( ~p K/l ) is the energy (three-momentum) of K ± or lepton l ∓ , ˆ p ST is the unitvector in the reconstructed direction of the CP -tagged D and m D is the nominal D mass. The U miss distributions are plotted in Fig. 4 for D → Keν and D → Kµν modes.In fits of the DT
Keν modes, signal shape is modeled using MC shape convolutedwith an asymmetric Gaussian and backgrounds are described with a 1st-order polyno-mial function. In fits of the DT
Kµν modes, signal shape is modeled using MC shapeconvoluted with an asymmetric Gaussian. Backgrounds of
Keν are modeled usingMC shape and their relative rate to the signals are fixed. Shape of
Kππ backgroundsare taken from MC simulations with convolution of a smearing Gaussian function; pa-rameters of the smearing function are fixed according to fits to the control sampleof D → Kππ events. Size of Kππ backgrounds are fixed by scaling the number of Kππ events in the control sample to the number in the signal region according tothe ratio estimated from MC simulations. Other backgrounds are described with a1st-order polynomial function.Finally, we obtain the preliminary result as y CP = − . ± . . ) ± . . ) . The result is compatible with the previous measurements [12]. This is the most precisemeasurement of y CP based on D D threshold productions. However, its precision isstill statistically limited. 7 (GeV) miss U -0.1 -0.05 0 0.05 0.1 E ve n t s / ( . ) (GeV) miss U -0.1 -0.05 0 0.05 0.1 E ve n t s / ( . ) n , Ke - K + K (GeV) miss U -0.1 -0.05 0 0.05 0.1 E ve n t s / ( . ) (GeV) miss U -0.1 -0.05 0 0.05 0.1 E ve n t s / ( . ) n , Ke - p + p (GeV) miss U -0.1 -0.05 0 0.05 0.1 E ve n t s / ( . ) (GeV) miss U -0.1 -0.05 0 0.05 0.1 E ve n t s / ( . ) n , Ke p p K (GeV) miss U -0.1 -0.05 0 0.05 0.1 E ve n t s / ( . ) (GeV) miss U -0.1 -0.05 0 0.05 0.1 E ve n t s / ( . ) n , Ke p K (GeV) miss U -0.1 -0.05 0 0.05 0.1 E ve n t s / ( . ) (GeV) miss U -0.1 -0.05 0 0.05 0.1 E ve n t s / ( . ) n , Ke w K (GeV) miss U -0.1 -0.05 0 0.05 0.1 E ve n t s / ( . ) (GeV) miss U -0.1 -0.05 0 0.05 0.1 E ve n t s / ( . ) n , Ke h K (GeV) miss U -0.1 -0.05 0 0.05 0.1 E ve n t s / ( . ) (GeV) miss U -0.1 -0.05 0 0.05 0.1 E ve n t s / ( . ) nm , K - K + K (GeV) miss U -0.1 -0.05 0 0.05 0.1 E ve n t s / ( . ) (GeV) miss U -0.1 -0.05 0 0.05 0.1 E ve n t s / ( . ) nm , K - p + p (GeV) miss U -0.1 -0.05 0 0.05 0.1 E ve n t s / ( . ) (GeV) miss U -0.1 -0.05 0 0.05 0.1 E ve n t s / ( . ) nm , K p p K (GeV) miss U -0.1 -0.05 0 0.05 0.1 E ve n t s / ( . ) (GeV) miss U -0.1 -0.05 0 0.05 0.1 E ve n t s / ( . ) nm , K p K (GeV) miss U -0.1 -0.05 0 0.05 0.1 E ve n t s / ( . ) (GeV) miss U -0.1 -0.05 0 0.05 0.1 E ve n t s / ( . ) nm , K w K (GeV) miss U -0.1 -0.05 0 0.05 0.1 E ve n t s / ( . ) (GeV) miss U -0.1 -0.05 0 0.05 0.1 E ve n t s / ( . ) nm , K h K Figure 4: Fits to U miss distributions in data for CP -tagged Keν and
Kµν modes.
In this paper, the preliminary BESIII results of the strong phase difference cos δ Kπ in D → Kπ decays and the mixing parameter y CP are reported. The measurementswere carried out based on the quantum-correlated technique in studying the processof D D pair productions of 2.92 fb − e + e − collision data collected with the BESIIIdetector at √ s = 3.773 GeV. The preliminary results are given ascos δ Kπ = 1 . ± . ± . ± . y CP = − . ± . ± . . Among them, the result of cos δ Kπ is the most accurate to date. In the future, globalfits can be implemented in order to best exploit BESIII data in the quantum-coherenceproductions [13]. 8 CKNOWLEDGEMENTS
The BESIII collaboration thanks the staff of BEPCII and the computing centerfor their strong support. This work is supported in part by Joint Funds of NationalNatural Science Foundation of China (11079008) and Natural Science Foundation ofChina (11275266).
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