Charm CPV: observation and prospects (Published as: Science Bulletin, 2020, 65(17):1428-1431, https://doi.org/10.1016/j.scib.2020.04.020) Charm CPV : observation and prospects Miroslav Saur · Fu-Sheng Yu 1 Introduction charm-quark system which, however, had never been discovered with a lot of efforts during the past decade. In physics, the symmetries and their violation always The LHCb collaboration eventually observed the charm provide deep insights into the Nature. The parity (P ) CPV in 2019 via measuring the difference of CP asym- symmetry represents the system is unchanged under metries of D0 ! K+K− and D0 ! π+π− with the the space reflection. The violation of parity, firstly pro- result of (1:54 ± 0:29) × 10−3 [1], with the significance posed by Lee and Yang and subsequently discovered in of 5.3σ. After the establishment of CPV in the strange- 1956, plays the key role in the understanding of the and bottom-quark systems, the observation of charm weak interaction which is one of the four basic forces of CPV is a milestone of particle physics. nature. The charge (C) symmetry describes a property between particles and their anti-particles. The violation of the combined charge-parity (CP ) symmetry was un- 2 LHCb and recent measurement expectedly observed in kaon meson decays in 1964. The C and CP violation (CPV ) are required to explore why Large Hadron Collider beauty experiment (LHCb) on there are much more matter than anti-matter in the Large Hadron Collider (LHC) is a dedicated heavy- Universe. flavour (particles containing c and b quarks) experiment The explanation of CPV was proposed by Kobayashi with a special focus on CPV measurements. Being a and Maskawa (KM) in 1973 by introducing three gener- single-arm forward spectrometer with excellent vertex, ations of quarks, or say six quarks, whereas only three interaction point and momentum resolution in com- quarks were established at the time. All the six quarks bination with high efficient particle identification sys- were found in the following twenty years. This theory tems and large cc cross-section, LHCb can study charm was finally manifested by the observation of CPV in physics, especially possible CP violating processes, with the bottom-quark meson system in 2001. The measured higher precision than previous dedicated B-factory ex- amount of CPV in the Standard Model (SM) of parti- periments. cle physics is about ten orders of magnitude smaller In the time period from 2011 to 2018, LHCb has col- −1 arXiv:2002.12088v3 [hep-ex] 21 Jul 2020 than required by the matter-antimatter asymmetry in lected 9 fb of data, roughly corresponding to the sam- the Universe. Therefore, it is important to search for ple of decays of 1010 D0 whose components are a charm new sources of CPV beyond the SM (BSM). The KM quark and an anti-up quark. Charmed mesons can be mechanism also predicts the existence of CPV in the produced as a direct result of proton-proton collisions (prompt production) or via weak decays of b-hadrons Miroslav Saur (semileptonic productions). In the case of studies using School of Physical Sciences, University of Chinese Academy 0 of Sciences, Beijing, 100000, China D mesons, prompt production is in fact a strong de- ∗ + 0 + E-mail: [email protected] cay D (2010) ! D π and charge conjugated decay Fu-Sheng Yu as well. Usage of this decays allows to determine ex- 0 School of Nuclear Science and Technology, Lanzhou univer- act charm charge of D meson according to the charge sity, Lanzhou, 730000, China of bachelor pion. Semileptonic process are then defined E-mail: [email protected] 0 0 + by the weak decay B ! D µ νµX and charge conju- 2 Miroslav Saur, Fu-Sheng Yu well approximated, up to the order O(10−6), as lin- ear combination of physical CP asymmetry ACP , de- tection asymmetry of D0 which is equal to zero due to charge conjugated final states, mother particle pro- duction asymmetry and detection asymmetry of tag- ging particle. These detection and production asym- metries are cancelled by equalising kinematics between K+K− and π+π− decay modes and then taking a dif- ference. This equalisation is done in three dimension of kinematic variables simultaneously after the removal of phase space regions with large intrinsic asymmetries due to the LHCb detector geometry. Final experimental formula is then written as following 0 + − 0 + − ∆ACP ≡ ACP (D ! K K ) − ACP (D ! π π ) dir equalised + − equalised + − Fig. 1 HFLAV fit of direct CPV parameter ∆aCP and indi- = Araw (K K ) − Araw (π π ): (2) ind rect CPV parameter aCP updated with the reported LHCb measurement. Reproduced from Ref. [4]. The difference of CP asymmetries in D0 ! K+K− and D0 ! π+π− are finally measured by LHCb as prompt −4 gated, where X stands for any allowed additional par- ∆ACP = [−18:2 ± 3:2 (stat.) ± 0:9 (syst.)] × 10 , semileptonic −4 ticles. In this case charm charge of D0 meson is deter- ∆ACP = [−9 ± 8 (stat.) ± 5 (syst.)] × 10 [1]. mined by the charge of muon. By combing both these results with the previous LHCb −1 Recently reported observation of CPV in the Charm measurements with the Run I data of 3 fb [2, 3], it sector by LHCb is based on the new Run 2 data analy- can be obtained that sis and subsequent combination of the obtained results ∆Acombined = (−15:4 ± 2:9) × 10−4; (3) with the previous measurements from Run 1 [2,3]. The CP 6 6 new analysis is based on 44 (9) × 10 and 14 (3) × 10 where the uncertainty includes statistical and system- 0 + − 0 + − D ! K K and D ! π π prompt (semileptonic) atic contributions. This result deviates from zero CP decays, respectively. This data set, corresponding to asymmetry hypothesis on 5.3σ level. This is the first −1 6 fb , was recorded from 2015 to 2018 at the collision observation of CP violation in the charm sector. energy 13 TeV. With the LHCb average of AΓ [4], the direct CP 0 Time dependent CP asymmetry of D decays is asymmetry can then be obtained as given by dir −4 ∆aCP = (−15:7 ± 2:9) × 10 , which shows the sensi- tivity of ∆ACP to the direct CPV . Finally, the com- 0 0 Γ(D (t) ! f) − Γ(D (t) ! f) bined fit of the direct and indirect CP asymmetries ACP (f; t) ≡ ; (1) Γ(D0(t) ! f) + Γ(D0(t) ! f) by the Heavy Flavour Averaging Groups (HFLAV) is shown in Fig. 1. The current world average result ex- where f is a final state and CP eigenstate, in the case cludes the no-CPV hypothesis on the level of 5.44σ. of reported analysis final state is K+K− or π+π− and D0 is the anti-particle of D0. This asymmetry can be also written as the combination of direct and indirect 3 Theoretical explanations and implications dir ht(f)i CP asymmetry effect: ACP (f) ≈ aCP (f)− τ(D0) AΓ (f), where ht(f)i denotes the mean decay time of D0 ! f In theory, CPV in D0 ! K+K− and π+π− results dir influenced by the experimental efficiency, aCP (f) is the from the interference between the tree and penguin am- 0 0 direct CP asymmetry, τ(D ) the D lifetime and AΓ plitudes of charm decays. It is difficult to calculate in the asymmetry between the D0 ! f and D0 ! f ef- the first-principle QCD methods due to the large non- fective decay widths. perturbative contributions at the charm scale. There- However,the ACP values, as defined above are not fore, the order of magnitude of predictions on the charm accessible directly by the experimental methods and CPV is meaningful. must be extracted from the data. Directly measurable Before 2019, several orders of magnitude of charm 0 value is the difference between raw yields, Araw, of D ! CPV have been predicted in literatures, ranging from K+K− and D0 ! K−K+ decays or between D0 ! 10−4 to 10−2. If persisting in using the perturbative + − 0 − + π π and D ! π π , respectively. Araw can be very QCD, CPV in charm decays is naively expected as Charm CPV : observation and prospects 3 we take PE ranging from E=2 to 2E. Under the fac- torization hypothesis, LLY proposed the factorization- assisted topological-amplitude approach which relates the penguin amplitudes to the tree amplitudes with- out any additional free parameters. Considering the uncertainties of input parameters, it is predicted that −3 ∆ACP = (−0:57 ∼ −1:87) × 10 [8], which is consis- tent with the latest result by the LHCb measurement. After the observation of charm CPV by LHCb in 2019, new explanations are explored either in the SM or in the BSM. In the SM picture, the measured result of ∆ACP can be explained by the non-perturbative final- state-interaction contributions from the rescattering ef- fects [11] or the near-by resonant effects [12]. Alterna- Fig. 2 Comparison between experimental measurements (in tively, given that the SM contribution to the charm black) and theoretical predictions (in blue) on ∆ACP in year. CPV is very small based on the heavy-quark expansion Experimental results are corresponding to the world-average and the perturbative QCD, the observed ∆A are ex- values for specific year as calculated by the HFLAV [4]. The CP theoretical approaches of CC and LLY are explained in text. plored by the BSM explanations, such as the flavour- The yellow band is the most recent experimental result for violating Z0 model, the two-Higgs-doublet model, and comparison.