We study glueball $G$ production in gluonic penguin decay $B\to G + X_s$, using the next-to-leading order $b\to s g^*$ gluonic penguin interaction and effective couplings of a glueball to two perturbative gluons. Subsequent decays of a scalar glueball are described by using techniques of effective chiral Lagrangian to incorporate the interaction between a glueball and pseudoscalar mesons. Mixing effects between the pure glueball with other mesons are considered. Identifying the $f_0(1710)$ to be a scalar glueball, we find that both the top and charm penguin to be important and obtain a sizable branching ratio for $B\to f_0(1710) + X_s$ of order $1.3\times 10^{-4} (f/0.07\mbox{GeV}^{-1})^2$, where the effective coupling strength $f$ is estimated to be $0.07$ GeV$^{-1}$ using experimental data for the branching ratio of $f_0(1710) \to K \overline K$ based on chiral Lagrangian estimate. An alternative perturbative QCD based estimation of $f$ is a factor of 20 larger, which would imply a much enhanced branching ratio. Glueball production from this rare semi-inclusive $B$ decay can be probed at the LHCb and Belle II to narrow down the allowed parameter space. Similar branching ratio is expected for the pseudoscalar glueball. We also briefly comment on the case of vector and tensor glueballs.
We study glueball G production in gluonic penguin decay B -> X_s G, using next-to-leading order b -> s g^* gluonic penguin interaction and an effective coupling of a glueball to two gluons. The effective coupling allows us to study the decay rate of a glueball to two pseudoscalars in the framework of chiral perturbation theory. Identifying the f_0(1710) to be a scalar glueball, we then determine the effective coupling strength with the branching ratio of f_0(1710) -> K KBar. We find that the charm penguin to be important and obtain a sizable branching ratio for Br(B -> X_s G) in the range of (…
We discuss the historical development of the gluonic B-penguin, its sensitivity to $H^+$ effects, and $\bsg\sim$ 10--15% as a possible solution to the $\Bsl$ and $n_C$ problems. The latter and the connection of the gluonic penguin to inclusive $B\to η^\prime+ X_s$ production through the gluon anomaly, with the intriguing prospect of 10% inclusive CP asymmetries, bring us to topics of current interest.
The $B\to ππ$ hadronic matrix element of the chromomagnetic dipole operator $O_{8g}$ (gluonic penguin) is calculated using the QCD light-cone sum rule approach. The resulting sum rule for $<ππ|O_{8g}|B>$ contains, in addition to the $O(α_s)$ part induced by hard gluon exchanges, a contribution due to soft gluons. We find that in the limit $m_b\to \infty$ the soft-gluon contribution is suppressed as a second power of $1/m_b$ with respect to the leading-order factorizable $B\to ππ$ amplitude, whereas the hard-gluon contribution has only an $α_s$ suppression. Nevertheless, at finite $m_b$, soft a…
We review the phenomenological and theoretical evidences for dynamical gluon mass generation and the main features of the glueball spectrum in (pure gauge) Yang-Mills theories. The mixing between glueball and conventional $\bar q q$ states in $f_0$ scalar mesons is discussed. For pseudoscalar mesons, the inclusion of the glue field in an effective low energy theory is presented leading to a third isoscalar $η''$ partner of the $η$ and $η'$. Branching ratios for processes involving $η''$ are given and, when available, compatible with data for $η(1405)$.
The strong isospin-breaking correction, Omega_{st}, which appears in estimates of the Standard Model value for the direct CP-violating ratio epsilon'/epsilon, is evaluated to next-to-leading order (NLO) in the chiral expansion using Chiral Perturbation Theory. The relevant linear combinations of the unknown NLO CP-odd weak low-energy constants (LEC's) which, in combination with 1-loop and strong LEC contributions, are required for a complete determination at this order, are estimated using two different models. It is found that, to NLO, Omega_{st}=0.08 +/- 0.05, significantly reduced from the …
We discuss the recent observation of f_0(980) in charmless B-decays and in gluon jets which hints toward a gluonic coupling of this meson similar to eta'. Further predictions on B-decays into scalar particles are presented. Charmless B decays also show a broad K Kbar (and possibly pi pi) S-wave enhancement which we relate to the 0^{++} glueball. These gluonic mesons represent a sizable fraction of the theoretically derived decay rate for b -> sg.
The gluonic widths of four leading glueball candidates are determined from their production in radiative quarkonium decays, allowing quantitative estimation of their glue content. Lattice predictions for the scalar and tensor channels seem to be in reasonable agareement with present data (allowing for mixing with $q \bar{q}$ states). However there is a glueball-like-state in the pseudoscalar spectrum whose mass is considerably lower than expected from lattice estimates.
The indirect evidence for gluonic objects in gluon jets is recalled, more accurate tests at the LHC are possible. Estimates of gluonic and quarkonic components of scalar mesons are presented, which could be improved by further studies, in particular of B and B_s decays. The results are consistent with the scalar glueball mixing into f_0(500) and f_0(1500). The study of symmetry relations for 2-body decay rates of charmonium χ_c is suggested as crucial test in the identification of q\bar q multiplets and glueballs. Further related results are discussed in the recent review \cite{Ochs:2013gi}.
Motivated by the newly observed resonance $X(2600)$ by BESIII Collaboration, we examine the trigluon glueball interpretation for it in the framework of QCD sum rules. We evaluate the mass spectra of the trigluon glueballs with quantum numbers $0^{-+}$ and $2^{-+}$ up to dimension 8 condensate in the operator product expansion. Our numerical results indicate that the mass of the $2^{-+}$ trigluon glueball is about $2.66\pm 0.06$ GeV, which is consistent with the mass of the X(2600) within the uncertainties, while $0^{-+}$ has a mass of $2.01\pm0.14$ GeV. The possible decay channels of the $2^{-…
The space-like penguin contributions to branching ratios and CP asymmetries in charmless decays of $B$ to two pseudoscalar mesons are studied using the next-to-leading order low energy effective Hamiltonian. Both the gluonic penguin and the electroweak penguin diagrams are considered. We find that the effects are significant.
We discuss the ``spectroscopy'' of gluonic states in systems with two space dimensions, using simple models to mimic the results of lattice gauge theory computations. We first discuss the quantum numbers of these systems, including charge conjugation. Two types of systems are discussed in detail: ``gluelumps'' which have a heavy adjoint color charge at the origin and glueballs which are composed entirely of glue. Both systems are discussed using the bag model and the flux tube model. For glueballs the model spectra are compared with the resulst of Teper. Both models capture many features of th…
We develop tools to determine the gluonic content of a resonance of known mass, width and $J^{PC}$ from its branching fraction in radiative quarkonium decays and production cross section in $γγ$ collisions. We test the procedures by applying them to known $q\bar{q}$ mesons, then analyze four leading glueball candidates. We identify inconsistencies in data for $J/ψ\to γf_0(1500)$ and $J/ψ\to γf_J(1710)$ whose resolution can quantify their glueball status.When $Γ(f_0(1500) \to γγ)$ and $Γ(f_J(1710) \to γγ)$ are known, the $n\bar{n}, s\bar{s},gg$ mixing angles can be determined. The enigmatic sit…
The space-like penguin contributions to branching ratios and CP asymmetries in charmless decays of $B_{c}$ to two pseudoscalar mesons are studied using the next-to-leading order low energy effective Hamiltonian and factorization approximation. Both the gluonic penguin and the electroweak penguin diagrams are considered. In addition the annihilation diagram contributions are also taken in account. We find that the space-like penguin effects are significant.
Signatures of dominant and central production of glueballs (binary gluonic mesons) in heavy ion and hadromic collisions are discussed. Search strategies are proposed.
We present a short survey of the theoretical expectations on glueballs and hybrids as well as of the present phenomenological status. The possibility to obtain new information on gluonic mesons from the study of gluon jets in comparison to quark jets is discussed.
We discuss states in the meson spectrum which have explicit gluonic components. Glueballs (with no valence quarks) and hybrid mesons (with valence quarks) are both reviewed. We present in some detail lattice simulation results. ( to appear in proceedings of QCD-20 years, Aachen Workshop)
The glueball-to-vacuum matrix elements of local gluonic operators in scalar, tensor, and pseudoscalar channels are investigated numerically on several anisotropic lattices with the spatial lattice spacing ranging from 0.1fm - 0.2fm. These matrix elements are needed to predict the glueball branching ratios in $J/ψ$ radiative decays which will help identify the glueball states in experiments. Two types of improved local gluonic operators are constructed for a self-consistent check and the finite volume effects are studied. We find that lattice spacing dependence of our results is very weak and t…
The space-like penguin contributions were ignored on little ground in many previous studies of nonleptonic B decays and CP violation. Taking the penguin-dominated channels $B^{-} _{u}\rightarrow \bar{K}^{0}π$ and $B^{-}_{u}\rightarrow K^{0} K^{-}$ for example, we illustrate the non-negligible effects of the space-like penguin diagrams on CP asymmetries. Some quali- tative remarks are given on the gluonic penguin picture and the direct CP violation in exclusive two-body decays of B mesons.
Hybrid charmonium with mass ~4 GeV could be produced via a c c.bar color-octet component in b->c c.bar s. These states could be narrow and could have a significant branching ratio to light hadrons, perhaps enhanced by glueballs. Decays to gluonic hadrons could make a sizable contribution to B->no charm decays. Experimental signatures and search strategies are discussed.
We argue that certain specific gluon excitations, other than conventional glueballs, can propagate freely outside of hadrons and glueballs. We begin with the result that the Abelian generators of $SU(N)$ QCD can be meaningfully isolated by the Cho-Faddeev-Niemi-Shabanov decomposition. It has already been shown by Cho \emph{et. al.} that the corresponding gluon excitations have a gauge transformation whose form indicates that they are physical entities of neutral colour charge. We contend that this colour neutrality permits them to propagate freely, albeit with an effective mass due to interact…
The lightest gluonic meson is expected with J^{PC}=0^{++}, calculations in full QCD point towards a mass of around 1 GeV. The interpretation of the scalar meson spectrum is hindered as some states are rather broad. In a largely model-independent analysis of pi+ pi- \to pi+ pi-, pi0 pi0 scattering in the region 600-1800 MeV a unique solution for the isoscalar S-wave is obtained. The resonances f_0(980), f_0(1500) and the broad f_0(600) or ``sigma'' are clearly identified whereas f_0(1370) is not seen at the level B(f_0(1370)\to pi pi)\gtrsim 10%. Arguments for the broad state to be a glueball a…
The penguin mediated processes $b\rightarrow s g$ and $b\rightarrow s l^+l^-$ are studied. In the Standard Model, for the leptonic modes improvement in experimental limits will put strigient bounds on the top mass, where the present limit from $b\rightarrow s μ^+μ^-$ is 390 GeV. For hadronic penguin processes, although the gluonic penguin dominates, we find the electroweak contribution are around 30\% for the upper range allowed top mass. The branching ratio for $B\rightarrow X_s ϕ$ is predicted to be in the range $(0.6\sim 2)\times 10^{-4}$. Effects of the charged Higgs in two Higgs doublet m…
We provide an overview of theoretical developments on hybrid mesons and glueballs in the last year at this turn of the millenium conference. Cracks in potential models of conventional mesons are developing. Hybrid meson adiabatic surfaces have been calculated and interpreted, experimental J^PC exotics have hybrid meson, four-quark state or non-resonant interpretations, and the strong decay mechanism of hybrids has been studied. All theoretical progress on hybrid mesons in the last year is mentioned. Overall features of glueballs are visited: decays and the successes of the large N_c limit. Two…
The correlator of the square of the Yang-Mills field-strength tensor corresponds to a scalar glueball, i.e., to a bound-state formed by gluonic ingredients only. It has quantum numbers 0++ and its mass, as predicted by different theoretical approaches, is expected to lie between 1 and 2 GeV. Here we restrict our considerations to the Born level, that is, we consider the correlator to zeroth order in the coupling. Gluonic self-interaction is taken into account indirectly by using non-perturbative gluon propagators. The employed closed expressions are motivated by lattice and Dyson-Schwinger stu…
A useful inequality is obtained if charmless strange B decays are assumed to be dominated by the gluonic penguin diagram and the tree diagram contribution is small but not negligible. The penguin-tree interference contribution which is linear in the tree amplitude is included but the direct tree contribution which is quadratic is neglected.
Given a resonance of known mass, width, and J^{PC}, we can determine its gluonic branching fraction, b(R->gg), from data on its production in radiative vector quarkonium decay, V -> gamma+R. For most resonances b(R->gg) is found to be O(10%), consistent with being q-qbar states, but we find that both pseudoscalars observed in the 1440 MeV region have b(R->gg) ~ 1/2 - 1, and b(f_0^{++}->gg) ~ 1/2. As data improves, b(R->gg) should be a useful discriminator between q-qbar and gluonic states and may permit quantitative determination of the extent to which a particular resonance is a mixture of gl…
Some recent developments in the phenomenology of the lightest scalar glueball are summarised. Tools for determining the gluonic content of a resonance of known mass, width and $J^{PC}$ from its branching fraction in radiative quarkonium decays and production cross section in $γγ$ collisions are presented. Two $q\bar{q} - G$ mixing schemes for $J^{PC} = 0^{++}$, inspired by the lattice, are shown to lead to similar phenomenology that may be tested at BEPC and in $γγ$ production at LEP2.
The constituent nature of candidate gluonic mesons can be studied by comparing their production in quark and gluon jets. The production rate for such mesons depends on the colour confinement processes at the end of the perturbative evolution. Whereas we expect enhanced production of hybrids in the fragmentation region of a gluon jet, the rate for glueballs depends on the relative importance of colour triplet and colour octet neutralization. These neutralization processes can be studied independently in events with large rapidity gaps. If octet processes turn out important the recently suggeste…
The existence of glueballs is predicted in QCD, the lightest one with quantum numbers J^{PC}=0^{++}, but different calculations do not well agree on its mass in the range below 1800 MeV. Several theoretical schemes have been proposed to cope with the experimental data which often have considerable uncertainties. Further experimental studies of the scalar meson sector are therefore important and we discuss recent proposals to study leading clusters in gluon jets and charmless B-decays to serve this purpose.
We study in next-to-leading order QCD hadronic penguin $B$ decays in the Standard and two-Higgs-doublet models. Although the gluonic penguin dominates, we find the electroweak contribution non-negligible. In the Standard Model, the branching ratio for $B \rightarrow X_s ϕ$ is predicted to be in the range $(0.6\sim 2)\times 10^{-4}$. The ranges of branching ratios for $B\rightarrow K ϕ$, $B\rightarrow K^*ϕ$, and $B_s\rightarrow ϕϕ$ are $(0.4\sim 2)\times 10^{-5}$, $(0.2\sim 1)\times 10^{-5}$, and $(0.15\sim 0.5)\times 10^{-5}$, respectively. The contribution from the charged Higgs boson in two …
The unexpectedly large branching ratios for $B\to η' K (η' X_s)$ decays could be of gluonic origin. We study the implications for $B\to ηK (ηX_s)$ and $P K (PX_s)$, where $P$ is the pseudoscalar glueball. In the mechanism proposed by Fritzsch, large branching ratios are predicted for these modes. The $B\to ηK$ rate is barely within the experimental limit, and $B\to P K$, $PX_s$ could be at the 0.1% and 1% level, respectively. Smaller but less definite results are found for the mechanism of $g^* \to η' g$ via the gluon anomaly.
A useful inequality is obtained if charmless strange B decays are assumed to be dominated by a $ΔI = 0$ transition like that from the gluonic penguin diagram and the contributions of all other diagrams including the tree, electroweak penguin and annihilation diagrams are small but not negligible. The interference contributions which are linear in these other amplitudes are included but the direct contributions which are quadratic are neglected.
We give the detailed analyses for the gluonic-penguin effect on the $\kp$ and $\pp$ decays of the $B$ meson. In the standard model, it is shown that the ratio $BR(B\A\kp)/BR(B\A\pp)$ takes the value $0.5\sim 3.0$ with the strongly depending on the CP violating phase $ϕ$ and the KM matrix element $|V_{ub}|$. We obtain the constraint on the form factor by using the experimental branching ratio. It is also found that, in the two-Higgs-doublet model, the charged Higgs contribution which could enhance the $B\A X_s\r$ decay does not a sizable effect on our processes. The effect of the final state in…
Applying perturbative QCD methods recently seen to give a good description of the two body hadronic decays of the B meson, we address the question of bound-state effects on the decay B into K* + gamma. Consistent with most analyses, we demonstrate that gluonic penguins, with photonic bremsstrahlung off a quark, change the decay rate by only a few percent. However, explicit off-shell b-quark effects normally discarded are found to be large in amplitude, although in the standard model accidents of phase minimize the effect on the rate. Using an asymptotic distribution amplitude for the K* and ju…
The most common decay used for measuring 2beta_s, the phase of Bs-Bsbar mixing, is Bs -> J/psi phi. This decay is dominated by the colour-suppressed tree diagram, but there are other contributions due to gluonic and electroweak penguin diagrams. These are often referred to as "penguin pollution" (PP) because their inclusion in the amplitude leads to a theoretical error in the extraction of 2beta_s from the data. In the standard model (SM), it is estimated that the PP is negligible, but there is some uncertainty as to its exact size. Now, phi_s^{c\bar{c}s} (the measured value of 2beta_s) is sma…
The recent observations of f_0(980) in charmless B-decays motivate further studies of scalar particle and glueball production in these processes. Amplitudes for charmless 2-body B decays involving the members of the scalar nonet are presented based on the symmetries of the dominant penguin contribution. Different scenarios for the lightest scalar nonet are investigated in view of the presently available data. We describe the evidence from B-decays for f_0(1500) with a flavour octet like mixing and the hints towards the members of the q qbar nonet of lowest mass. There is further support for th…
The inclusive nonleptonic transition rate of B meson in gluonic penguin channel is calculated in QCD using the heavy quark mass expansion. We found the branching ratio to be approximately 0.25%.
We systematically analyse the gluonic penguin-induced charmless decays $B \ra K_Xϕ$($K_X$ denotes the meson state $s\bar q \;(q=u\ {\rm or}\ d)$ ), in the standard model and the two-Higgs-doublet model. These processes, being induced at one-loop level, are of great importance in measuring the virtual top quark effect in the standard model, and also in searching for the non-standard signals in the low energy region. It is shown that the QCD effect is also significant in these processes, as in the weak radiative processes $B \ra X_s γ$. We also show that the charged Higgs contribution can not pr…
Based on the low-energy effective Hamiltonian with the generalized factorization, we calculate the new physics contributions to the branching ratios of the two-body charmless hadronic decays of $B_u$ and $B_d$ mesons induced by the new gluonic and electroweak charged-Higgs penguin diagrams in the general two-Higgs doublet models (models I, II and III). Within the considered parameter space, we find that: (a) the new physics effects from new gluonic penguin diagrams strongly dominate over those from the new $γ$- and $Z^0$- penguin diagrams; (b) in models I and II, new physics contributions to m…
We study the radiative charmless $B_{(s)}\to V(A)γ$ decays in perturbative QCD (pQCD) approach to the leading order in $α_s$ (here $V$ and $A$ denotes vector mesons and two kinds of axial-vector mesons: $^3P_1$ and $^1P_1$ states, respectively.). Our predictions of branching ratios are consistent with the current available experimental data. We update all $B_{(s)}\to V$ form factors and give the predictions for $B\to A$ form factors using the recent hadronic inputs. In addition to the dominant factorizable spectator diagrams, which is form factor like, we also calculate the so-called ``power s…
A variety of CP violating asymmetries in $B^0$ decays is predicted in the Standard Model in terms of CKM (Cabibbo-Kobayashi-Maskawa) complex phases. These phases can also be determined from rate measurements of certain $B^+$ and $B^-$ decays. We focus on the following processes: $B^0\toψK_S,~π^+π^-,~π^0π^0, ~ρ^{\pm}π^{\mp},~B_s\to D^+_s K^-,~π^0η, ~B^+\to D^0(\Dbar)K^+,~π^+π^0,~π^0 K^+,~ π^+ K^0,~ηK^+$ and their charge-conjugates. Complications due to gluonic-penguin and electroweak-penguin amplitudes are dealt with and are resolved. The importance of final state interaction phases in charged …
Based on the low energy effective Hamiltonian with generalized factorization, we calculate the new physics contributions to the branching ratios and CP-violating asymmetries of the two-body charmless hadronic decays $B \to PP, PV$ from the new strong and electroweak penguin diagrams in the TC2 model. The top-pion penguins dominate the new physics corrections, and both new gluonic and electroweak penguins contribute effectively to most decay modes. For tree-dominated decay modes $B \to ππ, ρπ, etc,$ the new physics corrections are less than 10%. For decays $B \to K^{(*)} π$, $K^{(*)} η$, $etc$,…
The 2--point functions for $ΔS=1$ current-current and QCD-penguin operators, as well as for the $\ds$ operator, are calculated at the next-to-leading order. The calculation is performed in two different renormalization schemes for $γ_5$, and the compatibility of the results obtained in the two schemes is verified. The scale- and scheme-invariant combinations of spectral 2--point functions and corresponding Wilson-coefficients are constructed and analyzed. For $ΔS=1$, the QCD corrections to the CP-conserving part, dominated by current-current operators, are 40\%--120\% at $q^2=\left(1-3\,\mbox{…
We update the profile of the CKM matrix. The apex (rhobar,etabar) of the Unitarity Triangle is given by means of a global fit. We propose to include therein sin2alpha from the CP-violating asymmetries in B0->rho+rho-, using isospin to discriminate the penguin contribution. The constraint from epsilon'/epsilon is briefly discussed. We study the impact from the measurement of the rare decay K+->pi+nunu-bar, and from a future observation of KL->pi0nunubar. The B system is investigated in detail, beginning with 2beta+gamma and gamma from B0->D(*)+-pi-+ and B+->D(*)0K+. A significant part of this p…
In left-right models the gluonic penguin contribution to b --> s s-bar s transition is enhanced by m_t/m_b due to the presence of (V+A) currents and by the larger values of loop functions than in the Standard Model. Together those may completely overcome the suppression due to small left-right mixing angle xi <~ 0.013. Two independent new phases in the B --> phi K_S decay amplitude appearing in a large class of left-right models may therefore modify the time dependent CP asymmetry in this decay mode by O(1) and explain the recent BaBar and Belle CP asymmetry measurements in this channel. This …
We discriminate gluonic hadrons from conventional $q\bar q$ states by surveying radial and orbital excitations of all I=0 and I=1 $n\bar n$ systems anticipated up to 2.1 GeV. We give detailed predictions of their quasi-two-body branching fractions and identify characteristic decay modes that can isolate quarkonia. Several of the ``missing mesons'' with L$_{q\bar q}=2$ and L$_{q\bar q}=3$ are predicted to decay dominantly into certain S+P and S+D modes, and should appear in experimental searches for hybrids in the same mass region. We also consider the topical issues of whether some of the rece…
In the framework of general two-Higgs-doublet models, we calculate the branching ratios of various inclusive charmless b decays by using the low energy effective Hamiltonian including next-to-leading order QCD corrections, and examine the current status and the new physics effects on the determination of the charm multiplicity $n_c$ and semileptonic branching ratio $B_{SL}$. Within the considered parameter space, the enhancement to the ratio $BR(b \to s g)$ due to the charged-Higgs penguins can be as large as a factor of 8 (3) in the model III (II), while the ratio $BR(b \to no charm)$ can be …
Based on the low-energy effective Hamiltonian, we calculate the new physics corrections to the branching ratio and the differential distributions of the rare decay $B \to X_s γγ$ induced by the new gluonic and electroweak charged-Higgs penguin diagrams in the general two-Higgs-doublet model with the restriction $λ_{ij}^{U,D}=0$ for $i\neq j$. Within the considered parameter space, we see the following: (a) the standard model predictions of ${\cal B}(B \to X_s γγ)$ and $A_{FB}$ have a moderate $m_s$ dependence; (b) in model III, the prediction of the branching ratio ${\cal B}(B \to X_s γγ)$ ran…
