Effective Lifetimes of BsDecays and their
Constraints on the B0
Robert Fleischer and Robert Knegjens
Nikhef, Science Park 105, NL-1098 XG Amsterdam, The Netherlands
Measurements of the effective lifetimes of Bs-meson decays, which only require
untagged rate analyses, allow us to probe the width difference ∆Γsand the CP-
violating phase φs of B0
smixing. We point out that the dependence of the
effective lifetime on non-linear terms in ∆Γsallows for a determination of φsand
∆Γsgiven a pair of Bsdecays into CP-even and CP-odd final states. Using recent
lifetime measurements of B0
this method and show how it complements the constraints in the φs–∆Γsplane
from other observables.
s→ K+K−and B0
s→ J/ψf0(980) decays, we illustrate
arXiv:1109.5115v1 [hep-ph] 23 Sep 2011
A promising avenue for New Physics (NP) to enter the observables of Bs-meson decays
is given by B0
originates from box topologies and is strongly suppressed. In the presence of NP, new
particles could give rise to additional box topologies or even contribute at the tree level.
Should these NP contributions also involve new CP-violating phases, the B0
phase φscould differ sizably from the tiny SM value of −2.1◦(see, for instance, Refs. [1,2]
and references therein).
A key channel for addressing this exciting possibility is B0
feature of this channel is that its final state contains two vector mesons and thereby
requires a time-dependent angular analysis of the J/ψ → µ+µ−and φ → K+K−decay
products [2,3]. Over the last couple of years, measurements at the Tevatron of CP-
violating asymmetries in “tagged” analyses (distinguishing between initially present B0
[4–6]. These results are complemented by the measurement of the anomalous like-sign
dimuon charge asymmetry at DØ, which was found to differ by 3.9σ from the SM
prediction . This summer, the LHCb collaboration has also joined the arena, reporting,
however, results that disfavour large NP effects . The above measurements, which we
will discuss in more detail below, are typically shown in the φs–∆Γsplane, where ∆Γs
is the width difference between the mass eigenstates of the Bs-meson system.
In this paper, we point out a new method for determining further constraints in the
φs–∆Γsplane using measurements of the effective lifetimes of Bsdecays. In particular, we
show that the information provided by the lifetimes of a pair of decays into CP-even and
CP-odd final states is sufficient to determine φsand ∆Γs. The advantage of this strategy
is that it only requires an “untagged” analysis, i.e. it is not necessary to distinguish
between initially present B0
Specifically, we will consider the B0
decays, which have final states with the CP eigenvalues +1 and −1, respectively. From
here on we shall abbreviate the latter decay as B0
the effective lifetimes of these channels are already available from the CDF and LHCb
collaborations [13–15]. For the theoretical interpretation of these results we also need
to address hadronic uncertainties. A closer look will reveal that these decays are well
suited in this respect. We will illustrate our method with the most recent data and shall
compare the resulting constraints in the φs–∆Γsplane with those from the alternative
measurements listed above.
The outline is as follows: in Section 2, we discuss the general formalism to calculate
effective lifetimes and show in Section 3 how the corresponding measurements can be
converted into contours in the φs–∆Γs plane. In Section 4, we turn to the hadronic
uncertainties affecting this analysis and their control through experimental data. The
constraints on the B0
tive lifetimes of the B0
where we also illustrate the impact of future lifetime measurements with errors at the
1% level. In Section 6, we give a collection of additional Bsdecays that can be added to
this analysis in the future. Finally, we summarize our conclusions in Section 7.
smixing. In the Standard Model (SM), the phenomenon of mixing
s→ J/ψφ. A characteristic
smesons) of the B0
s→ J/ψφ channel indicate possible NP effects in B0
smesons, which is experimentally advantageous.
s→ K+K−[9,10] and B0
s→ J/ψf0(980) [11,12]
s→ J/ψf0. First measurements of
s→ K+K−and B0
smixing parameters arising from the current data for the effec-
s→ J/ψf0channels are explored in Section 5,
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