Measurements of CKM angle phi1 with charmless penguins at Belle
aa r X i v : . [ h e p - e x ] O c t th International Conference on High Energy Physics, Philadelphia, 2008
Measurements of CKM angle φ with charmless penguins at Belle J. Dalseno for the Belle Collaboration
High Energy Accelerator Research Organization (KEK), Tsukuba, JAPAN
We present measurements of time-dependent CP violation parameters in B → K π , B → K S π + π − and B → K S K + K − decays. The latter two are extracted using time-dependent Dalitz plot analyses. These results are obtainedfrom a large data sample that contains 657 × B ¯ B pairs collected at the Υ(4 S ) resonance with the Belle detectorat the KEKB asymmetric-energy e + e − collider.
1. INTRODUCTION CP violation in the Standard Model (SM) arises from an irreducible complex phase in the Cabibbo-Kobayashi-Maskawa (CKM) quark-mixing matrix [1, 2]. Of recent interest is CP violation in b → q ¯ qs transitions whichproceeds by loop diagrams that may be affected by new particles in various extensions of the SM. Furthermore, the CP asymmetries in b → q ¯ qs transitions are predicted in the SM to be slightly higher than those observed in b → c ¯ cs transitions. However, current experimental measurements [3] tend to be lower than those for b → c ¯ cs transitionsmotivating more precise experimental determinations.The decay of the Υ(4 S ) produces a B ¯ B pair of which one ( B ) may be fully reconstructed while the other ( B )may reveal its flavour. The proper time interval between B and B is defined as ∆ t ≡ t Rec − t Tag and fromcoherent B ¯ B production in the Υ(4 S ) decay, the time-dependent decay rate for a quasi-two-body mode when B possesses flavour q ( B : q = +1, ¯ B : q = − | A (∆ t, q ) | = e −| ∆ t | /τ B τ B (cid:20) q ( A CP cos ∆ m d ∆ t + S CP sin ∆ m d ∆ t ) (cid:21) , (1)where τ B is the B lifetime and ∆ m d is the B ¯ B mass difference. This assumes no CP violation in mixing, | q/p | = 1,and that the B ¯ B lifetime difference is negligible. The parameter, A CP , denotes the direct CP violating componentand S CP represents mixing-induced CP violation. For time-dependent Dalitz plot analyses, the time-dependentdecay rate is written as | A (∆ t, q ) | = e −| ∆ t | /τ B τ B (cid:20) ( | A | + | ¯ A | ) − q ( | A | − | ¯ A | ) cos ∆ m d ∆ t + 2 q ℑ ( ¯ AA ∗ ) sin ∆ m d ∆ t (cid:21) . (2)The Dalitz-dependent amplitudes, A , can be written in the isobar approximation as a superposition of intermediatedecay channels, i , A ( s + , s − ) = X i a i F i ( s + , s − ) , ¯ A ( s − , s + ) = X i ¯ a i ¯ F i ( s − , s + ) , (3)where a i ≡ a i (1 + c i ) e i ( b i + d i ) for A and ¯ a i ≡ a i (1 − c i ) e i ( b i − d i ) for ¯ A are complex coefficients describing the rela-tive magnitudes and phases between the decay channels. The form factors, F i ( s + , s − ), depend on the Dalitz plotcoordinates, s ± , and describe the invariant mass and angular distribution probabilities. For a CP eigenstate, i , thetime-dependent CP violation parameters can be calculated as A CP ( i ) ≡ | ¯ a i | − | a i | | ¯ a i | + | a i | = − c i c i , and − η i S CP ( i ) ≡ − ℑ (¯ a i a ∗ i ) | a i | + | ¯ a i | = 1 − c i c i sin 2 φ eff1 ( i ) (4)and φ eff1 ( i ) ≡ arg( a i ¯ a ∗ i ) / d i is directly accessible as a fit parameter. Consequently, both A CP ( i ) and S CP ( i ) arerestricted to reside in the physical region. The relative fraction of each component can be calculated with, f i = ( | a i | + | ¯ a i | ) R F i ( s + , s − ) F ∗ i ( s + , s − ) ds + ds − R ( |A| + | ¯ A| ) ds + ds − . (5)14 th International Conference on High Energy Physics, Philadelphia, 2008
2. DATASET, DETECTOR AND BASIC ANALYSIS TECHNIQUE
These measurements of CP violating parameters are based on 657 × B ¯ B pairs collected with the Belle detec-tor [5] at the KEKB asymmetric-energy e + e − (3 . . × cm − s − , the collider produces the Υ(4 S ) resonance ( √ s = 10 .
58 GeV) with a Lorentz boost of βγ = 0 . z , which usually decays into a B ¯ B pair.Reconstructed B candidates are described with two kinematic variables: the beam-constrained mass, M bc ≡ q ( E CMSbeam ) − ( p CMS B ) and the energy difference, ∆ E ≡ E CMS B − E CMSbeam where E CMSbeam is the beam energy and E CMS B ( p CMS B ) is the energy (momentum) of the B meson all evaluated in the centre-of-mass system (CMS). The dominantbackground in the reconstruction of B is from continuum ( e + e − → q ¯ q ) events. Since their topology tends to bejet-like in contrast to the spherical B ¯ B decay, continuum can be suppressed with a Fisher discriminant based onmodified Fox-Wolfram moments [7]. This discriminant is combined with the polar angle of the B candidate in theCMS to form a likelihood ratio, R S / B , which separates continuum from B ¯ B events.Since the B and ¯ B mesons are approximately at rest in the Υ(4 S ) Enter-of-Mass System (CMS), the differencein decay time between the B ¯ B pair, ∆ t , can be determined from the displacement in z between the final state decayvertices, ∆ t ≃ ( z Rec − z Tag ) /βγc ≡ ∆ z/βγc . To obtain the ∆ t distribution, we reconstruct the tag-side vertex fromthe tracks not used to reconstruct B [8] and employ the flavour tagging routine described in Ref. [9]. The tagginginformation is represented by two parameters, the B flavour, q and r . The parameter, r , is an event-by-event,MC determined flavour-tagging dilution factor that ranges from r = 0 for no flavour discrimination to r = 1 forunambiguous flavour assignment.
3. TIME-DEPENDENT CP VIOLATION MEASUREMENT IN B → K π Direct CP violation has been observed in B → K + π − [10] and is found to be significantly different from thatin B ± → K ± π . This unexpected result may indicate the presence of new physics (NP) or poor understanding ofstrong interaction effects in B decays. A model-independent test for NP is possible via an isospin sum rule with highstatistics [11] which gives a relation among the direct CP violation asymmetries measured in all possible B → Kπ modes, i.e. B → K π , K + π − , B + → K + π and K π + , A K + π − + A K π + B ( K π + ) τ B B ( K + π − ) τ B + = A K + π B ( K + π ) τ B B ( K + π − ) τ B + + A K π B ( K π ) B ( K + π − ) . (6)Here, B represents the branching ratio of each decay mode and τ B + is the lifetime of the charged B meson. The sumrule’s theoretical precision is determined by SU(2) flavour symmetry, i.e. a few %, therefore the sum rule providesa clean test for new physics. As a fundamental input, the CP violation measurement in B → K π is currentlythe least known, experimentally. Since the branching fractions and CP asymmetries of other B → Kπ decay modeshave been measured to good precision [12], A K π is predicted with a small error. In addition to the B → K S π mode, we measure CP asymmetry in B → K L π decay for the first time, in order to maximize sensitivity to thedirect CP violation parameter, A K π .The signal yield of B → K S π events is found from a three-dimensional extended unbinned maximum likelihoodfit to M bc , ∆ E and R S / B to be 657 ±
37 events. For B → K L π , M bc can be calculated from the direction of the K L cluster while ∆ E cannot be calculated. The signal yield of 285 ±
52 events is extracted from a two-dimensionalfit to M bc and R S / B and has a significance of 3.7 σ including systematic uncertainties.As the vertex position of B → K L π cannot be determined and the vertex reconstruction efficiency of B → K S π is ∼
33% due to the long lifetime of the K S , these events can still be used to calculate A CP by integrating Eq. 1 over∆ t . We extract the CP parameters, A CP = +0 . ± .
13 (stat) ± .
06 (syst) , S CP = +0 . ± .
31 (stat) ± .
08 (syst) (7)24 th International Conference on High Energy Physics, Philadelphia, 2008 t (ps) ∆ -6 -4 -2 0 2 4 6 E ve n t s / ( . p s ) Tags B Tags B t (ps) ∆ -6 -4 -2 0 2 4 6 R a w A sy mm e t r y -1-0.8-0.6-0.4-0.200.20.40.60.81 Figure 1: The left plot shows the background subtracted fit to ∆ t for the good tags region, 0 . < r ≤ .
0, where the solid(dashed) curve represents B ( ¯ B ) tags. The right plot shows the B ¯ B raw asymmetry, ( N B − N ¯ B ) / ( N B + N ¯ B ), where N B ( N ¯ B ) is the number of signal B ( ¯ B ) tags in ∆ t . and the fit results for the ∆ t component is shown in Fig. 1. We find that the mixing induced component is consistentwith charmonium, S CP ( b → c ¯ cs ) = 0 . ± .
025 [3], and that there is a 1 . σ deviation between our measurement of A CP and the expectation from the isospin sum rule, A CP = − . ± .
06 [11].
4. TIME-DEPENDENT DALITZ PLOT CP VIOLATION MEASUREMENT IN B → K S π + π − The signal yield of B → K S π + π − events is found from a one-dimensional fit to ∆ E to be 1944 ±
98 events andthe resonances considered in the signal model (Eq. 3) are the K ∗± (892), K ∗± (1430), ρ (770), f (980), f (1270), f X (1300) and a non-resonant component. We obtain the CP parameters,Solution 1: − L = 18472 . f ( K ∗ +0 (1430) π − ) = 61 . ± . A CP ( ρ (770) K S ) = +0 . +0 . − . ± . ± . ,φ eff1 ( ρ (770) K S ) = (+20 . +8 . − . ± . ± . ◦ , A CP ( f (980) K S ) = − . ± . ± . ± . ,φ eff1 ( f (980) K S ) = (+12 . +6 . − . ± . ± . ◦ , Solution 2: − L = 18465 . f ( K ∗ +0 (1430) π − ) = 17 . ± . A CP ( ρ (770) K S ) = − . ± . ± . ± . ,φ eff1 ( ρ (770) K S ) = (+22 . ± . ± . ± . ◦ , A CP ( f (980) K S ) = +0 . ± . ± . ± . ,φ eff1 ( f (980) K S ) = (+14 . +7 . − . ± . ± . ◦ , (8)where the first error is statistical, the second is systematic and the third is the Dalitz plot signal model uncertainty.Figure 2 shows the fit results. The high K ∗ +0 (1430) π − fraction of Solution 1 is in agreement with some phenomeno-logical estimates [13] and may also be favoured by the total K − π S -wave phase shift when compared with thatmeasured by LASS [14]. As the likelihood difference is not found to be significant, we do not rule between thesesolutions where A CP is consistent with null asymmetry and φ eff1 agrees with charmonium.
5. TIME-DEPENDENT DALITZ PLOT CP VIOLATION MEASUREMENT IN B → K S K + K − The signal yield of B → K S K + K − is extracted to be 1269 ±
51 events from a two-dimensional fit to M bc and ∆ E in each r -bin. We consider the f (980), φ (1020), f X (1500), χ c , and a non-resonant component in the signal model.Four solutions with similar likelihood are found where two solutions arise from the interference between f (980) andthe non-resonant component and the other two from f X (1500) and the non-resonant component. Using externalinformation from B → K S π + π − , if the f X (1500) is the f (1500) for both B → K S π + π − and B → K S K + K − ,the ratio of branching fractions, B ( f (1500) → π + π − ) / B ( f (1500) → K + K − ), prefers the solution with the low f X (1500) K S fraction. Similarly the ratio, B ( f (980) → π + π − ) / ( B ( f (980) → π + π − ) + B ( f (980) → K + K − ))34 th International Conference on High Energy Physics, Philadelphia, 2008 t (ps) ∆ -6 -4 -2 0 2 4 6 E ve n t s / ( . p s ) Tags B Tags B t (ps) ∆ -6 -4 -2 0 2 4 6 R a w A sy mm e t r y -1-0.8-0.6-0.4-0.2-00.20.40.60.81 t (ps) ∆ -6 -4 -2 0 2 4 6 E ve n t s / ( . p s ) Tags B Tags B t (ps) ∆ -6 -4 -2 0 2 4 6 R a w A sy mm e t r y -1-0.8-0.6-0.4-0.2-00.20.40.60.81 (a) (b)Figure 2: Time-dependent Dalitz plot fit results for B → K S π + π − in (a), the ρ (770) region and (b), the f (980) region.The top plots show the ∆ t distribution for B (solid) and ¯ B (dashed) tags. These plots contain only good tags, 0 . We thank the KEKB group for excellent operation of the accelerator, the KEK cryogenics group for efficient solenoidoperations, and the KEK computer group and the NII for valuable computing and SINET3 network support. Weacknowledge support from MEXT and JSPS (Japan); ARC and DEST (Australia); NSFC (China); DST (India);MOEHRD and KOSEF (Korea); KBN (Poland); MES and RFAAE (Russia); ARRS (Slovenia); SNSF (Switzerland);NSC and MOE (Taiwan); and DOE (USA). References [1] N. Cabibbo, Phys. Rev. Lett. , 214 (1964).[2] M. Kobayashi and T. Maskawa, Prog. Theor. Phys. , 652 (1973).[3] E. Barberio et al. th International Conference on High Energy Physics, Philadelphia, 2008 110 -6 -4 -2 0 2 4 6 ∆ t (ps) ∆ t (ps) q=-1 -1-0.75-0.5-0.2500.250.50.751 -6 -4 -2 0 2 4 6 ∆ t (ps) Figure 3: Time-dependent Dalitz plot fit results for B → K S K + K − in the φ (1020) region. The left plot show the ∆ t distribution for B (blue) and ¯ B (red) tags for good tags, 0 . < r ≤ . 0. The right plot shows the B ¯ B raw asymmetry [4] A. B. Carter and A. I. Sanda, Phys. Rev. Lett. , 952 (1980); A. B. Carter and A. I. Sanda, Phys. Rev. D ,1567 (1981); I. I. Bigi and A. I. Sanda, Nucl. Phys. , 85 (1981).[5] A. Abashian et al. (Belle Collab.), Nucl. Instr. and Meth. A , 117 (2002).[6] S. Kurokawa and E. Kikutani, Nucl. Instr. and Meth. A , 1 (2003), and other papers included in this volume.[7] K. Abe et al. (Belle Collaboration), Phys. Rev. Lett. , 101801 (2001); K. Abe et al. (Belle Collaboration),Phys. Lett. B 511 , 151 (2001); S. H. Lee, K. Suzuki, et al. (Belle Collaboration), Phys. Rev. Lett. , 261801(2003).[8] H. Tajima et al. Nucl. Instr. and Meth. A , 370 (2004).[9] H. Kakuno et al. , Nucl. Instr. and Meth. A , 516 (2004).[10] B. Aubert et al. (BaBar Collab.), Phys. Rev. Lett. , 021603 (2007); S.-W. Lin et al. (Belle Collab.), Nature , 332 (2008).[11] M. Gronau, Phys. Lett. B , 82 (2005).[12] C. Amsler (Particle Data Group), Phys. Lett. B , 1 (2008).[13] V. L. Chernyak, Phys. Lett. B , 273 (2001).[14] D. Aston et al. (LASS Collab.), Nucl. Phys. B296