Impact of $$b \rightarrow s \ell \ell $$ anomalies on rare charm decays in non-universal $$Z'$$ models

In this work, we study the impact of $$b \rightarrow s \ell \ell $$ b → s ℓ ℓ , $$B_s - \bar{B_s}$$ B s - B s ¯ mixing and neutrino trident measurements on observables in decays induced by $$c \rightarrow u $$ c → u transition in the context of a non-universal $$Z'$$ Z ′ model which generates $$C^{\mathrm{NP}}_{9} <0$$ C 9 NP < 0 and $$C^{\mathrm{NP}}_9 = - \,C^{\mathrm{NP}}_{10} $$ C 9 NP = - C 10 NP new physics scenarios at the tree level. We inspect the effects on $$D^0 \rightarrow \pi ^0 \nu {\bar{\nu }}$$ D 0 → π 0 ν ν ¯ , $$D^+ \rightarrow \pi ^+ \nu {\bar{\nu }}$$ D + → π + ν ν ¯ and $$B_c \rightarrow B^+ \nu {\bar{\nu }} $$ B c → B + ν ν ¯ decays which are induced by the quark level transition $$c \rightarrow u \nu {\bar{\nu }}$$ c → u ν ν ¯ . The fact that the branching ratios of these decays are negligible in the standard model (SM) and the long distance effects are relatively smaller in comparison to their charged dileptons counterparts, they are considered to provide genuine null-tests of SM. Therefore the observation of these modes at the level of current as well as planned experimental sensitivities would imply unambiguous signature of new physics. Using the constraints on $$Z'$$ Z ′ couplings coming from a combined fit to $$b \rightarrow s \ell \ell $$ b → s ℓ ℓ , $$\varDelta M_s$$ Δ M s and neutrino trident data, we find that any meaningful enhancement over the SM value is ruled out in the considered framework. The same is true for $$D - {\bar{D}}$$ D - D ¯ mixing observable $$\varDelta M_D$$ Δ M D along with $$D^0 \rightarrow \mu ^+ \mu ^-$$ D 0 → μ + μ - and $$D^+ \rightarrow \pi ^+ \mu ^+ \mu ^-$$ D + → π + μ + μ - decay modes which are induced through $$c \rightarrow u \mu ^+ \mu ^-$$ c → u μ + μ - transition.

Probing new physics in class-I B-meson decays into heavy-light final states

With updated experimental data and improved theoretical calculations, several significant deviations are being observed between the Standard Model predictions and the experimental measurements of the branching ratios of $$ {\overline{B}}_{(s)}^0\to {D}_{(s)}^{\left(\ast \right)+}{L}^{-} $$ B ¯ s 0 → D s ∗ + L − decays, where L is a light meson from the set {π, ρ, K(∗)}. Especially for the two channels $$ {\overline{B}}^0\to {D}^{+}{K}^{-} $$ B ¯ 0 → D + K − and $$ {\overline{B}}_s^0\to {D}_s^{+}{\pi}^{-} $$ B ¯ s 0 → D s + π − , both of which are free of the weak annihilation contribution, the deviations observed can even reach 4–5σ. Here we exploit possible new-physics effects in these class-I non-leptonic B-meson decays within the framework of QCD factorization. Firstly, we perform a model-independent analysis of the effects from twenty linearly independent four-quark operators that can contribute, either directly or through operator mixing, to the quark-level b →$$ c\overline{u}d(s) $$ c u ¯ d s transitions. It is found that, under the combined constraints from the current experimental data, the deviations observed could be well explained at the 1σ level by the new-physics four-quark operators with γμ(1 − γ5) ⨂ γμ(1 − γ5) structure, and also at the 2σ level by the operators with (1 + γ5) ⨂ (1 − γ5) and (1 + γ5) ⨂ (1 + γ5) structures. However, the new-physics four-quark operators with other Dirac structures fail to provide a consistent interpretation, even at the 2σ level. Then, as two specific examples of model-dependent considerations, we discuss the case where the new-physics four-quark operators are generated by either a colorless charged gauge boson or a colorless charged scalar, with their masses fixed both at the 1 TeV. Constraints on the effective coefficients describing the couplings of these mediators to the relevant quarks are obtained by fitting to the current experimental data.

Equilibrium Spin Distribution From Detailed Balance

As the core ingredient for spin polarization, the equilibrium spin distribution function that eliminates the collision terms is derived from the detailed balance principle. The kinetic theory for interacting fermionic systems is applied to the Nambu–Jona-Lasinio model at quark level. Under the semi-classical expansion with respect to $$\hbar $$ ħ , the kinetic equations for the vector and axial-vector distribution functions are obtained with collision terms. For an initially unpolarized system, spin polarization can be generated at the first order of $$\hbar $$ ħ from the coupling between the vector and axial-vector charges. Different from the classical transport theory, the collision terms in a quantum theory vanish only in global equilibrium with Killing condition.

The mass-charge binding energy as an explanation for the superfine adjustment of the hadron and baryon masses

Quantum chromodynamics (QCD) describes how mass is created at the quark level. This mechanism is special, because the binding of quarks does not result in a mass loss or a release of energy, as in the case of the nuclear mass defect. Rather, mass is created by the binding of quarks. To achieve this binding, energy must be expended. At the same time, however, quarks are firmly bound to each other. Several authors have shown that the masses of the elementary particles as determined by means of QCD agree quite well with the experimentally determined values. In the following, superfine adjustment of the masses of the charged elementary particles is shown to be possible by considering the mass defect in terms of the mass-charge binding energy.

Combined theoretical study of the $$D^+ \rightarrow \pi ^+ \eta \eta $$ and $$D^+ \rightarrow \pi ^+ \pi ^0 \eta $$ reactions

We study the $$D^+ \rightarrow \pi ^+ \eta \eta $$ D + → π + η η and $$D^+ \rightarrow \pi ^+ \pi ^0 \eta $$ D + → π + π 0 η reactions, which are single Cabibbo suppressed and can proceed both through internal and external emission. The primary mechanisms at quark level are considered, followed by hadronization to produce three mesons in the $$D^+$$ D + decay, and after that the final state interaction of these mesons leads to the production of the $$a_0(980)$$ a 0 ( 980 ) resonance, seen in the $$\pi ^+ \eta $$ π + η , $$\pi ^0 \eta $$ π 0 η mass distributions. The theory has three unknown parameters to determine the shape of the distributions and the ratio between the $$D^+ \rightarrow \pi ^+ \eta \eta $$ D + → π + η η and $$D^+ \rightarrow \pi ^+ \pi ^0 \eta $$ D + → π + π 0 η rates. This ratio restricts much the sets of parameters but there is still much freedom leading to different shapes in the mass distributions. We call for a measurement of these mass distributions that will settle the reaction mechanism, while at the same time provide relevant information on the way that the $$a_0(980)$$ a 0 ( 980 ) resonance is produced in the reactions.

Theoretical study of the $$D^0 \rightarrow K^- \pi ^+ \eta $$ reaction

We develop a model to study the $$D^0 \rightarrow K^- \pi ^+ \eta $$ D 0 → K - π + η weak decay, starting with the color favored external emission and Cabibbo favored mode at the quark level. A less favored internal emission decay mode is also studied as a source of small corrections. Some pairs of quarks are allowed to hadronize producing two pseudoscalar mesons, which posteriorly are allowed to interact to finally provide the $$K^- \pi ^+ \eta $$ K - π + η state. The chiral unitary approach is used to take into account the final state interaction of pairs of mesons, which has as a consequence the production of the $$\kappa $$ κ ($$K^*_0(700)$$ K 0 ∗ ( 700 ) ) and the $$a_0(980)$$ a 0 ( 980 ) resonances, well visible in the invariant mass distributions. We also introduce the $$\bar{K}^{*0} \eta $$ K ¯ ∗ 0 η production in a phenomenological way and show that the s-wave pseudoscalar interaction together with this vector excitation mode are sufficient to provide a fair reproduction of the experimental data. The model provides the relative weight of the $$a_0(980)$$ a 0 ( 980 ) to the $$\kappa $$ κ excitation, and their strength is clearly visible in the low energy part of the $$K \pi $$ K π spectrum.

A New Description of Transverse Momentum Spectra of Identified Particles Produced in Proton-Proton Collisions at High Energies

The transverse momentum spectra of identified particles produced in high energy proton-proton p + p collisions are empirically described by a new method with the framework of the participant quark model or the multisource model at the quark level, in which the source itself is exactly the participant quark. Each participant (constituent) quark contributes to the transverse momentum spectrum, which is described by the TP-like function, a revised Tsallis–Pareto-type function. The transverse momentum spectrum of the hadron is the convolution of two or more TP-like functions. For a lepton, the transverse momentum spectrum is the convolution of two TP-like functions due to two participant quarks, e.g., projectile and target quarks, taking part in the collisions. A discussed theoretical approach seems to describe the p + p collisions data at center-of-mass energy s = 200 GeV , 2.76 TeV, and 13 TeV very well.

Relations between b → cτν decay modes in scalar models

As a consequence of the Ward identity for hadronic matrix elements, we find relations between the differential decay rates of semileptonic decay modes with the underlying quark-level transition b → cτν, which are valid in scalar models. The decay-mode dependent scalar form factor is the only necessary theoretical ingredient for the relations. Otherwise, they combine measurable decay rates as a function of the invariant mass-squared of the lepton pair q2 in such a way that a universal decay-mode independent function is found for decays to vector and pseudoscalar mesons, respectively. This can be applied to the decays $$ B\to {D}^{\ast}\tau v,{B}_s\to {D}_s^{\ast}\tau v,{B}_c\to J/\psi \tau v $$ B → D ∗ τv , B s → D s ∗ τv , B c → J / ψτv and B → Dτv, Bs → Dsτv, Bc → ηcτv, with implications for R(D(*)), $$ R\left({D}_s^{\left(\ast \right)}\right) $$ R D s ∗ , R(J/ψ), R(ηc), and ℬ(Bc → τv). The slope and curvature of the characteristic q2-dependence is proportional to scalar new physics parameters, facilitating their straight forward extraction, complementary to global fits.

Universal scale factors relating mesonic fields and quark operators

Scale factor matrices relating mesonic fields in chiral Lagrangians and quark-level operators of QCD sum-rules are shown to be constrained by chiral symmetry, resulting in universal scale factors for each chiral nonet. Built upon this interplay between chiral Lagrangians and QCD sum-rules, the scale factors relating the [Formula: see text] isotriplet scalar mesons to their underlying composite quark fields were recently determined. It is shown that the same technique when applied to [Formula: see text] isodoublet scalars reproduces the same scale factors, confirming the universality property and further validating this connection between chiral Lagrangians and QCD sum-rules, which can have nontrivial impacts on our understanding of the low-energy QCD, in general, and the physics of scalar mesons in particular.