Extraction of the weak angle gamma from B to charm decays
aa r X i v : . [ h e p - ph ] A p r Nikhef-2011-009
Extraction of the Weak Angle γ from B to Charm Decays Robert Fleischer a and Stefania Ricciardi ba Nikhef, Science Park 105, NL-1098 XG Amsterdam, The Netherlands b STFC Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire, OX11 0QX, UK
Abstract
We give a summary of the discussions in Working Group V of the CKM2010 workshop deal-ing with determinations of the angle γ of the unitarity triangle of the Cabibbo–Kobayashi–Maskawa matrix from B -meson decays into charmed final states. Summary of Working Group V6th International Workshopon the CKM Unitarity Triangle (CKM2010)Warwick, United Kingdom, 6–10 September 2010To appear in the Proceedings
March 2011
Introduction
The angle γ of the unitarity triangle (UT) of the Cabibbo–Kobayashi–Maskawa(CKM) matrix plays a central role for the testing of the flavour sector of the Stan-dard Model (SM). On the one hand, this angle can be extracted from B -meson decayswith contributions from loop (penguin) diagrams. On the other hand, it can also bedetermined by means of pure tree decays into final states with charm. The latteravenue was the topic of this working group. We had 12 talks [1]–[12], with mainlyexperimental discussions of time-dependent and time-integrated measurements of γ .The outline of this summary report follows closely the working group agenda. InSection 2, we make the case for a precise measurement of γ . In Sections 3 and 4, wediscuss new results from well-established methods and from new methods (proposedsince the CKM2008 workshop), respectively. In Section 5, we address the prospectsfor the measurement of γ at the LHCb experiment and beyond. Finally, we summarizeour concluding remarks in Section 6. For references to original papers, the reader isreferred to the contributions listed in [1]–[12]. γ Decays of B mesons into final states with charm offer a variety of strategies to de-termine γ . Here the sensitivity on this angle arises from interference effects between¯ b → ¯ c and ¯ b → ¯ u quark-level processes in decays of the kind B → DK . These decaysoriginate only from tree-diagram-like topologies, i.e. we have no contributions frompenguin diagrams, and involve only one weak phase difference. In addition to γ , alsoother B and D hadronic parameters enter the analyses, typically involving the ratioof colour-suppressed to colour-allowed amplitudes and CP-conserving strong phases.Several methods to extract all unknown parameters from the data were proposed,using combinations of several D modes or input from charm studies.In his talk [1], setting the stage for the discussions in our Working Group, JureZupan addressed the question: how clean are these determinations? The usual kindof reasoning is along the lines that these decays involve only tree-level amplitudes andare hence not affected by theoretical uncertainties. Moreover, they are considered toreceived no new-physics (NP) contributions and serve as standard candles for the SM.A potential source for theory errors is D – ¯ D mixing. Since this is a stronglysuppressed phenomenon in the SM, it leads to a small error for the determination of γ ,at most ∼ ◦ if it is completely neglected. However, if the D – ¯ D mixing parameters x D ( ∝ mass difference) and y D ( ∝ lifetime difference) are measured precisely, themixing effects can be taken into account. Consequently, D – ¯ D mixing does not leadto an irreducible uncertainty.The second potential source of theoretical uncertainty is related to electroweak1orrections, which may change the phase structure of the decay amplitudes throughbox-diagram topologies. However, the corresponding irreducible theoretical error isestimated as δγ/γ = O (10 − ), and is hence not any issue from the practical point ofview [1].Concerning the current status of the measurement of γ through B -meson decaysinto charmed final states, the error is still very large: γ = (cid:26) (cid:0) +21 − (cid:1) ◦ (CKMfitter Collaboration)(73 ± ◦ (UTfit Collaboration). (1)Interestingly, individual measurements are more precise than the CKMfitter average,which raises questions on the statistical procedures used. This was not discussed indetail within our working group. However, there was consensus that a larger datasample will reduce the disagreement between different statistical treatments.The current experimental precision is much beyond the B -factories design expec-tations, which is mainly due to the excellent performance of the accelerators andexperiments and to the use of the GGSZ method, which entered the scene at theCKM2003 workshop.Nevertheless, the determinations of γ from B decays into charmed final states havethe smallest theoretical uncertainties, but suffer from the largest experimental errorsamong all constraints for the UT. Let us next discuss new results from well-establishedmethods in more detail. Well-established methods exist for two distinct types of analyses: time-integrated,which access γ through measurements of direct CP violation in charged or self-taggedneutral B decays, and time-dependent, which extract the weak-phase 2 β ( s ) + γ frommeasurements of interference between B s ) decays with and without mixing. Time-integrated measurements have been successfully performed by the B -factoryexperiments and currently provide the best precision on γ . They are limited by sta-tistical uncertainties, hence the present knowledge of γ can be significantly improvedby additional measurements with larger B samples. It should be noted that the B -decay parameters do not depend on the D -decay mode (and vice-versa), thereforeexperiments can gain more than just statistics by extracting γ via a combined fit todifferent channels. Different D decay channels have been exploited by the Belle andBaBar collaborations, corresponding to three different time-integrated methods: the2LW method for CP eigenstates, the ADS method for doubly Cabibbo-supppresseddecays, and the GGSZ method for three-body self-conjugate final stats.Particularly interesting new results have been presented at this workshop for theADS method for B → D ( Kπ ) K decays for both the Belle [6] and the CDF [8]collaborations. This is a powerful method where the CP asymmetry is enhanced forfinal states with two opposite-charge kaons, because the two interfering amplitudeshave similar size.At CKM2010, Belle has reported the first evidence of the suppressed decay B − → D ( K + π − ) K − , obtained from the full data sample collected at the Υ(4 S ) resonance,corresponding to 7 . × B ¯ B pairs. The preliminary results on the relative rate, R ADS , of B − → D DCS K − to B − → D CF K − , R ADS = (cid:2) . ± . +0 . − . (syst.) (cid:3) × − , (2)corresponds to 3 . σ evidence for the suppresssed mode, while no significant CPasymmetry, A ADS = − . ± . +0 . − . (syst.) , (3)is observed between the B + and B − suppressed decays.Time-integrated methods are well-suited for hadron colliders, because they do notrequire B -tagging, hence their large B production can be fully exploited. However,selecting pure samples of fully hadronic B → DK decays requires detectors withexcellent trigger and PID capabilities. At this workshop, the CDF Collaborationpresented the first measurement of R ADS and A ADS at the Tevatron. Results arebased on a luminosity of 5 fb − and are in good agreement with existing B -factorymeasurements. These results supplement the recently published GLW analysis byCDF within a global programme to measure γ from tree-dominated processes. Theprecision of these measurements is comparable, even if not competitive yet, with thecurrent best measurements from the B factories, and will improve with the full datasample of (10–12) fb − , which is expected by the end of 2011. Most importantly,these results are a demonstration of the feasibility of these measurements at hadroncolliders.The BaBar Collaboration has recently published new results for all the threemethods (ADS, GLW and GGSZ) [7]. The measurements have been performed onthe full sample of 468 million B ¯ B pairs. The achieved precision on γ , around 15 ◦ , isdominated by the result achieved with the GGSZ method. The BaBar GGSZ analysisis based on B ± → DK ± , D ∗ K ± , and DK ∗± decays, followed by neutral D -mesondecays to K h + h − ( h = π, K ). The weak phase γ and other B -decay parameters areextracted from an amplitude fit to the Dalitz plot distributions of the D decays. The D and ¯ D decay amplitudes to K h + h − are modeled by the coherent sum of a non-resonant part and several intermidiate two-body decays that proceed through K h or Charge conjugation is implied everywhere, unless otherwise stated. + h − resonances. The uncertainties in the model introduce an additional systematicerror on γ . However, the result γ (mod180 ◦ ) = [68 ± ± ± ◦ (4)is still dominated by the statistical error. It can be compared to the Belle GGSZresult [6] γ (mod180 ◦ ) = (cid:2) . +10 . − . (stat.) ± . ± . (cid:3) ◦ , (5)which is obtained using D → K ππ decays only, but a larger data sample and a lesssophisticated decay model.The model error is hard to quantify, but can be avoided by using a model-independent approach. In the latter, the model dependence is lifted by relating the B yields to discrete measurements of the strong-phase difference, ∆ δ D , between D and ¯ D to K hh , in bins of the Dalitz plot. Only experimental observables are in-volved in this case, hence there are no model uncertainties. These measurements havebeen recently performed for different binning choices and for both D → K ππ and D → K KK at CLEO-c [5] with the full data-sample of quantum-correlated D ¯ D de-cays collected at the ψ (3770), which corresponds to 818 pb − . The model-independentapproach is expected to suffer from a small loss in statistical precision compared tothe model-dependent one, which is unbinned, hence makes optimal use of all availableinformation. This loss has been estimated to be about 10%. The CLEO-c uncertain-ties on the strong-phase parameters will also induce a systematic uncertainty on γ ,when a model-independent approach is adopted. This has been evaluated to be about(3–4) ◦ for B ± → D ( K K + K − ) K ± , and (2–4) ◦ for B ± → D ( K π + π − ) K ± , whichvaries within the given range according to the binning choice. These small residualerrors, which are due mainly to the limited size of the CLEO-c data sample, are ade-quate for the precision on γ which is expected at LHCb with the GGSZ method, andcould be further reduced with larger data samples.Other CLEO-c analyses have been presented at this workshop [5], which allow fora significant improvement in the precision for γ from time-integrated measurementsof B → DK decays. These include a new preliminary result on the strong-phasedifference ∆ δ D in D → Kπ , and the results on the coherence factor and on ∆ δ D inthe multibody decays, D → Kππ and D → Kπππ . Prospects for improving theseand other measurements of the D -decay parameters at future charm–tau factories,and their impact on the measurement of γ , have been discussed by Spradlin [10] atthis workshop. One clear message emerges: the contribution of physics at the charmthreshold is invaluable to the precise measurement of γ . Another well-established method to determine γ is by exploiting the interferencebetween ¯ b → ¯ c and b → u mediated transitions that is caused by B – ¯ B mixing and4ccurs when both the B and the ¯ B mesons can decay to a common final state. Atime-dependent analysis is required and is sensitive to the sum of the mixing phase,2 β , and the relative phase between the B and ¯ B decay amplitudes, γ .Abundant decays, such as B → D ( ∗ ) ∓ π ± , can be used. In this case, the b → u decay amplitude is doubly Cabibbo-suppressed, while the ¯ b → ¯ c transition is Cabibbo-favoured. Therefore, the magnitude of the ratio between the two, r = (cid:12)(cid:12)(cid:12)(cid:12) A ( ¯ B → D ( ∗ ) − π + ) A ( B → D ( ∗ ) − π + ) (cid:12)(cid:12)(cid:12)(cid:12) , (6)which governs the size of the CP violation effect, is expected naively to be about 2%.Because of this very small value, external input on r is required to extract the weakphase. Discussions at this workshop have focussed on these external measurementsand the associated systematic uncertainties.The BaBar Collaboration has estimated r from the ratio of the branching fractionsof B → D ∗ + s π − and B → D ∗− π + as follows [2]: r = s B ( B → D ∗ + s π − ) B ( B → D ∗− π + ) f D ∗ f D ∗ s tan( θ C ) = 0 . +0 . − . × (1 . ± . , (7)where the 30% systematic uncertainty accounts for possible non-factorizable, SU (3)-breaking corrections. Time-dependent measurements have been performed using 232million B ¯ B pairs, which is about half of the full data-sample. By combining re-sults from fully-recontructed B → D ( ∗ ) − π + , fully-reconstructed B → D − ( ∗ ) ρ + andpartially-reconstructed B → D ∗− π + decays, BaBar obtains | sin(2 β + γ ) | > . B → D ( ∗ ) − π + events from 386 million B ¯ B pairs, and partially recontructed B → D ∗− π + events from a larger data-sample of 657 million B ¯ B pairs. Results can be found inRef. [3]. A new measurement for the Dπ final state has been presented for the firsttime at this conference. Using SU (3) flavour-symmetry assumptions, Belle obtains r Dπ = [1 . ± . . ) ± . . ) ± . . )]% (8) r D ∗ π = [1 . ± . . ) ± . . ) ± . . )]% . (9)These are the most precise determination of r , but possible non-factorizable SU (3)-breaking effects are not completely accounted for in the theory error. Another promis-ing way to determine r is through the following isospin relation: r D ∗ π = s B ( B + → D ∗ + π ) B ( B → D ∗− π + ) τ B τ B + . (10)5n this case the measurement is limited by statistics, as only an upper limit is availablefor the branching fraction of the B + → D ∗ + π decay. With his method Belle finds r D ∗ π < .
051 (90% C.L.).BaBar has exploited also B decays that can exhibit larger interference effects,hence a larger value of r . These include B → D ∓ K π ± , where a time-dependentDalitz-plot analysis has been performed with 347 million B ¯ B pairs. The values of2 β + γ is obtained as a function of r . For r = 0 .
3, the result2 β + γ (mod180 ◦ ) = (83 ± ± ◦ (11)is obtained, where the central value has a weak dependence on r . Since 2008, a few new methods to measure γ have been proposed. Among these, themultibody B → DK + π − analysis is particularly well-suited for LHCb [1], because γ can be extracted by reconstructing D decays with only charged particles in the finalstate. In addition, the Dalitz plot of this B decay features a flavour-specific resonantdecay D ∗− (2460) → ¯ D π − . The interference of D ∗− (2460) K + with other resonancesin the B → DK + π − Dalitz plot, such as DK ∗ (892), allows γ to be extracted withbetter sensitivity compared to that estimated for the quasi two-body B → DK ∗ decay with a GLW/ADS method. Similarly to the quasi two-body determination,the multibody method requires the reconstruction of D decays to CP eigenstates andflavour-specific modes, but is based on the determination of relative decay amplitudes,rather than the determination of decay rates. The expected precision achievable atLHCb with this method has been recently re-evaluated using data yields extrapolatedfrom the 2010 data-taking. Approximately 700 B → DK + π − decays followed by thefavoured D → K + π − are expected in 1 fb − , from which γ can be determined with astatistical uncertainty of about 20 ◦ [9].Another interesting channel is B s → J/ψK S , which has been observed by CDFin the summer of 2010 and will be of interest for the LHCb experiment [11]. Thischannel is caused by ¯ b → ¯ cc ¯ d quark-level transitions and is the U -spin partner of the“golden” decay B d → J/ψK S . Thanks to the interference between tree and penguintopologies, which are not doubly Cabibbo-suppressed as in B d → J/ψK S , the UTangle γ can be determined through measurements of the CP-violating asymmetriesof B s → J/ψK S and the application of the U -spin symmetry. A first feasibilitystudy for LHCb shows that experimental sensitivity at the few-degree level can beobtained with an upgraded LHCb detector (see next section). Although interestingon its own, this determination of γ is not competitive in terms of precision withpure tree strategies. However, the measurement of CP violation in B s → J/ψK S allows also to determine hadronic penguin parameters and to control their impact on6he extraction of the B d – ¯ B d mixing phase φ d through a measurement of the mixing-induced CP violation in B d → J/ψK S . As discussed in [11], this will be the majorapplication of B s → J/ψK S at LHCb. Such an analysis is actually needed in orderto fully exploit LHCb’s impressive experimental precision for the determination of φ d from B d → J/ψK S , and will be an interesting study at an LHCb upgrade, which mayeventually allow us to resolve NP effects in B d – ¯ B d mixing. The B s system provides additional opportunities for the precise measurement of γ .Among these, the time-dependent measurement with B s → D ± s K ∓ decays is particu-larly promising. This measurement is unique to LHCb, because only LHCb has bothaccess to a large B s data-sample and the ability to resolve the fast B s – ¯ B s oscillations.The tree-level sensitivity to 2 β s + γ arises from the interference between the decaywith and without mixing. The value of 2 β s + γ can be converted to a measurementof γ because β s will be well-determined by measurements of B s → J/ψφ decays.This analysis presents some advantages in comparison with the time-dependentmeasurements from B d decays. It benefits from the expected sizeable width difference,∆Γ s , in the B s system, which provides additional sensitivity to γ through the inclusionof untagged events. It also benefits from the large interference in these decays, giventhat the ratio of the magnitude between the two interfering amplitudes is expectedto be approximately 0.4, which is large enough for it to be determined from data.By performing a simultaneous fit to B s → D s K and B s → D s π events, all physicalunknowns and experimental parameters can be extracted from data, so γ can bemeasured without theoretical uncertainties. In 2011, with 1 fb − , it is expected thatthe first measurements of the CP-violating observables will be performed [4]. However,an integrated luminosity of about 2 fb − at 7 TeV is required for an unambiguousextraction of γ from this mode. The achievable precision depends on the flavourtagging performance, but should be competitive with the LHCb results from thetime-integrated measurements.In addition to colour-allowed B s → D ± s K ∓ decays, also colour-suppressed B s → Dφ decays offer sensitivity to γ at tree-level. In this case, a time-integrated measure-ment of γ exploiting untagged decays has been proposed [1]. The untagged methodallows LHCb to exploit fully its statistical power and to mitigate the effect of thesmall branching fraction for this mode. If a sufficient number of different D decaysare used, there is enough experimental information to extract γ and all the hadronicparameters. Sensitivity studies performed at LHCb have evaluated that a statisticaluncertainty of about 20 ◦ on γ can be achieved by this method with 1 fb − . This levelof precision is comparable to the LHCb expectations for the other time-integratedmethods. 7he long-term prospects for the determinations of γ from B ( s ) → D ( s ) K decayswere discussed by Anton Poluektov [12]. Recently, two next generation e + e − facilitieshave been approved: the SuperB project in Italy and SuperKEKB in Japan. SuperBhas a design luminosity of 10 cm − s − and aims at 75 ab − , which is very similar tothe goals of SuperKEKB, with 8 × cm − s − and a goal of an integrated luminosityof 50 ab − . Both projects hope to start operation around 2015 and should take datauntil 2020. Concerning LHCb, a data sample of (6–7) fb − is expected to be collectedby 2016. There are plans to upgrade LHCb afterwards to run with an increasedluminosity of up to 2 × cm − s − , which would result in an expected data sampleof (50–100) fb − by 2020.In [12], a detailed comparison of the γ reach for SuperB (50 ab − ) and an upgradedLHCb experiment (50 fb − ) was given. The bottom line is that various independentmethods should allow measurements of γ with uncertainties at the (1–3) ◦ level, usingADS and GLW methods, B → D ( K S ππ ) K Dalitz analyses, self-tagging B → DKπ modes, and the B s → D s K channel, which is only accessible at LHCb. The overallsensitivity at the LHCb upgrade looks potentially better than that of SuperB, al-though potential backgrounds can reduce it. On the other hand, SuperB looks morestable with respect to “unfortunate” parameter combinations, where the sensitivitycan be significantly reduced.In order to fully exploit the B -decay data, it is desirable to have a large datasample, i.e. ∼ (10–20) fb − , at the charm threshold. Such data could be recorded atBES-III, a new dedicated charm-tau factory, or running SuperB at low energy. The determination of γ from B decays into charmed final states has continued toprogress. By the next CKM workshop, we expect new exciting experimental resultsfrom B -decay studies at hadron colliders. At this workshop, CDF has demonstratedthat analyses of B → DK modes are possible at hadron colliders. The correspond-ing new ADS/GLW results with 5 fb − are roughly competitive with those of the B factories, and the exploration continues, with an expected data set of (10–12) fb − bythe end of the Tevatron run in 2011.Concerning LHCb, we look forward to a variety of interesting measurements, withan expected uncertainty ∆ γ < ◦ by the end of 2012. The excellent tracking, PIDand trigger performance for these multi-hadron decay modes demonstrated with the < − of data analyzed in the summer of 2010 give us confidence that this canactually be achieved. The precise determination of γ continues to be a key target ofthe B -physics programme! 8 CKNOWLEDGEMENTS
We would like to thank all participants of our working group for excellent talks anddiscussions, as well as the organizers of CKM2010 for doing such a great job in hostingthis workshop at the University of Warwick.