LHCb Collaboration(Aaij, R. et al), Jaimes Elles, S. J., Jashal, B. K., Martinez-Vidal, F., Oyanguren, A., Rebollo De Miguel, M., et al. (2023). Measurement of the CKM angle γ using the B± → D*h± channels. J. High Energy Phys., 12(12), 013–32pp.
Abstract: A measurement of the CP-violating observables from B -> (DK +/-)-K-* and B-+/- -> D-*pi(+/-) decays is presented, where D-*(D) is an admixture of D-*0 and D-0 (D-0 and (0)) states and is reconstructed through the decay chains D-*-> D pi(0)/gamma and D -> KS0 pi+pi-/KS0K+K-. The measurement is performed by analysing the signal yield variation across the D decay phase space and is independent of any amplitude model. The data sample used was collected by the LHCb experiment in proton-proton collisions and corresponds to a total integrated luminosity of 9 fb(-1) at centre-of-mass energies of 7, 8 and 13 TeV. The CKM angle gamma is determined to be (69(-14)(+13))degrees using the measured CP-violating observables. The hadronic parameters r(B)(D)*(K +/-),r(B)(D)*(pi +/-),delta(D)(B)*(K +/-),delta(D)(B)*(pi +/-), which are the ratios and strong phase differences between favoured and suppressed B-+/- decays, are also reported.
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LHCb Collaboration(Aaij, R. et al), Jaimes Elles, S. J., Jashal, B. K., Martinez-Vidal, F., Oyanguren, A., Rebollo De Miguel, M., et al. (2024). A model-independent measurement of the CKM angle γ in partially reconstructed B±→D∗h± decays with D→K0Sh+h-(h=π,K). J. High Energy Phys., 02(2), 118–30pp.
Abstract: A measurement of CP-violating observables in B-+/-->(DK +/-)-K-& lowast; and B-+/--> D-& lowast;pi(+/-) decays is made where the photon or neutral pion from the D-& lowast;-> D gamma or D-& lowast;-> D pi(0) decay is not reconstructed. The D meson is reconstructed in the self-conjugate decay modes, D -> K-S(0)pi(+)pi(-) or D ->(KSK+K-)-K-0. The distribution of signal yields in the D decay phase space is analysed in a model-independent way. The measurement uses a data sample collected in proton-proton collisions at centre-of-mass energies of 7, 8, and 13 TeV, corresponding to a total integrated luminosity of approximately 9 fb(-1). The B-+/-->(DK +/-)-K-& lowast; and B-+/--> D-& lowast;pi(+/-) CP-violating observables are interpreted in terms of hadronic parameters and the CKM angle gamma, resulting in a measurement of gamma=(92(-17)(+21))degrees. The total uncertainty includes the statistical and systematic uncertainties, and the uncertainty due to external strong-phase inputs.
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LHCb Collaboration(Aaij, R. et al), Jaimes Elles, S. J., Jashal, B. K., Martinez-Vidal, F., Oyanguren, A., Rebollo De Miguel, M., et al. (2024). Search for CP violation in the phase space of D0 → KS0 K± π∓ decays with the energy test. J. High Energy Phys., 03(3), 107–20pp.
Abstract: A search for CP violation in D-0 -> (KSK+)-K-0 pi(-) and D-0 -> (KSK-)-K-0 pi(+) decays is reported. The search is performed using an unbinned model-independent method known as the energy test that probes local CP violation in the phase space of the decays. The data analysed correspond to an integrated luminosity of 5.4 fb(-1) collected in proton-proton collisions by the LHCb experiment at a centre-of-mass energy of root s = 13TeV, amounting to approximately 950 thousand and 620 thousand signal candidates for the D-0 -> (KSK-)-K-0 pi(+) and D-0 -> (KSK+)-K-0 pi(-) modes, respectively. The method is validated using D-0 -> K-pi(+)pi(-)pi(+) and D-0 -> K-S(0)pi(+)pi(-) decays, where CP-violating effects are expected to be negligible, and using background-enhanced regions of the signal decays. The results are consistent with CP symmetry in both the D-0 -> (KSK-)-K-0 pi(+) and the D-0 -> (KSK+)-K-0 pi(-) decays, with p-values for the hypothesis of no CP violation of 70% and 66%, respectively.
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Baker, M. J., Bordes, J., Hong-Mo, C., & Tsun, T. S. (2011). Mass Hierarchy, Mixing, CP-Violation And Higgs Decay – Or Why Rotation Is Good For Us. Int. J. Mod. Phys. A, 26(13), 2087–2124.
Abstract: The idea of a rank-one rotating mass matrix (R2M2) is reviewed detailing how it leads to ready explanations both for the fermion mass hierarchy and for the distinctive mixing patterns between up and down fermion states, which can be and have been tested against experiment and shown to be fully consistent with existing data. Further, R2M2 is seen to offer, as by-products: (i) a new solution to the strong CP problem in QCD by linking the theta-angle there to the Kobayashi-Maskawa CP-violating phase in the CKM matrix, and (ii) some novel predictions of possible anomalies in Higgs decay observable in principle at the LHC. A special effort is made to answer some questions raised.
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Bordes, J., Chan, H. M., & Tsun, T. S. (2010). A solution to the strong CP problem transforming the theta angle to the KM CP-violating phase. Int. J. Mod. Phys. A, 25(32), 5897–5911.
Abstract: It is shown that in the scheme with a rotating fermion mass matrix (i.e. one with a scale-dependent orientation in generation space) suggested earlier for explaining fermion mixing and mass hierarchy, the theta angle term in the QCD action of topological origin can be eliminated by chiral transformations, while giving still nonzero masses to all quarks. Instead, the effects of such transformations get transmitted by the rotation to the CKM matrix as the KM phase giving, for theta of order unity, a Jarlskog invariant typically of order 10(-5), as experimentally observed. Strong and weak CP violations appear then as just two facets of the same phenomenon.
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Baker, M. J., Bordes, J., Hong-Mo, C., & Tsun, T. S. (2012). Developing the Framed Standard Model. Int. J. Mod. Phys. A, 27(17), 1250087–45pp.
Abstract: The framed standard model (FSM) suggested earlier, which incorporates the Higgs field and three fermion generations as part of the framed gauge theory (FGT) structure, is here developed further to show that it gives both quarks and leptons hierarchical masses and mixing matrices akin to what is experimentally observed. Among its many distinguishing features which lead to the above results are (i) the vacuum is degenerate under a global su(3) symmetry which plays the role of fermion generations, (ii) the fermion mass matrix is “universal,” rank-one and rotates (changes its orientation in generation space) with changing scale mu, (iii) the metric in generation space is scale-dependent too, and in general nonflat, (iv) the theta-angle term in the quantum chromodynamics (QCD) action of topological origin gets transformed into the CP-violating phase of the Cabibbo-Kobayashi-Maskawa (CKM) matrix for quarks, thus offering at the same time a solution to the strong CP problem.
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Centelles Chulia, S., & Trautner, A. (2020). Asymmetric tri-bi-maximal mixing and residual symmetries. Mod. Phys. Lett. A, 35(35), 2050292–15pp.
Abstract: Asymmetric tri-bi-maximal mixing is a recently proposed, grand unified theory (GUT) based, flavor mixing scheme. In it, the charged lepton mixing is fixed by the GUT connection to down-type quarks and a T-13 flavor symmetry, while neutrino mixing is assumed to be tri-bi-maximal (TBM) with one additional free phase. Here we show that this additional free phase can be fixed by the residual flavor and CP symmetries of the effective neutrino mass matrix. We discuss how those residual symmetries can be unified with T-13 and identify the smallest possible unified flavor symmetries, namely (Z(13)xZ(13))(sic)D-12 and (Z(13)xZ(13))(sic)S-4. Sharp predictions are obtained for lepton mixing angles, CP violating phases and neutrinoless double beta decay.
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Bordes, J., Chan, H. M., & Tsou, S. T. (2021). delta(CP) for leptons and a new take on CP physics with the FSM. Int. J. Mod. Phys. A, 36, 2150236–22pp.
Abstract: A bonus of the framed Standard Model (FSM), constructed initially to explain the mass and mixing patterns of quarks and leptons, is a solution (without axions) of the strong CP problem by cancelling the theta-angle term theta(I) Tr(H-mu v H-mu v*) in coloura by a chiral transformation on a quark zero mode which is inherent in FSM, and produces thereby a CP-violating phase in the CKM matrix similar in size to what is observed.' Extending here to flavour, one finds that there are two terms proportional to Tr(G(mu v) G(mu v)*): (a) in the action from flavour instantons with unknown coefficient, say theta(I)', (b) induced by the above FSM solution to the strong CP-problem with therefore known coefficient theta(C)'. Both terms can be cancelled in the FSM by a chiral transformation on the lepton zero mode to give a Jarlskog invariant J' in the PMNS matrix for leptons of order 10(-2), as is hinted by the experiment. But if, as suggested in Ref. 2, the term theta(I)' is to be cancelled by a chiral transformation in the predicted hidden sector to solve the strong CP problem therein, leaving only the term theta(C)' to be cancelled by the chiral transformation on leptons, then the following prediction results: J' similar to -0.012 (delta(CP)'similar to (1.11)pi) which is (i) of the right order, (ii) of the right sign and (iii) in the range favoured by the present experiment. Together with the earlier result for quarks, this offers an attractive unified treatment of all known CP physics.
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