Houbing Jiang , Qiyun Li , Ke Li , Zhiqing Liu , …...Fix 4040and 4160 mass and width (PDG values);...

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Search for + βˆ’ β†’ ,, using data above + βˆ’ CM energy ~4 GeV 1 Houbing Jiang , Qiyun Li , Ke Li , Zhiqing Liu , ChangZheng Yuan 1 , Xingtao Huang Shandong university IHEP 1 2019.3.13

Transcript of Houbing Jiang , Qiyun Li , Ke Li , Zhiqing Liu , …...Fix 4040and 4160 mass and width (PDG values);...

Page 1: Houbing Jiang , Qiyun Li , Ke Li , Zhiqing Liu , …...Fix 4040and 4160 mass and width (PDG values); Three times iteration of the radiative correction procedure to get converge values

Search for 𝒆+π’†βˆ’ β†’ πœΈπŒπ’„πŸŽ,π’„πŸ,π’„πŸ using data above 𝒆+π’†βˆ’ CM energy ~4 GeV

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Houbing Jiang , Qiyun Li , Ke Li , Zhiqing Liu , ChangZheng Yuan1 , Xingtao Huang

Shandong universityIHEP1

2019.3.13

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β—†Motivation

β€’ We hope use 𝑒+π‘’βˆ’ β†’ π›Ύπœ’π‘π‘— to give more information about Y states ;

β€’ E1 radiative transitions from the higher-mass charmonium states are especially interesting. For example : we can proof if ψ(4160) is 2D state

β€’ Some work before this study;(CPC 39,041001) (PhysRevD.92.012011);

Phys. Rev. D 72, 054026

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Section I 𝒆+π’†βˆ’ β†’ πœΈπŒπ’„πŸ,π’„πŸ

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β—†DATA Set

β€’ Boss version boss703

β€’ DATA

21 energy points XYZ data

β€’ Signal MC

𝑒+π‘’βˆ’ β†’ π‘Œ(4260) β†’ π›Ύπœ’π‘1,2 P2GC1/P2GC2

πœ’π‘1 β†’ 𝛾J/πœ“ AV2GV

πœ’π‘2 β†’ 𝛾J/πœ“ T2GV

C.M 𝒔(MeV) L（pb-1οΌ‰

4009 4007.6 482.0

4180 4173.0 3189.0

4190 4189.3 521.9

4200 4199.6 523.7

4210 4209.7 511.2

4220 4218.8 508.2

4230 4226.3 1047.3

4237 4235.8 508.9

4246 4243.9 532.7

4260 4258.0 825.7

4270 4266.9 529.3

4360 4358.3 539.8

4420 4415.6 1028.9

4600 4599.5 566.9

C.M 𝒔(MeV) L（pb-1οΌ‰

4090 4085.5 52.8

4280 4277.8 174.5

4310 4307.9 45.1

4390 4387.4 55.6

4470 4467.1 111.1

4530 4427.1 112.1

4575 4574.5 48.9

Named DataSet I : DataSet II:

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β—† Event Selection

β€’ Initial selection:

➒ Charged track:N=2

➒ photon :good photons>=2;

➒ e , μ selection :

➒ The two photon candidates with the largest energies are retained;

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β€’ Further selection:

➒ Clearly πœ‚π½/πœ“ evnets, let M(𝛾𝛾) < 0.52 || M(𝛾𝛾) > 0.58 GeV;

β€’ After above selection,the inclusiveMC study show the dominant backgrounds come from Bhabha events.

β—† Event Selection for 𝒆+π’†βˆ’ channel

M(𝜸𝜸)@4180 DATA M(πœΈπ‘³π‘±/𝝍) >3.3GeV Signal MC M(πœΈπ‘³π‘±/𝝍) >3.3GeV

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β—†Suppress Bhabha events in 𝒆+π’†βˆ’ channel

β€’ Let Cos𝑒+𝛾𝐻>-0.9&& Cosπ‘’βˆ’π›Ύπ» >-0.9&&Cos𝑒+𝛾𝐿 <0.9&& Cosπ‘’βˆ’π›ΎπΏ <0.9 ;β€’ |Cos 𝛾𝐻 |<0.8 to remove Bhabha events;

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β€’ Further selection:

➒ Clearly πœ‚π½/πœ“ evnets, let M(𝛾𝛾) < 0.52 || M(𝛾𝛾) > 0.58 GeV;➒ Clearly πœ‹0 background, let | M(𝛾𝛾) –M(πœ‹0 )|>0.015GeV;

β€’ After above selection, the inclusiveMC study show the dominant backgrounds come from𝒆+π’†βˆ’ β†’ (π’πœΈ)𝝁+πβˆ’;

β—† Event Selection for 𝝁+πβˆ’ channel

Signal MCM(𝜸𝜸)@4180 DATA M(πœΈπ‘³π‘±/𝝍) >3.3GeV

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➒ Let |Cos 𝛾𝐻 |<0.8 to suppress dimu events;

β—†Suppress dimu events in 𝝁+πβˆ’ channel

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β—†Chisq4c cut

Chisq4c<40

➒ In πŒπ’„πŸ, πŒπ’„πŸ region:

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β—†M(πœΈπ‘³π‘±/𝝍) distribution@4180

β€’ Clearly, there are πœ’π‘1,2 events.

➒ After above cut:

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πœ’π‘1 MC

Scatter Plot of MC

β—†Photons distribution @4009

➒ Obviously, some πœ’π‘2 decay to 𝛾HJ/πœ“ at 4009 energy point. To πœ’π‘1 MC, also there is an overlap between the two photons distributions .so we decide to use two photons to search signal.

πœ’π‘2 MC

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β—†Photons distribution @4180

πœ’π‘1 MC

Scatter Plot of MC

➒ Obviously, the distribution of two photons is essentially without overlap,andalmost all πœ’π‘1,2 decay to low energy photon . So we use low energy photon to search signal

πœ’π‘2 MC

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β—†Signal extraction(DataSet I)

➒ For dataset I, We use fit method;

Fit Method

β€’ As analyzed above , we use both of the two photons to search signal at 4009 (2D- Fit), and use the low energy photon to search signal at others energy points.

β€’ Fit 𝑒+π‘’βˆ’ and πœ‡+πœ‡βˆ’ two channel Simultaneously.

β€’ Fit Shape:➒ @4009Signal use signal MC M(𝛾𝐿𝐽/πœ“) and M(𝛾𝐻𝐽/πœ“) 2-D shape ;Background use dimu or bhabha MC M(𝛾𝐿𝐽/πœ“) and M(𝛾𝐻𝐽/πœ“) 2-D shape;

➒ others Signal use signal MC M(𝛾𝐿𝐽/πœ“) fit to dataBackground 2-order Chebychev

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β—†Fit result @4009 (2-D simultaneously fit)

M(𝛾𝐻𝐽/πœ“)

M(𝛾𝐿𝐽/πœ“)

πœ‡+πœ‡βˆ’ 𝑒+π‘’βˆ’ combine

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β—†Fit result @4180 (simultaneously fit)

πœ‡+πœ‡βˆ’ 𝑒+π‘’βˆ’ combine

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➒ Using six xyz data to fill in large gaps between somehigh-statistic energy points , For dataset II,we use count method:

β€’ Define signal region: πœ’π‘1(3.49,3.53) πœ’π‘2(3.54,3.58) ,note the number of events as n;

β€’ Define sideband region (3.42,3.46) (3.6,3.64),note the number of events as b;

β€’ Statistical error:Suppose n and b follow Poisson distribution;

β—†Signal extraction(DataSet II)

C.M N_c1 N_c2 b

4090 2 0 7

4280 10 5 20

4310 2 4 3

4390 3 3 4

4470 8 0 6

4530 2 2 3

4575 1 0 1

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β—†Cross Section and lineshape of 𝒆+π’†βˆ’ β†’ πœΈπŒπ’„πŸ,π’„πŸ

➒ Firstly, we use πœ“ 4160 lineshape to get radiation correction factor;

β€’ Using follow fumula measure cross section:

➒ Fit to 𝒆+π’†βˆ’ β†’ πœΈπŒπ’„πŸ,π’„πŸ cross section:

β€’ Fit Method(likelihood Method): Define likelihood fuction:

@4180 We suppose the number of events follow Gaussion distribution; @ others We suppose the number of events follow possion distribution;

β„’ =ΰ·‘

i=1

𝐺(𝜎, 𝑁𝑒π‘₯𝑝)ΰ·‘

𝑖

𝑃(𝑁fit , 𝑁𝑒π‘₯𝑝)

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β—†The line shape of 𝒆+π’†βˆ’ β†’ πœΈπŒπ’„πŸ,π’„πŸ(Model I)

➒ Fit fuction(two coherent Breit-Wigner functions), because of the very similar line-shape ,we give a simultaneously（decay from same resonenceοΌ‰ fit:

πœŽπ‘‘π‘Ÿπ‘’π‘ π‘  = BW1+ π΅π‘Š2π‘’π‘–πœ™2

➒ Three times iteration of the radiative correction procedure to get converge values(For the first time , we use πœ“(4160) line-shape to get radiative correction factor)

β€’ 𝒆+π’†βˆ’ β†’ πœΈπŒπ’„πŸ (1+𝛿) βˆ— 𝑒𝑓𝑓 only πœ‡+πœ‡βˆ’

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𝒆+π’†βˆ’ β†’ πœΈπŒπ’„πŸ

𝒆+π’†βˆ’ β†’ πœΈπŒπ’„πŸ

β—†The line shape of 𝒆+π’†βˆ’ β†’ πœΈπŒπ’„πŸ,π’„πŸ(Model I-2-BW)

➒ Parameters➒ Fit result

Parameters I

M(R1) 3866.4Β± 326.6

Ξ“π‘‘π‘œπ‘‘(𝑅1) 523.1 Β± 87.9

Γ𝑒𝑒ℬ(𝑅1β†’ πœΈπŒπ’„πŸ)

2.8 Β± 0.7

Γ𝑒𝑒ℬ(𝑅1β†’ πœΈπŒπ’„πŸ)

4.2 Β± 0.7

M(R2) 4225.6 Β± 2.7

Ξ“π‘‘π‘œπ‘‘(𝑅2) 28.5 Β± 5.4

Γ𝑒𝑒ℬ(𝑅2β†’ πœΈπŒπ’„πŸ)

0.094 Β± 0.006

Γ𝑒𝑒ℬ(𝑅2β†’ πœΈπŒπ’„πŸ)

0.015 Β± 0.006

πœ™1(πœΈπŒπ’„πŸ) 79.2Β±0.3

πœ™2(πœΈπŒπ’„πŸ) 343.1Β±0.2

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β—†The line shape of 𝒆+π’†βˆ’ β†’ πœΈπŒπ’„πŸ,π’„πŸ(Model I-2-BW)

➒ Cross section 𝒆+π’†βˆ’ β†’ πœΈπŒπ’„πŸ(Data Set I)

𝒔 L(pb-1) 𝝐_𝒆𝒆 𝝐_𝒖𝒖 1+𝜹 πˆπ’…π’“π’†π’”π’”(𝒆𝒆)πˆπ’…π’“π’†π’”π’”(𝝁𝝁) Sig

4.0076 482.0 0.196 0.325 0.943 πŸ’. πŸβˆ’πŸ.πŸ“+πŸ‘.𝟎 πŸ“. πŸβˆ’πŸ.πŸ”

+𝟏.πŸ– 4.1𝝈

4.1783 3194.5 0.184 0.308 0.972 𝟐. πŸ—βˆ’πŸ.𝟎+𝟏.𝟏 πŸ‘. πŸ“βˆ’πŸŽ.πŸ”

+𝟎.πŸ” 7.6𝝈

4.1888 522.5 0.188 0.319 0.941 𝟎. πŸ“βˆ’πŸ.𝟐+𝟐.πŸ” πŸ’. πŸ•βˆ’πŸ.πŸ’

+𝟏.πŸ” 3.9𝝈

4.1989 524.6 0.196 0.329 0.898 𝟏. πŸ‘βˆ’πŸ.πŸ—+𝟐.πŸ‘ 𝟏. πŸ•βˆ’πŸ.𝟏

+𝟏.πŸ‘ 3.1𝝈

4.2092 518.1 0.201 0.338 0.839 𝟏. πŸ–βˆ’πŸ.πŸ“+𝟐.πŸ— 𝟏. πŸ•βˆ’πŸ.𝟏

+𝟏.πŸ’ -

4.2187 514.3 0.213 0.356 0.789 βˆ’πŸ. πŸβˆ’πŸ.𝟏+𝟐.πŸ“ 𝟏. πŸ‘βˆ’πŸ.𝟎

+𝟏.𝟐 -

4226.3 1047.3 0.212 0.360 0.819 βˆ’πŸ. πŸ•βˆ’πŸ.𝟐+𝟏.πŸ’ 𝟎. πŸβˆ’πŸŽ.πŸ“

+𝟎.πŸ” -

4.2357 530.6 0.204 0.347 0.970 βˆ’πŸŽ. πŸ’βˆ’πŸ.πŸ•+𝟐.𝟎 βˆ’πŸŽ.πŸβˆ’πŸŽ.πŸ”

+𝟎.πŸ• -

4.2438 537.4 0.188 0.316 1.127 𝟐. πŸ’βˆ’πŸ.πŸ—+𝟐.𝟐 βˆ’πŸ’.πŸ”βˆ’πŸ.πŸ’

+𝟏.πŸ“ -

4.258 825.7 0.164 0.275 1.291 πŸ‘. πŸ—βˆ’πŸ.πŸ•+𝟏.πŸ— 𝟏. πŸ‘βˆ’πŸŽ.πŸ”

+𝟎.πŸ• -

4.2668 529.3 0.152 0.258 1.336 𝟏. πŸŽβˆ’πŸ.πŸ“+𝟏.πŸ— 𝟎. πŸ•βˆ’πŸŽ.πŸ—

+𝟏.𝟏 -

4.3583 539.8 0.133 0.231 1.379 βˆ’πŸŽ. πŸβˆ’πŸ.πŸ–+𝟐.𝟏 𝟎. πŸ–βˆ’πŸŽ.πŸ•

+𝟎.πŸ— -

4.4156 1028.9 0.129 0.223 1.400 βˆ’πŸŽ. πŸ‘βˆ’πŸ.𝟏+𝟏.πŸ‘ 𝟐. πŸβˆ’πŸŽ.πŸ•

+𝟎.πŸ– -

4.5995 566.9 0.114 0.204 1.520 βˆ’πŸŽ. πŸβˆ’πŸ.πŸ”+𝟐.𝟎 𝟏. πŸ’βˆ’πŸŽ.πŸ•

+𝟎.πŸ— -

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β—†The line shape of 𝒆+π’†βˆ’ β†’ πœΈπŒπ’„πŸ,π’„πŸ(Model I-2-BW)

➒ Cross section 𝒆+π’†βˆ’ β†’ πœΈπŒπ’„πŸ(Data Set II)

𝒔 L(pb-1) 𝝐 1+𝜹 πˆπ’…π’“π’†π’”π’”

4.0855 52.8 0.238 0.990 βˆ’πŸ‘. πŸŽβˆ’πŸ‘.πŸ–+πŸ“.πŸ”

4.2778 174.5 0.180 1.356 πŸŽβˆ’πŸ.πŸ‘+𝟐.πŸ—

4.3079 45.1 0.174 1.369 𝟏. πŸβˆ’πŸ‘.𝟐+πŸ“.πŸ’

4.3874 55.6 0.170 1.384 𝟏. πŸ—βˆ’πŸ‘.πŸ’+πŸ“.𝟐

4.4671 111.1 0.163 1.428 πŸ’. πŸ–βˆ’πŸ.πŸ–+πŸ‘.πŸ”

4.4271 112.1 0.155 1.470 𝟎. πŸ“βˆ’πŸ.πŸ’+𝟐.πŸ‘

4.5745 48.9 0.154 1.503 𝟏. πŸβˆ’πŸ.πŸ–+πŸ‘.πŸ–

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β—†The line shape of 𝒆+π’†βˆ’ β†’ πœΈπŒπ’„πŸ,π’„πŸ(Model I-2-BW)

➒ Cross section 𝒆+π’†βˆ’ β†’ πœΈπŒπ’„πŸ(Data Set I)

𝒔 L(pb-1) 𝝐_𝒆𝒆 𝝐_𝒖𝒖 1+𝜹 πˆπ’…π’“π’†π’”π’”(𝒆𝒆)πˆπ’…π’“π’†π’”π’”(𝝁𝝁) Sig

4.0076 482.0 0.182 0.297 0.959 πŸπŸ‘. πŸβˆ’πŸ“.πŸ‘+πŸ”.𝟏 πŸ“. πŸ‘βˆ’πŸ.πŸ’

+𝟐.πŸ– 3.2𝝈

4.1783 3194.5 0.139 0.225 1.292 πŸ’. πŸ•βˆ’πŸ.πŸ–+𝟏.πŸ— πŸ’. πŸβˆ’πŸŽ.πŸ—

+𝟏.𝟎 5.4𝝈

4.1888 522.5 0.130 0.218 1.357 πŸ‘. πŸ•βˆ’πŸ’.𝟏+πŸ’.πŸ• 𝟐. πŸ–βˆ’πŸ.πŸ•

+𝟐.𝟎 -

4.1989 524.6 0.128 0.216 1.337 πŸ—. πŸ’βˆ’πŸ’.πŸ•+πŸ“.πŸ’ πŸ‘. πŸβˆ’πŸ.𝟏

+𝟐.πŸ” -

4.2092 518.1 0.148 0.249 1.069 πŸ—. πŸ•βˆ’πŸ“.πŸ–+πŸ”.πŸ“ 𝟏. πŸ•βˆ’πŸ.πŸ–

+𝟐.πŸ‘ -

4.2187 514.3 0.182 0.313 0.811 βˆ’πŸŽ. πŸ–βˆ’πŸ“.𝟏+πŸ“.πŸ– πŸ’. πŸ•βˆ’πŸ.𝟏

+πŸ‘.πŸ” -

4226.3 1047.3 0.202 0.338 0.749 βˆ’πŸ. πŸ‘βˆ’πŸ.πŸ”+𝟐.πŸ— βˆ’πŸŽ.πŸ–βˆ’πŸŽ.πŸ—

+𝟏.𝟏 -

4.2357 530.6 0.202 0.337 0.809 πŸ“. πŸ•βˆ’πŸ.𝟏+𝟐.πŸ— βˆ’πŸ.πŸ–βˆ’πŸ.𝟏

+𝟏.𝟐 -

4.2438 537.4 0.195 0.331 0.877 πŸ’. πŸ”βˆ’πŸ.πŸ”+πŸ’.𝟐 βˆ’πŸ.πŸβˆ’πŸ.πŸ”

+𝟏.πŸ— -

4.258 825.7 0.186 0.316 0.964 𝟐. πŸ“βˆ’πŸ‘.𝟎+πŸ‘.πŸ’ 𝟐. πŸ’βˆ’πŸ.πŸ’

+𝟏.πŸ” -

4.2668 529.3 0.177 0.299 1.001 πŸ“. πŸŽβˆ’πŸ‘.πŸ–+πŸ’.πŸ’ βˆ’πŸ‘.πŸ–βˆ’πŸ.πŸ”

+𝟏.πŸ• -

4.3583 539.8 0.149 0.251 1.167 𝟏. πŸ—βˆ’πŸ’.𝟎+πŸ’.πŸ” 𝟐. πŸ–βˆ’πŸ.πŸ•

+𝟐.𝟏 -

4.4156 1028.9 0.138 0.236 1.231 𝟏. πŸ‘βˆ’πŸ.πŸ”+πŸ‘.𝟎 πŸ’. πŸŽβˆ’πŸ.πŸ‘

+𝟏.πŸ“ 3.1𝝈

4.5995 566.9 0.117 0.208 1.380 βˆ’πŸ‘. πŸ”βˆ’πŸ.πŸ“+πŸ‘.𝟏 𝟎. πŸ•βˆ’πŸŽ.πŸ—

+𝟏.πŸ‘ -

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β—†The line shape of 𝒆+π’†βˆ’ β†’ πœΈπŒπ’„πŸ,π’„πŸ(Model I-2-BW)

➒ Cross section 𝒆+π’†βˆ’ β†’ πœΈπŒπ’„πŸ(Data Set II)

𝒔 L(pb-1) 𝝐 1+𝜹 πˆπ’…π’“π’†π’”π’”

4.0855 52.8 0.205 1.037 βˆ’πŸπŸ–. πŸβˆ’πŸ”.πŸ‘+πŸ—.𝟐

4.2778 174.5 0.213 1.038 βˆ’πŸ’. πŸ‘βˆ’πŸ‘.𝟎+πŸ‘.πŸ–

4.3079 45.1 0.196 1.099 πŸ—. πŸŽβˆ’πŸ”.πŸ—+𝟏𝟎.𝟐

4.3874 55.6 0.178 1.189 πŸ‘. πŸβˆ’πŸ“.πŸ•+πŸ–.πŸ•

4.4671 111.1 0.166 1.273 βˆ’πŸ”. πŸ”βˆ’πŸ.πŸ‘+πŸ‘.πŸ“

4.4271 112.1 0.157 1.321 𝟎. πŸ–βˆ’πŸ.πŸ’+πŸ’.𝟎

4.5745 48.9 0.152 1.361 βˆ’πŸ“. πŸ•βˆ’πŸ.πŸ”+πŸ’.πŸ”

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➒ Fit fuction: Suppose the line shape determined by πœ“ 4040 and πœ“ 4160 in 4~4.18GeV,we use(simultaneously fit ):

πœŽπ‘‘π‘Ÿπ‘’π‘ π‘  = π΅π‘Š πœ“ 4040 + π΅π‘Š πœ“ 4160 π‘’π‘–πœ™1 + π΅π‘Š(𝑅1)π‘’π‘–πœ™22;

➒ Fix πœ“ 4040 andπœ“ 4160 mass and width (PDG values);

➒ Three times iteration of the radiative correction procedure to get converge values (For the first time , we use πœ“(4160) line-shape to get radiative correction factor)

β€’ 𝒆+π’†βˆ’ β†’ πœΈπŒπ’„πŸ (1+𝛿) βˆ— 𝑒𝑓𝑓 only mumu

β—†The line shape of 𝒆+π’†βˆ’ β†’ πœΈπŒπ’„πŸ,π’„πŸ(Model II-3BW)

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β—†The line shape of 𝒆+π’†βˆ’ β†’ πœΈπŒπ’„πŸ,π’„πŸ

𝒆+π’†βˆ’ β†’ πœΈπŒπ’„πŸ

𝒆+π’†βˆ’ β†’ πœΈπŒπ’„πŸ

➒ Fitting result : ➒ Parameters:

Parameters I

M(πœ“ 4040 ) 4039(𝑓𝑖π‘₯𝑒𝑑)

Ξ“π‘‘π‘œπ‘‘(πœ“ 4040 ) 80(fixed)

Γ𝑒𝑒ℬ(πœ“ 4040 β†’ πœΈπŒπ’„πŸ) 0.8Β±0.3

Γ𝑒𝑒ℬ(πœ“ 4040 β†’ πœΈπŒπ’„πŸ) 1.6 Β±0.4

M(πœ“ 4160 ) 4191(fixed)

Ξ“π‘‘π‘œπ‘‘(πœ“ 4160 ) 70(fixed)

Γ𝑒𝑒ℬ(πœ“ 4160 β†’ πœΈπŒπ’„πŸ) 1.0 Β± 0.3

Γ𝑒𝑒ℬ(πœ“ 4160 β†’ πœΈπŒπ’„πŸ) 1.8 Β± 0.6

M(R2) 4244.8 Β± 6.3

Ξ“π‘‘π‘œπ‘‘(𝑅2) 83.2 Β± 14.8

Γ𝑒𝑒ℬ(𝑅2 β†’ πœΈπŒπ’„πŸ) 0.8 Β± 0.2

Γ𝑒𝑒ℬ(𝑅2 β†’ πœΈπŒπ’„πŸ) 1.5 Β± 0.8

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β—†The line shape of 𝒆+π’†βˆ’ β†’ πœΈπŒπ’„πŸ,π’„πŸ(Model II-3-BW)

➒ Cross section 𝒆+π’†βˆ’ β†’ πœΈπŒπ’„πŸ(Data Set I)

𝒔 L(pb-1) 𝝐_𝒆𝒆 𝝐_𝒖𝒖 1+𝜹 πˆπ’…π’“π’†π’”π’”(𝒆𝒆) πˆπ’…π’“π’†π’”π’”(𝝁𝝁)

4.0076 482.0 0.233 0.378 0.763 πŸ’. πŸ‘βˆ’πŸ.πŸ•+πŸ‘.𝟏 πŸ“. πŸ’βˆ’πŸ.πŸ•

+𝟏.πŸ—

4.1783 3194.5 0.220 0.375 0.778 πŸ‘. πŸβˆ’πŸ.𝟎+𝟏.𝟏 πŸ‘. πŸ“βˆ’πŸŽ.πŸ”

+𝟎.πŸ”

4.1888 522.5 0.222 0.374 0.783 𝟎. πŸ“βˆ’πŸ.πŸ‘+𝟐.πŸ” πŸ’. πŸ–βˆ’πŸ.πŸ’

+𝟏.πŸ”

4.1989 524.6 0.220 0.375 0.802 𝟏. πŸ‘βˆ’πŸ.πŸ—+𝟐.πŸ‘ πŸ‘. πŸ—βˆ’πŸ.πŸ’

+𝟏.πŸ”

4.2092 518.1 0.216 0.363 0.825 𝟏. πŸ•βˆ’πŸ.πŸ’+𝟐.πŸ• 𝟏. πŸ”βˆ’πŸ.𝟎

+𝟏.πŸ‘

4.2187 514.3 0.215 0.362 0.844 βˆ’πŸ. πŸŽβˆ’πŸ.𝟎+𝟐.πŸ‘ 𝟏. πŸβˆ’πŸŽ.πŸ—

+𝟏.𝟏

4226.3 1047.3 0.214 0.363 0.853 βˆ’πŸ. πŸ”βˆ’πŸ.𝟏+𝟏.πŸ‘ 𝟎. πŸβˆ’πŸŽ.πŸ“

+𝟎.πŸ”

4.2357 530.6 0.213 0.363 0.863 βˆ’πŸŽ. πŸ“βˆ’πŸ.πŸ–+𝟐.𝟐 βˆ’πŸŽ.πŸβˆ’πŸŽ.πŸ”

+𝟎.πŸ–

4.2438 537.4 0.214 0.349 0.875 𝟐. πŸ•βˆ’πŸ.𝟐+𝟐.πŸ“ βˆ’πŸ“.πŸ’βˆ’πŸ.πŸ–

+𝟏.πŸ•

4.258 825.7 0.207 0.347 0.917 πŸ’. πŸ‘βˆ’πŸ.πŸ—+𝟐.𝟐 𝟏. πŸ’βˆ’πŸŽ.πŸ•

+𝟎.πŸ–

4.2668 529.3 0.198 0.334 0.957 𝟏. πŸŽβˆ’πŸ.πŸ”+𝟐.𝟎 𝟎. πŸ–βˆ’πŸ.𝟎

+𝟏.𝟐

4.3583 539.8 0.122 0.210 1.577 βˆ’πŸŽ. πŸβˆ’πŸ.πŸ”+𝟐.𝟎 𝟎. πŸ–βˆ’πŸŽ.πŸ•

+𝟎.πŸ–

4.4156 1028.9 0.095 0.164 1.985 βˆ’πŸŽ. πŸ‘βˆ’πŸ.𝟏+𝟏.πŸ‘ 𝟐. πŸŽβˆ’πŸŽ.πŸ•

+𝟎.πŸ–

4.5995 566.9 0.054 0.097 3.244 βˆ’πŸŽ. πŸβˆ’πŸ.πŸ”+𝟐.𝟎 𝟏. πŸ‘βˆ’πŸŽ.πŸ•

+𝟎.πŸ—

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β—†The line shape of 𝒆+π’†βˆ’ β†’ πœΈπŒπ’„πŸ,π’„πŸ(Model II-3-BW)

➒ Cross section 𝒆+π’†βˆ’ β†’ πœΈπŒπ’„πŸ(Data Set II)

𝒔 L(pb-1) 𝝐 1+𝜹 πˆπ’…π’“π’†π’”π’”

4.0855 52.8 0.264 0.901 βˆ’πŸ. πŸ—βˆ’πŸ‘.πŸ•+πŸ“.πŸ“

4.2778 174.5 0.237 1.049 πŸŽβˆ’πŸ.πŸ‘+𝟐.πŸ—

4.3079 45.1 0.205 1.289 𝟏. πŸβˆ’πŸ‘.𝟐+πŸ“.𝟐

4.3874 55.6 0.135 2.004 𝟏. πŸ–βˆ’πŸ‘.πŸ‘+πŸ“.𝟎

4.4671 111.1 0.099 2.712 πŸ’. πŸ–βˆ’πŸ.πŸ•+πŸ‘.πŸ”

4.4271 112.1 0.089 3.240 𝟎. πŸ’βˆ’πŸ.πŸ‘:+𝟐.𝟏

4.5745 48.9 0.075 3.657 𝟏. πŸβˆ’πŸ.πŸ–+πŸ‘.πŸ–

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β—†The line shape of 𝒆+π’†βˆ’ β†’ πœΈπŒπ’„πŸ,π’„πŸ(Model II-3-BW)

➒ Cross section 𝒆+π’†βˆ’ β†’ πœΈπŒπ’„πŸ(Data Set I)

𝒔 L(pb-1) 𝝐_𝒆𝒆 𝝐_𝒖𝒖 1+𝜹 πˆπ’…π’“π’†π’”π’”(𝒆𝒆) πˆπ’…π’“π’†π’”π’”(𝝁𝝁)

4.0076 482.0 0.222 0.357 0.760 πŸπŸ‘. πŸ”βˆ’πŸ“.πŸ“+πŸ”.πŸ‘ πŸ“. πŸ”βˆ’πŸ.πŸ“

+πŸ‘.𝟎

4.1783 3194.5 0.208 0.339 0.779 πŸ“. πŸβˆ’πŸ.𝟎+𝟐.𝟏 πŸ’. πŸ•βˆ’πŸ.𝟎

+𝟏.𝟏

4.1888 522.5 0.206 0.350 0.780 πŸ’. πŸŽβˆ’πŸ’.πŸ“+πŸ“.𝟐 πŸ‘. πŸβˆ’.𝟏.πŸ–

+𝟐.𝟐

4.1989 524.6 0.209 0.349 0.797 πŸ—. πŸ•βˆ’πŸ’.πŸ—+πŸ“.πŸ” πŸ‘. πŸ’βˆ’πŸ.𝟐

+𝟐.πŸ•

4.2092 518.1 0.204 0.338 0.818 πŸ—. πŸβˆ’πŸ“.πŸ“+πŸ”.𝟐 𝟏. πŸ•βˆ’πŸ.πŸ•

+𝟐.𝟐

4.2187 514.3 0.201 0.337 0.838 βˆ’πŸŽ. πŸ•βˆ’πŸ’.πŸ“+πŸ“.𝟏 πŸ’. πŸβˆ’πŸ.𝟎

+𝟐.πŸ’

4226.3 1047.3 0.205 0.343 0.851 βˆ’πŸ. πŸβˆ’πŸ.𝟐+𝟐.πŸ“ βˆ’πŸŽ.πŸ•βˆ’πŸŽ.πŸ•

+𝟎.πŸ—

4.2357 530.6 0.203 0.335 0.864 πŸ“. πŸ‘βˆ’πŸ.𝟎+𝟐.πŸ” βˆ’πŸ.πŸ•βˆ’πŸŽ.πŸ—

+𝟏.𝟐

4.2438 537.4 0.197 0.332 0.880 πŸ’. πŸ“βˆ’πŸ‘.πŸ”+πŸ’.𝟐 βˆ’πŸ.πŸβˆ’πŸ.πŸ”

+𝟏.πŸ—

4.258 825.7 0.189 0.323 0.932 𝟐. πŸ”βˆ’πŸ‘.𝟏+πŸ‘.πŸ“ 𝟐. πŸ’βˆ’πŸ.πŸ’

+𝟏.πŸ”

4.2668 529.3 0.186 0.315 0.979 πŸ’. πŸ—βˆ’πŸ‘.πŸ•+πŸ’.πŸ‘ βˆ’πŸ‘.πŸ•βˆ’πŸ.πŸ“

+𝟏.πŸ”

4.3583 539.8 0.104 0.179 1.739 𝟏. πŸ—βˆ’πŸ‘.πŸ–+πŸ’.πŸ’ 𝟐. πŸ”βˆ’πŸ.πŸ”

+𝟏.πŸ—

4.4156 1028.9 0.075 0.135 2.263 𝟏. πŸ‘βˆ’πŸ.πŸ”+πŸ‘.𝟎 πŸ‘. πŸ–βˆ’πŸ.πŸ‘

+𝟏.πŸ“

4.5995 566.9 0.043 0.075 3.882 βˆ’πŸ‘. πŸ“βˆ’πŸ.πŸ“+πŸ‘.𝟏 𝟎. πŸ•βˆ’πŸ.𝟎

+𝟏.πŸ‘

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β—†The line shape of 𝒆+π’†βˆ’ β†’ πœΈπŒπ’„πŸ,π’„πŸ(Model II-3-BW)

➒ Cross section 𝒆+π’†βˆ’ β†’ πœΈπŒπ’„πŸ(Data Set II)

𝒔 L(pb-1) 𝝐 1+𝜹 πˆπ’…π’“π’†π’”π’”

4.0855 52.8 0.205 1.037 βˆ’πŸπŸ–. πŸβˆ’πŸ”.πŸ‘+πŸ—.𝟐

4.2778 174.5 0.213 1.038 βˆ’πŸ’. πŸ‘βˆ’πŸ‘.𝟎+πŸ‘.πŸ–

4.3079 45.1 0.196 1.099 πŸ—. πŸŽβˆ’πŸ”.πŸ—+𝟏𝟎.𝟐

4.3874 55.6 0.178 1.189 πŸ‘. πŸβˆ’πŸ“.πŸ•+πŸ–.πŸ•

4.4671 111.1 0.166 1.273 βˆ’πŸ”. πŸ”βˆ’πŸ.πŸ‘+πŸ‘.πŸ“

4.4271 112.1 0.157 1.321 𝟎. πŸ–βˆ’πŸ.πŸ’+πŸ’.𝟎

4.5745 48.9 0.152 1.361 βˆ’πŸ“. πŸ•βˆ’πŸ.πŸ”+πŸ’.πŸ”

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β—†Compare these two fit methods

β€’ βˆ’ log 𝐿 ：

2-BW βˆ’ log 𝐿 =165.5 3βˆ’BW βˆ’ log 𝐿 =173.8

Can’t distinguish these two methods;

β€’ For Resonance: Consistent with each other , Also consistent with 𝒆+ π’†βˆ’ β†’ 𝝅+ π…βˆ’π‘±/𝝍 channel;

Parameters（MeVοΌ‰ 𝒆+π’†βˆ’ β†’ πœΈπŒπ’„πŸ,𝟐

M(R2) 4225.6Β±2.6

Ξ“(R2) 28.5Β±5.4

2-BW 3-BW

Parameters(MeV) 𝒆+π’†βˆ’ β†’ πœΈπŒπ’„πŸ,𝟐

M(R1) 4247.2Β±6.2

Ξ“(R1) 82.5Β±14.1

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β„’~2683.2

β„’~1533.6

β„’~2221.5

β—†Confirm the dip around 4.23GeV

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β—†Systematic uncertainty（Cross SectionοΌ‰

β€’ The luminosity : measured using Bhabha events, with uncertainty 1.0%;

β€’ Tracking efficiency : 1% is assigned to each track, 2% in total ;

β€’ branching ratios : 0.6% for each channel 𝐽/πœ“ β†’ 𝑒+π‘’βˆ’ , 𝐽/πœ“ β†’ πœ‡+πœ‡βˆ’;

β€’ branching ratios : 3.5% for πœ’π‘1 β†’ 𝛾J/πœ“, 3.6% for πœ’π‘2 β†’ 𝛾J/πœ“;

β€’ Photon efficiency: each 1%, total 2%;

β€’ Fit to M(𝛾𝐿𝐽/πœ“) :➒ Change background shape 2nd β€”> 3nd ;

➒ Fit Range-----> （3.4,3.65οΌ‰->（3.45,3.7οΌ‰πŒπ’„πŸ ~πŸ’. πŸ–% πŒπ’„πŸ ~πŸ•. 𝟐%

β€’ Kinematic fit: The difference efficiency between before and after pull correction;

πŒπ’„πŸ~𝟐. πŸ’%, πŒπ’„πŸ~𝟐. πŸ‘%

Use 4180

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β€’ Radiative correction: Take the difference νœ€ βˆ— (1 + 𝛿) between two fit models as systematic uncertainty;πœ’π‘1~2.7% πœ’π‘2~1% @4180

β€’ Total systematic uncertainty : 𝑒+π‘’βˆ’ β†’ π›Ύπœ’π‘1 ~ 7.5% ;𝑒+π‘’βˆ’ β†’ π›Ύπœ’π‘2 ~ 8.9%;

β—†Systematic uncertainty (Cross Section)

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β—†Systematic uncertainty（Resonance Y(4220)οΌ‰

β€’ The CMS energies of all dataset: 1MeV for mass mesurement;

β€’ The difference of Two models(width and mass );

Parameters(MeV) 𝒆+π’†βˆ’ β†’ πœΈπŒπ’„πŸ,𝟐

M(Y(4220)) 4225.6 Β± 2.7 Β±20.2

Ξ“π‘‘π‘œπ‘‘(π‘Œ(4220)) 28.5 Β± 5.4 Β±54.7

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β—†Upper Limit for (significance <3𝝈)

β€’ To evaluate the upper limits of cross section at 90% C.L. :Define likelihood fuction:

β€’ 𝑁0 is the fixed number of signal events;

β€’ 𝐺 𝑁0, 𝑁0𝜎 is Gauss function, 𝜎 is systematic uncertainty ;

β€’ The upper limit on the cross section is calculated with following formula:

β„’(𝑁0) = ࢱ𝐺 𝑁0, 𝑁0𝜎 βˆ— β„’(𝑁) 𝑑𝑁

πœŽπ‘π‘œπ‘Ÿπ‘›π‘’π‘

=𝑁𝑒𝑝

β„’ βˆ™ ℬ βˆ™ πœ– βˆ™ (1 + 𝛿) βˆ™ (1 + 𝛿𝑉𝑃)

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β—†Upper Limit @4230

β€’ After consider to system uncertainty, we give the number of signal upper limit at 90% confidence level:

β€’ Total systematic uncertainty : 𝑒+π‘’βˆ’ β†’ π›Ύπœ’π‘1 ~ 8.5% ;𝑒+π‘’βˆ’ β†’ π›Ύπœ’π‘2 ~ 15.8%;

𝑒+π‘’βˆ’ β†’ π›Ύπœ’π‘1 𝑒+π‘’βˆ’ β†’ π›Ύπœ’π‘2

πœŽπ‘π‘œπ‘Ÿπ‘›π‘’π‘

< 0.8pb πœŽπ‘π‘œπ‘Ÿπ‘›π‘’π‘

< 1.4pb

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β—†Upper Limit (For <3𝝈)

β€’ After consider to system uncertainty, we give the number of signal upper limit at 90% confidence level:

𝑒+π‘’βˆ’ β†’ π›Ύπœ’π‘1 𝑒+π‘’βˆ’ β†’ π›Ύπœ’π‘2

C.M Sys error(%) Upper Limit(pb)

4210 8.6 2.8

4220 10.8 1.8

4230 8.5 0.8

4237 10.3 1.3

4246 18.2 0.9

4260 13.5 2.2

4270 10.7 2.4

4360 8.1 1.6

4420 8.1 2.0

4600 7.3 2.24

C.M Sys error(%) Upper Limit(pb)

4190 12.1 4.1

4200 9.7 5.7

4210 9.6 5.1

4220 13.5 6.3

4230 15.8 1.4

4237 11.9 1.4

4246 8.8 4.0

4260 8.9 3.1

4270 9.4 2.1

4360 10.8 4.7

4600 9.0 1.9

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39

Section II 𝒆+π’†βˆ’ β†’ πœΈπŒπ’„πŸŽ

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β—†DATA Set

β€’ Boss version boss703

β€’ DATA

XYZ data

C.M 𝒔(MeV) L（pb-1οΌ‰

4009 4007.6 482.0

4180 4173.0 3189.0

4190 4189.3 521.9

4200 4199.6 523.7

4210 4209.7 511.2

4220 4218.8 508.2

4230 4226.3 1047.3

4237 4235.8 508.9

4246 4243.9 532.7

4260 4258.0 825.7

4270 4266.9 529.3

4360 4358.3 539.8

4420 4415.6 1028.9

4600 4599.5 566.9

DataSet :

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β—†MC Samples for πŒπ’„πŸŽ β†’ 𝑲+π‘²βˆ’ 𝝅+π…βˆ’/ 𝝅+π…βˆ’ 𝝅+π…βˆ’

β€’ In PDG , πŒπ’„πŸŽ π’„π’‚π’π’Žπ’‚π’Šπ’π’π’š π’…π’†π’„π’‚π’š 𝒕𝒐 𝑲+π‘²βˆ’ 𝝅+π…βˆ’ , through the following channel:𝝅+π…βˆ’ 𝝅+π…βˆ’

πœ‹+πœ‹βˆ’ πœ‹+πœ‹βˆ’

𝐾+πΎβˆ’ πœ‹+πœ‹βˆ’

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β—†MC Samples for πŒπ’„πŸŽ β†’ 𝑲+π‘²βˆ’ 𝝅+π…βˆ’/ 𝝅+π…βˆ’ 𝝅+π…βˆ’

β€’ Signal MC 𝑒+π‘’βˆ’ β†’ π‘Œ(4260) β†’ π›Ύπœ’π‘0 P2GC0

➒ πœ‹+πœ‹βˆ’ πœ‹+πœ‹βˆ’

1. πœ’π‘0 β†’ πœ‹+πœ‹βˆ’ πœ‹+πœ‹βˆ’ ; PHSP

2. πœ’π‘0 β†’ 𝜌0πœ‹+πœ‹βˆ’ ;

3. πœ’π‘0 β†’ 𝑓0(980)𝑓0(980);

➒ 𝐾+πΎβˆ’ πœ‹+πœ‹βˆ’

1.πœ’π‘0 β†’ 𝑲+π‘²βˆ’πœ‹+πœ‹βˆ’ ; PHSP

2. πœ’π‘0 β†’ 𝐾0βˆ—(1430)0𝐾0

βˆ—(1430)0;

3. πœ’π‘0 β†’ 𝐾0βˆ—(1430)0𝐾2

βˆ—(1430)0+c.c. ;4. πœ’π‘0 β†’ 𝐾1(1270)

+ +c.c.;5. πœ’π‘0 β†’ 𝐾1(1400)

+ +c.c.;6. πœ’π‘0 β†’ 𝑓0(980)𝑓0(2200);7. πœ’π‘0 β†’ 𝑓0(1370)𝑓0(1710);8. πœ’π‘0 β†’ ΰ΄₯πΎβˆ—(892)0πœ‹βˆ’ 𝐾++c.c.;9. πœ’π‘0 β†’ ΰ΄₯πΎβˆ—(892)0 πΎβˆ— (892)0;

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β€’ Initial selection:➒ Charged tracks:

N=4➒ photon :

good photon>=1;➒ PID:

K: Prob(K)>Prob(πœ‹),Prob(K)>0.001πœ‹: Prob(πœ‹)>Prob(𝐾),Prob(πœ‹)>0.001

➒ Retain the photon with the large energy➒ 4C Kinematic fit:

Ο‡2 < 30 πœ’π‘0 β†’ 𝐾+πΎβˆ’ πœ‹+πœ‹βˆ’

Ο‡2 < 30 πœ’π‘0 β†’ πœ‹+πœ‹βˆ’ πœ‹+πœ‹βˆ’

β—† Event Selection

πœ’π‘0 β†’ 𝐾+πΎβˆ’ πœ‹+πœ‹βˆ’ πœ’π‘0 β†’ πœ‹+πœ‹βˆ’ πœ‹+πœ‹βˆ’

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β—†Background study in 𝑲+π‘²βˆ’ 𝝅+π…βˆ’ mode

β€’ background events mainly come from:

1. 𝑒+π‘’βˆ’ β†’ (𝑛)𝛾𝐼𝑆𝑅𝐾+πΎβˆ’ πœ‹+πœ‹βˆ’;

2. 𝑒+π‘’βˆ’ β†’ π›ΎπΌπ‘†π‘…πΎβˆ—ΰ΄₯πΎβˆ—;

3. 𝑒+π‘’βˆ’ β†’ (𝑛)π›ΎπΌπ‘†π‘…πΎβˆ’ πœ‹βˆ’πΎβˆ—+c.c.;

4. include πœ™ β†’ 𝐾+πΎβˆ’ background;5. include πœ‚β€² β†’ π›ΎπœŒ0(𝜌0 β†’ πœ‹+πœ‹βˆ’)background;6. include 𝜌0 β†’ πœ‹+πœ‹βˆ’ background;

β€’ For πœ™ β†’ 𝐾+πΎβˆ’ background in M(𝐾+πΎβˆ’ πœ‹+πœ‹βˆ’)∈ [3.2,3.6]：

β€’ M(𝐾+πΎβˆ’)>1.05 GeV

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β—†Background study in 𝑲+π‘²βˆ’ 𝝅+π…βˆ’ mode

β€’ πœ‚β€² background in M(𝐾+πΎβˆ’ πœ‹+πœ‹βˆ’)∈ [3.2,3.6] :

β€’ background events mainly come from:

1. 𝑒+π‘’βˆ’ β†’ (𝑛)𝛾𝐼𝑆𝑅𝐾+πΎβˆ’ πœ‹+πœ‹βˆ’;

2. 𝑒+π‘’βˆ’ β†’ π›ΎπΌπ‘†π‘…πΎβˆ—ΰ΄₯πΎβˆ—;

3. 𝑒+π‘’βˆ’ β†’ (𝑛)π›ΎπΌπ‘†π‘…πΎβˆ’ πœ‹βˆ’πΎβˆ—+c.c.;

4. include πœ™ β†’ 𝐾+πΎβˆ’ background;5. include πœ‚β€² β†’ π›ΎπœŒ0(𝜌0 β†’ πœ‹+πœ‹βˆ’)background;6. include 𝜌0 β†’ πœ‹+πœ‹βˆ’ background;

𝑴 πœΈπ…+π…βˆ’ > 𝟎. πŸ—πŸ•

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β—†Background study in 𝝅+π…βˆ’ 𝝅+π…βˆ’ mode

β€’ All combinations of π›Ύπœ‹+πœ‹βˆ’ pairs in M(πœ‹+πœ‹βˆ’ πœ‹+πœ‹βˆ’)∈ [3.2,3.6]

β€’ M(π›Ύπœ‹+πœ‹βˆ’_hh)

β€’ background events mainly come from: 1. 𝑒+π‘’βˆ’ β†’ (𝑛)π›ΎπΌπ‘†π‘…πœ‹

+πœ‹βˆ’πœ‹+πœ‹βˆ’;2. 𝑒+π‘’βˆ’ β†’ (𝑛)π›ΎπΌπ‘†π‘…πœ‹

+πœ‹βˆ’πœ‹+πœ‹βˆ’;3. include 𝜌0 β†’ πœ‹+πœ‹βˆ’ background;4. include πœ‚β€² β†’ π›Ύπœ‹+πœ‹βˆ’ background;

β€’ M(π›Ύπœ‹+πœ‹βˆ’_lh) β€’ M(π›Ύπœ‹+πœ‹βˆ’_ll)

|M(π›Ύπœ‹+πœ‹βˆ’)-M(πœ‚β€²)|>0.01GeV

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β—†Fit to M(𝝅+π…βˆ’ 𝝅+π…βˆ’) and M(π’Œ+π’Œβˆ’ 𝝅+π…βˆ’)

β€’ Fit Method: Fit two channel simultaneously;β€’ MC shape + 2nd polynomial;

πœ’π‘0 β†’ πœ‹+πœ‹βˆ’ πœ‹+πœ‹βˆ’πœ’π‘0 β†’ 𝐾+πΎβˆ’ πœ‹+πœ‹βˆ’

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β—†Fit to M(𝝅+π…βˆ’ 𝝅+π…βˆ’) and M(π’Œ+π’Œβˆ’ 𝝅+π…βˆ’)

β€’ Fit Method: Fit two channel simultaneously;β€’ MC shape + 2nd polynomial;

πœ’π‘0 β†’ πœ‹+πœ‹βˆ’ πœ‹+πœ‹βˆ’πœ’π‘0 β†’ 𝐾+πΎβˆ’ πœ‹+πœ‹βˆ’

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β—†Systematic uncertainty

β€’ The luminosity : measured using Bhabha events, with uncertainty 1.0%;

β€’ Tracking efficiency : 1% is assigned to each track, 4% in total ;

β€’ branching ratios : 8% for πœ’π‘0 β†’ π‘˜+π‘˜βˆ’ πœ‹+πœ‹βˆ’, 8% for πœ’π‘0 β†’ πœ‹+πœ‹βˆ’ πœ‹+πœ‹βˆ’;

β€’ PID: ,1.0% per kaon or pion ~ 4%;

β€’ Kinematic fit: The difference efficiency between before and after pull correction;

πœ’π‘0 β†’ π‘˜+π‘˜βˆ’ πœ‹+πœ‹βˆ’ ~6%, πœ’π‘0 β†’ πœ‹+πœ‹βˆ’ πœ‹+πœ‹βˆ’ ~2%;Use 4180

β€’ Radiative correction:use 𝑒+π‘’βˆ’ β†’ π›Ύπœ’π‘1 line shape, take the difference νœ€ βˆ— (1 + 𝛿)between 2-bw and 3-bw model as systematic uncertainty; ~2.7% ~1%

β€’ @4180 Total systematic uncertainty : πœ’π‘0 β†’ π‘˜+π‘˜βˆ’ πœ‹+πœ‹βˆ’ ~11.8% ;πœ’π‘0 β†’ πœ‹+πœ‹βˆ’ πœ‹+πœ‹βˆ’~10.9%;

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β—†Upper Limit

β€’ To evaluate the upper limits of cross section at 90% C.L. :Define likelihood fuction:

β€’ 𝑁0 is the fixed number of signal events;

β€’ 𝐺 𝑁0, 𝑁0𝜎 is Gauss function, 𝜎 is systematic uncertainty ;

β€’ The upper limit on the cross section is calculated with following formula:

β„’(𝑁0) = ࢱ𝐺 𝑁0, 𝑁0𝜎 βˆ— β„’(𝑁) 𝑑𝑁

πœŽπ‘π‘œπ‘Ÿπ‘›π‘’π‘

=𝑁𝑒𝑝

β„’ βˆ™ ℬ βˆ™ πœ– βˆ™ (1 + 𝛿) βˆ™ (1 + 𝛿𝑉𝑃)

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Upper limit @4180

β€’ Suppose 𝑒+π‘’βˆ’ β†’ π›Ύπœ’π‘0 follow 𝑒+π‘’βˆ’ β†’ π›Ύπœ’π‘1β€² line shape (P19), we generate signal MC samples ;

β€’ Similarly, After consider to systematic uncertainty,we give the number of signal upper limit at 90% confidence level:

β€’ πœŽπ‘π‘œπ‘Ÿπ‘›π‘’π‘ <2.4pb;

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β—†Summary

β€’ Using data above 𝑒+π‘’βˆ’ CM energy ~4 GeV, we observed 𝑒+π‘’βˆ’ β†’ π›Ύπœ’π‘1,𝑐2at 4180, evidence for 𝑒+π‘’βˆ’ β†’ π›Ύπœ’π‘1 at 4009@4190@4200,evidence for 𝑒+π‘’βˆ’ β†’ π›Ύπœ’π‘2 at 4009@4420;

β€’ Branch ratio(4180) about ℬ(𝑒+π‘’βˆ’ β†’ π›Ύπœ’π‘1/ 𝑒+π‘’βˆ’ β†’ π›Ύπœ’π‘2)β‰ˆ 0.767βˆ’0.242+0.258, there is a big

difference from theoretical prediction about πœ“(4160) E1 radiative transitions ;

β€’ Both 𝑒+π‘’βˆ’ β†’ π›Ύπœ’π‘1 and 𝑒+π‘’βˆ’ β†’ π›Ύπœ’π‘2 show there are a dip around 4230, which might be due to the interference of the Y(4220) resonance;

β€’ Using πœ’π‘0 β†’ 𝐾+πΎβˆ’ πœ‹+πœ‹βˆ’/ πœ‹+πœ‹βˆ’ πœ‹+πœ‹βˆ’ ,we don`t observe 𝑒+π‘’βˆ’ β†’ π›Ύπœ’π‘0 signal, upper limit of born cross sections are given;

Thanks!

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Back Up

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β—†MC for πŒπ’„πŸŽ β†’ 𝑲+π‘²βˆ’ 𝝅+π…βˆ’/ 𝝅+π…βˆ’ 𝝅+π…βˆ’

β€’ Decay card：

𝝅+π…βˆ’ 𝝅+π…βˆ’ 𝑲+π‘²βˆ’ 𝝅+π…βˆ’

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Scan data

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Fit result @4180&4190&4200

πœ‡+πœ‡βˆ’ 𝑒+π‘’βˆ’ combine

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Fit result @4210&4220&4230

πœ‡+πœ‡βˆ’ 𝑒+π‘’βˆ’

combine

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Fit result @4237&4246&4260

πœ‡+πœ‡βˆ’ 𝑒+π‘’βˆ’ combine

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Fit result @4270&4280&4360

πœ‡+πœ‡βˆ’ 𝑒+π‘’βˆ’ combine

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Fit result @4420&4600

πœ‡+πœ‡βˆ’ 𝑒+π‘’βˆ’

combine

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βˆ† βˆ’ log 𝐿 = 85.116Ndf=6Sig>10

Significance test

β€’ 𝒆+π’†βˆ’ β†’ πœΈπŒπ’„πŸ

β€’ 𝒆+π’†βˆ’ β†’ πœΈπŒπ’„πŸ

βˆ† βˆ’ log 𝐿 = 46.906Ndf=5Sig>10

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β—†Compare these two fit methods

β€’ βˆ’ log 𝐿 ：2-BW βˆ’ log 𝐿 =165.5 3βˆ’BW βˆ’ log 𝐿 =173.8

Can’t distinguish these two methods;

β€’ For Resonance: Consistent with each other , Also consistent with 𝒆+ π’†βˆ’ β†’ 𝝅+ π…βˆ’π‘±/𝝍 channel;

Parameters（MeVοΌ‰ 𝒆+π’†βˆ’ β†’ πœΈπŒπ’„πŸ,𝟐

M(R2) 4225.6Β±2.6

Ξ“(R2) 28.5Β±5.4

2-BW 3-BW

Parameters(MeV) 𝒆+π’†βˆ’ β†’ πœΈπŒπ’„πŸ,𝟐

M(R1) 4247.2Β±6.2

Ξ“(R1) 82.5Β±14.1

𝒆+ π’†βˆ’ β†’ 𝝅+ π…βˆ’π‘±/𝝍

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β—†MC for πŒπ’„πŸŽ β†’ 𝑲+π‘²βˆ’ 𝝅+π…βˆ’/ 𝝅+π…βˆ’ 𝝅+π…βˆ’

β€’ Decay card：

𝝅+π…βˆ’ 𝝅+π…βˆ’ 𝑲+π‘²βˆ’ 𝝅+π…βˆ’


LI - SIVACON Verteileranschluss / LI - SIVACON switchboard ...

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Digital Human Modeling with Applications - FAA Fire Safety Β· PDF fileDigital Human Modeling with Applications Zhiqing Cheng, ... β€’ CAESAR database ... Seating Comfort Modeling β€’

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Xiangtai Li, Xia Li, Ansheng You, Li Zhang, Guangliang ...

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METHODOLOGY ARTICLE Open Access HGTector: an ...stacks.cdc.gov/view/cdc/25290/cdc_25290_DS1.pdfgene transfers Qiyun Zhu1*, Michael Kosoy2 and Katharina Dittmar1* Abstract Background:

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lliHUi li i li!

Industrial Organization Taught by Dr. Prof. Fang Qiyun Textbook: Industrial Organization: A Strategic Approach Written by Jeffrey Church & Roger Ware.

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Operating Systems Lecture 2 Processes and Threads Adapted from Operating Systems Lecture Notes, Copyright 1997 Martin C. Rinard. Zhiqing Liu School of.

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Know more about... Zhiqing Zhang zhangzhiqing@wust.edu.cn zhiqing.zhang.wust@gmail.com.

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2.3 He Li (Rui Zhen Li)

2.3 He Li (Rui Zhen Li)

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Stem Li Li 12 4 09

Stem Li Li 12 4 09

FR:TI-LI TO:TI-LI C.

FR:TI-LI TO:TI-LI C.

Operating Systems Lecture 11 MIPS TLB Structure Adapted from Operating Systems Lecture Notes, Copyright 1997 Martin C. Rinard. Zhiqing Liu School of Software.

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Li Auto Inc. (β€œLi Auto” or the β€œCompany”) (Nasdaq: LI), an ...

Li Auto Inc. (β€œLi Auto” or the β€œCompany”) (Nasdaq: LI), an ...

Chi-Li-Chi-Li-Bon !

Chi-Li-Chi-Li-Bon !

CAMP LI-LO-LI LIFE

CAMP LI-LO-LI LIFE