Determining the photon polarization of the b → s γ using the B → K 1 ( 1270 ) γ → ( K ππ ) γ decay Andrey Tayduganov 1 , 2 Andrey.Tayduganov@th.u-psud.fr in collaboration with Emi Kou 1 and Alain Le Yaouanc 2 1 Laboratoire de l’Accélérateur Linéaire (LAL) 2 Laboratoire de Physique Théorique (LPT) Université Paris-Sud 11, France Osaka University, 1 November 2011 1 / 28
Outline Introduction: the b → s γ process and the photon polarization 1 The B → K 1 γ decay and polarization measurement 2 Basic idea and formalism Determination of λ γ in the DDLR method Strong interaction decays of the K 1 -mesons 3 Theoretical model Numerical results Sensitivity studies of λ γ measurement in the DDLR method 4 Statistical errors Theoretical uncertainties Future prospects of the photon polarization measurement 5 New Physics constraints combining various methods Conclusions and perspectives 6 2 / 28
Outline Introduction: the b → s γ process and the photon polarization 1 The B → K 1 γ decay and polarization measurement 2 Basic idea and formalism Determination of λ γ in the DDLR method Strong interaction decays of the K 1 -mesons 3 Theoretical model Numerical results Sensitivity studies of λ γ measurement in the DDLR method 4 Statistical errors Theoretical uncertainties Future prospects of the photon polarization measurement 5 New Physics constraints combining various methods Conclusions and perspectives 6 3 / 28
The b → s γ process and the photon polarization FCNC processes In the SM, Flavour Changing Neutral Current (FCNC) processes are forbidden at tree level. γ, Z u L γ µ d L W + µ → u ′ L U u † L U d d ′ L W + L µ Forbidden! | {z } V CKM s b ′ d L γ µ d L Z µ → d L U d † L U d d ′ L Z µ L | {z } 1 4 / 28
The b → s γ process and the photon polarization FCNC processes In the SM, Flavour Changing Neutral Current (FCNC) processes are forbidden at tree level. γ, Z u L γ µ d L W + µ → u ′ L U u † L U d d ′ L W + L µ Forbidden! | {z } V CKM s b ′ d L γ µ d L Z µ → d L U d † L U d d ′ L Z µ L | {z } 1 They can proceed only via loops. u , c , t γ R A µ X s ′ L σ µν q ν b ′ V ∗ W is V ib F 2 ( m i ) s b i = u , c , t large F 2 ( m t ) ⇒ B ( B → X s γ ) exp = ( 3 . 55 ± 0 . 24 ± 0 . 09 ) × 10 − 4 ( [HFAG(’10)] ) B → X s γ is sensitive to the effects of new physics beyond the SM 4 / 28
The b → s γ process and the photon polarization Why are we interested in measuring the photon polarization of b → s γ ? γ SM W s b V − A V − A 16 π 2 s σ µν q ν “ ” M ( b → s γ ) SM = 4 G F e m b 1 + γ 5 + m s 1 − γ 5 V ∗ b ε µ ∗ √ ts V tb F 2 2 2 2 | {z } | {z } b R → s L γ L b L → s R γ R In the SM, since m s / m b ≃ 0 . 02 ≪ 1, photons are predominantly left(right)-handed in the B ( B ) -decays. 5 / 28
The b → s γ process and the photon polarization Why are we interested in measuring the photon polarization of b → s γ ? ( δ d γ γ R SM NP RL ) 23 + ˜ s R ˜ b L W s s R b b L V − A V − A g ˜ 16 π 2 s σ µν q ν “ ” M ( b → s γ ) SM = 4 G F e m b 1 + γ 5 + m s 1 − γ 5 V ∗ b ε µ ∗ √ ts V tb F 2 2 2 2 | {z } | {z } b R → s L γ L b L → s R γ R In the SM, since m s / m b ≃ 0 . 02 ≪ 1, photons are predominantly left(right)-handed in the B ( B ) -decays. NP can induce new Dirac structures and lead to an excess of right(left)-handed photons, without contradicting with the measured B ( B → X s γ ) . ⇒ The measurement of the photon polarization could provide a test of physics beyond the SM, namely right-handed currents. 5 / 28
Photon polarization determination: 3 methods There are 3 methods proposed to measure the ratio M R / M L ( ≃ 0 in the SM): Method 1: time-dependent CP asymmetry in B 0 → K ∗ 0 ( → K S π 0 ) γ 1 [Atwood et al., Phys.Rev.Lett.79 (’97)] 2 |M L M R | S f γ = − ξ f |M L | 2 + |M R | 2 sin ( φ M − φ L − φ R ) Method 2: transverse asymmetries in B 0 → K ∗ 0 ( → K − π + ) ℓ + ℓ − 2 [Kruger&Matias, Phys.Rev.D71 (’05); Becirevic&Schneider, arXiv:1106.3283 (’11)] Re [ M R M ∗ Im [ M R M ∗ L ] L ] A ( 2 ) A ( im ) T = − |M R | 2 + |M L | 2 , = |M R | 2 + |M L | 2 T Method 3: K 1 three-body decay method in B → K 1 ( → K ππ ) γ [Gronau 3 et al., Phys.Rev.Lett.88, Phys.Rev.D66 (’02)] λ γ = |M R | 2 − |M L | 2 |M R | 2 + |M L | 2 6 / 28
Outline Introduction: the b → s γ process and the photon polarization 1 The B → K 1 γ decay and polarization measurement 2 Basic idea and formalism Determination of λ γ in the DDLR method Strong interaction decays of the K 1 -mesons 3 Theoretical model Numerical results Sensitivity studies of λ γ measurement in the DDLR method 4 Statistical errors Theoretical uncertainties Future prospects of the photon polarization measurement 5 New Physics constraints combining various methods Conclusions and perspectives 6 7 / 28
The B → K 1 γ decay and polarization measurement How to measure the polarization: basic idea The angular distribution of the three-body decay of K res in B → K res γ decay provides a direct determination of the K res ( ⇔ γ ) polarization [Gronau et al., Phys.Rev.Lett.88 (’02)] . NO helicity information 2 → 3-body K K ∗ B B K K ∗ γ γ z K 1 z π π π symmetric 8 / 28
The B → K 1 γ decay and polarization measurement How to measure the polarization: basic idea The angular distribution of the three-body decay of K res in B → K res γ decay provides a direct determination of the K res ( ⇔ γ ) polarization [Gronau et al., Phys.Rev.Lett.88 (’02)] . NO helicity information 2 → 3-body K K ∗ B B K K ∗ γ γ z K 1 z π π π symmetric There are two known K 1 ( 1 + ) states, decaying into K ππ final state via K ∗ π and ρ K modes: K 1 ( 1270 ) and K 1 ( 1400 ) . One of the decay channels B → K 1 γ , namely B + → K + 1 ( 1270 ) γ , is finally measured ( B = ( 4 . 3 ± 1 . 2 ) × 10 − 5 ), while B + → K + 1 ( 1400 ) γ is suppressed ( B < 1 . 5 × 10 − 5 ) [Belle, Phys.Rev.Lett.94 (’05)] . We investigate the feasibility of determining the photon polarization using the B → K 1 ( 1270 ) γ channel. 8 / 28
The B → K 1 γ decay and polarization measurement Formalism The decay distribution of B → K 1 γ → ( K ππ ) γ is given by the master formula: ds 13 ds 23 d cos θ ∝ 1 d Γ J | 2 ( 1 + cos 2 θ ) + λ γ 1 4 | � n · ( � J × � J ∗ )] cos θ 2 Im [ � λ γ = |M R | 2 − |M L | 2 |M R | 2 + |M L | 2 ≃ − 1 (+ 1 ) in the SM for B ( B ) respectively � J = C 1 ( s 13 , s 23 ) � p 1 − C 2 ( s 13 , s 23 ) � p 2 � p 1 × � ⇔ K 1 -decay helicity amplitude. z p 2 π ( � p 2 ) � n = | � p 1 × � p 2 | ; θ Since the final state interactions ; K ( � p 3 ) n · ( � J × � J ∗ ) is break T -parity and � T -odd, the amplitude must involve a ; y strong phase, coming from the x interference of at least 2 amplitudes. π ( � p 1 ) γ 9 / 28
Determination of λ γ in the DDLR method New method The decay distribution of B → K 1 γ → ( K ππ ) γ is given by the master formula: ds 13 ds 23 d cos θ ∝ 1 d Γ J | 2 ( 1 + cos 2 θ ) + λ γ 1 4 | � n · ( � J × � J ∗ )] cos θ 2 Im [ � Previous method of Gronau et al. In the original proposal by Gronau et al. , only the θ -dependence on the polarization was considered (up-down asymmetry): R 1 R 0 d Γ d Γ n · ( � J × � J ∗ )] 0 d cos θ d cos θ − − 1 d cos θ 3 R ds 13 ds 23 Im [ � d cos θ A up − down = = λ γ R 1 d Γ ds 13 ds 23 | � J | 2 R − 1 d cos θ 4 d cos θ 10 / 28
Determination of λ γ in the DDLR method New method The decay distribution of B → K 1 γ → ( K ππ ) γ is given by the master formula: ds 13 ds 23 d cos θ ∝ 1 d Γ J | 2 ( 1 + cos 2 θ ) + λ γ 1 4 | � n · ( � J × � J ∗ )] cos θ 2 Im [ � New method: DDLR (Davier, Duflot, Le Diberder, Rougé) In our work, we take into account the Dalitz variable ( s 13 , s 23 ) dependence, which carries the further information of the polarization (it was pointed out in the ALEPH analysis of τ → a 1 ( → πππ ) ν [Davier et al., Phys.Lett.B306 (’93)] ). In this method, we use the quantity, called ω : n · ( � J × � J ∗ )] cos θ ω ( s 13 , s 23 , cos θ ) ≡ 2 Im [ � | � J | 2 ( 1 + cos 2 θ ) [Kou,Le Yaouanc & A.T., Phys.Rev.D83 (’11)] 10 / 28
Determination of λ γ in the DDLR method Basic idea of the DDLR method Our PDF (i.e. the normalized decay width distribution) can be written as n · ( � J × � J ∗ )] cos θ ω ( s 13 , s 23 , cos θ ) ≡ 2 Im [ � W ( s 13 , s 23 , cos θ ) = f ( s 13 , s 23 , cos θ ) | � J | 2 ( 1 + cos 2 θ ) + λ γ g ( s 13 , s 23 , cos θ ) Using the maximum likelihood method, λ γ extraction from ω -distribution we obtain λ γ as a solution of the equation: λ γ = � ω � � ω 2 � N events ∂ ln L ω i X = 1 + λ γ ω i = 0 λ γ = − ∂ 2 ln L „ « 2 ω ∂λ γ σ − 2 = N � � i = 1 ∂λ γ 2 1 + λ γ ω One only has to sum ω and ω 2 over all N events Y W ( s i 13 , s i 23 , cos θ i ) L = the events ⇒ no fit is needed ! i = 1 N events 1 ω i ≡ g ( s i 13 , s i 23 , cos θ i ) / f ( s i 13 , s i 23 , cos θ i ) � ω n � ≡ X ω n i N events i = 1 Notice: resulting solution does not depend on f and g separately but only on their ratio ω . 11 / 28
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