Dalitz analyses with B Dh(h) decays at LHCb

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1 Available online at wwwscienceirectcom Nuclear an Particle Physics Proceeings (16) wwwelseviercom/locate/nppp alitz analyses with h(h) ecays at Wenbin Qian on behalf of the collaboration Laboratoire Annecy-le-Vieux e Physique es Particules Université e avoie, CNR/INP3, Annecy-le-Vieux, France Abstract We present stuies performe by the experiment with beauty to open charme meson ecays h(h ( ) ), h ( ) = π, Using the 1 fb 1 results of ± (hh ( ) ) h ±,1fb 1 results of ± ( π ± π π ) h ± an 1 fb 1 fb 1 results of moel-inepenent alitz plot analysis of ± ( hh) ± moes, γ is constraine to be (67 ± 1) Further measurements with multi-boy or ecays are presente in the proceeing The results inclue the moel-epenent measurements of ± ( hh) ± an the CP violation measurements of ± ( π) h ± an (hh ( ) ) eywors: CP violation, CM angle γ, alitz plot analysis 1 Introuction The Cabibbo-obayashi-Maskawa (CM) [1, ] angle γ = arg[v u Vub /(V cvcb )] is one of the least known parameters of the CM Unitarity Triangle (UT) Precise measurement of γ from tree-level interference is crucial to overconstrain the UT for the tanar Moel test The comparison between γ measure from treelevel an loop-level ecay amplitues may she light on new physics The angle γ can be accesse by many channels with interference between tree-level b c ecay amplitue A(b c) an b u ecay amplitue A(b u) where A(b u) A(b c) = r e i(δ γ), A( b ū) A( b c) = r e i(δ γ) r an δ are the amplitue ratio an strong phase ifference between the two transitions everal time-integrate methos to measure γ using h (h = π, ) are establishe, where inicates the coherent mixture of an states an is a ( )or ( ) These methos are categorise accoring to the ecay of : 1 Gronau-Lonon-Wyler (GLW) metho [3, 4]: ecays to -boy CP eigenstates, ie, π π / 15 Elsevier V All rights reserve Atwoo-unietz-oni (A) metho [5]: ecays to π where the favoure b c transition are with the oubly-cabibbo-suppresse π ecay, an the suppresse b u transition are with the Cabibbo-favoure π ecay 3 Giri-Grossman-offer-Zupan (GGZ) metho [6]: ecays to self-conjugate multi-boy final states, ie π π, 4 Grossman-Ligeti-offer (GL) metho [7]: the metho is similar as A metho, but with ecays to singly-cabibbo-suppresse three-boy final states, ie π All these ecay channels a sensitivity to γ measurement an it is important to combine them for better precision Measurements from abar experiment an elle experiment give their combinations of γ = ( ) [8] an γ = ( ) [9] respectively A combination of results from both experiments gives γ = (67±11) [1] Using its 1 fb 1 GLW an A measurements of ± (hh ( ) ) h ± [11], 1 fb 1 A measurement of ± ( π ± π π ) h ± [1] an 1 fb 1 [13] fb 1 [14] moel-inepenent GGZ results of ± ( hh) ±, the experiment performs the com-

2 W Qian / Nuclear an Particle Physics Proceeings (16) bination on γ [15] The CLEO inputs on system parameters [16] are use to further constrain the system Other external constraints inclue the mixing parameters [17] from the experiment an irect CP violation of an π π from HFAG [18] The 1-CL plot of γ combination is shown in Fig 1 The γ is constraine to be (67 ± 1) with δ /c 4 ] [GeV m CL % Preliminary 955% γ [ ] Figure 1: 1 - CL curve for γ combination from the experiment an r for to be ( ) an respectively In the following sections, new measurements from the experiment which are not yet inclue in the γ combinations are presente Moel epenent GGZ Measurement esies the moel-inepenent measurement of GGZ analysis using external inputs from CLEO with binne alitz plot [16], a moel-epenent analysis [19] is performe using moels from previous measurements by the abar experiment [, 1] Each resonant component an their interferences are explicitly escribe in the frame work of alitz plot technique The alitz plot istributions of π π from ± ± are shown in Fig We have aroun 64 ± ± an 887 ± π ± signals reconstructe base on 1 fb 1 ata A simultaneous fit with mass an alitz plot istributions of ± ± an ± π ± are performe to extract the Cartesian CP violation variables efine as: x ± = Re[r e i(δ ±γ) ], y ± = Im[r e i(δ ±γ) ], an the following results are obtaine: x = (7 ± ± 1)%, x = (84 ± 45 ± 9 ± 3)%, y = (13 ± ± 3)%, y = (3 ± 48 ± 9 ± 7)%, /c 4 ] [GeV m [GeV /c 4 ] m 1 3 [GeV /c 4 ] m Figure : alitz plot istributions of ( π π ) from (top) an (bottom) respectivly with 1 fb 1 ata m an m represent m( π ) an m( π ) where the first uncertainty is statistical, the secon is systematic an the thir is systematic uncertainties ue to alitz moelling It results in a γ value of ( ) The measurement is in agreement with the 1 fb 1 moel-inepenent results [13] 3 CP violation measurement with ( π) h The first GL analysis using singly-cabibbosuppresse ecays π is performe using 3fb 1 ata [] The ecays are ivie into eight categories accoring to the charge of meson, charge of kaon from ecays an type of bachelor particle h (π or ) ecays with same charge for meson an kaon from ecays are calle ame ign () an those with opposite charge are name as Opposite ign (O) The invariant mass istributions are shown in Fig 3 ( ) an Fig 4 ( ) for ± ( π) ± ecays

3 1366 W Qian / Nuclear an Particle Physics Proceeings (16) Entries / (15 MeV/c ) 3 1 xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx m([ π ] ) [MeV/c ] [ um, incl combinatorics ignal Mis-I π ] Entries / (15 MeV/c ) 3 1 xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx m([ π ] ) [MeV/c ] [ um, incl combinatorics ignal Mis-I π ] Entries / (15 MeV/c ) m([ π ] ) [MeV/c ] [ um, incl combinatorics ignal Mis-I π ] Entries / (15 MeV/c ) m([ π ] ) [MeV/c ] [ um, incl combinatorics ignal Mis-I π ] Figure 3: Invariant mass istributions of ( π ) an ( π ) The ata (black points) an the fitte moel (blue soli line) are shown ignal shape is shown as re ashe line; other components are inicate in the legen Figure 4: Invariant mass istributions of ( π ) an ( π ) respectively The ata (black points) an the fitte moel (blue soli line) are shown ignal shape is shown as re ashe line; other components are inicate in the legen We have reconstructe aroun 16 signals for ± ( π) ± an 318 signals for ± ( π) π ± The ecay withs of the eight categories are expresse as: Γ ± = z[1 r r r r κ cos(δ ± γ δ)], Γ ± O = z[r r r r κ cos(δ ± γ δ)], where r value is aroun 1 for ecays an 15 for π ecays; r is the amplitue ifference between π an π κ an δ are the coherence factor an average phase over certain alitz plot region an are taken from CLEO [3] The value of r, κ an δ epen on the alitz plot region chosen Two alitz plot regions are stuie an their values are summarise in Table 1 Table 1: r, δ an κ parameters from CLEO measurements [3] Parameters r (%) δ κ Whole alitz Region 59 ± ± ± 8 region 356 ± ± ± 16 even ratios are built from the eight yiels an their values are shown in Table where A i inicates the charge asymmetry efine as (Ni N i )/(N i N i ) an R i gives the ratios of flavour-average yiels between two processes liste in the subscript Table : Results for the observables measure in the whole alitz plot region an in the (89) ± region The first uncertainty is statistical an the secon is systematic Observable Whole alitz plot (89) ± region R π,/o 158 ± 58 ± 5 57 ± 13 ± 6 R /π, 9 ± 9 ± 4 84 ± 11 ± 3 R /π,o 66 ± 9 ± 56 ± 13 ± A, 4 ± 91 ± 18 6 ± 19 ± 9 A,O 33 ± 19 ± ± 8 ± 6 A π, 5 ± 4 ± 1 1 ± 8 ± 1 A π,o 5 ± 9 ± ± 43 ± 17 Using ratios liste in Table an inputs from CLEO liste in Table 1, scans of the χ probabilities over the γ r plane are performe for the whole alitz region an for the (89) ± region shown in Fig 5 The results are consistent with previous combination an will be valuable for the future global fits of the CM angle γ 4 CP violation stuies with (hh ( ) ) Results shown in previous sections are with the ecay channels of, similar analysis is also performe on self-tagge neutral ecays of ue to the broa with of (89), a ilution factor of (95 ±

4 W Qian / Nuclear an Particle Physics Proceeings (16) r 35 The measure results for the six ratios are r (a) γ A = , A s = , R = , Aππ = , Aππ s = , Rππ = The first uncertainty is statistical an the secon is systematic Ratios between the flavour-average partial withs of an s ecays with h h is efine as R hh s = Γ( (h h ) ) ) Γ( (h h ) ) Γ( s (h h ) ) ) Γ( s (h h ) ) The measure results are Figure 5: cans of the χ probabilities over the γ r plane for π moe The contours are the 1σ (ark blue), σ (meium blue) an 3σ (light blue) profile likelihoo contours The point is the result of γ combination shown in ec 1 The top plot shows the results using the whole alitz range an the bottom plot shows the results using only (89) region 3) is neee when extracting angle γ accoring to toy stuies base on the alitz plot structure of Using the 3 fb 1 ata, the invariant mass istributions of the reconstructe ( s) an ( s) caniates are shown in Fig 6 an Fig 7 respectively for ifferent ecay channels [4] The yiels of an s are obtaine through simultaneous fit to the invariant mass istributions We have 86σ an 58σ observation for the GLW moe of an π π The significance of A moe is 9σ Twelve ratios between ifferent yiels are calculate In the GLW moes, the relative partial ecay-rate asymmetry A hh (s) an ratio of flavour-average partial withs of the with the ecaying to a CP-even eigenstate R hh are given: A hh = Γ( (h h ) ) Γ( (h h ) ), Γ( (h h ) ) Γ( (h h ) ) A hh s = Γ( s (h h ) ) Γ( s (h h ) ), Γ( s (h h ) ) Γ( s (h h ) ) = Γ( CP ) ) Γ( CP ) Γ( ) ) Γ( ) R hh (b) γ R s = , Rππ s = For π ecay moes, the ratio of suppresse (π ) to favoure ( π ) ecay withs are measure separately for an : R = Γ( (π ) ) ) Γ( ( π ) ) ) = , R = Γ( (π ) ) ) = Γ( ( π ) ) 31 ) The - asymmetry A π with two kaons from the an the ecays having same charge is efine as: A π = Γ( ( π ) ) Γ( ( π ) ) Γ( ( π ) ) Γ( ( π ) ) imilar asymmetry A π s between s- s with two kaons having opposite charge is written as: A π s = Γ( s ( π ) ) Γ( s ( π ) ) Γ( s ( π ) ) Γ( s ( π ) ) The measure results are A π = , Aπ s = The measure ratios are use to extract information for γ measurement The pvalue from the profile likelihoo projecte over r ( ) an γ plane is shown in Fig 8 The results are compatible with the combination of γ shown in ec 1 The ratio of the amplitues of the ecay with b u an b c transitions is foun to be It is compatible an more accurate than previous results from abar [5]

5 1368 W Qian / Nuclear an Particle Physics Proceeings (16) Figure 6: Invariant mass istributions of ( π ),(π ), ( ) an (π π ) (from top to bottom) The ata (black points) an the fitte moel (black line) are shown The fitte components are inicate in the legen Figure 7: Invariant mass istributions of ( π ),(π ), ( ) an (π π ) (from top to bottom) The ata (black points) an the fitte moel (black line) are shown The fitte components are inicate in the legen

6 W Qian / Nuclear an Particle Physics Proceeings (16) Figure 8: Two-imensional projections of the pvalue in r ( )γ plane The contours show the 1σ (black), σ (meium grey) an 3σ (light grey) likelihoo The vertical line an hashe ban represent the best-fit value of γ an the 683% confience level interval shown in ec 1 5 Conclusion The experiment has performe abunant measurements to extract CM angle γ using beauty to open charm ecays Using the 1 fb 1 results of ± (hh ( ) ) h ±,1fb 1 results of ± ( π±π π ) h ± an 1fb 1 fb 1 results of moel-inepenent alitz plot analysis of ± ( hh) ± moes, γ is constraine to be (67 ± 1) Further measurements with multi-boy final states in or ecays are presente, these ecays inclue the 1fb 1 moel-epenent GGZ analysis, the first GL measurement using 3 fb 1 ata an the GLW/A measurements using ecays with 3 fb 1 ata The γ information extracte from these ecays are compatible with the γ combination results an will be use to further constrain angle γ References [1] N Cabibbo, Unitary symmetry an leptonic ecays, Phys Rev Lett 1 (1963) 531 [] M obayashi, T Maskawa, CP Violation in the Renormalizable Theory of Weak Interaction, Prog Theor Phys 49 (1973) 65 [3] M Gronau, Lonon, How to etermine all the angles of the unitarity triangle from s an s φ, Phys Lett 53 (1991) 483 [4] M Gronau, Wyler, On etermining a weak phase from charge ecay asymmetries, Phys Lett 65 (1991) 17 [5] Atwoo, I unietz, A oni, Enhance CP Violation with ( ) Moes an Extraction of the Cabibbo- obayashi-maskawa Angle γ, Phys Rev Lett 78 (1997) 357 [6] A Giri, Y Grossman, A offer, J Zupan, etermining γ using ± ± with multiboy ecays, Phys Rev 68 (3) 5418 [7] Y Grossman, Z Ligeti, A offer, Measuring γ in ± ± ( ) ecays, Phys Rev 67 (3) 7131 [8] J P Lees, et al, AAR Collaboration, Observation of irect CP violation in the measurement of the Cabibbo-obayashi- Maskawa angle γ with ± ( ) ( )± ecays, Phys Rev 87 (13) 515 [9] Trabelsi, elle collaboration, tuy of irect CP in charme ecays an measurement of the CM angle gamma at elle, arxiv:13133 [hep-ex] [1] A evan, et al, aar Collaboration an elle Collaboration, The Physics of the Factories, arxiv: [hep-ex] [11] R Aaij, et al, Collaboration, Observation of CPviolation in ecays, PhysLett 71 (1) 3 [1] R Aaij, et al, Collaboration, Observation of the suppresse A moes ± [π ± π π ] ± an ± [π ± π π ] π ±, Phys Lett 73 (13) 44 [13] R Aaij, et al, Collaboration, A moel-inepenent alitz plot analysis of ± ± with h h (h = π, ) ecays an constraints on the CM angle γ, Phys Lett 718 (1) 43 [14] R Aaij, et al, Collaboration, Moel-inepenent measurement of CP violation parameters in ± ( h h ) ± ecays, -CONF-13-4 [15] R Aaij, et al, Collaboration, Improve constraints on γ from ± ± ecays incluing first results on 1 ata, -CONF-13-4 [16] N Lowrey, et al, CLEO Collaboration, etermination of the π π an π π π Coherence Factors an Average trong-phase ifferences Using Quantum-Correlate Measurements, Phys Rev 8 (9) 3115 [17] R Aaij, et al, Collaboration, Observation of Oscillations, Phys Rev Lett 11 (13) 118 [18] Y Amhis, et al, Heavy Flavor Averaging Group, Averages of b-haron, c-haron, an τ-lepton properties as of early 1, arxiv: [hep-ex], with on line upate on [19] R Aaij, et al, Collaboration, Measurement of CP violation an constraints on the CM angle γ in ± ± with π π ecays, arxiv: [hep-ex] [] P el Amo anchez, et al, AAR Collaboration, Evience for irect CP Violation in the Measurement of the Cabbibo- obayashi-maskawa Angle γ with ( ) ( ) ecays, Phys Rev Lett 15 (1) 1181 [1] Aubert, et al, aar Collaboration, Improve measurement of the CM angle γ in ( ) ( ) ecays with a alitz plot analysis of ecays to π π an, Phys Rev 78 (8) 343 [] R Aaij, et al, collaboration, A stuy of CP violation in ± ± an ± π ± ecays with ± π final states, Phys Lett 733 (14) 36 [3] J Insler, et al, CLEO Collaboration, tuies of the ecays s π an s π, Phys Rev 85 (1) 916 [4] R Aaij, et al, collaboration, Measurement of CP violation parameters in ecays, arxiv: [hepex] [5] Aubert, et al, AAR Collaboration, earch for b u transitions in ecays, Phys Rev 8 (9) 311