Ⅰ. HIGHLIGHTS OF THE YEARRIKEN Accel. Prog. Rep. 49 (2016)Λb → p ℓ− ν̄ℓ and Λb → Λc ℓ− ν̄ℓ form factors from lattice QCD
with relativistic heavy quarks†
S. Meinel,∗1,∗2 W. Detmold,∗3 and C. Lehner∗4
The smallest and most uncertain element of theCabibbo-Kobayashi-Maskawa (CKM) quark mixing
matrix is Vub . Improved measurements of |Vub | are important because they constrain the length of the left
side of the (ρ̄, η̄) unitarity triangle, which lies opposite
the precisely known angle β 1) . The matrix element|Vcb | also plays a central role in ﬂavor physics, as it
normalizes the unitarity triangle and is the dominantsource of uncertainty in Standard-Model predictions ofthe kaon CP -violation parameter εK 2) .
Until recently, all direct determinations of |Vub | and|Vcb | were performed using measurements of B meson
semileptonic or leptonic decays at e+ e− colliders. For
both |Vub | and |Vcb |, there are tensions between themost precise extractions from exclusive and inclusive
semileptonic B decays; the 2014 Review of ParticlePhysics lists1)

dΓ/dq 2(ps−1 GeV−2 )|Vub |22.5,−3.

|Vcb |excl. = (39.5 ± 0.8) × 10
|Vcb |incl. = (42.2 ± 0.7) × 10

∗45101520810

dΓ/dq 2(ps−1 GeV−2 )|Vcb |2Λb → Λc µ− ν̄µ2.5
2.0
1.5
1.0
0.5
0.0

246q 2 (GeV2 )Fig. 1. Lattice QCD predictions for the Λb → p µ− ν̄µ andΛb → Λc µ− ν̄µ diﬀerential decay rates. The bands indicate the statistical-only and the total uncertainties.

|Vub |= 0.083 ± 0.004(expt) ± 0.004(lattice),|Vcb |
and, taking the 2014 PDG value for |Vcb | from exclusive
B decays,|Vub | = (3.27 ± 0.23) × 10−3 .
Because of the nonzero spin of the baryons, this analysis also provides important new constraints on possible right-handed currents beyond the Standard Model,
whose existence had been suggested as an explanation of the exclusive-inclusive tension in |Vub |4) . The
new measurement strongly disfavors this explanation3), demonstrating that powerful complementary constraints on physics beyond the Standard Model can bederived from baryonic b decays.

where the q 2 -ranges were chosen to cover the regionof the smallest uncertainties in our lattice QCD predictions. The combination of the LHCb measurementwith our calculation gives∗30.00dΓ(Λb →p µ− ν̄µ )dq 2dq 2
15 GeV2= (1.00 ± 0.09) × 10−2 ,∫ qmax2dΓ(Λb →Λc µ− ν̄µ )2dqdq 27 GeV2

∗20.5

3.02
∫ qmax∗11.0q 2 (GeV2 )The Large Hadron Collider allows new determinationsof |Vub | and |Vcb | using the baryonic decays Λb →p µ− ν̄µ and Λb → Λc µ− ν̄µ , provided that the relevant
Λb → p and Λb → Λc hadronic form factors can be calculated. In this work, we performed a precise lattice
QCD calculation of these form factors, utilizing lattice gauge-ﬁeld ensembles generated by the RBC andUKQCD Collaborations. Using our form factor results,
we can predict the Λb → p µ− ν̄µ and Λb → Λc µ− ν̄µdiﬀerential decay rates as functions of |Vub |2 and |Vcb |2 ,as shown in Fig. 1. The LHCb Collaboration has recently measured the following ratio of the partially integrated decay rates3) ,†1.50|Vub |excl. = (3.28 ± 0.29) × 10−3 ,−3,|Vub |incl. = (4.41 ± 0.15+0.15−0.17 ) × 10−3Λb → p µ− ν̄µ2.0References
1) K. A. Olive et al. [Particle Data Group], Chin. Phys. C38, 090001 (2014).
2) J. A. Bailey et al. [SWME Collaboration], Phys. Rev.
D 92, 034510 (2015).
3) R. Aaij et al. [LHCb Collaboration], Nature Phys. 11,743 (2015).
4) A. Crivellin, Phys. Rev. D 81, 031301 (2010).

Condensed from the article in Phys. Rev. D 92, 034503(2015)RIKEN Nishina Center
Department of Physics, University of ArizonaCenter for Theoretical Physics, Massachusetts Institute ofTechnology
Physics Department, Brookhaven National Laboratory- 13 -