New Physics or hadronic corrections

Transcription

1 New Physics or hadronic corrections in the B K μ + μ decay? Institute for Research in Fundamental Sciences (IPM) In collaboration with V. Chobanova, T. Hurth, N. Mahmoudi and D. Martinez Santos based on arxiv: & Rencontres de Moriond, QCD and High Energy Interactions La Thuile, Aosta valley, Italy March 25th April 1st, 2017

2 b s transitions Effective Hamiltonian for b sl + l transitions: chirality flipped operators (O i ) Most relevant for (semi-) leptonic decays Short-distance effects: Wilson coefficients C i μ (μ = m b ) o Calculated perturbatively up to NNLL o Contain all the contributions from scales higher than μ Long-distance effects: matrix elements of operators O i : o Require non-perturbative methods o Introduce the main theoretical uncertainties 1

3 Theoretical framework for B K l + l Effective Hamiltonian for b sl + l transitions: Matrix elements of B K l + l decay: K l + l sl H eff B : B K form factors V, A 0,1,2, T 1,2,3 or alternatively V λ, T λ, S (λ = helicity of K ) Helicity amplitudes: 2

4 Theoretical framework for B K l + l Effective Hamiltonian for b sl + l transitions: Matrix elements of B K l + l decay: K l + l had H eff B : H had eff contributes to b s ll through virtual photon exchange affect only the H V (λ) Helicity amplitudes: 3

5 Theoretical framework for B K l + l Effective Hamiltonian for b sl + l transitions: Matrix elements of B K l + l decay: K l + l had H eff B : In general naïve factorization not applicable Helicity amplitudes: 3

6 Theoretical framework for B K l + l Effective Hamiltonian for b sl + l transitions: Matrix elements of B K l + l decay: K l + l had H eff B : Helicity amplitudes: Beneke et al: ; Partial calculation from Khodjamirian et al

7 Theoretical framework for B K l + l Effective Hamiltonian for b sl + l transitions: Matrix elements of B K l + l decay: K l + l had H eff B : Helicity amplitudes: 3

8 Anomalies Three main LHCb anomalies observed in b sl + l decays: B K μ + μ angular observable P 5 (or S 5 ): 3.4σ tension with 3 fb 1 (2015) supported by Belle R K = BR(B + K + μ + μ )/BR(B + K + e + e ): 2.6σ tension in [1-6] GeV 2 bin BR(B s φμ + μ ): 3.2σ tension in [1-6] GeV 2 bin LHCb-TALK New Physics or underestimated hadronic uncertainties? 4

9 Model independent global fits Many b sl + l observables BR low B X s μ + μ BR high B X s μ + μ BR low B X s e + e BR high B X s e + e Global fits BR B s μ + μ BR B d μ + μ BR B K 0 μ + μ BR B + K + μ + μ R K BR B K e + e BR B K + μ + μ BR B s φ μ + μ B K 0 μ + μ : angular observables B s φ μ + μ : angular observables NP manifests itself in terms of shifts to the SM Wilson coefficients: C i μ = C i SM μ + δc i ( ) ( ) ( ) Global fits of Wilson coefficients C 7, C9, C10 Scanning over the values of δc i Minimizing χ 2 = O th O exp Σ th + Σ exp 1 O th O exp Guesstimate of unknown power corrections: Σ th + Σ exp 1 is the inverse covariance matrix Calculations done using SuperIso Leading Order QCDf of non-factorisable piece 1 + a k exp iφ k + b k q 2 with a k (b k ) varied between X%( 2.5) and +X%( 2.5) 6 GeV 2 exp iθ k 5

10 Fit results: single operator ( ) ( ) ( ) Global fit of Wilson coefficients C 7, C9, C10 Best fit when assuming NP in δc 9 (μ) ~ 1 Fits assuming two or more Wilson coefficients all have a best fit when δc 9 (μ) ~ 1 Several groups doing global fits (with similar results): based on latest LHCb data: Descotes-Genon, Hofer, Matias, Virto: ; Ciuchini, Fedele, Franco, Mishima, Paul, Silvestrini, Valli: ; Hurth, Mahmoudi, SN: ; Capdevila, Descotes-Genon, Hofer, Matias: ; Chobanova, Hurth, Mahmoudi, Martinez-Santos, SN:

11 Fit results for two operators: hadronic uncertainty dependence Stability of the fit with respect to hadronic uncertainties: 1. Different assumptions on the form factor uncertainties Filled area: global fit with normal form factor error Bharucha, Straub, Zwicky: Solid contour: removing form factor error correlations Dashed contour: 2 x form factor errors Dotted contour: 4 x form factor errors SM Only when assuming 4 x form factor errors tensions goes below 2σ 2. Different assumptions on the size of the non-factorisable power corrections Filled area: 10% power correction Solid contour: 60% power correction Guesstimate of unknown power corrections: Leading Order QCDf of non-factorisable piece 1 + a k exp iφ k + b k q 2 with a k (b k ) varied between X%( 2.5) and +X%( 2.5) 6 GeV 2 exp iθ k SM Tension not significantly reduced with 60% power correction 60% power corrections at amplitude level 17-20% on the observable level Large enough hadronic power corrections required to remove tension amount to more than 150% at the amplitude level in the critical bins (20-50% on the observable level) Ciuchini et al.:

12 Hadronic effects vs. New Physics Non-factorisable contributions appear in: A possible parametrisation of the non-factorisable power corrections Leading Order QCDf of non-factorisable piece + h λ(q 2 ) (λ = +,, 0) M. Ciuchini et al., S. Jäger and J. Camalich: It seems: h λ (0) C7 NP, h λ (1) C9 NP and h λ (2) term cannot be mimicked by C7,9 M. Ciuchini et al., However, λ = +,, 0 and V λ and T λ both have a q 2 dependence 8

13 Hadronic effects vs. New Physics Non-factorisable contributions appear in: A possible parametrisation of the non-factorisable power corrections Leading Order QCDf of non-factorisable piece + h λ(q 2 ) (λ = +,, 0) M. Ciuchini et al., S. Jäger and J. Camalich: It seems: h λ (0) C7 NP, h λ (1) C9 NP and h λ (2) term cannot be mimicked by C7,9 M. Ciuchini et al., However, λ = +,, 0 and V λ and T λ both have a q 2 dependence Mild q 4 -terms can rise due to form factor terms C 7 NP and C 9 NP can cause effects similar to h λ (0,1,2) 8

14 Hadronic effects vs. New Physics Hadronic power correction effect: New Physics effect: and similarly for C 7 NP effects can be embedded in the more general form of hadronic effects (0,1,2) We can do a fit for both hadronic quantities h +,,0 (18 parameters) and Wilson coefficients C NP 9 or C NP 7&9 (2 or 4 parameters) Due to the embedding of the two fits there can be a direct comparison of the fits with the Wilks test 9

15 Wilks test Fit to NP and power corrections using only B K μ + μ observables at low-q 2 to keep the embedding Comparison of the hadronic fit with the NP fit through likelihood ratio tests p-values can be obtained (via Wilks theorem) p-value indicates the significance of the new parameters added up to 8 GeV 2 observables δc 9 δc 7, δc 9 Hadronic fit Plain SM (4.1σ) (4.0σ) (2.7σ) δc (1.5σ) 0.45 (0.76σ) δc 7 & δc (0.52σ) Adding the hadronic parameters (16 more parameters) does not really improve the fits Strong indication that the NP interpretation is a valid option, even if the situation remains inconclusive 10

16 Outlook Outlook for identifying the origin of the anomalies: Assuming a possible future LHCb upgrade, with an integrated luminosity of 300 fb 1 o Scaling down the present LHCb uncertainties by a factor 10 o If data shows q 2 dependence which cannot be produced by any NP contribution, NP can be ruled out o Due to the embedding, the hadronic option cannot be ruled out in favour of the NP option although it would be peculiar if hadronic effects (h +,,0 (q 2 )) all conspired to mimic NP Crosscheck with other (clean) observable of ratios of decays to muons over electrons R μ/e o Deviations would indirectly confirm that the tension in P 5 is due to NP and would rule out the hadronic effects option Crosscheck with inclusive mode B X s μ + μ where power corrections can be estimated o If tension in P 5 due to NP effect in C 9, it is large enough to be checked at Belle-II Theory calculation of the non-factorisable power corrections o Complete calculation exists for B Kl + l Khodjamirian et al o Only partial calculations exist for B K l + l Khodjamirian et al Hurth, Mahmoudi, S.N Thank you for listening! 11

17 Backup

18 Hadronic corrections as shift to C 9 The effect of the power corrections could also be described through a q 2 -dependent shift in C 9 via

19 Hadronic corrections as shift to C 9 assuming h + (0) to be constrained The effect of the power corrections could also be described through a q 2 -dependent shift in C 9 via ( h + 0 /h (0) < 0.2)

20 New Physics fit using only low-q 2 B K μ + μ observables Fit with 2 parameters (complex C 9 ) low q 2 bins up to 6 GeV 2 low q 2 bins up to 8 GeV 2 Fit with 4 parameters (complex C 7 and C 9 ) low q 2 bins up to 6 GeV 2 low q 2 bins up to 8 GeV 2

21 Fit parameters of power corrections and shapes of the different corrections

22 Wilks test Comparison of the hadronic fit with the NP fit through likelihood ratio tests up to 6 GeV 2 observables δc 9 δc 7, δc 9 Hadronic fit Plain SM (2.8σ) (2.6σ) (1.9σ) δc (1.1σ) 0.37 (0.89σ) δc 7 & δc (0.86σ) up to 8 GeV 2 observables δc 9 δc 7, δc 9 Hadronic fit Plain SM (4.1σ) (4.0σ) (2.7σ) δc (1.5σ) 0.45 (0.76σ) δc 7 & δc (0.52σ)

23 Size of different contributions to the helicity amplitudes

24 Size of different contributions to the helicity amplitudes Assuming h + (0) to be constrained ( h + 0 /h (0) < 0.2)

25 B K l + l Observed in experiment: B K K + π l + l Angular behaviour of K + and π additional information on the helicity of K* Angular distribution described by four independent kinematic variables q 2 and three angles θ l, θ K, φ finalstate spis n 2 4 d 9 J cos cos d 32 2 dq d l d K 2 ( q, l, K, ) J i : functions of helicity amplitudes H V λ, H A λ, H P (or transversity amplitudes A L,R, A L,R, A 0 L,R, A t ) Besides the standard observables (BR, A FB, F L ) angular observables P i ( ) or Si constructed as ratios of different J i Minimize form factor dependence Sensitivity to certain Wilson coefficient Kruger, Matias: ; U. Egede et al.: ; W. Altmannshofer et al.: ; U. Egede et al.: ; Becirevic, Schneider: ; J. Matias et al.: ; S. Descotes-Genon et al.:

26 Angular coefficients

27 B K μ + μ observables Differential decay rate: dγ dq 2 = 3 4 J 1 J 2 /3 Forward Backward Asymmetry: A FB q d = [ 2 Γ 1 0 ] d cos θl / dγ = 3 dq 2 d cos θ l dq 2 8 J 6/ dγ dq 2 Forward-Backward Asymmetry zero-crossing: q 0 2 = 2m b C 7 eff Longitudinal Polarization Fraction: F L = 2J 2 c / dγ dq 2 C 9 eff + O(α s, Λ/m b ) Optimized obervables: U. Egede et al., JHEP 0811 (2008) 032 U. Egede et al.,jhep 1010 (2010) 056 J. Matias et al., JHEP 1204 (2012) 104 S. Descotes-Genon et al., JHEP 1305 (2013) 137 Or alternatively : S i = (J i s,c + J i s,c )/( dγ + d Γ dq 2 dq2) W. Altmannshofer et al., JHEP 0901 (2009) 019 P 5 in terms of helicity amplitudes:

28 Crosscheck: Future LHCb upgrade Identifying the origin of the anomalies: Assuming a possible future upgrade, with an integrated luminosity of 300 fb 1 o Scaling down the present LHCb uncertainties by a factor 10 o Assuming the current central values Fit with 2 parameters (complex C 9 ) low q 2 bins up to 6 GeV 2 low q 2 bins up to 8 GeV 2

29 Crosscheck: lepton non-universality in other observables Crosscheck with (clean) ratios R(μ/e) o Theoretically very clean compared to the angular observables Hiller, Kruger arxiv: , Altmannshofer, Straub arxiv: Using the best fit point for C 9 μ and C 9 e, make predictions of ratios of decays to muons versus electrons

30 Crosscheck: inclusive mode Crosschecking with the inclusive mode B X s μ + μ o Using the best fit point of C 7, C 9, C 10 we predict the branching ratio at low- and high-q 2 at 1,2 and 3σ ranges also for A FB o The black cross corresponds to the future Belle-II measurement assuming the best fit scenario o Expected uncertainty of 2.9% (4.1%) for the branching fraction in the low- (high-)q 2 region, absolute uncertainty of in the low-q 2 bin 1 (1 < q2 < 3.5 GeV 2 ), in the low-q 2 bin 2 (3.5 < q2 < 6 GeV 2 ) for the normalised A FB Hurth, Mahmoudi, S.N SM prediction Hurth, Mahmoudi, S.N Belle-II projection assuming best fit scenario NP effect of C 9 is large enough to be checked by the theoretically cleaner inclusive modes at Belle-II

31 Two operator fit: Full vs. Soft FF approach Different theoretical approaches Full form factor approach {C 9 C 10 } {C 9 C 9 } {C 9 μ C 9 e } χ 2 = 124 χ 2 = 123 χ 2 = 115 Soft form factor approach {C 9 C 10 } {C 9 C 9 } {C 9 μ C 9 e } χ 2 = 119 χ 2 = 119 χ 2 = 110

32 Dependence on experimental results: maximum likelihood vs. method of moment LHCb uses two different analysis methods for the angular observables Method of moments: larger uncertainties but more robust Most likelihood method: smaller uncertainties but involves model dependent assumptions How does the choice of method affect fit? fitting by considering only B K μ + μ observables most likelihood method of moments Tension of best fit point with SM is decreased with the method of moments mostly due larger (experimental) error of the method of moment results (central values very similar)

33 Dependence on experimental results: fit results when omitting S 5 Removing S 5 (P 5 ) from the global fit P 5 = S 5 F L (1 F L ) Filled area: global fit using all observables Solid contour: fit removing only S 5 Tension of best fit point is slightly reduced for C 9 but still more than 2σ It is not only S 5 (P 5 ) which drives C 9 to negative values

34 Dependence on experimental results: fit results when omitting R K Removing R K from the global fit Filled area: global fit using all observables Solid contour: fit removing only R K R K is the main measurement resulting in a best fit value for C 9 μ and C 9 e which are in more than 2σ tension with lepton universality

35 Motivation