Results On φ 2 From e + e − Colliders Pit Vanhoefer on behalf of the Belle Collaboration Max-Planck-Institut f¨ ur Physik, M¨ unchen BELLE pvanhoef at mpp.mpg.de φ 2 /α : Decays covered in this talk ( ρ , η ) a) B → ππ φ * * * V V ud V ud V V td V | | | | | | ub ub tb 2 * * * cd V cd V b) B → ρρ V V | | | | cd V | | V cb cb cb c) B 0 → ( ρπ ) 0 d) B 0 → a ± φ φ 1 π ∓ 3 1 0 (1,0) φ 2 from e + e − colliders 1 Pit Vanhoefer(MPI) FPCP 2013
Introduction • Measure properties of unitarity triangle to test CKM mechanism: 2 sides, 3 angles • Time-dependent decay rate of a B or a ¯ B meson decaying into common CP eigenstate P (∆ t ) = e −| ∆ t | /τ B 0 � � �� 1 + q S CP sin(∆ m d ∆ t ) + A CP cos(∆ m d ∆ t ) 4 τ B 0 1.5 excluded at CL > 0.95 excluded area has CL > 0.95 φ • A CP : direct CP violation ( = −C CP ) 3 1.0 ∆ ∆ m & m s d φ sin 2 • S CP : mixing induced CP violation 1 0.5 ∆ m d ε • q : flavor of B tag , q = +1 for B tag = B 0 φ K 2 φ φ η 1 0.0 3 φ 2 • τ B 0 : B life time φ V ub 2 -0.5 • ∆ m d : mass difference of B H and B L ε -1.0 K CKM φ • ∆ t : decay time difference of B CP and B tag φ sol. w/ cos 2 < 0 f i t t e r 1 3 Winter 12 (excl. at CL > 0.95) -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 ρ φ 2 from e + e − colliders 2 Pit Vanhoefer(MPI) FPCP 2013
✟ Mixing Induced ✟✟✟✟ CP � V td V ∗ � ✟ • φ 2 = arg CP in b → u transitions, tb accesible through mixing induced ✟ V ub V ∗ ud 0 0 e.g. interference between B → π + π − B f f B CP CP CP 0 0 B B u * —— V mixing induced ud d → ———— + W * V V V ub ub ud u B f CP b d d * V V V * 2 x and B → ¯ V B → π + π − tb td ub ud u * B ր V ud V V d td tb f CP = ρ ρ π π, d t b + W V ub 0 0 B W W B u + b ⇒ at tree level: d d b t d V V S CP = sin(2 φ 2 ) , A CP = 0 tb td φ 2 from e + e − colliders 3 Pit Vanhoefer(MPI) FPCP 2013
Living With Pollution b → u ( ρ , π , ...) at Tree level: S CP = sin(2 φ 2 ) and no direct ✟ CP ( A CP = 0 ) ✟ BUT more amplitudes (penguins) can contribute with different weak/strong phases + W V ub t b u b d * V V tb td u d + W g * V ud d d d d d d ⇒ φ 2 penguin pollution ⇒ ∆ φ 2 , A CP CP sin(2 φ eff � 1 − A 2 ⇒ measured observable φ eff S CP = ) = φ 2 + ∆ φ 2 2 2 with A CP � = 0 possible → extraction of ∆ φ 2 with isospin analysis is possible φ 2 from e + e − colliders 4 Pit Vanhoefer(MPI) FPCP 2013
Recover φ 2 • extraction of ∆ φ 2 with isospin analysis (remove penguin pollution) for unflavored isospin triplets, e.g. ρ, π Bose statistics: ⇒ I=0,2 (final states); A tree I=0,2; 00 penguin: I=0 only (gluon) 1 1 A A +- allows to formulate relations of the A +- 2 00 2 decay amplitudes A ∆ φ 2 A + − = A ( ¯ 2 e.g. ¯ B → ρ + ρ − ) A = A +0 -0 2 A + − + A 00 = A +0 1 • √ A + − + ¯ A 00 = ¯ 2 ¯ 1 A − 0 • √ M. Gronau and D. London, PRL 65 3381 (1990) • A +0 = ¯ A − 0 (no penguin) ⇒ geometrical considerations reveal ∆ φ 2 φ 2 from e + e − colliders 5 Pit Vanhoefer(MPI) FPCP 2013
Data Samples φ 2 from e + e − colliders 6 Pit Vanhoefer(MPI) FPCP 2013
B → π + π − BaBar PRD 87 052009(2013) Belle arXiv:1302.0551 467 × 10 6 B ¯ 772 × 10 6 B ¯ B pairs B pairs 160 160 160 160 Events / ps Events / ps Events / ps Events / ps 140 140 140 140 B A B AR 120 120 120 120 Preliminary Events / (1.5 ps) 100 100 100 100 q = +1 300 80 80 80 80 PRELIMINARY q = -1 60 60 60 60 40 40 40 40 250 20 20 20 20 0 0 0 0 -6 -6 -4 -4 -2 -2 0 0 2 2 4 4 6 6 -6 -6 -4 -4 -2 -2 0 0 2 2 4 4 6 6 ∆ ∆ t (ps) t (ps) ∆ ∆ t (ps) t (ps) 200 1 1 Asymmetry 0.8 0.8 150 0.6 0.6 100 BELLE 0.4 0.4 0.2 0.2 50 0 0 -0.2 -0.2 0 0 B B +N -0.4 -0.4 0.5 -N -0.6 -0.6 0 0 0 B B N N -0.8 -0.8 -0.5 -1 -1 -6 -6 -4 -4 -2 -2 0 0 2 2 4 4 6 6 -7.5 -5 -2.5 0 2.5 5 7.5 ∆ t (ps) t (ps) ∆ ∆ t (ps) S π + π − S π + π − = − 0 . 636 ± 0 . 082 ± 0 . 027 = − 0 . 68 ± 0 . 10 ± 0 . 03 CP CP A π + π − A π + π − = +0 . 328 ± 0 . 061 ± 0 . 027 = +0 . 25 ± 0 . 08 ± 0 . 02 CP CP ✟ ⇒ clear mixing induced ✟ CP and presence of penguins φ 2 from e + e − colliders 7 Pit Vanhoefer(MPI) FPCP 2013
B → π + π − C CP = −A CP World averages π + π - S CP H F A G H F A G π + π - S CP vs C CP H F AG H F A G CKM 2012 PRELIMINARY CKM 2012 C CP BaBar -0.68 ± 0.10 ± 0.03 PRELIMINARY arXiv:1206.3525 BaBar 0 Belle -0.64 ± 0.08 ± 0.03 CKM 2012 Belle HFAG CKM2012 preliminary LHCb LHCb -0.56 ± 0.17 ± 0.03 Average LHCb-CONF-2012-007 -0.65 ± 0.06 Average -0.2 HFAG correlated average -1 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.4 π + π - C CP H F A G H F A G CKM 2012 PRELIMINARY BaBar -0.25 ± 0.08 ± 0.02 -0.6 arXiv:1206.3525 Belle -0.33 ± 0.06 ± 0.03 CKM 2012 HFAG CKM2012 preliminary LHCb -0.11 ± 0.21 ± 0.03 LHCb-CONF-2012-007 -0.8 Average -0.29 ± 0.05 -0.8 -0.6 -0.4 -0.2 0 HFAG correlated average S CP -0.8 -0.6 -0.4 -0.2 0 0.2 Contours give -2 ∆ (ln L) = ∆χ 2 = 1, corresponding to 60.7 % CL for 2 dof ⇒ good agreements between experiments (prev. tension removed) φ 2 from e + e − colliders 8 Pit Vanhoefer(MPI) FPCP 2013
B → π 0 π 0 BaBar Belle PRD 87 052009(2013) PRL 94 181803 (2005) 467 × 10 6 B ¯ B pairs 275 × 10 6 B ¯ B pairs ) ) 150 150 2 2 Events / ( 5 MeV/ c Events / ( 5 MeV/ c ¯ B B 100 100 background substracted 50 50 0 0 5.2 5.2 5.22 5.22 5.24 5.24 5.26 5.26 5.28 5.28 2 2 m m (GeV/c (GeV/c ) ) ES ES � E 2 beam − p 2 m ES = M bc = B BaBar Belle B ( B 0 → π 0 π 0 ) × 10 6 2 . 3 +0 . 4 +0 . 2 1 . 83 ± 0 . 21 ± 0 . 13 − 0 . 5 − 0 . 3 A π 0 π 0 0 . 44 +0 . 53 0 . 43 ± 0 . 26 ± 0 . 05 − 0 . 52 ± 0 . 17 CP φ 2 from e + e − colliders 9 Pit Vanhoefer(MPI) FPCP 2013
B ± → π ± π 0 BaBar Belle PRD 76 091102 (2007) arxiv:1210.1348 (2012) 383 × 10 6 B ¯ B pairs 772 × 10 6 B ¯ B pairs 800 800 800 ) (a) 2 Events/(3.3MeV/c π π 0 ± 600 600 600 ± K π 0 400 400 400 200 200 200 background substracted signal enhanced 0 0 0 5.24 5.24 5.24 5.26 5.26 5.26 5.28 5.28 5.28 M bc ( GeV/c 2 ) ∆ E ( GeV ) 2 2 2 m m m (GeV/c (GeV/c (GeV/c ) ) ) ES ∆ E = E B rec − E beam BaBar Belle B ( B ± → π ± π 0 ) × 10 6 5 . 02 ± 0 . 46 ± 0 . 29 5 . 86 ± 0 . 26 ± 0 . 38 A π ± π 0 0 . 03 ± 0 . 08 ± 0 . 01 0 . 043 ± 0 . 043 ± 0 . 007 CP φ 2 from e + e − colliders 10 Pit Vanhoefer(MPI) FPCP 2013
B → ππ φ 2 /α constraints C K M f i t t e r CKM12 (prel.) CKM → π π B (BABAR) f i t t e r → π π B (Belle) CKM fit CKM12 (prel.) → π π B (WA) 1.0 0.8 0.6 p-value C K M f i t t e r CKM12 (prel.) 0.4 0.2 0.0 0 20 40 60 80 100 120 140 160 180 φ (deg) 2 WA: φ 2 /α = (87 . 1 +17 . 5 Belle: φ 2 ∈ [85 . 0 ◦ , 148 . 0 ◦ ] , Babar: α ∈ [71 ◦ , 109 ◦ ] , − 7 . 8 ) ◦ φ 2 from e + e − colliders 11 Pit Vanhoefer(MPI) FPCP 2013
B → ρρ helicity basis: • B → ρρ π π π π π π + + + + + + ρ → ππ • S → VV decay π π π π + + + + φ θ Hel θ Hel ֒ → superposition of CP even and ρ 0 ρ 0 0 π - B odd states ֒ → separation through helicity analy- π - sis • f L : fraction of longitudinal polarization(LP , pure CP even final states) � � 4 (1 − f L ) sin 2 θ 1 Hel sin 2 θ 2 f L cos 2 θ 1 Hel cos 2 θ 2 d 2 Γ 1 Hel = 9 1 Hel + d cos θ 1 Hel d cos θ 2 Hel Γ 4 naiv SM expectation: f L ∼ 1 − m 2 B ∼ 1 difficult to predict for color-suppressed mode V m 2 B 0 → ρ 0 ρ 0 • smaller statistics(exp.) less penguin pollution compared to B → ππ φ 2 from e + e − colliders 12 Pit Vanhoefer(MPI) FPCP 2013
B 0 → ρ + ρ − Helicity BaBar Belle PRD 76 052007 (2007) PRL 96 171801 (2006) 384 million B ¯ 275 million B ¯ B pairs B pairs (c) Events / (0.188) 200 100 0 -0.5 0 0.5 cos( θ ) i BaBar Belle B ( B 0 → ρ + ρ − ) × 10 6 (25 . 5 ± 2 . 1 +3 . 6 (22 . 8 ± 3 . 8 +2 . 3 − 3 . 9 ) − 2 . 6 ) 0 . 992 ± 0 . 024 +0 . 026 0 . 941 +0 . 034 f L − 0 . 040 ± 0 . 030 − 0 . 013 φ 2 from e + e − colliders 13 Pit Vanhoefer(MPI) FPCP 2013
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