1. Search for Four-Quark Hadrons in the Data from the Early Belle II Experiment
Todd Denning
Willamette University
(Dated: August 5, 2016)
The Belle II detector at the SuperKEK B-factory in Tsukuba, Japan, will examine e+
e−
collisions at
forty times greater instantaneous luminosity than the previous Belle detector. This increase opens
the door for analysis of unexplored physics, such as the higher energy bound states of b¯b quarks,
known as “bottomonium.” One of these bottomonium states is the Υ(6S) meson, currently the most
energetic form of bottomonium to have been discovered. Additionally, results from Belle indicate
the Υ(6S) may decay to a unique-charged four-quark state, called Z±
b . The process needed to
determine the feasibility of analyzing the decay Υ(6S) → π Z±
b , Z±
b → π±
Υ(pS), Υ(pS) → µ+
µ−
(where p = 1, 2, 3) during early Belle II operations is presented.
INTRODUCTION
The Belle Detector and KEK Accelerator
A B-factory, such as SuperKEKB, is a particle acceler-
ator that produces B-mesons from e+
e−
collisions. The
Belle II experiment will build upon the research that
was initially conducted by the original Belle experiment
from 1999-2008, which determined the effect of charge-
parity (CP) violation in B mesons, and contributed to
the 2008 Nobel Prize in physics. Additionally, the abil-
ity for Belle II to collect data at greater luminosities is
expected to improve measurements from previous exper-
iments, such as analyses of Υ(6S) decay and the study
of the “tetraquark” named Z±
b [1]. Given the greater
instantaneous luminosity of the accelerator and the up-
grades to the detector, there is hope to understand the
properties of these recently discovered particles. The ex-
pected ten-year run of SuperKEKB includes three differ-
ent phases: Phase 1, the bulk of which was completed
in 2016, involved testing background radiation detectors
and commissioning the beam. Phase 2, which is of par-
ticular interest for this study, and which has not yet
occurred, is expected to operate at the energy neces-
sary to produce Υ(6S) mesons. Phase 3 will eventu-
ally be the nominal operation for the full Belle II de-
tector. However, although Belle II operations have not
yet started, useful preliminary work involves simulating
data in order to understand and foresee potential prob-
lems associated with certain studies. This paper gives an
overview of the process of using Monte Carlo simulation
in order to determine the feasibility of studying the de-
cay Υ(6S) → π Z±
b , Z±
b → π±
Υ(pS), Υ(pS) → µ+
µ−
(where p = 1, 2, 3). Moreover, the value of such a study
allows researchers to plan the operations of Belle II over
its entire lifetime, and will give the collaboration foresight
into which studies need to be prioritized due to time and
budget concerns.
The Standard Model and Quarkonium
The Standard Model (SM) is the fundamental theory
that describes the particles that make up matter and the
forces that interact between them. Matter is composed of
quarks (q), which include up, down, top, bottom, strange,
and charm quarks, and leptons, such as electrons and
neutrinos. The bound states of quarks can include par-
ticles such as mesons, which are composed of a quark
and its antiquark (q¯q), and baryons such as protons and
neutrons, which are composed of three quarks. These
particles that are made entirely of quarks are referred to
as hadrons. Quarkonium is another name for the vary-
ing bound states of a quark and its antiquark, but the
term specifically refers to mesons formed either by a bot-
tom quark and an anti-bottom quark, known as “bot-
tomonium,” or a charm quark and an anti-charm quark,
known as “charmonium.” It has been recently discovered
that hadrons can be composed of four quarks as well. The
Z±
b particle is an example of this type of hadron, which
contributes to the interest in studying the aforementioned
decay.
Data Analysis
The ability to use software and programs specific to
high energy physics is of essential importance for this
study. A program called “EvtGen” simulates the par-
ticle physics decays that would occur under experimental
conditions [3]; “GEANT” then models these interactions
with the Belle II detector [2]. The Belle II analysis soft-
ware framework (basf2) is used to reconstruct the indi-
vidual particles, and the ROOT software package is used
to analyze the resulting data [4]. This is the framework
under which the ability to obtain a signal with varying
levels of luminosity occurs, and it also allows a distinc-
tion to be made between the reconstruction of physics
events in Phase 2 and 3. Not all of the detectors will be
commissioned until Phase 3. As such, the detector simu-
lation in GEANT employed different detector geometries
to account for the lack of vertex detector (VXD, PXD)
in Phase 2. Fig. 1 and 2 represent the number of VXD

2. 2
and PXD “hits” for Phase 2 and 3, respectively.
FIG. 1. Number of SVD hits for Phase 2, shown in red, and
Phase 3, shown in blue.
FIG. 2. Number of PXD hits for Phase 2, shown in red, and
Phase 3, shown in blue.
ANALYSIS
The main decay of interest in this study was Υ(6S) →
π Z±
b , Z±
b → π±
Υ(pS), Υ(pS) → µ+
µ−
, where the
branching fraction B(Υ(1S) → µ+
µ−
is approximately
2% [6]. This was referred to as the “exclusive” analysis,
where every other possible decay mode for Υ(6S) is not
considered. In order to get a better sense of the feasibility
of analyzing the Zb± states, it is necessary to look at cases
whereΥ(6S) is not restricted to only decaying to a pair of
two muons. This is called the “inclusive” analysis, given
by Υ(6S) → π+
X, Υ(6S) → π π±
X, where X represents
any appropriate particle that maintains charge conser-
vation. For both the exclusive and inclusive cases, the
signal particles of interest include Υ(1S), Υ(2S), Υ(3S),
and Z±
b (10610), Z±
b (10650), where the numbers associ-
ated with the Zb± in parentheses represent the mass of
the particles in question. Background sources in this anal-
ysis, conversely, come from unwanted q¯q events.
Exclusive Analysis
The exclusive decay Υ(6S) → π Z±
b , Z±
b →
π±
Υ(pS), Υ(pS) → µ+
µ−
yields an analysis that is rela-
tively clean, due to low background. Unfortunately, the
number of signal events is also low. This is due to the
small branching fraction, and therefore requires the use
of optimization parameters in order to find the best sig-
nal given varying amounts of background. This analy-
sis is ideal for Belle II because the integrated luminosity
of SuperKEKB will increase compared to the Belle ex-
periment, which will help to determine if studying this
particular decay is appropriate for Phase 2.
Exclusive Analysis Optimization
Determining the selection criteria to apply to the data
to optimize signal and reject background is of great im-
portance for both the exclusive and inclusive analysis.
An important optimization parameter is the number of
charged tracks that are reconstructed in the Belle II de-
tector. For the nTracks variable, the signal to background
ratio is optimized by requiring a value equal to 4. Figures
3 and 4 show the cuts that were applied to maximize the
Υ(1S) signal and nTracks, respectively. Additionally, the
Υ(1S) mass was optimized as well in order to remove in-
correctly reconstructed candidates whose massed do not
match the nominal values.
Inclusive Analysis
The inclusive decay Υ(6S) → π+
X, Υ(6S) → π π±
X,
unlike the exclusive decay, yields an analysis that has
much higher signal and background. Since the require-
ments on the reconstructed decay chain are less stringent,
it is expected that there will be more unwanted q¯q events.
Inclusive Analysis Optimization
Similar to the exclusive analysis, the inclusive analysis
optimization parameters include the Υ(pS) masses and
nTracks. However, two additional parameters, including
“R2” and “CosTBTO,” are needed. R2 is the ratio of
the second to zeroth Fox-Wolfram moment of the event
[7], and CosTBTO is the cosine of the angle between the
reconstructed Υ(6S) and the thrust axis of the event [8].

3. 3
FIG. 3. Signal optimization for the Υ(1S) mass, where cuts
of -160 MeV and +140 MeV from the nominal Υ(1S) mass [6]
were used.
FIG. 4. The optimized selection for nTracks is shown for
nTracks equal to four.
Figs. 5, 6, 7, and 8 show the various criteria for op-
timizing signal versus background for the Υ(pS) mass,
nTracks, R2, and CosTBTO, respectively.
FIG. 5. Signal optimization for the Υ(pS) mass, where cuts
of -20 MeV and +20 MeV were used to optimize signal and
reject background.
FIG. 6. The greatest optimization for nTracks was given at
nTracks >11

4. 4
FIG. 8. The best optimization for CosTBTO
FIG. 7. The best optimization for R2 is >0.8.
CALCULATING EFFICIENCIES
The goal of these analysis procedures is to determine
the feasibility of finding signals for the Zb± particles at
different amounts of integrated luminosity. After recon-
structing the inclusive and exclusive events, additional
cuts can be used to optimize the signal and background
for Zb± in the exclusive and inclusive cases.
The same process of maximizing the Zb± signal for the
exclusive case was done for the inclusive case. The results
of optimization, while removing signal events, reduces the
number of expected background events by orders of mag-
nitude, making it possible to attempt this analysis. The
technique for determining this feasibility involved using
Gaussian fits to determine the approximate area under
the Zb± mass peaks. Figures 9 and 10 show plots of the
Zb± mass signal from Υ(1S) reconstruction for the exclu-
sive and inclusive analyses, respectively, and the result-
ing Gaussian fits that were used to estimates their areas.
The same process, moreover, was used to reconstruct the
Zb± mass from Υ(2S) and Υ(3S). Based on these fits,
a “back-of-the-envelope” calculation of the efficiency was
found to range from 10-65%, but further study is required
to determine these values correctly. The resulting mean
values (¯x) and resolution (σ) values for all Υ(pS) modes
are summarized in Table 1.
FIG. 9. Signal peak for the exclusive Zb± mass with a Gaus-
sian fit
FIG. 10. Signal peak for the inclusive Zb± mass with a Gaus-
sian fit
As summarized in Table 1, there is a clear difference
between the signal resolution for the Zb± mass in the
exclusive and inclusive cases. The poor resolution of the
exclusive mode means that, with Phase 2 data, it will
be difficult to separate the wrong-pion combinations and
nearby Zb(10610) and Zb(10650) signals.

5. 5
Variable Υ(1S) Υ(2S) Υ(3S)
¯xE 10.60 GeV 10.60 MeV 10.61 GeV
σE 49.0 MeV 50.1 MeV 67.3 MeV
¯xI 10.61 GeV 10.61 GeV 10.61 GeV
σI 12.5 MeV 14.1 MeV 15.0 MeV
TABLE I. Resulting mean values (¯x) and resolution (σ) values
for all Υ(pS) modes, where E and I denote the exclusive and
inclusive cases, respectively.
CONCLUSION
In this study, an analysis of the exclusive and inclusive
modes for Υ(6S) was used to determine the feasibility of
studying the four-quark hadron called Zb± during early
Belle II operations. An analysis program called ROOT
was used to optimize the signal and background for Zb±
in the exclusive and inclusive modes in order to determine
the signal resolution for its mass, which was determined
to be too high for the exclusive case. The next steps
for this analysis are to work on improving the Zb± mass
resolution for the exclusive mode, properly calculate the
efficiency for studying these analyses, and to determine
the level of significance expected under various Phase 2
luminosity scenarios.
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