Recent Experimental Results on Leptonic D + (s) Decays, Semileptonic D Decays and Extraction of | V cd(s) |
aa r X i v : . [ h e p - e x ] N ov March 21, 2019
Recent Experimental Results on Leptonic D +( s ) Decays, Semileptonic D Decays and Extraction of | V cd ( s ) | Gang Rong Institute of High Energy Physics, CAS, Beijing, China
The recent experimental results on leptonic D +( s ) decays, semileptonic D decays, determinations of decay constants and form factors, as well as ex-tractions of | V cd | and | V cs | are briefly reviewed. Global analysis of all exist-ing measurements of leptonic D +( s ) decays and semileptonic D decays yields | V cd | = 0 . ± . | V cs | = 0 . ± . The 8th International Workshop on the CKM Unitarity Triangle (CKM2014),Vienna, Austria, September 8-12, 2014 Work supported in part by the National Natural Science Foundation of China (NSFC) under ContractNo.10935007. I would like to thank Yi Fang and Hailong Ma for many helpful discussions about thisexperimental review.
Introduction
In the Standard Model (SM) of particle physics, the decay rate of D +( s ) → ℓ + ν ℓ (where ℓ = e , µ , or τ ) relates to a product of the decay constant f D +( s ) and the Cabibbo-Kobayashi-Maskawa (CKM) matrix element V cd ( s ) byΓ( D +( s ) → ℓ + ν ℓ ) = G F π m ℓ m D +( s ) − m ℓ m D +( s ) f D +( s ) | V cd ( s ) | , (1)where G F is the Fermi coupling constant, m ℓ is the mass of the lepton, and m D +( s ) is themass of the D +( s ) meson. The differential rate of D → π ( K ) e + ν e decay relates to a productof decay form factor f π ( K )+ ( q ) and V cd ( s ) by d Γ dq = X G F π | ~p π ( K ) | | f π ( K )+ ( q ) | | V cd ( s ) | , (2)where q is square of the four-momenta transfer, ~p π ( K ) is the three-momentum of the π ( K )meson in the rest frame of the D meson, and X is a factor due to isospin, which equals to 1for D → π − e + ν e , D → K − e + ν e and D + → K e + ν e , and equals to 1 / D + → π e + ν e .With precision measurements of these decay rates one can more precisely determine thedecay constants f D +( s ) and form factors f π ( K )+ (0) as well as these CKM matrix elements. Theprecisely measured values of f D +( s ) and f π ( K )+ (0) can be used to validate LQCD calculationsfor these quantities, which can improve determinations of the CKM matrix elements | V ub | , | V td | , and | V ts | . As a consequence, the uncertainty in the overall constraint on the unitaritytriangle of the CKM matrix can be reduced. These can be used for more stringent test ofthe SM and search for New Physics beyond the SM. D +( s ) → ℓ + ν ℓ decays and decay constants f D +( s ) D +( s ) → ℓ + ν ℓ decays In 2014, the BESIII Collaboration made a measurement of D + → µ + ν µ decays by analyzing2.92 fb − data taken at 3.773 GeV. From 9 hadronic decay modes of D − meson, the BESIIICollaboration accumulated 1703054 ± D − tags. In this D − tag sample they observed409 . ± . D + → µ + ν µ decays and measured the branching fraction B ( D + → µ + ν µ ) = (3 . ± . ± . × − [1]. They also measured f D + | V cd | = 45 . ± . ± .
39 MeV and determined f D + = 203 . ± . ± .
8. In addition, they extracted | V cd | = 0 . ± . ± . D + decays for the first time.In 2013, the Belle Collaboration made new measurements of D + s → µ + ν µ and D + s → τ + ν τ decays. By analyzing 913 fb − data collected near 10.6 GeV, they measured B ( D + s → µ + ν µ ) = (0 . ± . ± . B ( D + s → τ + ν τ ) = (5 . ± . +0 . − . )% and determined f D + s = 255 . ± . ± . ± . .2 Decay constants f D +( s ) Historically the MARK-III, BES-I, BES-II, CLEO-c and BESIII Collaborations studiedthe leptonic D + decays, but only the BES-II, CLEO-c and BESIII Collaborations observedsignificant signal events for D + → µ + ν µ decays, and both the CLEO-c and BESIII Collabo-rations made precision measurements of this decay branching fraction. Table 1 summarizes B ( D + → µ + ν µ ) and some related quantities measured at the CLEO-c [4] and BESIII [1] ex-periments. The average of these two values of the measured branching fraction and relatedquantities [5] are also summarized in Table 1.Table 1: Summary of B ( D + → µ + ν µ ), f D + | V cd | , f D + and | V cd | . Quantity B ( D + → µ + ν µ ) (10 − ) f D + | V cd | (MeV) f D + (MeV) | V cd | CLEO-c [4] 3 . ± . ± .
09 N/A 206 . ± . ± . . ± . ± .
06 45 . ± . ± .
39 203 . ± . ± . . ± . ± . . ± .
17 45 . ± . ± .
15 203 . ± . ± . . ± . ± . Table 2 summarizes branching fractions for D + s → ℓ + ν ℓ decays and relative branchingratios for D + s → µ + ν µ decay measured at different experiments. These measurements can bedivided into three kinds of measurements, such as direct (D), precision (P), and relative (R)measurements, which are labeled as D, P and R in the last column of Table 2, respectively.The relative measurements of the branching fraction for D + s → µ + ν µ decay are determinedwith B ( D + s → φπ + ) = (4 . ± . f D +( s ) we separately consider all existing measurementsor some of these measurements of branching fractions for D +( s ) → ℓ + ν ℓ decays. Performingone free parameter, f D + s | V cs | , χ fit to all (DPR) of these measured branching fractions withinserting the well-measured m µ = (105 . ± . m τ = (1776 . ± . m D + s = (1968 . ± .
11) MeV, and τ D + s = (500 ± × − s [6] into Eq.(1) yields themeasured product f D + s | V cs | = 252 . ± . ± . f D + s | V cs | . These f D + s | V cs | are all listed in Table 3.Dividing f D + | V cd | = (45 . ± . ± .
15) MeV [5] by | V cd | = 0 . ± . f D + = (203 . ± . ± .
9) = (203 . ± .
7) MeV , which is obtained from both the BESIII [1] and CLEO-c [4] measurements of branchingfraction for D + → µ + ν µ decay. Similarly, dividing f D + s | V cs | = (252 . ± . ± .
8) MeVobtained by fitting all decay branching fractions listed in Table 2 by | V cs | = 0 . ± . f D + s = (258 . ± . ± .
8) = (258 . ± .
2) MeV . As a comparison Table 3 lists this f D + s and other values of f D + s determined by separatelyfitting the branching fractions in group DP and in group P, where the statistical and sys-2able 2: Summary of decay branching fractions B ( D + s → µ + ν µ ), B ( D + s → τ + ν τ ) andbranching ratio R B = B ( D + s → µ + ν µ ) /B ( D + s → φπ + ) measured at different experiments. Experiment B ( D + s → µ + ν µ ) (%) Note
BES-I [8] 1 . +1 . . − . − . DALEPH [9] 0 . ± . ± .
18 DCLEO-c [10] 0 . ± . ± .
017 PBaBar [11] 0 . ± . ± .
034 PBelle [3] 0 . ± . ± .
020 PExperiment R B B ( D + s → µ + ν µ ) (%) RBEATRICE [12] 0 . ± . ± .
04 1 . ± . ± . ± .
09 RCLEO-II [13] 0 . ± . ± .
035 0 . ± . ± . ± .
069 R
BaBar [14] . ± . ± .
006 0 . ± . ± . ± .
057 RExperiment B ( D + s → τ + ν τ ) (%)L3 [15] 7 . ± . ± . . ± . ± . . ± . ± .
84 DCLEO-c [17] 5 . ± . ± .
13 PBaBar [11] 5 . ± . ± .
49 PBelle [3] 5 . ± . +0 . − . P Table 3: f D + s | V cs | and f D + s determined by fitting different decay branching fractions ingroups of DPR, DP and P shown in Table 2. Group of B ( D + s → ℓ + ν ell ) DPR DP P f D + s | V cs | . ± . ± . . ± . ± . . ± . ± . f D + s . ± . . ± . . ± . tematic errors are combined together. With these determined values of f D + s and f D + wefind f D + s /f D + = 1 . ± . , which is 2 . σ ( σ is standard deviation) larger than the most precision value [ f D + s /f D + ] LQCD =1 . ± . ± .
003 calculated in LQCD [18]. Table 4 compares this determined ratio andother values of the ratio for which the values of f D + s are determined by fitting the branchingfractions in group DP and in group P. The last two ratios shown in Table 4 are larger thanthe predicted ratio calculated in LQCD [18] by 2 . σ and 2 . σ , respectively. D Decays
Recently, the BESIII Collaboration reported preliminary results on measurements of D → π − e + ν e and D → K − e + ν e decays. From 2.92 fb − data taken at 3.773 GeV, the BESIIICollaboration accumulated (279 . ± . × D tags with five hadronic decay modes. Inthis sample of D tags, they observed 6297 ±
87 and 70727 ±
278 signal events for D → π − e + ν e and D → K − e + ν e decays, respectively, and measured the branching fractions B ( D → π − e + ν e ) = (0 . ± . ± . B ( D → K − e + ν e ) = (3 . ± . ± f D + s /f D + determined with the values for f D + s shown in Table 3 andthe average value for f D + determined from B ( D + → µ + ν µ ) measured at the BESIII andCELO-c experiments. Group of B ( D + s → l + ν l ) DPR DP P f D + s /f D + . ± .
036 1 . ± .
036 1 . ± . . f π + (0) | V cd | = 0 . ± . ± . f K + (0) | V cs | = 0 . ± . ± . D → π − e + ν e decays.From a data sample taken near 10.6 GeV, they observed 5300 D → π − e + ν e decays andmeasured a relative branching ratio R B = B ( D → π − e + ν e ) /B ( D → K − π + ) = 0 . ± . ± . B ( D → π − e + ν e ) = (0 . ± . ± . ± . f π + (0) | V cd | = 0 . ± . ± . ± . f K + (0) = 0 . ± . ± . ± .
007 [21] by | V cs | = 0 . ± . f K + (0) | V cs | = 0 . ± . ± . ± . D → π − e + ν e , D → K − e + ν e , D + → π e + ν e and D + → K e + ν e by analyzing 818 pb − data taken at3.773 GeV. They measured f π + (0) | V cd | = 0 . ± . ± .
001 and f K + (0) | V cs | = 0 . ± . ± .
005 [22].The Belle Collaboration made measurements of D → π − e + ν e and D → K − e + ν e decays in 2006. By analyzing 282 fb − data taken at 10.58 GeV they measured the formfactors f π + ( q ) and f K + ( q ), and determined f π + (0) = 0 . ± . ± .
030 as well as f K + (0) =0 . ± . ± .
022 [23].Figure 1 shows comparison of these measured form factors along with theoretical pre-dictions for these two form factors. (0) π + f0.4 0.5 0.6 0.7 0.8 0.9 Experiment:Theory:AverageBESIII (2014)BaBar (2014)CLEO-c (2009)Belle (2006)HPQCD (2011)Fermilab/MILC/HPQCD (2005)Sum Rules (2009) -0.07+0.10 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± (0) π + f0.4 0.5 0.6 0.7 0.8 0.9 (0) K+ f Experiment:Theory:AverageBESIII (2014)BaBar (2007)CLEO-c (2009)Belle (2006)HPQCD (2013)HPQCD (2010)Fermilab/MILC/HPQCD (2005)Sum Rules (2009) -0.08+0.11 ± ± ± ± ± ± ± ± ± ± ± ± ± ± (0) K+ f Figure 1: Comparison of measured form factors along with theoretical predictions for these.Combining three measurements of f π ( K )+ (0) | V cd ( s ) | from the BaBar, BESIII and CLEO-c,we obtain the average [24] f π + (0) | V cd | = 0 . ± . , f K + (0) | V cs | = 0 . ± . , where the errors are the combined statistical and systematic errors together.4 Extractions of | V cd | and | V cs | Using the determined f D + | V cd | = 45 . ± . ± .
15 MeV shown in Table 1 and f D + s | V cs | =250 . ± . ± . f D + =(209 . ± .
3) MeV and f D + s = (248 . ± .
7) MeV from the Flavor Lattice Averaging Group,we find the CKM matrix elements | V cd | D + → µ + ν µ = 0 . ± . exp ± . LQCD and | V cs | D + s → ℓ + ν ℓ = 1 . ± . exp ± . LQCD . Similarly, with the measured f π + (0) | V cd | =0 . ± .
002 and f K + (0) | V cs | = 0 . ± .
004 together with [ f π + (0)] LQCD = 0 . ± .
029 [25]and [ f K + (0)] LQCD = 0 . ± .
019 [26] we extract the CKM matrix elements | V cd | D → πe + ν e =0 . ± . exp ± . LQCD and | V cs | D → πe + ν e = 0 . ± . exp ± . LQCD . Combiningthese | V cd ( s ) | D → π ( K ) eν e and | V cd ( s ) | D +( s ) → l + ν l together, we find [24] | V cd | = 0 . ± . , | V cs | = 0 . ± . . The above | V cd | and | V cs | are extracted from measurements of leptonic D +( s ) decays andsemi-leptonic D decays performed at the BaBar, Belle, BESIII and CLOE-c experiments.In these measurements of semi-leptonic D decays, the f π ( K )+ (0) | V cd ( s ) | were all measured byanalyzing differential rates of D → π ( K ) e + ν e decays.Beyond these four measurements of differential decay rates, many other experimentsmeasured some other quantities rather than the differential decay rates. In order to reducethe experimental uncertainties in | V cd | and | V cs | , several authors analyzed all existing mea-surements of these leptonic D +( s ) and semi-leptonic D decays to extract | V cd | and | V cs | . Byglobally analyzing all existing measurements together with the recent most precision valuesfor these form factors and decay constants calculated in LQCD, they extracted [5, 7] | V cd | = 0 . ± . , | V cs | = 0 . ± . , which are the most precise determinations of | V cd | and | V cs | up to date. Figure 2 showscomparison of these extracted | V cd | and | V cs | as well as other ones given by the HFAG ∗ along with the values from PDG2014. | cd |V0.16 0.18 0.2 0.22 0.24 0.26 Global anaylsisHFAG-charm’2014PDG14’2014PDG’2014Global fit in the SM 0.0045 ± ± ± ± ± ) µ ν + µ → + & D e ν + e π → (D ) µ ν + µ → + & D e ν + e π → (D interaction) ν ( interaction) ν & e ν + e π → (D | cd |V0.16 0.18 0.2 0.22 0.24 0.26 | cs |V0.92 0.94 0.96 0.98 1 1.02 Global anaylsisHFAG-charm’2014DELPHI at LEP-2PDG14’2014Global fit in the SM 0.011 ± ± ± -0.26+0.32 ± ± ) l ν + l → s+ & D e ν + Ke → (D ) l ν + l → s+ & D e ν + Ke → (D )s c → (W ) l ν + l → s+ & D e ν + Ke → (D | cs |V0.92 0.94 0.96 0.98 1 1.02 Figure 2: Comparison of the extracted | V cd | and | V cs | along with PDG2014 values. ∗ Personal communication with A. Zupanc. Summary
Analyzing all existing measurements of leptonic D +( s ) decays measured at different experi-ments yields f D + = 203 . ± . f D + s = 258 . ± . f D + s /f D + = 1 . ± . . σ . If only analyzing the branch-ing fractions for D + s → ℓ + ν ℓ decays measured at the BaBar, Belle and CELO-c experiments,these become to be f D + s = 257 . ± . f D + s /f D + = 1 . ± . . σ . The average of the measured f π ( K )+ (0) from the BaBar,Belle, BESIII and CLEO-c experiments are consistent within error with those calculated inLQCD, but with a factor of 3 (4) more precisions than that calculated in LQCD. Analyzingall measurements of the leptonic D +( s ) and semi-leptonic D decays together, in conjunctionwith the recent LQCD calculations for these form factors and decay constants, ones find | V cd | = 0 . ± . | V cs | = 0 . ± . | V cd | and | V cs | up to date. At present, the uncertainties of the extracted | V cd | and | V cs | are still dominated by the error of f π ( K )+ (0) calculated in LQCD. If these errors of f π ( K )+ (0) calculated in LQCD could be negligible, the relative accuracy of | V cd | and | V cs | from semi-leptonic D decays could reach to ∆ | V cd | / | V cd | ∼ .
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