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ATLAS Λ0b Baryon Studies
Dongliang Zhang (University of Michigan)
on behalf of ATLAS Collaboration
Hadron2015, Jefferson LabSeptember 13-18, 2015
Introduction Λ0b reconstruction Lifetime measurement Helicity study Λ0
b → ψ(2S)Λ0 Summary 1/18Λ0b baryon
q Λ0b is the lightest b-baryon
q m ∼ 5620 MeVq Beyond the reach of B-factoriesq Was less studied
q Lifetimeq Polarizationq Decay properties
q Included in this talk:
q Mass and lifetime measurement [Phys. Rev. D 87 (2013) 032002]q Λ0
b → J/ψΛ0 decay asymmetry parameter and helicity amplitude measurement [Phys.
Rev. D 89 (2014) 092009]q Observation of Λ0
b → ψ(2S)Λ0 decay and Γ(Λ0b → ψ(2S)Λ0)/Γ(Λ0
b → J/ψΛ0)measurement [arXiv:1507.08202 [hep-ex], submitted to Phys. Lett. B.]
Dongliang Zhang [UM] Hadron2015 14/09/2015
Introduction Λ0b reconstruction Lifetime measurement Helicity study Λ0
b → ψ(2S)Λ0 Summary 2/18ATLAS detector
Dongliang Zhang [UM] Hadron2015 14/09/2015
Introduction Λ0b reconstruction Lifetime measurement Helicity study Λ0
b → ψ(2S)Λ0 Summary 3/18J/ψ and Λ0 candidates
q J/ψ candidates
q Two combined muons, |η| < 2.5q Sufficient Inner Detector hitsq In J/ψ or ψ(2S) mass window
(MeV)µµm
2800 2900 3000 3100 3200 3300 3400
Candid
ate
s / 1
5 M
eV
0
10000
20000
30000
40000
50000
ATLAS
1 = 77 pbL
= 7 TeVs
q Λ0 candidates
q Two good ID tracks, pT > 400 MeVq pπ− and pπ+ combination, in Λ0
mass window
(MeV)πpm
1080 1090 1100 1110 1120 1130 1140 1150
Candid
ate
s / 3
.25 M
eV
0
20
40
60
80
100
120
140
1603
10×
ATLAS
1 = 77 pbL
= 7 TeVs
Dongliang Zhang [UM] Hadron2015 14/09/2015
Introduction Λ0b reconstruction Lifetime measurement Helicity study Λ0
b → ψ(2S)Λ0 Summary 4/18Λ0b reconstruction
q Λ0b fit
q mµ+µ− and mpπ− (mpπ+ ) fixed to J/ψ and Λ0 mass valuesq Dihadron vertex point to dimuon vertexq χ2/Ndof < 3
q Also fitted to B0d → J/ψ(µ+µ−)K 0
S (π+π−) hypothesis for B0d background
rejection cuts
q In lifetime measurementq Refitted Λ0
q pT > 3.5 GeVq Lxy > 10 mm
q PΛ0b− PB0
d> 0.05
Dongliang Zhang [UM] Hadron2015 14/09/2015
(MeV)0Λ ψJ/
M
5400 5500 5600 5700 5800 5900
Ca
nd
ida
tes /
17
Me
V0
50
100
150
200
250
300
350
400
450 candidates0
bΛ
candidates0
bΛ
ATLAS
1 = 4.9 fbL
= 7 TeVs
4074 Λ0b
4081 Λ0b
Introduction Λ0b reconstruction Lifetime measurement Helicity study Λ0
b → ψ(2S)Λ0 Summary 5/18Λ0b lifetime measurement
q Proper decay time
τ =Lxym
PDG
pT
q Mass-lifetime unbinned likelihood fit
L =N∏i=1
[fsigMs(mi |δmi )Ts(τi |δτ i )ws(δmi , δτ i ) + (1− fsig)Mb(mi |δmi )Tb(τi |δτ i )wb(δmi , δτ i )]
q Mass
q Ms(mi |δmi ): Gaussianq Mb(mi |δmi ): 1st order polynomial
q Proper decay time
q Ts(τi |δτ i ): exponential with efficiency correctionq Tb(τi |δτ i ):
– prompt: Dirac delta + symmetric exponential– non-prompt: two exponential
q ws,b(δmi , δτ i ) is the PDF for δmi and δτ i , from data and same for signal andbackground
Dongliang Zhang [UM] Hadron2015 14/09/2015
Introduction Λ0b reconstruction Lifetime measurement Helicity study Λ0
b → ψ(2S)Λ0 Summary 6/18Λ0b mass and lifetime
(MeV)0Λ ψJ/
m
5400 5500 5600 5700 5800 5900
Candid
ate
s / 1
7 M
eV
0
100
200
300
400
500
600
700
800 0.7 MeV± = 5619.7 bΛm
0.03± = 1.18 M
S
0.8 MeV± = 31.1 M
σ
57± = 2184 sigN
160± = 5970 bkg N
= 1.09dofN/2χ
= 7 TeVs1 = 4.9 fbL
Data
Fitted model
Signal
Background
ATLAS
(ps)τ
2 0 2 4 6 8 10 12
Candid
ate
s / 0
.46 p
s
10
210
310
0.036 ps± = 1.449 b
Λτ
0.02± = 1.05 τS
0.003 ps± = 0.117 τσ
= 1.09dofN/2χ
= 7 TeVs1 = 4.9 fbL
Data
Fitted model
Signal
Background
ATLAS
mΛ0b
= 5619.7± 0.7(stat)± 1.1(syst) MeV
τΛ0b
= 1.449± 0.036(stat)± 0.017(syst) ps
q Consistent with results from other experiments and theoretical predictions
q Main systematic uncertainty from muon trigger efficiency and Λ0 reconstructionbias
Dongliang Zhang [UM] Hadron2015 14/09/2015
Phys. Rev. D 87 (2013) 032002
Introduction Λ0b reconstruction Lifetime measurement Helicity study Λ0
b → ψ(2S)Λ0 Summary 7/18Λ0b → J/ψ(µ+µ−)Λ0(pπ−) decay
q Asymmetric decay
dN
d cos θ=
1
2(1 + P · αb cos θ)
q In subsequent decay:
q 4 helicity combination
Amplitude λΛ λJ/ψa+ = |a+|e iω+ 1/2 0a− = |a−|e iω− -1/2 0b+ = |b+|e iρ+ -1/2 -1b− = |b−|e iρ− 1/2 1
q Full PDF of Ω = (cos θ, φ, cos θ1, φ1, cos θ2, φ2):
w(Ω) =1
(4π)3
19∑i=0
f1i (~A)f2i (P, αΛ)Fi (Ω)
q 7 free parameters: P, 6 helicity parameters in ~A
Dongliang Zhang [UM] Hadron2015 14/09/2015
Introduction Λ0b reconstruction Lifetime measurement Helicity study Λ0
b → ψ(2S)Λ0 Summary 8/18Parametrization
q For αb measurement, using P = 0, reduced to 6 terms (i = 0, 2, 4, 6, 18, and 19)
q Parameters ~A
q αb = |a+|2 − |a−|2 + |b+|2 − |b−|2
q k+ = |a+|√|a+|2+|b+|2
q k− = |b−|√|a−|2+|b−|2
q ∆+ = ω+ − ρ+
q ∆− = ω− − ρ−
i f1i Fi
0 1 12 (k2
+ + k2− − 1) + αb(k2
+ − k2−) cos θ1
4 14
[(3k2− − 3k2
+ − 1) + 3αb(1− k2− − k2
+)] 0.5(3 cos2 θ2 − 1)
6 − 14
[(k2+ + k2
− − 1) + αb(3 + k2+ − k2
−)] 0.5(3 cos2 θ2 − 1) cos θ1
18 3√2
[ 1−αb2
√k2−(1− k2
−) cos(−∆−)− 1+αb2
√k2
+(1− k2+) cos(∆+)] sin θ1 sin θ2 cos θ2 cos(φ1 + φ2)
19 − 3√2
[ 1−αb2
√k2−(1− k2
−) sin(−∆−)− 1+αb2
√k2
+(1− k2+) sin(∆+)] sin θ1 sin θ2 cos θ2 sin(φ1 + φ2)
Dongliang Zhang [UM] Hadron2015 14/09/2015
Introduction Λ0b reconstruction Lifetime measurement Helicity study Λ0
b → ψ(2S)Λ0 Summary 9/18Method of moments
q Least square fit
χ2 =∑i
∑j
(〈Fi 〉expected − 〈Fi 〉)V−1ij (〈Fj〉expected − 〈Fj〉)
q 〈Fj〉 measured from dataq Vij is the covariance matrix
q 〈Fi 〉expected depends on the parameters ~A
〈Fi 〉expected(~A) =
∫Fi (Ω′)
∫T (Ω′,Ω)w(~A,Ω) dΩdΩ′
=∑j
1
(4π)3
∫∫f1j(~A)f2j(αΛ)Fi (Ω′)T (Ω′,Ω)Fj(Ω) dΩ′dΩ
=∑j
f1j(~A)f2j(αΛ)Cij
q The effects of detector are in Cij
q T (Ω′,Ω) is the resolution and efficiency function
Dongliang Zhang [UM] Hadron2015 14/09/2015
Introduction Λ0b reconstruction Lifetime measurement Helicity study Λ0
b → ψ(2S)Λ0 Summary 10/18Efficiency correction from MC
Cij=1
(4π)3
∫∫Fi (Ω′)Fj(Ω)T (Ω′,Ω) dΩ′dΩ
≈ εTNmc
Nmc∑n=1
Fi (Ω′n)Fj(Ωn)
1θcos
1 0.5 0 0.5 1
Fra
ctio
n /
0.1
0
0.02
0.04
0.06
0.08
0.1
Flat PDF
=1b
α
=0.3b
α
=1b
α
ATLAS
Simulation
2θcos
1 0.5 0 0.5 1
Fra
ctio
n /
0.1
0
0.02
0.04
0.06
0.08
0.1
Flat PDF
=1b
α
=0.3b
α
=1b
α
ATLAS
Simulation
Dongliang Zhang [UM] Hadron2015 14/09/2015
Introduction Λ0b reconstruction Lifetime measurement Helicity study Λ0
b → ψ(2S)Λ0 Summary 11/18Event selection & Background
q 2011 7 TeV data
q Λ0b selection
q Exclude tracks from primary vertexq τ > 0.35 psq Loose B0
d veto: PΛ0b> PB0
d
q 5560 < m < 5680 MeV
q Combinatorial background
q Estimated from sidebands (SB)
q Peaking background
q B0d → J/ψ(µ+µ−)K 0
S (π+π−)q Yield from the mass fitq 〈Fi 〉 from Mont Carlo
Parameter [5340, 5900] MeV [5560, 5680] MeVNsig 1400± 50 1240± 40NComb 1090± 80 234± 16NB0
d210± 90 73± 30
Dongliang Zhang [UM] Hadron2015 14/09/2015
[MeV])
0Λ(0ΛψJ/
m
5400 5500 5600 5700 5800 5900
Eve
nts
/ 1
0 M
eV
0
50
100
150
200
250
300
Data 2011
Fitted modelSignal
bkgd0
BComb. bkg 50± = 1400 sigN
90± = 210 d
0B
N
80± = 1090 Comb.N
) = 0.892χProb(
ATLAS 1
L dt = 4.6 fb∫ = 7 TeV, s0
bΛ+0bΛ
Left SB Right SB
2F
1 0.5 0 0.5 1
Events
/ 0
.1
0
50
100
150
200
[5560, 5680] MeV
[5400, 5520] MeV
[5720, 5840] MeV
ATLAS
1 L dt = 4.6 fb∫ = 7 TeV, s
cos θ1
Introduction Λ0b reconstruction Lifetime measurement Helicity study Λ0
b → ψ(2S)Λ0 Summary 12/18Results
Fit resultsαb= 0.30± 0.16(stat)± 0.06(syst)
k+ = 0.21+0.14−0.21(stat)± 0.13(syst)
k− = 0.13+0.20−0.13(stat)± 0.15(syst)
corresponding to
|A( 1/2, 0)| = 0.17+0.12−0.17 ± 0.09
|A(−1/2,−1)| = 0.59+0.06−0.07 ± 0.03
|A(−1/2, 0)| = 0.79+0.04−0.05 ± 0.02
|A( 1/2, 1)| = 0.08+0.13−0.08 ± 0.06
Main systematic uncertaintiesq MC statistics
q Background shape modeling
bα
1 0.5 0 0.5 1
valu
em
in
2 χ
0
10
20
30
40
50
60bΛ + bΛ
=0.30bestbα
)=3.15bestbα(
min
2χ
ATLAS
1 L dt = 4.6 fb∫ = 7 TeV, s
2σ
3σ
pQCD: −(0.14 ∼ 0.17)
HQET: 0.78
LHCb 0.05± 0.17± 0.07
q Between two theory predictions
q Consistent with LHCb results
Dongliang Zhang [UM] Hadron2015 14/09/2015
Correlation
Parameter αb k+ k−αb 1 0.41 −0.19k+ 1 0.20k− 1
Phys. Rev. D 89 (2014) 092009
Ref: LHCb [Phys. Lett. B 724 (2013) 27]; pQCD [Phys. Rev. D 65 (2002) 074030]; HEQT [Phys. Lett. B 614 (2005) 165173];
Introduction Λ0b reconstruction Lifetime measurement Helicity study Λ0
b → ψ(2S)Λ0 Summary 13/18Λ0b → ψ(2S)Λ0 selection
q Fiducial rangeq pT(Λ0
b) > 10 GeV, |η(Λ0b)| < 2.1 (Kinematic range)
q pT(µ±) > 4 GeV, |η(µ±)| < 2.3q pT(Λ0) > 2.5 GeV
q Other selectionc cutsq pT(π−) > 0.45 GeVq τ > 0.35 ps, P(Λ0
b) > P(B0d )
)) [MeV]0
Λ(0
Λ ψm(J/
5400 5500 5600 5700 5800 5900
Events
/ 1
0 M
eV
0
200
400
600
800
1000
1200
1400 ATLAS1 = 8 TeV, 20.6 fbs
0
bΛ + 0bΛ
130± = 6940 sigN
Data
Fitted model
signal0bΛ
reflection0
B
) [MeV]0
S Kψm(J/
5100 5200 5300 5400 5500
Events
/ 1
0 M
eV
0
100
200
300
400
500 ATLAS1 = 8 TeV, 20.6 fbs
84± = 854 sigN
Data
Fitted model
signal0
B
reflection0bΛ
Dongliang Zhang [UM] Hadron2015 14/09/2015
Λ0b → J/ψΛ0 B0
d → J/ψK 0S
Introduction Λ0b reconstruction Lifetime measurement Helicity study Λ0
b → ψ(2S)Λ0 Summary 14/18Λ0b → ψ(2S)Λ0 selection
)) [MeV]0
Λ(0
Λ(2S) ψm(
5400 5500 5600 5700 5800
Events
/ 1
5 M
eV
0
50
100
150
200
250
300ATLAS
1 = 8 TeV, 20.6 fbs0
bΛ + 0bΛ
38± = 603 sigN
Data
Fitted model
signal0bΛ
reflection0
B
) [MeV]0
S(2S) Kψm(
5100 5200 5300 5400 5500
Events
/ 1
5 M
eV
0
20
40
60
80
100
ATLAS1 = 8 TeV, 20.6 fbs
28± = 124 sigN
Data
Fitted model
signal0
B
reflection0bΛ
q Simultaneous Λ0b and B0
d mass fit
q Signal: modified Gaussian p(x) = exp[−0.5 · x1+1/(1+0.5·x)], x = |(m −m0)/σ|q B0
d and Λ0b reflection using MC templates
q Non-resonant background: exponential functions
Dongliang Zhang [UM] Hadron2015 14/09/2015
Λ0b → ψ(2S)Λ0 B0
d → ψ(2S)K 0S
Introduction Λ0b reconstruction Lifetime measurement Helicity study Λ0
b → ψ(2S)Λ0 Summary 15/18
) [MeV]
µ+µm(
2700 2800 2900 3000 3100 3200 3300 3400
Events
/ 2
0 M
eV
0
500
1000
1500
2000
2500ATLAS
1 = 8 TeV, 20.6 fbs0
bΛ + 0bΛ
120± = 9770 sigN
Data
Fitted model
signalψJ/
Background
) [MeV]
µ+µm(
3400 3500 3600 3700 3800 3900 4000 4100 4200
Events
/ 2
0 M
eV
0
20
40
60
80
100
120
140
160
180ATLAS
1 = 8 TeV, 20.6 fbs0
bΛ + 0bΛ
45± = 724 sigN
Data
Fitted model
(2S) signalψ
Background
) [MeV]
πm(p
1060 1080 1100 1120 1140 1160 1180
Events
/ 2
MeV
0
500
1000
1500
2000
2500 ATLAS1 = 8 TeV, 20.6 fbs
0Λ ψ J/→
0bΛ
120± = 7710 sigN
Data
Fitted model
signal0
Λ
Background
) [MeV]
πm(p
1060 1080 1100 1120 1140 1160 1180
Events
/ 2
MeV
0
50
100
150
200
250
ATLAS1 = 8 TeV, 20.6 fbs
0Λ(2S) ψ →
0bΛ
38± = 702 sigN
Data
Fitted model
signal0
Λ
Background
Dongliang Zhang [UM] Hadron2015 14/09/2015
Introduction Λ0b reconstruction Lifetime measurement Helicity study Λ0
b → ψ(2S)Λ0 Summary 16/18Branching ratio
q Yields from fits
Λ0b → J/ψΛ0 B0 → J/ψK0
S Λ0b → ψ(2S)Λ0 B0 → ψ(2S)K0
S
Nsig 6940± 130 854± 84 603± 38 124± 28
msig [MeV] 5620.4± 0.4 5274.7± 2.3 5618.2± 1.2 5272.4± 4.9
σsig [MeV] 19.7± 0.5 19.2± 2.2 14.3± 1.1 16.7± 4.1
q Acceptance correction Ncor = Nsig/Aq Efficiency (Aeff) and acceptance (Akin) in fiducial range
pT(Λ0b) > 10 GeV, |η(Λ0
b)| < 2.1
pT(µ±) > 4 GeV, |η(µ±)| < 2.3
pT(Λ0) > 2.5 GeV
Channel Aeff [%] Akin [%]
Λ0b → J/ψΛ0 4.16± 0.02 7.57± 0.06
Λ0b → ψ(2S)Λ0 4.30± 0.03 9.61± 0.07
Dongliang Zhang [UM] Hadron2015 14/09/2015
Introduction Λ0b reconstruction Lifetime measurement Helicity study Λ0
b → ψ(2S)Λ0 Summary 17/18Branching ratio
In kinematic range pT(Λ0b) > 10 GeV, |η(Λ0
b)| < 2.1:
Γ(Λ0b → ψ(2S)Λ0)
Γ(Λ0b → J/ψΛ0)
=Ncor(Λ0
b → ψ(µ+µ−)Λ0)
Ncor(Λ0b → J/ψ(µ+µ−)Λ0)
· B(J/ψ → `+`−)
B(ψ(2S)→ `+`−)
= 0.501± 0.033(stat)± 0.016(syst)± 0.011(B)
q B(J/ψ → µ+µ−) = 0.05961± 0.00033 [PDG]
q B(ψ(2S)→ µ+µ−) = B(ψ(2S)→ e+e−) = 0.00789± 0.00017 [PDG]
q Systematic uncertainties
q Signal extraction fits (2.8%)q MC statistics (1.3%)q Λ0
b polarization model (1.1%)
q In the range 0.5–0.8 for B meson decays; smaller than calculation 0.8± 0.1 [Phys.
Rev. D 88 (2013) 114018]
Dongliang Zhang [UM] Hadron2015 14/09/2015
arXiv:1507.08202 [hep-ex]
Introduction Λ0b reconstruction Lifetime measurement Helicity study Λ0
b → ψ(2S)Λ0 Summary 18/18Summary
q Studying Λ0b production and decay using ATLAS data
q Lifetime measurement
mΛ0b
= 5619.7± 0.7(stat)± 1.1(syst) MeV
τΛ0b
= 1.449± 0.036(stat)± 0.017(syst) ps
q αb measurement
αb = 0.30± 0.16(stat)± 0.06(syst)
|a+| = 0.17+0.12−0.17(stat)± 0.09(syst)
|a−| = 0.59+0.06−0.07(stat)± 0.03(syst)
|b+| = 0.79+0.04−0.05(stat)± 0.02(syst)
|b−| = 0.08+0.13−0.08(stat)± 0.06(syst)
q Observation of Λ0b → ψ(2S)Λ0 and the measured branching ratio
Γ(Λ0b → ψ(2S)Λ0)
Γ(Λ0b → J/ψΛ0)
= 0.501± 0.033(stat)± 0.016(syst)± 0.011(B)
Dongliang Zhang [UM] Hadron2015 14/09/2015
Backup 19/18Backup: Efficiency correction of lifetime measurement
’ (ps)τ
0 1 2 3 4 5 6
Effic
iency
0.018
0.02
0.022
0.024
0.026
0.028
56 ps± = 113 bΛ
c
ATLAS
Simulation
= 7 TeVs
bΛ
c
’τ
e’) ~ τ(ε
(ps)trueτ
0 1 2 3 4 5 6
Effic
iency
0.03
0.035
0.04
0.045
0.05
43 ps± = 94 dB
c
ATLAS
Simulation
= 7 TeVs
dB
c
’τ
e’) ~ τ(ε
Dongliang Zhang [UM] Hadron2015 14/09/2015
Backup 20/18Backup: B0
d lifetime measurement
(MeV)S
KψJ/M
5100 5150 5200 5250 5300 5350 5400 5450 5500
Candid
ate
s / 1
3 M
eV
0
500
1000
1500
2000
2500
3000
3500
4000 0.2 MeV± = 5279.6 dBM
0.01± = 1.11 M
S
0.2 MeV± = 27.8 M
σ
110± = 17530 sigN
65± = 10069 bkg N
= 1.03dofN/2χ
= 7 TeVs1 = 4.9 fbL
Data
Fitted model
Signal
Background
ATLAS
(ps)τ
2 0 2 4 6 8 10 12 14
Candid
ate
s / 0
.46 p
s
10
210
310
410 0.012 ps± = 1.509
dBτ
0.02± = 1.06 τS
0.003 ps± = 0.107 τσ
= 1.03dofN/2χ
= 7 TeVs1 = 4.9 fbL
Data
Fitted model
Signal
Background
ATLAS
Dongliang Zhang [UM] Hadron2015 14/09/2015
Backup 21/18Backup: full PDF
i f1i f2i Fi0 a+a∗+ + a−a
∗− + b+b∗+ + b−b
∗− 1 1
1 a+a∗+ − a−a∗− + b+b∗+ − b−b
∗− P cos θ
2 a+a∗+ − a−a∗− − b+b∗+ + b−b
∗− αΛ cos θ1
3 a+a∗+ + a−a∗− − b+b∗+ − b−b
∗− P αΛ cos θ cos θ1
4 −a+a∗+ − a−a∗− + 1
2b+b∗+ + 1
2b−b
∗− 1 1
2(3 cos2 θ2 − 1)
5 −a+a∗+ + a−a∗− + 1
2b+b∗+ −
12b−b
∗− P 1
2(3 cos2 θ2 − 1) cos θ
6 −a+a∗+ + a−a∗− −
12b+b∗+ + 1
2b−b
∗− αΛ
12
(3 cos2 θ2 − 1) cos θ1
7 −a+a∗+ − a−a∗− −
12b+b∗+ −
12b−b
∗− P αΛ
12
(3 cos2 θ2 − 1) cos θ cos θ1
8 −3Re(a+a∗−) P αΛ sin θ sin θ1 sin2 θ2 cosφ1
9 3Im(a+a∗−) P αΛ sin θ sin θ1 sin2 θ2 sinφ1
10 − 32Re(b−b
∗+) P αΛ sin θ sin θ1 sin2 θ2 cos(φ1 + 2φ2)
11 32Im(b−b
∗+) P αΛ sin θ sin θ1 sin2 θ2 sin(φ1 + 2φ2)
12 − 3√2Re(b−a
∗+ + a−b
∗+) P αΛ sin θ cos θ1 sin θ2 cos θ2 cosφ2
13 3√2Im(b−a
∗+ + a−b
∗+) P αΛ sin θ cos θ1 sin θ2 cos θ2 sinφ2
14 − 3√2Re(b−a
∗− + a+b∗+) P αΛ cos θ sin θ1 sin θ2 cos θ2 cos(φ1 + φ2)
15 3√2Im(b−a
∗− + a+b∗+) P αΛ cos θ sin θ1 sin θ2 cos θ2 sin(φ1 + φ2)
16 3√2Re(a−b
∗+ − b−a
∗+) P sin θ sin θ2 cos θ2 cosφ2
17 − 3√2Im(a−b
∗+ − b−a
∗+) P sin θ sin θ2 cos θ2 sinφ2
18 3√2Re(b−a
∗− − a+b∗+) αΛ sin θ1 sin θ2 cos θ2 cos(φ1 + φ2)
19 − 3√2Im(b−a
∗− − a+b∗+) αΛ sin θ1 sin θ2 cos θ2 sin(φ1 + φ2)
Dongliang Zhang [UM] Hadron2015 14/09/2015
Backup 22/18
q MC weighted using the fit results
2F
1 0.5 0 0.5 1
Events
/ 0
.1
0
20
40
60
80
100
120
140
160
180
200
databΛ+bΛ0
bΛReweighted 0
bΛPythia
Background
test prob: 0.982χATLAS
1 L dt = 4.6 fb∫ = 7 TeV, s
4F
0.5 0 0.5 1
Events
/ 0
.05
0
50
100
150
200
250
300
350
databΛ+bΛ0
bΛReweighted 0
bΛPythia
Background
test prob: 0.572χATLAS
1 L dt = 4.6 fb∫ = 7 TeV, s
6F
1 0.5 0 0.5 1
Events
/ 0
.04
0
50
100
150
200
250
databΛ+bΛ0
bΛReweighted 0
bΛPythia
Background
test prob: 0.802χATLAS
1 L dt = 4.6 fb∫ = 7 TeV, s
18F
0.4 0.2 0 0.2 0.4
Events
/ 0
.02
0
20
40
60
80
100
120
140
databΛ+bΛ0
bΛReweighted 0
bΛPythia
Background
test prob: 0.0632χATLAS
1 L dt = 4.6 fb∫ = 7 TeV, s
Dongliang Zhang [UM] Hadron2015 14/09/2015
cos θ112 (3 cos2 θ2 − 1)
12 sin θ1 sin θ2 cos θ2 cos(φ1 + φ2) 1
2 sin θ1 sin θ2 cos θ2 sin(φ1 + φ2)
Backup 23/18Sidebands comparison
4F
0.5 0 0.5 1
Eve
nts
/ 0
.1
0
100
200
300
400
[5560, 5680] MeV
[5400, 5520] MeV
[5720, 5840] MeV
ATLAS
1 L dt = 4.6 fb∫ = 7 TeV, s
6F
1 0.5 0 0.5 1
Eve
nts
/ 0
.04
0
100
200
300
[5560, 5680] MeV
[5400, 5520] MeV
[5720, 5840] MeV
ATLAS
1 L dt = 4.6 fb∫ = 7 TeV, s
18F
0.4 0.2 0 0.2 0.4
Eve
nts
/ 0
.05
0
100
200
300[5560, 5680] MeV
[5400, 5520] MeV
[5720, 5840] MeV
ATLAS
1 L dt = 4.6 fb∫ = 7 TeV, s
19F
0.4 0.2 0 0.2 0.4
Eve
nts
/ 0
.05
0
100
200
300[5560, 5680] MeV
[5400, 5520] MeV
[5720, 5840] MeV
ATLAS
1 L dt = 4.6 fb∫ = 7 TeV, s
Dongliang Zhang [UM] Hadron2015 14/09/2015
12 (3 cos2 θ2 − 1) 1
2 (3 cos2 θ2 − 1) cos θ1
12 (sin θ1 sin θ2 cos θ2 cos(φ1 + φ2) 1
2 (sin θ1 sin θ2 cos θ2 sin(φ1 + φ2)
Backup 24/18
q Other angular variables
θcos
1 0.5 0 0.5 1
Fra
ctio
n /
0.1
0
0.02
0.04
0.06
0.08
0.1
Flat PDF
=1b
α
=0.3b
α
=1b
α
ATLAS
Simulation
[rad]1
φ
3 2 1 0 1 2 3
/16
) ra
dπ
Fra
ctio
n /
(
0
0.01
0.02
0.03
0.04
0.05
0.06
Flat PDF
=1b
α
=0.3b
α
=1b
α
ATLAS
Simulation
[rad]2
φ
3 2 1 0 1 2 3
/16
) ra
dπ
Fra
ctio
n /
(
0
0.01
0.02
0.03
0.04
0.05
0.06
Flat PDF
=1b
α
=0.3b
α
=1b
α
ATLAS
Simulation
[rad]2
φ+1
φ
3 2 1 0 1 2 3
/16
) ra
dπ
Fra
ctio
n /
(
0
0.01
0.02
0.03
0.04
0.05
Flat PDF
=1b
α
=0.3b
α
=1b
α
ATLAS
Simulation
Dongliang Zhang [UM] Hadron2015 14/09/2015
Backup 25/18Backup: Λ0
b → ψ(2S)Λ0 selection
Λ0b and Λ0
b
) [MeV]0
Λ ψm(J/
5400 5500 5600 5700 5800 5900
Events
/ 1
0 M
eV
0
100
200
300
400
500
600
700
800ATLAS
1 = 8 TeV, 20.6 fbs0bΛ
89± = 3523 sigN
Data
Fitted model
signal0bΛ
reflection0
B
) [MeV]0
Λ ψm(J/
5400 5500 5600 5700 5800 5900
Events
/ 1
0 M
eV
0
100
200
300
400
500
600
700ATLAS
1 = 8 TeV, 20.6 fbs0
bΛ
92± = 3414 sigN
Data
Fitted model
signal0
bΛ
reflection0
B
Threshold function
A · (m −mp −mπ−)B · exp[C · (m −mp −mπ−) + D · (m −mp −mπ−)2]
Dongliang Zhang [UM] Hadron2015 14/09/2015
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