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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- system which, however, had never been discovered with a lot of efforts during the past decade. In physics, the and their violation always The LHCb collaboration eventually observed the charm provide deep insights into the . The (P ) CPV in 2019 via measuring the difference of CP asym- 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 which is one of the four basic forces of CPV is a milestone of . nature. The (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 decays in 1964. The C and CP violation (CPV ) are required to explore why beauty experiment (LHCb) on there are much more than anti-matter in the Large Hadron Collider (LHC) is a dedicated heavy- . flavour (particles containing c and b ) 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 resolution in com- quarks were established at the . 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 (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- 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 can be mechanism also predicts the existence of CPV in the produced as a direct result of -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: miroslav.saur@.ch 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 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 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 . 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. vector-like quark models [13–15]. Due to the non-perturbative physics at the charm ∗ αs(µc) |VubVcb| −4 scale, it is difficult to use the observed CPV to reliably ACP ∼ π |V V ∗ | = O(10 ). On the contrary, If us cs search for new physics. On the contrary, the study of taking the unknown non-perturbative contributions to charm CPV could be used to test and understand the be arbitrarily large, the charm CPV could be as large as non-perturbative behaviour of the SM. The additional 10−2, to be consistent with the experimental results in progress in theory and also more precise experimental 2011 when ∆A was measured to be (−0.82 ± 0.24)% CP measurements are needed. by LHCb [5]. Due to the limit of space of this article, relevant references can be seen in [6]. The most inter- esting thing is that only two papers, written by Cheng 4 Impact and prospect for the future and Chiang (CC) [7] and Li, L¨uand Yu (LLY) [8], quan- −3 0 + − 0 titatively predicted ∆ACP at the order of 10 before Although the combination of D → K K and D → the observation. They are much smaller than the experi- π+π− was expected to be one of the best probes of mental measurements in 2011 and 2012, but manifested CPV in charm, many other studies are possible or even 0 0 0 + by the recent LHCb result. The comparison between the already ongoing, such as D → KSKS and D → experimental measurements and the theoretical predic- K+K−π+ [6], to test and understand the dynamics of tions by CC and LLY are shown in Fig. 2. charm decay and to search for new physics beyond the To predict the charm CPV , one should reliably ob- SM. Due to their generally rich decays structure multi- tain the tree amplitudes first, to understand the dy- body decays offer additional interesting possibility how namics at the charm scale, and then calculate the pen- to look for CPV signatures. However, at the same time guin amplitudes reasonably. Including all the strong- such a studies generally require more complicated anal- interaction effects, especially the non-perturbative con- ysis methods and higher recorded luminosity. Another tributions, the topological diagrammatic approach works interesting measurement is being performed to investi- well for hadronic charm-meson decays by extracting gate a novel effect of CPV in charmed meson decaying 0 the tree amplitudes from the data of branching frac- into KS, which comes from mother decay and daugh- tions [7–9]. CC pointed out that the upper bound of ter mixing with predicted values reaching the available ∆ACP in the SM is −0.25% [9] which is more than 2σ experimental sensitivity [16]. away from the experimental result at that time. Later The LHCb detector is currently going through the on, they assumed that the penguin-exchange diagram substantial upgrade which will allow to record data is identical to the W -exchange diagram, PE = E, so with 5 higher luminosity than during the years −3 that ∆ACP = (−1.39±0.04)×10 or (−1.51±0.04)× 2015-2018. This, in combination with the new full soft- 10−3 [7], and updated with similar results in [10]. To ware trigger, a crucial point for the charm physics, give a reasonable uncertainty of the CC approach, con- will allow LHCb to achieve an unprecedented preci- sidering the possible difference between PE and E, sion in the heavy flavour sector CPV measurements. 4 Miroslav Saur, Fu-Sheng Yu

Table 1 Overview of the recorded and predicted values for 2. LHCb collaboration, R. Aaij, B. Adeva, M. Adi- promptly produced D0 → K+K− and D0 → π+π− yields nolfi, et al., Measurement of CP asymmetry in during the different data-taking periods at LHCb. All val- D0 → K−K+ and D0 → π−π+ decays, JHEP 07 (2014) ues are corresponding to the trigger-level yields within the 041, arXiv:1405.2797. LHCb acceptance. Last column shows expected precision of 3. LHCb collaboration, R. Aaij, C. Abellan Beteta, the ∆ACP measurements with the corresponding yields. Re- B. Adeva, et al., Measurement of the difference of produced from Ref. [17]. time-integrated CP asymmetries in D0 → K−K+ and 0 − + −1 D → π π decays, Phys. Rev. Lett. 116 (2016) 191601, Sample [fb ] Yield yield σ(∆ACP ) 0 + − 0 + − arXiv:1602.03160. D → K K D → π π [%] 4. Heavy Flavor Averaging Group, Y. Amhis, Sw. Banerjee, Run 1-2 (9) 52 × 106 17 × 106 0.03 E. Ben-Haim et al., Averages of b-hadron, c-hadron, and Run 1-3 (23) 280 × 106 94 × 106 0.013 τ- properties as of summer 2016, Eur. Phys. J. Run 1-4 (50) 1 × 109 305 × 106 0.01 C77 (2017) 895, arXiv:1612.07233, updated results and Run 1-5 (300) 4.9 × 109 1.6 × 109 0.003 plots available at https://hflav.web.cern.ch. 5. LHCb, R. Aaij, C. Abellan Beteta, B. Adeva, et al., Evidence for CP violation in time-integrated D0 → − + This opens a door to measure possible CPV effects h h decay rates, Phys. Rev. Lett. 108 (2012) 111602, arXiv:1112.0938. in rare decays, e.g. radiative and semi-leptonic decays. 6. H.-N. Li, C.-D. L, and F.-S. Yu, Implications on the first Another dedicated heavy-flavour experiment is Belle II, observation of charm cpv at lhcb, arXiv:1903.10638. which started taking data in 2019, from which contri- 7. H.-Y. Cheng and C.-W. Chiang, SU(3) symmetry break- butions to CPV measurements are expected, especially ing and CP violation in D → PP decays, Phys. Rev. D86 (2012) 014014, arXiv:1205.0580. results from the decays with neutral particles in the fi- 8. H.-n. Li, C.-D. Lu, and F.-S. Yu, Branching ratios and nal states. Another substantial upgrade of the LHCb is direct CP asymmetries in D → PP decays, Phys. Rev. planned for the time period after 2030, with additional D86 (2012) 036012, arXiv:1203.3120. ten fold increase of luminosity. The LHCb is currently 9. H.-Y. Cheng and C.-W. Chiang, Direct CP violation in two-body hadronic charmed meson decays, Phys. expected to be the only dedicated heavy-flavour experi- Rev. D 85 (2012) 034036, arXiv:1201.0785, [Erratum: ment taking data during that time period. Table 1 sum- Phys.Rev.D 85, 079903 (2012)]. marises current and expected future trigger-level yields 10. H.-Y. Cheng and C.-W. Chiang, Revisiting and sensitivity in promptly produced D0 → K+K− and in d → pp and vp decays, Phys. Rev. D 100 (2019) 093002, 0 + − arXiv:1909.03063. D → π π decays. 11. Y. Grossman and S. Schacht, The emergence of the In summary, the first experimental observation of ∆U = 0 rule in charm physics, JHEP 07 (2019) 020, CP violation in the charm sector was done with an arXiv:1903.10952. amazing sensitivity obtained by LHCb in 2019. This 12. A. Soni, Resonance enhancement of Charm CP, arXiv:1905.00907. is a milestone in the high energy physics. The result is 13. M. Chala, A. Lenz, A. V. Rusov, and J. Scholtz, δa CP consistent with the theoretical predictions by CC and within the standard model and beyond, JHEP 07 (2019) LLY. It is expected that more precise measurements 161, arXiv:1903.10490. and more theoretical studies in the near future will help 14. A. Dery and Y. Nir, Implications of the LHCb discovery of CP violation in charm decays, JHEP 12 (2019) 104, us to deeply understand the dynamics at the charm arXiv:1909.11242. scale and to explore the new physics effects. 15. L. Calibbi, T. Li, Y. Li, and B. Zhu, Simple model for large CP violation in charm decays, B-physics anoma- lies, muon g-2, and , arXiv:1912.02676. 5 Acknowledgement 16. F.-S. Yu, D. Wang, and H.-n. Li, CP asymmetries in charm decays into neutral , Phys. Rev. Lett. 119 This work is partially supported by the National Nat- (2017) 181802, arXiv:1707.09297. 17. LHCb collaboration, R. Aaij, B. Adeva, M Adinolfi, et al., ural Science Foundation of China under Physics case for an LHCb Upgrade II — Opportuni- Grants No.U1732101 and 11975112, by Gansu Natural ties in flavour physics, and beyond, in the HL-LHC era, Science Fund under grant No.18JR3RA265, by the Fun- arXiv:1808.08865. damental Research Funds for the Central Universities under Grant No. lzujbky-2019-55 and by the University of Chinese Academy of Sciences scholarship for Inter- national students.

References

1. LHCb collaboration, R. Aaij, C. Abellan Beteta, M. Adi- nolfi, et al., Observation of CP violation in charm decays, Phys. Rev. Lett. 122 (2019) 211803, arXiv:1903.08726.