Nonfactorizable Contributions Research Articles

Nonfactorizable charming-loop contribution to FCNC Bs→γl+l− decay

We present the first theoretical calculation of nonfactorizable charm-quark loop contributions to the Bs→γl+l− amplitude. We calculate the relevant form factors, HA,VNF(k′2,k2), and provide convenient parametrizations of our results in the form of fit functions of two variables, k′2 and k2, applicable in the region below hadron resonances, k′2<MJ/ψ2 and k2<Mϕ2. We report that factorizable and nonfactorizable charm contributions to the Bs→γl+l− amplitude have opposite signs. To compare the charm and the top contributions, it is convenient to express nonfactorizable charming loop contribution as a nonuniversal (i.e., dependent on the reaction) q2-dependent correction ΔNFC7(q2) to the Wilson coefficient C7. For the Bs→γl+l− amplitude, the correction is found to be positive, ΔNFC7(q2)/C7>0. Published by the American Physical Society 2024

Evidence of the singly Cabibbo suppressed decay Λc+→pπ0

Evidence for the singly Cabibbo suppressed decay Λc+→pπ0 is reported for the first time with a statistical significance of 3.7σ based on 6.0 fb−1 of e+e− collision data collected at center-of-mass energies between 4.600 and 4.843 GeV with the BESIII detector at the BEPCII collider. The absolute branching fraction of Λc+→pπ0 is measured to be (1.56−0.58+0.72±0.20)×10−4. Combining with the branching fraction of Λc+→nπ+, (6.6±1.3)×10−4, the ratio of the branching fractions of Λc+→nπ+ and Λc+→pπ0 is calculated to be 3.2−1.2+2.2. As an important input for the theoretical models describing the decay mechanisms of charmed baryons, our result indicates that the nonfactorizable contributions play an essential role and their interference with the factorizable contributions should not be significant. In addition, the absolute branching fraction of Λc+→pη is measured to be (1.63±0.31stat±0.11syst)×10−3. Published by the American Physical Society 2024

Study of Bs0→TT(a2(1320), K2*(1430), f2(1270), f2′(1525)) in the perturbative QCD approach

In the present study, the calculations of two-body decays Bs0→TT [T denotes tensor mesons, a2(1320), K2*(1430), f2(1270), f2′(1525)] in the perturbative QCD approach are presented. The ensuing predictions encompass branching ratios, polarization fractions, and direct CP violations, all elucidated in comprehensive detail. It is discerned that (1) for pure annihilation decay, the longitudinal polarization is around 90.0%, whereas the transverse polarizations manifest comparatively diminutive magnitudes. (2) The direct CP asymmetry is directly proportional to the interference between the tree and penguin contributions. For most of the decays investigated within this discourse, the direct CP asymmetry remains modest in magnitude. (3) There are precisely six distinct categories of Feynman diagrams for Bs0→TT, because the tensor mesons cannot be produced through the (V±A) currents or (S±P) density, thereby prohibiting factorizable emission diagrams. The nonfactorizable and annihilation contributions are ascertained to be pivotal in these decay modes. The calculated branching ratios of our calculation for Bs0→TT are at the order of 10−6 and 10−7, which can be tested in the LHCb and Belle II experiments. (4) Mixing exists for the f2(1270) and f2′(1525), just as the η and η′ mixing, the branching ratios about the mixing angle θ are given in this work. However, it is different from f1(1285)−f1(1420), the mixing angle is notably small, thereby resulting in only marginal alterations in the decay branching ratios. Published by the American Physical Society 2024

Radiative B to tensor meson decays at NLO in SCET

The radiative B to tensor meson decays are studied at next-to-leading order in soft-collinear effective theory (SCET). The SCET allows the systematic treatment of factorizable and non-factorizable contributions along with the resummation of large perturbative logarithms. We performed a two-step matching and determined the soft-overlap function and branching ratios for these B to tensor meson decays. In the case of , the numerical value of the branching ratio lies close to its experimental measurements. The estimated values of the branching ratios of Cabibbo–Kobayashi–Maskawa suppressed decays are significantly small compared to that of , but still could be measured in some ongoing and future B physics experiments.

Non-factorizable virtual corrections to Higgs boson production in weak boson fusion beyond the eikonal approximation

Non-factorizable virtual corrections to Higgs boson production in weak boson fusion at next-to-next-to-leading order in QCD were estimated in the eikonal approximation [1]. This approximation corresponds to the expansion of relevant amplitudes around the forward limit. In this paper we compute the leading power correction to the eikonal limit and show that it is proportional to first power of the Higgs boson transverse momentum or the Higgs boson mass over partonic center-of-mass energy. Moreover, this correction can be significantly enhanced by the rapidity of the Higgs boson. For realistic weak boson fusion cuts, the next-to-eikonal correction reduces the estimate of non-factorizable contributions to fiducial cross section by (20) percent.

Resonance contributions from χ c0 in charmless three-body hadronic B meson decays* *Supported by the National Natural Science Foundation of China (11235005, 11847141, 12105112), the Natural Science Foundation of Jiangsu Education Committee (21KJB140027), and the Natural Science Foundation of Huaiyin Institute of Technology (21HGZ012).

Within the framework of perturbative QCD factorization, we investigate the nonfactorizable contributions to the factorization-forbidden quasi-two-body decays with . We compare our predicted branching ratios for the decay with available experiment data as well as predictions by other theoretical studies. The branching ratios of these decays are consistent with data and other theoretical predictions. However, in the Cabibbo-suppressed decays with , the values of the branching ratios are of the order of and . The ratio between the decays and and the distribution of branching ratios for different decay modes in invariant mass are considered in this study.

Measurement of the branching fraction of the singly Cabibbo-suppressed decay Λc+→ΛK+

We report a branching fraction measurement of the singly Cabibbo-suppressed decay Λc+→ΛK+ using a data sample collected with the BESIII detector at the BEPCII storage ring. The data span center-of-mass energies from 4.599 to 4.950 GeV and correspond to an integrated luminosity of 6.44 fb−1. The branching fraction of Λc+→ΛK+ relative to that of the Cabibbo-favored decay Λc+→Λπ+ is measured to be R=B(Λc+→ΛK+)B(Λc+→Λπ+)=(4.78±0.34±0.20)%. Combining with the world-average value of B(Λc+→Λπ+), we obtain B(Λc+→ΛK+)=(6.21±0.44±0.26±0.34)×10−4. Here the first uncertainties are statistical, the second systematic, and the third comes from the uncertainty of the Λc+→Λπ+ branching fraction. This result, which is more precise than previous measurements, does not agree with theoretical predictions, and suggests that nonfactorizable contributions have been underestimated in current models.Received 9 August 2022Accepted 16 November 2022DOI:https://doi.org/10.1103/PhysRevD.106.L111101Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasBranching fractionHadronic decaysParticle decaysPhysical SystemsCharmed baryonsTechniquesPrecision measurementsParticles & Fields

Investigating the color-suppressed decays Λb→Λψ in the perturbative QCD approach

The nonleptonic two-body ${\mathrm{\ensuremath{\Lambda}}}_{b}\ensuremath{\rightarrow}\mathrm{\ensuremath{\Lambda}}\ensuremath{\psi}$ decays with $\ensuremath{\psi}=J/\ensuremath{\psi}$ or $\ensuremath{\psi}(2S)$ are investigated based on the perturbative QCD approach. These are color-suppressed processes in which the nonfactorizable contributions are confirmed to be dominant. Angular momentum conservation allows us to describe the concerned decays by four independent complex helicity amplitudes. It is observed that the negative-helicity states for the $\mathrm{\ensuremath{\Lambda}}$ baryon are preferred as expected in the left-handed nature of the charged-current interaction. The obtained results for the helicity amplitudes are used to compute the branching ratios and various observable parameters, which are then compared to the existing theoretical predictions and experimental data. In particular, we predict the ratio $\mathcal{R}=\frac{\mathcal{B}({\mathrm{\ensuremath{\Lambda}}}_{b}\ensuremath{\rightarrow}\mathrm{\ensuremath{\Lambda}}\ensuremath{\psi}(2S))}{\mathcal{B}({\mathrm{\ensuremath{\Lambda}}}_{b}\ensuremath{\rightarrow}\mathrm{\ensuremath{\Lambda}}J/\ensuremath{\psi})}=0.4{7}_{\ensuremath{-}0.00}^{+0.02}$ in comparison with $0.508\ifmmode\pm\else\textpm\fi{}0.023$ from the Particle Data Group at the level of 1 standard deviation. We also briefly explore the long-distance contributions to the semileptonic ${\mathrm{\ensuremath{\Lambda}}}_{b}\ensuremath{\rightarrow}\mathrm{\ensuremath{\Lambda}}{l}^{+}{l}^{\ensuremath{-}}$ decays in the kinematic regions where the dilepton invariant masses are around the $J/\ensuremath{\psi}$ and $\ensuremath{\psi}(2S)$ resonances.

Two-body baryonic Bu,d,s and Bc to charmless final state decays

We study the rates and direct $CP$ violations of two-body baryonic ${\overline{B}}_{u,d,s}\ensuremath{\rightarrow}{\mathbf{\text{B}}\overline{\mathbf{\text{B}}}}^{\ensuremath{'}}$ and ${B}_{c}^{\ensuremath{-}}\ensuremath{\rightarrow}{\mathbf{\text{B}}\overline{\mathbf{\text{B}}}}^{\ensuremath{'}}$ decays, where the final state baryons include low-lying octet and decuplet baryons. We incorporate topological amplitude formalism and the factorization approach. Asymptotic relations at large ${m}_{b}$ are used to simplify decay amplitudes. Using the most up-to-date data on ${\overline{B}}^{0}\ensuremath{\rightarrow}p\overline{p}$ and ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}\mathrm{\ensuremath{\Lambda}}\overline{p}$ decay rates as inputs, rates and direct $CP$ violations of ${\overline{B}}_{u,d,s}\ensuremath{\rightarrow}{\mathbf{\text{B}}\overline{\mathbf{\text{B}}}}^{\ensuremath{'}}$ decays are revised and predicted. It is interesting that the results on rates satisfy all existing experimental bounds and some are close to the bounds. Factorization diagrams contribute to penguin-exchange, exchange, annihilation, and penguin-annihilation amplitudes. Although the resulting penguin-exchange factorization amplitudes are sizable, the rest suffer from severe chiral suppression and are sensitive to nonfactorizable contributions. As the ${\overline{B}}_{s}\ensuremath{\rightarrow}p\overline{p}$ decay is governed by exchange and penguin annihilation amplitudes, the rate predicted in factorization calculation is very rare, but it can be enhanced by including nonfactorizable contributions. The case where the rate is enhanced to saturate the present experimental bound through the enhancement on exchange or penguin-annihilation amplitudes is discussed. As annihilation modes ${B}_{c}^{\ensuremath{-}}\ensuremath{\rightarrow}{\mathbf{\text{B}}\overline{\mathbf{\text{B}}}}^{\ensuremath{'}}$ decays from factorization calculation are found to be very rare, but they can be enhanced by including nonfactorizable contributions as well. Small direct $CP$ violations of pure penguin modes in $\mathrm{\ensuremath{\Delta}}S=\ensuremath{-}1$ ${\overline{B}}_{u,d,s}\ensuremath{\rightarrow}{\mathbf{\text{B}}\overline{\mathbf{\text{B}}}}^{\ensuremath{'}}$ decays are robust predictions of the SM, while vanishing direct $CP$ violations of exchange modes in ${\overline{B}}_{u,d,s}\ensuremath{\rightarrow}{\mathbf{\text{B}}\overline{\mathbf{\text{B}}}}^{\ensuremath{'}}$ decays and in all ${B}_{c}^{\ensuremath{-}}\ensuremath{\rightarrow}{\mathbf{\text{B}}\overline{\mathbf{\text{B}}}}^{\ensuremath{'}}$ decay modes are null tests of the SM.

Searching systematics for nonfactorizable contributions to and hadronic decays

The two-body weak decays / and are examined using isospin analysis to study nonfactorizable contributions. After determining strong interaction phases and obtaining factorizable contributions from spectator-quark diagrams for N c =3, we determine nonfactorizable isospin amplitudes from the experimental data for these modes. Our results support the universality of the ratio of nonfactorizable isospin reduced amplitudes for these decays within experimental errors. To demonstrate that these systematics are not coincidental, we also plot our results w. r. t. this ratio.

Nonleptonic two-body decays of Λb→Λcπ , ΛcK in the perturbative QCD approach

We study the color-allowed $\Lambda_b\rightarrow \Lambda_c \pi, \Lambda_cK$ decays in the perturbative QCD approach (PQCD) to lowest order in strong coupling constant $\alpha_s$. Both the factorizable and nonfactorizable contributions are taken into account in our calculations. It is found that these processes are dominated by the factorizable contributions, while the important nonfactorizable contributions can enhance the branching ratios by about 30$\%$. The decay branching ratios are predicted to be $\mathcal{B}(\Lambda_b\rightarrow \Lambda_c \pi)=6.7^{+4.1}_{-3.8}\times 10^{-3}$ and $\mathcal{B}(\Lambda_b\rightarrow \Lambda_c K)=5.0^{+4.0}_{-3.0}\times 10^{-4}$, where the uncertainties arise from the baryon light-cone distribution amplitudes (LCDAs), the heavy charm quark and charmed baryon masses, and the hard scales. It is shown that the asymmetry parameters in the two decays are approximately equal to -1, which is expected as in the heavy quark limit and the soft meson limit. Our predictions are consistent with the recent experimental data within errors. The obtained numerical results are also compared to those in the other theoretical approaches when they are available.

Time-reversal asymmetries and angular distributions in \u039bb \u2192 \u039bV

We study the spin correlations to probe time-reversal (T) asymmetries in the decays of Λb→ ΛV (V = ϕ, ρ0, ω, K∗0). The eigenstates of the T-odd operators are obtained along with definite angular momenta. We obtain the T-odd spin correlations from the complex phases among the helicity amplitudes. We give the angular distributions of Λb→ Λ(→ pπ−)V (→ PP′) and show the corresponding spin correlations, where P(′) are the pseudoscalar mesons. Due to the helicity conservation of the s quark in Λ, we deduce that the polarization asymmetries of Λ are close to −1. Since the decay of Λb→ Λϕ in the standard model (SM) is dictated by the single weak phase from the product of CKM elements, {V}_{tb}{V}_{ts}^{ast } , the true T and CP asymmetries are suppressed, providing a clean background to test the SM and search for new physics. In the factorization approach, as the helicity amplitudes in the SM share the same complex phase, T-violating effects are absent. Nonetheless, the experimental branching ratio of Br(Λb→ Λϕ) = (5.18 ± 1.29) × 10−6 suggests that the nonfactorizable effects or some new physics play an important role. By parametrizing the nonfactorizable contributions with the effective color number, we calculate the branching ratios and direct CP asymmetries. We also explore the possible T-violating effects from new physics.

Doubly Cabibbo-suppressed decays of antitriplet charmed baryons

Doubly Cabibbo-suppressed (DCS) nonleptonic weak decays of antitriplet charmed baryons are studied systematically in this work. The factorizable and nonfactorizable contributions can be classified explicitly in the topological-diagram approach and treated separately. In particular, the evaluation of nonfactorizable terms is based on the pole model in conjunction with current algebra. All three types of relevant non- perturbative parameters contributing factorizable and nonfactorizable terms are estimated in the MIT bag model. Branching fractions of all the DCS decays are predicted to be of order 10−4 ∼ 10−6. In particular, we find that the three modes {Xi}_c^{+}to {Sigma}^{+}{K}^0,{Sigma}^0{K}^{+} and {Xi}_c^0to {Sigma}^{-}{K}^{+} are as large as (1 ∼ 2) × 10−4, which are the most promising DCS channels to be measured. We also point out that the two DCS modes {Xi}_c^{+}to {Sigma}^{+}{K}^0 and {Xi}_c^0to {Sigma}^0{K}^0 are possible to be distinguished from {Xi}_c^{+}to {Sigma}^{+}{K}_S and {Xi}_c^0to {Sigma}^0{K}_S . The decay asymmetries for all the channels with a kaon in their final states are found to be large in magnitude and negative in sign.

A puzzle in varvec{bar{B}_{(s)}^0 rightarrow D_{(s)}^{(*)+} lbrace pi ^-, K^-rbrace } decays and extraction of the varvec{f_s/f_d} fragmentation fraction

We provide updated predictions for the hadronic decays bar{B}_s^0rightarrow D_s^{(*)+} pi ^- and bar{B}^0rightarrow D^{(*)+} K^-. They are based on {mathcal {O}}(alpha _s^2) results for the QCD factorization amplitudes at leading power and on recent results for the bar{B}_{(s)} rightarrow D_{(s)}^{(*)} form factors up to order mathcal{O}(Lambda _mathrm{QCD}^2/m_c^2) in the heavy-quark expansion. We give quantitative estimates of the matrix elements entering the hadronic decay amplitudes at order mathcal{O}(Lambda _mathrm{QCD}/m_b) for the first time. Our results are very precise, and uncover a substantial discrepancy between the theory predictions and the experimental measurements. We explore two possibilities for this discrepancy: non-factorizable contributions larger than predicted by the QCD factorization power counting, and contributions beyond the Standard Model. We determine the f_s/f_d fragmentation fraction for the CDF, D0 and LHCb experiments for both scenarios.

Revisiting nonfactorizable contributions to factorization-forbidden decays of B mesons to charmonium * * Supported in part by the National Natural Science Foundation of China (11605060, 11547020), the Natural Science Foundation of Hebei Province (A2019209449) and Department of Education of Hebei Province (BJ2016041)

Motivated by the large rates of decays observed by the and Belle collaborations, we investigate the nonfactorizable contributions to these factorization-forbidden decays, which can occur through a gluon exchange between the system and the spectator quark. Our numerical results demonstrate that the spectator contributions are capable of producing a large branching ratio consistent with the experiments. As a by-product, we also study the Cabibbo-suppressed decays, such as and the U-spin-related decay, which have so far received less theoretical and experimental attention. The calculated branching ratios reach the order of , which is within the scope of the Belle-II and LHCb experiments. Further, the -asymmetry parameters are also calculated for these decays. The obtained results are compared with the available experimental data and numbers from other predictions. We also investigate the sources of theoretical uncertainties in our calculation.

Analysis of the strong decays of Pc(4312) as a pentaquark molecular state with QCD sum rules * * Supported by National Natural Science Foundation (11775079)

In this article, we tentatively assign Pc(4312) to be the pentaquark molecular state with the spin-parity , and discuss the factorizable and non-factorizable contributions in the two-point QCD sum rules for the molecular state in detail to prove the reliability of the single pole approximation in the hadronic spectral density. We study its two-body strong decays with the QCD sum rules, and special attention is paid to match the hadron side with the QCD side of the correlation functions to obtain solid duality. We obtain the partial decay widths and , which are compatible with the experimental value of the total width, and support assigning to be the pentaquark molecular state.

Hadronic weak decays of the charmed baryon Ωc

Two-body hadronic weak decays of the charmed baryon $\Omega_c$, including Cabibbo-favored (CF), singly Cabibbo-suppressed (SCS) and doubly Cabibbo-suppressed (DCS) modes, are studied systematically in this work. To estimate nonfactorizable contributions, we work in the pole model for the $P$-wave amplitudes and current algebra for the $S$-wave amplitudes. Among all the channels decaying into a baryon octet and a pseudoscalar meson, $\Omega_c\to \Xi^0\overline{K}^0$ is the only allowed CF mode. The predicted branching fraction of order $3.8\%$ and large and positive decay asymmetry of order $0.50$ indicate that a measurement of this mode in the near future is promising. Proceeding through purely nonfactorizable contributions, the SCS mode $\Omega_c\to\Lambda^0\overline{K}^0$ and DCS mode $\Omega_c\to\Lambda^0 \eta$ are predicted to have branching fractions as large as $0.8\%$ and $0.4\%$, respectively. The two DCS modes $\Omega_c\to\Sigma^0\eta$ and $\Omega_c\to\Lambda^0\pi^0$ are suggested to serve as new physics searching channels for their vanishing SM background.

Two-body weak decays of doubly charmed baryons

The hadronic two-body weak decays of the doubly charmed baryons ${\mathrm{\ensuremath{\Xi}}}_{cc}^{++},{\mathrm{\ensuremath{\Xi}}}_{cc}^{+}$, and ${\mathrm{\ensuremath{\Omega}}}_{cc}^{+}$ are studied in this work. To estimate the nonfactorizable contributions, we work in the pole model for the $P$-wave amplitudes and current algebra for $S$-wave ones. For the ${\mathrm{\ensuremath{\Xi}}}_{cc}^{++}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}_{c}^{+}{\ensuremath{\pi}}^{+}$ mode, we find a large destructive interference between factorizable and nonfactorizable contributions for both $S$- and $P$-wave amplitudes. Our prediction of $\ensuremath{\sim}0.70%$ for its branching fraction is smaller than the earlier estimates in which nonfactorizable effects were not considered, but agrees nicely with the result based on an entirely different approach, namely, the covariant confined quark model. On the contrary, a large constructive interference was found in the $P$-wave amplitude by Dhir and Sharma, leading to a branching fraction of order (7--16)%. Using the current results for the absolute branching fractions of $({\mathrm{\ensuremath{\Lambda}}}_{c}^{+},{\mathrm{\ensuremath{\Xi}}}_{c}^{+})\ensuremath{\rightarrow}p{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}$ and the LHCb measurement of ${\mathrm{\ensuremath{\Xi}}}_{cc}^{++}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}_{c}^{+}{\ensuremath{\pi}}^{+}$ relative to ${\mathrm{\ensuremath{\Xi}}}_{cc}^{++}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{c}^{+}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{+}$, we obtain $\mathcal{B}({\mathrm{\ensuremath{\Xi}}}_{cc}^{++}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}_{c}^{+}{\ensuremath{\pi}}^{+}{)}_{\text{expt}}\ensuremath{\approx}(1.83\ifmmode\pm\else\textpm\fi{}1.01)%$ after employing the latest prediction of $\mathcal{B}({\mathrm{\ensuremath{\Xi}}}_{cc}^{++}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Sigma}}}_{c}^{++}{\overline{K}}^{*0})$. Our prediction of $\mathcal{B}({\mathrm{\ensuremath{\Xi}}}_{cc}^{++}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}_{c}^{+}{\ensuremath{\pi}}^{+})\ensuremath{\approx}0.7%$ is thus consistent with the experimental value but in the lower end. It is important to pin down the branching fraction of this mode in future study. Factorizable and nonfactorizable $S$-wave amplitudes interfere constructively in ${\mathrm{\ensuremath{\Xi}}}_{cc}^{+}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}_{c}^{0}{\ensuremath{\pi}}^{+}$. Its large branching fraction of order 4% may enable experimentalists to search for the ${\mathrm{\ensuremath{\Xi}}}_{cc}^{+}$ through this mode. That is, the ${\mathrm{\ensuremath{\Xi}}}_{cc}^{+}$ is reconstructed through the ${\mathrm{\ensuremath{\Xi}}}_{cc}^{+}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}_{c}^{0}{\ensuremath{\pi}}^{+}$ followed by the decay chain ${\mathrm{\ensuremath{\Xi}}}_{c}^{0}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}\ensuremath{\rightarrow}p{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}$. Besides ${\mathrm{\ensuremath{\Xi}}}_{cc}^{+}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}_{c}^{0}{\ensuremath{\pi}}^{+}$, the ${\mathrm{\ensuremath{\Xi}}}_{cc}^{+}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}_{c}^{+}({\ensuremath{\pi}}^{0},\ensuremath{\eta})$ modes also receive large nonfactorizable contributions to their $S$-wave amplitudes. Hence, they have large branching fractions among ${\mathrm{\ensuremath{\Xi}}}_{cc}^{+}\ensuremath{\rightarrow}{\mathcal{B}}_{c}+P$ channels. Nonfactorizable amplitudes in ${\mathrm{\ensuremath{\Xi}}}_{cc}^{++}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}_{c}^{\ensuremath{'}+}{\ensuremath{\pi}}^{+}$ and ${\mathrm{\ensuremath{\Omega}}}_{cc}^{+}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}_{c}^{\ensuremath{'}+}{\overline{K}}^{0}$ are very small compared to the factorizable ones owing to the Pati-Woo theorem for the inner $W$-emission amplitude. Likewise, nonfactorizable $S$-wave amplitudes in ${\mathrm{\ensuremath{\Xi}}}_{cc}^{+}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}_{c}^{\ensuremath{'}+}({\ensuremath{\pi}}^{0},\ensuremath{\eta})$ decays are also suppressed by the same mechanism.

Two-body hadronic weak decays of antitriplet charmed baryons

We study Cabibbo-favored (CF) and singly Cabibbo-suppressed (SCS) two-body hadronic weak decays of the antitriplet charmed baryons ${\mathrm{\ensuremath{\Lambda}}}_{c}^{+}$, ${\mathrm{\ensuremath{\Xi}}}_{c}^{0}$, and ${\mathrm{\ensuremath{\Xi}}}_{c}^{+}$ with more focus on the last two. Both factorizable and nonfactorizable contributions are considered in the topologic diagram approach. The estimation of nonfactorizable contributions from $W$-exchange and inner $W$-emission diagrams relies on the pole model and current algebra. The nonperturbative parameters in both factorizable and nonfactorizable parts are calculated in the MIT bag model. Branching fractions and up-down decay asymmetries for all the CF and SCS decays of antitriplet charmed baryons are presented. The prediction of $\mathcal{B}({\mathrm{\ensuremath{\Xi}}}_{c}^{+}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}^{0}{\ensuremath{\pi}}^{+})$ agrees well with the measurements inferred from Belle and CLEO, while the calculated $\mathcal{B}({\mathrm{\ensuremath{\Xi}}}_{c}^{0}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}^{\ensuremath{-}}{\ensuremath{\pi}}^{+})$ is too large compared to the recent Belle measurement. We conclude that these two ${\mathrm{\ensuremath{\Xi}}}_{c}\ensuremath{\rightarrow}\mathrm{\ensuremath{\Xi}}{\ensuremath{\pi}}^{+}$ modes cannot be simultaneously explained within the current-algebra framework for $S$-wave amplitudes. This issue needs to be resolved in future study. The long-standing puzzle with the branching fraction and decay asymmetry of ${\mathrm{\ensuremath{\Lambda}}}_{c}^{+}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}^{0}{K}^{+}$ is resolved by noting that only the type-II $W$-exchange diagram contributes to this mode. We find that not only does the calculated rate agree with experiment but also the predicted decay asymmetry is consistent with the SU(3)-flavor symmetry approach in sign and magnitude. Likewise, the CF mode ${\mathrm{\ensuremath{\Xi}}}_{c}^{0}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Sigma}}}^{+}{K}^{\ensuremath{-}}$ and the SCS decays ${\mathrm{\ensuremath{\Xi}}}_{c}^{0}\ensuremath{\rightarrow}p{K}^{\ensuremath{-}}$, ${\mathrm{\ensuremath{\Sigma}}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ proceed only through type-II $W$ exchange. They are predicted to have large and positive decay asymmetries. These features can be tested in the near future.

Mixed QCD-electroweak corrections to Higgs production via gluon fusion in the small mass approximation

We compute the mixed QCD-electroweak corrections to the cross section for the production of a Higgs boson via gluon fusion, in the limit of a small mass of the electroweak gauge bosons. This limit is regular and we calculate it by setting the W, Z masses to zero in the Feynman rules for their propagators. Our analytic results provide an independent check, in a non-trivial limit, of a recent exact computation for the three-loop mixed QCD and electroweak virtual corrections [1] and the corresponding contribution to the cross section in the soft-virtual approximation [2]. From our calculation in the small mass approximation, we can infer the second term in the expansion of the cross section around the threshold limit with its exact dependence on the masses of the W, Z bosons. Furthermore we find that in the small mass approximation the non-factorizable contributions from the real radiation, so far unknown for full gauge boson mass dependence, are modest in comparison to the known factorizable and virtual contributions to the full mathcal{O}left({alpha}_s^3{alpha}^2right) mixed QCD and electroweak cross-section. This furnishes a new phenomenological test of estimates [3] for the mixed QCD and electroweak corrections, which were based on the hypothesis of factorization of QCD and electroweak corrections.