Developments in Exclusive b sl + l Decays

Transcription

1 Developments in Exclusive b sl + l Decays Danny van Dyk NIKHEF Theory Seminar November 13th, 2014 q f et FOR 1873 D. van Dyk (Siegen) Exclusive b sl + l / 43

2 Motivation Basics of the B = S = 1 Effective Field Theory Overview of Exclusive b sl + l Decays Development: Λ b Λ( Nπ)l + l Development: Charmonium Resonances in B Kl + l Conclusion D. van Dyk (Siegen) Exclusive b sl + l / 43

3 Motivation D. van Dyk (Siegen) Exclusive b sl + l / 43

4 Search for effects of physics beyond the Standard Model the Standard Model of particle physics describes nature very well however: beyond SM physics seems likely, since the SM does not allow for neutrino oscillations... has no candidate for dark matter... has no explanation for the emergence of different flavours consequence: search for the effects of new physics, either directly, i.e., in the production of new particles at very high energies... indirectly, i.e., as loop effects in e.g. b-quark decays D. van Dyk (Siegen) Exclusive b sl + l / 43

5 Top-down vs. bottom-up in flavour physics Top-down start with a New Physics model calculate effects on observables constrain model parameters from data Bottom-up for a given process: categorize all possible effects of new physics introduce effective couplings C i, and determine their SM values constrain C i from data if deviations from SM expectations are found, search for a model or models that can explain these specific deviations D. van Dyk (Siegen) Exclusive b sl + l / 43

6 Bottom-up and Effective Field Theories effective field theories (EFTs) describe the same effects up to a limiting scale µ as the respective full field theory but uses fewer degrees of freedom example 4-fermi theory: includes the dynamics of leptons and neutrino as in the SM in particular the µ decay but W is not a dynamical degree of freedom effective field theories are very compatible with the bottom-up approach example 4-fermi theory: operator [ēγ ρ (1 γ 5 )ν e ] [ ν µ γ ρ (1 γ 5 )µ] has effective coupling G F natural extension: introduce further operators with anomalous spin structures (i.e. beyond the SM) constrain their additional effective couplings from data (4-fermi: Michel parameter studies) D. van Dyk (Siegen) Exclusive b sl + l / 43

7 Basics of the B = S = 1 Effective Field Theory D. van Dyk (Siegen) Exclusive b sl + l / 43

8 b sl + l Transitions b sl + l is a flavour-changing neutral current (FCNC) forbidden at tree level in the SM leading term arises at the one-loop level examples: s l s l W t W ν W t γ/z b l b l D. van Dyk (Siegen) Exclusive b sl + l / 43

9 Effective Field Theory for b sl + l FCNCs remove heavy fields (SM: t, W, Z, beyond:?) as dynamical degrees of freedom technical term: to integrate out new 4-fermion operators emerge with currents at different coordinates non-local effective field theory, described by effective hamiltonian H eff expand H eff in terms of local operators (OPE) illustration at hand of W propagator: 1 MW 2 = 1 p2 MW 2 [1 + p2 M 2 W ( )] p 4 + O MW 4 focus on leading-power term only next-to-leading-power suppressed by p 2 /M 2 W s W l s l t ν 1 MW 2 C i +... b W l b l D. van Dyk (Siegen) Exclusive b sl + l / 43

10 Effective Hamiltonian universal b s effective Hamiltonian H eff = 4G ] F [V tb Vts C i O i + O (V ub Vus) + h.c. 2 i describes all b s transitions, including b sc c b sγ b sl + l model-independent correlations between observables Some b sl + l, b sγ modes B K l + l B Kl + l B s µ + µ B K γ B X s l + l B X s γ exclusive decay modes: final state is fully specified D. van Dyk (Siegen) Exclusive b sl + l / 43

11 Effective Operators Radiative and semileptonic operators O 7(7 ) = em b 4π [ sσµν P R(L) b]f µν O 9(9 ) = α e 4π [ sγµ P L(R) b][ lγ µ l] O 10(10 ) = α e 4π [ sγµ P L(R) b][ lγ µ γ 5 l] O 7,9,10 dominantly contribute to b sl + l in the SM couplings of O 7 small, O 9,10 vanish in the SM suppressing spin structures other than V ± A Four-quark operators dominant background O 1 = [ cγ µ T a P L b][ sγ µ T a c] O 2 = [ cγ µ P L b][ sγ µ c] O (1) Wilson coefficients, contribute α e suppressed via off-shell photon D. van Dyk (Siegen) Exclusive b sl + l / 43

12 Renormalization Group Equations evaluate hadronic matrix elements O i at µ b m b typical scale for the problem α s (m b ) still reasonably small perturbation series under control match (that is read off ) C i at scale µ 0 M W, m t C 7,9,10 emerge at one-loop order, C 2 at tree level α e and α s corrections under control however, C i (µ 0) O i µb wildly inacurate solution: Renormalization Group Improved Perturbation Theory C i (µ 0) C i (µ b ) = j [U(µ b, µ 0)] ij C j (µ 0) next-to-next-to-leading-logarithm (N 2 LL) result resums large logarithms α n s ln m (µ b /µ 0), 2 n m 0 electroweak corrections start to play important role [Bobeth/Gorbahn/Stamou ] C 10 matching now computed to α 2 s [Hermann/Misiak/Steinhauser ] D. van Dyk (Siegen) Exclusive b sl + l / 43

13 Overview of Exclusive b sl + l Decays D. van Dyk (Siegen) Exclusive b sl + l / 43

14 Wilson coefficients and amplitudes at µ = 4.2 GeV to NNLL accuracy C 7 C 9 C 10 C 1 C typically, the b sl + l decay amplitudes looks like [ A C 9 ± C m2 b F T (q 2 ] ) q 2 F (q 2 ) C 7 F (q 2 ) + with hadronic matrix elements, F, F T and F cc schematically: [ C 2 C ] 1 F cc... 6 b s b s A l l + qq l l D. van Dyk (Siegen) Exclusive b sl + l / 43

15 Comparison of Exclusive Decays decay # kin. variables # hadr. matr. elem. sensitivity B s l + l 0 1 constant C 10( ) B Kl + l form factors C 7( ), C 9( ), C 10( ) B K l + l form factors C 7( ), C 9( ), C 10( ) Λ b Λl + l form factors C 7( ), C 9( ), C 10( ) will focus on semileptonic decays with increasing # of kinematic variables, the # of observables rises (good) however: # of hadronic matrix elements rises too (bad) each exclusive decay has its own individual set of hadronic matrix elements for semileptonic decays with one final statehadron, had. mat. elements are functions of only q 2 : dilepton mass squared : for naivly factorizing amplitudes (for semileptonic decays, massless leptons are assumed) D. van Dyk (Siegen) Exclusive b sl + l / 43

16 Optimized Observables design observables that e.g. probe right-chiral leptons amplitude A can be decomposed w/ respect to lepton chirality left-chiral leptons: A L C 9 C 10 right-chiral leptons: A R C 9 + C 10 C 9,10! several groups working on optimal bases of angular observables, with focus on B K l + l decays aims reduce form factor uncertainties at low q 2 : P i [Descotes-Genon/Matias/Virto and references therein] reduce form factor uncertainties at high q 2 : H (i) T [Bobeth/Hiller/DvD and references therein] extract form factor ratios from data [Bobeth/Hiller/DvD , ] D. van Dyk (Siegen) Exclusive b sl + l / 43

17 Pollution by cc States all exclusive b sl + l processes face severe problem of hadronic ( cc) resonances in dilepton spectrum hadronic operators give rise to b s cc, hadronizes to H b X s ψ(n)[ l + l ] systematically include effects via hadronic two-point function T (q 2 ) C 7 O 7 T (q 2 ) different approaches to obtain T (q 2 ), depending on kinematics methods and their domain of validity small q 2 m 2 b: QCD-improv. Factorization (QCDF) [Beneke/Feldmann/Seidel hep-ph/ and hep-ph/ ] large q 2 m 2 b: Operator Product Expansion (OPE) [Grinstein/Pirjol hep-ph/ , Beylich/Buchalla/Feldmann ] all q 2 : hadronic dispersion relation (model-dependent) [Khodjamirian et al , , Lyon/Zwicky ] reviewing these works is another talk; some details in the backups D. van Dyk (Siegen) Exclusive b sl + l / 43

18 State of Model-Independent Analysis [Beaujean/Bobeth/DvD Eur.Phys.J. C74 (2014) 2897 (Err. ibid)] does not yet include today s preprint by Altmannshofer and Straub D. van Dyk (Siegen) Exclusive b sl + l / 43

19 Model-Independent Framework Definition of model-independent for the purpose of this work: Basis of Operators O i include as many O i beyond SM as needed/as few as possible balancing act, test statistically if choice of basis describes data well! Wilson Coefficients C i treat C i as uncorrelated, generalized couplings constrain their values from data model builders: confront new physics models with constraints D. van Dyk (Siegen) Exclusive b sl + l / 43

20 Fit Scenarios SM(ν-only) fix C 7,9,10 to SM values (NNLL) fix C 7 = m s/m b C 7, fix C 9,10 = 0 fit nuisance parameters, use informative priors form factors: light-cone sum rules [Khodjamirian/Mannel/Pivovarov/Wang 10] power corrections: power-counting assumptions CKM: tree-level fit [UTfit] quark masses [PDG] D. van Dyk (Siegen) Exclusive b sl + l / 43

21 Fit Scenarios SM Basis fix C 7 = m s /m b C 7, fix C 9,10 = 0 fit C 7,9,10 fit nuisance parameters, use informative priors form factors: light-cone sum rules [Khodjamirian/Mannel/Pivovarov/Wang 10] power corrections: power-counting assumptions CKM: tree-level fit [UTfit] quark masses [PDG] D. van Dyk (Siegen) Exclusive b sl + l / 43

22 Fit Scenarios SM+SM Basis fit C 7,9,10 fit C 7,9,10 fit nuisance parameters, use informative priors form factors: light-cone sum rules [Khodjamirian/Mannel/Pivovarov/Wang 10] power corrections: power-counting assumptions CKM: tree-level fit [UTfit] quark masses [PDG] D. van Dyk (Siegen) Exclusive b sl + l / 43

23 Sensitivity to Fit Parameters Wilson coefficients C 7( ) C 9( ) C 10( ) 93 individual measurements experiments B s µ + µ CP-avg. time-int. BR CMS,LHCb B X s γ CP-avg. BR BaBar,Belle,CLEO B X s l + l CP-avg. BR BaBar,Belle B K γ CP-avg. BR + 2 time-dep. CP asymm. BaBar,Belle,CLEO B K l + l CP-avg. BR + 7 angular observables ATLAS,BaBar,Belle,CDF,CMS,LHCb B Kl + l CP-avg. BR BaBar,Belle,CDF,LHCb Form factors interplay between B X s{γ, l + l } and B K {γ, l + l } some B K l + l obs. form-factor insensitive by construction some B K l + l obs. dominantly sensitive to form factor ratios D. van Dyk (Siegen) Exclusive b sl + l / 43

24 Further Theory Constraints Form factors from lattice QCD (LQCD) B K form factors available from LQCD data only at high q 2 : GeV 2 no data points given reproduce 3 data points from z-parametrization q 2 {17, 20, 23} GeV 2 use as constraint, incl. covariance matrix [HPQCD arxiv: ] data f + f q 2 [GeV 2 ] B K Form factor (FF) relation at q 2 = 0 FF V, A 1 ξ +... [Charles et al. hep-ph/ ] no α s corrections [Burdmann/Hiller hep-ph/ , Beneke/Feldmann hep-ph/ ] Large Energy Limit: V (0) = (1.33 ± 0.4) A 1 (0) LCSR constraint: ξ (0) = , to avoid ξ (q 2 ) A 0 (q 2 ) < 0. see also FF fits by [Hambrock/Hiller/Schacht/Zwicky ] D. van Dyk (Siegen) Exclusive b sl + l / 43

25 The B K l + l Anomaly LHCb measurement [ ] not considering data at 6 GeV 2 q 2 14 GeV 2 deviation from SM prediction in form factor-free obs. P 5 [1,6] LHCb uses one SM prediction (DGHMV) [Descotes-Genon/Hurth/Matias/Virto ] P 5 1.0, LHCb DGHMV JC BBvD however: further SM prediction exist, much larger uncertainty (JC) [Jäger/Camalich ] our take on SM prediction P 5 [1,6] = (BBvD) however, also consider later slides difference: treatment of unknown power corrections (form factor corrections, cc resonances) D. van Dyk (Siegen) Exclusive b sl + l / 43

26 Results SM(ν-only) Goodness of fit largest pulls at best-fit point 3.4σ F L [1,6], BaBar σ F L [1,6], ATLAS σ P 4 [14.18,16], LHCb σ B [16,19.21], Belle σ A FB [16,19], ATLAS 2013 obtain p value of 0.12 Summary good fit, no New Physics signal we find power corrections on top of QCDF results at large recoil D. van Dyk (Siegen) Exclusive b sl + l / 43

27 Parametrization of Power Large Recoil six parameters ζ L(R) χ for the [1, 6] bin A L(R) χ (q 2 ) ζ L(R) χ A L(R) χ (q 2 ), χ =,, 0 on top of QCDF correction to transversity amplitudes χ = 0 χ = χ = prior tension diluted by parameters ζ L(R) χ shift by 20% for ζ L, shift by +10% for ζ L 0 few percents for ζ R χ ζ Lχ K improved understanding of power corrections desirable D. van Dyk (Siegen) Exclusive b sl + l / 43

28 Results (SM Basis) flipped sign SM like C C7 C C9 post HEP 13 (selection) with B X s {γ, l + l } B s µ + µ from LHCb and CMS same data as [Descotes-Genon/Matias/Virto ] exclusive decays limited: only B K l + l! only LHCb data! only q 2 [1, 6]GeV 2 : Standard Model, : best-fit point red-shaded areas: regions of 68%, 95%, 99% prob., full dataset blue solid lines: regions of 68%, 95%, 99% prob., selection best-fit point similar to [Descotes-Genon et al ] less tension, only 2.5σ C 9 C SM ± 0.7 D. van Dyk (Siegen) Exclusive b sl + l / 43

29 Results (SM Basis) flipped sign SM like C : Standard Model, : best-fit point C7 C C9 post HEP 13 (full) SM-like uncertainty reduced by 2 compared to 2012 SM at the border of 1σ flipped-sign barely allowed at 1σ (26% of evidence) cannot confirm NP findings ζ L(R) χ in (C 7, C 9 ) [Descotes-Genon et al ] as in SM(ν-only) p value: 0.12 (@SM-like sol.) red-shaded areas: regions of 68%, 95%, 99% prob., full dataset blue solid lines: regions of 68%, 95%, 99% prob., selection D. van Dyk (Siegen) Exclusive b sl + l / 43

30 Results (SM+SM Basis) C A B C D C B C D A C A D C B C C C10 : Standard Model, : best-fit points, (light-) red: 68% CL (95% CL) for full dataset four solutions A through D A = SM like, 37% of ev. D = SM SM, 34% of ev. B, C suppressed: 14% and 15% of evidence for A (SM-like sol.) p value 0.07 C 9 C9 SM = 0.8 ± σ deviation from SM ζχ L(R) decrease wrt. SM(ν-only) and SM basis D. van Dyk (Siegen) Exclusive b sl + l / 43

31 (Statistical) Model Comparison model comparison using Bayes factor results compare scenarios only at SM-like solution A( ) adjust priors to contain only A( ) SM(ν-only) wins over SM basis: odds of 48:1 (43:1 with lattice inputs) SM(ν-only) wins over SM+SM basis: odds of 401:1 (143:1 with lattice inputs) SM(ν-only) draws against highly-spec. scenario where NP only enters C 9(9 ) D. van Dyk (Siegen) Exclusive b sl + l / 43

32 Development: Λ b Λ( Nπ)l + l [based on Böer/Feldmann/DvD ] D. van Dyk (Siegen) Exclusive b sl + l / 43

33 Why Λ b Λ B K l + l is being measured with increasing precision. Why spend effort on Λ b Λ? pro arguments, sorted from weakest to strongest D. van Dyk (Siegen) Exclusive b sl + l / 43

34 Why Λ b Λ B K l + l is being measured with increasing precision. Why spend effort on Λ b Λ? pro arguments, sorted from weakest to strongest independent confirmation of results: same b sl + l operators, different hadronic matrix elements D. van Dyk (Siegen) Exclusive b sl + l / 43

35 Why Λ b Λ B K l + l is being measured with increasing precision. Why spend effort on Λ b Λ? pro arguments, sorted from weakest to strongest independent confirmation of results: same b sl + l operators, different hadronic matrix elements Γ Λ ev: small width approximation fully applicable (compare B Kπl + l where non-res. P -wave contributions are unconstrained) D. van Dyk (Siegen) Exclusive b sl + l / 43

36 Why Λ b Λ B K l + l is being measured with increasing precision. Why spend effort on Λ b Λ? pro arguments, sorted from weakest to strongest independent confirmation of results: same b sl + l operators, different hadronic matrix elements Γ Λ ev: small width approximation fully applicable (compare B Kπl + l where non-res. P -wave contributions are unconstrained) fewer hadronic matrix elements (2 in HQET limit, 1 in SCET limit) D. van Dyk (Siegen) Exclusive b sl + l / 43

37 Why Λ b Λ B K l + l is being measured with increasing precision. Why spend effort on Λ b Λ? pro arguments, sorted from weakest to strongest independent confirmation of results: same b sl + l operators, different hadronic matrix elements Γ Λ ev: small width approximation fully applicable (compare B Kπl + l where non-res. P -wave contributions are unconstrained) fewer hadronic matrix elements (2 in HQET limit, 1 in SCET limit) doubly weak decay: complementary constraints on b sl + l physics with respect to B K l + l D. van Dyk (Siegen) Exclusive b sl + l / 43

38 Kinematics and Decay Topology Λ b (p) Λ(k) [ N(k 1 ) π(k 2 )] l + (q 1 ) l (q 2 ) 3 independent decay angles cos θ Λ cos θ l k q k q cos ϕ k q only for unpolarized Λ b Momenta q = q 1 + q 2 q = q 1 q 2 k = k 1 + k 2 k = k 1 k 2 D. van Dyk (Siegen) Exclusive b sl + l / 43

39 Λ b Λ Hadronic Matrix Elements In General using (overall 10) helicity form factors (FFs) [compare Feldmann/Yip ] schematically: ε (λ) Λ Γ Λ b fλ Γ (q 2 ) for lepton mass m l 0 this reduces to 8 independent FFs results for all FFs expected from the lattice in the long run Within HQET heavy quark spin symmmetry reduces matrix elements to 2 FFs at leading power known from Lattice QCD [Detmold/Lin/Meinel/Wingate ] Within SCET applicable when E Λ = O (m b ) matrix elements reduce further to 1 single FF estimates from SCET sum rules [Feldmann/Yip ] D. van Dyk (Siegen) Exclusive b sl + l / 43

40 Λ Nπ Hadronic Matrix Element Λ Nπ is a parity-violating weak decay branching fraction B[Λ Nπ] = (99.7 ± 0.1)% [PDG, our naive average] equations of motions reduce independent matrix elements to 2 we choose to express them through decay width Γ Λ parity-violating coupling α within small width approximation, Γ Λ cancels α well known from experiment: α pπ = ± [PDG average] D. van Dyk (Siegen) Exclusive b sl + l / 43

41 Angular Distribution of Λ b Λ[ Nπ]l + l we define the angular distribution as 8π 3 d 4 Γ dq 2 dcos θ l dcos θ Λ dϕ K(q2, cos θ l, cos θ Λ, ϕ) when considering only SM and chirality-flipped operators K = 1 ( K 1ss sin 2 θ l + K 1cc cos 2 θ l + K 1c cos θ l ) + cos θ Λ ( K2ss sin 2 θ l + K 2cc cos 2 θ l + K 2c cos θ l ) + sin θ Λ sin ϕ ( K 3sc sin θ l cos θ l + K 3s sin θ l ) + sin θ Λ cos ϕ ( K 4sc sin θ l cos θ l + K 4s sin θ l ) no further observables possible up to mass-dimension six K n K n(q 2 ) D. van Dyk (Siegen) Exclusive b sl + l / 43

42 Angular Observables matrix elements parametrized through 8 transversity amplitudes A λ χ M A R 1, A R 1, A R 0, A R 0, and (R L) λ dilepton chirality χ transversity state, similar as in B K l + l M third component of dilepton angular momentum D. van Dyk (Siegen) Exclusive b sl + l / 43

43 Angular Observables matrix elements parametrized through 8 transversity amplitudes A λ χ M λ dilepton chirality A R 1, A R 1, A R 0, A R 0, and (R L) χ transversity state, similar as in B K l + l M third component of dilepton angular momentum express angular observables through transversity amplitudes, e.g. K 1cc = 1 [ A R A R (R L) ] K 2c = α [ A R A R (R L) ]. full list in the backups D. van Dyk (Siegen) Exclusive b sl + l / 43

44 Simple Observables start with integrated decay width Γ = 2K 1ss + K 1cc define further observables X as weighted (ω X ) integrals X = 1 d 3 Γ Γ d cos θ l d cos θ Λ dϕ ωx(cos θ l, cos θ Λ, ϕ)d cos θ l d cos θ Λ dϕ A leptonic forward-backward asymmetry K 1c A l FB = 3 2 2K 1ss + K 1cc with ω A l FB = sign cos θ l D. van Dyk (Siegen) Exclusive b sl + l / 43

45 Simple Observables start with integrated decay width Γ = 2K 1ss + K 1cc define further observables X as weighted (ω X ) integrals X = 1 d 3 Γ Γ d cos θ l d cos θ Λ dϕ ωx(cos θ l, cos θ Λ, ϕ)d cos θ l d cos θ Λ dϕ A leptonic forward-backward asymmetry K 1c A l FB = 3 2 2K 1ss + K 1cc with ω A l FB = sign cos θ l B fraction of longitudinal dilepton pairs F 0 = 2K1ss K1cc 2K 1ss + K 1cc with ω F0 = 2 5 cos 2 θ l D. van Dyk (Siegen) Exclusive b sl + l / 43

46 Simple Observables start with integrated decay width Γ = 2K 1ss + K 1cc define further observables X as weighted (ω X ) integrals X = 1 d 3 Γ Γ d cos θ l d cos θ Λ dϕ ωx(cos θ l, cos θ Λ, ϕ)d cos θ l d cos θ Λ dϕ C hadronic forward-backward asymmetry A Λ FB = 1 2K 2ss + K 2cc 2 2K 1ss + K 1cc with ω A l FB = sign cos θ Λ D. van Dyk (Siegen) Exclusive b sl + l / 43

47 Simple Observables start with integrated decay width Γ = 2K 1ss + K 1cc define further observables X as weighted (ω X ) integrals X = 1 d 3 Γ Γ d cos θ l d cos θ Λ dϕ ωx(cos θ l, cos θ Λ, ϕ)d cos θ l d cos θ Λ dϕ C hadronic forward-backward asymmetry A Λ FB = 1 2K 2ss + K 2cc 2 2K 1ss + K 1cc with ω A l FB = sign cos θ Λ D combined forward-backward asymmetry A lλ K 2c FB = 3 4 2K 1ss + K 1cc with ω A l FB = sign cos θ Λ sign cos θ l D. van Dyk (Siegen) Exclusive b sl + l / 43

48 New Types of Constraints assume C 9(9 ) free floating, and C 10(10 ) = CSM 10(10 ) ( 4, 0) 4 existing constraints ρ ± 1 blue banded constraints 2 C9 ' C9 black square: SM point D. van Dyk (Siegen) Exclusive b sl + l / 43

49 New Types of Constraints assume C 9(9 ) free floating, and C 10(10 ) = CSM 10(10 ) ( 4, 0) 4 2 existing constraints ρ ± 1 ρ 2 blue banded constraints insensitive (not shown) C9 ' C9 black square: SM point D. van Dyk (Siegen) Exclusive b sl + l / 43

50 New Types of Constraints assume C 9(9 ) free floating, and C 10(10 ) = CSM 10(10 ) ( 4, 0) C9 ' existing constraints ρ ± 1 ρ 2 blue banded constraints insensitive (not shown) new constraints ρ 3 purple banded constraints C9 black square: SM point D. van Dyk (Siegen) Exclusive b sl + l / 43

51 New Types of Constraints assume C 9(9 ) free floating, and C 10(10 ) = CSM 10(10 ) ( 4, 0) C9 ' existing constraints ρ ± 1 ρ 2 blue banded constraints insensitive (not shown) new constraints ρ 3 ρ 4 purple banded constraints gold hyperbolic constraint C9 black square: SM point D. van Dyk (Siegen) Exclusive b sl + l / 43

52 Development: Charmonium Resonances in B Kl + l D. van Dyk (Siegen) Exclusive b sl + l / 43

53 Experimental Situation in 2013 LHCb announced observation of a resonance beyond ψ(3770) in dilepton spectrum of B + K + µ + µ [LHCb ] to paraphrase Douglas Adams: this made a lot of people very irritated and has been widely regarded as a bad move experiment performed model-dependent decomposition Candidates / (25 MeV/c 2 ) LHCb data total nonresonant interference resonances background m µ + µ [MeV/c 2 ] theory side did never claim absence of resonances in low recoil region LHCb s non-resonant curve OPE prediction same resonances as in e + e hadrons expected in B K ( ) l + l spetrum D. van Dyk (Siegen) Exclusive b sl + l / 43

54 Known Charmonia with J P = 1 Charmonium states apologies, cannot find source of plots 1 S 0 3 S 1 1 P 1 3 P 0 3 P 1 3 P 2 1 D 2 3 D 1 3 D 2 3 D 3 charged ψ(4415) Mass, GeV ψ(4040) χ c2 (2P) ψ(2s) η c (2S) h c χ χ c2 c1 χ c0 ψ(4160) ψ(3770) η c J/ψ charged K.Chilikin (ITEP) Quarkonium(-like) states at Belle Moriond QCD, / 21 D. van Dyk (Siegen) Exclusive b sl + l / 43

55 Known Charmonia with J P = 1 Charmonium states apologies, cannot find source of plots 1 S 0 3 S 1 1 P 1 3 P 0 3 P 1 3 P 2 1 D 2 3 D 1 3 D 2 3 D 3 charged Mass, GeV ψ(4415) X (4160) ψ(4040) X (3940) ψ(2s) η c (2S) h c Y (3915) χ c2 (2P) X (3872) χ χ c2 c1 χ c0 Y (4660) Y (4360) Y (4260) ψ(4160) X (3820) ψ(3770) η c J/ψ charged K.Chilikin (ITEP) Quarkonium(-like) states at Belle Moriond QCD, / 21 D. van Dyk (Siegen) Exclusive b sl + l / 43

56 Open Questions where are the other resonances beside ψ(4160)? to what extent is quark-hadron duality violated? B K l + l to the rescue! what is the value of H (1) T? what is the value of S 7? can we learn more about the q 2 spectrum when combining exclusive b sl + l data? D. van Dyk (Siegen) Exclusive b sl + l / 43

57 Conclusion D. van Dyk (Siegen) Exclusive b sl + l / 43

58 Summary and Outlook exclusive b sl + l decays are interesting channels to probe for new physics effects and to simultaneously understand old physics data has become very precise; we have already started to infer hadronic physics from data however: disentangling right-handed currents from cc contributions will be difficult measurements in the decay channel Λ b Λ( Nπ)l + l will be helpful will offer novel types of new physics constraints on account of different hadronic matrix element, it will either confirm or challenge the current results offered in the mesonic decay channels increasing precision in B Kl + l will need to be met by further understanding of the charmonium spectrum we might need to reconsider modelling the spectrum not discussed: B Kπl + l [Das/Jung/Hiller/Shires ], B s ϕl + l,... D. van Dyk (Siegen) Exclusive b sl + l / 43

59 Backup Slides D. van Dyk (Siegen) Exclusive b sl + l / 43

60 Large Recoil (I) QCD Factorization (QCDF) + Soft Collinear Effective Theory (SCET) calculate qq loops perturbatively, expand in 1/m b, 1/E K relate matrix elements to universal hadronic quantities: Light Cone Distribution Amplitudes (LCDAs) form factors decay constants [Beneke/Feldmann 00, Beneke/Feldmann/Seidel 01 & 04] Light Cone Sum Rules (LCSR) calculate cc, ccg on the light cone for q 2 4m 2 c achieves resummation of soft gluon effects use analycity of amplitude to relate results to q 2 < M 2 ψ uses many of the same inputs as QCDF+SCET D. vanincludes Dyk (Siegen) parts of QCDF+SCETExclusive results b sl + l / 43

61 Large Recoil (I) QCD Factorization (QCDF) + Soft Collinear Effective Theory (SCET) calculate qq loops perturbatively, expand in 1/m b, 1/E K relate matrix elements to universal hadronic quantities: Light Cone Distribution Amplitudes (LCDAs) form factors decay constants [Beneke/Feldmann 00, Beneke/Feldmann/Seidel 01 & 04] Combination of QCDF+SCET and LCSR Results not yet! no studies yet to find impact on optimized observables at large recoil! LCSR results are not included in following discussion D. van Dyk (Siegen) Exclusive b sl + l / 43

62 Low Recoil OPE [Grinstein/Pirjol 04, Beylich/Buchalla/Feldmann 11] i d 4 xe iqx K T {O i (0), j e.m. µ (x)} B = j,k C i,j,k (q 2 /m 2 b, µ) O j (k) µ b s b s b s qq l l = q q q 2 l l OP E l l Operators k = 3 form factors, α s corrections known, absorbed into effective Wilson coefficients C 7,9 C eff 7,9 k = 4 absent k = 5 Λ 2 /m 2 b 2% corrections, first new had. matrix elements explicitly: < 1% for q 2 = 15GeV 2 [Beylich/Buchalla/Feldmann] D. van Dyk (Siegen) Exclusive b sl + l / 43

63 Λ b Λ( Nπ)l + l Angular Observables. K 1ss = 1 [ ] A R A R A R A R (R L) K 1cc = 1 [ ] A R A R (R L) ( ) K 1c = Re A R 1 A R (R L) 1 K 2ss = α ( ) 2 Re A R 1 A R + 1 2AR 0 A R + (R L) 0 ( ) K 2cc = α Re A R 1 A R + (R L) 1 K 2c = α [ ] A R A R 1 2 (R L) K 3sc = α ( ) Im A R 2 1 A R 0 AR 1 A R + (R L) 0 K 3s = α ( ) Im A R 2 1 A R 0 AR 1 A R + (R L) 0 K 4sc = α ( ) Re A R 2 1 A R 0 AR 1 A R + (R L) 0 K 4s = α ( ) Re 2 AR 1 A R (R L) 0 A R 1 A R 0 D. van Dyk (Siegen) Exclusive b sl + l / 43

64 At Low Recoil: Amplitudes when q 2 = O ( m 2 b ) A L(R) 1 A L(R) 0 = 2NC L(R) + f V s = + 2NC L(R) + f V 0 m Λb + m Λ s q 2 A L(R) 1 A L(R) 0 = +2NC L(R) f A s+ = 2NC L(R) f A 0 m Λb m Λ s q 2 with s ± = (m Λb ± m Λ ) 2 q 2 ( C R(L) + = (C 9 + C 9 ) + 2κm bm Λb C R(L) = κ as in [Grinstein/Pirjol hep-ph/ ] ) q 2 (C 7 + C 7 ) ± (C 10 + C 10 ) ( (C 9 C 9 ) + 2κm ) bm Λb q 2 (C 7 C 7 ) ± (C 10 C 10 ) D. van Dyk (Siegen) Exclusive b sl + l / 43

65 At Low Recoil: ρs when q 2 = O ( m 2 b ) ρ ± 1 = C 79 ± C C 10 ± C 10 2 ρ 2 = Re (C 79 C10 C 7 9 C 10 ) i Im (C 79C7 9 + C 10C10 ) ρ ± 3 = 2 Re ((C 79 ± C 7 9 )(C 10 ± C 10 ) ) ρ 4 = ( C 79 2 C C 10 2 C 10 2) i Im (C 79 C10 C 7 9 C 10). D. van Dyk (Siegen) Exclusive b sl + l / 43