LHCb Collaboration(Aaij, R. et al), Garcia Martin, L. M., Henry, L., Jashal, B. K., Martinez-Vidal, F., Oyanguren, A., et al. (2020). Measurement of CP observables in B+/- -> DK+/- and B+/- -> D pi+/- with D -> KS0 K+/- pi-/+ decays. J. High Energy Phys., 06(6), 058–25pp.
Abstract: Measurements of CP observables in B-+/- -> DK +/- and B-+/- -> D pi (+/-) decays are presented, where D represents a superposition of D-0 and D<overbar>0 states. The D meson is reconstructed in the three-body final states KS0K +/- pi -/+ and KS0K -/+ pi +/-. The analysis uses samples of B mesons produced in proton-proton collisions, corresponding to an integrated luminosity of 1.0, 2.0, and 6.0 fb(-1) collected with the LHCb detector at centre-of-mass energies of <mml:msqrt>s</mml:msqrt> = 7, 8, and 13 TeV, respectively. These measurements are the most precise to date, and provide important input for the determination of the CKM angle gamma.
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Hansen, M. T., Romero-Lopez, F., & Sharpe, S. R. (2020). Generalizing the relativistic quantization condition to include all three-pion isospin channels. J. High Energy Phys., 07(7), 047–49pp.
Abstract: We present a generalization of the relativistic, finite-volume, three-particle quantization condition for non-identical pions in isosymmetric QCD. The resulting formalism allows one to use discrete finite-volume energies, determined using lattice QCD, to constrain scattering amplitudes for all possible values of two- and three-pion isospin. As for the case of identical pions considered previously, the result splits into two steps: the first defines a non-perturbative function with roots equal to the allowed energies, E-n(L), in a given cubic volume with side-length L. This function depends on an intermediate three-body quantity, denoted K-df;3, which can thus be constrained from lattice QCD input. The second step is a set of integral equations relating K-df,K-3 to the physical scattering amplitude, M-3. Both of the key relations, E-n(L) <-> K-df,K-3 and K-df,K-3 <-> M-3, are shown to be block-diagonal in the basis of definite three-pion isospin, I-pi pi pi, so that one in fact recovers four independent relations, corresponding to I-pi pi pi = 0; 1; 2; 3. We also provide the generalized threshold expansion of K-df,K-3 for all channels, as well as parameterizations for all three-pion resonances present for I-pi pi pi = 0 and I-pi pi pi = 1. As an example of the utility of the generalized formalism, we present a toy implementation of the quantization condition for I-pi pi pi = 0, focusing on the quantum numbers of the omega and h(1) resonances.
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Aguilera-Verdugo, J. J., Hernandez-Pinto, R. J., Rodrigo, G., Sborlini, G. F. R., & Torres Bobadilla, W. J. (2021). Causal representation of multi-loop Feynman integrands within the loop-tree duality. J. High Energy Phys., 01(1), 69–26pp.
Abstract: The numerical evaluation of multi-loop scattering amplitudes in the Feynman representation usually requires to deal with both physical (causal) and unphysical (non-causal) singularities. The loop-tree duality (LTD) offers a powerful framework to easily characterise and distinguish these two types of singularities, and then simplify analytically the underling expressions. In this paper, we work explicitly on the dual representation of multi-loop Feynman integrals generated from three parent topologies, which we refer to as Maximal, Next-to-Maximal and Next-to-Next-to-Maximal loop topologies. In particular, we aim at expressing these dual contributions, independently of the number of loops and internal configurations, in terms of causal propagators only. Thus, providing very compact and causal integrand representations to all orders. In order to do so, we reconstruct their analytic expressions from numerical evaluation over finite fields. This procedure implicitly cancels out all unphysical singularities. We also interpret the result in terms of entangled causal thresholds. In view of the simple structure of the dual expressions, we integrate them numerically up to four loops in integer space-time dimensions, taking advantage of their smooth behaviour at integrand level.
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LHCb Collaboration(Aaij, R. et al), Henry, L., Jashal, B. K., Martinez-Vidal, F., Oyanguren, A., Remon Alepuz, C., et al. (2021). Measurement of the CKM angle gamma in B-+/- -> DK +/- and B-+/- -> D pi(+/-) decays with D -> K(S)(0)h(+)h(-). J. High Energy Phys., 02(2), 169–36pp.
Abstract: A measurement of CP-violating observables is performed using the decays B-+/- -> DK +/- and B-+/- -> D pi(+/-), where the D meson is reconstructed in one of the self-conjugate three-body final states K-S(0)pi(+)pi(-) and (KSK+K-)-K-0 (commonly denoted K(S)(0)h(+)h(-)). The decays are analysed in bins of the D-decay phase space, leading to a measurement that is independent of the modelling of the D-decay amplitude. The observables are inter- preted in terms of the CKM angle gamma. Using a data sample corresponding to an integrated luminosity of 9 fb(-1) collected in proton-proton collisions at centre-of mass energies of 7, 8, and 13 TeV with the LHCb experiment, gamma is measured to be (68.7(-5.1)(+5.2))degrees. The hadronic parameters r(B)(DK), r(B)(D pi), delta(DK)(B), and delta(D pi)(B), which are the ratios and strong-phase differences of the suppressed and favoured B-+/- decays, are also reported.
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LHCb Collaboration(Aaij, R. et al), Henry, L., Jashal, B. K., Martinez-Vidal, F., Oyanguren, A., Remon Alepuz, C., et al. (2021). Measurement of the CKM angle gamma and Bs0-Bs0bar mixing frequency with Bs0 -> Ds-/+ h +/ pi+/- pi-/+ decays. J. High Energy Phys., 03(3), 137–46pp.
Abstract: The CKM angle gamma is measured for the first time from mixing-induced CP violation between Bs0 -> Ds -/+ K pi +/- pi -/+ and Bs0bar -> Ds +/- K -/+ pi -/+ pi +/- decays reconstructed in proton-proton collision data corresponding to an integrated luminosity of 9 fb(-1) recorded with the LHCb detector. A time-dependent amplitude analysis is performed to extract the CP-violating weak phase gamma – 2 beta (s) and, subsequently, gamma by taking the Bs0-Bs0bar mixing phase beta (s) as an external input. The measurement yields gamma = (44 +/- 12) degrees modulo 180 degrees, where statistical and systematic uncertainties are combined. An alternative model-independent measurement, integrating over the five-dimensional phase space of the decay, yields gamma = (44 -13+20) degrees modulo 180 degrees. Moreover, the Bs0-Bs0bar oscillation frequency is measured from the flavour-specific control channel Bs0 -> Ds- pi+ pi+ pi- to be m(s) = (17.757 +/- 0.007(stat) +/- 0.008(syst)) ps(-1), consistent with and more precise than the current world-average value.
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