CKM ELEMENTS FROM semileptonic b decays

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1 CKM ELEMENTS FROM semileptonic b decays paolo gambino università di torino & INFN Munich May 2016

2 Importance of Vxb Vcb plays an important role in the determination of UT!! " K x V cb and in the prediction of FCNC: V tb V ts 2 V cb 2h i 1+O( 2 ) where it often dominates the theoretical uncertainty. Vub/Vcb constrains directly the UT Since several years, exclusive decays prefer smaller Vub and Vcb Relation to semitauonic anomaly (3.9σ)?

3 Inclusive semileptonic B decays OPE allows us to write inclusive observables as double series in Λ/mb and αs M i =M (0) i + s M (1) s 2 (2) i + M i + M (,0) i + s M (,1) µ 2 i + M (G,0) i + s M (G,1) µ 2 G i m 2 b + M (D,0) i 3 D m 3 b + M (LS,0) i 3 LS m 3 b m 2 b +... µ 2 π ( µ ) = 1 2M B ( ) 2 b B B b id µ µ G 2 µ ( ) = 1 2M B B b i 2 σ µνg µν b B v v v v µ OPE valid for inclusive enough measurements, away from perturbative singularities semileptonic width, moments Current fits includes 6 non-pert parameters mb,c µ 2,G 3 D,LS and all known corrections up to O(Λ 3 /mb 3 )

4 Extraction of the OPE parameters El spectrum hadronic mass spectrum Global shape parameters (first moments of the distributions) tell us about m b, m c and the B structure, total rate about V cb OPE parameters describe universal properties of the B meson and of the quarks useful in many applications (rare decays, V ub,...)

5 Latest semileptonic fit Alberti, Healey, Nandi, PG kinetic scheme calculation based on ; hep-ph/ includes all O(αs 2 ) and O(αs/mb 2 ) corrections reassessment of theoretical errors, realistic correlations following Schwanda, PG, external constraints: precise heavy quark mass determinations, mild constraints on μ 2 G from hyperfine splitting and ρ 3 LS from sum rules Previous global fits: Buchmuller, Flaecher hep-ph/ , Bauer et al, hep-ph/ (1S scheme)

6 charm mass determinations Hoang et al 13 our default choice sum rules studies of σ(e + e - hadrons) almost all at NNNLO Remarkable improvement in recent years. mc can be used as precise input to fix mb instead of radiative moments

7 fit results m kin b m c (3 GeV) µ 2 3 D µ 2 G 3 LS BR c 10 3 V cb Alberti et al, Without mass constraints m kin b (1GeV) 0.85 m c (3GeV) = ± GeV 0.45 results depend little on assumption for correlations and choice of inputs, 1.8% determination of Vcb r D 3 HGeV 3 L leptonic r D 3 HGeV 3 L all cuts 20-30% determination of the OPE parameters hadronic no high cuts m p 2 HGeV 2 L m p 2 HGeV 2 L

8 Results: bottom mass Alberti et al. H2014L Kuehn et al. H2009L Bodenstein et al. H2012L HPQCD H2014L Penin, Zerf H2014L Beneke et al. H2014L HPQCD,NRQCD H2014L Hoang et al. H2012L Lucha et al. H2013L Ê Ê Ê Ê Ê Ê Ê Ê Ê m b Hm b L HGeVL The fit gives mb kin (1GeV)=4.553(20)GeV scheme translation _ error _ mb kin (1GeV)=mb(mb)+0.37(3)GeV mb(mb)=4.183(37)gev

9 higher order effects Reliability of the method depends on our ability to control higher order effects. Quark-hadron duality violation would manifest as inconsistency in the fit. Purely perturbative corrections complete at NNLO, small residual error (kin scheme)melnikov,biswas,czarnecki,pak,pg Mixed corrections perturbative corrections to power suppressed coefficients completed at O(αs/mb 2 ) Becher, Boos, Lunghi, Alberti, Ewerth, Nandi, PG, Mannel,Pivovarov, Rosenthal

10 Higher power corrections Proliferation of non-pert parameters and powers of 1/m c starting 1/m 5. At 1/m b 4 Mannel,Turczyk,Uraltsev can be estimated by Lowest Lying State Saturation approx by truncating B O 1 O 2 B = X n B O 1 n n O 2 B see also Heinonen,Mannel LLSA might set the scale of effect, but large corrections to LLSA have been found in some cases (Mannel, Uraltsev, PG, 2012) In LLSA good convergence of the HQE. We used LLSA as loose constraint in the fit including higher powers, Healey, Turczyk, PG PRELIMINARY V cb = (42.09 ± 0.77) 10 3 Very stable V cb

11 Prospects Theoretical uncertainties already dominant O(α s /m b3 ) calculation under way O(1/m Q 4,5 ) effects need further investigation but small effect on V cb NNNLO corrections to total width feasible, needed for 1% uncertainty? Electroweak corrections New observables in view of Belle-II: FB asymmetry proposed by Turczyk Lattice QCD information on local matrix elements is the next frontier

12 New results for B Dlv f.f. fnal/milc hpqcd

13 Global fit to B Dlν D.Bigi, PG preliminary f+ Babar 2009 Belle 2015 MILC-FNAL HPQCD χ 2 /dof=22/ f form factors f + HzL Hupper plotl and f 0 HzL Hlower plotl

14 Global fit to B Dlν Vcb =40.62(0.97) 10-3 preliminary (BGL,N=2) Vcb =40.49(0.96) 10-3 preliminary (BGL,N=3,4) based on z-expansion with strong unitarity constraints using other channels Boyd,Grinstein,Lebed & Caprini,Lellouch,Neubert 1997 assumes no correlation between FNAL and HPQCD, 3% syst error on Babar data, correct treatment of last bin, no finite size bin effect, updated Belle results CLN parameterization gives Vcb = 40.85(95)10-3 but terrible fit (p-value < 10-4 ) when lattice results for f0 are included. FNAL: f0/f+(1)=0.753(3) CLN: We re getting too precise for using CLN without errors!! Non-zero recoil lattice results are crucial: only zero recoil leads to Vcb =39.6(2.1) 10-3 (BGL) 40.0(1.1) 10-3 (CLN) Very precise R(D)=0.302(3), 1.9σ from HFAG average

15 Exclusive B D * lv At zero recoil, where rate vanishes, the ff is!!!! Thanks to measurement of slopes and shape parameters, exp error only ~1.3%! The ff F(1) cannot be experimentally determined. Lattice QCD is the best hope to compute it. Only one unquenched Lattice calculation:!! F(1) = A apple1+o F(1) =0.906(13) 1 m 2 c +... Vcb =39.04(49)exp(53)lat(19)QED % error (adding in quadrature) Bailey et al (FNAL/MILC) ~2.9σ or ~8% from inclusive determination

16 Prospects for exclusive V cb Most experimental B D (*) results tied up with CLN don t include CLN error: also R(D * ) should have larger uncertainty. New exp analyses under way, more at Belle-II. Need for more lattice calculations and extension of B D * ff to non-zero recoil. Matching at 1/m Q 3 for lattice discretization effects under study by FNAL/MILC. Simulations at physical pion mass and m b a 1? Heavy quark sum rules (with BPS arguments) favor smaller F(1)=0.86(2) leading to agreement with inclusive. Difficult to improve, how good is BPS limit? QED/EW corrections: SD log OK, SD remainder tiny if G μ employed, soft/ collinear radiation subtracted out by Photos, intermediate photons (IR finite) are structure dependent: lattice calculations? exp cuts? relevance of Coulomb enhancement for B 0 decay rate? New channels (Bc, Bs, Λ b ) at Belle-II and LHCb, better understanding of D **

17 B Xulv and cuts Experiments often use kinematic cuts to avoid the b clv background:! m X < M D E l > (M B2 -M D2 )/2M B q 2 > (M B -M D ) 2... The cuts destroy convergence of the OPE that works so well in b c. OPE expected to work only away from pert singularities! Rate becomes sensitive to local b-quark wave function properties like Fermi motion. Dominant nonpert contributions can be resummed into a SHAPE FUNCTION f(k+). Equivalently the SF is seen to emerge from soft gluon resummation! Luke

18 How to access the SF? d 3 dp + dp de = G2 F V ub Z dkc(e,p +,p,k)f (k)+o m b Subleading SFs Predictions based on resummed pqcd! DGE, ADFR OPE constraints + parameterization without/with resummation! GGOU, BLNP Fit semileptonic (and radiative) data SIMBA, NNVub

19 Vub determinations Inclusive: 5% total error HFAG 2014 Average V DGE 4.52(16)(16) BLNP 4.45(16)(22) GGOU 4.51(16)(15) UT fit (without direct Vub): Vub=3.62(12) 10-3 CLEO (E e ) 4.21 ± BELLE sim. ann. (m, q 2 ) X 4.50 ± BELLE (E e ) 4.93 ± BABAR (E e ) 4.50 ± BELLE multivariate (p*) 4.60 ± BABAR (m <1.55) X 4.29 ± BABAR (m <1.7)! Recent experimental results are theoretically cleanest (2%) but based on background modelling. Signal simulation also relies on theoretical models X 4.09 ± BABAR (m <1.7, q >8) X 4.32 ± BABAR (P + <0.66) 4.24 ± 0.26 ± 0.32 BABAR (m, q 2 fit, p*>1gev) X 4.42 ± BABAR (p*>1.3gev) 4.41 ± Average +/- exp + theory - theory 4.51 ± χ 2 /dof = 8.8/10 (CL = %) P. Gambino, P. Giordano, G. Ossola, N. Uraltsev JHEP 0710:058,2007 (GGOU) HFAG PDG V [ 10 ub -3 ]

20 NEW preliminary Babar endpoint analysis High sensitivity of the BR on the shape of the signal in the endpoint region. GGOU: V ub = y.skovpen, eps-ph 2015

21 Functional forms About 100 forms considered in GGOU, large variety, double max discarded. Small uncertainty (1-2%) on V ub A more systematic method by Ligeti et al. arxiv: Plot shows 9 SFs that satisfy all the first three moments 21

22 The NNVub Project K.Healey, C. Mondino, PG, Use Artificial Neural Networks to parameterize shape functions without bias and extract Vub from theoretical constraints and data, together with HQE parameters in a model independent way (without assumptions on functional form). Similar to NNPDF. Applies to b ulv, b sγ, b sl+l-! Belle-II will be able to measure some kinematic distributions, thus constraining directly the shape functions. NNVub will provide a flexible tool to analyse data.

23 NNVub GGOU(2007)

24 Prospects Belle-II from kinematic distributions include all relevant information check signal dependence at endpoint full phase space implementation of NNLO and α s /m b 2 corrections At Belle-II we can expect to bring inclusive V ub at same level as V cb

25 f0! Du, MITP workshop 2015

26 Recent lattice B π RBC/UKQCD FNAL/MILC p=0.02 Fnal FNAL 3.72(16) 10-3 only 4.3% error 2.2σ from inclusive RBC/UKQCD 3.61(32) σ from inclusive LCSR 3.32(26) σ from inclusive LHCb depends on V cb employed but low

27 Recent lattice results Prospects: further improvements in LQCD, much more BelleII, B s Klv and other and LHCb

28 visual summary 5.0 B D * FNAL V cb inclusive 10 3 V ub V ub inclusive GGOU (HFAG) B π FNAL/MILC B D global fit i i i utfit(sm) i reasonable consistency among exclusive channels! not all results on the same footing! 3.0 Λ b p/λ b Λ c V cb

29 New physics? The difference in Vcb incl vs excl D * with FNAL/MILC form factor is large: 3σ or about 8%. The perturbative corrections to inclusive Vcb total 5%, the power corrections about 4%. Right Handed currents now excluded since V cb incl V cb V cb B!D V cb 1 V cb B!D V cb 1+ Chen,Nam,Crivellin,Buras,Gemmler,Isidori,... = R Ṽ cb V cb 0.08 Most general SU(2) invariant dim 6 NP (without RH neutrino) _ can explain results, but it is incompatible with Z bb data Explaining Vub tension is easier Crivellin, Pokorski

30 RH currents don t help R. van de Water

31 UUT analysis in CMFV models ε K ΔM s V ub V cb CMFV = ± Blanke, Buras

32 Summary Improvements of OPE approach to s.l. decays continue. O(α s Λ 2 /m b2 ) effects implemented. No sign of inconsistency in this approach so far, competitive mb determination. Exclusive/incl. tension in Vcb remains (3σ, 8%) only in the D * channel. The D channel is becoming competitive and is compatible with both. The remaining tension calls for new lattice analyses and new data (ongoing Belle analysis, Belle-II) Exclusive/incl tension in Vub seems receding because of new FNAL/ MILC and HPQCD results and of preliminary Babar results. Significant progress will come with Belle-II and LHCb data (B τv etc). New physics explanations less constrained for Vub than for Vcb., but right handed current disfavoured. RH currents don t help. Belle-II will improve precision and allow for consistency checks of our methods, especially for inclusive Vub. LHCb potential (for exclusives) greater than expected.

33 back-up slides

34 Theoretical errors Theoretical errors are generally the dominant ones in the fits. We estimate them in a conservative way, mimicking higher orders by varying the parameters by fixed amounts: mc,b 8MeV, αs(mb) 0.018, 7% in 1/m 2 parameters, 30% in 1/m 3 parameters New corrections have been within theor. uncertainties so far.

35 Extrapolation to zero recoil, possible parameterization effect (qualitative & exaggerated picture) F(w) V cb w Babar form factor shape from

36 A global comparison , Phys Rept»Vub» BLNP DGE»Vub» only theory errors (without common parametric) 3.5 ADFR GGOU analysis analysis common inputs (except ADFR) Overall good agreement SPREAD WITHIN THEORY ERRORS NNLO BLNP still missing: will push it up a bit Systematic offset of central values: normalization? to be investigated»vub» analysis GGOU