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

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

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

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)

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, …).

B → D*ℓν Lattice: no 2015 updates FNAL/MILC Nf=2+1 Relativistic b-quark (HQET inspired) PRD 14, 1403.0635 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 0.4-0.6% 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 0707.0582 («step scaling» method) Kronfeld 2014

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, 1206.2296+HFAG 12 Gambino Schwanda 1307.4551 -resulting smaller FF implies higher |Vcb| (closer to inclusive) -Much larger th error (More than twice on |Vcb|)

B → D ℓν: 2015 news Two new lattice Nf=2+1 calculations at non-zero recoil with massive leptons → Fermilab/MILC 1503.07237 2) HPQCD 1505.03925 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/9412324

Comparing with data HPQCD reduction errors underway (matching procedure…) HPQCD 1505.03925 HPQCD Fermilab/MILC Fermilab/MILC B →D* with 2009 Babar data

More recent Belle determination 1510.03657 BGL parameterization NPB 461 (1996) 493 Slightly more precise (more lattice input) 1503.07237, 1505.03925 CLN parameterization NPB 530 (1998) 153 1503.07237

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

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

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|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:0906.2498 [hep-lat]

|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:0906.2498 [hep-lat]

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 1503.01421 see also Y. Amhis ‘s talk PDG 2014

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 1311.5420 Corrections for the ρ lineshape in B → π π ℓ ν experimental distribution Kang et al. 1312.1193 BSM: Right-handed currents for B → ρ ℓ ν (data disfavoured) Bernlochner, Ligeti,Turczyk 1408.2516

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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

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)

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

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 Rosner1509.02220 exp th 1.4σ higher than from baryon decay

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)