Nonfactorizable Diagrams Research Articles

Phenomenological studies on neutral B-meson decays into J/psi f_1 and eta _c f_1

The axial-vector mesons f_1(1285) and f_1(1420) are particularly viewed as the mixtures of flavor states f_n and f_s with mixing angle varphi . In order to determine this angle, we study the B_{d,s}^0rightarrow J/psi f_1(1285,1420) and B_{d,s}^0rightarrow eta _c f_1(1285,1420) decays in perturbative QCD (PQCD) approach, including the effects of vertex corrections, nonfactorizable diagrams and penguin operators. Not only the branching fractions, but also the direct CP asymmetries and the polarization fractions are calculated. It is found that the branching fractions of these decays are large enough to be measured in the running LHCb and Belle-II experiments. Moreover, in comparison with the observed {mathcal {B}}(B_{d,s}^0 rightarrow J/psi f_1(1285)), B_s^0 rightarrow (J/psi , eta _c) f_1(1420) decays have large branching fractions, which could be measured promisingly through f_1(1420) rightarrow K_S^0 K^pm pi ^mp in experiments. We also propose several ratios that could be used to further constrain the absolute value of the mixing angle varphi , but its sign cannot be determined yet in these decays. The direct CP asymmetries of these decays indicate the penguin pollution in the B_d^0 rightarrow (J/psi , eta _c) f_1 decays cannot be neglected. We acknowledge that there are large theoretical uncertainties arising from the distribution amplitudes of axial-vector mesons and charmonium states, and more precise nonperturbative parameters are called. The comparisons between our results and future experimental data would help us to understand the nature of f_1 states and to test the PQCD approach.

Two-particle contributions and nonlocal effects in the QCD sum rules for the axial vector tetraquark candidate Zc(3900)

In this article, we study the [Formula: see text] with the QCD sum rules in details by including the two-particle scattering state contributions and nonlocal effects between the diquark and antidiquark constituents. The two-particle scattering state contributions cannot saturate the QCD sum rules at the hadron side, the contribution of the [Formula: see text] plays an unsubstitutable role, we can saturate the QCD sum rules with or without the two-particle scattering state contributions. If there exists a repulsive barrier or spatial distance between the diquark and antidiquark constituents, the Feynman diagrams can be divided into the factorizable and nonfactorizable diagrams. The factorizable diagrams consist of two-colored clusters and lead to a stable tetraquark state. The nonfactorizable Feynman diagrams correspond to the tunneling effects, which play a minor important role in the QCD sum rules, and are consistent with the small width of the [Formula: see text]. It is feasible to apply the QCD sum rules to study the tetraquark states, which begin to receive contributions at the order [Formula: see text], not at the order [Formula: see text].

Tetraquark-adequate formulation of QCD sum rules

We study details of QCD sum rules \`a la Shifman-Vainshtein-Zakharov for exotic tetraquark states. We point out that duality relations for correlators involving exotic currents have fundamental differences compared with the duality relations for the correlators of bilinear quark currents: namely, the $O(1)$ and $O({\ensuremath{\alpha}}_{s})$ (${\ensuremath{\alpha}}_{s}$ the strong coupling constant) terms in the operator product expansion for the exotic correlators exactly cancel against the contributions of the two-meson states on the hadron side of QCD sum rules. As a result, the tetraquark properties turn out to be related to the specific nonfactorizable parts of the exotic Green functions; the relevant nonfactorizable diagrams start at order $O({\ensuremath{\alpha}}_{s}^{2})$.

Branching ratios, CP asymmetries and polarizations of Brightarrow psi (2S) V decays

We analyze the non-leptonic decays B/B_srightarrow psi (2S) V with V=(rho , omega , K^{*}, phi ) by employing the perturbative QCD (pQCD) factorization approach. Here the branching ratios, the CP asymmetries and the complete set of polarization observables are investigated systematically. Besides the traditional contributions from the factorizable and non-factorizable diagrams at the leading order, the next-to-leading order (NLO) vertex corrections could also provide considerable contributions. The pQCD predictions for the branching ratios of the B_{(s)}rightarrow psi (2S)K^{*}, psi (2S)phi decays are consistent with the measured values within errors. As for Brightarrow psi (2S) rho , psi (2S) omega decays, the branching ratios can reach the order of 10^{-5} and could be measured in the LHCb and Belle-II experiments. The numerical results show that the direct CP asymmetries of the considered decays are very small. Thus the observation of any large direct CP asymmetry for these decays will be a signal for new physics. The mixing-induced CP asymmetries in the neutral modes are very close to sin 2beta _{(s)}, which suggests that these channels can give a cross-check on the measurement of the Cabbibo–Kobayashi–Maskawa (CKM) angle beta and beta _s. We find that the longitudinal polarization fractions f_0 are suppressed to sim 50% due to the large non-factorizable contributions. The magnitudes and phases of the two transverse amplitudes mathcal {A}_{parallel } and mathcal {A}_{perp } are roughly equal, which is an indication for the approximate light-quark helicity conservation in these decays. The overall polarization observables of Brightarrow psi (2S) K^{*0} and B_srightarrow psi (2S) phi channels are also in good agreement with the experimental measurements as reported by LHCb and BaBar. Other results can also be tested by the LHCb and Belle-II experiments.

The S-wave resonance contributions in the B^{0}_{s} decays into psi (2S,3S) plus pion pair

The three-body decays B^0_s rightarrow psi (2S,3S) pi ^+ pi ^- are studied based on the perturbative QCD approach. With the help of the nonperturbative two-pion distribution amplitudes, the analysis is simplified into the quasi-two-body processes. Besides the traditional factorizable and nonfactorizable diagrams at the leading order, the next-to-leading order vertex corrections are also included to cancel the scale dependence. The f_0(980), f_0(1500) resonance contributions as well as the nonresonant contributions are taken into account using the presently known pi pi time-like scalar form factor for the sbar{s} component. It is found that the predicted B^0_s rightarrow psi (2S) pi ^+ pi ^- decay spectra in the pion pair invariant mass shows a similar behavior as the experiment. The calculated S-wave contributions to the branching ratio of B^0_s rightarrow psi (2S) pi ^+ pi ^- is 6.0times 10^{-5}, which is in agreement with the LHCb data mathcal {B}(B^0_s rightarrow psi (2S) pi ^+ pi ^-)=(7.2pm 1.2)times 10^{-5} within errors. The estimate of mathcal {B}(B^0_s rightarrow psi (3S) pi ^+ pi ^-) can reach the order of 10^{-5}, pending the corresponding measurements.

Anatomy of the perturbative QCD approach to the baryonic decaysΛb→pπ,pK

We calculate the $CP$-averaged branching ratios and $CP$-violating asymmetries for the two-body charmless hadronic decays ${\ensuremath{\Lambda}}_{b}\ensuremath{\rightarrow}p\ensuremath{\pi}$, $pK$ in the perturbative QCD (pQCD) approach to lowest order in ${\ensuremath{\alpha}}_{s}$. The baryon distribution amplitudes involved in the factorization formulas are considered to the leading twist accuracy, and the distribution amplitudes of the proton are expanded to the next-to-leading conformal spin (i.e., ``P'' waves), the moments of which are determined from QCD sum rules. Our work shows that the contributions from the factorizable diagrams in ${\ensuremath{\Lambda}}_{b}\ensuremath{\rightarrow}p\ensuremath{\pi}$, $pK$ decays are much smaller compared to the nonfactorizable diagrams in the conventional pQCD approach. We argue that this reflects the estimates of the ${\ensuremath{\Lambda}}_{b}\ensuremath{\rightarrow}p$ transition form factors in the ${k}_{T}$ factorization approach, which are found to be typically an order of magnitude smaller than those estimated in the light-cone sum rules and in the nonrelativistic quark model. As an alternative, we adopt a hybrid pQCD approach, in which we compute the factorizable contributions with the ${\ensuremath{\Lambda}}_{b}\ensuremath{\rightarrow}p$ form factors taken from the light-cone QCD sum rules. The nonfactorizable diagrams are evaluated utilizing the conventional pQCD formalism, which is free from the endpoint singularities. The predictions worked out here are confronted with the recently available data from the CDF Collaboration on the branching ratios and the direct $CP$ asymmetries for the decays ${\ensuremath{\Lambda}}_{b}\ensuremath{\rightarrow}p\ensuremath{\pi}$ and ${\ensuremath{\Lambda}}_{b}\ensuremath{\rightarrow}pK$. The asymmetry parameter $\ensuremath{\alpha}$ relevant for the anisotropic angular distribution of the emitted proton in the polarized ${\ensuremath{\Lambda}}_{b}$ baryon decays is also calculated for the two decay modes.

Bs → ρ(ω)K* with the perturbative QCD approach

Bs → ρ(ω)K* decays are useful to determine the Bs distribution amplitude, as well as constrain the CKM phase angle α. We study these decays within the perturbative QCD approach. In this approach, we derive factorizable and non-factorizable diagrams, as well as annihilation diagrams. We find that the branching ratio for Bs → ρ+K*− is of the order of 10−5 and there is a large direct CP violation in . Our predictions are consistent with those from other methods and current experiments.

Polarization,CPasymmetry, and branching ratios inB→K*K*with the perturbative QCD approach

We study the charmless rare decays $B\ensuremath{\rightarrow}{K}^{*}{K}^{*}$ within the perturbative QCD picture. We calculate not only factorizable and nonfactorizable diagrams, but also annihilation ones. Our predictions are the following: The longitudinal polarization fraction vary from 75% to 99% depending on channels, the branching ratios are of order ${10}^{\ensuremath{-}7}$ for ${B}^{0}({\overline{B}}^{0})\ensuremath{\rightarrow}{K}^{*0}{\overline{K}}^{*0}$ and ${B}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}{K}^{*\ifmmode\pm\else\textpm\fi{}}{\overline{K}}^{*0}({K}^{*0})$, much bigger than that for ${B}^{0}({\overline{B}}^{0})\ensuremath{\rightarrow}{K}^{*+}{K}^{*\ensuremath{-}}$(${10}^{\ensuremath{-}8}$). The direct $\mathrm{CP}$ asymmetry in ${B}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}{K}^{*\ifmmode\pm\else\textpm\fi{}}{\overline{K}}^{*0}({K}^{*0})$ and ${B}^{0}({\overline{B}}^{0})\ensuremath{\rightarrow}{K}^{*+}{K}^{*\ensuremath{-}}$ is about $\ensuremath{-}15%$ and $\ensuremath{-}65%$ if we choose $\ensuremath{\alpha}({\ensuremath{\varphi}}_{2})$ as $95\ifmmode^\circ\else\textdegree\fi{}$. The direct $\mathrm{CP}$ violation in ${B}^{0}({\overline{B}}^{0})\ensuremath{\rightarrow}{K}^{*0}{\overline{K}}^{*0}$ decays is negligible if there is not strong final state interactions. Our predictions will be tested in the future $B$ experiments.

Charmless decaysB→ππ,πKandKKin broken SU(3) symmetry

Charmless B decay modes $B \to \pi \pi, \pi K$ and $KK$ aresystematically investigated with and without flavor SU(3) symmetry. Independent analyses on $\pi \pi$ and $\pi K$ modes both favor a large ratio between color-suppressed tree ($C$) and tree ($T)$ diagram, which suggests that they are more likely to originate from long distance effects. The sizes of QCD penguin diagrams extracted individually from $\pi\pi$, $\pi K$ and $KK$ modes are found to follow a pattern of SU(3) breaking in agreement with the naive factorization estimates. Global fits to these modes are done under various scenarios of SU(3)relations. The results show good determinations of weak phase $\gamma$ in consistency with the Standard Model (SM), but a large electro-weak penguin $(P_{\tmop{EW}})$ relative to $T + C$ with a large relative strong phase are favored, which requires an big enhancement of color suppressed electro-weak penguin ($P_{\tmop{EW}}^C$) compatible in size but destructively interfering with $P_{\tmop{EW}}$ within the SM, or implies new physics. Possibility of sizable contributions from nonfactorizable diagrams such as $W$-exchange ($E$), annihilation($A$) and penguin-annihilation diagrams($P_A$) are investigated. The implications to the branching ratios and CP violations in $K K$modes are discussed.

Study of color suppressed modesB0→D(*)0η(′)

The color suppressed modes ${B}^{0}\ensuremath{\rightarrow}{D}^{(*)0}{\ensuremath{\eta}}^{(\ensuremath{'})}$ are analyzed in the perturbative QCD approach. We find that the dominant contribution is from the nonfactorizable diagrams. The branching ratios calculated in our approach for ${B}^{0}\ensuremath{\rightarrow}{D}^{(*)0}\ensuremath{\eta}$ agree with current experiments. By neglecting the gluonic contribution, we predict that the branching ratios of ${B}^{0}\ensuremath{\rightarrow}{D}^{(*)0}{\ensuremath{\eta}}^{\ensuremath{'}}$ are comparable in size to those for ${B}^{0}\ensuremath{\rightarrow}{D}^{(*)0}{\ensuremath{\pi}}^{0},$ but smaller than those for ${B}^{0}\ensuremath{\rightarrow}{D}^{(*)0}\ensuremath{\eta}.$

Charged Higgs boson production in bottom-gluon fusion

We compute the complete next-to-leading order SUSY-QCD corrections for the associated production of a charged Higgs boson with a top quark via bottom-gluon fusion. We investigate the applicability of the bottom parton description in detail. The higher order corrections can be split into real and virtual corrections for a general two Higgs doublet model and into additional massive supersymmetric loop contributions. We find that the perturbative behavior is well under control. The supersymmetric contributions consist of the universal bottom Yukawa coupling corrections and nonfactorizable diagrams. Over most of the relevant supersymmetric parameter space the Yukawa coupling corrections are sizable, while the remaining supersymmetric loop contributions are negligible.

Λb→ΛJ/ψdecay in perturbative QCD

We calculate the amplitudes involved in the heavy baryon nonleptonic decay $\Lambda_b \rar \Lambda J/\psi$ using perturbative QCD factorization theorem, which are expressed as convolutions of hard $b$ quark decay amplitudes with the $\Lambda_b$ baryon, $\Lambda$ baryon and $J/\psi$ meson distribution amplitudes. It is found that nonfactorizable contributions dominate over factorizable ones. Because of soft cancellation in pairs of nonfactorizable diagrams, the $\Lambda_b \rar \Lambda J/\psi$ decay is characterized by a large scale, such that perturbative QCD is applicable. Employing the distribution amplitudes determined in our previous works and from QCD sum rules, we derive the branching ratio $B(\Lambda_b \rar \Lambda J/\psi)=(1.7 \sim 5.3)\times 10^{-4}$ in agreement with data. We predict an asymmetry parameter $\alpha= -0.17 \sim -0.14$ associated with the anisotropic angular distribution of the $\Lambda$ baryons produced in polarized $\Lambda_b$ baryon decays.