1. Update on |Vxb| determination
Giulia Ricciardi
Lio International Conference on models and
dark matter,
23-27 /11/2015, IPNL, Lyon, France

2. Twenty years of CKM refinement
M. Calvi, Southempton, 1999
LEP 1999
Inclusive
PDG 2015
Beauty Factories
interlude
Error reduction not
The End
PDG 2015

3. Overview Inclusive-exclusive determinations of
|Vcb| & |Vub| and related puzzles
Focus on
2015 update & news
Prospects

4. Exclusive | Vcb| determination
Massless leptons limit
Luke’s theorem
Rather preferred: less suppressed
exp rate and high-order corrections
Non perturbative corrections beyond HM limit (m= mb, mc)

5. Lattice
unless mba << 1 discretization errors out of control and no direct simulation is possible. As of today
mb ~ 1/a
Ways out:
effective theories (HQET, NRQCD) that eliminate high degrees of freedom (systematic expansion in 1/mb )
simulations with lighter mass O(1/mc) and extrapolation to mb, or interpolation to HQET point
Each approach introduces new source of errors (matching of HQET to QCD, renormalization, control of extrapolation, …).

6. B → D*ℓν Lattice: no 2015 updates
FNAL/MILC Nf=2+1
Relativistic b-quark
(HQET inspired)
PRD 14,
PRD 09
Bailey, lattice 14
B → D*ℓν Lattice: no 2015 updates
PRD
Same analysis,
higher stats, smaller a, …
+ HFAG data
Experimental data taken at non-zero recoil due to kinematic suppression
At this level of precision, important to extend unquenched calculations to non-zero recoil
In principle, errors from discretization
reducibleby going to finer lattice spacings
or by using a more improved Fermilab action
Subleading error appearing at the %
even more nontrivial to improve.
Largest error from discretization,
Estimated taking the difference between
HQET description of LGT and QCD
only quenched results at the non-recoil point de Divitiis et al
(«step scaling» method)
Kronfeld 2014

7. LCSR
All sum rules based on the general idea of calculating a relevant quark-current correlation function and relating it to the hadronic parameters of interest via a dispersion relation.
B → D*ℓν no 2015 updates
More recent zero-recoil SR calculations have incorporated higher order effects and an improved estimates of inelastic corrections in the sum rule
Gambino, Mannel, Uraltsev, HFAG 12
Gambino Schwanda
-resulting smaller FF implies higher |Vcb| (closer to inclusive)
-Much larger th error (More than twice on |Vcb|)

8. B → D ℓν: 2015 news
Two new lattice Nf=2+1 calculations at non-zero recoil with massive leptons →
Fermilab/MILC
2) HPQCD
based on NRQCD action for bottom and the HISQ action for charm quarks
form factors calculated for a range of
recoil momenta
dependence on momentum transfer
parameterized using z -expansion BGL
hep-ph/

9. Comparing with data HPQCD reduction errors underway
(matching procedure…)
HPQCD
HPQCD
Fermilab/MILC
Fermilab/MILC B →D*
with 2009 Babar data

10. More recent Belle determination 1510.03657
BGL parameterization NPB 461 (1996) 493
Slightly more precise (more lattice input) ,
CLN parameterization NPB 530 (1998) 153

11. Inclusive decays B Xc l ν
HQE for sufficiently inclusive quantities (total width, moments of kinematical distributions) away from perturbative singularities
Double series in αs and 1/m
𝑚 𝑐 2 ∼ Λ QCD 𝑚 𝑏
STATUS
Completed 𝑂(𝑎𝒔𝟐) corrections
to leading term (parton model) Aquila et al 05, Pak et al 08, Biswas et al 10
to power suppressed coefficients 0(𝛼 𝑠 2 Λ2 𝑚𝑏2 ) Becher et al 07, Alberti et al 12-13, Mannel et al 14
Neglecting perturbative corrections, i.e. working at tree level
computed and estimated up order 𝑂( 1 𝑚 𝑏 5 ) Gremm et al 96, Dassinger et al 06, Mannel et al 10,
Heinonen et al 14

12. |Vcb| summary Fading disagreement (2015 results) ? Exclusive
most precise
Error
below 2%
Fading disagreement (2015 results) ?

13. A. Crivellin 15

14. |Vub| exclusive determination
Traditionally extracted by the decay B → π ℓ ν
(only a single form factor in massless limit)
Non-pert th predictions for 𝑓+ usually confined to regions of q2
arXiv:  [hep-lat]

15. |Vub| exclusive determination
Traditionally extracted by the decay B → π ℓ ν
(only a single form factor in massless limit)
Non-pert th predictions for 𝑓+ usually confined to regions of q2
Latest lattice determinations
higher values
agreement with
indirect fits
arXiv:  [hep-lat]

16. new exclusive players Λ0b → p µ ν Ratio of relevant form factors
lattice 2+1 flavors of
dynamical domain-wall
fermions, RBC &
UKQCD
Configurations
Detmond, Lehner, Meinel
see also Y. Amhis ‘s talk
PDG 2014

17. new exclusive players B → ω ℓ ν, B → ρ ℓ ν
2015 LCSR ff computation
available-
at q2 <12 GeV +2013Belle(2012 Babar) data
consistently lower, about 10%;
possible S-wave background not separated in exp analysis of B → ρ ℓ ν; estimated 5% change Meissner, Wang
Corrections for the ρ lineshape in B → π π ℓ ν experimental distribution
Kang et al
BSM: Right-handed currents for B → ρ ℓ ν (data disfavoured)
Bernlochner, Ligeti,Turczyk

18. A. Crivellin 15

19. Inclusive |Vub|
large b → c background (|Vcb/Vub|2 ≈100 )
Need experimental phase space cuts to reduce background;
in general
mX << EX
Phase space regions where OPE fails become dominant; new unwelcome effects (with respect to semileptonic b → c):
Final gluon radiation strongly inhibited: soft and collinear singularities
perturbative expansion of spectra affected by large logarithms
asn log2n(2 EX/mX)
to be resummed at all orders in PT
non–perturbative effects related to a small vibration of the b quark in the B meson (Fermi motion) enhanced Xu

20. Experimental progress
Belle & Babar results access 90% data
Theoretical approaches
predictions based on parameterizations of shape function, and OPE constraints
several cuts Bosch, Lange, Neubert , Paz (BLNP), Gambino, Giordano, Ossola, Uraltsev (GGOU)
mX-q2 cut Bauer, Ligeti, Luke (BLL)
Lepton momentum spectrum Leibovich, Low, Rothstein (LLR), Lange, Neubert, Paz (LNP)
global fit Ligeti, Stewart, Tackmann
predictions based on resummed pQCD
Andersen, Gardi (DGE),
Aglietti, Di Lodovico, Ferrera , GR (ADFR)

21. |Vub| determination status
Long standing
tension
~2-3σ
Babar inclusive average

22. Leptonic decays Experimental branching fractions consistent with SM
Still quite large syst errors
and background
Several th determination of fB with lattice or QCD SR
Rosner
exp th
1.4σ higher than from
baryon decay

23. Conclusions Latest episode of “The |Vxq| saga”
fading |Vcb| puzzle: one out of two discrepancies
|Vub| determination-prone experiments: significant advances, more expected
new exclusive measurements (B → ρ/ω lν, baryon decays, ecc.) limited by theory uncertainties
possible pushing th improvements in lattice (Non zero recoil B-> D*,QED error…)
inclusive benefits: higher statistics, better: b→ c background subtraction, separation B+,-/0 (WA), q2 tail (duality)…
prospective smaller errors in in experimental b.f. for leptonic B decays (BelleII)