MEASUREMENT OF THE ANGLE φ 1 (β) AND B B MIXING (RECENT RESULTS FROM BaBar AND Belle) Kazuo Abe KEK, Tsukuba, Japan

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1 Physics in Collision - Zeuthen, Germany, June 26-28, 23 MEASUREMENT OF THE ANGLE φ 1 (β) AND B B MIXING (RECENT RESULTS FROM BaBar AND Belle) Kazuo Abe KEK, Tsukuba, Japan ABSTRACT Recent results from BaBar an Belle experiments on B B mixing an sin 2φ 1 are presente. Accuracy of m measurements has reache 1.2%. Higher orer effects within the Stanar Moel or possible new physics effect that might appear in the B B mixing through non-zero Γ/Γ, CP violation, or CP T violation have been explore. The BaBar an Belle results on sin 2φ 1 from the b c cs moes are in goo agreement with each other an a combine result with an accuracy of 8% is in goo agreement with a global CKM fit. A simple average of the sin 2φ 1 values that were measure in the penguin-loop ominate ecay moes, φk S, η K S, an K + K K S, shows about 2.5σ eviation from the Stanar Moel. 15

2 1 e + e Υ(4S) B B A scheme of proucing Υ(4S) in an asymmetric-energy e + e collisin, that is use at PEP-II an KEKB, enables separation of the ecay verteces of the two B mesons. PEP-II operates at 9 GeV e 3.1 GeV e + corresponing to z 26µm, while KEKB operates at 8 GeV e 3.5 GeV e + corresponing to z 2µm. Since the size of interaction region in the z irection is much larger than these z ( 7mm at KEKB), the reference of the proper time must be the ecay point of the other B (See Fig. 1). Conservation of charge-conjugation in the Υ(4S) B B ecay forces z e - e + B rec B tag Figure 1: Schematical rawing of e + e KEKB. Υ(4S) B B process at PEP-II an the time structure of B B system to stay as ψ(t) = B > B > B > B > at any t until one B meson ecays. This feature is use to etermine the flavor of the reconstructe B at t =. 2 B B Mixing Mass an flavor eigenstates of the neutral B meson states are expresse by B 1 >= p B > +q B >, B 2 >= p B > q B >. (1) Well efine time epenence of (B 1, B 2 ) an flavor-specific ecays of (B, B ) lea to the B B oscillation. Probabilities of observing the two B mesons as having the opposite-flavor (OF) or having the same-flavor (SF) at t are expresse by P OF e t/τ B 4τ B [1 + cos( m t)], P SF e t/τ B [1 cos( m t)]. (2) 4τ B The mixing parameters can be obtaine either by reconstructing one B in flavorspecific moes such as D ( ) π, D ( ) ρ, D ( ) lν, an flavor-tagging the other B using information of remaining tracks in the event, or by using ilepton events. For the sin 2φ 1 measurement, we reconstruct one B as CP eigenstates such as J/ψK S. The OF-SF asymmetries that were measure by Belle [1] an BaBar [2] are shown in 16

3 (OS-SS)/(OS+SS) Z (µm) (OF SF)/(OF+SF) D*l ν m = ps t (ps) (OF SF)/(OF+SF) Haronic m = ps t (ps) A( z) z (µm) Figure 2: Belle m measurements base on 32 million B B. From left to right, ileptons, semileptonic ecays, haronic ecays, an partially reconstructe D π ecays. Fig. 2 an 3. The results are summarize in Figure 4. A combine result of BaBar an Belle is m =.54 ±.7 ps 1 which ominates the worl average of m =.52 ±.6 ps 1. Events /.24 ps 4 2 (a) Events /.24 ps (b) Asymmetry 1.5 BABAR A mix 1.5 BABAR c) Asymmetry /.24 ps (c) t (ps) t (ps) t (ps) Figure 3: BaBar m measurements. From left to right, ileptons (23M B B), semileptonic ecays (23M B B), haronic ecays (32M B B). 3 B B mixing in Stanar Moel In the Stanar Moel, box-iagram is responsible for B B mixing, an expresse as m = m H m L = 2 M 12 where M 12 = G2 F m 2 W η B m B B B fb 2 S 12π 2 (m 2 t /m2 W )(V t V tb) 2. (3) Here B 1 an B 2 are reefine as B H an B L. Extraction of V t from m is ominate by a large uncertainty in f B BB = 23 ± 4 MeV [3]. Improve lattice QCD calculations an m s measurements are waite. The mixing also has an absorptive part Γ = Γ L Γ H = 2 Γ 12, which is tiny in the Stanar Moel. Γ 12 M Γ 12 Γ 3π 2 m 2 b m 2 W 1 S (m 2 t /m 2 W ) (±3%). (4) 17

4 ARGUS+CLEO (χ ).49±.32 ps -1 ALEPH (3 analyses).446±.26±.19 ps -1 DELPH (5).519±.18±.11 ps -1 L3 (3).444±.28±.28 ps -1 OPAL (5).479±.18±.15 ps -1 CDF (4).495±.33±.27 ps -1 BABAR ilepton/π s (23M BB) BABAR D*lν (23M BB) BABAR haronic (32M BB) BELLE ilepton (32M BB) BELLE D*lν (32M BB) BELLE haronic (32M BB) BELLE D*π (32M BB).493±.12±.9 ps ±.18±.13 ps ±.16±.1 ps -1.53±.8±.1 ps ±.12±.15 ps ±.17±.11 ps -1.59±.17±.2 ps -1 Worl average.52±.6 ps m (ps -1 ) Figure 4: Present status of m measurements. Any eviation will be ifficult to explain in the Stanar Moel, which of course makes this measurement very interesting. For non-zero Γ, the time-epenent ecay rates for the flavor-specific state (B f( f)) must be moifie as [1 ± cos( m t)] [ cosh Γ ] t ± cos( m t) 2 while for CP eigenstate (B f CP, CP -even (CP -o)), it must be moifie as [1 ± sin 2φ 1 sin( m t)] [ cosh Γ t cos 2φ 1 sinh Γ ] t ± sin 2φ 1 sin( m t). 2 2 (6) CP violation in the B B mixing leas to q/p 1 an it is relate to Γ 12 an M 12 as 1 q ( ) Γ12 p 2 Im. (7) M 12 In the Stanar Moel, q/p is less than 1 3 because Γ 12 /M an φ M12 φ Γ12 = π + O(m 2 c /m2 b ). Probabilities of observing the SF events are given for ++ an combinations separately by P++ SF = p/q 2 P SF an P SF = q/p 2 P SF. Thus a charge asymmetry in the SF events appears if CP is violate. (5) 18

5 CP T violation leas to p p an/or q q where the B meson states are escribe by B H >= p B > +q B >, B L >= p B > q B >. We introuce variables θ an φ where q/p = tan( θ 2 )eiφ, an q /p = cot( θ 2 )eiφ. The time epenence of the OF ecay is moifie as 1+cos( m t) [1+ cos θ 2 +(1 cos θ 2 ) cos( m t) 2Im(cos θ) sin( m t)]. (8) A time-epenent asymmetry in the OF events can appear if CP T is violate [4]. 4 Results of Γ/Γ, q/p, cos θ BaBar has performe a global fit to the fully reconstructe haronic events from the 88M B B sample an extracte Γ/Γ, q/p, Re(cos θ), an Im(cos θ) [5]. BaBar also obtaine q/p from the ilepton events in the 23M B B sample [6]. Belle etermine Im(cos θ) an Re(cos θ) using the ilepton events in the 32M B B sample [1]. Results are summarize in Table 1. Table 1: Results of Γ/Γ, q/p, cos θ. The parameter z is equivalent to cos θ. sgn(reλ CP ) = +1 in SM. Reλ CP / λ CP.672 ±.68. ata variables result BaBar haronic sgn(reλ CP ) Γ/Γ.8 ±.37 ±.18 q/p 1.29 ±.13 ±.11 Reλ CP / λ CP Rez.14 ±.35 ±.34 Imz.38 ±.29 ±.25 BaBar ileptons q/p.998 ±.5 ±.7 Belle ileptons Im(cos θ).3 ±.1 ±.3 Re(cos θ). ±.12 ±.1 5 sin 2φ 1 from J/ψK S an other b c cs ecays Asymmetry of time-epenent ecay rates between (B f) an ( B f) for the final state f = f = f CP is expresse by a f (t) = Γ( B (t) f) Γ(B (t) f) Γ( B (t) f) + Γ(B (t) f) = 2Imλ f λ f sin( mt) + λ f 2 1 λ f cos( mt). (9) Information of CP violation is in a quantity λ f. Namely Imλ f results in mixingassiste CP violation, an λ f 1 results in irect CP violation. The λ f is efine 19

6 as λ f = (q/p) < f H B > / < f H B > where the B B mixing contribution is given by q/p = (VtbV t )/(V tb Vt) which is equal to e 2iφ 1 in the Stanar Moel. For the J/ψK S final state (Fig. 5 followe by K K S ), λ is given by λ(j/ψk S ) = V tbv t V tb V t η ( VcbV cs JψKS Vcb V cs ) ( V cv cs V csv c ). (1) Here η f is CP eigenvalue of the f state. We obtain Imλ(J/ψK S ) = sin 2φ 1 an Imλ(J/ψK L ) = sin 2φ 1. B c _ c s _ J/ψ K Figure 5: Diagram for B J/ψK S. Methos for the event selections are given in etail in references [7] an [8]. The results presente here are base on the ata set of 88M B B for BaBar an 85M B B for Belle. Both group use J/ψK S, ψ K S, χ c1 K S, η c K S, J/ψK, an J/ψK L final states. Except for the J/ψK L final state, the caniate events peak in the mass istributions for reconstructe B mesons. For the J/ψK L events, twoboy ecay of B must be assume since the K L energy cannot be etecte. BaBar uses the energy-ifference, E, between reconstructe B an beam energy, whereas Belle uses the center-of-mass momentum of reconstructe B, p B. They are shown in Fig. 6. Extraction of sin 2φ 1 from the t istributions are one by maximize a likelihoo L = i P i (i each caniate event). The probability of each caniate event is escribe by P i = [f sig P sig ( t )R sig ( t t ) + (1 f sig )P bkg ( t )R bkg ( t t )] t (11) where f sig is signal fraction of caniate event, P sig an P bkg are the probability ensity functions, an R sig an R bkg are the t resolutions. The t istributions an asymmetries are shown in Fig. 7 together with their fit results. The BaBar results are sin 2φ 1 =.741 ±.67 ±.34 an λ =.948 ±.51 ±.3, while the Belle results are sin 2φ 1 =.719 ±.74 ±.35 an λ =.95 ±.49 ±.25. A combine result is sin 2φ 1 =.734 ±.55. Fig. 8 shows an allowe region of (ρ-η) plane from the sin 2φ 1 measurement an from a global CKM fit without using sin 2φ 1. Agreement is excellent. 11

7 Events / 2.5 MeV/c 2 Events / 2 MeV B J/ψK S ψ(2s)k S χ c1k S η ck S J/ψK Backgroun m ES (GeV/c 2 ) J/ψK L signal J/ψX backgroun Non-J/ψ backgroun a) b) Number of events / (.5 GeV/c) events Purity = 63 % J/Ψ K L (834 events) J/Ψ K L X BG, K L etecte J/Ψ X BG, other combinatorial BG p cms B (GeV/c) E (MeV) Figure 6: (Left) Beam-energy substitute mass istribution for the η CP = 1 final states an E istribution for the J/ψK L final state for BaBar. (Right) Beamenergy substitute mass istribution for the η CP = 1 final states an p B istribution for the J/ψK L final state for Belle. Entries /.6 ps Raw Asymmetry B tags B tags Backgroun Raw Asymmetry Entries /.6 ps B tags B tags Backgroun 1/N N/( t).2.1 qξ f =+1 qξ f = 1 Raw Asymmetry.5 (a)combine.5.5 (b)(cc_ )K S (ξ f = 1).5.5 (c) J/ψK L (ξ f =+1).5 ()Non-CP sample t (ps) t (ps) t (ps) t (ps) Figure 7: BaBar t istributions an asymmetries for CP -o final states (far-left) an J/ψK L state (2n-left). Belle t istributions for a sum of B -tagge J/ψK L an B -tagge CP -o states (labele as qξ f = +1) an for a sum of B -tagge J/ψK L an B -tagge CP -o states (labele as qξ f = 1) (2n-right). Far-right are Belle asymmetries for qξ f = +1 an qξ f = + 1 samples combine (a), each separately (b) an (c), an for non-cp sample (). 111

8 1 m m s & m ε K η V ub /V cb sin 2β WA ε K -1 C K M f i t t e r ρ Figure 8: Shae area are for 1σ an 2σ regions from the BaBar-Belle combine value of sin 2φ 1. 9% (5%) CL contours from a global CKM fit are also shown. 6 sin 2φ 1 from loop iagram ecays 6.1 φk S The B φk S ecay has only b ss s penguin contribution in the Stanar Moel (Fig. 9). Leaing term has a CKM factor of V cb V cs (P c P t ) = Aλ 2 (P c P t ), where B u _,c _,t _ s _ s s _ φ K Figure 9: Stanar Moel contribution to B φk S. P q are the penguin amplitues. This is same as the CKM factor for B J/ψK S. Next-to-leaing term V ub Vus (P u P t ) = Aλ 4 (ρ iη)(p u P t ) has a ifferent phase, but is suppresse by λ 2 5%. Since η φks = 1, sin 2φ 1 measure in this moe shoul be the same as that for the J/ψK S in the Stanar Moel. In orer to allow room for new physics, we parameterize the asymmetry istribution by where a f ( t) = S f sin( m t) + A f cos( m t) (12) S f = 2Imλ f λ f ( η f sin 2φ 1 in SM), A f = C f = λ f 2 1 ( in SM). (13) λ f

9 Any eviation woul be an inication of new physics in penguin loop. The BaBar results base on 84M B B [9] are S φks =.18 ±.51 ±.7 an A φks = +.8 ±.38 ±.12, whereas the Belle results base on 85M B B [1] are S φks =.73 ±.64 ±.22 an A φks =.56 ±.41 ± η K S This moe is contribute by b ss s penguin, b s penguin, an b u tree iagrams (Fig. 1). In the Stanar Moel, presence of aitional b s penguin u _,c _,t _ s _ η s B s _ K u _,c _,t _ s _ K B _ η u _ η u B s _ K Figure 1: Stanar Moel contributions to B η K S. oes not cause any change from the φk S case, an only ifference is the aitional b u tree iagram which is only 5% effect. Since η η K S = 1, we expect to have S f sin 2φ 1. The BaBar results base on 88.9M B B [11] are S η K S = +.2±.34±.3b an A η K S =.1 ±.23 ±.3, whereas the Belle results base on 85M B B [1] are S η K S = +.71 ± an A η K S = +.26 ±.22 ± K + K K S This ecay is contribute by b s penguin an b u tree iagrams (Fig. 11). The Belle analysis for this ecay moe shows that the b u tree contribution u _,c _,t _ s _ u u _ s s b s _ u u _ s s _ Figure 11: Stanar Moel contributions to B K + K K S. is negligible an furthermore CP content of the final state is preominantly even (η K + K K S = +1) [1]. Therefore we expect S f sin 2φ 1. The results base on 85M B B are S K + K K S =.49 ±.43 ±.11 an A K + K K S =.4 ±.33 ±.1. Fig. 12 summarizes the ( η f S f ) measurements for the penguin loop ecays. An average sin 2φ 1 of those three penguin ecays is.19 ±.2, about 2.5σ off the 113

10 BABAR φk S -.18±.51±.7 BELLE φk S -.73±.64±.22 BABAR η K S.2±.34± BELLE.71± η K S BELLE.49±.43±.11 K + K - K S penguin loop WA.19±.2 sin 2φ 1 WA.73± η f S f Figure 12: Summary of η f S f measurements for the penguin loop ecays. Stanar Moel. We are entering an exciting era for exploring new physics through sin 2φ 1 measurements in ifferent ecay moes. 7 sin 2φ 1 from other moes 7.1 J/ψπ In this moe, the tree an penguin contributions are of comparable size(fig. 13). The CKM factors are V cb Vc = Aλ 3 for the tree, an V cb Vc(P c P t ) = Aλ 3 (P c P t ) an V ub Vu(P u P t ) = Aλ 3 (ρ iη)(p u P t ) for the penguins, respectively. In an B c _ J/ψ c _ π _ b u _,c _,t _ Figure 13: Stanar Moel contributions to B J/ψπ. B c c J/ψ π 114

11 extreme case of ignoring the penguin, we obtain S f sin 2φ 1 since η J/ψπ = +1. If a eviation is seen, presence of penguin shoul be suspecte first. The BaBar results base on 88M B B [12] are S J/ψπ = +.5±.49±.16 an A J/ψπ =.38±.41±.9, whereas the Belle results base on 85M B B [13] are S J/ψπ =.93±.49±.8 an A J/ψπ =.25 ±.39 ± D + D an D + D These moes have similar penguin pollution as J/ψπ (Fig. 14). The CKM factors are V cb Vc = Aλ 3 for the tree, an V cb Vc(P c P u ) = Aλ 3 (P c P u ) an V tb Vt(P t P u ) = Aλ 3 (1 ρ + iη)(p t P u ) for the penguins, respectively. BaBar angular c D (*)+ - B b - c - D (*)- b u _,c _,t D (*)+ c B c _ D (*)- Figure 14: Stanar Moel contributions to B D ( )+ D ( ). analysis [15] showe that CP content of the D + D final state is preominantly even (η D + D +1). In an extreme case of ignorin the penguin, we obtain S f sin 2φ 1. The D + D final state is not a CP eigenstate. In an extreme case of ignoring the penguin, we obtain S ± f = S f sin 2φ 1. The BaBar results base on 88M B B [14] are 8 Summary S D ± D =.24 ±.69 ±.12, S D D =.82 ±.75 ±.14 A ± D D = +.22 ±.37 ±.1, A D D = +.47 ±.4 ±.12. (14) Precision of m has reache 1.2%. Attempt for observing higher orer effect an possible new physics effects in B B mixing are vigorously explore. The m measurements are an important testing groun for the t measurement an flavortagging. Precision of sin 2φ 1 has reache 8%. Statistical error still ominates. It is in goo agreement with a global CKM fit (without sin 2φ 1 ). λ is consistent with 1 in b c cs ecays as expecte in the Stanar Moel. New physics search by sin 2φ 1 measurements in penguin loops is well uner way. sin 2φ 1 measurements for penguin pollute ecays were also pushe to fin useful information. 115

12 References 1. N. Hasting et al., Phys. Rev. D 67, 524 (23); K. Hara et al., Phys. Rev. Lett. 89, (22); T. Tomura et al., Phys. Lett. B (22); Y. Zheng et al., Phys. Rev D 67, 924 (23). 2. B. Aubert et al. Phys. Rev. Lett. 88, (22); B. Aubert et al. Phys. Rev. Lett. 88, (22); B. Aubert et al, hep-ex/ K. Hagiwara et al. (Particle Data Group), Phys. Rev. D 66, 11 (22). 4. See, for example, A. Mohapatra, M. Satpathy, K. Abe, an Y. Sakai, Phys. Rev. D 58, 363 (1998). 5. hep-ex/ B. Aubert et al., Phys. Rev. Lett. 88, (22). 7. B. Aubert et al. Phys. Rev. Lett. 89, 2182 (22). 8. K. Abe et al. Phys. Rev. D 66, 7112 (22). 9. Talk presente at Morion Conference (March 23). 1. K. Abe et al. Phys. Rev. D 67, 3112(R) (23). 11. B. Aubert et al. hep-ex/ B. Aubert et al. hep-ex/ K. Abe et al. Belle-CONF B. Aubert et al. hep-ex/ Talk presente at FPCP (June 23). 116