Annihilation Topologies Research Articles

Zooming into CP violation in B(s)→ hh decays

The LHCb collaboration has recently reported the first observation of CP violation in the penguin-dominated {B}_s^0 → K−K+ decay and further new measurements, indicating differences between the direct CP asymmetries of both the {B}_s^0 → K−K+, {B}_d^0 → π−K+ and the {B}_d^0 → π−π+, {B}_s^0 → K−π+ modes. We show that these puzzling differences can be accommodated through sizeable penguin annihilation and exchange topologies in the Standard Model, and constrain them. Utilising the U-spin symmetry, we extract the angle γ of the unitarity triangle from the CP asymmetries in the {B}_s^0 → K−K+, {B}_d^0 → π−π+ system alone, finding gamma =left({65}_{-7}^{+11}right){}^{circ} , in perfect agreement with the determination from tree-level B → DK decays. The {B}_s^0-{overline{B}}_s^0 mixing phase ϕs can be extracted from CP violation measurements in {B}_s^0 → K−K+ in a clean way. We present a new strategy and extract ϕs = −(3.6 ± 5.4)°. This result is in agreement with the determination from {B}_s^0 → J/ψϕ decays. New CP-violating contributions would influence these determinations differently. Hence it is interesting to keep monitoring both as the experimental picture sharpens.

Study on pure annihilation type B→Vγ decays

We investigate the pure annihilation type radiative $B$ meson decays $B^0 \to \phi \gamma$ and $B_s \to \rho^0(\omega)\gamma$ in the soft-collinear effective theory. We consider three types of contributions to the decay amplitudes, including the direct annihilation topology, the contribution from the electro-magnetic penguin operator and the contribution of the neutral vector meson mixings. The numerical analysis shows that the decay amplitudes are dominated by the $\omega-\phi$ mixing effect in the $B^0 \to \phi\gamma$ and $B_s \to \omega\gamma$ modes. The corresponding decay branching ratios are enhanced about three orders of magnitudes relative to the pure annihilation type contribution in these two decay channels. The decay rate of $B_s \to \rho^0\gamma$ is much smaller than that of $B_s \to \omega\gamma$ because of the smaller $\rho^0-\phi$ mixing. The predicted branching ratios $B(B^{0}\rightarrow\phi\gamma)=(3.99^{+1.67}_{-1.46} )\times10^{-9},\,B(B_s\rightarrow\omega\gamma)=(2.01^{+0.81}_{-0.71} )\times10^{-7}$ are to be tested by the Belle-II and LHC-b experiments.

Resonant assisted annihilation

Assisted annihilation is a novel mechanism to generate viable sub-GeV thermal dark matter, where a pair of stable dark matter annihilates with an assister to Standard Model states. Typically such 3 → 2 annihilation topologies are flux suppressed compared to 2 → 2 processes. In this paper, we explore the possibility of a resonant 3 → 2 assisted annihilation dominantly driving the freeze-out of dark matter. We demonstrate that in a simple multipartite scalar extension of the Standard Model this can be realized in certain regions of parameter space to provide viable dark matter relic density, in agreement with observation. We demonstrate that for photophilic assisters parts of the parameter space are already constrained by indirect detection experiments and the measurements of CMB anisotropies while substantial regions remain beyond the present limit.

The branching fraction calculations of Bc+ → ψ(2S)π+, Bc+ → J/ψK+ and Bc+ → J/ψDs+ decays relative to that of the Bc+ → J/ψπ+ mode

The weak decay of [Formula: see text] into [Formula: see text], [Formula: see text] and [Formula: see text] mesons, observed by LHCb collaboration for the first time, are calculated in the model which takes into account the “factorizable” contributions and “nonfactorizable” corrections. The decays of [Formula: see text] mesons into charmonia and light hadrons are expected to be well described by the factorization approximation. In the standard model, [Formula: see text], [Formula: see text] decays occur through only the tree-level diagrams and so there are no CP violation in these channels. The decay [Formula: see text] is expected to proceed mainly via a [Formula: see text] transition because the [Formula: see text] decay has identical final state and similar event topology, where it is chosen as the relative branching fraction channel. The ratio of branching fractions [Formula: see text] is of particular interest since the CKM matrix element is suppressed by a factor [Formula: see text], in which the [Formula: see text] occur through [Formula: see text] transition, but the dominant amplitude of the decay [Formula: see text] is a [Formula: see text] transition. The decay [Formula: see text] is examined by color-allowed, color-suppressed spectator and weak annihilation diagrams. The weak annihilation topology, in contrast to decays of other beauty hadrons, is not suppressed and can contribute significantly to the decay amplitude. Because of the [Formula: see text], [Formula: see text] and [Formula: see text] branching fractions are calculated relative to the [Formula: see text] decay, this decay mode is estimated separately, the ratio between them are [Formula: see text], [Formula: see text] and [Formula: see text], respectively, that are compatible with the experimental data.

D \u2192 \u03c1\u2113+\u2113\u2212 decays in the QCD factorization approach

We consider rare semileptonic decays of a heavy D-meson into a light vector meson in the framework of QCD factorization. In contrast to the corresponding B-meson decays, the naive factorization hypothesis does not even serve as a first approximation. Rather, the decay amplitudes appear to be dominated by non-factorizable dynamics, e.g. through annihilation topologies, which are particularly sensitive to long-distance hadronic contributions. We therefore pay particular attention to intermediate vector-meson resonances appearing in quark-loop and annihilation topologies. Compared to the analogous B-meson decays, we identify a number of effects that result in very large theoretical uncertainties for differential decay rates. Some of these effects are found to cancel in the ratio of partially integrated decay rates for transversely and longitudinally polarized ρ mesons. On the phenomenological side this implies a very limited potential to constrain physics beyond the Standard Model by means of these decays.

Nonleptonic charmless decays of Bc→TP,TV in the perturbative QCD approach

Two-body charmless hadronic $B_c$ decays involving a light $1^3\!P_2$-tensor($T$) meson are investigated for the first time within the framework of perturbative QCD(pQCD) at leading order, in which the other meson is the lightest pseudoscalar($P$) or vector($V$) state. The concerned processes can only occur through the pure weak annihilation topology in the standard model. We predict the CP-averaged branching ratios and polarization fractions of those considered decays in Cabibbo-Kobayashi-Maskawa(CKM) favored and suppressed modes. Phenomenologically, several modes$-$such as the $B_c \to K_2^*(1430) K$ and the CKM-favored $B_c \to TV-$have large decay rates of $10^{-6}$, which are expected to be detected at Large Hadron Collider experiments in the near future. Moreover, all of the $B_c \to TV$ modes are governed by the longitudinal amplitudes in the pQCD calculations and the corresponding fractions vary around $78\%$-$98\%$. A confirmation of these results could prove the reliability of the pQCD approach used here and further shed some light on the annihilation decay mechanism.

Study of the weak annihilation contributions in charmless varvec{B_srightarrow VV} decays

In this paper, in order to probe the spectator-scattering and weak annihilation contributions in charmless B_srightarrow VV (where V stands for a light vector meson) decays, we perform the chi ^2-analyses for the endpoint parameters within the QCD factorization framework, under the constraints from the measured bar{B}_{s}rightarrow rho ^0phi , phi K^{*0}, phi phi and K^{*0}bar{K}^{*0} decays. The fitted results indicate that the endpoint parameters in the factorizable and nonfactorizable annihilation topologies are non-universal, which is also favored by the charmless Brightarrow PP and PV (where P stands for a light pseudo-scalar meson) decays observed in previous work. Moreover, the abnormal polarization fractions f_{L,bot }(bar{B}_{s}rightarrow K^{*0}bar{K}^{*0})=(20.1pm 7.0)%,(58.4pm 8.5)% measured by the LHCb collaboration can be reconciled through the weak annihilation corrections. However, the branching ratio of bar{B}_{s}rightarrow phi K^{*0} decay exhibits a tension between the data and theoretical result, which dominates the contributions to chi _mathrm{min}^2 in the fits. Using the fitted endpoint parameters, we update the theoretical results for the charmless B_srightarrow VV decays, which will be further tested by the LHCb and Belle-II experiments in the near future.

Anatomy of B → D D ¯ $$ B\to D\overline{D} $$ decays

The decays $B_d^0\rightarrow D_d^-D_d^+$ and $B_s^0\rightarrow D_s^-D_s^+$ probe the CP-violating mixing phases $\phi_d$ and $\phi_s$, respectively. The theoretical uncertainty of the corresponding determinations is limited by contributions from penguin topologies, which can be included with the help of the $U$-spin symmetry of the strong interaction. We analyse the currently available data for $B^0_{d,s}\rightarrow D_{d,s}^-D_{d,s}^+$ decays and those with similar dynamics to constrain the involved non-perturbative parameters. Using further information from semileptonic $B_d^0\rightarrow D_d^-\ell^+\nu_{\ell}$ decays, we perform a test of the factorisation approximation and take non-factorisable $SU(3)$-breaking corrections into account. The branching ratios of the $B_d^0\rightarrow D_d^-D_d^+$, $B_s^0\rightarrow D_s^-D_d^+$ and $B_s^0\rightarrow D_s^-D_s^+$, $B_d^0\rightarrow D_d^-D_s^+$ decays show an interesting pattern which can be accommodated through significantly enhanced exchange and penguin annihilation topologies. This feature is also supported by data for the $B_s^0\rightarrow D_d^-D_d^+$ channel. Moreover, there are indications of potentially enhanced penguin contributions in the $B_d^0\rightarrow D_d^-D_d^+$ and $B_s^0\rightarrow D_s^-D_s^+$ decays, which would make it mandatory to control these effects in the future measurements of $\phi_d$ and $\phi_s$. We discuss scenarios for high-precision measurements in the era of Belle II and the LHCb upgrade.

Bcexclusive decays to charmonium and a light meson at next-to-leading order accuracy

In this paper, we study the ${B}_{c}$-meson exclusive decays to S-wave charmonia and light pseudoscalar or vector mesons, i.e., $\ensuremath{\pi}$, $K$, $\ensuremath{\rho}$, and ${K}^{*}$ at the next-to-leading order (NLO) in the QCD coupling. The nonfactorizable contribution is included, which is absent in traditional naive factorization. Numerical results show that NLO QCD corrections markedly enhance the branching ratio with a $K$ factor of 1.75 for ${B}_{c}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}{\ensuremath{\eta}}_{c}{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$ and 1.31 for ${B}_{c}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}J/\ensuremath{\psi}{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$ using certain input parameters. And the theoretical uncertainties for their branching ratios are reduced compared with that of direct tree-level calculation. In order to investigate the asymptotic behavior, the analytic form is obtained in the heavy quark limit, i.e., ${m}_{b}\ensuremath{\rightarrow}\ensuremath{\infty}$. We note that annihilation topologies contribute trivia in this limit, and the corrections at leading order in $z={m}_{c}/{m}_{b}$ expansion come from form factors and hard spectator interactions. At last, some related phenomenologies are also discussed.

Flavor dependence of annihilation parameters in QCD factorization

For $B_{d,s} \to \pi^\mp K^\pm$ and $K^{(\ast)} K^{(\ast)}$ decays, the flavor symmetry breaking effects may be particularly small since the final state interactions should be the same between the corresponding $B_d$ and $B_s$ decays due to the charge conjugation symmetry of the final states. This is consistent with the newly measured direct CP asymmetry of $B_s \to \pi^+ K^-$. These decays are thus supposed to be important in testing the Standard Model and in probing new physics effects. However, the observation of pure annihilation decay $B_s \to \pi^+ \pi^-$ appears to imply a large annihilation scenario with $\rho_A \sim 3$, in contrast to the case of $\rho_A \sim 1$ in $B_{u,d}$ decays in the framework of QCD factorization. This seems to indicate unexpectedly large flavor symmetry breaking effects between the annihilation amplitudes of $B_s$ and $B_{u,d}$ decays. This apparent contradiction could be resolved by noticing that there is a priori no reason to justify the common practice of assuming the universality of annihilation parameters for different Dirac structures of effective operators. We then argue that, for $B_{d,s} \to \pi^\mp K^\pm$ decays, the flavor symmetry breaking effects of annihilation amplitudes have all been included in the initial state decay constants and are thus small. But the flavor symmetry breaking effects in $B_{d,s} \to K^{(\ast)} K^{(\ast)}$ decays are likely to be much larger, as part of the annihilation topologies of $B_s \to K K$ decay could be related to $B_s \to \pi^+ \pi^-$ decay. Therefore when new physics effects are searched for in these decay channels, care must be taken to consider the potentially large flavor symmetry breaking effects in more details.

Study of the pure annihilationBc→A2A3decays

In this work, we calculate the {\it CP}-averaged branching ratios and the polarization fractions of the charmless hadronic $B_c \to A_2 A_3$ decays within the framework of perturbative QCD(pQCD) approach, where $A$ is either a light $^3P_1$ or $^1P_1$ axial-vector meson. These thirty two decay modes can occur through the annihilation topology only. Based on the perturbative calculations and phenomenological analysis, we find the following results: (a) the branching ratios of the considered thirty two $B_c\to A_2 A_3$ decays are in the range of $10^{-5}$ to $10^{-8}$; (b) $B_c\to a_1 b_1$, $\ov{K}_1^0 K_1^+$ and some other decays have sizable branching ratios and can be measured at the LHC experiments; (c) the branching ratios of $B_c \to A_2(^1P_1) A_3(^1P_1)$ decays are generally much larger than those of $B_c \to A_2(^3P_1) A_3(^3P_1)$ decays with a factor around (10 $\sim$ 100); (d) the branching ratios of $B_c \to \ov{K}_1^0 K_1^+$ decays are sensitive to the value of $\theta_K$, which will be tested by the running LHC and forthcoming SuperB experiments; (e) the large longitudinal polarization contributions govern most considered decays and play the dominant role.

Implications of the recent measurement of pure annihilation [formula omitted] decays in QCD factorization

The CDF 3.7 sigma evidence of pure annihilation Bs→π+π− decays, if confirmed, would imply a large annihilation scenario in the QCD factorization approach. This is somewhat unexpected as the large annihilation scenario was disfavored in previous studies. In this Letter we reinvestigate the role of annihilation topology in QCD factorization. We find that it is not easy to reach the CDF central value of Bs→π+π− decays when other decay channels are considered. Our analysis also reveals that, for well-measured charmless B decays into two final pseudoscalar mesons, the QCD factorization predictions with large annihilation parameters show good agreement with the experimental data except Bs→K+K− and Bd→K0K¯0 decays. Though other possibilities cannot be excluded, this may indicate that the SU(3) flavor symmetry breaking should be taken into account for the annihilation topology. In addition, there are different annihilation topologies, so that somewhat different annihilation parameters may be chosen for different final states and different annihilation topologies. If so, the predictive power of the QCD factorization method may be rather limited for many decay channels.

Studies on charmless hadronic Bc → AV(VA) decays in the perturbative QCD approach

We study the charmless hadronic Bc → AV(VA) decays in the perturbative QCD(pQCD) approach, where A is either a 3P1 or a 1P1 axial-vector meson and V stands for the vector meson. All considered 30 decay channels can only occur through the annihilation topologies in the standard model. Based on the perturbative calculations and the phenomenological analysis, we find the following results: (i) the CP-averaged branching ratios of the considered Bc decays are in the range of 10−5–10−9 in the standard model; (ii) many considered decay modes, such as Bc → a1(1260)+ω, b1(1235)ρ, (K1(1270), K1(1400))K* and ρ+f1(1285), have sizable branching ratios, say around 10−6, and within the reach of the LHCb experiments; (iii) the longitudinal polarization fractions of most considered decays are large, ∼0.9 in magnitude; (iv) the pQCD predictions for several decays involving mixtures of 3P1 and/or 1P1 mesons are highly sensitive to the values of the mixing angles, which will be tested by the ongoing LHC and forthcoming Super-B experiments; (v) the CP-violating asymmetries of these considered Bc decays are absent naturally in the standard model because of the involved pure tree topology.

QCD factorization for charmless hadronicBsdecays revisited

Branching fractions and CP-violating asymmetries of charmless $\bar B_s\to PP, VP, VV$ decays (P and V denoting pseudoscalar and vector mesons, respectively) are re-examined in the framework of QCD factorization (QCDF). We take into account subleading power corrections to the penguin annihilation topology and to color-suppressed tree amplitudes that are crucial for resolving the CP puzzles and rate deficit problems with penguin-dominated two-body decays and color-suppressed tree-dominated $\pi^0\pi^0$ and $\rho^0\pi^0$ modes in the $B_{u,d}$ sector. Many of the $B_s\to h_1h_2$ decays can be related to $B_d\to h_1h_2$ ones via U-spin or SU(3) symmetry. Some useful model-independent relations can be derived and tested. Mixing-induced CP asymmetries for many of the penguin-dominated decays are predicted to be very small in the standard model. They are sensitive to New Physics and offer rich possibilities of new discoveries. Measurements of direct CP-violating asymmetries can be used to discriminate QCDF from other competing approaches such as pQCD and soft-collinear effective theory.

Branching ratios andCPasymmetries ofB→a1(1260)πanda1(1260)Kdecays

We present the studies of the decays $B\ensuremath{\rightarrow}{a}_{1}(1260)\ensuremath{\pi}$ and ${a}_{1}(1260)K$ within the framework of QCD factorization. Because of the G-parity, unlike the vector meson, the chiral-odd two-parton light-cone distribution amplitudes of the ${a}_{1}$ are antisymmetric under the exchange of quark and antiquark momentum fractions in the SU(2) limit. The branching ratios for ${a}_{1}\ensuremath{\pi}$ modes are sensitive to tree-penguin interference. The resultant $\mathcal{B}({B}^{0}\ensuremath{\rightarrow}{a}_{1}^{\ifmmode\pm\else\textpm\fi{}}{\ensuremath{\pi}}^{\ensuremath{\mp}})$ are in good agreement with the data. However, using the current Cabibbo-Kobayashi-Maskawa angles, $\ensuremath{\beta}=22.0\ifmmode^\circ\else\textdegree\fi{}$ and $\ensuremath{\gamma}=59.0\ifmmode^\circ\else\textdegree\fi{}$, our results for the mixing-induced parameter $S$ and ${\ensuremath{\alpha}}_{\mathrm{eff}}$ differ from the measurements of the time-dependent $CP$ asymmetries in the decay ${B}^{0}\ensuremath{\rightarrow}{a}_{1}^{\ifmmode\pm\else\textpm\fi{}}{\ensuremath{\pi}}^{\ensuremath{\mp}}$ at about the $3.7\ensuremath{\sigma}$ level. This puzzle may be resolved by using a larger $\ensuremath{\gamma}\ensuremath{\gtrsim}80\ifmmode^\circ\else\textdegree\fi{}$. For ${a}_{1}K$ modes, the annihilation topologies give sizable contributions and are sensitive to the first Gegenbauer moment of the leading-twist tensor (chiral-odd) distribution amplitude of the ${a}_{1}$ meson. The $B\ensuremath{\rightarrow}{a}_{1}K$ amplitudes resemble the corresponding $B\ensuremath{\rightarrow}\ensuremath{\pi}K$ ones very much. Taking the ratios of corresponding $CP$-averaged ${a}_{1}K$ and $\ensuremath{\pi}K$ branching ratios, we can extract information relevant to the electroweak penguins and annihilations. The existence of new physics in the electroweak penguin sector and final-state interactions during decays can thus be explored.

Exclusive Charmless B Decays in QCD

The problem of hadronic input in charmless nonleptonic B decays is discussed. QCD sum rules and their light-cone versions (LCSR) provide an important part of this input, such as the decay constant $f_B$ and $B\to \pi$ form factor. Employing the LCSR technique, the $B\to \pi\pi$ hadronic matrix elements with emission, penguin and annihilation topologies are calculated, with no evidence for large nonfactorizable effects and/or strong phases.

Study of B c → D π in the perturbative QCD approach

We investigate the branching ratios and direct CP asymmetries of $B_c^+\to D^0\pi^+$ and $B_c^+\to D^+\pi^0$ decays in the PQCD approach. All the diagrams with emission topology or annihilation topology are calculated strictly. A branching ratio of $10^{-6}$ and $10^{-7}$ for $B_c^+\to D^0\pi^+$ and $B_c^+\to D^+\pi^0$ decay is predicted, respectively. Because of the different weak phase and strong phase from penguin operator and two kinds of tree operator contributions, we predict a possible large direct CP violation: $A^{\rm dir}_{cp} (B_c^\pm \to D^0 \pi^\pm)\approx -50%$ and $A^{\rm dir}_{cp} (B_c^\pm \to D^\pm \pi^0)\approx 25%$ when $\gamma=55^\circ$, which can be tested in the coming LHC.

Annihilation effects inB→ππfrom QCD light-cone sum rules

Using the method of QCD light-cone sum rules, we calculate the $B\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}$ hadronic matrix elements with annihilation topology. We obtain a finite result, including the related strong phase. Numerically, the annihilation effects in $B\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}$ turn out to be small with respect to the factorizable emission mechanism. Our predictions, together with the earlier sum rule estimates of emission and penguin contributions, are used for the phenomenological analysis of $B\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}$ channels. We predict a $\ensuremath{\Delta}I=1/2$ transition amplitude which significantly differs from this amplitude extracted from the current data.

Weak annihilation topologies and final state interactions inD→PPdecays

We study two-body D -> PP decays, assuming that each decay process go through the bare amplitude followed by elastic SU(3) rescattering, where the bare amplitude consists of (i) the color-allowed and color-suppressed factorization amplitudes and (ii) the short-distance weak annihilation amplitudes. We have performed the \chi^2 fit on 14 branching ratios of D -> PP decays in the formalism of the above mentioned model. The final state interactions can be well accounted for by the short-distance annihilation topologies and SU(3) rescatterings. The two SU(3) rescattering phase differences are \delta \equiv \delta_{27}-\delta_{8} \simeq -46^\circ and \sigma \equiv \delta_{27}-\delta_{1} \simeq -21^\circ, where \delta_{27}, \delta_{8} and \delta_{1}are the rescattering phases of final states corresponding to the representations 27, 8 and 1, respectively. We find that the D^0 -> K^0 \bar{K}^0 decay occurs mainly due to the nonzero short-distance weak annihilation effects, originating from SU(3) symmetry-breaking corrections to the distribution amplitudes of the final-state kaons, but receives tiny effects from other modes via SU(3) rescattering. Our results are in remarkable accordance with the current data.

Publisher’s Note: Annihilation in factorization-suppressedBdecays involving a1P11meson and search for new-physics signals [Phys. Rev. D72, 034009 (2005)

The recent measurements of large transverse fractions in B \to \phi K^* decays represent a challenge for theory. It was shown that the QCD penguin annihilation could contribute to the transverse amplitudes such that the observation could be accounted for in the Standard Model. However, if one resorts to new physics for resolutions, then the relevant 4-quark operators should be tensor-like or scalar-like. We show that the same annihilation effects could remarkably enhance the longitudinal rates of factorization-suppressed B\to h_1(1380) K^*, b_1(1235) K^* modes to be (12.0^{+4.1}_{-3.0})\times 10^{-6} and (7.0\pm 3.5)\times 10^{-6}, respectively, but attend to be cancelled in the transverse components. Nevertheless, the transverse fractions of B\to h_1(1380) K^* can become sizable due to new-physics contributions. The measurements of these decays can thus help us to realize the role of annihilation topologies in charmless B decays and offer a theoretically clean window to search for the evidence of new physics.