c-Conf-97-278-T.ps,/usr/people/preprint/covers/cover_2.ps,p-Conf-97-278-T.ps F Fermi National Accelerator Laboratory FERMILAB-Conf-97/278-T Beautiful CP Violation Isard Dunietz Fermi National Accelerator Laboratory P.O. Box 500, Batavia, Illinois 60510 October 1997 Presented at the b20 Conference, IIT, Chicago, June, 1997 Operated by Universities Research Association Inc. under Contract No. DE-AC02-76CH03000 with the United States Department of Energy Disclaimer This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, expressed or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any speci�c commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or re ect those of the United States Government or any agency thereof. Distribution Approved for public release; further dissemination unlimited. hep-ph/9709448 24 Sep 1997 F E R M IL A B { C O N F { 9 7 / 2 7 8 { T h ep -p h / 9 7 0 9 4 4 8 B e a u t if u l C P V io la t io n I s a r d D u n ie t z F e r m i N a tio n a l A c c e le ra to r L a b o ra to r y , P .O . B o x 5 0 0 , B a ta v ia , IL 6 0 5 1 0 A b s t r a c t . C P v io la tio n is o b serv ed to d a te o n ly in K 0 d eca y s a n d is p a ra m eteri- za b le b y a sin g le q u a n tity �. B eca u se it is o n e o f th e lea st u n d ersto o d p h en o m en a in th e S ta n d a rd M o d el a n d h o ld s a clu e to b a ry o g en esis, it m u st b e in v estig a ted fu rth er. H ig h ly sp ecia lized sea rch es in K 0 d eca y s a re p o ssib le. E � ects in B d eca y s a re m u ch la rg er. In a d d itio n to th e tra d itio n a l B d ! J = K S ; � + � � a sy m m etries, C P v io la tio n co u ld b e sea rch ed fo r in a lrea d y ex istin g in clu siv e B d a ta sa m p les. T h e ra p id B s � B s o scilla tio n s ca n cel in u n ta g g ed B s d a ta sa m - p les, w h ich th erefo re a llo w fea sib ility stu d ies fo r th e o b serv a tio n o f C P v io la tio n a n d th e ex tra ctio n o f C K M elem en ts w ith p resen t v ertex d etecto rs. T h e fa v o red m eth o d fo r th e ex tra ctio n o f th e C K M a n g le is sh o w n to b e u n fea sib le a n d a so lu tio n is p resen ted in v o lv in g strik in g d irect C P v io la tio n in ch a rg ed B d e- ca y s. N o v el m eth o d s fo r d eterm in in g th e B s m ix in g p a ra m eter � m a re d escrib ed w ith o u t th e tra d itio n a l req u irem en t o f a v o r-sp eci� c � n a l sta tes. I IN T R O D U C T IO N M o re th a n th irty y ea rs a fter its d isco v ery, C P v io la tio n rem a in s a m y stery. O u r en tire k n o w led g e a b o u t it ca n b e su m m a rized b y th e sin g le p a ra m eter � [1 ]. C P v io la tio n is n o t ju st a q u a in t tin y e� ect o b serv ed in K 0 d eca y s, b u t is o n e o f th e n ecessa ry in g red ien ts fo r b a ry o g en esis [2 ]. W ith in th e C K M m o d el, it is co n n ected a lso to th e q u a rk -m ix in g a n d h iera rch y o f q u a rk m a sses. A su ccessfu l th eo ry o f C P v io la tio n w ill h a v e fa r-rea ch in g ra m i� ca tio n s in co sm o lo g y a n d h ig h en erg y p h y sics. A t p resen t, w e a re n o t a b le to a n sw er ev en th e q u estio n ra ised b y W o lfen stein m o re th a n 3 0 y ea rs a g o : Is C P v io la tio n d u e to a n ew su p erw ea k in tera ctio n , w h ich w o u ld sh o w u p essen tia lly o n ly in m ix in g -in d u ced p h en o m en a ? O r a re th ere d irect C P v io la tin g e� ects? T h ere ex ists a m u ltitu d e o f scen a rio s fo r C P v io la tio n , a ll co n sisten t w ith �. W h a t is n eed ed is th e o b serv a tio n o f m a n y in d ep en d en t C P v io la tin g e� ects. T h is w o u ld b e in v a lu a b le in d irectin g u s to w a rd a m o re fu n d a m en ta l u n d ersta n d in g o f C P v io la tio n , in a n a lo g y to th e http://xxx.lanl.gov/abs/hep-ph/9709448 history of parity violation. There a variety of measurements guided us to the successful V � A theory [3]. Searches for (direct) CP violation in K and hyperon decays are impor- tant [1,4]. Because the expected e�ects are either tiny for processes with sizable BR's or could be large but then involve tiny BR's O(10�11), ingenious experimental techniques are being developed to overcome those handicaps. A whole class of additional independent CP measurements can be obtained from studies of b-hadron decays. Although CP violation may not be (entirely) due to the CKM model, that model serves here as a guide. Decays of b-hadrons can access large CKM phases and thus large CP violation, because the b-quark is a member of the third generation. There are many proposed methods that involve large CP violating e�ects [5]. This talk focuses on recently discussed phenomena, some of which can be studied with presently existing data sam- ples. First, (semi-)inclusive B decays are expected to exhibit CP violation and CKM parameters can be extracted [6{8]. Even the Bs mixing-parameter �m could be determined from such avor-nonspeci�c �nal states, in addition to the conventional methods [9,10]. Second, untagged Bs data samples are predicted to exhibit CP violation and permit the extraction of CKM parameters, as long as the Bs width di�erence is signi�cant [11]. The far-reaching physics potential of the Bs ! J= � process is touched upon. The third topic explains why the favorite method for determining the CKM angle , pioneered by Gronau-London-Wyler (GLW) [12], is unfeasible. The CKM parameter can be cleanly extracted [13], however, when one incorporates the striking, direct CP violating e�ects in B ! D0=D0 transitions [14], which were not considered by GLW. II EXCLUSIVE AND INCLUSIVE B DECAYS Traditional methods involve exclusive modes such as J= KS [15], � +�� [16{18], and study the rate-asymmetry between Bd(t) ! J= KS; �+�� 6= Bd(t) ! J= KS; �+�� : (1) The e�ective BR is tiny � 10�5, but the asymmetries are large O(1). How does this large asymmetry come about? The unmixed Bd could decay into J= KS directly, Bd ! J= KS. The CP conjugated process is the direct decay, Bd ! J= KS. To excellent accuracy, those two direct decay rates are equal. The Bd could mix �rst into a Bd and then decay to J= KS;Bd(t) ! Bd ! J= KS. The CP conjugated process is the mixing-induced Bd(t) ! Bd ! J= KS transition. Again, to excellent accuracy, the magnitudes of the two mixing-induced amplitudes are the same. The large CP violation predicted in the CKM model occurs because of the interference of the direct and mixing-induced amplitudes. To form the asymmetry, it is not su�cient to reconstruct the �nal state J= KS. One must be able to distinguish those reconstructed events as originating from an initial Bd versus Bd (referred to as tagging). Initially (at t = 0) the neutral B meson has no time to mix. At t = 0 there is no mixing-induced amplitude and thus no CP violation. There is almost no loss in measuring the asymmetry by not considering J= KS events within the �rst Bd lifetime or so. While the rate is largest during that time-interval, the asymmetry is tiny and needs large proper times to build itself up [18,19]. Triggering on detached vertices is thus more e�cient for such CP violation studies than one might think naively. Inclusive B samples are many orders of magnitude larger than the exclusive ones and can be accessed by vertexing. The time-dependent, totally inclusive asymmetry, I(t) � �(B 0(t) ! all) � �(B0(t) ! all) �(B0(t) ! all) + �(B0(t) ! all) ; (2) is CP violating [7,8]. That appears to be rather puzzling, especially because the CPT theorem guarantees that the totally inclusive width is the same for particle and antiparticle. That CPT stranglehold is removed, because B0 �B0 mixing provides an additional amplitude and thus novel interference e�ects. The totally inclusive CP asymmetry I(t) is related to the wrong-sign asymmetry [20,21] �(B0(t) ! W) � �(B0(t) ! W) �(B0(t) ! W) + �(B0(t) ! W) = �a = �Im �12 M12 ; (3) where W denotes \wrong-sign" avor-speci�c modes that come only from B 0 ! W and never from B0 ! W; such as W = `�X and W = D+s n ��;��;a�1 o for Bs decays [W = D (�)D(�)�s ;DD KX;J= K � for Bd de- cays]. The data samples for the I(t) asymmetries exist already. For instance, the SLD collaboration determined the lifetime ratio of neutral to charged b- hadrons by an inclusive topological vertex analysis [22]. The polarization of Z0 provides a large forward-backward asymmetry of b production and thus an e�ective initial avor-tag [23] and it is clear that SLD can study inclusive asymmetries. Similarly, the LEP experiments are able to study I(t) by using their b-enriched samples and optimal avor-tagging algorithms. CDF has several million high PT-leptons, which are highly enriched in b content. The data sample of detached vertices on the other hemisphere allows CDF to study I(t). The newly installed vertex detector at CLEO permits meaningful studies, because the I(t) asymmetry becomes signi�cant only after a few Bd lifetimes, see Eq. (4) below. For �� = 0, the explicit time dependence is [7] -0.10 -0.05 0.00 0.05 0.10 0.0 0.5 1.0 1.5 2.0 t / τ(Bs) I(t) FIGURE 1. The totally inclusive CP asymmetry of Bs(t) ! all, with a = 0:01;�� = 0 and x = 20 (see Eqs. (2),(4)). I(t) = a � x 2 sin�mt� sin2 �mt 2 � ; (4) where x � �m=�. The observable a can thus be extracted from a study of I(t). For Bs mesons, that extraction o�ers a signi�cant statistical gain over the conventional method [Eq. (3)]. The factor of x=2 enhances I(t) over a by an order of magnitude, which corresponds to a statistical gain of O(102). There is another gain, because all Bs decays are used rather than avor-speci�c Bs modes that must be e�ciently distinguished from Bd modes. The distinc- tion involves stringent selection criteria. The reason is that the wrong-sign asymmetry [Eq. (3)] is time-independent, and the wrong-sign Bd asymmetry is an order of magnitude larger than the Bs one, within the CKM model. Thus, for instance, the high-p (-PT) leptons must originate from Bs decays and not from Bd decays. This can be achieved by either studying wrong-sign Bs modes at very short proper times [24], or by inferring the existence of a Ds, or by observing such primary kaons that signi�cantly enrich the Bs content, or by a combination of the above. In contrast, the unique time-dependence of I(t) provides automatic discrimination. For the Bs meson at least, the time- dependent inclusive asymmetry may be more e�ective in extracting the CP violating observable a than the conventional wrong-sign asymmetry. Figure 1 shows what to expect for the choice x = 20 and where New Physics is allowed to enhance a = j�12=M12j � 0:01. The observation of a non- vanishing I(t) proves CP violation and in addition allows a determination of the Bs � Bs mixing parameter �m from avor-nonspeci�c �nal states. The traditional methods for extracting �m require avor-speci�c �nal states and tagging [9,10]. We will mention later on additional ways to extract �m with avor-nonspeci�c �nal states. Within the CKM model, the totally inclusive asymmetries are tiny O(10�3) for Bd and O(10�4) for Bs [25,26]. The ability to select speci�c quark tran- sitions enhances the asymmetries by orders of magnitude, at times to the � (10�20)% level [7]. Such selections permit extractions of CKM phases and to conduct the study in either a time-integrated or time-dependent fashion.1 Those analyses should be pursued whenever feasible. There exist unitarity constraints, which allow systematic cross-checks. Future B detectors will be able to more fully explore the potential with such semi-inclusive data samples. III PHYSICS WITH (UNTAGGED) BS MESONS One conventional way to determine the CKM angle is the time-dependent study of tagged (�) Bs (t) ! D�s K� processes [27], and in the neglect of penguin amplitudes (�) Bs (t) ! �0KS;!KS transitions [17,18,28]. It requires avor- tagging and the ability to trace the rapid �mt-oscillations. The requirements are problematic: (a) Flavor-tagging is at present only a few percent e�cient at hadron accel- erators [29].2 (b) Resolution of �mt-oscillations is feasible for x �<20 with present vertex technology [9], but LEP experiments reported [10], x �>15 : (5) Though �mt-oscillations may be too rapid to be resolved at present, such large �m may imply a sizable width di�erence �� [31]. Non-perturbative e�ects may further enhance �� considerably [32]. Perhaps �� will be the �rst observable Bs �Bs mixing e�ect [11], which would circumvent problems (a) and (b). The �mt-terms cancel in the time-evolution of untagged Bs [11], f(t) � �(Bs(t) ! f) + �(Bs(t) ! f) = ae��Lt + be��Ht ; (6) which is governed by the two exponentials e��Lt and e��Ht alone. That fact permits many non-orthodox CP violating studies and extractions of CKM parameters [11]: (1) Consider �nal states with de�nite CP parity, fCP , such as � 0KS;!KS; :::: If the untagged time-evolution fCP (t) is governed by both exponentials e ��Lt and e��Ht, then CP violation has occured [11]. The measurement of fCP (t) 1) For Bs mesons, �m could be extracted from such more re�ned studies. 2) Though, in principle almost all B-decays could be avor-tagged [30]. allows even the extraction of CKM parameters [11,33]. The physics of the J= � �nal state is very instructive. The time-evolution of untagged J= � could show CP violating e�ects [33]. The (�) Bs! J= � has CP-even and CP- odd amplitudes, (�) A + and (�) A� respectively. Angular correlations [34] allow to measure the interference terms between CP-even and CP-odd amplitudes, which for untagged data samples is proportional to [33], � e��Ht � e��Lt � �22� ; where � � 0:22: (7) The observation of such a non-vanishing term would prove CP violation and would permit the extraction of the CKM parameter �. Note that the observ- able depends optimally on the width di�erence. Those interference terms once tagged allow the measurement of �m, even though J= � is a avor-nonspeci�c �nal state [34]. To demonstrate the point most sharply, neglect CP violation and set �� = 0. Then A+(t) � e�imLt and A�(t) � e�imHt. The observable A+(t)A��(t) � ei�mt depends on �m � mH �mL. Ref. [35] describes yet another method for measuring �m without avor-speci�c �nal states. (2) After several Bs lifetimes, the long-lived B H s � Bs �Bs will be signi�- cantly enriched over the short-lived BLs . Consider then �nal states f that can be fed from both Bs and Bs, and that are non-CP-eigenstates. CP violation is proven if the time evolution of untagged f(t) di�ers from untagged f(t), f(t) 6= f(t) ) CP violation : (8) Furthermore, the CKM angle can be extracted from time-dependent studies of D�s K �(t); (�) D0 �(t) [11].3 CP violating e�ects and CKM extractions can be enhanced by studying D(�;��)�s K ��(t) [36]. In summary, neither avor-tagging nor exquisite tracing of �mt-oscillations are necessary, only a large ��. IV DIRECT CP VIOLATION AND EXTRACTING CKM ANGLES The favorite method (particularly at �(4S) factories) for determining has been developed by Gronau, London and Wyler (GLW) [12] and requires the measurements of the six rates B� ! D0K�;D0K� and D0CP K�. Here D0CP denotes that the D 0 is seen in CP eigenstates with either CP-even 3) The determination of from (�) D0 �(t) and D0 CP �(t) as presented in Ref. [11] must include the e�ect of doubly-Cabibbo suppressed (�) D0 decay-amplitudes [14,13]. A(B� ! D0K�) = A(B+ ! D 0 K +) p 2A(B+ ! D0 CP K +) p 2A(B� ! D0 CP K �) A(B� ! D 0 K �) A(B+ ! D0K+) 2 FIGURE 2. The traditional GLW method for extracting the CKM angle . (K+K�;�+��; :::) or CP-odd (KS�;KS� 0; :::) parity. The GLW method fo- cuses on the CP violating rate di�erence of B+ ! D0CP K+ versus B� ! D0CP K � [37], which can reach at best the 10% level and is probably signi�- cantly smaller. In principle, the GLW method is a great idea. However, new CLEO data indicate that the method is unfeasible, and that the largest CP violating e�ect has been overlooked [14,13]. Once the e�ect has been incorporated, the CKM angles can be cleanly extracted [13]. Let us review the original GLW method, point out the problem, and show how it can be overcome. Consider CP even D0CP , for which D0CP = 1p 2 (D0 + D 0 ) : (9) Then p 2A(B� ! D0CP K�) = A(B� ! D0K�) + A(B� ! D 0 K�) ; (10) and that amplitude triangle is shown in Figure 2. The weak phase di�erence of the two interfering amplitudes is . GLW argued that the magnitudes of each of the sides of the triangle can be measured (being proportional to the square roots of the respective rates), and thus claimed that the amplitude triangle can be fully reconstructed. Figure 2 has not been drawn to scale. The B� ! D0K� amplitude is an order of magnitude smaller than the B� ! D0K� one, which can be seen as follows [13]. The CKM factors suppress the amplitude ratio by about 1/3. The D 0 K� is color-suppressed while D0K� is also color-allowed, yielding another suppression factor of about 1/4. Nothing changes when the CP conjugated �nal states are considered, except that the CKM elements have to be complex conjugated. Apparently, the CP-conjugated triangle can also be determined, see Figure 2. The A(B+ ! D0K+) is rotated by 2 with respect to A(B� ! D0K�); and apparently the angle can be extracted. Note that the only CP violation in all these processes occurs in �(B+ ! D0CP K+) 6= �(B� ! D0CP K�) (11) while there is no CP violation in �(B+ ! D0K+) = �(B� ! D0K�) ; and (12) �(B+ ! D0K+) = �(B� ! D0K�) : (13) In principle this argument is correct, but in practice the largest direct CP violating e�ects (residing in those processes) will be seen in [14,13] B+ ! D0K+ 6= B� ! D0K� : (14) The D 0 produced in the B� ! D0K� process is seen in its non-leptonic, Cabibbo-allowed modes f, such as K+��;K��. It was assumed that the kaon avor unambiguously informs on the initial charm avor. This assumption overlooked the doubly-Cabibbo-suppressed D0 ! f process which leads to the same �nal state B� ! D0[! f]K�. Further, CLEO has measured [38] ����� A(D0 ! f) A(D 0 ! f) ����� � 0:1 ; (15) which maximizes the interference, ����� A(B� ! K�D0[! f]) A(B� ! K�D0[! f]) ����� � 1 ; (16) A(B� ! K�[f]) = A(B� ! K�D0[! f]) + A(B� ! K�D0[! f]) : (17) The conditions are ideal for striking direct CP violating e�ects. They require that the interfering amplitudes be comparable in size (Eq. (16)), that the weak phase di�erence be large ( in our case), and that the relative �nal- state-phase di�erence be signi�cant. It is an experimental fact that large �nal state phases occur in many D decays [39]. This enables us to engineer large CP violating e�ects by optimally weighting relevant sections of generalized Dalitz plots. The traditional focus on CP eigenmodes of D0CP automatically excludes this so potent source of �nal-state interaction phases. The orthodox method [37,12] accesses only the �nal-state phase di�erence residing in B� ! D0K� versus B� ! D0K�, which is expected to be signi�cantly more feeble [40]. The CKM angle can be cleanly extracted once one incorporates the �ndings of this section [13], because penguin amplitudes are absent. The extraction of and the observation of CP violation is optimized by combining detailed (experimental) investigations of D0 decays with B� decays to (�) D0 [13]. This provides yet another reason for accurate measurements of D0 decays. Note also that observation of direct CP violation (as advocated in this section) would rule out superweak scenarios as the only source for CP violation. V CONCLUSION CP violation has been observed only in K0 decays and is parameterizable by a single quantity �. It is one of the necessary ingredients for baryogenesis [2], and within the CKM model is related to the quark-mixing and hierarchy of quark masses. It is one of the least understood phenomena in high energy physics and a very important one. Just as the successful V �A theory of parity violation [3] emerged from a synthesis of many independent parity violating measurements, so a more fundamental understanding of CP violation will pro�t from many independent observations of CP violation. This talk thus emphasized that CP violation should not only be searched in traditional exclusive Bd ! J= KS;�+�� rate asymmetries. Observable CP violating e�ects could be present in (semi-)inclusive B decays, and could be searched for with existing data samples. The time-evolutions of untagged Bs data samples have no rapid �mt-oscillations. Still CP violation could be observed and CKM parameters extracted as long as �� is sizable. Many striking direct CP violating e�ects in B decays are possible. The observation of CP violation and CKM extraction are optimized by detailed studies of D decays. VI ACKNOWLEDGEMENTS This work was supported in part by the Department of Energy, Contract No. DE-AC02-76CH03000. REFERENCES 1. B. Winstein and L. Wolfenstein, Rev. Mod. Phys. 65, 1113 (1993). 2. A.D. Sakharov, JETP Lett. 5, 24 (1967). 3. R.P. Feynman and M. Gell-Mann, Phys. Rev. 109, 193 (1958); E.C.G. Sudar- shan and R. Marshak, Phys. Rev. 109, 1860 (1958). 4. G. Buchalla, hep-ph/9612307. 5. 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