Measuring CP violation in B0
→ φφ with LHCb
J. F. Libby on behalf of the LHCb Collaboration∗
University of Oxford
Sensitivity studies to the CP -violating parameters of the decay B0s → φφ with the LHCb exper-
iment are presented. The decay proceeds via a b → sss̄ gluonic-penguin quark transition, which
is sensitive to contributions from beyond the Standard Model particles. A time-dependent angular
analysis of simulated data leads to an expected statistical uncertainty of 6◦ on any new physics
induced CP -violating phase for a sample corresponding to 2 fb−1 of integrated luminosity. The
expected precision on sin 2β from the related decay B0 → φK0S is also discussed.
I. INTRODUCTION
The amplitude for the decay B0s → φφ is dominated
by gluonic-penguin quark transitions b → sss̄ (Fig. 1).
Gluonic-penguin processes are sensitive to beyond the
Standard Model particles that contribute within the loop.
The e+e− B-factories have measured sin 2β in nine B0
gluonic penguin decay modes, such as B0 → φK0S and
B0 → η′K0S [1]. All the measurements of sin 2β from
these modes have values below that measured in b →
cc̄s transitions, but no individual measurement shows a
significant deviation.
The decay B0s → φφ is predicted to have a CP -
violating phase less than 1◦ within the SM [2]. The
dependence on Vts in both the mixing and decay am-
plitudes leads to a cancellation of the B0s -mixing phase.
Therefore, if any significant CP -violation is measured
in B0s → φφ decays it is an unambiguous signature of
new physics. The decay is of a pseudoscalar meson to
two vector mesons, which leads to the final state being
a CP -even and CP -odd admixture. Therefore, a time-
dependent angular analysis is required to extract the CP -
violating parameters of the decay.
The paper is organized as follows. Section II contains a
brief description of the LHCb experiment. The predicted
event yields and background estimations are described
FIG. 1: The main diagram contributing to the decay B0s →
∗Electronic address: j.libby1@physics.ox.ac.uk
in Section III. The CP sensitivity study is presented in
Section IV. The LHCb prospects with the related mode
B0 → φK0S are discussed in Section V. The conclusions
are given in Section VI.
II. THE LHCb EXPERIMENT
The Large Hadron Collider (LHC) collides protons
at a centre-of-mass energy of 14 TeV. The LHC pro-
duces 1012 bb̄ quark pairs per nominal year of data-taking
(107 s) when operating at an instantaneous luminosity of
2×1032 cm−2s−1.1 The LHCb spectrometer [3, 4] instru-
ments one forward region about the pp collision point.
The forward geometry captures approximately one-third
of all B hadrons produced and increases the probability
of both B hadrons from the bb̄ pairs being within the
acceptance, which improves the efficiency of flavour tag-
ging.
A silicon vertex detector, with sensors perpendicular to
the beam axis, is situated close to the interaction region
in a secondary vacuum. The detector provides accurate
determination of primary and secondary vertices leading
to a proper-time resolutions of approximately 40 fs in
hadronic B-decays such as B0s → φφ. Tracking stations
either side of a 1.2 T dipole magnet produce momentum
measurements with an accuracy of a few parts per mille.
There are two Ring-Imaging Čerenkov detectors, with 3
different radiators, that allow identification of K± from
π± over the momentum range 1 to 100 GeV/c.
In addition, the detector includes an electromagnetic
calorimeter, a hadron calorimeter and a muon detector.
These components are critical for identifying large trans-
verse momentum, pT , electrons, photons, hadrons and
muons from B-hadron decay in the initial hardware stage
(Level-0) of the LHCb trigger. The Level-0 trigger re-
duces the 40 MHz collision rate to 1 MHz. All data is
then transferred from the detector to a dedicated CPU
farm where the Higher Level Trigger (HLT) algorithms
are performed. Initially an association between the high
1 This luminosity optimises the number of single interactions per
bunch crossing.
http://arxiv.org/abs/0704.1392v1
mailto:j.libby1@physics.ox.ac.uk
hmBsT
Entries  4808
Mean    5.369
RMS    0.02572
Bs mass [GeV/c2]
4.8 5 5.2 5.4 5.6 5.8
hmBsT
Entries  4808
Mean    5.369
RMS    0.02572
m Bs true
FIG. 2: The B0s mass of candidates reconstructed in the signal
(blue) and inclusive bb̄ simulation samples (red) before trigger
selections. The normalisations are arbitrary.
pT objects that satisfy the Level-0 trigger and tracks with
large impact parameter to the primary vertex is sought.
If this is successful, exclusive and inclusive HLT algo-
rithms are executed resulting in a 2 kHz output rate to
disk.
III. EVENT SELECTION AND BACKGROUND
ESTIMATION
The estimation of B0s → φφ yields and background
has been performed on simulated data. The simulation
of the pp collisions and subsequent hadronisation is per-
formed by the PYTHIA generator [5]. The decay of any
B hadrons produced is simulated by EVTGEN [6] and the
detector response is performed by GEANT4 [7]. The re-
sulting data are processed by the complete LHCb recon-
struction software. A dedicated sample containing events
with a B0s → φφ decay is used to evaluate the selection
efficiency. Minimum bias events are selected rarely by
the Level-0 trigger and the HLT. Therefore, an inclusive
sample of 34 million events containing bb̄ quark pairs is
used to estimate the background. Due to the very large
number of bb̄ pairs that will be produced at LHCb, the
inclusive bb̄ sample only corresponds to approximately
15 minutes of data taking at the nominal instantaneous
luminosity; this leads to large uncertainties on the back-
ground estimates.
The selection process begins with the identification of
φ candidates reconstructed from two oppositely charged
kaons. Particle identification and pT requirements are
placed on the K± and they must be consistent with pro-
duction at a common vertex. The mass of the K+K−
must be within 20 MeV/c2 of the φ mass; the mass in-
terval corresponds to approximately ±3σmφ , where σmφ
is the mass resolution.
B-meson candidates are reconstructed in events with
two or more φ candidates with a pT > 1.2 GeV/c
2. The
B-meson candidates must be consistent with production
at a common vertex and this vertex must be well sepa-
rated from the primary vertex. The B0s candidate mass
distribution is shown in Fig. 2 for signal and background
samples. Events within 40 MeV/c2 of the B0s mass are
considered as signal; the mass interval corresponds to
approximately ±3σmB , where σmB is the mass resolu-
tion. Once Level-0 and HLT trigger selections have been
applied there are 4000 signal events expected in every
2 fb−1 of integrated luminosity, which corresponds to
one nominal year of LHC operation. The event yield
is calculated assuming the measured branching fraction
B(B0s → φφ) = (14
−5(stat.) ± 6(syst.)) × 10
−6 [8]; the
measured value lies within theoretically predicted range
[9, 10]. The background remaining in the bb̄ inclusive
simulation sample is found to consist of combinatoric B0s
candidates. The background-to-signal ratio is bounded
to lie between 0.4 to 2.1 at the 90% confidence level,
with a central value of 0.9.
IV. B0s → φφ CP SENSITIVITY
The magnitude of any new physics induced CP -phase,
φNP , is extracted from a time-dependent analysis of
the differential cross section with respect to the three
transversity angles defined in Fig 3. The amplitude for
the decay can be written in terms of three helicity am-
plitudes Hλ(t) where λ = 0,±1. The helicity amplitudes
are related to the transversity basis by A0(t) = H0(t),
A||(t) =
(H+1 +H−1) and A⊥(t) =
(H+1 −H−1).
The amplitudes A0 and A|| are CP even and A⊥ is CP
odd. The differential cross section is then given by:
dΓ(t)
dχd cos θ1d cos θ2
= |A0(t)|
2f1(χ, θ1, θ2)|A||(t)|
2f2(χ, θ1, θ2) + |A⊥(t)|
2f3(χ, θ1, θ2)
+ ℑ(A∗0(t)A⊥(t))f4(χ, θ1, θ2) + ℜ(A
0(t)A||(t))f5(χ, θ1, θ2) + ℑ(A
||(t)A⊥(t))f6(χ, θ1, θ2) (1),
where fi (i = 1 − 6) are even angular functions as re-
quired by Bose symmetry [11]. The time-dependent fac-
tors of these angular functions are sensitive to any CP -
violating phase. In principle the CP -violating phase can
χ=ϕ1+ ϕ2
FIG. 3: A schematic of the definition of the transversity angles
θ1, θ2 and χ.
accep
Entries  4663
Mean    2.675
RMS     1.343
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
accep
Entries  4663
Mean    2.675
RMS     1.343
Acceptabnce
Proper time (ps)
FIG. 4: The variation of the acceptance as a function of the
proper-time, τ . The acceptance function fit to the simulated
data is ǫ(τ ) = 0.084τ
0.027+τ3
be different between the three transversity amplitudes.
However, to simplify the analysis it has been assumed
to be equal. Significant fine-tuning of the phases would
be required for no effects to be observed if new physics
induced phases are present. The time-dependent terms
also depend on the strong phase differences δ||,0 between
A(t)⊥ and A(t)||,0, the relative magnitudes of the three
amplitudes and the mass (lifetime) differences between
the B0s mass eigenstates, ∆ms (∆Γs).
Simulated data are generated to follow the differential
distribution given in Eqn. 1 with the value of φNP cho-
sen to be 0.2 rad. The strong phases are assumed to be
δ|| = 0 and δ0 = π; these values are motivated by näıve
factorization [12]. The magnitudes of the transversity
amplitudes are set to the values measured in the anal-
ogous channel for B0 decays B0 → K∗φ [13, 14]. The
value of ∆ms is taken to be 17 ps
−1 [15] and ∆Γs/Γ is
set to be 0.15, compatible with current experimental con-
straints [16] and theoretical expectations [17]. The signal
sample size has a mean of 4000 events corresponding to
an integrated luminosity of 2 fb−1.
The following experimental effects are also simulated.
• The background is assumed to be at level 90%
of the signal with flat transversity angle and mass
distributions, and an exponential lifetime distribu-
tions.
• The tagging power, ǫ(1− 2ω), where ǫ is the tag-
ging efficiency and ω is the mistag rate, is assumed
to be 9% which has been found in simulation stud-
ies of other B0s hadronic decays [18]. This is signif-
icantly better than that for B0 modes because the
kaon associated with the B0s hadronisation is also
used.
• The proper-time acceptance measured from the
signal simulation sample is shown in Fig. 4. The
reduced acceptance for short lifetimes is the result
of trigger and selection requirements on the impact
parameters of the B daughters.
• The proper time and B0
mass resolutions are
estimated to be 40 fs and 12 MeV/c2, respectively.
These resolutions are estimated from the signal
simulation sample used for the selection studies.
• The angular acceptance and resolution are as-
sumed to be flat and to have negligible effect, re-
spectively; this assumption is motivated by the
studies of related channel B0s → Jψφ [19].
phi_s
-0.4 -0.2 0 0.2 0.4 0.6 0.8
Prob       1
Constant  1.373± 20.59 
Mean      0.006382± 0.1941 
Sigma     0.004403± 0.1002 
Prob       1
Constant  1.373± 20.59 
Mean      0.006382± 0.1941 
Sigma     0.004403± 0.1002 
phi_s
-0.4 -0.2 0 0.2 0.4 0.6 0.8
A RooPlot of "phi_s"
φNP (rad)
FIG. 5: The distribution of fitted value of φNP for 500 simu-
lated B0s → φφ experiments.
Five-hundred samples of signal and background events
are generated and a maximum likelihood fit is performed
on each one. The parameters φNP , δ||, δ0 and the mag-
nitude of the transversity amplitudes are extracted from
the fit; all other parameters are fixed. The distribution
of the fitted value of φNP for these 500 experiments is
shown in Fig 5. The average error on φNP is 0.1 rad
(5.7◦). The pull distribution of the true value subtracted
from the fitted value divided by the uncertainty is nor-
Sets of 500 experiments are produced varying the input
parameters assumed. The variation of the uncertainty
on φNP as a function of the B(B
s → φφ), signal-to-
background ratio and ∆Γs/Γs is given in Table I. The
variation of the assumed B leads to the expected statisti-
cal scaling of the uncertainty. The uncertainty on φNP is
not degraded significantly until the background-to-signal
TABLE I: The variation of the uncertainty on φNP as a
function of the branching fraction, background-to-signal ra-
tio (B/S) and ∆Γs/Γs.
B (×10−5) σ(φNP )
0.35 13◦
0.7 8.1◦
1.4 5.7◦
2.1 4.6◦
B/S σ(φNP )
0 5.5◦
0.9 5.7◦
2 6.1◦
5 7.2◦
∆Γs/Γs σ(φNP )
0.05 7.2◦
0.15 5.7◦
0.05 4.9◦
ratio is greater than three. Increasing the value of ∆Γs/Γ
leads to a reduction in the uncertainty because enhanced
interference from the lifetime difference among the am-
plitudes increases the sensitivity to φNP . The values of
φNP , the proper-time resolution and the relative magni-
tudes of the transversity amplitudes are also varied; all
these had negligible effect on the sensitivity to φNP .
V. B0 → φK0S CP SENSITIVITY
Simulation studies of the decay B0 → φK0S have also
been performed. The expected yield per 2 fb−1 of in-
tegrated luminosity is 800 events. These yields do not
include K0S daughters without measurements in the sili-
con vertex detector, approximately two-thirds ofK0S from
these decays, which are not reconstructed in the current
HLT algorithms. Algorithms to perform this reconstruc-
tion are currently being developed. The background-to-
signal ratio is estimated to be 2.4 from the bb̄ inclusive
simulation.
A time-dependent analysis of the B0 → φK0S is re-
quired to extract the sensitivity to sin 2β. A toy sim-
ulation study is performed to extract the sensitivity to
sin 2β. The tagging power is assumed to be 5% and the
proper-time resolution is taken to be 60 fs from the simu-
lated signal sample. A 10% K+K− S-wave contribution
is also included in the fit. The uncertainty on sin 2β is
expected to be 0.32 for a data sample corresponding to
2 fb−1 of integrated luminosity.
VI. CONCLUSIONS
Sensitivity studies to CP -violation in the decay B0s →
φφ have been presented. A sample of data corresponding
to an integrated luminosity of 2 fb−1 gives an uncertainty
of 6◦ on any new physics induced CP phase. Varying the
assumptions used within reasonable ranges changes the
predicted statistical uncertainty between 4◦ and 13◦. The
largest statistical uncertainty results from decreasing the
branching fraction by a factor of four. The measurement
of sin 2β from the B0 → φK0S has also been investigated.
The sensitivity is expected to be 0.32 with a data set
corresponding to 2 fb
of integrated luminosity; this is
of the same order as the current sensitivity of the e+e−
B-factories [20, 21]. Therefore, in conclusion, B0s → φφ
is the most sensitive mode with which to study gluonic-
penguin B decays with LHCb.
[1] E. Barberio et al. (Heavy Flavour Averaging Group),
http://www.slac.stanford.edu/xorg/hfag .
[2] M. Raidal, Phys. Rev. Lett 89, 231803 (2002).
[3] LHCb Technical Proposal, LHCb Collaboration,
CERN/LHCC 98-4 (1998).
[4] LHCb Reoptimized Detector Design and Performance,
LHCb Collaboration, CERN/LHCC 2003-040 (2003).
[5] T. Sjöstrand, L. Lönnblad and S. Mrenna,
hep-ph/0108264.
[6] D. Lange, Nucl. Instr. and Meth. A462 (2001) 152.
[7] S. Agostinelli et al. (GEANT4 Collaboration), Nucl. In-
str. and Meth. A506 (2003) 250.
[8] D. Acosta et al. (CDF Collaboration), Phys. Rev. Lett.
95, 031801 (2005).
[9] Y.-H. Chen et al., Phys. Rev. D 59, 074003 (1999).
[10] X. Q. Li, G. R. Lu and Y. D. Yang, Phys. Rev. D 68,
114015 (2005) [Erratum-ibid D 71, 019902 (2005)].
[11] B. de Paula et al., LHCb-2007-047.
[12] M. Bauer, B. Stech and M. Wirbel, Z. Phys. C 34, 103
(1987).
[13] B. Aubert et al. (BABAR Collaboration), Phys. Rev.
Lett. 93 231804 (2004).
[14] K.-F. Chen et al. (Belle Collaboration), Phys. Rev. Lett.
94 221804 (2005).
[15] A. Abulencia et al. (CDF Collaboration), Phys. Rev.
Lett. 97 242003 (2006).
[16] G. Weber, these proceedings.
[17] C. Tarantino, hep-ph/0702235.
[18] M. Calvi, O. Leroy and M. Musy, LHCb-2007-058.
[19] L. Fernandez, CERN-THESIS-2006-042.
[20] K.-F. Chen et al. (Belle Collaboration), hep-ex/0608039.
[21] B. Aubert et al. (BABAR Collaboration),
hep-ex/0607112.
http://www.slac.stanford.edu/xorg/hfag
http://arxiv.org/abs/hep-ph/0108264
http://arxiv.org/abs/hep-ph/0702235
http://arxiv.org/abs/hep-ex/0608039
http://arxiv.org/abs/hep-ex/0607112

  Sensitivity studies to the CP-violating parameters of the decay Bs->phi phi
with the LHCb experiment are presented. The decay proceeds via a b->s s anti-s
gluonic-penguin quark transition, which is sensitive to contributions from
beyond the Standard Model particles. A time-dependent angular analysis of
simulated data leads to an expected statistical uncertainty of 6 degrees on any
new physics induced CP-violating phase for a sample corresponding to 2 fb^{-1}
of integrated luminosity. The expected precision on sin2beta from the related
decay Bd->phi K0S is also discussed.

Measuring CP violation in B0
→ φφ with LHCb
J. F. Libby on behalf of the LHCb Collaboration∗
University of Oxford
Sensitivity studies to the CP -violating parameters of the decay B0s → φφ with the LHCb exper-
iment are presented. The decay proceeds via a b → sss̄ gluonic-penguin quark transition, which
is sensitive to contributions from beyond the Standard Model particles. A time-dependent angular
analysis of simulated data leads to an expected statistical uncertainty of 6◦ on any new physics
induced CP -violating phase for a sample corresponding to 2 fb−1 of integrated luminosity. The
expected precision on sin 2β from the related decay B0 → φK0S is also discussed.
I. INTRODUCTION
The amplitude for the decay B0s → φφ is dominated
by gluonic-penguin quark transitions b → sss̄ (Fig. 1).
Gluonic-penguin processes are sensitive to beyond the
Standard Model particles that contribute within the loop.
The e+e− B-factories have measured sin 2β in nine B0
gluonic penguin decay modes, such as B0 → φK0S and
B0 → η′K0S [1]. All the measurements of sin 2β from
these modes have values below that measured in b →
cc̄s transitions, but no individual measurement shows a
significant deviation.
The decay B0s → φφ is predicted to have a CP -
violating phase less than 1◦ within the SM [2]. The
dependence on Vts in both the mixing and decay am-
plitudes leads to a cancellation of the B0s -mixing phase.
Therefore, if any significant CP -violation is measured
in B0s → φφ decays it is an unambiguous signature of
new physics. The decay is of a pseudoscalar meson to
two vector mesons, which leads to the final state being
a CP -even and CP -odd admixture. Therefore, a time-
dependent angular analysis is required to extract the CP -
violating parameters of the decay.
The paper is organized as follows. Section II contains a
brief description of the LHCb experiment. The predicted
event yields and background estimations are described
FIG. 1: The main diagram contributing to the decay B0s →
∗Electronic address: j.libby1@physics.ox.ac.uk
in Section III. The CP sensitivity study is presented in
Section IV. The LHCb prospects with the related mode
B0 → φK0S are discussed in Section V. The conclusions
are given in Section VI.
II. THE LHCb EXPERIMENT
The Large Hadron Collider (LHC) collides protons
at a centre-of-mass energy of 14 TeV. The LHC pro-
duces 1012 bb̄ quark pairs per nominal year of data-taking
(107 s) when operating at an instantaneous luminosity of
2×1032 cm−2s−1.1 The LHCb spectrometer [3, 4] instru-
ments one forward region about the pp collision point.
The forward geometry captures approximately one-third
of all B hadrons produced and increases the probability
of both B hadrons from the bb̄ pairs being within the
acceptance, which improves the efficiency of flavour tag-
ging.
A silicon vertex detector, with sensors perpendicular to
the beam axis, is situated close to the interaction region
in a secondary vacuum. The detector provides accurate
determination of primary and secondary vertices leading
to a proper-time resolutions of approximately 40 fs in
hadronic B-decays such as B0s → φφ. Tracking stations
either side of a 1.2 T dipole magnet produce momentum
measurements with an accuracy of a few parts per mille.
There are two Ring-Imaging Čerenkov detectors, with 3
different radiators, that allow identification of K± from
π± over the momentum range 1 to 100 GeV/c.
In addition, the detector includes an electromagnetic
calorimeter, a hadron calorimeter and a muon detector.
These components are critical for identifying large trans-
verse momentum, pT , electrons, photons, hadrons and
muons from B-hadron decay in the initial hardware stage
(Level-0) of the LHCb trigger. The Level-0 trigger re-
duces the 40 MHz collision rate to 1 MHz. All data is
then transferred from the detector to a dedicated CPU
farm where the Higher Level Trigger (HLT) algorithms
are performed. Initially an association between the high
1 This luminosity optimises the number of single interactions per
bunch crossing.
http://arxiv.org/abs/0704.1392v1
mailto:j.libby1@physics.ox.ac.uk
hmBsT
Entries  4808
Mean    5.369
RMS    0.02572
Bs mass [GeV/c2]
4.8 5 5.2 5.4 5.6 5.8
hmBsT
Entries  4808
Mean    5.369
RMS    0.02572
m Bs true
FIG. 2: The B0s mass of candidates reconstructed in the signal
(blue) and inclusive bb̄ simulation samples (red) before trigger
selections. The normalisations are arbitrary.
pT objects that satisfy the Level-0 trigger and tracks with
large impact parameter to the primary vertex is sought.
If this is successful, exclusive and inclusive HLT algo-
rithms are executed resulting in a 2 kHz output rate to
disk.
III. EVENT SELECTION AND BACKGROUND
ESTIMATION
The estimation of B0s → φφ yields and background
has been performed on simulated data. The simulation
of the pp collisions and subsequent hadronisation is per-
formed by the PYTHIA generator [5]. The decay of any
B hadrons produced is simulated by EVTGEN [6] and the
detector response is performed by GEANT4 [7]. The re-
sulting data are processed by the complete LHCb recon-
struction software. A dedicated sample containing events
with a B0s → φφ decay is used to evaluate the selection
efficiency. Minimum bias events are selected rarely by
the Level-0 trigger and the HLT. Therefore, an inclusive
sample of 34 million events containing bb̄ quark pairs is
used to estimate the background. Due to the very large
number of bb̄ pairs that will be produced at LHCb, the
inclusive bb̄ sample only corresponds to approximately
15 minutes of data taking at the nominal instantaneous
luminosity; this leads to large uncertainties on the back-
ground estimates.
The selection process begins with the identification of
φ candidates reconstructed from two oppositely charged
kaons. Particle identification and pT requirements are
placed on the K± and they must be consistent with pro-
duction at a common vertex. The mass of the K+K−
must be within 20 MeV/c2 of the φ mass; the mass in-
terval corresponds to approximately ±3σmφ , where σmφ
is the mass resolution.
B-meson candidates are reconstructed in events with
two or more φ candidates with a pT > 1.2 GeV/c
2. The
B-meson candidates must be consistent with production
at a common vertex and this vertex must be well sepa-
rated from the primary vertex. The B0s candidate mass
distribution is shown in Fig. 2 for signal and background
samples. Events within 40 MeV/c2 of the B0s mass are
considered as signal; the mass interval corresponds to
approximately ±3σmB , where σmB is the mass resolu-
tion. Once Level-0 and HLT trigger selections have been
applied there are 4000 signal events expected in every
2 fb−1 of integrated luminosity, which corresponds to
one nominal year of LHC operation. The event yield
is calculated assuming the measured branching fraction
B(B0s → φφ) = (14
−5(stat.) ± 6(syst.)) × 10
−6 [8]; the
measured value lies within theoretically predicted range
[9, 10]. The background remaining in the bb̄ inclusive
simulation sample is found to consist of combinatoric B0s
candidates. The background-to-signal ratio is bounded
to lie between 0.4 to 2.1 at the 90% confidence level,
with a central value of 0.9.
IV. B0s → φφ CP SENSITIVITY
The magnitude of any new physics induced CP -phase,
φNP , is extracted from a time-dependent analysis of
the differential cross section with respect to the three
transversity angles defined in Fig 3. The amplitude for
the decay can be written in terms of three helicity am-
plitudes Hλ(t) where λ = 0,±1. The helicity amplitudes
are related to the transversity basis by A0(t) = H0(t),
A||(t) =
(H+1 +H−1) and A⊥(t) =
(H+1 −H−1).
The amplitudes A0 and A|| are CP even and A⊥ is CP
odd. The differential cross section is then given by:
dΓ(t)
dχd cos θ1d cos θ2
= |A0(t)|
2f1(χ, θ1, θ2)|A||(t)|
2f2(χ, θ1, θ2) + |A⊥(t)|
2f3(χ, θ1, θ2)
+ ℑ(A∗0(t)A⊥(t))f4(χ, θ1, θ2) + ℜ(A
0(t)A||(t))f5(χ, θ1, θ2) + ℑ(A
||(t)A⊥(t))f6(χ, θ1, θ2) (1),
where fi (i = 1 − 6) are even angular functions as re-
quired by Bose symmetry [11]. The time-dependent fac-
tors of these angular functions are sensitive to any CP -
violating phase. In principle the CP -violating phase can
χ=ϕ1+ ϕ2
FIG. 3: A schematic of the definition of the transversity angles
θ1, θ2 and χ.
accep
Entries  4663
Mean    2.675
RMS     1.343
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
accep
Entries  4663
Mean    2.675
RMS     1.343
Acceptabnce
Proper time (ps)
FIG. 4: The variation of the acceptance as a function of the
proper-time, τ . The acceptance function fit to the simulated
data is ǫ(τ ) = 0.084τ
0.027+τ3
be different between the three transversity amplitudes.
However, to simplify the analysis it has been assumed
to be equal. Significant fine-tuning of the phases would
be required for no effects to be observed if new physics
induced phases are present. The time-dependent terms
also depend on the strong phase differences δ||,0 between
A(t)⊥ and A(t)||,0, the relative magnitudes of the three
amplitudes and the mass (lifetime) differences between
the B0s mass eigenstates, ∆ms (∆Γs).
Simulated data are generated to follow the differential
distribution given in Eqn. 1 with the value of φNP cho-
sen to be 0.2 rad. The strong phases are assumed to be
δ|| = 0 and δ0 = π; these values are motivated by näıve
factorization [12]. The magnitudes of the transversity
amplitudes are set to the values measured in the anal-
ogous channel for B0 decays B0 → K∗φ [13, 14]. The
value of ∆ms is taken to be 17 ps
−1 [15] and ∆Γs/Γ is
set to be 0.15, compatible with current experimental con-
straints [16] and theoretical expectations [17]. The signal
sample size has a mean of 4000 events corresponding to
an integrated luminosity of 2 fb−1.
The following experimental effects are also simulated.
• The background is assumed to be at level 90%
of the signal with flat transversity angle and mass
distributions, and an exponential lifetime distribu-
tions.
• The tagging power, ǫ(1− 2ω), where ǫ is the tag-
ging efficiency and ω is the mistag rate, is assumed
to be 9% which has been found in simulation stud-
ies of other B0s hadronic decays [18]. This is signif-
icantly better than that for B0 modes because the
kaon associated with the B0s hadronisation is also
used.
• The proper-time acceptance measured from the
signal simulation sample is shown in Fig. 4. The
reduced acceptance for short lifetimes is the result
of trigger and selection requirements on the impact
parameters of the B daughters.
• The proper time and B0
mass resolutions are
estimated to be 40 fs and 12 MeV/c2, respectively.
These resolutions are estimated from the signal
simulation sample used for the selection studies.
• The angular acceptance and resolution are as-
sumed to be flat and to have negligible effect, re-
spectively; this assumption is motivated by the
studies of related channel B0s → Jψφ [19].
phi_s
-0.4 -0.2 0 0.2 0.4 0.6 0.8
Prob       1
Constant  1.373± 20.59 
Mean      0.006382± 0.1941 
Sigma     0.004403± 0.1002 
Prob       1
Constant  1.373± 20.59 
Mean      0.006382± 0.1941 
Sigma     0.004403± 0.1002 
phi_s
-0.4 -0.2 0 0.2 0.4 0.6 0.8
A RooPlot of "phi_s"
φNP (rad)
FIG. 5: The distribution of fitted value of φNP for 500 simu-
lated B0s → φφ experiments.
Five-hundred samples of signal and background events
are generated and a maximum likelihood fit is performed
on each one. The parameters φNP , δ||, δ0 and the mag-
nitude of the transversity amplitudes are extracted from
the fit; all other parameters are fixed. The distribution
of the fitted value of φNP for these 500 experiments is
shown in Fig 5. The average error on φNP is 0.1 rad
(5.7◦). The pull distribution of the true value subtracted
from the fitted value divided by the uncertainty is nor-
Sets of 500 experiments are produced varying the input
parameters assumed. The variation of the uncertainty
on φNP as a function of the B(B
s → φφ), signal-to-
background ratio and ∆Γs/Γs is given in Table I. The
variation of the assumed B leads to the expected statisti-
cal scaling of the uncertainty. The uncertainty on φNP is
not degraded significantly until the background-to-signal
TABLE I: The variation of the uncertainty on φNP as a
function of the branching fraction, background-to-signal ra-
tio (B/S) and ∆Γs/Γs.
B (×10−5) σ(φNP )
0.35 13◦
0.7 8.1◦
1.4 5.7◦
2.1 4.6◦
B/S σ(φNP )
0 5.5◦
0.9 5.7◦
2 6.1◦
5 7.2◦
∆Γs/Γs σ(φNP )
0.05 7.2◦
0.15 5.7◦
0.05 4.9◦
ratio is greater than three. Increasing the value of ∆Γs/Γ
leads to a reduction in the uncertainty because enhanced
interference from the lifetime difference among the am-
plitudes increases the sensitivity to φNP . The values of
φNP , the proper-time resolution and the relative magni-
tudes of the transversity amplitudes are also varied; all
these had negligible effect on the sensitivity to φNP .
V. B0 → φK0S CP SENSITIVITY
Simulation studies of the decay B0 → φK0S have also
been performed. The expected yield per 2 fb−1 of in-
tegrated luminosity is 800 events. These yields do not
include K0S daughters without measurements in the sili-
con vertex detector, approximately two-thirds ofK0S from
these decays, which are not reconstructed in the current
HLT algorithms. Algorithms to perform this reconstruc-
tion are currently being developed. The background-to-
signal ratio is estimated to be 2.4 from the bb̄ inclusive
simulation.
A time-dependent analysis of the B0 → φK0S is re-
quired to extract the sensitivity to sin 2β. A toy sim-
ulation study is performed to extract the sensitivity to
sin 2β. The tagging power is assumed to be 5% and the
proper-time resolution is taken to be 60 fs from the simu-
lated signal sample. A 10% K+K− S-wave contribution
is also included in the fit. The uncertainty on sin 2β is
expected to be 0.32 for a data sample corresponding to
2 fb−1 of integrated luminosity.
VI. CONCLUSIONS
Sensitivity studies to CP -violation in the decay B0s →
φφ have been presented. A sample of data corresponding
to an integrated luminosity of 2 fb−1 gives an uncertainty
of 6◦ on any new physics induced CP phase. Varying the
assumptions used within reasonable ranges changes the
predicted statistical uncertainty between 4◦ and 13◦. The
largest statistical uncertainty results from decreasing the
branching fraction by a factor of four. The measurement
of sin 2β from the B0 → φK0S has also been investigated.
The sensitivity is expected to be 0.32 with a data set
corresponding to 2 fb
of integrated luminosity; this is
of the same order as the current sensitivity of the e+e−
B-factories [20, 21]. Therefore, in conclusion, B0s → φφ
is the most sensitive mode with which to study gluonic-
penguin B decays with LHCb.
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