e University of Manchester
October 16, 2018
CP Violation and Mixing in Multi-body D decays Samuel Harnew on behalf of LHC b School of Physics and AstronomyThe University of Bristol, Bristol, UK
We present recent LHCb results and future prospects for CP violationand mixing measurements in multi-body charm decays. The complex am-plitude structure of multi-body decays provides unique sensitivity to CPviolation localised in certain phase space regions. A model-independentsearch in the phase space of D → π + π − π + π − and D → K + K − π + π − de-cays showed no evidence for localised CP violation. If one assumes the noCP violation hypothesis, the probability of getting the observed results is9 .
1% and 41%, respectively.The model-independent determination of gamma from B → DK re-quires external input to account for the interference of D and D am-plitudes to the same final state. Previously this input could only be ob-tained at the charm threshold, but recently it has been proposed that D mixing can provide complimentary information. For the example of D → K + π − π + π − decays, it is shown that charm mixing can be usedto considerably improve current constraints on the coherence factor andaverage strong phase difference, with existing data.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 LHCb detector [1] is a single-arm forward spectrometer covering a unique pseudo-rapidity range 2 < η <
5. The detector is specialised for the study of b and c quarks,making it ideal for measurements of CP violation (CPV) and mixing in the charm sec-tor. Essential to the study of hadronic decay modes are two Ring Imaging Cherenkovdetectors that provide particle identification, crucial for suppressing backgrounds.The tracking system provides an excellent impact parameter resolution, importantfor identifying heavy flavour decays at trigger level.Multi-body charm decays offer the opportunity to study CPV effects localisedin phase space, providing sensitivity to phenomena that might get ‘washed out’ inglobal decay rate asymmetries. In Sec. 2 we present a search for local CPV in D → π + π − π + π − and D → K + K − π + π − decays.Quantum-correlated data provide important information on charm interferenceparameters that play a crucial role in the precision measurement of gamma from B → DK and related decays, where the details of the analysis depends on the finalstate of the D [12, 13, 14, 15, 16, 17]. In Sec. 3 we discuss the possibility of constrainingthe D → K − π + π − π + coherence factor R K πD and average strong phase difference δ K πD [10] using input from D mixing [8]. It is thought that such a measurement isalready possible with data collected at LHCb. LHCb has performed searches for local CP asymmetries in several multi-body decaymodes. Recent results on three body decays are discussed by Sam Gregson in theseproceedings under the title “Direct CP violation in the decays D + → φπ + and D + s → K s π + ”. Here we present a search for local CP asymmetries in the four body D → π + π − π + π − and D → K + K − π + π − decays [2]. These decays are singly Cabibbosuppressed, so contain contributions from both loop and tree diagrams. The loopdiagrams are particularly sensitive to new physics which may enhance CP violatingeffects [7].The analysis was performed using 1fb − of data collected by LHCb during 2011. D mesons are reconstructed from the decay chains D ∗ + → D π + s and D ∗− → D π − s where the charge of the slow pion, π s , identifies the flavour of the D meson at pro-duction. The analysis uses the ‘Miranda method’ [9] which has been used in manysimilar searches. The multi-body phase space is split into N independent volumes,and the variable S iCP gives the significance of CPV in volume i . The number of D → f events in volume i is given by N i ( D ) with an uncertainty σ i ( D ), where f represents a given final state. The equivalent quantities for the CP conjugate process1re N i ( D ) and σ i ( D ). S iCP = N i ( D ) − αN i ( D ) (cid:113) α (cid:0) σ i ( D ) + σ i ( D ) (cid:1) α = (cid:80) i N i ( D ) (cid:80) i N i ( D ) (2.1)The quantity α is used to remove any global asymmetry. This includes removingsensitivity to global CPV, but also any D D production and global detection asym-metries. Describing the kinematics of four body decays requires 5 dimensions, makingit difficult to visualise the variation of S iCP across this space. Fig. 2 shows the S iCP distribution for the 3 body D + → K + K − π + decay [3]. The phase space is partitionedto give a similar number of events in each volume. A similar method is used to par-tition the five dimensional phase space of D → π + π − π + π − and D → K + K − π + π − decays.In the case of no CPV, one would expect the S iCP to be distributed as a gaussian,with mean 0 and unity width. To identify the presence of CPV the squared S iCP aresummed to form a χ statistic with N bins − χ = (cid:88) i (cid:0) S iCP (cid:1) , (2.2)from which a p-value is calculated. The p-value gives the probability of gettinga larger χ than the one measured, assuming the no CPV hypothesis is true. Todemonstrate the method, two sets of simulated signal events (ignoring detector reso-lution effects) have been generated; the first contains no local CP asymmetries, whilethe second contains a phase difference of 10 o between the D → a (1260) + π − and D → a (1260) − π + decays. Fig. 1 shows the S iCP distribution for both cases; the ex-ample with no CPV yields a p-value of 85 . . × − . CP S -5 0 5 E n t r i e s / . Simulation CP S -5 0 5 E n t r i e s / . Simulation
Figure 1: The S CP distribution for (left) toy data generated with no CPV (right) toydata generated with CPV. 2n the analysis of LHCb data, signal yields are extracted from a 2D maximumlikelihood fit in m ( hhhh ) and ∆ m = m ( π s hhhh ) − m ( hhhh ), where h represents a pionor a kaon candidate. Fig. 2 shows a 1D projection of this fit for the D → π − π + π − π + channel. The signal yields in D → π − π + π − π + and D → K − K + π − π + decays are330 ,
000 and 57 , ] c [MeV/ m D
140 145 150 ) c C a nd i d a t e s / ( . M e V / Data - p + p + p - p fi D Random soft pionCombinatorial
LHCb
Data - p + p + p - p fi D Random soft pionCombinatorial ) /c (GeV + p - K m ) / c ( G e V + K - K m C P S -3-2-10123 LHCb (b)
Figure 2: (left) ∆ m projection of a 2D fit in m ( π + π − π + π − ) and ∆ m , superimposedwith the signal candidates. Fits include various sources of backgrounds that aredescribed in [2]. (right) S CP variation across the Dalitz plot for D + → K + K − π + .To check for any experimental biases that could fake the presence of local CPV, theCabibbo favoured D → K − π + π − π + decay is used as a control channel. In 2 . χ / dof = 113 . / S iCP distribution for both search channels is shown in Fig. 3; D → K − K + π − π + has a χ / NDF = 42 . /
31 giving a p-value of 9 . D → π − π + π − π + has a χ / NDF = 130 . /
127 giving a p-value of 41%. Neither shows evidence of local CPV. D → K + π − π + π − complex interfer-ence parameter using D mixing This section introduces a method that uses D mixing to constrain the coherence factorand average strong phase difference [8]. Here we discuss application to the final state K + π − π + π − where existing measurements can be considerably improved.In the suppressed decay D → K + π − π + π − there are two dominant amplitudes;a doubly Cabibbo suppressed (DCS) diagram on one hand, and a time dependantamplitude which proceeds via D mixing and a Cabibbo favoured (CF) diagram on theother. Having two amplitudes of a comparable magnitude makes this the perfect placeto study the interference effects between DCS and CF diagrams. Information on these3 P S -4 -2 0 2 4 E n t r i e s / . - p + p + p - p fi D LHCb CP S -4 -2 0 2 4 E n t r i e s / . + p - p + K - K fi D LHCb
Figure 3: The S CP distribution for (left) D → π + π − π + π − decays (right) D → K + K − π + π − decays, both superimposed with a gaussian distribution of mean 0 andunity width.interference effects are needed to constrain the CP violating phase γ in B + → DK + and similar decay modes. These can be conveniently parameterised by the complexinterference parameter Z f [8], which is related to the coherence factor, R fD , andaverage strong phase difference, δ fD [10, 11] through Z f = R fD e − iδ fD . The magnitudeof Z f lies in the range [0 ,
1] and gives a measure of how much the interference effectsare diluted from integrating over phase-space. The argument of Z f gives a weightedaverage of the strong phase difference between the CF and DCS amplitudes.In an experimental measurement of the suppressed decay, one usually uses thefavoured D → K − π + π − π + as a normalisation channel. The theoretical expressionfor the ratio of decay rates is given by, r ( t ) = R ( D ( t ) → f ) R (cid:0) D ( t ) → f (cid:1) = r Df + r Df (cid:0) y Re Z f + x Im Z f (cid:1) Γ t + x + y t ) , (3.1)which represents the ratio of rates integrated over all phase space. The dimensionlessquantities x and y are the usual D mixing parameters and Γ gives the average widthof the D mass eigenstates.A measurement of the constant term in Eq. 3.1 allows r Df to be constrained, andΓ has been well measured previously [6]. Therefore, through the linear term of Eq. 3.1there is sensitivity to b = y Re Z f + x Im Z f . It is therefore possible to constrain Z f given external input on x and y [5]. These constrains follow a straight line in the Im Z f − Re Z f plane which is smeared out by any uncertainty on x , y or b .A simulation study based on plausible D → K + π − π + π − event yields in LHCb’s2011+2012 dataset leads to the constraints in the Z K π plane shown in Fig. 4. Theresults are shown in two separate parameterisations; cartesian coordinates Re Z K π - Im Z K π , and polar coordinates R K πD - δ K πD . Also shown in the figure are the4onstraints set by CLEO-c [4] and a combination of these with the simulated data.This indicates that considerable improvements on Z K π are possible with currentlyavailable datasets. Toy Simulation Cleo-c Combination C a r t e s i a n P o l a r Figure 4: The figures show constraints on Z f from (left) simulated data generatedwith the Cleo-c central values of Z f using expected statistics from LHCb with 3fb − of data (centre) Cleo-c using threshold data (right) a combination of simulated andthreshold data. The top row parameterises the constraints in the preferred Re Z f - Im Z f coordinates, whereas the bottom row uses the R fD - δ fD . Multi-body charm decays have a complex underlying amplitude structure that canlead to localised regions of CP violation across phase space. In D decays this cangive enhanced sensitivity to CPV in charm, a possible signature of new physics.In B + → DK + decays, one can use the variation of the strong phase to enhancesensitivity to the CP violating phase γ .LHCb performed a model independent search for local CPV in D → K − K + π − π + and D → π − π + π − π + decays using 1fb − of data collected in 2011. Assuming there isno CPV, the probability of obtaining the observed results is calculated as 9 .
1% and51% for the D → K − K + π − π + decay and D → π − π + π − π + decay, respectively. Thisindicates no evidence for local CPV in either search channel.The complex interference parameter plays an important role in measuring the CPviolating phase γ in B + → DK + and similar decay modes. Previous constraints on Z K π , or equivalently R K πD and δ K πD , were set at CLEO-c using data at the charmthreshold. It has been shown that constrains on complex interference parameter canalso be found using D mixing, and a combination of these with existing results couldgreatly improve the statistical uncertainty on its measurement. References [1] R. Aaij et al. (LHCb collaboration), “The LHCb detector at the LHC”, JINST , S08005 (2008).[2] R. Aaij et al. (LHCb collaboration), “Search for CP violation in D → π − π + π − π + decays”, LHCb-CONF-2012-019.[3] R. Aaij et al. (LHCb collaboration), “Search for CP violation in D + → K + K − π + decays”, Phys. Rev.
D84 , 112008 (2011).[4] Lowrey, N. et al. (CLEO collaboration), Phys. Rev. D80, 031105 (2009).[5] Heavy Flavour Averaging Group, “ D mixing results allowing for CPV”, 2012, .[6] J. Beringer et al. (Particle Data Group), Phys. Rev. D86, 010001 (2012).[7] Y. Grossman, A. L. Kagan, and Y. Nir, “New physics and CP violation in singlyCabibbo suppressed D decays”, Phys. Rev.
D75 , 036008 (2007).[8] S. Harnew and J. Rademacker , “Charm mixing as input for model-independentdeterminations of the CKM phase gamma”, 2013, arXiv:1309.0134v3.[9] I. Bediaga et al. , “On a CP anisotropy measurement in the Dalitz plot”,
Phys.Rev.
D80 , 096006 (2009).[10] D. Atwood and A. Soni, “Role of charm factory in extracting CKM phase infor-mation via B → DK ”, Phys. Rev.
D68 , 033003 (2003).[11] A. Giri, Y. Grossman, A. Soer, J. Zupan, “Determining γ using B → DK withmultibody D decays”, Phys. Rev.
D68 , 054018 (2003).612] M. Gronau, D. Wyler, “On determining a weak phase from CP asymmetries incharged B decays”,
Phys. Lett.
B265 , 172176 (1991).[13] M. Gronau, D. London, “How to determine all the angles of the unitarity trianglefrom B d → DK s and B s → Dφ ”, Phys. Lett.
B253 , 483-488 (1991).[14] D. Atwood, I. Dunietz, A. Soni, “ B → KD ( D ) modes and extraction of theCabibbo-Kobayashi-Maskawa angle γ ”, Phys. Rev. Lett. , 32573260 (1997).[15] A. Giri, Y. Grossman, A. Soffer, J. Zupan, “Determining γ using B ± → DK ± with multibody D decays”, Phys. Rev.
D68 , 054018 (2003).[16] A. Poluektov et al. , “Measurement of φ with Dalitz plot analysis of B ± → D ( ∗ ) K ± decays”, Phys. Rev.
D70 , 072003 (2004).[17] J. Rademacker, G. Wilkinson, “Determining the unitarity triangle γ with afour-body amplitude analysis of B + → ( K + K − π + π − ) D K ± decays”, Phys. Lett.