This document describes a study measuring the fraction of J/ψ mesons originating from Υ(1P), Υ(2P), and Υ(3P) decays as a function of pT(J/ψ) using data collected by the LHCb experiment at center-of-mass energies of 7 and 8 TeV. The analysis involves determining yields of J/ψ mesons and yields from Υ decays to J/ψ in different pT bins. Monte Carlo simulations are used to calculate efficiencies and compare data distributions. Results include improved precision on previous LHCb measurements of these fractions and a measurement of the Υ1(3P) mass.

1. Production of b at
p
s =7 and 8 TeV
Vanya Belyaev, Concezio Bozzi, Hans Dijkstra, Sasha Mazurov
ICHEP approval session
6 June 2014
1/23

2. Motivation
Bound bb states, which can be produced in different spin configurations, are an
ideal laboratory for QCD tests. It’s like a hydrogen atom in QCD.
States with parallel quark spins (S=1):
S-wave state.
P-wave b states, composed by 3 spin states
b(0;1;2).
can be readily produced in the radiative decays
of b.
b(3P) state recently observed by ATLAS, D0 and
LHCb.
This study:
1 Measurement of (NS) (N=1, 2, 3) fraction
originating from b decays as function of pT().
Provides valuable information on Color-Octet
matrix elements.
2 Measurement of b(3P) mass.
2/23

3. Previous analysis
“Production of (1S) mesons from b decays in pp collisions at p
s = 1:8 TeV” at CDF, arXiv:hepex/9910025.
“Observation of a new b state in radiative transitions to (1S) and (2S)
at ATLAS”, arXiv:1112.5154
“Measurement of the fraction of (1S) originating R
from b(1P) in pp
p
collisions at
s =7 TeV”, arXiv:1209.0282,
L = 32 pb1
“Observation of the b(3P) state at LHCb in pp collisions at
p
s =7 TeV”,
LHCb-CONF-2012-020,
R
L = 0:9 fb1.
100
90
80
70
60
50
40
30
20
10
6 7 8 9 10 11 12 13 14 15
¡ (1S) (GeV/c)
T
p
(1P) (%)
b (1S) from c ¡ Fraction of
0
LHCb
s = 7 TeV
300 LHCb preliminary
250
200
150
100
50
0 0.5 1 1.5 2
2) ) (GeV/c −
μ + g ) − m(μ
−
μ + m(μ
Candidates / 20 MeV/c2
0
s = 7 TeV
­1
0.9 fb
0 0.5 1 1.5 2
Pull
4
2
0
­2
­4
b(3P)
3/23

4. In this study
The results in this study extend the statistical precision of previous LHCb
measurements and add considerably more decays and higher transverse
momentum regions. The measurement of (3S) fraction in radiative b(3P)
decay was performed for the first time.
In each pT() bin calculate:
(pp!b(mP)X)Br(b(mP)!(nS)
)
(pp!(nS)X) =
Nb(mP)!(nS)
N(nS)
(nS)
b(mP)!(nS)
for each (nS); n = 1; 2; 3 and b(mP);m = 1; 2; 3
Get N from fits: N from m(+) and Nb!
from
[m(+
) m(+)] (for better resolution)
Compute efficiency from Monte-Carlo simulation
4/23

5. Content
1 Datasets
2 Determination of yields
3 Determination of b yields in the following decays:
b(1; 2; 3P) ! (1S)
b(2; 3P) ! (2S)
b(3P) ! (3S)
4 Measuring of b1(3P) mass
5 Monte-Carlo efficiencies
6 Systematic uncertainties
7 Results
5/23

6. Datasets
Full 2011 dataset at
p
s =7 TeV.
R
L = 1 fb1
Full 2012 dataset at
p
s =8 TeV.
R
L = 2 fb1
Monte-Carlo simulation of b inclusive decays, generated 62 106
events.
6/23

7. The selection
Almost the same cuts as are used in the study “Measurement of production
p
in pp collisions at
s = 2:76 TeV”, arXiv:1402.2539
Description Requirement
rapidity 2:0 y 4:5
Track fit quality 2=ndf 4
Track pT 1 GeV=c
+ vertex probability 0:5%
Luminous region jzPVj 0:5m and x2
PV + y2
PV 100mm2
Kullback-Leibler distance 5000
Muon and hadron hypotheses logLh 0
Muon probability ProbNN 0:5
Trigger lines:
L0 L0DiMuon
HLT1 Hlt1DiMuonHighMass
HLT2 HLT2DiMuonB
7/23

8. The fit model
p
s = 7 TeV
6 p+
T 12 GeV=c
9 10 11
30000
25000
20000
15000
10000
5000
0
Candidates/(40 MeV=c2)
m+
GeV=c2
(1S)
(2S)
(3S)
+ transverse momentum intervals, GeV=c
6 – 40
p
s = 7 TeV
p
s = 8 TeV
N(1S) 283,300 600 659,600 900
N(2S) 87,500 400 203,300 600
N(3S) 50,420 290 115,300 400015
3 Double Crystal Ball functions for signal yields. Tails’ parameters are
fixed from simulation.
Exponential function for combinatorial background.
8/23

9. b selection
In this study photons reconstructed using the calorimeter information.
Another approach uses photon conversions in e+e pairs—this method
has better invariant mass resolution, but requires more statistics.
Cuts on
:
Transverse momentum of
pT (
) 600 MeV=c
Polar angle of
in the +
rest frame cos
0
Confidence level of
CL(
) 0:01
Dimuon mass windows:
9 10 11
35000
30000
25000
20000
15000
10000
5000
0
Candidates/(12 MeV=c2)
m+
GeV=c2
9/23

10. b1;2(1; 2; 3P) ! (1S)
fit model (1)
10 10.5
1000
800
600
400
200
0
4
2
0
-2
-4
Candidates/(20 MeV=c2)
m+
m+ + mPDG
(1S)
h
GeV=c2
i
p
b(1P) s = 7 TeV
b(2P)
b1 b2 b(3P)
One Crystal Ball (CB) for each b1;2(1P; 2P; 3P) state: 6 CB in total
Exclude the study of b0 due to its low radiative branching ratio.
Product of exponential and linear combination of polynomials for
combinatorial background.
10/23

11. b1;2(1; 2; 3P) ! (1S)
fit model (2)
Free parameters: yields and background
parameters.
Fixed parameter: b1(1P) to the value
measured on combined 2011 and 2012
datasets.
Linked parameters for b1 and b2
signals:
b2(jP) = b1(jP) + mPDG
b2(jP), j=1,2
b2(3P) = b1(3P) + mtheory
b2(3P)
Nb = Nb1 + (1 )Nb2
( is fixed to 0.5)
b2 = b1
Other linked parameters:
b1(2P) = b1(1P) + mPDG
b1(2P)
b1(3P) = b1(1P) + mb1(3P)
(mb1(3P) measured in this study)
Fixed parameters from MC study:
b1(1P), b1(2P)
b1(1P)
, b1(3P)
b1(1P)
and n parameters of CB.
(1S) transverse momentum intervals, GeV=c
14 – 40
p
s = 7 TeV
p
s = 8 TeV
Nb(1P) 2090 80 5070 130
Nb(2P) 450 50 1010 80
Nb(3P) 150 40 220 60
11/23

12. b fits
LHCb p
s = 7 TeV
10 10.5
1000
800
600
400
200
0
Candidates/(20 MeV=c2)
m+
m+ + mPDG
(1S)
GeV=c2
LHCb p
s = 8 TeV
10 10.5
2500
2000
1500
1000
500
0
Candidates/(20 MeV=c2)
m+
m+ + mPDG
(1S)
GeV=c2
LHCb p
s = 7 TeV
10.2 10.4 10.6 10.8 11
250
200
150
100
50
0
Candidates/(20 MeV=c2)
m+
m+ + mPDG
(2S)
GeV=c2
LHCb p
s = 7 TeV
10.2 10.4 10.6 10.8 11
600
500
400
300
200
100
0
Candidates/(20 MeV=c2)
m+
m+ + mPDG
(2S)
GeV=c2
LHCb p
s = 7 TeV
10.5 10.6 10.7
30
25
20
15
10
5
0
Candidates/(20 MeV=c2)
m+
m+ + mPDG
(3S)
GeV=c2
LHCb p
s = 8 TeV
10.5 10.6 10.7
80
70
60
50
40
30
20
10
0
Candidates/(20 MeV=c2)
m+
m+ + mPDG
(3S)
GeV=c2
12/23

13. Mass of b1(3P) in b ! (3S)
decay
LHCb p
s = 7 and 8 TeV
10.5 10.6 10.7
100
80
60
40
20
0
Candidates/(20 MeV=c2)
m+
m+ + mPDG
(3S)
GeV=c2
The measured on the combined 2011 and 2012 datasets
mb1(3P)=10;510 2 (stat) 6 (syst)MeV=c2 is consistent with the mass
measured in another study with converted photons—
10;515:7 3:1 (stat)+1:5
2:1 (syst) MeV=c2 (very preliminary results).
ATLAS measured b1 and b2 mass barycenter for
mb2 mb1 = 12 MeV=c2 and = 0:5:
mb(3P) = 10;530 5 (stat) 9 (syst) MeV=c2
D0: mb(3P) = 10;551 14 (stat) 17 (syst) MeV=c2
13/23

14. Data— Monte Carlo comparison
A comparison of the distribution of the relevant observables used in this
analysis was performed on real and simulated data, in order to assess the
reliability of Monte Carlo in computing efficiencies
0.06
0.05
0.04
0.03
0.02
0.01
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0.06
0.05
0.04
0.03
0.02
0.01
0
pT [(1S)]
b(1P) b(2P) b(3P)
GeV=c2
pT [b(1P)]
b(1P) b(2P) b(3P)
GeV=c2
pT [(1S)]
GeV=c2
pT [b(2P)]
GeV=c2
pT [(1S)]
GeV=c2
pT [b(3P)]
GeV=c2
b(1P) b(2P) b(3P)
2 of decay tree fitter 2 of decay tree fitter 2 of decay tree fitter
0 0.2 0.4 0.6 0.8 1
0.1
0.08
0.06
0.04
0.02
0.1
0.08
0.06
0.04
0.02
0
0.08
0.06
0.04
0.02
0.06
0.05
0.04
0.03
0.02
0.01
0
0 0.2 0.4 0.6 0.8 1
0.2
0.15
0.1
0.05
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
-0.02
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
0.1
0.08
0.06
0.04
0.02
0
-0.02
0 0.2 0.4 0.6 0.8 1
0 2 4
0
0 2 4
0
0 2 4
-0.02
0 10 20 30
0 10 20 30
0 10 20 30
15 20 25 30 35
0
15 20 25 30 35
0
15 20 25 30 35
0
confidence level
confidence level
confidence level
Arbitrary units
Arbitrary units
Arbitrary units
Arbitrary units
Arbitrary units
Arbitrary units
Arbitrary units
Arbitrary units
Arbitrary units
Arbitrary units
Arbitrary units
Arbitrary units
b(1P) b(2P) b(3P)
The agreement is generally very good.
14/23

15. Monte-Carlo photon reconstruction efficiency
b(1P) ! (1S)
p
s =7 TeV
p
s =8 TeV
b(3P) ! (1S)
p
s =7 TeV
p
s =8 TeV
b(3P) ! (2S)
p
s =7 TeV
p
s =8 TeV
20 30 40
30
25
20
15
10
5
25
20
15
10
5
30
25
20
15
10
5
0
Efficiency, %
p(2S)
T [ GeV=c]
30
25
20
15
10
5
25
20
15
10
5
25
20
15
10
5
0
b(2P) ! (1S)
p
s =7 TeV
p
s =8 TeV
b(2P) ! (2S)
p
s =7 TeV
p
s =8 TeV
b(3P) ! (3S)
p
s =7 TeV
p
s =8 TeV
20 25 30 35 40
Efficiency, %
p(3S)
T [ GeV=c]
10 20 30 40
0
Efficiency, %
p(1S)
T [ GeV=c]
20 30 40
0
Efficiency, %
p(2S)
T [ GeV=c]
10 20 30 40
0
Efficiency, %
p(1S)
T [ GeV=c]
10 20 30 40
0
Efficiency, %
p(1S)
T [ GeV=c]
Photon is more energetic as pT()
increases so it is reconstructed more
efficiently.
15/23

16. Systematic uncertainties
Since this analysis measures the fraction of (nS) particles originating from b decays, most
systematic uncertainties cancel in the ratio and only residual effects need to be taken into account.
Systematic uncertainties on the event yields are mostly due to the fit model of and b invariant
masses, while the ones on the efficiency are due to the photon reconstruction and the unknown
initial polarization of b and particles.
The uncertainty related to the fit model estimated by the previous study “Production of Jp
= and
mesons in pp collisions at
s = 8 TeV”, arXiv:1304.6977
Systematic due to photon reconstruction taken from the previous works based on “Study of 0=
reconstruction efficiency with 2011 data”, LHCb-INT-2012-001.
fraction uncertainties common to all b decays (%)
fit model 0:7
reconstruction 3
16/23

17. Systematic uncertainties— Polarization
The polarization is expected to be small. “Measurement of the (1S),
p
Y2S and (3S) polarizations in pp collisions at
s = 7 TeV”,
arXiv:1209.2922.
The uncertainty related to the unknown polarization of b mesons was
estimated using the prescription described in the LHCb paper
“Measurement of the relative rate of prompt c0, c1 and c2 production at p
s = 7TeV” (thanks to Edwige Tournefier) that is based on the analytical
calculations in HERA “Production of the Charmonium States and p
c1 c2
in Proton Nucleus Interactions at
s = 41.6-GeV”
In the previous study the uncertainty due to polarization is dominated 20%.
This study shows that this uncertanty is less than 9%.
17/23

18. Summary of systematic uncertainties
T
Summary of fraction systematic uncertainties (%)
(maximum deviations that were found in pbins):
b fit model b polarization
b(1P) ! (1S)
+4:3
5:8
+5:1
4:0
b(2P) ! (1S)
+4:8
6:2
+5:8
6:8
b(3P) ! (1S)
+19:6
16:6
+6:9
6:7
b(2P) ! (2S)
+2:3
7:0
+8:7
7:8
b(3P) ! (2S)
+19:7
19:9
+4:5
4:2
b(3P) ! (3S)
+20:9
27:6
+6:4
7:5
18/23

19. fractions in b !
decays
p
s =7 TeV
p
s =8 TeV
b(1P) ! (1S)
b(2P) ! (1S)
b(3P) ! (1S)
10 20 30 40
50
45
40
35
30
25
20
15
10
5
0
(1S) fraction, %
p(1S)
T [ GeV=c]
p
s =7 TeV
p
s =8 TeV
b(2P) ! (2S)
b(3P) ! (2S)
10 20 30 40
60
50
40
30
20
10
0
(2S) fraction, %
p(2S)
T [ GeV=c]
p
s =7 TeV
p
s =8 TeV
b(3P) ! (3S)
10 20 30 40
100
90
80
70
60
50
40
30
20
10
0
(3S) fraction, %
p(3S)
T [ GeV=c]
Outer error bars show statistical and systematics errors, inner error bars — only statistical errors.
Unexpected huge fraction of (3S) ( 50%) originated from b(3P)
19/23

20. (1S) fractions in b(1P) ! (1S)
decays
In agreement with the previous LHCb result.
b(1P) ! (1S)
p
s =7 TeV
p
s =8 TeV
p
s =7 TeV (2010)
10 20 30 40
50
45
40
35
30
25
20
15
10
5
0
(1S) fraction, %
p(1S)
T [ GeV=c]
Outer error bars show statistical and systematics errors, inner error bars — only statistical errors.
20/23

21. Summary
Measured fractions of (1; 2; 3S) originated from b decays. About 40%
of come from b, with mild dependence on transverse momentum.
The measurement of (3S) fraction in radiative b(3P) decay was
performed for the first time.
This analysis improves significantly the statistical precision of the
previous work and adds more decays and transverse momentum regions.
Measured mass of b(3P) is 10; 510 2 (stat) 6 (stat) MeV=c2,
consistent with another determination which uses converted photons.
Request approval to go to paper
Thanks to our referees Mikhail Shapkin and Olivier Deschamps
Documentation:
TWiki page
Analysis Note: LHCb-ANA-2014-004
Paper draft available
21/23

22. Backup
22/23

23. yields as function of pT
106
105
104
103
102
(1S)
p
s =7 TeV
p
s =8 TeV
0 10 20 30 40 50
106
105
104
103
102
(3S)
0 10 20 30 40 50
106
105
104
103
(2S)
0 10 20 30 40 50
102
Events
pT() [ GeV=c]
Events
pT() [ GeV=c]
Events
pT() [ GeV=c]
p
s =7 TeV
p
s =8 TeV
p
s =7 TeV
p
s =8 TeV
Yields normalized by bin width and luminosity.
The small difference between 7 and 8 TeV data is due to the production
cross-sections, which are expected to be about 10% larger.
23/23