QCD factorization of the four-lepton decay $$B^-\rightarrow \ell \bar{\nu }_\ell \ell ^{(\prime )} \bar{\ell }^{(\prime )}$$

Motivated by the first search for the rare charged-current B decay to four leptons, $$\ell \bar{\nu }_\ell \ell ^{(\prime )} \bar{\ell }^{(\prime )}$$ ℓ ν ¯ ℓ ℓ ( ′ ) ℓ ¯ ( ′ ) , we calculate the decay amplitude with factorization methods. We obtain the $$B\rightarrow \gamma ^*$$ B → γ ∗ form factors, which depend on the invariant masses of the two lepton pairs, at leading power in an expansion in $$\Lambda _\mathrm{QCD}/m_b$$ Λ QCD / m b to next-to-leading order in $$\alpha _s$$ α s , and at $$\mathcal {O}(\alpha _s^0)$$ O ( α s 0 ) at next-to-leading power. Our calculations predict branching fractions of a few times $$10^{-8}$$ 10 - 8 in the $$\ell ^{(\prime )} \bar{\ell }^{(\prime )}$$ ℓ ( ′ ) ℓ ¯ ( ′ ) mass-squared bin up to $$q^2=1~$$ q 2 = 1 GeV$$^2$$ 2 with $$n_+q>3~$$ n + q > 3 GeV. The branching fraction rapidly drops with increasing $$q^2$$ q 2 . An important further motivation for this investigation has been to explore the sensitivity of the decay rate to the inverse moment $$\lambda _B$$ λ B of the leading-twist B meson light-cone distribution amplitude. We find that in the small-$$q^2$$ q 2 bin, the sensitivity to $$\lambda _B$$ λ B is almost comparable to $$B^- \rightarrow \mathrm {\ell }^- \bar{\nu }_{\mathrm {\ell }}\gamma $$ B - → ℓ - ν ¯ ℓ γ when $$\lambda _B$$ λ B is small, but with an added uncertainty from the light-meson intermediate resonance contribution. The sensitivity degrades with larger $$q^2$$ q 2 .

Decay amplitudes to three hadrons from finite-volume matrix elements

We derive relations between finite-volume matrix elements and infinite-volume decay amplitudes, for processes with three spinless, degenerate and either identical or non-identical particles in the final state. This generalizes the Lellouch-Lüscher relation for two-particle decays and provides a strategy for extracting three-hadron decay amplitudes using lattice QCD. Unlike for two particles, even in the simplest approximation, one must solve integral equations to obtain the physical decay amplitude, a consequence of the nontrivial finite-state interactions. We first derive the result in a simplified theory with three identical particles, and then present the generalizations needed to study phenomenologically relevant three-pion decays. The specific processes we discuss are the CP-violating K → 3π weak decay, the isospin-breaking η → 3π QCD transition, and the electromagnetic γ* → 3π amplitudes that enter the calculation of the hadronic vacuum polarization contribution to muonic g − 2.

Measurement of the CKM angle γ in B± → DK± and B± → Dπ± decays with D → $$ {K}_{\mathrm{S}}^0 $$h+h−

A measurement of CP-violating observables is performed using the decays B± → DK± and B± → Dπ±, where the D meson is reconstructed in one of the self-conjugate three-body final states $$ {K}_{\mathrm{S}}^0 $$ K S 0 π+π− and $$ {K}_{\mathrm{S}}^0 $$ K S 0 K+K− (commonly denoted $$ {K}_{\mathrm{S}}^0 $$ 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 γ. 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, γ is measured to be $$ \left({68.7}_{-5.1}^{+5.2}\right){}^{\circ} $$ 68.7 − 5.1 + 5.2 ° . The hadronic parameters $$ {r}_B^{D K},{r}_B^{D\pi},{\delta}_B^{D K},\kern0.5em \mathrm{and}\kern0.5em {\delta}_B^{D\pi} $$ r B DK , r B Dπ , δ B DK , and δ B Dπ , which are the ratios and strong-phase differences of the suppressed and favoured B± decays, are also reported.

Factorization at subleading power and endpoint divergences in h → γγ decay. Part II. Renormalization and scale evolution

Building on the recent derivation of a bare factorization theorem for the b-quark induced contribution to the h → γγ decay amplitude based on soft-collinear effective theory, we derive the first renormalized factorization theorem for a process described at subleading power in scale ratios, where λ = mb/Mh « 1 in our case. We prove two refactorization conditions for a matching coefficient and an operator matrix element in the endpoint region, where they exhibit singularities giving rise to divergent convolution integrals. The refactorization conditions ensure that the dependence of the decay amplitude on the rapidity regulator, which regularizes the endpoint singularities, cancels out to all orders of perturbation theory. We establish the renormalized form of the factorization formula, proving that extra contributions arising from the fact that “endpoint regularization” does not commute with renormalization can be absorbed, to all orders, by a redefinition of one of the matching coefficients. We derive the renormalization-group evolution equation satisfied by all quantities in the factorization formula and use them to predict the large logarithms of order $$ {\alpha \alpha}_s^2{L}^k $$ αα s 2 L k in the three-loop decay amplitude, where $$ L=\ln \left(-{M}_h^2/{m}_b^2\right) $$ L = ln − M h 2 / m b 2 and k = 6, 5, 4, 3. We find perfect agreement with existing numerical results for the amplitude and analytical results for the three-loop contributions involving a massless quark loop. On the other hand, we disagree with the results of previous attempts to predict the series of subleading logarithms $$ \sim {\alpha \alpha}_s^n{L}^{2n+1} $$ ∼ αα s n L 2 n + 1 .

$$\omega \rightarrow 3\pi $$ and $$\omega \pi ^{0}$$ transition form factor revisited

In light of recent experimental results, we revisit the dispersive analysis of the $$\omega \rightarrow 3\pi $$ ω → 3 π decay amplitude and of the $$\omega \pi ^0$$ ω π 0 transition form factor. Within the framework of the Khuri–Treiman equations, we show that the $$\omega \rightarrow 3\pi $$ ω → 3 π Dalitz-plot parameters obtained with a once-subtracted amplitude are in agreement with the latest experimental determination by BESIII. Furthermore, we show that at low energies the $$\omega \pi ^0$$ ω π 0 transition form factor obtained from our determination of the $$\omega \rightarrow 3\pi $$ ω → 3 π amplitude is consistent with the data from MAMI and NA60 experiments.

The cross section of $$e^+e^-\rightarrow \Lambda \overline{\Sigma }{}^0+\text {c.c.}$$ as a litmus test of isospin violation in the decays of vector charmonia into $$\Lambda \overline{\Sigma }{}^0+\text {c.c.}$$

Under the aegis of isospin conservation, the amplitudes in Born approximation, i.e., considering the only one-photon-exchange mechanism, of the decay $$\psi \rightarrow \Lambda \overline{\Sigma }{}^0+\text {c.c.}$$ ψ → Λ Σ ¯ 0 + c.c. , where $$\psi $$ ψ is a vector charmonium, and of the reaction $$e^+e^-\rightarrow \Lambda \overline{\Sigma }{}^0+\text {c.c.}$$ e + e - → Λ Σ ¯ 0 + c.c. at the $$\psi $$ ψ mass, are parametrized by the same electromagnetic coupling. It follows that, the modulus of such a coupling can be extracted from the data on the two observables: the decay branching fraction and the annihilation cross section. By considering the first two vector charmonia, $$J/\psi $$ J / ψ and $$\psi (2S)$$ ψ ( 2 S ) , it is found that, especially in the case of $$\psi (2S)$$ ψ ( 2 S ) , there is a substantial discrepancy between the values of the modulus of the same electromagnetic coupling extracted from the branching ratio and the cross section. We propose, as a possible explanation for such a disagreement, the presence in the decay amplitude of isospin-violating contributions driven by two different mechanisms, that, however, appear to be more favored in the $$\psi (2S)$$ ψ ( 2 S ) than in the $$J/\psi $$ J / ψ decays.

Hawking-Moss transition with a black hole seed

We extend the concept of Hawking-Moss, or up-tunnelling, transitions in the early universe to include black hole seeds. The black hole greatly enhances the decay amplitude, however, order to have physically consistent results, we need to impose a new condition (automatically satisfied for the original Hawking-Moss instanton) that the cosmological horizon area should not increase during tunnelling. We motivate this conjecture physically in two ways. First, we look at the energetics of the process, using the formalism of extended black hole thermodynamics; secondly, we extend the stochastic inflationary formalism to include primordial black holes. Both of these methods give a physical substantiation of our conjecture.

The fate of the axial anomaly in a finite field theory

The conservation of the vector current and the axial anomaly responsible for the [Formula: see text] decay amplitude are obtained in leading order within the Taylor–Lagrange formulation of fields considered as operator-valued distributions. As for gauge theories, where this formulation eliminates all divergences and preserves gauge symmetry, it is shown that the different contributions can be evaluated directly in four-dimensional space–time, with no restrictions whatsoever on the four-momentum of the internal loop, and without the need to introduce any additional nonphysical degrees of freedom like Pauli–Villars fields. We comment on the similar contributions responsible for the decay of the Higgs boson into two photons.