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Reports from the Large Hadron Collider experiments
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m^2 K+K– (GeV^2 /c^4 )3B+ data
B+ model
B– data
B– model0.0.asymmetry/(0.03 GeV/c2 )0.0.0cos θhel > 0
cos θhel < 0–0.–0.–0.–0.
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mπ+π– (GeV/c^2 )1.2 1.New sources of CP violation (CPV)
are needed to explain the absence of
antimatter in our matter-dominated
universe. The LHCb collaboration has
reported new results describing CPV in
B+ → π+K+K– and B+ → π+π+π– decays. Until
very recently, all observations of CPV
in B mesons were made in two-body
and quasi-two-body decays; however,
it has long been conjectured that the
complex dynamics of multi-body decays
could give rise to other manifestations.
For CPV to occur in B decays, compet-
ing decay amplitudes with different
weak phases (which change sign under
CP) and strong phases (which do not)
are required. The weak phase differ-
ences are tied to fundamental param-
eters of the Standard Model (SM), but
the strong phase difference can arise
from loop-diagram contributions,
final-state re-scattering effects, and
phases associated with intermediate
resonant structure.
The three-body B decays under study
proceed mainly via various intermedi-
ate resonances – effectively, a cascade
of two-body decays – but also include
contributions from non-resonant
three-body interactions. The phase
space is two-dimensional (it can be
fully described by two kinematic
variables) and its size allows a rich
tapestry of resonant structures to
emerge, bringing quantum-mechan-
ical interference into play. Much as in
Young’s double-slit experiment, the
total amplitude comprises the sum of
all possible decay paths. The interference
pattern and its phase variation could
contribute to CPV in regions where res-
onances overlap.
One of the most intriguing LHCb
results was the 2014 observation of
large CPV effects in certain phase-space
regions of B+ → π+K+K– and B+ → π+π+π–
decays. In the new analysis, these effects
are described with explicit amplitude
models for the first time (figure 1). A
crucial step in the phenomenological
description of these amplitudes is to
include unitarity-conserving couplings
between final states, most notably ππ
and KK. Accounting for these is essentialFig. 1. Left: yields of B+ → π+K+K– and B– → π–K–K+ showing a clear asymmetry in the region of phase space
dominated by re-scattering effects. Right: the CP asymmetry between B+ → π+π+π– and B– → π–π–π+ decays in a
region of phase space including the ρ(7 70)^0 and f 2 (1270), divided according to whether the cosine of the helicity
angle is positive (blue) or negative (red). (cosθhel > 0 if, in the rest frame of the B, the pion with the same charge
as the B has higher momentum than its oppositely charged counterpart.) The bands indicate the full spread of
the isobar, K-matrix and quasi-model-independent models used to describe the decays.LHCb
Three-body B
+
decays violate CPThis is
the first
observation
of CP violation
in the
interference
between
intermediate
statesof an amplitude analysis, found in the
ππ ↔ KK re-scattering amplitude; the
first observation of CPV in the interfer-
ence between intermediate states, seen
in the overlap between the dominant
spin-1 ρ(770)^0 resonance and the π+π+
S-wave; and the first obser vation of CPV
involving a spin-2 resonance of any kind,
found in the decay B+ → f 2 (1270)π+. These
results provide significant new insights
into how CPV in the SM manifests in
practice, and motivate further study,
particularly into the strong-phase-
generating QCD processes that govern
CP violation.Further reading
LHCb Collaboration 2014 Phys. Rev. D 90
112004.
LHCb Collaboration 2018 LHCb-PAPER-
2018-051.
LHCb Collaboration 2019 LHCb-PAPER-
2019-017.
LHCb Collaboration 2019 LHCb-PAPER-
2019-018.to accurately model the complex S-wave
component of the decays, which is the
configuration where there is no relative
angular momentum between a pair of
oppositely-charged final-state particles,
and which contains broad resonances
that are difficult to model. Three com-
plementary approaches were deployed to
describe the complicated spin- 0 S-wave
component of the B+ → π+π+π– decay:
the classical isobar model, which
explicitly associates a line-shape with
a clear physical interpretation to each
contribution in the phase space; the
K-matrix method, which takes data
from scattering experiments as an input;
and finally a quasi-model-independent
approach, in which the S-wave magni-
tude and phase are extracted directly
from the data.
LHCb’s amplitude analyses of these
decays are based on data from Run 1 of
the LHC and contain several ground-
breaking results, including the largest
CP asymmetry in a single componentCCJulAug19_Energyfrontiers_v4.indd 15 27/06/2019 15: