Analysis of the charmless decay B 0 in the LHCb experiment Diego - PowerPoint PPT Presentation

CKM matrix and α with B 0 → ρπ decays Experimental context Selection of B 0 → ρπ decays D 0 → K − π + π 0 studies Analysis of the charmless decay B 0 → ρπ in the LHCb experiment Diego Alejandro Roa Romero O. Deschamps, R. Lef` evre, P. Perret Laboratoire de Physique Corpusculaire - Universit´ e Blaise Pascal December 2011 Analysis of the charmless decay B 0 → ρπ in the LHCb experiment Diego Roa 1

CKM matrix and α with B 0 → ρπ decays Experimental context Selection of B 0 → ρπ decays D 0 → K − π + π 0 studies Contents CKM matrix and α with B 0 → ρπ decays 1 Experimental context 2 Selection of B 0 → ρπ decays 3 D 0 → K − π + π 0 studies 4 Analysis of the charmless decay B 0 → ρπ in the LHCb experiment Diego Roa 2

CKM matrix and α with B 0 → ρπ decays Experimental context Selection of B 0 → ρπ decays D 0 → K − π + π 0 studies Quarks in the Standard Model In the Standard Model, we find six quarks coming in three generations: u c t d s b These are the mass eigenstates composing the hadrons (valence quarks), except for the top quark which weakly decays before hadronizing As the weak interaction eigenstates are different from the mass eigenstates, the W bosons couple quarks of different generations Analysis of the charmless decay B 0 → ρπ in the LHCb experiment Diego Roa 3

CKM matrix and α with B 0 → ρπ decays Experimental context Selection of B 0 → ρπ decays D 0 → K − π + π 0 studies CKM matrix The transformation from the mass eigenstates basis ( q ) to the weak interaction one ( q ′ ) can be represented by a 3 × 3 unitary matrix, the Cabbibo-Kobayashi-Maskawa matrix: d ′       V ud V us V ub d  = s ′ V cd V cs V cb s      b ′ V td V ts V tb b +− W The weak coupling between two mass eigenstates ( ij ) then q i V ij depends on the matrix element V ij of the CKM matrix. q j Analysis of the charmless decay B 0 → ρπ in the LHCb experiment Diego Roa 4

CKM matrix and α with B 0 → ρπ decays Experimental context Selection of B 0 → ρπ decays D 0 → K − π + π 0 studies Unitary Triangle Unitarity implies that the matrix elements satisfy � V ij V ∗ jk = δ ik ∀ i , k = 1 , 2 , 3 j We are particularly interested in one of those relations V cd V ∗ cb + V td V ∗ tb + V ud V ∗ ub = 0 η The representation of this relation in the complex plane is a triangle. The * * V V V td V ud ub tb α * * V V V cd V cb angle α is related with CP violation cd cb in B mesons: no CP violation would mean a flat triangle, i.e. α = π . β γ ρ 0 1 Analysis of the charmless decay B 0 → ρπ in the LHCb experiment Diego Roa 5

CKM matrix and α with B 0 → ρπ decays Experimental context Selection of B 0 → ρπ decays D 0 → K − π + π 0 studies Constraints on the unitary triangle Concerning α The combination of the measurements gives: α = (89.0 ± 4 . 4 4 . 2 ) ◦ The global fit, excluding α measurements, gives: α = (92.9 ± 3 . 6 5 . 1 ) ◦ Analysis of the charmless decay B 0 → ρπ in the LHCb experiment Diego Roa 6

CKM matrix and α with B 0 → ρπ decays Experimental context Selection of B 0 → ρπ decays D 0 → K − π + π 0 studies b → u transitions To measure α we have to use decays involving b → u transitions: � − V td V ∗ � tb α = arg V ud V ∗ ub In these processes the main contributions come from diagrams at tree level of weak origin and penguin diagrams involving QCD and weak factors: d d d d _ { } { } 0 0 B B π 0 π W u b d b u,c,t g W u } } + ρ 0 d ρ u u Analysis of the charmless decay B 0 → ρπ in the LHCb experiment Diego Roa 7

CKM matrix and α with B 0 → ρπ decays Experimental context Selection of B 0 → ρπ decays D 0 → K − π + π 0 studies Decay channels The channels involving b → u transitions are B 0 → ππ , B 0 → ρπ and B 0 → ρρ (branching ratios between 7 · 10 − 7 and 2.4 · 10 − 5 ) We focus on B 0 → ρπ → π + π − π 0 which should lead to the best experimental sensitivity We will see in the following slides: how the decay amplitudes can be written in terms of α , how the phase space can be expressed, how the time evolution of a | B 0 > state can be written according to B 0 − ¯ B 0 mixing, and finally how to extract α . Analysis of the charmless decay B 0 → ρπ in the LHCb experiment Diego Roa 8

CKM matrix and α with B 0 → ρπ decays Experimental context Selection of B 0 → ρπ decays D 0 → K − π + π 0 studies Decay amplitude We can express the total amplitude of B 0 → π + π − π 0 as the combination of the amplitudes of B 0 → π + − 0 ρ − +0 Factorizing the penguin and tree parts, the amplitudes can be expressed as A j = V ∗ ub V ud T j − V ∗ tb V td P j where “ j ” represents the decay to ρ + π − , ρ − π + or ρ 0 π 0 In terms of α e i β A j = e − i α T j − P j Isospin decomposition leads to − 1 P + − + P − + � � = P 00 2 Analysis of the charmless decay B 0 → ρπ in the LHCb experiment Diego Roa 9

CKM matrix and α with B 0 → ρπ decays Experimental context Selection of B 0 → ρπ decays D 0 → K − π + π 0 studies B 0 → 3 π amplitude The total amplitude A 3 π of the B 0 → 3 π decay is � f j A j A 3 π = i The factors f j account both for pure form factors and the angular distributions associated to the spin of the ρ vector meson This point is very important and determines the way α will be extracted Analysis of the charmless decay B 0 → ρπ in the LHCb experiment Diego Roa 10

CKM matrix and α with B 0 → ρπ decays Experimental context Selection of B 0 → ρπ decays D 0 → K − π + π 0 studies Parametrization of the phase space Initially, there are 12 degrees of freedom corresponding to the 4-momentums of the 3 pions 4-momentum conservation between the initial B meson and the decay products imposes 4 relations The nature of the decay products being known, their invariant masses give 3 more relations As the B meson is a scalar, the orientation of the decay plane is isotropic and any choice of the 3 Euler angles is equivalent The phase space can then be represented by only 2 parameters: s + = m 2 π + π 0 , s − = m 2 π − π 0 and the factors f j can be expressed as functions of s + and s − Analysis of the charmless decay B 0 → ρπ in the LHCb experiment Diego Roa 11

CKM matrix and α with B 0 → ρπ decays Experimental context Selection of B 0 → ρπ decays D 0 → K − π + π 0 studies B 0 − ¯ B 0 mixing We can describe the B 0 system by the flavour eigenstates | B 0 > = | ¯ B 0 > = | b ¯ bd > and | ¯ d > that can be written as linear combinations of the mass eigenstates: p | B 0 > + q | ¯ B 0 > | B L > = p | B 0 > − q | ¯ B 0 > | B H > = with | p | 2 + | q | 2 = 1 The time evolution of a | B 0 > state, prepared as such at t = 0, is given by (the formula for ¯ B 0 ( t ) is similar) � � ∆ mt � | B 0 > + i p � ∆ mt � � B 0 > | B 0 ( t ) > = e − imt e − Γ t | ¯ 2 × cos q sin 2 2 with: m = ( M H + M L ) / 2, ∆ m = M H − M L and Γ = (Γ H + Γ L ) / 2 assuming: ∆Γ = ∆Γ H − Γ L << Γ and ∆ m Analysis of the charmless decay B 0 → ρπ in the LHCb experiment Diego Roa 12

CKM matrix and α with B 0 → ρπ decays Experimental context Selection of B 0 → ρπ decays D 0 → K − π + π 0 studies Amplitude distribution The decay amplitude distribution as a function of phase space and proper time can be expressed as (here for an initial B 0 ) e − Γ t / 2 cos (∆ mt M ( t , s + , s − ) ) A 3 π ( s + , s − ) = 2 psin (∆ mt ie − Γ t / 2 q )¯ A 3 π ( s + , s − ) + 2 π π - π + 0 MonteCarlo Dalitz Plot for B to d × 6 10 30 - s The distribution as a function of 25 ( s + ; s − ) is called a Dalitz plot 20 The strategy to extract α is to fit 15 the time dependent Dalitz plot 10 obtained on flavour tagged (initial 5 B 0 or initial ¯ B 0 ) decays × 6 10 0 0 5 10 15 20 25 30 + s Analysis of the charmless decay B 0 → ρπ in the LHCb experiment Diego Roa 13

CKM matrix and α with B 0 → ρπ decays Experimental context Selection of B 0 → ρπ decays D 0 → K − π + π 0 studies Example of time dependent Dalitz plots Example of Dalitz plots for an initial B 0 and various ranges of proper time: 0 < t < 3ps 3ps < t < 6ps 1800 1600 300 1400 250 1200 200 1000 800 150 600 100 400 50 200 0 0 30 30 s - 25 s - 25 × 10 6 × 10 6 20 20 15 30 15 30 25 25 10 20 + 10 20 + 15 s 15 s 5 10 5 10 5 5 0 0 0 0 6ps < t < 9ps 9ps < t < 12ps 60 7 50 6 5 40 4 30 3 20 2 10 1 0 0 30 30 s - 25 s - 25 × 10 6 × 10 6 20 20 30 30 15 15 25 25 + + 10 20 10 20 15 s 15 s 5 10 5 10 5 5 0 0 0 0 Analysis of the charmless decay B 0 → ρπ in the LHCb experiment Diego Roa 14

CKM matrix and α with B 0 → ρπ decays Experimental context Selection of B 0 → ρπ decays D 0 → K − π + π 0 studies The Large Hadron Collider pp collisions √ s = 7 TeV 1.1 fb − 1 recorded in LHCb in 2011 Analysis of the charmless decay B 0 → ρπ in the LHCb experiment Diego Roa 15