Measurement of the angle g (f 3 ) at the e + e - B-factories

Transcription

1 Measurement o the angle g 3 at the e + e - -actories Matteo Rama Laboratori Nazionali di Frascati Flavor Physics & CP Violation 13 May -4 13, uzios Rio de Janeiro razil

2 The angle g CM is 3x3 unitary matrix 4 parameters ater ad hoc choice o quark ield phases: 3 real and 1 CP violating phase [Wolenstein parametrization] V ub e iγ From the unitarity o V: Unitarity Triangle Measurement o g at e + e - -actories - FPCP 13

3 Measurement o g with color allowed A 1 V cb V us Aλ 3 color suppressed A V ub V cs Aλ 3 ρ + iη g is measured in the intererence o the two amplitudes unknowns: γ, r b, δ b +δ theoretically clean most sensitive method to constrain g at present similar principle applies to several other processes: + π,, s s, A tot = A 1 + A = A 1 + A + A 1 A cos φ hadronic parameters extracted with g measured at charm actories δ b + δ = r b A + + A φ = γ + δ strong phase rom and decay Measurement o g at e + e - -actories - FPCP 13 3

4 Extraction o g using decays ierent methods depending on inal state: GLW [M. Gronau,. London,. Wyler, PL53, ; PL 65, ] to two-body CP eigenstates + -, p + p - even, s p, s w odd AS to doubly Cabibbo suppressed decays + p -, + p - p, GGSZ alitz [. Atwood, I. unietz, A. Soni, PRL 78, ] [. Atwood et al., PRL78, ; A. Giri et al., PR68, ] to 3-body decays s p + p -, s + -, p + p - p, etc. alitz plot itted to determine how the strong phase o decay amplitude varies over the alitz plane model independent analysis most powerul method nowadays ierent decays ±, * ±, * ± and lavour-tagged *. They depend on mode-dependent hadronic actors r b, d b Strategy: combine as many channels as possible to improve the overall sensitivity Measurement o g at e + e - -actories - FPCP 13 4

5 The -actories dataset TOTAL: ab 1 at Y4S ~ Measurement o g at e + e - -actories - FPCP 13 5

6 The GGSZ method The intererence varies as unction o the position in the alitz plot V cb + S p p Vub S p p Spp m A m +, m A m, m + = A A m, m + + r b e iδ b γ A m +, m A + m, m + = A + + A m +, m + r b e iδ b+γ A m, m + A m -,m + is measured with a alitz plot analysis o high statistics samples o lavour-tagged and The + and - yields are measured as a unction o the position in the alitz plot ML it Unknowns: g, rb and d b S S m m m p Measurement o g at e + e - -actories - FPCP 13 6 m pp A m, m + m

7 Reconstructed decay modes ecays + * [ p ] + * [ g] + * + [ s p] S pp 468M 657M 468M 657M 3 468M 657M 468M 386M S 468M 468M 3 468M 468M [ S pp] * p, S pp Signal region deined by E and M bc p * * E E E * * beam mbc Ebeam p both aar and elle it signal vs alitz plot position using likelihoode, M bc,event shape vars Measurement o g at e + e - -actories - FPCP 13 7

8 Measurement o x ±,y ± Measurement o g at e + e - -actories - FPCP 13 8 Extract the cartesian coordinates instead o g, r b, d b likelihood unbiased and Gaussian-shaped using x,y Im Re * * y x y x Im Re * * y x y x, m m A x ±,y ± 4 variables, 3 indep. x + +y + =x - +y - x+,y+ x-,y- * * elle - aar - x = r b cosδ b γ y = r b sinδ b γ the contours do not include the alitz model errors x-,y- x+,y+

9 From x ±,y ± to g: aar Combine, *, * with S p + p - and S + - Use requentist method to derive the physical parameters g, r b, d b rom x ±,y ± PRL15, total error exp. sys. alitz model sys. 3.5s stat signiicance o CPV γ = 68 ± 14 ± 4 ± 3 mod 18 stat syst model Measurement o g at e + e - -actories - FPCP 13 9

10 From x ±,y ± to g: elle Combine and * with S p + p - Use requentist method to derive the physical parameters g, r b, d b rom x ±,y ± PR81, 11 1 * γ r b δ b γ r b δ b combined 3.5s stat signiicance o CPV γ = ± 3.6 ± 8.9 mod 18 stat syst model Measurement o g at e + e - -actories - FPCP 13 1

11 Model independent analysis Model-independent measurement o g. Proposed by A. Giri et al. [Phys Rev ]. Pioneered by elle. divide the S pp alitz plot in k bins symmetric w.r.t. the m + vs m axis express the ± ± yields in each bin i in terms o x ±, y ± and parameters c i, s i c i, s i are measured by CLEO exploiting the quantum coherence in ψ 377 extract x ±, y ± rom ML it to ± ± yields in all bins ± ± yields rom lav.-tagged spp extracted rom it to the ± yields measured by CLEO [PR8, 116 1] N i ± = h ±i + r b i + i i x ± c i ± y ± s i Measurement o g at e + e - -actories - FPCP 13 11

12 Model independent measurement dierence PR85, γ = ± 4.1 ± 4.3 mod 18 stat exp sys c i,s i errors r b =.145 ±.3 ±.1 ±.11 δ b = 19.9 ± 15. ± 3.8 ± 4.7 uncertainty in c i, s i can be reduced at ESIII and possible next generation charm-tau actories Measurement o g at e + e - -actories - FPCP 13 1

13 GLW method Measurement o g at e + e - -actories - FPCP to + -, p + p - CP+ and sp, sw, s CP- measure + and - yields to determine the GLW observables: R CP CP CP cos cos 1 b b b r r d g A CP CP CP CP CP CP b b R r d sing sin 4 observables, 3 independent unknowns: g, d b, r b

14 GLW reconstructed decay modes, * * p and * g, * + -, p + p - CP+, sp, sw, s, sh CP- PR8,74 1 very challenging at hadronic colliders - * - p s π, s η CM 1 + * + p s π, s η CM 1 Measurement o g at e + e - -actories - FPCP 13 14

15 * * CP- CP+ CP- CP+ CP- CP+ GLW results M. arbach s talk M. arbach s talk Measurement o g at e + e - -actories - FPCP 13 15

16 Why not g rom GLW alone The GLW observables can be expressed in terms o the cartesian coordinates x ±,y ± : x ± = R CP+ 1 A CP+ R CP 1 A CP /4 r b = x ± + y ± = R CP+ + R CP / arxiv:11.84 good constraint on x ± comparable to GGSZ method when in same size dataset very loose constraint on y ± + γ x, y x +, y + Measurement o g at e + e - -actories - FPCP 13 16

17 AS method Measurement o g at e + e - -actories - FPCP to + p -, + p - p, + p + p + p -, doubly-cabibbo-supp. * * * * suppressed suppressed avored avored + + same inal state large intererence ~O1 Measures + and - yields to determine the AS observables: ] [ ] [ ] [ ] [ A AS AS b b R r r / sin sin g d d ] [ ] [ ] [ ] [ R AS g d d cos cos b b b r r r r A A r arg A A d r + p - =.6 measured at CLEOc/ESIII

18 AS reconstructed decay modes h=,p ecays h + * [ p ]h + * [ g]h + * + [ s p] + p - 467M 77M 467M 77M 3 467M 77M 379M p - p 474M example:, + p A AS =.8 ± A AS = Measurement o g at e + e - -actories - FPCP 13 18

19 AS * * results * *[g] *[p ] * *[g] *[p ] 3p p p p p 3p pp p p p p M. arbach s talk M. arbach s talk M. arbach s talk M. arbach s talk * * p results available in backup slide LHCb dominates the, p mode. Final states with neutrals diicult in hadronic environment Measurement o g at e + e - -actories - FPCP 13 19

20 Why not g rom AS alone The AS observables can be expressed in terms o the cartesian coordinates x ±,y ± : arxiv:11.84 x + r cosδ + y r sinδ = Γ ± π Γ π ± + γ x, y x +, y + x ±,y ± are delocalized over two circles Note: or * the circles associated to * p and * g are centered at opposite points r cos δ, ±r sin δ and g can be extracted in principle up to discrete ambiguities. GLW + AS can constrain g Note: uncertainty on the values o r and δ are neglected Measurement o g at e + e - -actories - FPCP 13

21 * * aar GLW+AS+GGSZ combination Combination o GGSZ+GLW+AS in two stages I. combine the GGSZ, GLW and AS ± * * ± observables 34 in total to II. extract the combined x ±,y ± 4 or each mode transorm the combined x ±,y ± into the physically relevant quantities g, {r b, d b } ** stage I GGSZ GGSZ+GLW GGSZ+GLW+AS contours or * and * in PR87, results: z x + iy external input required or the hadronic parameters r π, δ π, r ππ, δ ππ, k ππ Measurement o g at e + e - -actories - FPCP 13 1

22 aar GLW+AS+GGSZ combination stage II x ±,y ± ** g, {r b, d b } ** with requentist stat procedure γ = modulo 18 exp+p model sys = ±4 CPV signiicance: 5. 9σ GGSZ alone 4.σ. GGSZ+GLW 5.4σ PR87, up to r b % = r +1.9 b % = Measurement o g at e + e - -actories - FPCP 13

23 elle GLW+AS+GGSZ combination Combination o GGSZ mod. dep.+glw+as +* observables - requentist stat procedure up to Trabelsi@CM1 arxiv: GGSZ: γ = GGSZ + AS : γ = 68 ± GGSZ + AS + GLW: γ = : +.63 r b = r b = r b = Measurement o g at e + e - -actories - FPCP 13 3

24 elle and aar combination Combination o aar and elle: GGSZ mod. dep.+glw+as with, * and *aar only. Frequentist stat procedure. aar and elle model errors assumed uncorrelated. rom: Physics o the Factories, to be submitted to EPJC. aar elle aar+elle aar elle aar+elle aar + elle: γ = 67 ± 11 mod 18 o r b =.1 ±.11 δ b = mod 18 o aar elle aar+elle Measurement o g at e + e - -actories - FPCP 13 4

25 mixing and CPV in and p Several interesting studies on the eect o mixing and CPV in the extraction o g with * * and * p Eect o mixing Y. Grossman, Z. Ligeti, A. Soer, PR67, ; PR7, A. ondar, A. Poluektov, V. Vorobiev, PR8, alitz mod ind Eect o CPV in decays W. Wang, PRL11, GLW M. Martone and J. Zupan, arxiv: GLW. hattacharya,. London, M. Gronau, J. L. Rosner, arxiv: GLW A. ondar, A. olgov, A. Poluektov, V. Vorobiev arxiv: alitz Corrections or mixing and CPV not considered in aar and elle * * combinations eects expected to be small at present -actories although some may not be completely negligible eects more and more important at LHCb and at elle Measurement o g at e + e - -actories - FPCP 13 5

26 Summary Sensitivity to g 3 dominated by the ± ± decays so ar aar and elle have reconstructed all the most sensitive decay modes using all or almost all their inal datasets aar GLW+AS+GGSZ combination: γ = mod 18 exp+p model sys = ±4 elle GLW+AS+GGSZ combination: γ = +15 mod actories average: γ = 67 ± 11 mod 18 o Measurement o g at e + e - -actories - FPCP 13 6

27 ACUP Measurement o g at e + e - -actories - FPCP 13 7

28 ependence o sg on r b the error on g at ixed x,y uncertainty scales roughly as 1/r b same x,y errors but smaller r b larger uncertainty on g Measurement o g at e + e - -actories - FPCP 13 8

29 * p AS measurements Measurement o g at e + e - -actories - FPCP 13 9