RIKEN Accel. Prog. Rep. 50 (2017)

Ⅱ-5. Hadron Physics (Theory)Λb → Λ + − form factors, diﬀerential branching fraction, andangular observables from lattice QCD with relativistic b quarks†
W. Detmold∗1 and S. Meinel∗2,∗3
Decays of bottom hadrons involving the ﬂavorchanging neutral-current transition b → s + − arehighly suppressed in the Standard Model, so that
small eﬀects from new physics could cause signiﬁcantchanges in the observed decay rates and angular distributions. The recent precise experimental resultsfrom LHCb for the mesonic decays B → Kμ+ μ− ,B → K ∗ μ+ μ− , and Bs → φμ+ μ− indeed show somedeviations from the available Standard-Model predictions, but it remains unclear whether these deviations
are caused by new fundamental physics or by problems
with the calculations of the hadronic contributions1) .
The baryonic decay mode Λb → Λ(→ p π)+ −
can shed new light on these puzzles. Similarly toB → K ∗ (→ K π)+ − , this decay provides a wealthof angular observables that can be used to disentangle the contributions from individual operators in theb → s + − eﬀective Hamiltonian2) . At the same time,
the theoretical description of Λb → Λ(→ p π)+ − iscleaner than that of B → K ∗ (→ K π)+ − becausethe Λ is stable under the strong interactions.
The Λb → Λ(→ p π)+ − diﬀerential decay rate depends on the hadronic matrix elementsΛ(p , s )| s γ μ b |Λb (p, s),

Λ(p , s )| s γ γ5 b |Λb (p, s),Λ(p , s )| s iσ μν qν b |Λb (p, s),Λ(p , s )| s iσ μν qν γ5 b |Λb (p, s),μ(1)
(2)
(3)
(4)

which can be decomposed into ten form factors. In thiswork, we performed a precise lattice QCD determination of these form factors, utilizing lattice gauge-ﬁeld
ensembles generated by the RBC and UKQCD Collaborations. Based on these form factors, we then calculated the Λb → Λ(→ p π)+ − diﬀerential decay rate
and the complete set of angular observables (for unpolarized Λb ) in the Standard Model. Our results for thediﬀerential branching fraction dB/dq 2 = τΛb dΓ/dq 2
and for the lepton-side forward-backward asymmetry
AFB are shown in Fig. 1. Also included in the plots are
the measurements of these observables from the LHCbCollaboration3) .
In the high-q 2 region from 15 to 20 GeV2 , the magnitude of the lepton-side forward-backward asymmetry measured by LHCb is smaller than the theoreticalvalue by 3.3σ. The measured diﬀerential branching
†∗1
∗2
∗3

Condensed from the article in Phys. Rev. D 93, 074501(2016)
Center for Theoretical Physics, Massachusetts Institute ofTechnology
RIKEN Nishina Center
Department of Physics, University of Arizona- 132 -

1.6

dB −7
[10 GeV−2 ]
dq 2

1.4
1.2
1.00.80.6
0.4
0.20.0051015201520q [GeV ]220.4

AFB = 32 K̂1c0.2
0.0
−0.2
−0.4
0510q [GeV ]22Fig. 1. The Λb → Λ(→ p π)+ − diﬀerential branching
fraction (top) and lepton-side forward-backward asymmetry (bottom). The cyan and magenta curves (without and with q 2 -binning) show the Standard-Model predictions obtained from the form factors computed in lattice QCD; the black data points are the experimental results from LHCb3) . The regions near q 2 ∼ m2J/ψ , m2ψ ,where resonant long-distance eﬀects are dominant, areexcluded from the analysis.

fraction exceeds the theoretical value by 1.6σ. Whilethe latter deviation is not yet statistically signiﬁcant,it is in the opposite direction to what has been observed mesonic B decays1) . More precise experimental
results, including for the branching ratio of the normalization mode Λb → J/ψ Λ, would be very useful inclarifying this aspect of the results.
References
1) T. Blake, G. Lanfranchi, D. M. Straub, Prog. Part.
Nucl. Phys. 92, 50 (2017).
2) P. Böer, T. Feldmann, D. van Dyk, JHEP 1501, 155(2015).
3) R. Aaij et al. [LHCb Collaboration], JHEP 1506, 115(2015).