Rb measurement at CEPC MC Level Bo Li Outline Introduction Rb Double tagging method B-tagging performance Method I/O test Effect of c , uds and Cb 2 Introduction Rb : the relative decay width of Z into b quarks Based on the CEPC MC samples: Zbb, Zcc, Zuds Produced from FSClasser ~110k events

By using the Double tagging method 3 Introduction Double Tagging Method The two jets are divided into two hemispheres according to the plane perpendicul ar to the thrust axis Double tagging method : The ratio of one jet tagged as b jet The ratio of both jets tagged as b jets = + + ( 1 ) 2 h 2

2 2 = + + ( 1 ) h The are gotten from MC samples The , , are gotten from DATA samples 4 Rb method Double Tagging Method = + + ( 1 ) 2 h Get from MC

2 2 2 2 = + + ( 1 ) = h ( ) 1 LEP measurement 0.21594 0.00066 Syst error : ~0.2% Major systematics is hemisphere tag correlations CEPC Expected Syst error (0.02%)

hemisphere tag correlations depends on b tagging efficiency with a high b-tagging efficiency above 80% and rejection of charm and light jet above 90% Rb method Get From Mixed MC Sample Double Tagging Method = + + ( 1 ) 2 h Get from MC

2 2 2 2 = + + ( 1 ) = h ( ) 1 ratio of jet tagged as b jet in Hemisphere I = + + ( 1 The ) h = + + ( 1 The of ) jettagged

ratio as b jet in Hemisphere J h 2 = 6 B-tagging method The default algorithm is based on the LCFIPlus: combines more th an 60 variables to calculate the b jet probability by BDT method B-tagging method for hemisphere I: Calculating the b jet probability based on the number of ve rtex B-tagging method for hemisphere J: Calculating the b jet probability based on the number of l epton(we set >=1 lepton)

7 B-tagging method B-tagging method for hemisphere I: Calculating the b jet probability based on the number of vertex b jet efficiency and c, light jet rejection >0.45 >0.5 >0.6 >0.7 >0.8 >0.9 8 B-tagging method B-tagging method for hemisphere J: Calculating the b jet probability based on the numb er of lepton 9 Correlation

Factor 2D B_likelihood zbb 2 = I : Prob>0.45 >0.5 >0.6 >0.7 >0.8 >0.9 hemisphere J J : Prob>0.45 >0.5 >0.6 >0.7 >0.8 >0.9 Working point J hemisphere I W or

kin g Correlation Factors ~ 1 po in tJ Work oi nt p g n i I

Working point I 10 Rb method I/O test The ratio of jet tagged as b jet in Hemisphere I The ratio of jet tagged as b jet in Hemisphere J Following this procedure, we can meausere the Rb, b 11 The Z hadronic pseudoDATA is mixed by MC samples: Zbb sample, Zcc sample, Zll sample We set Rb=0.2, Rb=0.4, Rb=0.6 as the Input Rb to mix the DATA 11 Method

I/O test Input Rb=0.2, 0.4, 0.6. Btag work points: Prob>0.45 >0.5 >0.6 >0.7 >0.8 >0.9 Input Rb=0.2 Input Rb=0.4 Input Rb=0.6 12 Method Effect of c uds and Cb Input theory Rb=0.2158, Btag Prob work points: Prob>0.45 >0.5 >0.6 >0.7 >0.8 >0.9 I/O test with c 10%, uds 10%, Cb 10%

(Measured Rb-0.2158)/0.2158 Prob>0.45 Prob>0.50 Prob>0.60 Prob>0.70 Prob>0.8 Prob>0.9 c 10% 1.03% 0.82% 0.51%

0.31% 0.18% 0.08% uds 10% 0.36% 0.29% 0.19% 0.13% 0.09% 0.06%

Cb 10% 10.54% 10.51% 10.47% 10.45% 10.43% 10.42% 13 Plan Both the B-tagging efficiency for Z->bb and rejection for Z->cc, Z->uds

are good for method The double tagging method procedure works well as shown in I/O test The b tagging correlation factors ~ 1 Next step : Increase the statistics to reduce the effect from c uds and Cb Study on the systematic errors such as the gluon splitting, charm physics modeling 14 Back up

15 Method Effect of Cb Follow the procedure in : Measurement of Rb and Br(b X) at LEP Using Double-Tag X) at LEP Using Double-Tag X) at LEP Using Double-Tag Methods (L3 Collaboration) In section 4.3.3 Systematics from Hemisphere Correlation 1. The normalized distribution of for all hemispheres, N(). 2. The single-hemisphere tagging efficiency as a function of , (). 3. The normalized distribution of in a co-tagged hemisphere, C(). A co-tagged hemisphere is the one opposite to a tagged hemisphere, regardless of whether it is itself tagged. Angular effects: =cos; = QCD effects: =Energy_jet 16

Method Effect of Cb I : Prob>0.45 J : Prob>0.45 pt : 1.00904 d0: 0.99996 z0 : 1.00035 signd0 : 1.00074 signz0 : 0.999531 Thrust : 1.0032 Thrust_theta : 1.0021

Thrust_phi : 1.00006 Energy : 1.00149 Px : 1.00171 Py : 1.00154 Pz : 1.00086 ntrk : 0.999593 nclu : 0.99983 charge : 1.00037 mass : 1.00031 Ptot : 1.00449 Rapidity :

1.00563 17 Method I : Prob>0.45 : Jet_Pt Effect of Cb J : Prob>0.45 pt : 1.00904 18 Method I : Prob>0.45

Effect of Cb J : Prob>0.45 : Thrust Thrust : 1.0032 19 Method I : Prob>0.45 Effect of Cb J : Prob>0.45 Thrust_theta : 1.0021

20 Method I : Prob>0.45 Effect of Cb J : Prob>0.45 : Jet_ 21 Method I : Prob>0.45 Effect of Cb J : Prob>0.45

Thrust_phi : 1.00006 22 Method I : Prob>0.45 Effect of Cb J : Prob>0.45 : Jet_mass 23 Method Effect of Cb

I : Prob>0.9 J : Prob>0.9 pt : 1.04939 d0 : 1.0004 z0 : 1.0044 signd0 : 1.00092 signz0 : 0.998709 Thrust : 1.00788 Thrust_theta : 1.02492 Thrust_phi : 0.999965 Energy : 1.00962 Px :

1.01379 Py : 1.01177 Pz : 1.01045 ntrk : 1.00303 nclu : 1.00089 charge : 1.00152 mass : 1.00137 Ptot : 1.01527 Rapidity : 1.032 24

Check the measured Rb and effb in DATA are different from the Input Truth Rb and effb at Prob>0.9 The is got by MC samples: Zbbsample2, Zccsample2, Zllsample2 So if DATA sample1sample2 which means the MC is different from the DATA The difference as a Ratio: Eff in DATA/ Eff in MC1. difference between DATA and MC are very small 2. and differences are big at Prob>0.9 : which may come from the very low statistics after B-tagging which will lead to the difference in the IO test 3. effect is very small, as The Zllrejction at four work point are ~100% 25 Check

Input Rb=0.3 We redo the IO test by DATA and MC with same Zcc sample Zcc DATA Sample Zcc MC Sample Zcc DATA Sample= Zcc MC Sample We can see the differences of measured Rb and effb between DATA and MC are smaller 26 Check Input Rb=0.5 Zcc DATA Sample= Zcc MC Sample 27 Check

Input Rb=0.7 Zcc DATA Sample= Zcc MC Sample 28