Weak Annihilation Research Articles

Theoretical overview on heavy flavor physics at LHCb

Precise prediction of the heavy hadrons decay amplitudes is of great importance in the determination of the parameters of KM matrix and searching for new physics signals beyond the standard model. Due to the high accuracy of the B meson decay constants, the structure dependent QED corrections should be taken into account for B→μ+μ− decays due to the power enhancement, but this effect is numerically negligible for B→τ+τ−. The radiative leptonic decays and double radiative decays are the best channels to determine the B meson distribution amplitudes, but one should systematically deal with the power corrections to reduce the uncertainty. The heavy-to-light form factors is one of the most important nonperturbative quantities, and an improved method to improve the theoretical accuracy is to fit the form factors using combined data from Lattice and light-cone sum rules which works well at large recoil region. The power suppressed weak annihilation contribution is phenomenologically important in the nonleptonic decays, and the previously neglected hard-collinear gluon exchange diagrams have the potential to cancel the endpoint singularity arising from the hard gluon exchange. Therefore, more endeavors need to be paid to this topic.

Exploring dark matter spike distribution around the Galactic centre with stellar orbits

ABSTRACT Precise measurements of the stellar orbits around Sagittarius A* have established the existence of a supermassive black hole (SMBH) at the Galactic centre (GC). Due to the interplay between the SMBH and dark matter (DM), the DM density profile in the innermost region of the Galaxy, which is crucial for the DM indirect detection, is still an open question. Among the most popular models in the literature, the theoretical spike profile proposed by Gondolo & Silk (GS hereafter) is well adopted. In this work, we investigate the DM spike profile using updated data from the Keck and Very Large Telescope (VLT) telescopes considering that the presence of such an extended mass component may affect the orbits of the S-stars in the GC. We examine the radius and slope of the generalized Navarro–Frenk–White (NFW) spike profile, analyse the Einasto spike, and discuss the influence of DM annihilation on the results. Our findings indicate that an initial slope of γ ≳ 0.92 for the generalized NFW spike profile is ruled out at a 95 per cent confidence level. Additionally, the spike radius Rsp larger than 21.5 pc is rejected at 95 per cent probability for the Einasto spike with α = 0.17, which also contradicts the GS spike model. The constraints with the VLT/GRAVITY upper limits are also projected. Although the GS NFW spike is well constrained by the Keck and VLT observation of S2, an NFW spike with a weak annihilation cusp may still be viable, as long as the DM annihilation cross-section satisfies $\left\langle \sigma v \right\rangle \gtrsim 7.7\times 10^{-27}~{\rm cm^3\, s^{-1}} (m_{\rm DM}/100~{\rm GeV})$ at 95 per cent level.

On weak annihilators and nilpotent associated primes of skew PBW extensions

We investigate the notions of weak annihilator and nilpotent associated prime defined by Ouyang and Birkenmeier (Weak annihilator over extension rings, 2012) in the setting of skew PBW extensions. We extend several results formulated in the literature concerning annihilators and associated primes of commutative rings and skew polynomial rings to a more general setting of algebras not considered before. We exemplify our results with families of algebras appearing in the theory of enveloping algebras, noncommutative algebraic geometry, and theoretical physics. Finally, we present some ideas for future research.

Dispersive constraints on fermion masses

We demonstrate that fermion masses in the Standard Model (SM) can be constrained by the dispersion relations obeyed by hadronic and semileptonic decay widths of a fictitious heavy quark $Q$ with an arbitrary mass. These relations, imposing stringent connections between the high-mass and low-mass behaviors of decay widths, correlate a heavy quark mass and the chiral symmetry breaking scale. Given the known input from leading-order heavy quark expansion and a hadronic threshold for decay products, we solve for a physical heavy quark decay width. It is shown that the charm (bottom) quark mass $m_c= 1.35$ GeV ($m_b= 4.0$ GeV) can be determined by the dispersion relation for the $Q\to du\bar d$ ($Q\to c\bar ud$) decay with the threshold $2m_\pi$ ($m_\pi+m_D$), where $m_\pi$ ($m_D$) denotes the pion ($D$ meson) mass. Requiring that the dispersion relation for the $Q\to su\bar d$ ($Q\to d\mu^+\nu_\mu$, $Q\to u\tau^-\bar\nu_\tau$) decay with the threshold $m_\pi+m_K$ ($m_\pi+m_\mu$, $m_\pi+m_\tau$) yields the same heavy quark mass, $m_K$ being the kaon mass, we constrain the strange quark (muon, $\tau$ lepton) mass to be $m_s= 0.12$ GeV ($m_\mu=0.11$ GeV, $m_\tau= 2.0$ GeV). Moreover, all the predicted decay widths corresponding to the above masses agree with the data. It is pointed out that our formalism is similar to QCD sum rules for probing resonance properties, and that the Pauli interference (weak annihilation) provides the higher-power effect necessary for establishing the solutions of the hadronic (semilaptonic) decay widths. This work suggests that the parameters in the SM may not be free, but arranged properly to achieve internal dynamical consistency.

Shedding new light on weak annihilation B-meson decays

We identify a novel leading-power contribution to the pure weak annihilation non-leptonic B-meson decay amplitudes, which arises from the hard-collinear gluon exchange between the light quark of the bottom meson and the final-state active partons. This interesting observation is naturally expected to shed new light on deciphering rapidity divergences in the convolution integrals of the soft-collinear factorization formulae. Subsequently we explore an intriguing enhancement mechanism due to the penguin contractions of the current-current operators from the weak effective Hamiltonian, which yields the significant impacts on the CP violating observables.

ACP[D(s)0,+→Vγ] from a large O8 contribution

$CP$ violation in $\mathrm{\ensuremath{\Delta}}{A}_{\mathrm{CP}}=\ensuremath{-}0.154(29)$, in the ${D}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}/{K}^{+}{K}^{\ensuremath{-}}$ system, is established, and its central value is 1 order of magnitude above the naive Standard Model (SM) estimate. It remains unclear whether this is due to currently incalculable strong interaction matrix elements or genuine new physics, such as a shift in ${\mathcal{O}}_{8}$ with a weak phase. We show that interference of the long-distance (LD) terms with the ${\mathcal{O}}_{8}$ matrix element can give rise to ${A}_{CP}^{D\ensuremath{\rightarrow}V\ensuremath{\gamma}}=\mathrm{few}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ (for reference values $\mathrm{Im}[{C}_{8}^{\mathrm{NP}}]\ensuremath{\approx}{10}^{\ensuremath{-}3}$). In addition, it is pointed out that the ratio of left- to right-handed (photon polarization) LD amplitudes is measurable in time-dependent $CP$ asymmetries. We argue that both theory and experimental consideration favor weak annihilation (WA) as the dominant LD contribution. More definite progress could be achieved by either computing the radiative corrections to WA or the measurement of the charged modes ${D}_{(d,s)}^{+}\ensuremath{\rightarrow}(\ensuremath{\rho},{K}^{*}{)}^{+}\ensuremath{\gamma}$ and ${D}_{s}\ensuremath{\rightarrow}{\ensuremath{\rho}}^{+}\ensuremath{\gamma}$.

Rare decays of the B s –meson into four charged leptons in the framework of the Standard Model

In the framework of the Standard Model we present new theoretical predictions for the branching ratios, double and single differential distributions and forward—backward leptonic asymmetries for the decay. In our consideration we take into account the —resonance contribution; the main contributions of four charmonium resonances : and —resonant contribution from and ‘tails’ contributions from and resonances; non—resonant contribution of the - pairs, bremsstrahlung and the contribution of the weak annihilation. We provide the prediction for the branching ratio of decay with and without the —resonance contribution. We use the model of vector meson dominance (VMD) for calculation of resonances contributions and take into account all substantive terms in amplitude that was not considered in the previously papers.

Estimating QCD-factorization amplitudes through SU(3) symmetry in Brightarrow P P decays

We estimate the potential size of the weak annihilation amplitudes in QCD factorization as allowed by experimental data. To achieve this goal, we establish a connection between the amplitudes in the QCD factorization and the so-called topological and SU(3)-invariant descriptions. Our approach is based purely on the analysis of the tensor structure of the decay amplitudes. By focusing on the processes Brightarrow P P and considering data from CP asymmetries and branching fractions, we perform a global fit to the SU(3)-irreducible quantities assuming minimal theoretical bias. Subsequently we translate the outcome to the QCD factorization decomposition, and find that the most constrained weak annihilation amplitudes are below 0.04. However, in view of the large uncertainties in several of the experimental input parameters, values up to sim 0.3 are allowed in certain cases.

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)}^0to {D}_{(s)}^{left(ast right)+}{L}^{-} decays, where L is a light meson from the set {π, ρ, K(∗)}. Especially for the two channels {overline{B}}^0to {D}^{+}{K}^{-} and {overline{B}}_s^0to {D}_s^{+}{pi}^{-} , 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 → coverline{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.

Probing QCD dynamics and the standard model with {D}_{(s)}^{+}to {P}_1^{+}{P}_2^0gamma decays

We compute 10 radiative three-body decays of charged charmed mesons {D}^{+}to {P}_1^{+}{P}_2^0gamma and {D}_sto {P}_1^{+}{P}_2^0gamma , P1,2 = π, K, in leading order QCDF, HHχPT and the soft photon approximation. We work out decay distributions and asymmetries in the standard model and with new physics in the electromagnetic dipole operators. The forward-backward asymmetry is suitable to probe the QCD frameworks, in particular the s-channel dependent weak annihilation contributions in QCDF against the markedly different resonance structure in HHχPT. These studies can be performed with Cabibbo-favored modes Ds → π+π0γ, {D}^{+}to {pi}^{+}{overline{K}}^0gamma and {D}_sto {K}^{+}{overline{K}}^0gamma with mathcal{O}left({10}^{-4}-{10}^{-3}right)hbox{-} mathrm{level} branching ratio, which are standard model-like and induced by different hadronic dynamics. Understanding of the latter can therefore be improved in a data-driven way and sharpens the interpretation of standard model tests. Singly Cabibbo-suppressed modes such as D+ → π+π0γ, Ds → π+K0γ, Ds → K+π0γ with branching ratios within ∼ 10−5–10−4 are sensitive to new physics that can be signalled in the forward-backward asymmetry and in the CP-asymmetry of the rate, ideally in the Dalitz region but also in single differential distributions. Results complement those with neutral D0→ P1P2γ decays.

Disentangling QCD and new physics in D \u2192 \u03c0\u2113+\u2113\u2212

In this paper we consider the decay D+ → π+ℓ+ℓ−, addressing in particular the resonance contributions as well as the relatively large contributions from the weak annihilation diagrams. For the weak annihilation diagrams we include known results from QCD factorisation at low q2 and at high q2, adapting the existing calculation for B decays in the Operator Product Expansion. The hadronic resonance contributions are obtained through a dispersion relation, modelling the spectral functions as towers of Regge-like resonances in each channel, as suggested by Shifman, imposing the partonic behaviour in the deep Euclidean. The parameters of the model are extracted using e+e− → (hadrons) and τ → (hadrons) + ντ data as well as the branching ratios for the resonant decays D+ → π+R(R → ℓ+ℓ−), with R = ρ, ω, and ϕ. We perform a thorough error analysis, and present our results for the Standard Model differential branching ratio as a function of q2. Focusing then on the observables FH and AFB, we consider the sensitivity of this channel to effects of physics beyond the Standard Model, both in a model independent way and for the case of leptoquarks.

Impact of weak annihilation contribution on rare semileptonic B + → π + ℓ + ℓ − decay

In the Standard Model, b → s and b → d flavor-changing neutral currents (FCNCs) are not allowed at the tree level and are induced by loop effects. We consider the rare semileptonic B + → π + ℓ + ℓ − decay, where ℓ = e, μ is a charged lepton. The dilepton invariant-mass spectrum and decay rate for B + → π + ℓ + ℓ − are calculated in the effective Hamiltonian approach in two cases — by taking into account the weak annihilation diagrams and without this contribution. Our predictions for the branching fraction of the B + → π + ℓ + ℓ − decay, being dependent on the choice of the B → π form factors, are in agreement with the existing LHCb results within experimental uncertainties. Moreover, accounting for the weak annihilation contributions allows us to get a better agreement with the experimental data on the entire q 2-distribution in the kinematically allowed region, in particular, in its lowest q 2-part. This provides an alternative description of the data than a previous analysis, in which the low-q 2 enhancement seen experimentally was obtained through the long-distance contributions from the light vector mesons.

The heavy quark expansion for inclusive semileptonic charm decays revisited

The Heavy Quark Expansion (HQE) has become an extremely powerful tool in flavor physics. For charm decays, where the expansion parameters αs(mc) and ΛQCD/mc are bigger than for bottom decays, it remains to be seen if the HQE can be applied with similar success. Nevertheless, to make optimal use of the plethora of data already available and coming in the near future, a better understanding of HQE for charm decays is crucial. This paper discusses in detail how the HQE for charm decays is set up, what is the role of four-quark (weak annihilation) operators and how this compares to the well understood bottom decays. Subtleties concerning radiative corrections and the charm mass scheme are briefly discussed. An experimental study of the relevant HQE hadronic matrix elements will then show if the HQE expansion for charm converges well enough. Besides serving as an important cross check for inclusive B decays, in the end, this study might open the road for inclusive |Vcs| and |Vcd| extractions.

Finite-dimensional right alternative superalgebras with semisimple strongly alternative even part

The class of finite-dimensional unital right alternative superalgebras with semisimple strongly alternative even part over an algebraically closed field are studied. We introduce the concept of weak annihilator of a superalgebra and prove that it is a superideal, and the superalgebra itself splits into the direct sum of its weak annihilator and a superalgebra with a zero weak annihilator. We also classify superalgebras with zero weak annihilator in this class of superalgebras.

Rare radiative decays of vector and axial-vector Bc mesons to (Ds, D*s, Ds1) final states

In this work, we use the QCD sum rule method to study the radiative decays of the vector and axial-vector $B_c$ mesons to each of three charmed strange mesons, $D_s$, $D^*_s$ and $D_{s1}$, through their dominant weak annihilation channels. We calculate all relevant transition form factors, which are used to estimate the branching fractions at different channels. The order of branching ratios are obtained to be in the order of $ 10^{-6} - 10^{-5} $, which may be checked via differnet experiments.

Erratum to: Study of B c + decays to the K+K−π+ final state by using B s 0 , χ c0 and D0 resonances and weak annihilation nonresonant topologys

The author’s affiliation reported in JHEP 12 (2017) 019 was incorrectly named. The actual name is Urmia University.

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.

Study of Bc+ decays to the K+K\u2212\u03c0+ final state by using Bs0, \u03c7c0 and D0 resonances and weak annihilation nonresonant topologys

In this research the weak decay of Bc+ decays to the K+K−π+ final state, which is being observed by LHCb collaboration for the first time, is calculated in the quasi-two-body decays which takes the Bs0, χc0 and D0 resonances and weak annihilation nonresonant contributions into account. In this process, the Bc+ meson decays first into Bs0π+, χc0π+ and D0π+ intermediate states, and then the Bs0, χc0 and D0 resonances decay into K+K− components, which undergo final state interaction. The mode of the Bc+ → D0(→K−π+)K+ is also associated with the calculation, in this mode the intermediate resonance D0 decays to the K−π+ final mesons. The resonances Bs0, χc0 and D0 effects in the Bc+ → Bs0(→K+K−)π+, Bc+ → χc0(→K+K−)π+ and Bc+ → D0(→K+K−)π+, D0(→ K−π+)K+ decays are described in terms of the quasi-two-body modes. There is a weak annihilation nonresonant contribution in which Bc+ decays to the K+K−π+ directly, so the point-like 3-body matrix element leftlangle {K}^{+}{K}^{-}{pi}^{+}left|uoverline{d}right|0rightrangle is also considered. The decay mode of the {B}_c^{+}to {overline{K}}^{ast 0}(892){K}^{+} is contributed to the annihilation contribution. The branching ratios of quasi-two-body decays expand in the range of (2.12 ± 0.61) × 10−6 to (7.56 ± 1.71) × 10−6.

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.

Application of the light-front holographic wavefunction for heavy-light pseudoscalar meson in Bd,s → Dd,sP decays

In this paper we extend our analyses of the decay constant and distribution amplitude with an improved holographic wavefunction to the heavy-light pseudoscalar mesons. In the evaluations, the helicity-dependence of the holographic wavefunction is considered; and an independent mass scale parameter is employed to moderate the strong suppression induced by the heavy quark. Under the constraints from decay constants and masses of pseudoscalar mesons, the χ2-analyses for the holographic parameters exhibit a rough consistence with the results obtained by fitting the Regge trajectory. With the fitted parameters, the results for the decay constants and distribution amplitudes are presented. We then show their application in evaluating the Bd,s→Dd,sP decays, in which the power-suppressed spectator scattering and weak annihilation corrections are first estimated. Numerically, the spectator scattering and weak annihilation corrections present a negative shift of about 0.7% on the branching fractions; while, the predictions are still larger than the experimental data. Such small negative shift confirms the estimation based on the power counting rules.