Search for new physics in three-body charmless B mesons decays

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1 Search for new physics in three-body charmless B mesons decays Emilie Bertholet Advisors: Eli Ben-Haim, Matthew Charles LPNHE-LHCb group emilie.bertholet@lpnhe.in2p3.fr November 17, 2017 Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

2 Overview 1 General introduction 2 Study of a method of extraction of the CKM-angle γ 3 Dalitz-plot analysis of B 0 K 0 SK + K Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

3 Contents 1 General introduction 2 Study of a method of extraction of the CKM-angle γ 3 Dalitz-plot analysis of B 0 K 0 SK + K Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

4 Weak interaction and CKM matrix Transitions between different types of quarks in the SM weak interaction (W ± bosons). b V cb c b W + s W + CKM-matrix 3 3 complex unitarity matrix parametrised by 3 angles and 1 phase (only source of CP violation in the SM) V ud V us V ub V CKM = V cd V cs V cb V td V ts V tb Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

5 Weak interaction and CKM matrix Wolfenstein parametrisation: 3rd order development in λ = V us λ 0.23, A 0.8, ρ 0.14, η λ 2 /2 λ Aλ 3 (ρ iη) V CKM = λ 1 λ 2 /2 Aλ 2 + O(λ 4 ) Aλ 3 (1 ρ iη) Aλ 2 1 u c t V ud V us V ub V CKM = V cd V cs V cb V td V ts V tb d s b Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

6 Weak interaction and CKM matrix Wolfenstein parametrisation: 3rd order development in λ = V us λ 0.23, A 0.8, ρ 0.14, η λ 2 /2 λ Aλ 3 (ρ iη) V CKM = λ 1 λ 2 /2 Aλ 2 + O(λ 4 ) Aλ 3 (1 ρ iη) Aλ 2 1 u c t V ud V us V ub V CKM = V cd V cs V cb V td V ts V tb d s b Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

7 Weak interaction and CKM matrix Wolfenstein parametrisation: 3rd order development in λ = V us λ 0.23, A 0.8, ρ 0.14, η λ 2 /2 λ Aλ 3 (ρ iη) V CKM = λ 1 λ 2 /2 Aλ 2 + O(λ 4 ) Aλ 3 (1 ρ iη) Aλ 2 1 u c t V ud V us V ub V CKM = V cd V cs V cb V td V ts V tb d s b Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

8 Weak interaction and CKM matrix Wolfenstein parametrisation: 3rd order development in λ = V us λ 0.23, A 0.8, ρ 0.14, η λ 2 /2 λ Aλ 3 (ρ iη) V CKM = λ 1 λ 2 /2 Aλ 2 + O(λ 4 ) Aλ 3 (1 ρ iη) Aλ 2 1 u c t V ud V us V ub V CKM = V cd V cs V cb V td V ts V tb d s b Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

9 Weak interaction and CKM matrix Wolfenstein parametrisation: 3rd order development in λ = V us λ 0.23, A 0.8, ρ 0.14, η λ 2 /2 λ Aλ 3 (ρ iη) V CKM = λ 1 λ 2 /2 Aλ 2 + O(λ 4 ) Aλ 3 (1 ρ iη) Aλ 2 1 u c t V ud V us V ub V CKM = V cd V cs V cb V td V ts V tb d s b Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

10 Weak interaction and CKM matrix Wolfenstein parametrisation: 3rd order development in λ = V us λ 0.23, A 0.8, ρ 0.14, η λ 2 /2 λ Aλ 3 (ρ iη) V CKM = λ 1 λ 2 /2 Aλ 2 + O(λ 4 ) Aλ 3 (1 ρ iη) Aλ 2 1 u c t V ud V us V ub V CKM = V cd V cs V cb V td V ts V tb d s b Nothing in the SM explains the hierarchy in the transitions!!! Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

11 Unitarity triangle and the γ angle CKM matrix is unitary: i j V ij V ik = δ jk V ij V kj = δ jk Unitarity triangle V ud V ub + V cd V cb + V td V tb = 0 ρ + i η = V udvub V cd Vcb. γ = arg [ V udv ub V cd V cb b u highly suppressed: great precision on γ measurement is difficult to achieve. Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31 ]

12 Why measure γ? Measure CKM parameters: SM V CKM unitary. SM+NP maybe not? We need to test unitarity and self-consistency over-constrain the triangle α = [deg] β = [deg] γ = [deg] Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

13 Why measure γ? Measure CKM parameters: SM V CKM unitary. SM+NP maybe not? We need to test unitarity and self-consistency over-constrain the triangle Measure γ: from tree decays from loop decays [charmless] γ is the least known CKM parameter to date. α = [deg] β = [deg] γ = [deg] Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

14 Three-body decay formalism: Dalitz Plane 3-body decay 2 free parameters the phase space lies on a plane Partial width of the decay dγ = 1 1 (2π 3 ) 32M 2 M 2 ds 12 ds 23 with s ij = mij 2 = (m i + m j ) 2 s 12 + s 23 + s 13 = M 2 + m1 2 + m2 2 + m3 2 Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

15 Three-body decay formalism: Dalitz Plane 3-body decay 2 free parameters the phase space lies on a plane Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

16 The framework of Dalitz plot analysis Experimentally, we use an isobar approximation which models the total amplitude as resulting from a coherent sum of amplitudes A (s 12, s 23 ) = N j=1 c j e iφ j F j (s 12, s 23 ) Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

17 The framework of Dalitz plot analysis Experimentally, we use an isobar approximation which models the total amplitude as resulting from a coherent sum of amplitudes A (s 12, s 23 ) = N j=1 c j e iφ j F j (s 12, s 23 ) Isobar parameters Coefficients describing the relative magnitude and phase of the different decay channels. Contains only the weak dynamics. Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

18 The framework of Dalitz plot analysis Experimentally, we use an isobar approximation which models the total amplitude as resulting from a coherent sum of amplitudes A (s 12, s 23 ) = Isobar parameters Coefficients describing the relative magnitude and phase of the different decay channels. Contains only the weak dynamics. N j=1 c j e iφ j F j (s 12, s 23 ) DP-dependent dynamical amplitudes Functions describing the strong dynamics. Lineshape: propagators = Breit- Wigner or more complicated functions. Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

19 So why study all this? Why study charmless B meson decays? Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

20 So why study all this? Why study charmless B meson decays? Penguin and tree contributions can have similar size Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

21 So why study all this? Why study charmless B meson decays? Penguin and tree contributions can have similar size { CP violation NP searches Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

22 So why study all this? Why study charmless B meson decays? Penguin and tree contributions can have similar size { CP violation NP searches Why Dalitz-plot (DP) analysis? Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

23 So why study all this? Why study charmless B meson decays? Penguin and tree contributions can have similar size { CP violation NP searches Why Dalitz-plot (DP) analysis? Gives information on the resonant structure. Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

24 So why study all this? Why study charmless B meson decays? Penguin and tree contributions can have similar size { CP violation NP searches Why Dalitz-plot (DP) analysis? Gives information on the resonant structure. Gives access to many observables: Branching ratios Direct and indirect CP asymmetries Direct access to phases Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

25 Contents 1 General introduction 2 Study of a method of extraction of the CKM-angle γ 3 Dalitz-plot analysis of B 0 K 0 SK + K Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

26 Method overview Most precise measurement of γ comes from decays like B DK dominated by tree processes (SM-like measurement). We studied a method to extract γ from charmless loop processes (new physics sensitive) developed by London et al. Phys.Lett. B728 (2014) b W + s b?? s γ is extracted combining the information coming from 5 charmless 3-body decays modes of B mesons under the assumption of SU(3) flavour symmetry. B 0 K S K S K S B 0 K + π 0 π B + K + π + π B 0 K S K + K B 0 K S π + π Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

27 Theoretical amplitudes Under SU(3) flavour symmetery the penguin diagrams and tree diagrams are proportional for b s transitions P (C) EW = κ T (C) Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

28 Theoretical amplitudes Under SU(3) flavour symmetery the penguin diagrams and tree diagrams are proportional for b s transitions P (C) EW = κ T (C) Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

29 Theoretical amplitudes Under SU(3) flavour symmetery the penguin diagrams and tree diagrams are proportional for b s transitions P (C) EW = κ T (C) Constant: function of CKM matrix elements and Wilson coefficients Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

Wilson coefficients SU(3) flavour symmety implies using fully symmetrised amplitudes.

30 Theoretical amplitudes Under SU(3) flavour symmetery the penguin diagrams and tree diagrams are proportional for b s transitions P (C) EW = κ T (C) Constant: function of CKM matrix elements and Wilson coefficients SU(3) flavour symmety implies using fully symmetrised amplitudes. Mathematics of symmetrisation will be discussed later. Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

31 Theoretical amplitudes The theoretical amplitudes for each mode can be expressed in terms of 2A (B 0 K + π 0 π ) fs = be iγ κc, 2A (B 0 K 0 π + π ) fs = de iγ P uce iγ a + κd, 2A (B 0 K + K 0 K ) fs = α SU(3) ( ce iγ P uce iγ a + κb), A (B 0 K 0 K 0 K 0 ) fs = α SU(3) ( P uce iγ + a). Parameter counting for 5 modes (and 4 modes) Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

32 Theoretical amplitudes The theoretical amplitudes for each mode can be expressed in terms of 5 effective diagrams: a, b, c, d and P uc. 2A (B 0 K + π 0 π ) fs = be iγ κc, 2A (B 0 K 0 π + π ) fs = de iγ P uce iγ a + κd, 2A (B 0 K + K 0 K ) fs = α SU(3) ( ce iγ P uce iγ a + κb), A (B 0 K 0 K 0 K 0 ) fs = α SU(3) ( P uce iγ + a). Parameter counting for 5 modes (and 4 modes) 5 magnitudes + 4 relative strong phases Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

33 Theoretical amplitudes The theoretical amplitudes for each mode can be expressed in terms of 5 effective diagrams: a, b, c, d and P uc. The weak phase γ 2A (B 0 K + π 0 π ) fs = be iγ κc, 2A (B 0 K 0 π + π ) fs = de iγ P uce iγ a + κd, 2A (B 0 K + K 0 K ) fs = α SU(3) ( ce iγ P uce iγ a + κb), A (B 0 K 0 K 0 K 0 ) fs = α SU(3) ( P uce iγ + a). Parameter counting for 5 modes (and 4 modes) 5 magnitudes + 4 relative strong phases + γ Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

34 Theoretical amplitudes The theoretical amplitudes for each mode can be expressed in terms of 5 effective diagrams: a, b, c, d and P uc. The weak phase γ α SU(3) 2A (B 0 K + π 0 π ) fs = be iγ κc, 2A (B 0 K 0 π + π ) fs = de iγ P uce iγ a + κd, 2A (B + K + π + π ) fs = ce iγ P uce iγ a + κb, 2A (B 0 K + K 0 K ) fs = α SU(3) ( ce iγ P uce iγ a + κb), A (B 0 K 0 K 0 K 0 ) fs = α SU(3) ( P uce iγ + a). Parameter counting for 5 modes (and 4 modes) 5 magnitudes + 4 relative strong phases + γ + α SU(3) Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

35 Theoretical amplitudes The theoretical amplitudes for each mode can be expressed in terms of 5 effective diagrams: a, b, c, d and P uc. The weak phase γ α SU(3) 2A (B 0 K + π 0 π ) fs = be iγ κc, 2A (B 0 K 0 π + π ) fs = de iγ P uce iγ a + κd, 2A (B + K + π + π ) fs = ce iγ P uce iγ a + κb, 2A (B 0 K + K 0 K ) fs = α SU(3) ( ce iγ P uce iγ a + κb), A (B 0 K 0 K 0 K 0 ) fs = α SU(3) ( P uce iγ + a). Parameter counting for 5 modes (and 4 modes) 5 magnitudes + 4 relative strong phases + γ + α SU(3) 11 (10) theoretical parameters. Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

36 Observables From the extracted the amplitudes of the 5 (4) modes we can construct observables X = M fs 2 + M fs 2 Effective branching ratio averaged on flavour Parameter counting for 5 modes (and 4 modes) X is available for all modes: 5 (4) parameters Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

37 Observables From the extracted the amplitudes of the 5 (4) modes we can construct observables X = M fs 2 + M fs 2 Y = M fs 2 M fs 2 Effective branching ratio averaged on flavour Direct CP asymmetry Parameter counting for 5 modes (and 4 modes) X is available for all modes: 5 (4) parameters Y is available for all modes: 5 (4) parameters Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

38 Observables From the extracted the amplitudes of the 5 (4) modes we can construct observables X = M fs 2 + M fs 2 Y = M fs 2 M fs 2 Z = Im[M M fs ] fs Effective branching ratio averaged on flavour Direct CP asymmetry Indirect CP asymmetry Parameter counting for 5 modes (and 4 modes) X is available for all modes: 5 (4) parameters Y is available for all modes: 5 (4) parameters Z is available for self-conjugate modes: 3 parameters Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

39 Observables From the extracted the amplitudes of the 5 (4) modes we can construct observables X = M fs 2 + M fs 2 Y = M fs 2 M fs 2 Z = Im[M M fs ] fs Effective branching ratio averaged on flavour Direct CP asymmetry Indirect CP asymmetry Parameter counting for 5 modes (and 4 modes) X is available for all modes: 5 (4) parameters Y is available for all modes: 5 (4) parameters Z is available for self-conjugate modes: 3 parameters 13 (11) observables. Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

40 Observables From the extracted the amplitudes of the 5 (4) modes we can construct observables X = M fs 2 + M fs 2 Y = M fs 2 M fs 2 Z = Im[M M fs ] fs Effective branching ratio averaged on flavour Direct CP asymmetry Indirect CP asymmetry Parameter counting for 5 modes (and 4 modes) X is available for all modes: 5 (4) parameters Y is available for all modes: 5 (4) parameters Z is available for self-conjugate modes: 3 parameters 13 (11) observables. With 11 (10) theoretical parameters and 13 (11) observables γ can be extracted from a fit. Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

41 Extraction of γ from a single point in phase space Likelihood scan on γ with a single point on the DP Pick a point amplitudes observables combination. Fix γ to consecutive values and minimise χ 2, floating the other parameters (a, b...). 11 theoretical parameters and 13 observables covariance matrix. Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

42 Extraction of γ from a single point in phase space Likelihood scan on γ with a single point on the DP Pick a point amplitudes observables combination. Fix γ to consecutive values and minimise χ 2, floating the other parameters (a, b...). χ NOT REAL DATA γ [rad] 11 theoretical parameters and 13 observables covariance matrix. Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

43 Extraction of γ from a single point in phase space Likelihood scan on γ with a single point on the DP Pick a point amplitudes observables combination. Fix γ to consecutive values and minimise χ 2, floating the other parameters (a, b...). χ NOT REAL DATA γ [rad] 11 theoretical parameters and 13 observables covariance matrix. Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

44 Extraction of γ from a single point in phase space Likelihood scan on γ with a single point on the DP Pick a point amplitudes observables combination. Fix γ to consecutive values and minimise χ 2, floating the other parameters (a, b...). χ NOT REAL DATA γ [rad] 11 theoretical parameters and 13 observables covariance matrix. Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

45 Extraction of γ from a single point in phase space Likelihood scan on γ with a single point on the DP Pick a point amplitudes observables combination. Fix γ to consecutive values and minimise χ 2, floating the other parameters (a, b...). χ NOT REAL DATA γ [rad] 11 theoretical parameters and 13 observables covariance matrix. Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

46 Extraction of γ from a single point in phase space Likelihood scan on γ with a single point on the DP Pick a point amplitudes observables combination. Fix γ to consecutive values and minimise χ 2, floating the other parameters (a, b...). χ NOT REAL DATA etc... Prefered value of γ γ [rad] 11 theoretical parameters and 13 observables covariance matrix. Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

47 Extraction of γ from a set of N correlated points Similar method. (11N 1) theoretical parameters and 13N observables. (13N 13N) covariance matrix, contains the correlations between the different points. Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

48 Extraction of γ from a set of N correlated points Similar method. The more points we add, the larger the covariance matrix becomes. (11N 1) theoretical parameters and 13N observables. (13N 13N) covariance matrix, contains the correlations between the different points. Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

49 Extraction of γ from a set of N correlated points Similar method. The more points we add, the larger the covariance matrix becomes. (11N 1) theoretical parameters and 13N observables. (13N 13N) covariance matrix, contains the correlations between the different points. The result depends on the choice of points Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

50 Choice of points on the Dalitz plane In theory, we can extract γ using as many points as we want on Dalitz plane. In practice, the number of points is limited because of large correlations between points that make the covariance matrix singular. Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

51 Choice of points on the Dalitz plane In theory, we can extract γ using as many points as we want on Dalitz plane. In practice, the number of points is limited because of large correlations between points that make the covariance matrix singular. Pathological example corr = Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

52 Choice of points on the Dalitz plane In theory, we can extract γ using as many points as we want on Dalitz plane. In practice, the number of points is limited because of large correlations between points that make the covariance matrix singular. Pathological example corr = We found that the maximum number of points we can use is 3. Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

53 Symmetrisation methods ] 2 [GeV s Figure: Symmetrisation 1 example. s 13 2 [GeV ] Figure: Kinematic boundaries of the different modes. Symmetrisation method 1: with invariant masses A fs = A(s 13, s 23 ) Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

54 Symmetrisation methods ] 2 [GeV s Figure: Symmetrisation 1 example. s 13 2 [GeV ] Figure: Kinematic boundaries of the different modes. Symmetrisation method 1: with invariant masses A fs = A(s 13, s 23 )+A(s 23, s 13 ) + A(s 12, s 23 ) + A(s 23, s 12 ) + A(s 13, s 12 ) + A(s 12, s 23 ) Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

55 Symmetrisation methods ] 2 [GeV s Figure: Symmetrisation 1 example. s 13 2 [GeV ] Figure: Kinematic boundaries of the different modes. Symmetrisation method 1: with invariant masses A fs = 1 6 (A(s 13, s 23 )+A(s 23, s 13 ) + A(s 12, s 23 ) + A(s 23, s 12 ) + A(s 13, s 12 ) + A(s 12, s 23 )) Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

56 Symmetrisation methods Helicity angle Use cos θ ij instead of s ij as parameters. The cos θ ij = f (s 12, s 23, s 13 ). With this set of parameters all the planes size the same. Figure: For the decay B abc, θ ab is the angle between a and c in the rest frame of a and b Symmetrisation method 2: with helicity angles A fs A(c 21, c 23, c 31 ) + A(c 23, c 21, c 13 ) + A(c 12, c 31, c 23 ) + A(c 32, c 13, c 21 ) + A(c 31, c 12, c 32 ) + A(c 13, c 32 c 12 ) Notice that c ij = cos θ ij = c ji Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

Symmetrisation method 2: with helicity angles A fs A(c 21, c 23, c 31 ) + A(c 23, c 21, c 13 ) + A(c 12, c 31, c 23 ) + A(c 32, c

57 Symmetrisation methods Figure: Jacobian of the transformation (s 13, s 23 ) (c 12, c 23 ) for K S K S K S. Figure: Representation of the symmetrised K S K S K S plane in terms of cosine helicity angles using symmetrisation 2. Symmetrisation method 2: with helicity angles A fs A(c 21, c 23, c 31 ) + A(c 23, c 21, c 13 ) + A(c 12, c 31, c 23 ) + A(c 32, c 13, c 21 ) + A(c 31, c 12, c 32 ) + A(c 13, c 32 c 12 ) Notice that c ij = cos θ ij = c ji Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

58 Results: 4 modes, symmetrisation 1 γ extracted from 201 random 3-points combinations with full correlations using symmetrisation 1 #evts γ scan minima Minima Entries 1366 Mean Std Dev γ [deg] min Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

59 Results: 4 modes, symmetrisation 1 γ extracted from 201 random 3-points combinations with full correlations using symmetrisation 1 #evts γ scan minima Minima Entries 1366 Mean Std Dev γ [deg] min Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

60 Results: 4 modes, symmetrisation 1 γ extracted from 201 random 3-points combinations with full correlations using symmetrisation 1 #evts γ scan minima Minima Entries 1366 Mean Std Dev minima γ [ ] γ [deg] min Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

61 Results: 4 modes, symmetrisation 1 γ extracted from 201 random 3-points combinations with full correlations using symmetrisation 1 #evts Compatible with γ from trees: γ scan minima Minima Entries 1366 Mean Std Dev minima γ [ ] γ [deg] min Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

62 Contents 1 General introduction 2 Study of a method of extraction of the CKM-angle γ 3 Dalitz-plot analysis of B 0 K 0 SK + K Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

63 Introduction The LPNHE group is involved in studies of B 0 d,s K S hh (h = π, K) Measurement of BF(Bd,s 0 K S h + h ) with 3 fb 1 of Run 1 data. Time-independent, untagged, Dalitz-plot analysis of B 0 KSK 0 + K. Louis Henry s thesis Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

64 Measured branching fractions with 3fb 1 of data BF(B 0 d,s K S h + h ) Paper arxiv: v1, accepted on JHEP 6 modes 3 spectra Measured relative to B 0 K 0 Sπ + π B 0 s modes measured for the 1st time in LHCb: all modes observed except B 0 K 0 SK + K ( 3σ) Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

65 Dalitz-plot analysis of B 0 K 0 SK + K Reference resonance model from BaBar. Resonance Lineshape mass (MeV) width (MeV) φ(1020) RBW ± ± 0.04 gk f0(980) Flatté 965± 10 = 4.12 ± 0.33 gπ f0(1500) RBW 1505±6 109± 7 f 2(1525) RBW 1720± 6 135± 8 f0(1710) RBW 1525± χc0 RBW ± ± 0.6 NR(S-wave) 2nd order polynomial - - NR(P-wave) 2nd order polynomial - - Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

66 Dalitz-plot analysis of B 0 K 0 SK + K Reference resonance model from BaBar fits to data with randomised initial values of parameters. Add/remove contributions depending on the likelihood and goodness of fit. Resonance Lineshape mass (MeV) width (MeV) φ(1020) RBW ± ± 0.04 gk f0(980) Flatté 965± 10 = 4.12 ± 0.33 gπ f0(1500) RBW 1505±6 109± 7 f 2(1525) RBW 1720± 6 135± 8 f0(1710) RBW 1525± χc0 RBW ± ± 0.6 NR(S-wave) 2nd order polynomial - - NR(P-wave) 2nd order polynomial - - Louis thesis results Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

67 Dalitz-plot analysis of B 0 K 0 SK + K Reference resonance model from BaBar fits to data with randomised initial values of parameters. Add/remove contributions depending on the likelihood and goodness of fit. Resonance Lineshape mass (MeV) width (MeV) φ(1020) RBW ± ± 0.04 gk f0(980) Flatté 965± 10 = 4.12 ± 0.33 gπ f0(1500) RBW 1505±6 109± 7 f 2(1525) RBW 1720± 6 135± 8 f0(1710) RBW 1525± χc0 RBW ± ± 0.6 NR(S-wave) 2nd order polynomial - - NR(P-wave) 2nd order polynomial - - Multiple soutions! isobar contribution Louis thesis results FF in % Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

68 Analysis in progress Previous analysis: Multiple solutions implying several isobar parameters. Yields similar to B-factories but not better. Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

69 Analysis in progress Previous analysis: Multiple solutions implying several isobar parameters. Yields similar to B-factories but not better. How can we improve the results? Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

70 Analysis in progress Previous analysis: Multiple solutions implying several isobar parameters. Yields similar to B-factories but not better. How can we improve the results? Use more data (we already doubled the dataset). Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

71 Analysis in progress Previous analysis: Multiple solutions implying several isobar parameters. Yields similar to B-factories but not better. How can we improve the results? Use more data (we already doubled the dataset). Use tagging information. Tagging information may reduce ambiguities and so the number of solutions. Gain in sensitivity. Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

72 Analysis in progress Previous analysis: Multiple solutions implying several isobar parameters. Yields similar to B-factories but not better. How can we improve the results? Use more data (we already doubled the dataset). Use tagging information. Include more contributions to the model. Tagging information may reduce ambiguities and so the number of solutions. Gain in sensitivity. LHCb has better sensitivity in some regions of the Dalitz plane than B-factories. Add resonances in these regions. Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

73 Adding components Study the effect of adding a new resonance to the model that could model the NR (P wave): a 0 (980) (isospin triplet). Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

74 Adding components Study the effect of adding a new resonance to the model that could model the NR (P wave): a 0 (980) (isospin triplet). Fits to data using various models 1 BaBar model. 2 Baseline model (BaBar with simplified NR P-wave). 3 Baseline model + a 0 0(980) + no NR P-wave. 4 Baseline resonances + a 0 0(980) + flat NR. 5 Baseline resonances - f 0 (1710) + a 0 0(980) + flat NR. For each of the above models we used the fit results for the isobar parameters to generate signal-only toys. Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

75 Adding components 2. Baseline 1. BaBar 3. a00 (980), no NR-P Emilie Bertholet (LPNHE) 4. a00 (980), Flat NR 3-body charmless B decays 5. Idem 4. without f0 (1710) November 17, / 31

76 Adding components 2. Baseline 1. BaBar a00 (980) imitates the P-wave (to some extent) 3. a00 (980), no NR-P Emilie Bertholet (LPNHE) 4. a00 (980), Flat NR 3-body charmless B decays 5. Idem 4. without f0 (1710) November 17, / 31

77 Fit results with the different models Summary of tested models model number of resonances varying parameters minimum NLL number of solutions BaBar Baseline a 0 0 (980) without PolNR_P a0 0 (980) with Flat NR a0 0 (980) with Flat NR without f0(1710) Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

78 Fit results with the different models Summary of tested models model number of resonances varying parameters minimum NLL number of solutions BaBar Baseline a 0 0 (980) without PolNR_P a0 0 (980) with Flat NR a0 0 (980) with Flat NR without f0(1710) The addition a 0 0 (980) decreases the number of solutions. Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

79 Fit results with the different models Summary of tested models model number of resonances varying parameters minimum NLL number of solutions BaBar Baseline a 0 0 (980) without PolNR_P a0 0 (980) with Flat NR a0 0 (980) with Flat NR without f0(1710) The addition a 0 0 (980) decreases the number of solutions. Fit fractions (in %) φ(1020) f0(980) f0(1500) f 2(1525) f0(1710) χc0 PolNR_S0 PolNR_S1 PolNR_S2 a 0 0 (980) φ(1020) f0(980) f0(1500) f 2(1525) f0(1710) χc PolNR_S PolNR_S PolNR_S a0 0 (980) Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

80 Fit results with the different models Summary of tested models model number of resonances varying parameters minimum NLL number of solutions BaBar Baseline a 0 0 (980) without PolNR_P a0 0 (980) with Flat NR a0 0 (980) with Flat NR without f0(1710) The addition a 0 0 (980) decreases the number of solutions. Fit fractions (in %) φ(1020) f0(980) f0(1500) f 2(1525) f0(1710) χc0 PolNR_S0 PolNR_S1 PolNR_S2 a 0 0 (980) φ(1020) f0(980) f0(1500) f 2(1525) f0(1710) χc PolNR_S PolNR_S PolNR_S a0 0 (980) The addition a 0 0 (980) increases (much) f 0 (980) fit fraction. Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

$Results are encouraging: statistical error (using only input from BaBar) at the level of < 10 Experimental aspects of B physics: B 0 KS0 K + K Work on the amplitude analysis and branching fraction$

81 Conclusion Phenomenological part: measurement of γ in charmless B decays Close to be finalised (article in preparation) Found 6 solutions for γ, one is compatible with that from tree-dominated decays Results are encouraging: statistical error (using only input from BaBar) at the level of < 10 Experimental aspects of B physics: B 0 KS0 K + K Work on the amplitude analysis and branching fraction measurement in progress Adding more data and using more sophisticated methods and models we hope to: obtain a first observation of Bs0 KS0 K + K decays gain sensitivity to more observables in the amplitude analysis Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 31

83 BACKUP Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 7

84 B K S hh diagrams Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 7

85 Measuring γ with B DK processes Super clean: loop diagrams contribution O(10 7 ) 2 competing diagrams with relative phase θ and suppression factor r B Γ 1 + r B e iθ 2 = 1 + 2r B cos(θ) Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 7

86 Error propagation and χ 2 function Covariance matrix of the observables: V XYZ V XYZ (s 1, s 2 ) = G T (s 1, s 2 ) V a G(s 1, s 2 ) G(s 1, s 2 ): matrix of the derivatives of the isobar parameters V a : covariance matrix of the isobar parameters Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 7

87 Error propagation and χ2 function Covariance matrix of the observables: VXYZ VXYZ (s1, s2 ) = G T (s1, s2 ) Va G(s1, s2 ) G(s1, s2 ): matrix of the derivatives of the isobar parameters Va : covariance matrix of the isobar parameters Covariance matrix of 2 points A and B VXYZ (s1a, s2a ; s1b, s2b ) = G T (s1a, s2a ; s1b, s2b ) Va G(s1A, s2a ; s1b, s2b ). Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, /7

88 Error propagation and χ2 function Covariance matrix of the observables: VXYZ VXYZ (s1, s2 ) = G T (s1, s2 ) Va G(s1, s2 ) G(s1, s2 ): matrix of the derivatives of the isobar parameters Va : covariance matrix of the isobar parameters Covariance matrix of 2 points A and B VXYZ (s1a, s2a ; s1b, s2b ) = G T (s1a, s2a ; s1b, s2b ) Va G(s1A, s2a ; s1b, s2b ). χ2 function 1 X χ2 = X T VXYZ exp th Xmode1 Xmode1 exp th Y Ymode1 X = mode1... Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, /7

89 Error propagation and χ2 function Covariance matrix of the observables: VXYZ VXYZ (s1, s2 ) = G T (s1, s2 ) Va G(s1, s2 ) G(s1, s2 ): matrix of the derivatives of the isobar parameters Va : covariance matrix of the isobar parameters Covariance matrix of 2 points A and B VXYZ (s1a, s2a ; s1b, s2b ) = G T (s1a, s2a ; s1b, s2b ) Va G(s1A, s2a ; s1b, s2b ). χ2 function exp th Xmode1 Xmode1 exp th Y Ymode1 X = mode1 1 X χ2 = X T VXYZ We need to compute the inverse of VXYZ Emilie Bertholet (LPNHE) 3-body charmless B decays... November 17, /7

90 Isobar model in more details Fj L N (s 12,s 23 ) {}}{ A (s 12, s 23 ) = c j e iθ j R j (m)x L ( p )X L ( q )T j (L, p, q) j=1 R j (m) is the resonance mass term (also called lineshape). m is the invariant mass of the decay products of the resonance. Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 7

91 Isobar model in more details Fj L N (s 12,s 23 ) {}}{ A (s 12, s 23 ) = c j e iθ j R j (m)x L ( p )X L ( q )T j (L, p, q) j=1 R j (m) is the resonance mass term (also called lineshape). m is the invariant mass of the decay products of the resonance. X L are Blatt-Weisskopf angular momentum barrier factors. T j are the Zemach tensors which describe the angular distributions. L is the spin of the resonance. p is the momentum of the bachelor particle (the particle not belonging to the resonance) evaluated in the rest frame of the B meson. p and q are the momenta of the bachelor particle and one of the resonance daughters, respectively, both evaluated in the rest frame of the resonance. Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 7

92 Fit fractions The fit fractions are defined the by following equation DP FF j ( M j(s 1, s 2 ) 2 + M j (s 1, s 2 ) 2 )ds 1 ds 2 DP ( M (s 1, s 2 ) 2 + M (s 1, s 2 ) 2 )ds 1 ds 2 The interference fit fractions quantify the interferences between different states. They are given by DP FF jk 2Re (M j(s 1, s 2 )Mk (s 1, s 2 ) + M j (s 1, s 2 ) M k (s 1, s 2 ))ds 1 ds 2 DP ( M (s 1, s 2 ) 2 + M (s 1, s 2 ) 2 )ds 1 ds 2 With these definitions FF j + FF jk = 1 j j<k Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 7

93 Measured branching fractions with 3fb 1 of data Emilie Bertholet (LPNHE) 3-body charmless B decays November 17, / 7

Introduction to Dalitz-plot

Introduction to Dalitz-plot Gagan Mohanty Student Seminar @ TIFR January 7, 01 Few Diversions Hierarchical expansion of CKM (1983) + O( 4) magnitudes d s b phases d s b u c t u c t 3 A triangle at the