To understand the rare decay Bs→π+π−ℓ+ℓ−

Motivated by the LHCb measurement, we analyze the Bs→π+π−ℓ+ℓ− decay in the kinematics region where the pion pairs have invariant masses in the range 0.5–1.3 GeV and muon pairs do not originate from a resonance. The scalar π+π− form factor induced by the strange s¯s current is predicted by the unitarized approach rooted in the chiral perturbation theory. Using the two-hadron light-cone distribution amplitude, we then can derive the Bs→π+π− transition form factor in the light-cone sum rules approach. Merging these quantities, we present our results for differential decay width which can generally agree with the experimental data. More accurate measurements at the LHC and KEKB in future are helpful to validate our formalism and determine the inputs in this approach

Radiative leptonic Bc→γℓν¯ decay in effective field theory beyond leading order

We study the radiative leptonic Bc→γℓν¯ decays in nonrelativistic QCD effective field theory, and we explore the contribution from a fast-moving photon. As a result, interactions between the photon and the heavy quarks can be integrated out, resulting in the factorization formula for the decay amplitude. We calculate not only the relevant short-distance coefficients at leading order and next-to-leading order in αs , but also the nonrelativistic corrections at the order |v|2 in our analysis. We find that the QCD corrections can significantly decrease the branching ratio, and this is of great importance in extracting the long-distance operator matrix elements of Bc . For phenomenological application, we present our results for the photon energy, lepton energy and lepton-neutrino invariant mass distribution

Neutron–proton effective mass splitting in neutron-rich matter at normal density from analyzing nucleon–nucleus scattering data within an isospin dependent optical model

The neutron–proton effective mass splitting in asymmetric nucleonic matter of isospin asymmetry δ and normal density is found to be mn−p⁎≡(mn⁎−mp⁎)/m=(0.41±0.15)δ from analyzing globally 1088 sets of reaction and angular differential cross sections of proton elastic scattering on 130 targets with beam energies from 0.783 MeV to 200 MeV, and 1161 sets of data of neutron elastic scattering on 104 targets with beam energies from 0.05 MeV to 200 MeV within an isospin dependent non-relativistic optical potential model. It sets a useful reference for testing model predictions on the momentum dependence of the nucleon isovector potential necessary for understanding novel structures and reactions of rare isotopes

"Bare Cross Section" of "Measurement of the e+e−→π+π−\mathrm e^+\mathrm e^-\rightarrow\mathrm\pi^+\mathrm\pi^- Cross Section between 600 and 900 MeV Using Initial State Radiation"

Bare cross section $\sigma^\mathrm{bare}(e^+e^-\to\pi^+\pi^-(\gamma_\mathrm{FSR}))$ of the process $e^+e^-\to\pi^+\pi^-$ measured using the initial state radiation method. The data is corrected concerning final state radiation and vacuum polarization effects. The final state radiation is added using the Schwinger term at born level

"Covariance Matrix of the Pion Form Factor" of "Measurement of the e+e−→π+π−\mathrm e^+\mathrm e^-\rightarrow\mathrm\pi^+\mathrm\pi^- Cross Section between 600 and 900 MeV Using Initial State Radiation"

Statistical covariance matrix of the pion form factor $|F_\pi|^2$

"Pion Form Factor" of "Measurement of the e+e−→π+π−\mathrm e^+\mathrm e^-\rightarrow\mathrm\pi^+\mathrm\pi^- Cross Section between 600 and 900 MeV Using Initial State Radiation"

Pion form factor $|F_\pi|^2$ measured using the initial state radiation method. The data is corrected concerning vacuum polarization effects

"Table 1" of "Measurement of the e+e−→π+π−\mathrm e^+\mathrm e^-\rightarrow\mathrm\pi^+\mathrm\pi^- Cross Section between 600 and 900 MeV Using Initial State Radiation"

Results of the BESIII measurement of the cross section $\sigma^{\rm bare}_{\pi^+\pi^-(\gamma_{\rm FSR})} \equiv \sigma^{\rm bare}(e^+e^-\rightarrow\pi^+\pi^-(\gamma_{\rm FSR}))$ and the squared pion form factor $|F_\pi|^2$. The errors are statistical only. The value of $\sqrt{s'}$ represents the bin center. The 0.9$\%$ systematic uncertainty is fully correlated between any two bins

"Bare Cross Section" of "Measurement of the e+e−→π+π−\mathrm e^+\mathrm e^-\rightarrow\mathrm\pi^+\mathrm\pi^- Cross Section between 600 and 900 MeV Using Initial State Radiation"

Bare cross section $\sigma^\mathrm{bare}(e^+e^-\to\pi^+\pi^-(\gamma_\mathrm{FSR}))$ of the process $e^+e^-\to\pi^+\pi^-$ measured using the initial state radiation method. The data is corrected concerning final state radiation and vacuum polarization effects. The final state radiation is added using the Schwinger term at born level

"Pion Form Factor" of "Measurement of the e+e−→π+π−\mathrm e^+\mathrm e^-\rightarrow\mathrm\pi^+\mathrm\pi^- Cross Section between 600 and 900 MeV Using Initial State Radiation"

Pion form factor $|F_\pi|^2$ measured using the initial state radiation method. The data is corrected concerning vacuum polarization effects

"Covariance Matrix of the Bare Cross Section" of "Measurement of the e+e−→π+π−\mathrm e^+\mathrm e^-\rightarrow\mathrm\pi^+\mathrm\pi^- Cross Section between 600 and 900 MeV Using Initial State Radiation"

Statistical covariance matrix of the bare cross section $\sigma^\mathrm{bare}(e^+e^-\to\pi^+\pi^-(\gamma_\mathrm{FSR}))$