TTime-dependent CP violation in B decays at Belle Luka Santelj ∗ † Jozef Stefan Institute, Ljubljana, SloveniaE-mail: [email protected]
Using the full data sample collected with the Belle detector at the KEKB asymmetric-energy e + e − collider, we present three recent measurements of time-dependent CP violation in B decays, anda measurement of branching fraction of the B → ρ ρ decay. We studied B → ω K decays andmeasured the values of CP violation parameters in B → ω K S to be A ω K S = . ± . ( stat ) ± . ( syst ) and S ω K S = + . ± . ( stat ) ± . ( syst ) , which gives the first evidence of CP vi-olation in this decay. In addition, we measured the direct CP violation in B + → ω K + to be A CP ( B + → ω K + ) = . ± . ( stat ) ± . ( syst ) , and two branching fractions B ( B → ω K ) =( . ± . ( stat ) ± . ( syst )) × − and B ( B + → ω K + ) = ( . ± . ( stat ) ± . ( syst )) × − (preliminary). From the measurement of CP violation parameters in the B → η (cid:48) K decay weobtain S η (cid:48) K = . ± . ( stat ) ± . ( syst ) and A η (cid:48) K = + . ± . ( stat ) ± . ( syst ) (pre-liminary), which are the world’s most precise values to date. Measuring CP violating param-eters in the B → π + π − decay gives A π + π − = + . ± . ( stat ) ± . ( syst ) and S π + π − = − . ± . ( stat ) ± . ( syst ) . This result is used in an isospin analysis to constrain the φ angle of the unitarity triangle, with which we rule out the region 23 . ◦ < φ < . ◦ at the 1 σ confidence level. The measured branching fraction of the B → ρ ρ decay is B ( B → ρ ρ ) =( . ± . ( stat ) ± . ( syst )) × − , with the fraction of longitudially polarized ρ mesonsbeing f L = . + . − . ± .
13. From the same measurement we obtain also the first evidence ofthe B → f ρ decay, by measuring B ( B → f ρ ) × B ( f → π + π − ) = ( . ± . ( stat ) ± . ( syst )) × − . Using this result in an isospin analysis we obtain φ = ( . ± . ) ◦ . The European Physical Society Conference on High Energy Physics -EPS-HEP201318-24 July 2013Stockholm, Sweden ∗ Speaker. † On behalf of the Belle Collaboration. c (cid:13) Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. http://pos.sissa.it/ a r X i v : . [ h e p - e x ] D ec ime-dependent CP violation in B decays at Belle Luka Santelj
1. Introduction
Measuring the parameters of the unitarity triangle (UT) provides a major test of the Stan-dard Model (SM), in particular of the Cabibbo-Kobayashi-Maskawa (CKM) description of flavorchanging currents and CP violation. Angles of the UT related to B u , d decays can be determinedby measuring CP asymmetries in various B meson decays, and this was the main motivation forconstruction of two so-called B factory experiments, Belle and BaBar. In the previous decadeboth experiments have confirmed the complex phase of the CKM matrix as the main source of CPviolation.In these proceedings we present two recent measurements related to the φ angle of the UT,mainly motivated by their sensitivity to possible New Physics contributions, and two measurementsof the φ angle. All measurements are based on the data sample containing 772 millions B ¯ B pairscollected by the Belle experiment [1] , during its full data taking period (1999-2010).Angles φ and φ can be determined by measuring time-dependent asymmetry between decaysof B and ¯ B mesons into a common CP eigenstate f CP [2]. At the Belle experiment pairs of B mesons are produced in asymmetric energy collisions of electrons and positrons, through the ϒ ( S ) → B tag B CP → f tag f CP process. Since a B meson pair is in a quantum coherent state, a decayof B tag into a flavor specific final state f tag at t tag , determines the flavor of B CP at t tag . In this casethe CP asymmetry is given by a CP ( ∆ t ) = Γ ( B ( ∆ t ) → f CP ) − Γ ( ¯ B ( ∆ t ) → f CP ) Γ ( B ( ∆ t ) → f CP ) + Γ ( ¯ B ( ∆ t ) → f CP ) = A f cos ∆ M ∆ t + S f sin ∆ M ∆ t , (1.1)where ∆ t is the time difference between decays of B tag and B CP , ∆ M is the mass difference betweenthe two B mass eigenstates ( B L and B H ), and A f and S f are the so-called CP violation parameters,which can be within the SM related with the UT angles.
2. Measurement of branching fractions and CP violation parameters in B → ω K decays The B → ω K S decays are sensitive to the φ = arg ( − V cd V ∗ cb ) / ( V td V ∗ tb ) interior angle of the UT.The decay proceeds dominantly by the b → s ¯ qq penguin diagram, and within the SM we expect A ω K S = S ω K S = sin 2 φ , neglecting other contributing CKM-suppressed amplitudes with adifferent weak phase. However, the contribution of these CKM-suppressed amplitudes may not benegligible, resulting in a non-zero A ω K S and in a deviation of S ω K S from sin 2 φ . Several theoreticalmethods were used to estimate the effect of these amplitudes, indicating the expected value of S ω K S slightly higher than sin 2 φ [3]. However, current experimental measurements indicate the opposite[4, 5, 6], which might be a consequence of a contribution of new heavy particles in the loop of thepenguin diagram [7].In this measurement, we have also measured the direct CP violating parameter A CP in the B + → ω K + decay, defined as A CP = Γ ( B − → ω K − ) − Γ ( B + → ω K + ) Γ ( B − → ω K − ) + Γ ( B + → ω K + ) , (2.1) Here B ( t ) ( ¯ B ( t ) ) denote states that were at t = B ( ¯ B ) states, but later get mixed due to B − ¯ B mixing. ime-dependent CP violation in B decays at Belle Luka Santelj where again a deviation from the expected asymmetry could be an indication of New Physics.Furthermore, the measurement of the branching fractions provides an important test of the QCDfactorization (QCDF) and perturbative QCD (pQCD) approaches.To obtain the two branching fractions and CP violation parameters we perform a seven-dimensional unbinned extended maximum likelihood fit to M bc , ∆ E (two kinematic variables of thereconstructed B meson), R s / b (event topology variable), m π (invariant mass of the reconstructed ω ), H π (helicity angle), ∆ t and q (where q = + q = −
1) for B tag = B ( ¯ B )). The fit is performedsimultaneously to B → ω K S and B + → ω K + data samples, sharing common calibration factors.Following this, the model shape is fixed and the A CP ( B + → ω K + ) parameter is obtained from twofurther fits to extract the number of B + and B − events. The preliminary results are [8]: B ( B → ω K ) = ( . ± . ( stat ) ± . ( syst )) × − , B ( B + → ω K + ) = ( . ± . ( stat ) ± . ( syst )) × − , A ω K S = . ± . ( stat ) ± . ( syst ) , S ω K S = + . ± . ( stat ) ± . ( syst ) , A CP ( B + → ω K + ) = . ± . ( stat ) ± . ( syst ) , (2.2)where the first uncertainty is statistical and the second is systematic. The latter is dominated byuncertainties of the ∆ t resolution function parameters for A ω K S and S K S , and by parameters of thebackground PDF shape for the branching fractions. The comparison of data distributions and thefitted PDF is shown in figure 1. The results given in (2.2) are the world’s most precise measure-ments of the branching fractions and CP violation parameters in B → ω K decays. The observedvalues of A ω K S and S ω K S differ from zero with a significance of 3.1 standard deviations, whichgives the first evidence of CP violation in the B → ω K S decay. ] E v en t s /[ . G e V / c ] [GeV/c bc M5.25 5.26 5.27 5.28 5.29 5.3 R e s i dua l s N o r m a li s ed -202 ] E v en t s /[ . G e V / c ] [GeV/c0.73 0.75 0.77 0.79 0.81 0.83 R e s i dua l s N o r m a li s ed -202 E v en t s /[ . s ] q = +1q = -1 [ps]-7.5 -5 -2.5 0 2.5 5 7.5 B + N B N B - N B N -0.500.5 Figure 1: Left two:
Distribution of reconstructed events in M bc and m π (black points) along with the fittedPDF (the full line). The dashed line shows contribution of the q ¯ q background (from e + e − → q ¯ q ( q = u , d , s , c ) events), the dotted line of the B ¯ B background. Right:
Distributions of reconstructed events in ∆ t (eventswith q = + q = − q = + q = − ime-dependent CP violation in B decays at Belle Luka Santelj
3. Measurement of CP violation parameters in B → η (cid:48) K decay The B → η (cid:48) K decay is another decay that proceeds dominantly through the b → s ¯ qq transi-tion, for which within the SM we expect A η (cid:48) K = S η (cid:48) K = − ξ f sin 2 φ (where ξ f = − (+ ) for B → η (cid:48) K S ( B → η (cid:48) K L )). Theoretically this is the cleanest mode to measure CP violation param-eters in a b → s ¯ qq process, as the contributions from the CKM suppressed diagrams are expectedto be (cid:46) .
02 for both S η K and A η (cid:48) K [3].In the first part of the analysis, event reconstruction and signal fraction estimation, we studyseparately B → η (cid:48) K S and B → η (cid:48) K L events. To obtain the fraction of signal events we study thedistribution of events in M bc , ∆ E and R s / b for K S events, and the distribution in p cmsB ( B candidatemomentum in the center-of-mass system), r (quality of the B candidate flavor information) and R s / b for K L events. Altogether we reconstruct 2503 ± B → η (cid:48) K S signal events, and 1041 ± B → η (cid:48) K L signal events, where the uncertainties are statistical only. Following this, we performan unbinned maximum likelihood fit to extract the values of CP violation parameters from themeasured ∆ t , q distribution of events. Our preliminary results are S η (cid:48) K = + . ± . ( stat ) ± . ( syst ) , A η (cid:48) K = + . ± . ( stat ) ± . ( syst ) , (3.1)where the first uncertainty is statistical and the second is systematic. The main contribution to thelatter comes from the uncertainties in the ∆ t resolution function parameters for S η (cid:48) K , and from thetag-side interference effect for A η (cid:48) K . The comparison of data distribution and the fitted PDF isshown in figure 2. The measured values of S η (cid:48) K and A η (cid:48) K are the world’s most precise values ofCP violation parameters in this particular decay, as well as among all b → s ¯ qq transition dominateddecays. They are consistent with previous measurements [9, 10] and with the SM prediction. E n t r i e s / . G e V E [GeV] -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 E n t i r e s / . G e V -8 -6 -4 -2 0 2 4 6 8 E v en t s ( / . s ) q = +1q = -1 -8 -6 -4 -2 0 2 4 6 8 A sy mm e t r y -0.500.5 Preliminary
Figure 2: Left two:
Distribution of reconstructed B → η (cid:48) K S events in M bc and ∆ E (black points) alongwith the fitted PDF (the red). The yellow area shows contribution of the q ¯ q background, and the blue area ofthe B ¯ B background. Right:
Distribution of the reconstructed events in ∆ t (events with q = + q = − q = + q = − ime-dependent CP violation in B decays at Belle Luka Santelj
4. Measurements of φ angle in B → π + π − and B → ρ ρ decays Decays B → π + π − and B → ρ ρ are sensitive to φ = arg ( − V td V ∗ tb ) / ( V ud V ∗ ub ) . At the treelevel we expect A f = S f = sin 2 φ . However, penguin contributions can give rise to direct CPviolation, A f (cid:54) =
0, and also pollute the measurement of φ . Despite this, it is still possible to obtainthe value of φ with a SU ( ) isospin analysis, by considering the set of three B → hh decays ( h = π or h = ρ ), related via isospin symmetry [11]. Belle recently updated measurements of CP violationparameters in the B → π + π − decay and of branching fraction of the B → ρ ρ decay to the fulldata sample, and the values obtained were used to provide new constraints on φ . B → π + π − decay To obtain the values of S π + π − and A π + π − a seven-dimensional fit to L + K π , L − K π ( π , K separa-tion likelihood function), M bc , ∆ E , R s / b , ∆ t and q is performed. The main background contributioncomes from e + e − → q ¯ q ( q = u , d , s , c ) events. In total we reconstruct 2964 ±
88 signal events, andthe following values of CP violation parameters are obtained [12] A π + π − = + . ± . ( stat ) ± . ( syst ) , S π + π − = − . ± . ( stat ) ± . ( syst ) , (4.1)where the first uncertainty is statistical and the second is systematic. The comparison of data distri-bution in ∆ t with the fitted PDF is shown in figure 3. The values given in (4.1) are the world’s mostprecise values of CP violation parameters in this decay. Using these values, and input from otherBelle measurements (branching fractions of B → π + π − , B + → π + π [13] and B → π π [14]decays), an isospin analysis is performed to constrain φ . Obtained difference 1-CL (confidencelevel) is plotted in figure 3, for a range of φ . The region 23 . ◦ < φ < . ◦ is ruled out at the 1 σ level, including systematic uncertainties. E v en t s / ( . s ) q = +1q = -1 -7.5 -5 -2.5 0 2.5 5 7.5 B + N B N B - N B N -0.500.5 - C L Figure 3: Left:
Distribution of reconstructed events in ∆ t (events with q = + q = − q = + q = − Right:
Difference 1-CL,plotted for a range of φ . The dashed line indicate the 1 σ exclusion level. . 5 ime-dependent CP violation in B decays at Belle Luka Santelj B → ρ ρ decay Measuring the branching fraction of the B → ρ ρ decay is quite challenging due to its lowvalue and the presence of other, largely unknown, four-pion final states. In addition, due to twovector particles in the final state, a helicity analysis is needed in order to separate the longitudinaland transverse polarization amplitudes, with even and odd CP eigenvalues respectively.We perform an unbinned maximum likelihood fit to a six-dimensional distribution of recon-structed candidates in m π + π − , m π + π − (invariant masses of reconstructed ρ s ), cos θ hel , cos θ hel (he-licity angles), and R s / b . The results are [15] B ( B → ρ ρ ) = ( . ± . ( stat ) ± . ( syst )) × − , f L = . + . − . ( stat ) ± . ( syst ) , (4.2)where B is a branching fraction and f L is a fraction of longitudinally polarized ρ mesons. Thebranching fraction is measured with a significance of 3 . B ( B → f ρ ) × B ( f → π + π − ) = ( . ± . ( stat ) ± . ( syst )) × − , (4.3)with a significance of 3 . B → f ρ decay.Using the values of B ( B → ρ ρ ) and f L , along with the world average values [6] of B ( B → ρ + ρ − ) , f + − L , A ρ + ρ − , S ρ + ρ − , B ( B + → ρ + ρ ) and CP violation parameters A ρ ρ , S ρ ρ from BaBarmeasurement [16], an isospin analysis is performed to constrain φ . We obtain φ = ( . ± . ) ◦ ,at a 1 σ confidence level. References [1] A. Abashian et al. (Belle Collaboration), Nucl. Instrum. Methods Phys. Res. A , 117 (2002).[2] I. Bigi and A. Sanda,
CP Violation , Cambridge University Press, Cambridge (2009)[3] C. -K. Chua, “Theoretical review on sin 2 β ( φ ) from b → s penguins”, arXiv:0807.3596 [hep-ph].[4] Y. Chao et al. (Belle Collaboration), Phys. Rev. D , 091103(R) (2007).[5] B. Aubert et al. (BaBar Collaboration), Phys. Rev. D , 052003 (2009).[6] Y. Amhis et al. , 241 (1997).[8] V. Chobanova et al. (Belle Collaboration), arXiv:1311.6666 [hep-ex].[9] K.-F. Chen et al. (Belle Collaboration), Phys. Rev. Lett. , 031802 (2007).[10] B. Aubert et al. (BaBar Collaboration), Phys. Rev. D , 052003 (2009).[11] R. Fleischer, arXiv:hep-ph/9809216v1.[12] J. Dalseno et al. (Belle Collaboration), arXiv:1302.0551v2 [hep-ex].[13] Y.-T. Duh et al. (Belle Collaboration), Phys. Rev. D , 031103(R) (2012).[14] Y. Chao et al. (Belle Collaboration), Phys. Rev. Lett. , 181803 (2005).[15] P. Vanhoefer et al. (Belle Collaboration), arXiv:1212.4015v2 [hep-ex].[16] B. Aubert et al. (BaBar Collaboration), Phys. Rev. D , 052007 (2007)., 052007 (2007).