Nuclear Physics B Proceedings Supplement 00 (2014) 1–6
Supplement
Study of b-hadron to J/ψh
+h
−decays
Liming Zhang (on behalf of the LHCb Collaboration)
Physics Department, Syracuse University, Syracuse, New York 13244-1130, USA
Abstract
Using data collected by the LHCb detector corresponding to an integrated luminosity of 3 fb−1, several types of b-hadron toJ/ψh+h−decays are studied. Reported are the most recent results including amplitude analyses ofB0s and B0→ J/ψπ+π−decays, precision measurement of lifetime ratio ofΛ0btoB0usingΛ0b→J/ψpK−, and first observation of a Cabibbo-suppressed decayΛ0b→J/ψpπ−. Studies of f0(980) andf0(500) substructure are also discussed inπ+π− final states.
Keywords: Standard Model, Amplitude analysis, HEQ,BLifetime, Cabibbo-suppressed decay, LHCb, Scalar mesons
1. Introduction
1
Decays B0s and B0 → J/ψh+h−, where h is either
2
a pion or kaon, are useful for CPviolation measure-
3
ments [1, 2] and B0s, in particular, is used for New
4
Physics searches [3]. (Charged conjugated modes are
5
also used when appropriate.) In order to best exploit
6
these decays, a better understanding of the final state
7
composition is necessary. The study of b-baryon char-
8
monium decays is of considerable interest both to probe
9
the dynamics of heavy flavour decay processes and to
10
search for the effects of physics beyond the Standard
11
Model.
12
Here, we report the recent studies performed using
13
the run I data collected by the LHCb detector [4], cor-
14
responding to an integrated luminosity of 3 fb−1. There
15
are also other decays I didn’t cover, especially B0s [5]
16
and B0 → J/ψK+K− [6] that have been studied with
17
the 1 fb−1 LHCb data. Thanks to theJ/ψ → µ+µ−de-
18
cays, for same number of final particles charmonium
19
modes generally have higher reconstruction and trigger
20
efficiencies than hadronic modes at LHCb.
21
2. Amplitude analyses ofB0
(s) → J/ψ π+π−decays
22
The decay also provides an excellent environment for
23
study of the light scalar states which decay to a π+π−
24
pair, e.g. f0(980) and f0(500) also calledσ. Figure 1
25
shows the leading order diagrams for the two decays,
26
where only s¯scontent is involved in theB0s decays and
27
dd¯in theB0decays. We have used time-integrated am-
28
plitude analysis on both channels to understand the res-
29
onant structure andCPcomponents of the decays using
30
data of an integrated luminosity of 3 fb−1.
31
b
W-
c
}
q
}
c J/
q
q p p
+B q
0}
-
Figure 1: Leading order diagram forB0qdecays intoJ/ψπ+π−, where q=sord.
The decay B0s or B0 → J/ψπ+π−withJ/ψ → µ+µ−
32
is described by 4 variables, chosen to be theπ+π−mass
33
and three helicity angles. Zhang and Stone developed
34
a new theoretical approach which includes all four vari-
35
ables and enables the measurement of the fractions of
36
CP-even and -odd transversity states [7]1. Since one of
37
the particles in the final state, the J/ψ, has spin 1, its
38
three decay amplitudes must be considered, while the
39
π+π−system is described as the coherent sum of reso-
40
nant and possibly nonresonant amplitudes.
41
The invariant mass of the selected J/ψπ+π− combi-
42
nations is shown in Fig. 2, where the dimuon is con-
43
strained to theJ/ψ mass [8]. There are 27 400B0s and
44
18 800B0 signal events within±20 MeV of the respec-
45
tive peaks. The invariant masses ofπ+π−are shown in
46
Fig. 3 and 4 for theB0s andB0candidates, respectively,
47
superimposed with fit function and each resonance con-
48
tribution. The two decays show very distinct spectra.
49
The B0s decays can be described by 5 resonances:
50
f0(980), f0(1500),f0(1790), f2(1270) and f20(1525) [9].
51
Another solution with a significant nonresoance compo-
52
nent along with these five resonances also describe the
53
data equally well. Even though the two solutions have
54
quite different fit fractions for the f0(980), the largest
55
final state component. Similar fractions are found for
56
the two spin-2 states in both solutions, and the total D-
57
wave fraction is 2.3%. As only perpendicular transver-
58
sity components of the two spin-2 states areCP-even,
59
we set the upper limit ofCP-even fraction< 2.3% at
60
95% confidence level (CL).
61
The B0 decays can be described by 6 reso-
62
nances:ρ(770), f0(500), f2(1270),ω(782),ρ(1450) and
63
ρ(1700) [10]. The largest two contributions with fit
64
fractions are ρ(770) of (63.1±2.2+−2.23.4)% and f0(500)
65
of (22.2±1.2+−3.52.6)%. Whenever two uncertainties are
66
quoted, the first is statistical and the second is system-
67
atic. TheCP-even fraction is 56%.
68
3. Substructure of the f0(980) and f0(500) mesons
69
Scalar mesons, especially the f0(980), are not well
70
understood. Their masses do not follow the expectation
71
in the na¨ıve quark model that the state containing two
72
strange quarks is heavier than the state containing only
73
one, in stark contrast to the vector mesons [8]. Stone
74
and Zhang [11] suggested the use ofB→J/ψf0decays
75
to discern theqq¯or tetraquark [12], i.e. [qq][ ¯qq], nature¯
76
of scalar mesons. In theqq¯model, the f0(980), denoted
77
as f0, and the f0(500), denoted asσ, are considered as a
78
mixture of light and strange quarks governed by a single
79
1The approach is applied here after integrating over the decay time.
) [MeV]
π-
π+
ψ m(J/
5300 5400 5500
Combinations/ (5 MeV)
0 1000 2000 3000 4000 5000 6000
7000 LHCb
Figure 2: Invariant mass ofJ/ψπ+π−combinations. The data have been fitted with double Crystal Ball signals and several background functions. The (red) solid curve shows theB0ssignal, the (purple) dot- dashed curve isB0signal, the (brown) dotted line shows the combina- torial background, the (green) short-dashed line shows theB−back- ground, the (light blue) long-dashed line is the sum ofB0s →J/ψη0, B0s →J/ψφwithφ→π+π−π0backgrounds and theΛ0b →J/ψK−p reflection, the (black) dot-long dashed curve is theB0 →J/ψK−π+ reflection and the (blue) solid curve is the total.
mixing angleφ, so that their wave functions are
80
|f0i = cosφ|ssi¯ +sinφ|nni¯
|σi = −sinφ|ss¯i+cosφ|n¯ni, where|n¯ni ≡ 1
√ 2
|uui¯ +|ddi¯
. (1)
When these states are viewed asqqq¯ q¯states the wave functions becomes
|f0i= 1
√ 2
[su][ ¯s¯u]+[sd][ ¯sd]¯
, |σi=[ud][ ¯ud].¯ (2) Here the tetraquark states are consider to be unmixed,
81
for which there is some justification with a mixing angle
82
estimate of<5◦[12]2.
83
Two ratios of decay widths suggested by Stone and Zhang [11] as discriminates between the two and four quark models are tested by the LHCb data. Table 1 shows the predictions of the two ratios compared be- tween the qq¯ and the tetraquark models. LHCb mea- sures both ratios of branching fraction are consistent with zero, as
B
B0s →J/ψf0(500),f0(500)→π+π− B
B0s →J/ψf0(980),f0(980)→π+π− <3.4% (3)
2The LHCb result usingB0s →J/ψπ+π−decays shown in Table 2 gives tetraquark mixing angle<7.7◦at 90% CL.
Table 1: Ratios of decay widths and predictions of the value forrB0
(s)in either theq¯qmodel, or the tetraquark model. The form-factors are notated asFij, and the phase space factorΦij, whereiindicates eitherσorf0andjindicates eitherB0orB0s.
Mode ratio qq¯ tetraquark
Γ(B0s→J/ψσ) Γ(B0s→J/ψf0)
=
|Fσ B0
s
(m2J/ψ)|2
|Ff0
B0 s
(m2J/ψ)|2 Φσ
B0 s
Φf0
B0 s
× r
B0s
r
B0s
= tan
2φ r
B0s
= 0
Γ(B0→J/ψf0) Γ(B0→J/ψσ)
=
|Ff0 B0(m2J/ψ)|2
|Fσ
B0(m2J/ψ)|2 ΦBf00
ΦσB0
× r
B0r
B0= tan
2φ r
B0=
12) [GeV]
π-
π+
m(
0.5 1 1.5 2
Events/ (20 MeV)
1 10 102
103
104
Data LHCb
Fit Signal Background
(980) f0
(1525) f’2
(1270) f2
(1500) f0
(1790) f0 NR
Figure 3: Invariant mass ofπ+π−fromB0scandidates.
at 90% CL, and B
B0→J/ψf0(980),f0(980)→π+π− B
B0→J/ψf0(500),f0(500)→π+π− =(0.6+−0.4−2.60.7+3.3)%.
(4) To interpret the results, we useB(f0(980)→π+π−)=
84
(0.46±0.06) andB(f0(980)→π+π−) = 23, and phase
85
space ratio Φσ
Φf0 = 1.25. The interpretation of the re-
86
sults is listed in Table 2. With current data, the pureqq¯
87
gives a consistent picture where both channels give up-
88
per limit on the mixing phase. Using the pure tetraquark
89
model, the measuredrB0is inconsistent with the predic-
90
tion of 50% at the 8 standard deviation level. Thus we
91
have ruled outf0(980) andf0(500) being pure tetraqaurk
92
state. The mixing ofqq¯ and tetraquark for the scalar
93
mesons is also possible [12]. In the calculations, we
94
use the form factor ratios equal to 1. Both two and
95
four quark models give the same prediction for the
96
decay width ratio of B0s → J/ψf0 to B0 → J/ψσ.
97
Using LHCb measured values, Ref. [11] verified that
98
|Ff0
B0s(m2J/ψ)/FσB0(m2J/ψ)|=0.99+−0.040.13consistent with 1.
99
) [GeV]
π-
π+
m(
0.5 1 1.5 2
Combinations / (18.6 MeV)
0 200 400 600 800 1000 1200 1400
Data Fit Signal Background
(770) ρ
(500) f0
(1270) f2
(782) ω
(1450) ρ
(1700) ρ
0
KS
LHCb
Figure 4: Invariant mass ofπ+π−fromB0candidates.
Table 2: Interpretation of the results for substructure of the f0(980) andf0(500) mesons using either theq¯qmodel or the tetraquark model, where the upper limits are at 90% CL.
Model B0s →J/ψπ+π− B0→J/ψπ+π− qq¯ |φ|<7.7◦ |φ|<17◦ Tetraquark rB0
s <1.8% rB0=(1.1+−0.7−0.71.2+6.0)%
4. Precision measurement ofΛ0
btoB0lifetime ratio
100
The heavy quark expansion (HQE) theory, first de-
101
veloped in 1986 [13], is used to extract values of|Vub|
102
and|Vcb|from inclusiveB−andB0semileptonic decays,
103
so its verification is of prime importance. It leads to
104
a theoretical prediction for the decay width, and hence
105
lifetime, for each b-flavored hadron [14]. One such
106
set of predictions was [15] that τ(B0s)/τ(B0) ≈ 1.0,
107
τ(B−)/τ(B0)≈1.1 andτ(Λ0b)/τ(B0)≈0.96. The theory
108
was improved by further calculations. For example, in
109
the case of the ratio of lifetimes of theΛ0bbaryon,τ(Λ0b),
110
to the B0 meson,τ(B0), differences of only a few per-
111
cent were expected [16, 17], as the corrections of order
112
O(1/m2b) andO(1/m3b) effects are both small.
113
Experimental tests of the HQE using lifetime mea-
114
) [MeV]
pK-
ψ m(J/
5500 5600 5700
Candidates / (4 MeV)
10 102
103
104 (a) LHCb
) [MeV]
K-
π+
ψ m(J/
5200 5250 5300 5350 5400
Candidates / (4 MeV)
102
103
104
(b) LHCb
Figure 5: Fits to the invariant mass spectrum of (a)J/ψpK−and (b)J/ψπ+K−combinations. TheΛ0bandB0signals are shown by the (magenta) solid curves. The (black) dotted lines are the combinatorial backgrounds, and the (blue) solid curves show the totals. In (a) theB0s →J/ψK+K− andB0 → J/ψπ+K−reflections, caused by particle misidentification, are shown with the (brown) dot-dot-dashed and (red) dot-dashed shapes, respectively, and the (green) dashed shape represents the doubly misidentifiedJ/ψK+pfinal state, where the kaon and proton masses are swapped.
In (b) theB0s→J/ψπ+K−mode is shown by the (red) dashed curve and the (green) dot-dashed shape represents theΛ0b→J/ψpK−reflection.
surements started in the 1990’s. Measurements at LEP
115
indicated thatτ(Λ0b)/τ(B0) was significantly lower than
116
the prediction: in 2003 one widely quoted average of
117
all data gave 0.798±0.052 [18], while another gave
118
0.786±0.034 [19].
119
More recent measurements showed indications that a
120
higher value is possible [20], although the uncertainties
121
of these measurements are large. The LHCb collabora-
122
tion performed measurements of the lifetime ratio uti-
123
lizing theΛ0b→J/ψpK−decay using 1 fb−1of data [21]
124
and then updated with 3 fb−1 sample [22]. ThisΛ0bde-
125
cay mode was first seen by LHCb. For similar decay
126
width, this decay mode has much better reconstruction
127
efficiency than theJ/ψΛ final state [23], as it contains
128
four charged tracks from theΛ0bdecay vertex. Only the
129
3 fb−1measurement is discussed here.
130
In this measurement theΛ0bdecay time distribution is
131
compared to that ofB0 → J/ψK−π+ decays. The re-
132
constructed invariant mass distributions for both modes
133
are shown in Fig. 5. For B0 candidates the invariant
134
π+K−mass was required to be within±100 MeV of the
135
K∗0(892) mass. There are approximately 50 000Λ0bsig-
136
nal events and 340 000B0signal events.
137
The decay time acceptances obtained from the sim-
138
ulations are shown in Fig. 6(a). The individual accep-
139
tances in both cases exhibit the same behaviour of de-
140
creasing below 1 ps. The ratio of the decay time accep-
141
tances is shown in Fig. 6(b). The yield ofbhadrons for
142
both decay modes is determined by fitting the candidate
143
invariant mass distributions in each decay time bin. The
144
resulting signal yields as a function of decay time are
145
shown in Fig. 7.
146
Acceptance (arbitrary scale)
0.5 1
1.5
LHCb Simulation
Acceptance ratio
(b) (a)
t [ps]
0 2 4 6 8
0.8 1 1.2
1.4
LHCb Simulation
Figure 6: (a) Decay time acceptances (arbitrary scale) from sim- ulation for (green) circles Λ0b → J/ψpK−, and (red) open-boxes B0 →J/ψK∗0(892) decays. (b) Ratio of the decay time acceptances betweenΛ0b→J/ψpK−andB0→J/ψK∗0(892) decays obtained from simulation. The (blue) line shows the result of the linear fit.
t [ps]
0 2 4 6
Yield / (0.3 ps)
102
103
104
105
LHCb
Figure 7: Decay time distributions forΛ0b→J/ψpK−shown as (blue) circles, andB0 →J/ψK∗0(892) shown as (green) squares. For most entries the error bars are smaller than the points.
The ratio of lifetimes is determined asτ(Λ0b)
τ(B0) =0.974±
147
0.006±0.004. Multiplying the lifetime ratio byτ(B0)=
148
1.519 ±0.007 ps, the Λ0b baryon lifetime is τ(Λ0b) =
149
1.479±0.009±0.010 ps. A summary of Λ0b lifetime
150
measurements done since 1990 is shown in Fig. 8.
1 1.2 1.4 1.6
Experiment
-] ψpK LHCb 1/fb (2013) [J/
Λ] ψ CMS (2012) [J/
Λ] ψ ATLAS (2012) [J/
Λ] ψ D0 (2012) [J/
Λ] ψ CDF (2011) [J/
-] π
+
Λc
CDF (2010) [ Λ] ψ D0 (2007) [J/
D0 (2007) [Semileptonic decay]
DLPH (1999) [Semileptonic decay]
ALEP (1998) [Semileptonic decay]
OPAL (1998) [Semileptonic decay]
CDF (1996) [Semileptonic decay]
τ (ps) τ(Β )0
-] ψpK LHCb 3/fb (2014) [J/
1.479±0.009±0.010 ps 1.415±0.027±0.006 ps 1.468±0.009±0.008 ps
LHCb 1/fb (2014) [J/ψΛ] LHCb (2014) Average
Figure 8: Summary of measuredΛ0blifetimes. The vertical dashed line shows the world averageB0lifetime.
151
5. First observation of Cabibbo-suppressed decay
152
Λ0
b → J/ψpπ−
153
LHCb has first observed the Cabibbo-suppressed de- cayΛ0b → J/ψpπ−using a data sample corresponding to an integrated luminosity of 3 fb−1[24]. A prominent signal is observed and the branching fraction relative to the decay modeΛ0b→J/ψpK−is determined to be
B(Λ0b→ J/ψpπ−)
B(Λ0b→J/ψpK−) =0.0824±0.0025(stat)±0.0042(syst).
The measured ratio is consistent with the expectation
154
computed using relative CKM matrix elements and
155
phase space factors. Figure 9 shows the distribution of
156
Λ0b→ J/ψpπ−andΛ0b→J/ψpK−masses.
157
2] [MeV/c
π-
ψp
mJ/
5500 5600 5700
2 Candidates per 5 MeV/c
0 200 400 600 800 1000 1200 1400
LHCb DataΛb→J/ψpπ-
pK-
ψ
→J/
Λb
B reflections Combinatorial Total
2] [MeV/c
pK-
ψ
mJ/
5500 5600 5700
2 Candidates per 5 MeV/c
10 102
103
Data pK- ψ
→J/
Λb B reflections Combinatorial Total
LHCb
Figure 9: Distribution of (top)Λ0b → J/ψpπ−and (bottom)Λ0b → J/ψpK−masses with fit projections overlaid.
A search for direct CPviolation is performed. The difference in the CP asymmetries between these two de-
cays is found to be
ACP(Λ0b→ J/ψpπ−)− ACP(Λ0b →J/ψpK−)
=(+5.7±2.4 (stat)±1.2 (syst))%,
which is compatible with CP symmetry at the 2.2σ
158
level.
159
6. Conclusion
160
Using the 3 fb−1data sample, LHCb has used various
161
b-hardon toJ/ψh+h−decays to test the Standard Model
162
and search for New Physics, as well as understand the
163
scalar mesons.
164
ACKNOWLEDGEMENTS
165
I thank the U.S. National Science Foundation for sup-
166
port.
167
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