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Stocchi, A.

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New evaluation of the CKM-matrix and Unitarity

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New evaluation of the CKM-matrix and UnitarityA. StocchiTo cite this version:A. Stocchi. New evaluation of the CKM-matrix and Unitarity. S. Recksiegel, A. Hoang, S.Paul. 8 th International Conference ”Heavy Quarks & Leptons” (HQL2006), Oct 2006, Munich,Germany. pp.345-354, 2006. <in2p3-00291133>HAL Id: in2p3-00291133http://hal.in2p3.fr/in2p3-00291133Submitted on 26 Jun 2008HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.L’archive ouverte pluridisciplinaire HAL, estdestine´e au de´poˆt et a` la diffusion de documentsscientifiques de niveau recherche, publie´s ou non,e´manant des e´tablissements d’enseignement et derecherche franc¸ais ou e´trangers, des laboratoirespublics ou prive´s.Proceedings of theVIIIth International Workshop onHeavy Quarks and LeptonsHQL06October 2006Deutsches Museum, MunichEditorsS. Recksiegel, A. Hoang, S. PaulOrganized by the Physics Department of the Technical University of Munichand the Max-Planck Institute for Physics, MunichThis document is part of the proceedings ofHQL06, the full proceedings are available fromhttp://hql06.physik.tu-muenchen.deNew evaluation of CKM Matrix and UnitarityTriangle parametersAchille StocchiLaboratoire de l’Acce´le´rateur Line´aire,IN2P3-CNRS et Universite´ de Paris-Sud,Orsay Cedex, Franceon behalf of the UTfit Coll. 11 IntroductionThe analysis of the Unitarity Triangle (UT) is one of the key places where the flavoursector of the Standard Model (SM) can be tested with great precision, hence it pro-vides a powerful and maybe unique opportunity to look for sizeable effects beyond theSM. In fact, the successes of the B factories - even well beyond the original expecta-tions - and recently of the Tevatron in the B0s sector, have provided the UT analysiswith a rich set of measurements, thus allowing for a precise determination of the pa-rameters of the Cabibbo-Kobayashi-Maskawa (CKM) matrix and, more importantly,for non trivial checks of the internal consistency of the SM flavour picture.In this paper we will start showing the present knowledge of the Unitarity Tri-angle fit in the Standard Model and we will continue presenting the status of theUnitarity Triangle analysis beyond the Standard Model using a model independentparametrization of the New Physics effects in |∆F | =2 processes. For these analy-ses we make use of the most recent determinations of theoretical and experimentalparameters (updated to Summer 2006). The results and the plots presented in thispaper can be found at the URL http://www.utfit.org, where they are continuouslyupdated.2 Unitarity Triangle in the Standard ModelBefore the B factories came into play, UT fits were performed by only using mea-surements of the sides and of the indirect CP violation parameter !K of neutral Kaonsystem. The B factories in few years of measurements completely changed the sce-nario by providing determinations of all the UT angles, in particular the long awaited1M. Bona, M. Ciuchini, E. Franco, V. Lubicz, G. Martinelli, F. Parodi, M. Pierini, P. Roudeau,C. Schiavi, L. Silvestrini, V. Sordini, A. Stocchi, V. Vagnoni1A. Stocchi New evaluation of CKM Matrix and Unitarity Triangle parametersβ from b → ccs modes, but also - quite unexpectedly since the penguin pollution inthe B0 → pi+pi− decay mode became evident - the α angle. Even more surprisingly,the B factories have been able to close the circuit by providing measurements of theγ angle, even if with large errors so far.Here below we briefly describe the most relevant measurements entering our SMUT fit:• The rates of charmed and charmless semileptonic B decays which allow to mea-sure the ratio |Vub| / |Vcb|.• The mass difference between the light and heavy mass eigenstates of the B0−B0system ∆md.• The mass difference of the B0s−B0s system ∆ms, compared to ∆md, ∆md/∆ms.• The εK parameter, which measures CP violation in the neutral kaon system.• β from b→ ccs modes and from B0 → D0pi0.• The angle α, that can be obtained from the B → pipi and B → ρρ decays,assuming the SU(2) flavour symmetry and neglecting the contributions of elec-troweak penguins. It can also be obtained using a time-dependent analysis ofB → (ρpi)0 decays on the Dalitz plane. The combination of the BaBar andBelle results including all the three methods gives already a quite precise mea-surement; just restricting to the SM solution, we get α = (92 ± 7)◦ at 68%probability.• The angle γ that can be extracted from the tree-level decays B → DK, usingthe fact that a charged B can decay into a D0(D0)K final state via a Vcb(Vub)mediated process. CP violation occurs if the D0 and the D0decay to thesame final state. The same argument can be applied to B → D∗K and B →DK∗ decays. Three methods have been proposed: the Gronau-London-Wylermethod (GLW), which consists in reconstructing the neutral D meson in a CPeigenstate: B± → D0CP±K±, the Atwood-Dunietz-Soni method (ADS), whichconsists in forcing the D0(D0) meson, coming from the Cabibbo-suppressed(Cabibbo-allowed) b→ u (b→ c) transition to decay into the Cabibbo-allowed(Cabibbo-suppressed) Kpi final state - thus looking at the interference betweentwo amplitudes of similar size; the Dalitz method, consisting in studying theinterference between the b→ u and the b→ c transitions using the Dalitz plotofD mesons reconstructed into three-body final states (such asD0 → Kspi−pi+).The advantage of this last method is that the full sub-resonance structure ofthe three-body decay is considered, including interferences such as those usedfor GLW and ADS methods plus additional interferences due to the overlap2A. Stocchi New evaluation of CKM Matrix and Unitarity Triangle parametersρ-1 -0.5 0 0.5 1η-1-0.500.51γβαsmΔdmΔ dmΔKεcbVubVηFigure 1: Determination of ρ and η from constraints on |Vub| / |Vcb|, ∆md, ∆ms, εK ,β, γ, and α. 68% and 95% total probability contours are shown, together with 95%probability regions from the individual constraints.between broad resonances in some regions of the Dalitz plot. The combinationof the BaBar and Belle analyses, including all the three methods, yields thetwo-fold result γ = (82± 19)◦ ∪ (−98± 19)◦ at 68% probability.For more details on the SM analysis see [1] (for similar work see [2]). In Tab. 1 wesummarize the values of the relevant input parameters used in the SM fit, as well asthe output of the fit including all the constraints. A graphical view of the fit result inthe (ρ, η) plane is shown in Fig. 1. From the plot it is clearly visible how impressivethe success of the CKM picture is in describing CP violation in the SM: all the variousmeasurements do agree in constraining the apex of the UT at an astonishing level.However, by looking in more detail at Fig. 1, it is interesting to note that the 95%probability regions depicted by the sin 2β and |Vub| / |Vcb| constraints, two of the mostprecise ones used in the fit, show just a bare agreement. In particular, in our analysiswe find that while the experimental value of sin 2β is in good agreement with the restof the fit, the same does not hold for |Vub| / |Vcb|, which is rather on the high side. Itcan be shown that this is due to a large value of the inclusive determination of |Vub|.Unless this discrepancy should be considered as a hint of NP, it has to be explainedby the uncertainties of the theoretical approaches needed to determine |Vub| [3].3A. Stocchi New evaluation of CKM Matrix and Unitarity Triangle parametersParameter Value Gaussian (σ) Uniform (half-width)λ 0.2258 0.0014 -|Vcb|(excl.) 41.3× 10−3 1.0× 10−3 1.8× 10−3|Vcb|(incl.) 41.6× 10−3 0.7× 10−3 -|Vub|(excl.) 35.0× 10−4 4.0× 10−4 -|Vub|(incl.) 44.9× 10−4 3.3× 10−4 -∆md 0.507 ps−1 0.005 ps−1 -∆ms 17.77 ps−1 0.12 ps−1 -fBs√BˆBs 262 MeV 35 MeV -ξ =fBs√BˆBsfBd√BˆBd1.23 0.06 -BˆK 0.79 0.04 0.08εK 2.280× 10−3 0.013× 10−3 -fK 0.160 GeV fixed∆mK 0.5301 ×10−2 ps−1 fixedsin 2β 0.675 0.026 -mt 163.8 GeV 3.2 GeV -mb 4.21 GeV 0.08 GeV -mc 1.3 GeV 0.1 GeV -Parameter Output Parameter Outputρ 0.163± 0.028 η 0.344± 0.016α[◦] 92.7± 4.2 β[◦] 22.2± 0.9γ[◦] 64.6± 4.2 ∆ms [ps−1] 17.77± 0.12sin 2β 0.701± 0.022 Imλt [10−5] 13.8± 0.7Vub[10−3] 3.68± 0.14 Vcb[10−2] 4.16± 0.06Vtd[10−3] 8.50± 0.27 |Vtd/Vts| 0.208± 0.007Rb 0.381± 0.014 Rt 0.904± 0.028Table 1: Top: values of the relevant inputs used in the SM UT fit. The inputs fromthe α and γ measurements are not shown since we make use of the experimentallikelihoods (see text). Bottom: SM UT fit results.4A. Stocchi New evaluation of CKM Matrix and Unitarity Triangle parametersdBC0 1 2 3 4 5 6]o [ dBφ-80-60-40-20020406080]o [ dBφsBC0 1 2 3 4 5 6]o [ sBφ-80-60-40-20020406080]o [ sBφFigure 2: Bounds on the CBq −φBq planes, from the NP generalized UT fit: 68% and95% probability regions.3 New Physics AnalysisSince the mixing processes are described by a single amplitude, they can be parame-terized without loss of generality in terms of two parameters quantifying the differenceof the amplitude with respect to the SM one. In the case of B0q −B0q mixing we defineCBq e2iφBq =〈B0q |H fulleff |B0q〉〈B0q |HSMeff |B0q〉, (q = d, s)where HSMeff includes only the SM box diagrams, while Hfulleff includes also the NPcontributions. In the absence of NP, we have that CBq = 1 and φBq = 0. Theexperimental quantities determined from the B0q −B0q mixings are related to their SMcounterparts and the NP parameters by the following relations:∆mexpq = CBq∆mSMq , βexp = βSM + φBd ,αexp = αSM − φBd , βexps = βSMs − φBs.For the K0 −K0 mixing is instead convenient to introduce a single parameter:C"K =Im[〈K0|H fulleff |K0〉]Im[〈K0|HSMeff |K0〉],which implies the following relation for the measured value of εK :εexpK = C"K εSMK .5A. Stocchi New evaluation of CKM Matrix and Unitarity Triangle parametersdBC0 2 4 6Probability density00.00050.001Probability densityProbability density]o[dBφ-50 0 50Probability density00.00050.0010.00150.002Probability densityProbability densitysBC0 2 4 6Probability density00.00050.001Probability densityProbability density]o[sBφ-50 0 50Probability density00.050.1-310×Probability densityProbability densityK∈C-2 0 2Probability density00.0010.002Probability densityProbability densityρ-1 -0.5 0 0.5 1η-1-0.500.51γηFigure 3: 1D distributions showing the constraints on φBq , CBq and C"K comingfrom the NP generalized analysis. The bottom-right plot shows instead the 68% and95% confidence contours in the ρ − η plane as resulting from the NP generalizedfit, superimposed to the 95% confidence regions determined by the |Vub| / |Vcb| and γconstraints only.∆mK is not considered since the long distance effects are not well under control.With these definitions, NP effects which enter the present analysis are parameterizedin terms of 5 real quantities: CBd, φBd, CBs, φBs and C"K .The results of the fit are summarized in Tab. 2. For more details on the NPanalysis see [4]. For other recent works on the same subject see [5]. The bounds onthe two φB vs CB planes are given in Fig. 2. The distributions for CBq , φBq and C"Kare shown in Fig. 3, and in the same figure also the fit result in the ρ − η plane isdepicted. We see that the non-standard solution for the UT with its vertex in thethird quadrant, which was present in previous analyses, is now absent thanks to theimproved value of ASL by the BaBar Collaboration [6] and to the measurement ofACH by the D0 Collaboration [7]. Furthermore, the measurement of ∆ms stronglyconstrains CBs, so that it is already known better than CBd . Finally, ACH and ∆Γsprovide the first relevant constraints on φBs .6A. Stocchi New evaluation of CKM Matrix and Unitarity Triangle parametersParameter Output Parameter Output Parameter OutputCBd 1.24± 0.43 φBd[◦] −3.0± 2.0 CBs 1.15± 0.36φBs[◦] (−3± 19) ∪ (94± 19) C"K 0.91± 0.15ρ 0.87± 0.056 η 0.370± 0.036 α[◦] 92± 9β[◦] 24.4± 1.8 γ[◦] 63± 8 Imλt[10−5] 14.8± 1.4Vub[10−3] 4.00± 0.24 Vcb[10−2] 4.15± 0.07 Vtd[10−3] 8.39± 0.59|Vtd/Vts| 0.205± 0.015 Rb 0.416± 0.026 Rt 0.896± 0.061sin 2β 0.752± 0.040 sin 2βs 0.039± 0.004Parameter Output Parameter Output Parameter Outputρ 0.153± 0.030 η 0.347± 0.018 α[◦] 91.3± 4.8β[◦] 22.3± 0.9 γ[◦] 66.3± 4.8 sin 2βs 0.037± 0.002Table 2: Top: determination of UT and NP parameters from the NP generalized fit.Bottom: determination of UUT parameters from the constraints on α, β, γ, |Vub/Vcb|,and ∆md/∆ms (UUT fit).4 Universal Unitarity TriangleIn the context of Minimal Flavour Violation (MFV) extensions of the SM [8,9], it ispossible to use the so called Universal Unitarity Triangle (UUT) construction in orderto determine the parameters of the CKM matrix independently of NP effects [10]. Forthis purpose one has to use all the constraints from tree-level processes and from theangle measurements, as well as the ∆md/∆ms ratio, which in MFV scenarios areNP-free. Instead, !K , ∆md and ∆ms may receive NP contributions, because of theshifts δSK0 and δSB0 of the Inami-Lim functions in the K-K and Bd,s-Bd,s mixings.With only one Higgs doublet or at small tanβ these two contributions are forced tobe equal. Instead, for large tanβ, the two quantities are in general different. In bothcases, one can use the output of the UUT given in Tab. 2 and graphically representedin Fig. 4 to constrain δSK,B0 . We get δS0 = δSK0 = δSB0 = −0.16±0.32 for small tanβ,while for large tanβ we obtain δSB0 = 0.05 ± 0.67 and δSK0 = −0.18 ± 0.37. Thesebounds can be translated into lower bounds on the MFV scale [11]: Λ > 5.5 TeV at95% probability for small tanβ and Λ > 5.1 TeV at 95% probability for large tanβ.7A. Stocchi New evaluation of CKM Matrix and Unitarity Triangle parametersρ-1 -0.5 0 0.5 1η-1-0.500.51γβαsmΔdmΔcbVubVηFigure 4: Determination of ρ and η from the constraints on α, β, γ, |Vub/Vcb|, and∆md/∆ms (UUT fit).5 ConclusionsIn this paper we have presented updated analyses of the Unitarity Triangle in theStandard Model and beyond, using all the relevant measurements available from theB factories and the Tevatron. Despite the great number of measurements employedin the fit, and the remarkable precision achieved with some of them, the SM is stillshowing an impressive degree of consistency.We have performed an analysis with a model-independent approach able to de-scribe general extensions of the SM with loop-mediated contributions to FCNC pro-cesses. We have shown how the redundant set of measurements nowadays availableallow for a simultaneous determination of the CKM parameters, together with theNP contributions to |∆F | = 2 processes in the K0, B0 and B0s sectors.Furthermore, we have performed a Universal Unitarity Triangle analysis, showingthat it is possible to constrain the UUT parameters with excellent accuracy. In thisway, we have been able to put limits on new scale in Minimal Flavour Violationscenarios, in the large and small tanβ scenarios, up to about 5-6 TeV.Bibliography[1] M. Bona et al. [UTfit Collaboration], JHEP 0507, 028 (2005), [arXiv:hep-ph/0501199]; M. Ciuchini et al., JHEP 0107 (2001) 013 [arXiv:hep-ph/0012308].8A. Stocchi New evaluation of CKM Matrix and Unitarity Triangle parameters[2] J. Charles et al., Eur. Phys. J. C 41 (2005) 1 [hep-ph/0406184]; updates athttp://ckmfitter.in2p3.fr/.[3] M. Bona et al. [UTfit Collaboration], [arXiv:hep-ph/0606167].[4] M. Bona et al. [UTfit Collaboration], JHEP 0603, 080 (2006), [arXiv:hep-ph/0509219];[5] Z. Ligeti, M. Papucci and G. Perez, Phys. Rev. Lett. 97 (2006) 101801[arXiv:hep-ph/0604112]; Y. Grossman, Y. Nir and G. Raz, arXiv:hep-ph/0605028;F. J. Botella, G. C. Branco and M. Nebot, arXiv:hep-ph/0608100.[6] B. Aubert et al. [BABAR Collaboration], Phys. Rev. Lett. 96 (2006) 251802[arXiv:hep-ex/0603053].[7] D0 Collaboration, D0 Conference note 5189; see also G. Borissov, “D0 results onCP violation phase in Bs system”. ICHEP06, Moscow (Russia)[8] M. Blanke et al., arXiv:hep-ph/0604057.[9] G. Isidori and P. Paradisi, arXiv:hep-ph/0605012.[10] A. J. Buras et al., Phys. Lett. B 500, 161 (2001) [arXiv:hep-ph/0007085].[11] G. D’Ambrosio et al., Nucl. Phys. B 645, 155 (2002) [arXiv:hep-ph/0207036].9A. Stocchi New evaluation of CKM Matrix and Unitarity Triangle parameters10

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