B --> rho K* decays and other rare vector-vector modes
B → ρK∗ decays and other rare vector-vector modes ∗
G. Vasseur†
DSM/DAPNIA/SPP, CEA/Saclay, F-91191 Gif-sur-Yvette, France
The recent analyses of the following rare vector-vector decays of the B meson are presented:
∗, ωK∗, ωρ, ωω, and ωφ charmless final states. The latest results indicate that the fraction of
longitudinal polarization is about 0.5 in penguin-dominated modes and close to 1 for tree-dominated
modes.
I. MOTIVATION
The search for rare charmless hadronic decays of the
B meson to vector-vector final states has become a quite
active field in the experiments at the B factories, Belle
at KEK and BABAR at SLAC. As a lot of these decays
have not yet been seen, the first goal of these studies
is to observe such modes and measure their branching
fraction. The measurements can then be compared to
theoretical predictions.
The direct CP-violation asymmetry in these modes
can also be measured. It is defined as ACP = (Γ
Γ+)/(Γ−+Γ+), where the superscript on the total width
Γ indicates the sign of the b-quark charge in the B me-
son. Some modes can be used for further CP studies. In
fact, the result on B+ → ρ+K∗0 has already been used
to constrain the effect of the penguin amplitude on the
measurement of the angle α of the unitarity triangle from
B0 → ρ+ρ− using SU(3) flavor symmetry [1].
A hot topic is the measurement of the fraction of lon-
gitudinal polarization. The helicity angles θ1 and θ2 of
the two vector mesons are defined as the angles between
the vector meson direction in the B meson rest frame
and the direction of one of its decay product in the vec-
tor meson rest frame, as illustrated on one example in
Fig. 1. Integrating over the φ angle between the decay
planes of the two vector mesons, the fraction of longitu-
dinal polarization fL can be extracted from the angular
θK*0 θρ +K*0
FIG. 1: Definition of the helicity angles in the case of the
vector-vector B+ → ρ+K∗
decay.
∗Presented at the 4th International Workshop on the CKM Uni-
tariry Triangle, Nagoya, Japan, December 12-16, 2006. Preprint
DAPNIA-06-601.
†Electronic address: georges.vasseur@cea.fr
dependence of the decay rate, which is proportional to
(1− fL) sin
2 θ1 sin
2 θ2 + fL cos
2 θ1 cos
2 θ2.
A value of fL close to unity of order (1−O(
2 )) is ex-
pected for light vector mesons from helicity conservation.
This is expected to be true for both tree and penguin dia-
grams. However the experimental situation is more com-
plex. If fL has indeed been measured close to 1 in the
tree-dominated B → ρρ modes [2], it is surprisingly close
to 0.5 in the penguin-dominated B → φK∗ modes [3].
This effect is not yet understood. There are several possi-
ble explanations, either within the Standard Model, such
as rescattering in the final state, contribution from anni-
hilation or electroweak penguin diagrams, and transverse
gluon [4], or in new physics outside the Standard Model.
To have a better picture, it is important to measure other
vector-vector modes, both tree-dominated, like B → ωρ
and B0 → ωω, and penguin-dominated like B → ρK∗
and B → ωK∗.
The recent studies of the B → ρK∗ modes are reviewed
in section II, the ones involving an ω meson in section III.
Charge-conjugate modes are implied throughout.
II. B → ρK
MODES
A. Introduction
The B → ρK∗ charmless decays proceed through
dominant gluonic penguin loops and doubly Cabibbo-
suppressed tree processes, as shown in Fig. 2. The ex-
ternal tree diagram is only possible with a K∗+, and the
color-suppressed internal tree diagram with a ρ0. Hence
B+ → ρ+K∗0 is pure penguin.
According to isospin symmetry, the two modes with a
charged ρ are expected to have a branching fraction twice
as large as the two modes with a neutral ρ.
FIG. 2: Feynmann diagrams for the B → ρK∗ decay: gluonic
penguin, external tree and internal tree diagrams.
http://arxiv.org/abs/0704.0364v1
mailto:georges.vasseur@cea.fr
B. Results from Belle
Mbc (GeV/c
∆E (GeV)
FIG. 3: Projections of Mbc for events in the ∆E signal region
(left) and of ∆E in the Mbc signal region (right). The solid
curves show the results of the fit. The dashed curve is the
signal contribution. The hatched histograms represent the
continuum background. The sum of the b → c and continuum
background component is shown as dot-dashed lines.
0.4 0.8 1.2 1.6 2.0
M(π+π0) (GeV/c2)
0.64 0.84 1.04 1.24 1.44
M(K+π-) (GeV/c2)
FIG. 4: Signal yields obtained from the Mbc-∆E distribution
in bins of M(π+π0) (left) for events in the K∗0 region and in
bins of M(K+π−) (right) for events in the ρ+ region. The
points with error bars show the data. Solid curves show the
results of the fit. Hatched histograms are for the nonresonant
component.
Belle was the first experiment in 2005 to publish a re-
sult on the observation of the B+ → ρ+K∗0 mode [5],
on a sample of 275 millions of BB̄ pairs. A signal of
B+ → π+π0K+π− is extracted from the e+e− → qq̄
continuum and BB̄ backgrounds in an extended un-
binned maximum-likelihood fit using the B meson beam-
constrained mass Mbc and energy difference ∆E, as
shown in Fig 3.
The B+ → ρ+K∗0 signal is extracted by fits to Mbc
and ∆E in bins of the vector meson masses M(π+π0)
and M(K+π−), as shown in Fig 4. This is necessary
because there is a large nonresonant ρKπ background,
which gives a continuum in the distribution of M(K+π−).
Nethertheless there is a clear B+ → ρ+K∗0 signal of
85± 16 events with a significance of 5.2 σ.
As for fL, it is obtained by fitting simultaneously the
signal yields obtained from Mbc-∆E fits in bins of the two
helicity angles, assuming an S-wave Kπ system in the
ρKπ background. The results for the branching fraction
and fL in B
→ ρ+K∗0 are:
B = (8.9± 1.7± 1.2) 10−6,
fL = 0.43± 0.11
+0.05
−0.02.
The value found for fL is similar to the one found in φK
and its error is about twice as large as in φK∗.
C. Results from BABAR
 (GeV)0π+πm
0.5 1 1.5E
 (GeV)0π+πm
0.5 1 1.5E
 (GeV)-π+πm
0.6 0.8 1 1.2 1.4E
 (GeV)-π+πm
0.6 0.8 1 1.2 1.4E
 (GeV)-π+Km
0.8 1 1.2 1.4E
 (GeV)-π+Km
0.8 1 1.2 1.4E
 (GeV)-π+Km
0.8 1 1.2 1.4E
 (GeV)-π+Km
0.8 1 1.2 1.4E
FIG. 5: sPlots for the ππ (top) and Kπ (bottom) invariant
masses in the B+ → ρ+K∗
(left) and B0 → ρ0K∗
/B0 →
f0(980)K
∗0 (right) analyses. The points with error bars show
the data. The solid curve shows the signal and nonresonant
background contribution, the dashed curve is the nonreso-
nant background contribution (ρKπ except for the top right
plot where it represents the sum of f0(1370)K
∗, ππK∗, and
ππKπ). The arrows show the standard mass windows used
in the final fit.
More recently BABAR published an anlysis of all four
B → ρK∗ modes [6], performed on a sample of 232 mil-
lions of BB̄ pairs. It is based on an unbinned maximum-
likelihood fit, using seven variables: the B meson energy-
substituted mass mES and energy difference ∆E, a neural
network output or a Fischer discriminant combining sev-
eral event shape variables, the two vector meson masses,
and the two helicity angle cosines. The fit allows the
simultaneous extraction of the branching ratio and the
fraction of longitudinal polarization.
The major challenge in the analysis comes from the
nonresonant backgrounds, which share the same final
state as the signal. They are studied by enlarging the
vector meson mass windows, as illustrated in Fig. 5. As
in Belle, a large ρKπ background is seen in the mKπ dis-
tribution in the B+ → ρ+K∗0 mode. The Kπ system in
this background is measured to be mostly S-wave. The
situation is even more complex in the B0 → ρ0K∗0 mode,
since in addition to the ρKπ background there are sev-
eral contributions seen in the mππ distribution for a ρ
in contrast to the one for a ρ+. The f0(980) can be seen
clearly. In fact B → f0(980)K
∗, which is a scalar-vector
TABLE I: Results from BABAR on the B → ρK∗ modes: signal yield with its statistical uncertainty, significance (systematic un-
certainties included), branching fraction (90% confidence level upper limit in parentheses), fraction of longitudinal polarization
and direct CP asymmetry. (The numbers in brackets are not quoted as measurements.)
Mode Signal yield Significance (σ) B(×10−6) fL ACP
∗+ 51± 24 2.5 < 6.1 (3.6± 1.7± 0.8) [0.9 ± 0.2]
∗+ 60± 24 1.6 < 12.0 (5.4± 3.6± 1.6)
∗0 194± 29 7.1 9.6± 1.7± 1.5 0.52 ± 0.10± 0.04 −0.01 ± 0.16± 0.02
∗0 185± 30 5.3 5.6± 0.9± 1.3 0.57 ± 0.09± 0.08 0.09 ± 0.19± 0.02
a) b)
c) d)
 (GeV)ESm
 (GeV)ESm
5.25 5.26 5.27 5.28 )2 (GeV/cESm )2 (GeV/cESm
5.26 5.27 5.28 5.29
FIG. 6: Projections of mES of events passing a signal likeli-
hood threshold for (a) B+ → ρ0K∗
, (b) B+ → ρ+K∗
, (c)
∗+, (d) B0 → ρ0K∗
, (e) B+ → f0(980)K
∗+, and
(f) B0 → f0(980)K
∗0. The points with error bars show the
data. The solid curve is the fit function, the dashed curve
is the total background contribution, and the dotted curve is
the continuum background contribution.
mode, is considered as another signal to be measured in
the same maximum-likelihood fit. Also present are con-
tributions from the f0(1370) and nonresonant ππ. The
yields of the nonresonant backgrounds are fitted in the
enlarged mass windows, then extrapolated to the stan-
dard ones and fixed in the final fit with the standard mass
windows.
The projection plots in the B mass shown in Fig. 6 il-
lustrate the extraction of the signal from the continuum
and BB̄ backgrounds in the four B → ρK∗ channels and
the two B → f0(980)K
∗ modes. Table I summarizes the
results. No significant enough signals are observed for
B0 → ρ−K∗+ and B+ → ρ0K∗+, where upper limits at
the 90 % confidence level are set on the branching ratios.
For the latter a related signal B+ → f0(980)K
∗+ is ob-
served with a significance of 5.0 σ and a measured branch-
ing fraction of (5.2 ± 1.2 ± 0.5) 10−6. In B+ → ρ+K∗0,
the result is in very good agreement with the result from
Belle, with a similar precision. The B0 → ρ0K∗0 mode is
observed for the first time. The ratio between the branch-
ing fractions in these two modes is compatible with the
factor 2 expected from isospin symmetry.
The value of ACP is measured in the two significant
modes to be compatible with 0, as expected since there is
one dominant diagram. Finally fL is found close to 0.5 in
these two modes. It is compatible with the measurement
from Belle and has about the same precision. It is again
similar to the value found for φK∗.
III. MODES WITH ω
40 +ρω
10 ωω
20 *0Kω
20 0ρω
40 +ρω
20 ωω
 E (GeV)  ∆
-0.2 -0.1 0 0.1 0.2
 (GeV/cESM
5.25 5.26 5.27 5.28 5.29
20 0fω
FIG. 7: Projections of ∆E (left) and mES (right) of events
passing a signal likelihood threshold for, from top to bottom,
∗0, B+ → ωK∗
, B0 → ωρ0, B+ → ωρ+, B0 →
ωω, B0 → ωφ, and B0 → ωf0(980). The points with error
bars show the data. The solid curve is the fit function, the
dashed curve is the signal contribution, and the dot-dashed
curve is the background contribution.
TABLE II: Results from BABAR on modes involving an ω meson: signal yield with its statistical uncertainty, significance
(systematic uncertainties included), branching fraction (90% confidence level upper limit in parentheses), fraction of longitudinal
polarization and direct CP asymmetry. (The numbers in brackets are not quoted as measurements.)
Mode Signal yield Significance (σ) B(×10−6) fL ACP
∗0 55± 20 2.4 < 4.2 (2.4± 1.1± 0.7) [0.71 ± 0.25]
∗+ 8± 16 0.4 < 3.4 (0.6± 1.3± 1.0)
−18± 16 0.6 < 1.5 (−0.6± 0.7+0.8−0.3)
+ 156± 32 5.7 10.6± 2.1+1.6−1.0 0.82 ± 0.11± 0.02 0.04 ± 0.18± 0.02
→ ωω 48+24−19 2.1 < 4.0 (1.8
−0.9 ± 0.4) [0.71 ± 0.25]
→ ωφ 3.1±+4.4−8.5 0.3 < 1.2 (0.1± 0.5± 0.1)
    ρθcos
-0.5 0 0.5
|    ωθ|cos
0 0.5 1
FIG. 8: Projections of the helicity-angle cosines for ω (left)
and ρ+ (right) of events passing a signal likelihood threshold
from the fit for B+ → ωρ+ decays. The points with error bars
show the data. The solid curve is the fit function, the dashed
curve is the signal contribution, and the dot-dashed curve is
the background contribution.
On the same sample of 232 millions of BB̄ pairs,
BABAR has also recently published a search for several
vector-vector modes involving an ω meson [7]: B0 →
ωK∗0, B+ → ωK∗+, B0 → ωρ0, B+ → ωρ+, B0 → ωω,
and B0 → ωφ. The related vector-scalar mode B0 →
ωf0(980) was also searched for. An earlier search for
B → ωK∗ and B → ωρ on 89 millions of BB̄ pairs
resulted in the first observation of the B+ → ωρ+ chan-
nel [8].
The analysis is also based on an extended unbinned
maximim-likelihood fit using the same seven variables as
in the previous section. Nonresonant ππ and Kπ back-
grounds are fixed in the fit as determined from extrap-
olations from higher-mass regions. The projection plots
of ∆E and mES of Fig. 7 illustrate the extraction of the
signal from the continuum and BB̄ backgrounds in all
these modes. In most of them, no significant enough sig-
nal is seen. The only channel where a significant signal is
observed is B+ → ωρ+. Its measured branching fraction
is about 2 standard deviations smaller than the one of
B+ → ρ+ρ0 [2], while these two branching fractions are
naively expected to be equal. Table II summarizes the
results in all the modes. To calculate the branching frac-
tion, fL is left free in the fit for the three modes with a
signal significance greater than 2σ and is fixed otherwise.
Upper limits at the 90 % confidence level are set on the
branching fractions for the modes other than B+ → ωρ+.
The maximum-likelihood fit also provides the value of
fL in B
→ ωρ+, which is found to be 0.82 ± 0.11, a
high value expected for this tree-dominated mode. This
is illustrared in the projection plots of the helicity angle
cosines shown in Fig. 8. The direct CP asymmetry is also
measured and found to be compatible with 0.
IV. CONCLUSION
In summary, improved analyses with explicit consider-
ation of nonresonant backgrounds have been performed
on several charmless hadronic vector-vector decays of
the B meson. The B+ → ωρ+, B+ → ρ+K∗0, and
B0 → ρ0K∗0 modes have been observed and measured in
the past few years. Improved upper limits have been set
on the branching fraction of other vector-vector modes.
The recent results on vector-vector modes have also
brought more pieces to the polarization puzzle. The
penguin-dominated B+ → ρ+K∗0 and B0 → ρ0K∗0
modes have a fraction of longitudinal polarization of
about 0.5 like φK∗, while the tree-dominated B+ → ωρ+
mode has one closer to 1 like ρρ. As a lot of charmless
vector-vector modes have not yet been observed, new re-
sults can be expected with more data.
[1] M. Beneke et al., Phys. Lett. B 638, 68 (2006).
[2] A. Somov, contribution to this conference.
[3] K.F. Chen, contribution to this conference.
[4] G.W.S. Hou, contribution to this conference.
[5] J. Zhang et al., Phys. Rev. Lett. 95, 141801 (2005).
[6] B. Aubert et al., Phys. Rev. Lett. 97, 201801 (2006).
[7] B. Aubert et al., Phys. Rev. D 74, 051102 (2006).
[8] B. Aubert et al., Phys. Rev. D 71, 031103 (2005).
