$S$-wave contribution to rare $D^0\to {\pi }^{+}{\pi }^{-}{\ell }^{+}{\ell }^{-}$ decays in the Standard Model and sensitivity to New Physics

Abstract

Physics of the up-type flavour offers unique possibilities of testing the Standard Model (SM) compared to the down-type flavour sector. Here, we discuss SM and New Physics (NP) contributions to the rare charm-meson decay $D^0\to {\pi }^{+}{\pi }^{-}{\ell }^{+}{\ell }^{-}$. In particular, we discuss the effect of including the lightest scalar isoscalar resonance in the SM picture, namely, the $f_0(500)$, which manifests in a big portion of the allowed phase space. Other than showing in the total branching ratio at an observable level of about $20\%$, the $f_0(500)$ resonance manifests as interference terms with the vector resonances, such as at high invariant mass of the leptonic pair in distinct angular observables. Recent data from LHCb optimize the sensitivity to $P$-wave contributions, that we analyse in view of the inclusion of vector resonances. We propose the measurement of alternative observables which are sensitive to the $S$-wave and are straightforward to implement experimentally. This leads to a new set of null observables, that vanish in the SM due to its gauge and flavour structures. Finally, we study observables that depend on the SM interference with generic NP contributions from semi-leptonic four-fermion operators in the presence of the $S$-wave.

References in corpus (67)

• Weak Decays Beyond Leading Logarithms
• $B\to V{\ell }^{+}{\ell }^{-}$ in the Standard Model from Light-Cone Sum Rules
• Weak form factors for heavy meson decays: an update
• From controversy to precision on the sigma meson: a review on the status of the non-ordinary $f_0(500)$ resonance
• Kaon Decays in the Standard Model
• Observation of $CP$ violation in charm decays
• Precise determination of the f0(600) and f0(980) pole parameters from a dispersive data analysis
• STCF Conceptual Design Report: Volume 1 -- Physics & Detector
• Rare Charm Decays in the Standard Model and Beyond
• Measurement of e+e- -> pi+pi- cross section with CMD-2 around rho-meson
• B_l4 decays and the extraction of |V_ub|
• General Analysis of B -> K^(*) l^+ l^- Decays at Low Recoil
• $B^0$ and $B_s^0$ decays into $J/\psi$ $f_0(980)$ and $J/\psi$ $f_0(500)$ and the nature of the scalar resonances
• Prospects of discovering new physics in rare charm decays
• Comprehensive Amplitude Analysis of $\gamma \gamma \to {\pi }^{+}{\pi }^{-},{\pi }^0{\pi }^0$ and $\overline{K}K$ below 1.5 GeV
• Flavor & new physics opportunities with rare charm decays into leptons
• Radiative Weak Decays of Charm Mesons
• Measurement of the resonant and CP components in ${\overline{B}}^0\to J/\psi {\pi }^{+}{\pi }^{-}$ decays
• The $c\to u\gamma$ Contribution to Weak Radiative Charm Decay
• Evidence for new interference phenomena in the decay D+ to K- pi+ mu+ nu
• Precise measurement of the $f_s/f_d$ ratio of fragmentation fractions and of $B_s^0$ decay branching fractions
• A model-independent analysis of final-state interactions in \bar B_{d/s}^0 --> J/psi pi pi
• Charm Physics Confronts High-$p_T$ Lepton Tails
• A new parametrization for the scalar pion form factors
• Impact of $B\to K_0^{\ast }{\ell }^{+}{\ell }^{-}$ on the New Physics search in $B\to K^{\ast }{\ell }^{+}{\ell }^{-}$ decay
• On $D\to X_u{l}^{+}{l}^{-}$ within the Standard Model and Frameworks like the Littlest Higgs Model with T Parity
• Disentangling the Decay Observables in $B^{-}\to {\pi }^{+}{\pi }^{-}{\ell }^{-}{\bar{\nu }}_{\ell }$
• Standard Model prediction and new physics tests for D0 -> h+h-l+l- (h=π,K; l=e,μ)
• Effects of Littlest Higgs model in rare D meson decays
• Observation of $B_s^0\to J/\psi f_0(980)$ and Evidence for $B_s^0\to J/\psi f_0(1370)$
• The New Physics Reach of Null Tests with $D\to \pi \ell \ell$ and $D_s\to K\ell \ell$ Decays
• The mass of the sigma pole
• Chiral Dynamics and S-wave Contributions in Semileptonic B decays
• Analysis of the D+ --> K- pi+ e+ nu_e decay channel
• Null tests from angular distributions in $D\to P_1{P}_2{l}^{+}{l}^{-}$, $l=e,\mu$ decays on and off peak
• The effect of S-wave interference on the $B^0\to K^{\ast 0}{\ell }^{+}{\ell }^{-}$ angular observables
• Rare charm $\mathbf{c}\to \mathbf{u}\mathbf{\nu }\bar{\mathbf{\nu }}$ dineutrino null tests for ${\mathbf{e}}^{+}{\mathbf{e}}^{-}$-machines
• Observation of $D^0$ meson decays to ${\pi }^{+}{\pi }^{-}{\mu }^{+}{\mu }^{-}$ and $K^{+}{K}^{-}{\mu }^{+}{\mu }^{-}$ final states
• On CP Asymmetries in Two-, Three- and Four-Body D Decays
• Amplitude Analyses of $D^0\to {\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ and $D^0\to K^{+}{K}^{-}{\pi }^{+}{\pi }^{-}$ Decays
• Observation of $D^{+}\to f_0(500)e^{+}{\nu }_e$ and Improved Measurements of $D\to \rho e^{+}{\nu }_e$
• Theoretical and experimental status of rare charm decays
• Measurement of the time-integrated $CP$ asymmetry in $D^0\to K^{-}{K}^{+}$ decays
• $D\to \rho {\ell }^{+}{\ell }^{-}$ Decays in the QCD Factorization Approach
• Resonant and nonresonant contributions to the weak $D\to V{l}^{+}{l}^{-}$ decays
• Final-state interactions in the CP asymmetries of charm-meson two-body decays
• Higher-order Wilson coefficients for c $\to$ u transitions in the Standard Model
• Search for the rare decays $D\to h(h^{\prime })e^{+}{e}^{-}$
• Analysis of D+ to K- pi+ e+ nu_e and D+ to K- pi+ mu+ nu_mu Semileptonic Decays
• Measurement of angular and CP asymmetries in $D^0\to {\pi }^{+}{\pi }^{-}{\mu }^{+}{\mu }^{-}$ and $D^0\to K^{+}{K}^{-}{\mu }^{+}{\mu }^{-}$ decays
• Disentangling QCD and New Physics in $D^{+}\to {\pi }^{+}{\ell }^{+}{\ell }^{-}$
• K_L to π^+ π^- e^+ e^-
• K^+ -> pi^+pi^0e^+e^-: a novel short-distance probe
• Search for $CP$ violation through an amplitude analysis of $D^0\to K^{+}{K}^{-}{\pi }^{+}{\pi }^{-}$ decays
• Differential branching fraction and angular moments analysis of the decay $B^0\to K^{+}{\pi }^{-}{\mu }^{+}{\mu }^{-}$ in the $K_{0,2}^{\ast }(1430{)}^0$ region
• K->pipie+e- decays and chiral low-energy constants
• Branching fraction and charge asymmetry measurements in B to J/psi pi pi decays
• The f0(1370) controversy from dispersive meson-meson scattering data analyses
• Modelling theoretical uncertainties in phenomenological analyses for particle physics
• Angular analysis of $D^0\to {\pi }^{+}{\pi }^{-}{\mu }^{+}{\mu }^{-}$ and $D^0\to K^{+}{K}^{-}{\mu }^{+}{\mu }^{-}$ decays and search for $CP$ violation
• Light-Cone Sum Rules for $S$-wave $B\to K\pi$ Form Factors
• Search for rare decays of $D^0$ mesons into two muons
• $B\to D_0^{\ast }$ and $B_s\to D_{s0}^{\ast }$ form factors from QCD light-cone sum rules
• A complete description of P- and S-wave contributions to the $B^0\to K^{+}{\pi }^{-}{\ell }^{+}{\ell }^{-}$ decay
• Radiative three-body D-meson decays in and beyond the standard model
• Cabibbo Allowed D -> K pi gamma Decays
• Probing QCD dynamics and the standard model with $D_{(s)}\to P^{+}{P}^0\gamma$ decays

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• Search for $D^0$ meson decays to ${\pi }^{+}{\pi }^{-}{e}^{+}{e}^{-}$ and $K^{+}{K}^{-}{e}^{+}{e}^{-}$ final states
• Search for resonance-enhanced $CP$ and angular asymmetries in the ${\Lambda }_c^{+}\to p{\mu }^{+}{\mu }^{-}$ decay at LHCb
• New opportunities for rare charm from $Z\to c\bar{c}$ decays
• Measurement of the $D^0\to K^{-}{\pi }^{+}{e}^{+}{e}^{-}$ branching fraction and search for $D^0\to {\pi }^{+}{\pi }^{-}{e}^{+}{e}^{-}$ and $D^0\to K^{+}{K}^{-}{e}^{+}{e}^{-}$ decays at Belle