e University of Manchester
May 11, 2018
Studies of charmed states in amplitude analyses at LHCb
Paras Naikon behalf of the LHCb Collaboration
School of PhysicsUniversity of Bristol, Bristol, United Kingdom
Amplitude analysis is a powerful tool to study the properties of in-termediate resonances produced in the decays of B mesons. At LHCbwe have studied B ± → X (3872) K ± , where X (3872) → J/ψπ + π − , todetermine the quantum numbers of the X (3872), and B ± → ppK ± tolearn more about ( cc ) → pp transitions. We also exploit the spin of the J/ψ to perform amplitude analyses of the decays B s ) → J/ψπ + π − and B s ) → J/ψK + K − . Our results use 1.0 fb − of data taken in 2011 from √ s = 7 TeV pp collisions, provided by the LHC.PRESENTED AT The 6 th International Workshop on Charm Physics (CHARM 2013)Manchester, UK, 31 August – 4 September, 2013 The workshop was supported by the University of Manchester, IPPP, STFC, and IOP a r X i v : . [ h e p - e x ] N ov Introduction
The dominant weak decay b → c results in the production of charmed states in B meson decays that can be well-explored by the LHCb experiment. The following isa summary of how exploiting charmed states in B decays at LHCb has lead to abetter understanding of both. Our results use 1.0 fb − of data from √ s = 7 TeV pp collisions, provided by the LHC in 2011. This data was collected by the LHCbdetector (described in Refs. [1, 2]). X (3872) quantum numbersvia B ± → X (3872) K ± decays [3] The X (3872) was discovered in B + decays ∗ by the Belle experiment in 2003 [4], andhas been confirmed by several other experiments [5, 6, 7]. X (3872) production hasmost recently been studied at the LHC [8, 9], however the nature of the X (3872)remains unclear. The open explanations for this state are conventional charmoniumand exotic states such as D ∗ D molecules [10], tetra-quarks [11], or their mixtures[12]. To determine the best explanation, we need to determine the quantum numbers J (total angular momentum), P (parity), and C (charge-conjugation) of the X (3872).The CDF experiment analyzed three-dimensional (3D) angular correlations in asample of inclusively-reconstructed X (3872) → J/ψπ + π − , J/ψ → µ + µ − decays [13].A χ fit of J P C hypotheses to the binned 3D distribution of the
J/ψ and ππ helicityangles ( θ J/ψ , θ ππ ) [14, 15, 16], and the angle between their decay planes, excluded allspin-parity assignments except for 1 ++ or 2 − + . The Belle collaboration concluded thattheir data were equally well described by the 1 ++ and 2 − + hypotheses, by studyingone-dimensional distributions in three different angles [17]. The BaBar experimentused information from X (3872) → ωJ/ψ , ω → π + π − π events to favor the 2 − + hypothesis, which had a confidence level (CL) of 68%, over the 1 ++ hypothesis, butthe latter was not ruled out (CL = 7%) [18].The angular correlations in the B + decay carry significant information about the X (3872) quantum numbers. A first analysis of the complete five-dimensional an-gular correlations of the B + → X (3872) K + , X (3872) → J/ψπ + π − , J/ψ → µ + µ − decay chain has been performed using the 2011 LHCb data sample. A fit to thedata yields 313 ± B ± → X (3872) K ± candidates. To discriminate between the1 ++ and 2 − + assignments we use the likelihood-ratio test, which in general providesthe most powerful test between two hypotheses [19]. The probability distributionfunction (PDF) for each J P C hypothesis, J X , is defined in the 5D angular spaceΩ ≡ (cos θ X , cos θ ππ , ∆ φ X,ππ , cos θ J/ψ , ∆ φ X,J/ψ ) by the normalized product of the ex-pected decay matrix element ( M ) squared and of the reconstruction efficiency ( (cid:15) ), ∗ The inclusion of charge-conjugate states is implied in this proceeding. ] ++ (1 L )/ -+ (2 L = -2 ln[ t -200 -100 0 100 200 N u m be r o f e x pe r i m en t s / b i n data t -+ =2 PC Simulated J ++ =1 PC Simulated J
LHCb
Figure 1:
Distribution of the test statistic t for the simulated experiments with J P C = 2 − + (black circles on the left) and with J P C = 1 ++ (red triangles on the right). A Gaussian fitto the 2 − + distribution is overlaid (blue solid line). The value of the test statistic for thedata, t data , is shown by the solid vertical line. PDF(Ω | J X ) = |M (Ω | J X ) | (cid:15) (Ω) /I ( J X ), where I ( J X ) = (cid:82) |M (Ω | J X ) | (cid:15) (Ω) d Ω. θ X isthe X (3872) helicity angle, and ∆ φ X,ππ = φ X − φ ππ and ∆ φ X,J/ψ = φ X − φ J/ψ are theangles between the X (3872) decay plane and ππ or J/ψ decay planes, respectively.We follow the approach adopted in Ref. [13] to predict the matrix elements.We define a test statistic t = − − + ) / (cid:32)L(1 ++ )]. The background in the datais subtracted in the log-likelihoods using the sPlot technique [20]. Positive (negative)values of the test statistic for the data, t data , favor the 1 ++ (2 − + ) hypothesis. Thevalue of the test statistic observed in the data is t data = +99, favoring the 1 ++ hypothesis. The value of t data is compared with the distribution of t in the simulatedexperiments to determine a p -value for the 2 − + hypothesis via the fraction of simulatedexperiments yielding a value of t > t data . As shown in Fig. 1, the distribution of t isreasonably well approximated by a Gaussian function. Based on the mean and rootmean square spread of the t distribution for the 2 − + experiments, this hypothesis isrejected with a significance of 8 . σ . Integrating the 1 ++ distribution from −∞ to t data gives CL (1 ++ ) = 34%. This unambiguously establishes that J P C for the X (3872)state is 1 ++ . 2 Study of the pp charmonium resonances in B ± → ppK ± decays [21] The B + → ppK + decay offers a clean environment to study cc states and charmonium-like mesons that decay to pp , and to search for glueballs or exotic states. Measure-ments of intermediate charmonium-like states, such as the X (3872), are important toclarify their nature [3, 22] and to determine their partial width to pp , which is crucialto predict the production rate of these states in dedicated experiments [23]. BaBarand Belle have previously measured the B ± → ppK ± branching fraction, includingcontributions from the J/ψ and η c (1 S ) intermediate states [24, 25]. The LHCb datasample allows the study of substructures in the B + → ppK + decays with a sampleten times larger than those available at previous experiments.The signal yields for the charmonium contributions, B + → ( cc ) K + → ppK + , aredetermined by fitting the pp invariant mass distribution of B + → ppK + candidateswithin the B + mass signal window, | M ppK + − M B + | < /c . An unbinnedextended maximum likelihood fit to the pp invariant mass distribution, shown inFig. 2, is performed over the mass range 2400 − /c . We define the ratio ofbranching fractions for each resonant “mode” as follows: R (mode) = B ( B + → mode K + → ppK + ) B ( B + → J/ψ K + → ppK + ) , (1)where “mode” corresponds to the intermediate η c (1 S ), ψ (2 S ), η c (2 S ), χ c (1 P ), h c (1 P ), X (3872), or X (3915) states.Final results for all intermediate modes are given in Ref. [21]. The total branchingfraction, its charmless component ( M pp < . /c ) and the branching fractionsvia the resonant cc states η c (1 S ) and ψ (2 S ) relative to the decay via a J/ψ interme-diate state are: B ( B ± → ppK ± ) total B ( B + → J/ψK + → ppK + ) = 4 . ± .
19 (stat) ± .
14 (syst) , B ( B ± → ppK ± ) M pp < . /c B ( B + → J/ψK + → ppK + ) = 2 . ± .
10 (stat) ± .
08 (syst) , R ( η c (1 S )) = 0 . ± .
035 (stat) ± .
027 (syst) , R ( ψ (2 S )) = 0 . ± .
012 (stat) ± .
009 (syst) . The branching fractions obtained are compatible with the world average values [26].3 c [MeV/ pp M ) c C a nd i d a t es / ( M e V / LHCb P u ll Figure 2:
Invariant mass distribution of the pp system for B + → ppK + candidates withinthe B + mass signal window, | M ( ppK + ) − M B + | < /c . The dotted lines representthe Gaussian and Voigtian functions (red) and the dashed line the smooth function (green)used to parametrize the signal and the background, respectively. The bottom plot showsthe pulls. We combine our upper limit for X (3872) with the known value for B ( B + → X (3872) K + ) × B ( X (3872) → J/ψπ + π − ) = (8 . ± . × − [26] to obtain the limit B ( X (3872) → pp ) B ( X (3872) → J/ψπ + π − ) < . × − . This limit challenges some of the predictions for the molecular interpretations ofthe X (3872) state and is approaching the range of predictions for a conventional χ c (2 P ) state [27, 28]. Using our result and the η c (2 S ) branching fraction B ( B + → η c (2 S ) K + ) × B ( η c (2 S ) → KKπ ) = (3 . +2 . − . ) × − [26], a limit of B ( η c (2 S ) → pp ) B ( η c (2 S ) → KKπ ) < . × − is obtained. 4 Amplitude analyses of B s ) → J/ψh + h − decays[29, 30, 31, 32] Measurement of mixing-induced CP violation in B s decays is critical for probingphysics beyond the Standard Model. Final states that are CP eigenstates with largerates and high detection efficiencies are very useful for such studies. For example, the B s → J/ψf (980), f (980) → π + π − decay mode, a CP-odd eigenstate, was discoveredby the LHCb collaboration [33] and subsequently confirmed by several experiments[34]. We use only J/ψ → µ + µ − decays, so our final state has four charged tracks givingus a high detection efficiency. LHCb has used this mode to measure the CP violatingphase φ s [35], which complements measurements in the J/ψφ final state [36, 37]. It ispossible that a larger π + π − mass range could also be used for such studies. In orderto fully exploit the J/ψπ + π − final state for measuring CP violation, it is importantto determine its resonant and CP content. This motivated a “modified Dalitz plot”analysis of the B s → J/ψπ + π − decay. Modified Dalitz plot analysis differs from aclassical Dalitz plot analysis [38] because the J/ψ in our final state has spin-1 andits three decay amplitudes must be considered. We also perform modified Dalitz plotanalyses of other B s ) → J/ψh + h − decays ( h = π or K ).In these analyses, we apply a formalism similar to that used in Belle’s analysis of B → K − π + χ c decays [39]. The decay of B s ) → J/ψh + h − , where J/ψ → µ + µ − ,can be described by four variables. We choose the invariant mass squared of J/ψh + ( m ( J/ψh + )), the invariant mass squared of h + h − ( m ( h + h − )), the J/ψ helicity angle( θ J/ψ ), and the angle between the
J/ψ and h + h − decay planes ( χ ) in the B s ) restframe. The χ distribution has little structure, so we analyze the decay process afterintegrating over χ , which eliminates several interference terms. The m ( h + h − ) vs. m ( J/ψh + ) distributions are shown for the B s ) → J/ψπ + π − and B s ) → J/ψK + K − decays in Fig. 3. We model the decay with a series of resonant and non-resonantamplitudes. The data are then fitted with the coherent sum of these amplitudes.Detailed results of all B s ) → J/ψh + h − modified Dalitz plot analyses are availablein Refs. [29, 30, 31, 32]. The π + π − system in B s → J/ψπ + π − is shown to bedominantly in an S-wave state, and the CP-odd fraction in this B s decay is shownto be greater than 0.977 at 95% confidence level, meaning that B s → J/ψπ + π − decays can be used for studies of mixing-induced CP violation in a large ππ invariant-mass range. In addition, we report the first measurement of the B s → J/ψπ + π − branching fraction relative to B s → J/ψφ as (19 . ± . ± . B → J/ψK + K − decay. The branching fraction is determined tobe B ( B → J/ψK + K − ) = (2 . ± . ± . × − . We also set an upper limit of B ( B → J/ψφ ) < . × − at the 90% CL, an improvement of about a factor offive with respect to the previous best measurement [40].5a) ) (GeV ) + π ψ (J/ m
15 20 25 ) ( G e V ) - π + π ( m LHCb (b) ) ) (GeV + K (cid:115) (J/ m
15 20 ) ) ( G e V - K + ( K m LHCb (c) ) ) (GeV + πψ (J/ m
10 15 20 25 ) ) ( G e V - π + π ( m LHCb (d) ] ) [GeV + K ψ (J/ m
15 20 ] ) [ G e V - K + ( K m LHCb
Figure 3: Invariant mass-squared distributions of h + h − vs. J/ψh + for the decays(a) B s → J/ψπ + π − , (b) B s → J/ψK + K − , (c) B → J/ψπ + π − , and (d) B → J/ψK + K − . Note that in this figure we use mass units where we have defined c = 1. ACKNOWLEDGEMENTS
We express our gratitude to our colleagues in the CERN accelerator departmentsfor the excellent performance of the LHC. We thank the technical and adminis-trative staff at the LHCb institutes. We acknowledge support from CERN andfrom the national agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); NSFC(China); CNRS/IN2P3 and Region Auvergne (France); BMBF, DFG, HGF andMPG (Germany); SFI (Ireland); INFN (Italy); FOM and NWO (The Netherlands);SCSR (Poland); MEN/IFA (Romania); MinES, Rosatom, RFBR and NRC “Kurcha-tov Institute” (Russia); MinECo, XuntaGal and GENCAT (Spain); SNSF and SER(Switzerland); NAS Ukraine (Ukraine); STFC (United Kingdom); NSF (USA). Wealso acknowledge the support received from the ERC under FP7. The Tier1 com-puting centres are supported by IN2P3 (France), KIT and BMBF (Germany), INFN(Italy), NWO and SURF (The Netherlands), PIC (Spain), GridPP (United King-dom). We are thankful for the computing resources put at our disposal by YandexLLC (Russia), as well as to the communities behind the multiple open source softwarepackages that we depend on. 6 eferences [1] A. A. Alves Jr. et. al. (LHCb Collaboration), JINST, , S08005 (2008).[2] R. Aaij et. al. , JINST, , P04022 (2013).[3] R. Aaij et. al. (LHCb Collaboration), Phys. Rev. Lett. , 222001 (2013).[4] S.-K. Choi et al. (Belle collaboration), Phys. Rev. Lett. , 262001 (2003).[5] D. Acosta et al. (CDF collaboration), Phys. Rev. Lett. , 072001 (2004).[6] V. M. Abazov et al. (D0 collaboration ), Phys. Rev. Lett. , 162002 (2004).[7] B. Aubert et al. (BaBar collaboration), Phys. Rev. D71 , 071103 (2005).[8] LHCb collaboration, R. Aaij et al. , Eur. Phys. J.
C72 , 1972 (2012).[9] CMS collaboration, S. Chatrchyan et al. , JHEP , 154 (2013).[10] N. A. Tornqvist, Phys. Lett. B590 , 209 (2004).[11] L. Maiani, F. Piccinini, A. D. Polosa, and V. Riquer, Phys. Rev.
D71 , 014028(2005).[12] C. Hanhart, Y. Kalashnikova, and A. Nefediev, Eur. Phys. J.
A47 , 101 (2011).[13] A. Abulencia et al. (CDF collaboration), Phys. Rev. Lett. , 132002 (2007).[14] M. Jacob and G. Wick, Annals Phys. , 404 (1959).[15] J. D. Richman, An experimenter’s guide to the helicity formalism ,CALT-68-1148 (ExperimentersGuideToTheHelicityFormalism.pdf, available athttp://charm.physics.ucsb.edu/people/richman/) (1984).[16] S. U. Chung, Phys. Rev.
D57 , 431 (1998).[17] S.-K. Choi et al. (Belle collaboration), Phys. Rev.
D84 , 052004 (2011).[18] P. del Amo Sanchez et al. (BaBar collaboration), Phys. Rev.
D82 , 011101 (2010).[19] F. James,
Statistical methods in experimental physics , World Scientific Publish-ing, 2006.[20] M. Pivk and F. R. Le Diberder, Nucl. Instrum. Meth.
A555
356 (2005).[21] R. Aaij et. al. (LHCb Collaboration), Euro. Phys. Journal
C73 , 2462 (2013).722] N. Brambilla et al. , Eur. Phys. J.
C71 et al. , AIP Conf. Proc.
549 (2011).[24] BaBar collaboration, B. Aubert et al. , Phys. Rev.
D72 , (2005) 051101[25] Belle collaboration, J. Wei et al. , Phys. Lett.
B659 , (2008) 80.[26] J. Beringer et al. (Particle Data Group), Phys. Rev.
D86
D77
D77 et. al. (LHCb Collaboration), Phys. Rev.
D86 , 052006 (2012).[30] R. Aaij et. al. (LHCb Collaboration), Phys. Rev.
D87 , 072004 (2013).[31] R. Aaij et. al. (LHCb Collaboration), Phys. Rev.
D87 , 052001 (2013).[32] R. Aaij et. al. (LHCb Collaboration), Phys. Rev.
D88 , 072005 (2013).[33] R. Aaij et. al. (LHCb Collaboration), Phys. Lett.
B698 , 115 (2011).[34] J. Li et al. (Belle collaboration), Phys. Rev. Lett. , 121802 (2011).[35] R. Aaij et al. (LHCb collaboration), Phys. Lett.
B707
497 (2012).[36] R. Aaij et al. (LHCb collaboration), Phys. Rev. Lett. et al. (CDF collaboration), Phys. Rev.
D85 , 072002 (2012).[38] R. Dalitz, Phil. Mag. et al. (Belle collabration), Phys. Rev. D78 et al. (Belle collaboration), Phys. Rev.