aa r X i v : . [ h e p - e x ] S e p hep-ex/October 23, 2018 Measurements of T -odd observables Maurizio Martinellion behalf the LHCb collaboration
Laboratoire de Physique des Hautes Energies´Ecole Polytechnique F´ed´erale de Lausanne, CH-1015 Lausanne, Switzerland
The study of T -odd observables using four-body hadronic final statesof charm meson decays provides complementary insight to measuring CP asymmetries via decay rate asymmetries. New results based on the fullLHCb dataset are presented. PRESENTED AT The 7th International Workshop on Charm Physics(CHARM 2015)Detroit, MI, 18-22 May, 2015
Introduction
Violation of CP symmetry in charm meson decays is expected to be extremely smallin the Standard Model (SM) [1, 2], although recent calculations do not exclude effectsup to a few times 10 − [3, 4, 5]. This small CP violation effect in the SM leaves roomfor beyond-SM effects that, even if small, could produce an asymmetry significantlylarger than that predicted from the SM. The large samples of charm meson decaysrecorded at LHCb, enable the search for CP violation at the sub-percent level, henceapproaching the largest SM predictions.Three kinds of search are usually pursued in probing CP violation. These involveinterference effects between the decay amplitudes, between the mixing and the de-cay amplitudes, and in the mixing amplitudes [1]. In the present contribution, analternative approach using triple-product correlations is shown. CP violation and T -odd correlations The search for CP violation in the charm sector is particularly interesting since thecontribution from SM is expected to be very small. Any large effect can therefore beassociated to new particles and phenomena. In this frame, it is important to studyvarious decay channels and exploit alternative and complementary techniques.Most of the searches for CP violation in the charm sector are made with two-bodyparticle decays [6, 7]. While favoured by the very large statistics already collectedby the experiments, these channels do not offer the rich variety of interfering contri-butions from which CP violation can arise in multi-body decays. Furthermore, thepresence of independent measurable momenta in the final state allows the explorationof new techniques, such as the one using triple-products.The study of triple-products, and T -odd observables in particular, offers a dif-ferent point of view on CP violation. This technique has been initially proposed byValencia [8] for quasi-two-body B mesons decays, but is valid for other hadrons aswell. Valencia observed that a CP -violating phase difference appears when studyingtriple-product correlations of decay rates of a particle decay A B = Γ( k · ǫ × ǫ > − Γ( k · ǫ × ǫ < N B ∝ sin(∆ δ + ∆ φ ) , (1)where ∆ δ and ∆ φ represent the differences of strong and weak phases, respectively.The observable A B is therefore sensitive to CP violation but also to differences inphases introduced by strong interactions. Since the latter are independent of CP , onecan build a similar asymmetry for the charged-conjugate decay that will only differin the sign of the weak phases A B ∝ sin(∆ δ − ∆ φ ) , (2)1nd extract a CP -violating observables from the combination of the above asymme-tries a T − oddCP = 12 (cid:0) A B + A B (cid:1) ∝ cos ∆ δ sin ∆ φ. (3)It should be noted that the so-built observable has a complementary feature to thecommon decay rate asymmetries among charged-conjugate processes a CP ∝ sin ∆ δ sin ∆ φ. (4)While the latter needs a sizeable difference in the interfering amplitudes’ strong phasesto be sensitive to CP violation (sin ∆ δ = 0), the former has maximum sensitivity whenthere is not such difference.The simplest way to define a triple-product T -odd observable is by using threeindependent momentum or spin variables from the decay. In the case of spinlessparticles in the final state, at least four particles are needed ( A → abcd ), and the T -odd observable can be built as a triple-product of three out of the four momentain the center-of-mass frame of the decay C T = ~p a · ~p b × ~p c . (5)The two asymmetries A T = Γ( C T > − Γ( C T < A T = Γ( − C T > − Γ( − C T < CP -violating observable a T -odd CP = 12 (cid:0) A T − A T (cid:1) , (7)which differs with respect to Eq. 3 for a ‘minus’ sign due to a conventional choice inthe definition of A T .One advantage of this technique over those comparing the decay rates of chargedconjugate decays is that it does not suffer from any flavour-dependent asymmetry.The asymmetries A T and A T are indeed measured separately on charged-conjugatedecays, and any tagging or particle reconstruction asymmetry is cancelled in theratio. Since these effects are the source of the largest systematic uncertainties in theanalyses that compare the decay rates of charged conjugate decays, the systematicsuncertainties in this technique are usually very small.2 Previous searches
The first attempts at searching for CP violation by using triple-product correla-tions in charm decays were made by FOCUS [9] with a few hundreds of events in D → K + K − π + π − , D + → K S K + π + π − and D + s → K S K + π + π − decays ∗ , obtaininga sensitivity ranging from 5% to 7%.The first measurement reaching the sub-percent sensitivity was made by BaBar [10,11], that obtained sensitivities ranging from 0.5% to 1% on the same channels withabout 50,000 and 20,000 D and D +( s ) decays, respectively. None of the experimentsobserved significant deviations from zero. The LHCb experiment searched for CP violation using T -odd correlations in D → K + K − π + π − decays [12]. The triple-product is defined by using the momenta of threeout of the four daughters in the D rest frame ( C T ≡ ~p K + · ~p π + × ~p π − ). A sample of170,000 D decays is found in 3 fb − of data recorded by the LHCb detector in 2011and 2012, when selecting them through partial reconstruction of semileptonic decaysof the B meson ( B → D µ − X , where X indicates any system composed of chargedand neutral particles). The charge of the muon is used to identify the flavour of the D meson. The distributions of the D meson candidates in four different regions definedby D flavour and C T value being greater or less then zero are shown in Figure 1.The four samples shown in the plot are fitted simultaneously to a model made of twoGaussian distributions for signal and and exponential shape for background. Theasymmetry parameters are extracted directly from the fit.Three measurements of CP violation are performed: (i) integrated; (ii) in bins ofthe phase space; (iii) in bins of decay time. The phase space is divided in 32 binsdefined by means of a Cabibbo-Maksymowicz parametrisation [13], while 5 bins areused in decay time. The criterium used to define the bins guarantees a consistentnumber of events per bin. The result of the integrated measurement is a T -odd CP = (1 . ± . ± . × − . (8)For the binned methods, the asymmetry is calculated in each bin and a χ withrespect to the hypothesis of a T -odd CP = 0 is used to estimate the level at which CP isconserved. These results are shown in Figure 2.Useful information can also be extracted by the non- CP -violating asymmetries A T ∗ Throughout this document the use of charge conjugate reactions is implied, unless otherwiseindicated. c ) [GeV/ − π + π − K + (K m ) c C a nd i d a t e s / ( . M e V / >0) T (C (a) D LHCb P u ll − ] c ) [GeV/ − π + π − K + (K m ) c C a nd i d a t e s / ( . M e V / <0) T (C (b) D LHCb P u ll − ] c ) [GeV/ − π + π − K + (K m ) c C a nd i d a t e s / ( . M e V / >0) T C(- D(c)
LHCb P u ll − ] c ) [GeV/ − π + π − K + (K m ) c C a nd i d a t e s / ( . M e V / <0) T C(- D(d)
LHCb P u ll − Figure 1: Distributions of the K + K − π + π − invariant mass in the four samples definedby D ( D ) flavour and the sign of C T ( C T ). The results of the fit are overlaid as asolid line, and a dashed line is used for representing the background. The normalisedresiduals (pulls) of the difference between the fit results and the data points, dividedby their uncertainties, are shown on top of each distribution.and A T . The integrated measurement shows a significant deviation from zero, A T = ( − . ± . ± . × − A T = ( − . ± . ± . × − . (9)While these asymmetries are flat in D decay time, they show significant deviationfrom the average values in different regions of the phase space, with local asymme-tries values ranging from -30% to 30%, as shown in Figure 3. These effects can beinterpreted as being due to the various resonant contributions that produce differentasymmetries as a result of final state interactions in different regions of the phasespace. This is not the only possible explanation though, following a recent interpre-tation of triple-product asymmetries [14], part of them can be explained as a signalof P violation. 4 hase space region ] - [ C P - odd T a − − − − (a)LHCb /ndf = 26.4/32 χ -1 − − ] - [ C P - odd T a − − − − decay time [ps] D (b) LHCb/ndf = 1.3/4 χ Figure 2: Distributions of a T -odd CP in (a) 32 bins of the phase space and (b) 4 bins of D decay time. A χ with respect to the a T -odd CP = 0 hypothesis is calculated and shownin the plot with the relevant number of degrees of freedom. Phase space region ] - [ T A -40-30-20-10010203040 (a)LHCb Phase space region ] - [ T A -40-30-20-10010203040 (b)LHCb Figure 3: Distributions of (a) A T and (b) A T in 32 bins of the phase space.An interesting feature of this measurement is that, by definition, the systematicuncertainties are very small. A detailed study is presented in the LHCb analysis,where the largest uncertainty on a T -odd CP is due to detector bias as estimated from acontrol sample of B → D ( K − π + π + π − ) µ − X decays. This is conservatively assignedas the statistical uncertainty of the measurement on this sample, since no significantbias is observed. For the A T and A T measurements, the background from prompt D decays and flavour misidentification are the largest sources of uncertainty, butthey cancel in a T -odd CP . Cross-checks were made on particles reconstruction efficiency,particle identification and tagging efficiency, none of them affecting the measurement.5 Conclusions
The triple-product correlations provide alternative and complementary measurementswith which to search for CP violation in multi-body particle decays. Recent studiessuggest that these correlations can be used to probe C and P symmetries as well [14],and that they can be used to probe CP violation systematically in differential decaydistributions [15].The LHCb collaboration searched for CP violation using T -odd correlations in D → K + K − π + π − decays, finding a T -odd CP = (1 . ± . ± . × − . Thisresult is consistent with the previous ones from BaBar and FOCUS collaborations,and has the best sensitivity so far. All of them show no sign of CP violation.This observable is affected by systematic uncertainties that are very small, andtherefore is appropriate for the study of very large data samples expected at LHCbafter LHC Run 2 ( ∼
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