Recent results of charm physics
at BESIII
Huijing Li1*
1. Henan Normal University* lihuijing@htu.edu.cn(On behalf of BESIII Collaboration)
Aug. 25 th, 2021
The 20 th Lomonosov Conference
on Elementary Particle Physics
Moscow State University
Aug. 19-25 th, 2021

Outline✍ Introduction✍ (Semi-) leptonic decays$p 𝑫$𝒔 → 𝝉 𝝂𝝉•3𝝉
𝝉$ → 𝒆$ 𝝂𝒆 𝝂

arXiv: 2106.02218 [hep-ex]•3𝝉𝝉$ → 𝝅$ 𝝅𝟎 𝝂

arXiv: 2105.07178 [hep-ex], accepted by PRD3𝝉𝝉$ → 𝝅$ 𝝂$p 𝑫$𝒔 → 𝝁 𝝂𝝁•arXiv: 2102.11734 [hep-ex], accepted by PRD

p 𝑫(𝒔) → 𝑷𝒍$ 𝝂𝒍 (𝑷 = 𝜼, 𝑿, 𝑲𝟏 𝟏𝟐𝟕𝟎 ' ) PRL124(2020)231801✍ Hadronic decays

PRD104(2021)012003
arXiv: 2102.10850 [hep-ex]

p 𝑫 → 𝑲𝟎𝑺,𝑳 𝝅$ 𝝅'

PRL124(2020)241802; PRD101(2020)112002

p 𝑫 → 𝑲𝟎𝑺,𝑳 𝑲$ 𝑲'

PRD102(2020)052008

p 𝑫 → 𝑲$ 𝝅$ 𝝅$ 𝝅' 𝐚𝐧𝐝 𝑫 → 𝑲' 𝝅$ 𝝅𝟎 JHEP05(2021)164
p 𝑫$ → 𝑲$ 𝝅$ 𝝅' 𝝅𝟎
PRL125(2020)141802✍ Summary2

Main goals
In the SM:[1]𝑫(𝒔) semi-leptonic decay[1]𝑫(𝒔) pure leptonic decay[1]೧ᅘႻഀഐ˪ ШഁИ ഒЩ𝚪(𝑫$𝒔೹ᅇᅘ១→ 𝒍$ 𝝂𝒍 ) ∝ഋႻ೺Ⴛഃᄮቑᆴ𝒇𝑫"ྻᅓ
𝟐

𝒔= 𝑽𝒄𝒅 𝒔𝟐೧ᅘႻេႱኜഀഐᆣ˪ ШഔИ ഁИ ഒЩ೹ᅇᅘ១ഋႻ೺ႻྻᅓഐഃႻᄺ ԕഐႳԡഐᆣ˪

𝚪 𝑫(𝒔) → 𝑷 𝒍$ 𝝂𝒍 ∝ 𝒇$ 𝒒𝟐𝟐

ೳ= 𝑽𝒄𝒅 𝒔v Decay constant 𝒇𝑫$ , form factor 𝒇"(𝟎): calibrate Lattice QCD(𝒔)v CKM matrix element |𝑽𝒄𝒅(𝒔) |: test the unitarity of the CKM matrix
v Lepton flavor universality (LFU) test.
[1] Hai-Bo Li, and Xiao-Rui Lyu, arXiv: 2103.00908 [hep-ex].

3𝟐

Hadronic decays of charm mesons[1], 𝟎 isu Strong phase measurement with quantum correlated 𝝍 𝟑𝟕𝟕𝟎 → 𝑫𝟎 𝑫
crucial in the model-independent determinations of 𝜸/𝝓𝟑 and charm
mixing/direct CPV.
• In the SM, CP violation is studied by measuring CKM matrix,
represented by unitarity triangle in complex plane. The angle is the only
one that can be extracted from tree-level processes, for which theu Probe non-perturbative QCD•

Help to understand hadron
spectra•η

contribution of non-SM effect is small.
HFLAV
PDG 2021

0.60.4

Study SU(3) flavor symmetry
α0.200γβcontours hold 68%, 95% CL

0.2

0.4

0.6

0.81ρ4

Beijing Electron Positron Collider (BEPCII) in China
A double-ring collider with high luminosity
Center-of-mass energy: 2.0 – 4.95 GeV

LinacSouthBESIIIdetector

2004: started BEPCII upgrade,
BESIII construction
2008: test run
2009-now: BESIII physics run• 1989-2004(BEPC):
𝑳𝐩𝐞𝐚𝐤 = 𝟏. 𝟎×𝟏𝟎𝟑𝟏 /𝐜𝐦𝟐 𝐬• 2009-now(BEPCII)
𝑳𝐩𝐞𝐚𝐤 = 𝟏. 𝟎×𝟏𝟎𝟑𝟑 /𝐜𝐦𝟐 𝐬(Achieved on Apr. 5th, 2016)
5BESIII Detector
From inner to outside[1]:Helium-based multilayer
drift chamber (MDC):
Plastic scintillator
time-of-flight (TOF):
CsI (Tl) electromagnetic
calorimeter (EMC):
Superconducting
solenoidal magnet:
Muon Chamber(MUC):[1] M. Ablikim et al. (BESIII Collaboration), Nucl. Instr. Meth. A614, 345 (2010).

6𝑫𝟎(A) and 𝑫A
𝒔 data set at BESIII𝒔(𝐆𝐞𝐕)

Integrated luminosity

𝟑. 𝟕𝟕𝟑

𝟐. 𝟗𝟑 𝐟𝐛*𝟏𝒔(𝐆𝐞𝐕)

Integrated luminosity(𝐩𝐛*𝟏 )𝟒. 𝟏𝟕𝟖𝟑𝟏𝟖𝟗. 𝟎 ± 𝟎. 𝟗 ± 𝟑𝟏. 𝟗

𝟒. 𝟏𝟖𝟗𝟓𝟐𝟔. 𝟕 ± 𝟎. 𝟏 ± 𝟐. 𝟐

𝟒. 𝟏𝟗𝟗𝟓𝟐𝟔. 𝟎 ± 𝟎. 𝟏 ± 𝟐. 𝟏

𝟒. 𝟐𝟎𝟗𝟓𝟏𝟕. 𝟏 ± 𝟎. 𝟏 ± 𝟏. 𝟖

𝟒. 𝟐𝟏𝟗𝟓𝟏𝟒. 𝟔 ± 𝟎. 𝟏 ± 𝟏. 𝟖

𝟒. 𝟐𝟐𝟔𝟏𝟎𝟒𝟕. 𝟑 ± 𝟎. 𝟏 ± 𝟏𝟎. 𝟐

Decay chain of interest,𝟎𝒆"𝒆* → 𝝍 𝟑𝟕𝟕𝟎 → 𝑫𝟎 𝑫𝒆"𝒆* → 𝝍 𝟑𝟕𝟕𝟎 → 𝑫"𝑫*∓𝒆"𝒆* → 𝑫∗±𝒔 𝑫𝒔

𝐓𝐨𝐭𝐚𝐥: 𝟔. 𝟑𝟐 𝐟𝐛'𝟏

7

𝝅'𝝅'

Tag

Analysis technique
Similar for the hadronic decays
𝑲$𝑫'$𝒆𝝍 𝟑𝟕𝟕𝟎𝑫$'𝒆

Signal𝑿l Single tag (ST):fully reconstruct one 𝑫'
𝚫𝑬 = 𝑬𝑫' − 𝑬𝐛𝐞𝐚𝐦
𝑴𝐁𝐂 =𝑬𝟐𝐛𝐞𝐚𝐦 − 𝒑𝑫' 𝟐
PRL124(2020)231801

Tag

p Double tag (DT):in the recoil ST 𝑫'(𝒔) ,analyze the signal 𝑫$(𝒔)𝐌𝐌𝟐 = 𝑬𝟐𝐦𝐢𝐬𝐬 − 𝒑𝐦𝐢𝐬𝐬 𝟐
𝑬𝐦𝐢𝐬𝒔 = 𝑬𝐜𝐦 −𝒑𝑫'(𝒔)

𝟐𝒆$

4.178
GeV𝒆'𝑫∗$𝒔
𝑫$𝒔𝑿Signal𝜸(𝝅𝟎 )l Single tag (ST):fully reconstruct one 𝑫'𝒔
𝑴𝐫𝐞𝐜 =𝑬𝐜𝐦 −𝒑𝑫"𝒔arXiv: 2102.11734 [hep-ex]+ 𝑴𝟐𝑫(𝒔) − 𝑬𝑿

𝝅'

𝑫'𝒔

Charge conjugatedprocesses are implied
The signal branching
fraction:𝐬𝐢𝐠𝐧𝐚𝐥𝑵𝐃𝐓
𝑩𝐬𝐢𝐠 = 𝐒𝐓
𝑵𝑫(𝒔) ×𝝐𝐬𝐢𝐠

𝑲'

𝑲$

#$

𝑲 𝑲 𝝅

𝟐𝟐+ 𝒎𝟐𝑫"𝒔− −𝒑𝑫"𝒔

PRD104(2021)012003$

𝑲# 𝑲$ 𝝅$𝒑𝐦𝐢𝐬𝐬 = −𝒑𝑫'(𝒔) − 𝒑𝑿
𝑼𝐦𝐢𝐬𝐬 = 𝑬𝐦𝐢𝐬𝐬 − 𝒑𝐦𝐢𝐬𝐬𝐭𝐚𝐠
𝑴𝐁𝐂 (𝐆𝐞𝐕/𝒄𝟐 )or other variables

𝑴𝐫𝐞𝐜 (𝐌𝐞𝐕/𝒄𝟐 )𝟐𝐌𝐈𝐧𝐯 (𝐌𝐞𝐕/𝒄𝟐 )8"Pure leptonic 𝑫𝒔 decays
In the SM :೧ᅘႻഀ೹ᅇᅘ១ഐ˪ ШഁИ ഒЩT𝝂𝚪 𝑫T→𝒍𝒍(𝒔)=𝑮𝟐𝑭 𝒇𝟐𝑫1(𝒔)𝟖𝝅ഋႻ೺Ⴛ

ഃᄮቑᆴ

𝑽𝒄𝒅 𝒔𝟐ྻᅓ𝒎𝟐𝒍 𝒎𝑫1𝒔𝒎𝟐𝒍
𝟏− 𝟐𝒎𝑫1(𝒔)𝟐9AAA𝑫A→𝝉𝝂𝐯𝐢𝐚
𝝉
→𝒆𝝂𝒆 𝝂) 𝝉𝒔𝝉
arXiv: 2106.02218 [hep-ex]✍ 𝑬𝐭𝐨𝐭𝐞𝐱𝐭𝐫𝐚 : the total energy of the good EMC showers, excluding those associated with the ST𝐨𝑫'𝒔 candidates and those within 𝟓 of the initial direction of the positron.
𝐧𝐨𝐧'𝑫2𝐭𝐨𝐭
𝐭𝐨𝐭✍ DT yield in signal 𝑬𝐞𝐱𝐭𝐫𝐚 < 𝟎. 𝟒 GeV : 𝑵𝐃𝐓 = 𝑵𝐃𝐓 − 𝑵𝐃𝐓 𝒔

Signal peak

K0SK-

200

400
200

K0SK-/+/-

100

K0SK+/-/-

150/+/-/-

400
300

100
50

200
50/-d200
150
100
50

100
100/-/0d400/-d’ 0500K-/+/-

300

al/-d’ + -/ /d

200

200

0.5

1

1.5

2

Data" →𝝉𝑩𝑫Best
𝟓. 𝟐𝟕 ± 𝟎. 𝟏𝟎𝐬𝐭𝐚𝐭. ± 𝟎. 𝟏𝟐𝐬𝐲𝐬𝐭. %fit " 𝝂 =𝒔𝝉200-

1000The background yield of 𝑫$𝒔$→ 𝑿 𝒆 𝝂𝒆 is extrapolated
from the fit to 𝑬𝐭𝐨𝐭
𝐞𝐱𝐭𝐫𝐚> 𝟎. 𝟔 GeV.

-K+K /-/0

600

500

100

Events / (0.1 GeV)

800

-K+K /-1000"𝑲𝟎𝑿𝒆" 𝝂𝒆𝑳 𝒆 𝝂𝒆− 𝑵𝐃𝐓− 𝑵𝐃𝐓

non-Ds bkg

100
0.5

1

1.5

20D+sAXe+i e bkg

0.5

1

1.5

E totextra (GeV)

2The
D AmostK e i bkgprecise result to date+s-0 +e
L
D AK0S/- bkg for DsAK0SK

10AAA 𝟎)
𝑫A→
𝝉𝝂
𝐯𝐢𝐚𝝉
→𝝅𝝅 𝝂𝝉𝒔𝝉
arXiv: 2105.07178 [hep-ex], accepted by PRD• Simultaneous fit to the 𝐌𝐌 𝟐 for six energy points shared with a common leptonic
branching fraction.
Signal yields: 𝟏𝟕𝟒𝟓 ± 𝟖𝟒

𝐌𝐌𝟐 = 𝑬𝟐𝐦𝐢𝐬𝐬 − 𝒑𝐦𝐢𝐬𝐬 𝟐𝑬𝐦𝐢𝐬𝒔 = 𝑬𝐜𝐦 −𝒑𝑫'𝒔

𝟐𝑩𝑫"𝒔 →𝝉"𝝂𝝉 = 𝟓. 𝟐𝟗 ± 𝟎. 𝟐𝟓𝐬𝐭𝐚𝐭. ± 𝟎. 𝟐𝟎𝐬𝐲𝐬𝐭. %+ 𝑴𝟐𝑫𝒔 − 𝑬𝜸 − 𝑬𝝅3 𝝅𝟎𝒑𝐦𝐢𝐬𝐬 = −𝒑𝑫'𝒔 − 𝒑𝜸 − 𝒑𝝅3 𝝅𝟎11AAA)
AA
𝑫A→
𝝉𝝂
𝐯𝐢𝐚
𝝉
→
𝝅𝝂and𝑫→𝝁𝝂𝝁𝒔𝝉𝝉𝒔
arXiv: 2102.11734 [hep-ex], accepted by PRD• An unbinned simultaneous maximum likelihood fit to two-dimensional distributions
Only show @ 4.178 GeVµ-likeFor all data samples
𝐬𝐢𝐠𝐧𝐚𝐥

𝑵𝑫"→𝝉"𝝂 = 𝟗𝟒𝟔$𝟒𝟔'𝟒𝟓𝒔

𝝉𝐬𝐢𝐠𝐧𝐚𝐥

𝑵𝑫"→𝝁"𝝂 = 𝟐𝟏𝟗𝟖 ± 𝟓𝟓𝒔

𝝁p-like𝟐𝑴𝐢𝐧𝐯 𝑫(𝒔 𝐌𝐞𝐕/𝒄𝑴𝟐𝐦𝐢𝐬𝐬 𝐆𝐞𝐕/𝒄𝟐

𝟐$'𝟐
𝑩 𝑫$𝒔 → 𝝉 𝝂𝝉 = 𝟓. 𝟐𝟏 ± 𝟎. 𝟐𝟓𝐬𝐭𝐚𝐭. ± 𝟎. 𝟏𝟕𝐬𝐲𝐬𝐭. ×𝟏𝟎$'𝟑 The most precise to date.
𝑩 𝑫$𝒔 → 𝝁 𝝂𝝁 = 𝟓. 𝟑𝟓 ± 𝟎. 𝟏𝟑𝐬𝐭𝐚𝐭. ± 𝟎. 𝟏𝟔𝐬𝐲𝐬𝐭. ×𝟏𝟎
12

Lepton flavor universality•Combine results from BESIII measurements and PDG2020
PDG2020

PTEP2020(2020)083C01

5.48±0.23

CLEO

PRD79(2009)052002, oe i5.30±0.47±0.22

CLEO

PRD80(2009)112004, oli5.52±0.57±0.21

CLEOPRD79(2009)052001, o/ i

6.42±0.81±0.18

BaBarPRD82(2010)091103, oe,µi

5.00±0.35±0.49

BelleJHEP09(2013)139, oe,µ, / i

5.70±0.21±0.31

BESIII 0.482 fb-1 PRD94(2016)072004, o/i3.28±1.83±0.37

BESIII 6.32 fb-1

arXiv:2102.11734 [hep-ex], o/ i 5.21±0.25±0.17

BESIII 6.32 fb-1

arXiv:2105.07178 [hep-ex], oli 5.29±0.25±0.20

BESIII 6.32 fb-1

arXiv:2106.02218 [hep-ex], oe i 5.27±0.10±0.12-2024++B(Ds A o io) (×10-2)$e $𝚪(𝑫𝒔 → 𝝉 𝝂𝝉 )𝑹𝝉/𝝁 ==$e𝚪(𝑫$𝒔 → 𝝁 𝝂𝝁 )𝒎𝟐𝝉"𝒎𝟐𝝉"
𝟏− 𝟐𝒎𝑫 "𝒔𝒎𝟐𝝁" 𝟏 −𝒎𝟐𝝁"𝟐𝟐𝒎𝟐𝑫"𝒔6= 𝟗. 𝟔𝟕 ± 𝟎. 𝟑𝟒

𝟗. 𝟕𝟓 ± 𝟎. 𝟎𝟏(SM prediction)

No LFU violation in 𝝉 − 𝝁 flavors with thecurrent precision.

13

Comparison of decay constant 𝒇𝑫"𝒔"
𝑩 𝑫"
𝑽𝒄0𝒔 → 𝒍 𝝂𝒍 ∝ 𝒇𝑫$𝒔𝟐• Input 𝑽𝒄𝒔 = 𝟎. 𝟗𝟕𝟑𝟐𝟎 ± 𝟎. 𝟎𝟎𝟎𝟏𝟏 from CKM global fit
ETM(2+1+1)
FMILC(2+1+1)
FLAG19(2+1+1)

PRD91(2015)054507
PRD98(2018)074512
arXiv:1902.08191 [hep-lat]247.2±4.1
249.9±0.4249.9±0.5

HFLAV18
CLEO
CLEO
CLEO
BaBar
Belle
BESIII 0.482 fb-1
CLEOBaBar
Belle
BESIII 3.19 fb-1
BESIII 6.32 fb-1
BESIII 6.32 fb-1
BESIII 6.32 fb-1
BESIII 6.32 fb-1

EPJC81(2021)226
PRD79(2009)052002, oe i
PRD80(2009)112004, oli
PRD79(2009)052001, o/ i
PRD82(2010)091103, oe,µi
JHEP09(2013)139, oe,µ, / i
PRD94(2016)072004, µ i
PRD79(2009)052001, µ i
PRD82(2010)091103, µ i
JHEP09(2013)139, µ i
PRL122(2019)071802, µ i
arXiv:2102.11734 [hep-ex], µ i
arXiv:2102.11734 [hep-ex], o/ i
arXiv:2105.07178 [hep-ex], oli
arXiv:2106.02218 [hep-ex], oe i254.5±3.2251.8±11.2±5.3
257.0±13.3±5.0
277.1±17.5±4.0
244.6±8.6±12.0
261.1±4.8±7.2
245.5±17.8±5.1
256.7±10.2±4.0
264.9±8.4±7.6
248.8±6.6±4.8
253.0±3.7±3.6
249.8±3.0±3.8
249.7±6.0±4.2
251.6±5.9±4.9251.1±2.4±3.00100fD+s [MeV]

20030014

Comparison of |𝑽𝒄𝒔 |• Input 𝒇𝑫"𝒔 = 𝟐𝟒𝟗. 𝟗 ± 𝟎. 𝟓 from LQCD calculations
CKMFitter

PTEP2020(2020)083C01

0.97320±0.00011

EPJC81(2021)226
HFLAV18
PRD79(2009)052002, oei
CLEO
PRD80(2009)112004, oli
CLEO
PRD79(2009)052001, o/i
CLEO
PRD82(2010)091103, oe,µi
BaBar
JHEP09(2013)139, oe,µ,/i
Belle
BESIII 0.482 fb-1 PRD94(2016)072004, µi
PRD79(2009)052001, µi
CLEO
PRD82(2010)091103, µi
BaBar
JHEP09(2013)139, µi
Belle-1 PRL122(2019)071802, µi
BESIII 3.19 fb
BESIII 6.32 fb-1 arXiv:2102.11734 [hep-ex], µi
BESIII 6.32 fb-1 arXiv:2102.11734 [hep-ex], o/i
BESIII 6.32 fb-1 arXiv:2105.07178 [hep-ex], oli
BESIII 6.32 fb-1 arXiv:2106.02218 [hep-ex], oei-10|Vcs|

0.969±0.010
0.981±0.044±0.021
1.001±0.052±0.019
1.079±0.068±0.016
0.953±0.033±0.047
1.017±0.019±0.028
0.956±0.069±0.020
1.000±0.040±0.016
1.032±0.033±0.029
0.969±0.026±0.019
0.985±0.014±0.014
0.973±0.012±0.015
0.972±0.023±0.016
0.980±0.023±0.019
0.978±0.009±0.012

115

Semi-leptonic 𝑫(𝒔) decay
In the SM೧ᅘႻេႱ
ኜ೹ᅇᅘ១ ೺ Ⴛഀഐᆣ˪ ШഔИ ഁИ ഒЩ𝒅𝚪𝑮𝟐𝑭 𝒑𝟑=𝑿𝒇" 𝒒𝟐𝟐𝟑𝒅𝒒
𝟐𝟒𝝅𝟐

𝑽𝒄𝒅 𝒔ഃႻᄺ ԕഐႳԡ𝟐ഋႻ

ྻᅓ
ഐ
ഐᆣ˪

ೳ

, 𝟎 , 𝜼(3) ; 𝑿 =, (𝑿 = 𝟏 𝐟𝐨𝐫 𝑲*, 𝝅*, 𝑲

𝟏𝐟𝐨𝐫 𝝅𝟎 )𝟐16

𝑫A → 𝜼𝝁A 𝝂𝝁𝒆$ 𝒆' → 𝝍 𝟑𝟕𝟕𝟎 → 𝑫$ 𝑫' 2.93 fb-1 @3.773 GeV= (𝟏𝟓𝟐𝟐. 𝟓 ± 𝟐. 𝟏)×𝟏𝟎𝟑

ü 𝜼 → 𝜸𝜸ü Unbinned fit to 𝑼𝐦𝐢𝐬𝐬
𝐬𝐢𝐠𝐧𝐚𝐥𝑵𝐃𝐓= 𝟐𝟑𝟒 ± 𝟐𝟐𝑩𝑫"→𝜼𝝁"𝝂𝝁 = 𝟏𝟎. 𝟒 ± 𝟏. 𝟎𝐬𝐭𝐚𝐭. ± 𝟎. 𝟓𝐬𝐲𝐬𝐭. ×𝟏𝟎'𝟒

𝑹𝝁/𝒆 =𝑩𝑫"→𝜼𝝁"𝝂𝝁

𝐄𝐯𝐞𝐧𝐭𝐬/(𝟔 𝐌𝐞𝐕)

𝐬𝐢𝐠𝐧𝐚𝐥No. of single tags: 𝑵𝐒𝐓

PRL124(2020)231801

𝐒𝐢𝐠. > 𝟏𝟎𝝈−𝟎. 𝟏

𝟎. 𝟎𝟎. 𝟏

𝑼𝐦𝐢𝐬𝐬 (𝐆𝐞𝐕)= 𝟎. 𝟗𝟏 ± 𝟎. 𝟏𝟑
𝐏𝐃𝐆
𝑩𝑫"→𝜼𝒆"𝝂𝒆

SM prediction: (𝟎. 𝟗𝟕 − 𝟏. 𝟎𝟎)
No LFU violation within current sensitivity.

17

First measurement on dynamics of 𝑫$ → 𝜼𝝁$ 𝝂•

𝝁 decay𝜼Form factor 𝒇$ 𝒒𝟐

Partial decay rates

𝜼𝒇$ 𝟎 𝑽𝒄𝒅 = 𝟎. 𝟎𝟖𝟕 ± 𝟎. 𝟎𝟎𝟖𝐬𝐭𝐚𝐭. ± 𝟎. 𝟎𝟎𝟐𝐬𝐲𝐬𝐭.

PRL124(2020)231801

𝜼𝒇$ 𝒒𝟐 is parameterized by thetwo parameter series expansion.

𝜼𝒇$ 𝟎 = 𝟎. 𝟑𝟗 ± 𝟎. 𝟎𝟒𝐬𝐭𝐚𝐭. ± 𝟎. 𝟎𝟏𝐬𝐲𝐬𝐭.
𝑽𝒄𝒅 = 𝟎. 𝟐𝟒𝟐 ± 𝟎. 𝟎𝟐𝟐𝐬𝐭𝐚𝐭. ± 𝟎. 𝟎𝟎𝟔𝐬𝐲𝐬𝐭. ± 𝟎. 𝟎𝟑𝟑𝐭𝐡𝐞𝐨𝐫𝐲18

𝑫𝟎 → 𝑲𝟏 𝟏𝟐𝟕𝟎 b 𝒆A 𝝂𝒆arXiv: 2102.10850 [hep-ex]

ü 𝑲𝟏 𝟏𝟐𝟕𝟎 ' → 𝑲' 𝝅$ 𝝅'ü Two-dimensional unbinned extended maximum-likelihood simultaneous fits shared withthe same value of [𝑩𝑫𝟎→𝑲𝟏 𝟏𝟐𝟕𝟎 2 𝒆"𝝂𝒆 ⋅ 𝑩𝑲𝟏 𝟏𝟐𝟕𝟎 2→𝑿→𝑲2𝝅"𝝅2 ].
𝐬𝐢𝐠𝐧𝐚𝐥𝐒𝐢𝐠. > 𝟏𝟎𝝈𝑵𝐃𝐓= 𝟏𝟎𝟗. 𝟎 ± 𝟏𝟐. 𝟓'𝟑𝑩𝑫𝟎→𝑲𝟏 𝟏𝟐𝟕𝟎 2 𝒆"𝝂𝒆 = 𝟏. 𝟎𝟗 ± 𝟎. 𝟏𝟑$𝟎.𝟎𝟗'𝟎.𝟏𝟑 ± 𝟎. 𝟏𝟐𝐞𝐱. ×𝟏𝟎

𝚪𝑫𝟎→𝑲𝟏 𝟏𝟐𝟕𝟎 2𝒆"𝝂𝒆𝚪𝑫"→𝑲W 𝟏(𝟏𝟐𝟕𝟎)𝟎𝒆"𝝂𝒆= 𝟏. 𝟐𝟎 ± 𝟎. 𝟎𝟐𝐬𝐭𝐚𝐭. ± 𝟎. 𝟏𝟒𝐬𝐲𝐬𝐭. ± 𝟎. 𝟎𝟒𝐞𝐱.

Agrees with unity as
predicted by isospin
symmetry.
19

A
𝑫A→𝑿𝒆
𝝂𝒆𝒔
PRD104(2021)012003

ü 𝑿 means inclusive decays

ü Sort recoil-side selected tracks into eighteen momentum (𝒑𝒆 ) bins for 𝒑𝒆 > 𝟐𝟎𝟎 𝐌𝐞𝐕/𝒄𝐬𝐢𝐠𝐧𝐚𝐥

ü The signal yield 𝑵𝑫" →𝑿𝒆"𝝂 = 𝑵𝒑𝒆Y𝟐𝟎𝟎 𝐌𝐞𝐕/𝒄 + 𝑵𝒑𝒆\𝟐𝟎𝟎 𝐌𝐞𝐕/𝒄 (𝐞𝐱𝐭𝐫𝐚𝐩𝐨𝐥𝐚𝐭𝐞)𝒔𝐬𝐢𝐠𝐧𝐚𝐥

𝑵𝑫" →𝑿𝒆"𝝂 = 𝟏𝟔𝟔𝟒𝟖 ± 𝟑𝟐𝟔𝒔𝒆𝒆$'𝟐
𝑩 𝑫$𝒔 → 𝑿𝒆 𝝂𝒆 = (𝟔. 𝟑𝟎 ± 𝟎. 𝟏𝟑𝐬𝐭𝐚𝐭. ± 𝟎. 𝟏𝟎𝐬𝐲𝐬𝐭. )×𝟏𝟎

𝚪𝑫"𝒔 →𝑿𝒆"𝝂𝒆𝚪𝑫𝟎→𝑿𝒆"𝝂𝒆= 𝟎. 𝟕𝟗𝟎 ± 𝟎. 𝟎𝟏𝟔𝐬𝐭𝐚𝐭. ± 𝟎. 𝟎𝟐𝟎𝐬𝐲𝐬𝐭.

• Consistent with the prediction of 0.813

extrapolate• Supports the conclusion that thedifference in the semileptonic decay
widths of 𝑫$𝒔) and 𝑫𝟎 𝒄3
𝒖 mesons𝒔 (𝒄ecan be accounted for within theStandard model by non-spectator
interactions.
20

Hadronic decaysThe 𝝍 𝟑𝟕𝟕𝟎 has a 𝑪 = −𝟏 quantum number

3𝟎𝒆$ 𝒆' → 𝝍 𝟑𝟕𝟕𝟎 → 𝑫𝟎 𝑫and this is conserved in the strong decay inwhich two neutral 𝑫 mesons are produced.
Hence, the two neutral mesons have anantisymmetric wave function. This also meansthat the two 𝑫 mesons do not decay
independently of one another.
3 𝟎 pair will be a quantum-correlated state
The 𝑫𝟎 𝑫21

𝑫 → 𝑲𝟎𝑺,𝑳 𝝅A 𝝅b
PRL124(2020)241802; PRD101(2020)112002

3 𝟎 quantum correlation à Directly measure the strong-phase difference• 𝝍 𝟑𝟕𝟕𝟎 → 𝑫𝟎 𝑫
3 𝟎 decays à The key inputs for a binned model-independent𝚫𝜹𝑫 between 𝑫𝟎 and 𝑫determination of the CKM angle 𝜸/𝝓𝟑 with 𝑩 decays.
• 𝒄𝒊 and 𝒔𝒊 are the amplitude-weightedaverages of 𝐜𝐨𝐬 𝚫𝜹𝑫 and 𝐬𝐢𝐧 𝚫𝜹𝑫 overeach Dalitz plot bin.
• The estimated uncertainties on 𝜸/𝝓𝟑 :between 0.7° and 1.2°.

𝑫 → 𝑲𝟎𝑺 𝝅$ 𝝅'Equal 𝚫𝜹𝑫 binnings

Optimal 𝚫𝜹𝑫 binnings Modified optimal 𝚫𝜹𝑫 binnings

22𝑫 → 𝑲𝟎𝑺,𝑳 𝑲A 𝑲b
PRD102(2020)052008• Equal 𝚫𝜹𝑫 binnings scheme: with2/3/4 pairs of bins.

𝑪𝑷 − 𝐞𝐯𝐞𝐧 𝐯𝐬. 𝑲𝟎𝑺 𝑲$ 𝑲'

𝑪𝑷 − 𝐨𝐥𝐝 𝐯𝐬. 𝑲𝟎𝑺 𝑲$ 𝑲'• 𝒎± : 𝒎 𝑲𝟎𝑺 𝑲± .
• The estimated uncertainties on 𝜸/𝝓𝟑 : 2.3°, 1.3°, and 1.3° for 2, 3, 4
pairs of bins schemes.
𝑫 → 𝑲𝟎𝑺 𝑲$ 𝑲'

23

𝑫 → 𝑲A 𝝅A 𝝅A 𝝅b 𝐚𝐧𝐝 𝑫 → 𝑲b 𝝅A 𝝅𝟎JHEP05(2021)164• A 𝝌𝟐 fit：obtain the coherence factors (𝑹) and the average strong-phase differences (𝜹𝐃 )𝑹𝑲𝟑𝝅 = 𝟎. 𝟓𝟐$𝟎.𝟏𝟐'𝟎.𝟏𝟎

𝑫 → 𝑲$ 𝝅$ 𝝅$ 𝝅'

𝑫 → 𝑲' 𝝅$ 𝝅𝟎

𝑹𝑲𝝅𝝅𝟎 = 𝟎. 𝟕𝟖 ± 𝟎. 𝟎𝟒
𝜹𝑲𝟑𝝅= (𝟏𝟔𝟕$𝟑𝟏𝑫'𝟏𝟗 )°𝟎𝜹𝑲𝝅𝝅= (𝟏𝟗𝟔$𝟏𝟒𝑫'𝟏𝟓 )°• 𝚫𝝌𝟐 𝐬𝐜𝐚𝐧𝐬: 𝚫𝝌𝟐 = 𝟐. 𝟑𝟎, 𝟔. 𝟏𝟖, 𝟏𝟏. 𝟖𝟑 intervals correspond to 68.3%, 95.4%, and 99.7%
confidence levels in the 2D parameter space:• Besides, the phase space of 𝑫 → 𝑲$ 𝝅$ 𝝅$ 𝝅' is divided into four bins. Based on thisresults, the estimated uncertainty on 𝜸/𝝓𝟑 is around 6°.
24

𝑫A → 𝑲A 𝝅A 𝝅b 𝝅𝟎
PRL125(2020)141802• The naive expectation for the doubly Cabibbo-suppressed (DCS) decay rate relative to its
Cabibbo-favored (CF) counterpart 𝑹 = 𝑩 𝐃𝐂𝐒 /𝑩(𝐂𝐅) is of the order 𝐭𝐚𝐧𝟒 𝜽𝑪 ~𝟎. 𝟐𝟗%
level, where 𝜽𝑪 is the Cabibbo mixing angle.
• 2D fits for all events; simultaneous 2D fits for 𝝎 events
All events

Sig. = 𝟐𝟑. 𝟑𝝈"" " 2 𝟎""→𝑲 𝝅 𝝅 𝝅
𝑵𝑫= 𝟑𝟓𝟎 ± 𝟐𝟐
𝐃𝐓→𝑲 𝝎
𝑵𝑫= 𝟗. 𝟐$𝟒.𝟎
𝐃𝐓'𝟑.𝟒Sig. = 𝟑. 𝟑𝝈25

PRL125(2020)141802'𝟓𝑩𝑫"→𝑲"𝝎 = 𝟓. 𝟕$𝟐.𝟓'𝟐.𝟏 𝐬𝐭𝐚𝐭. ± 𝟎. 𝟐𝐬𝐲𝐬𝐭. ×𝟏𝟎

𝑩∗𝑫"→𝑲"𝝅"𝝅2𝝅𝟎 = 𝟏. 𝟏𝟑 ± 𝟎. 𝟎𝟖𝐬𝐭𝐚𝐭. ± 𝟎. 𝟎𝟑𝐬𝐲𝐬𝐭. ×𝟏𝟎'𝟑*Remove contributions from𝜼/𝝎/𝝓 → 𝝅$ 𝝅' 𝝅𝟎• The ratio 𝑩 𝐃𝐂𝐒 /𝑩(𝐂𝐅) :𝑩∗𝑫"→𝑲"𝝅"𝝅2𝝅𝟎= 𝟏. 𝟖𝟏 ± 𝟎. 𝟏𝟓 % = 𝟔. 𝟐𝟖 ± 𝟎. 𝟓𝟐 𝐭𝐚𝐧𝟒 𝜽𝑪𝐏𝐃𝐆
3 " 2 " " 𝟎
𝑩𝑫 →𝑲 𝝅 𝝅 𝝅This ratio is significantly larger than the values 𝟎. 𝟐𝟏~𝟎. 𝟓𝟖 % from other DCS
decays, which implies that there is a massive isospin symmetry violation• The asymmetry:±± ± ∓ 𝟎→𝑲 𝝅 𝝅 𝝅𝑨𝑫=
𝑪𝑷𝑩𝑫"→𝑲"𝝅"𝝅2𝝅𝟎 − 𝑩𝑫2→𝑲2𝝅2𝝅"𝝅𝟎= (−𝟎. 𝟎𝟒 ± 𝟎. 𝟎𝟔𝐬𝐭𝐚𝐭. ± 𝟎. 𝟎𝟏𝐬𝐲𝐬𝐭. )𝑩𝑫"→𝑲"𝝅"𝝅2𝝅𝟎 + 𝑩𝑫2→𝑲2𝝅2𝝅"𝝅𝟎No evidence for CP violation is found.
26

Summary✍ With 2.93 𝐟𝐛'𝟏 @ 3.773 GeV and 6.32 fb-1 from 4.178-4.226 GeV data samples, BESIII
have studied• pure and semi-leptonic 𝑫(𝒔) decays, which provide precision calibration of LQCD
and precision measurements of CKM matrix elements.
• charm hadronic decays, which are key labs to understand non-perturbative QCD,
and provide important inputs to model-independent determination of CKM
angle 𝜸/𝝓𝟑 and charm mixing/CPV.
✍ In the near future, BESIII will collect 20 𝐟𝐛'𝟏 @ 3.773 GeV data sample, and another3 fb-1 @ 4.178 GeV[1], the single precisions will be further improvedà a new era ofprecision charm physics.

[1] M. Ablikim et al., Chin. Phys. C 44, 040001 (2020).

27

Backup28

• Form factor 𝒇" 𝟎 with input 𝑽𝒄𝒔 𝐂𝐊𝐌𝐟𝐢𝐭𝐭𝐞𝐫n Single pole model
𝒇$𝒒𝟐

n ISGW2 model

𝒇$ 𝟎=
𝟏 − 𝒒𝟐 /𝑴𝟐𝐩𝐨𝐥𝐞n Modified pole modeln Series expansion

𝒇$ 𝒒𝟐 = 𝒇$ 𝒒𝟐𝐦𝐚𝐱

𝒇$𝒒𝟐

=𝒓𝟐 𝟐
𝟏+𝒒𝐦𝐚𝐱 − 𝒒𝟐
𝟏𝟐'𝟐

𝒇$ 𝟎
𝒒𝟐
𝟏− 𝟐
𝑴𝐩𝐨𝐥𝐞

𝒒𝟐
𝟏−𝜶 𝟐
𝑴𝐩𝐨𝐥𝐞

9𝟏𝒇" 𝒕 =𝒂 (𝒕 )(𝟏 + j 𝒓𝒌 𝒕𝟎 𝒛 𝒕, 𝒕𝟎𝑷 𝒕 𝚽 𝒕, 𝒕𝟎 𝟎 𝟎
𝒌8𝟏29𝒌)