QCD Counting Research Articles

BaryonicBMeson Decays

We review the two- and three-body baryonicBdecays with the dibaryon (BB′¯) as the final states. Accordingly, we summarize the experimental data of the branching fractions, angular asymmetries, andCPasymmetries. Using theW-boson annihilation (exchange) mechanism, the branching fractions ofB⟶BB′¯are shown to be interpretable. In the approach of perturbative QCD counting rules, we study the three-body decay channels. In particular, we review theCPasymmetries ofB⟶BB′¯M, which are promising to be measured by the LHCb and Belle II experiments. Finally, we remark the theoretical challenges in interpretingBB−⟶pp¯ρ−andBB−⟶pp¯μ−ν¯μ.

Revisiting semileptonic B−→pp¯ℓ−ν¯ℓ decays

We systematically revisit the baryonic four-body semileptonic decays of $B^- \to {\bf B}\bar{\bf B}'\ell^- \bar{\nu}_{\ell}$ by the perturbative QCD counting rules with ${\bf B}$ representing octet baryons and $\ell=e,\mu$. We study the transition form factors of $B^- \to {\bf B} \bar{\bf B}'$ in the limit of $(p_{\bf B}+p_{\bar{\bf B}'})^2 \to \infty $ with the three-body $\bar{B}\to {\bf B}\bar{\bf B}' M$ and $B^- \to p\bar{p} \mu^- \bar{\nu}_{\mu}$ data along with $SU(3)_f$ flavor symmetry. We calculate the decay branching ratios and angular asymmetries as well as the differential decay branching fractions of $B^- \to p \bar{p} \ell^- \bar{\nu}_{\ell}$. In particular, we find that our new result of ${\cal B}( B^- \to p \bar{p} \ell^- \bar{\nu}_{\ell})=(5.21\pm0.34)\times 10^{-6}$, which is about one order of magnitude lower than the previous theoretical prediction of $(10.4\pm2.9)\times 10^{-5}$, agrees well with both experimental measurements of $(5.8^{+2.6}_{-2.3})\times 10^{-6}$ and $(5.3\pm0.4)\times 10^{-6}$ by the Belle and LHCb Collaborations, respectively. We also evaluate the branching ratios and angular asymmetries in other channels of $B^- \to {\bf B}\bar{\bf B}\ell^- \bar{\nu}_{\ell}$, which can be tested by the ongoing experiments at LHCb and BelleII.

Using QCD counting rules to identify the production of gluonium

The empirical identification of bound states of gluons has remained a central goal of hadron spectroscopy. We suggest an experimentally challenging, but model–independent way to assess which zero charge, isospin-zero mesons have a large gluonium light-front wavefunction component in the quark and gluon Fock space of QCD. Our method exploits QCD counting rules which relate the power-law fall-off of production amplitudes at high momentum transfer to the meson's twist (dimension minus spin of its minimum interpolating operators). Scalar 0+ glueballs composed of two valence gluons with zero internal orbital angular momentum have twist τ=2. In contrast, quark-antiquark |qq¯〉 scalar mesons have twist τ≥3 since they have nonzero orbital angular momentum, and multi-quark states such as |qqq¯q¯〉 tetraquarks yield twist τ≥4. Thus, the production cross section for both |qq¯〉 and |qqq¯q¯〉 mesons will be suppressed by at least one power of momentum transfer relative to glueball production. For example, in single inclusive particle hadroproduction AB→CX, the cross section for glueball production at high transverse momentum pT and fixed xT=2pTs will dominate higher twist mesons by at least two powers of pT.Similarly, in exclusive production processes at large CM energy and fixed CM angle, the glueball rate dominates by a power of s: we illustrate the method with a simple reaction, e−e+→ϕf0 where the f0 can be tested to be a glueball versus another type of scalar meson.

Radiative and semileptonic B decays involving higher K-resonances in the final states

We study the radiative and semileptonic B decays involving a spin-J resonant \(K_{J}^{(*)}\) with parity (−1)J for \(K_{J}^{*}\) and (−1)J+1 for K J in the final state. Using large energy effective theory (LEET) techniques, we formulate \(B\to K_{J}^{(*)}\) transition form factors in the large recoil region in terms of two independent LEET functions \(\zeta_{\perp}^{K_{J}^{(*)}}\) and \(\zeta_{\parallel}^{K_{J}^{(*)}}\), the values of which at zero momentum transfer are estimated in the BSW model. According to the QCD counting rules, \(\zeta_{\perp,\parallel}^{K_{J}^{(*)}}\) exhibit a dipole dependence in q 2. We predict the decay rates for \(B\to K_{J}^{(*)}\gamma\), \(B\to K_{J}^{(*)}\ell^{+}\ell^{-}\) and \(B\to K_{J}^{(*)}\nu \bar{\nu}\). The branching fractions for these decays with higher K-resonances in the final state are suppressed due to the smaller phase spaces and the smaller values of \(\zeta^{K_{J}^{(*)}}_{\perp,\parallel}\). Furthermore, if the spin of \(K_{J}^{(*)}\) becomes larger, the branching fractions will be further suppressed due to the smaller Clebsch–Gordan coefficients defined by the polarization tensors of the \(K_{J}^{(*)}\). We also calculate the forward–backward asymmetry of the \(B\to K_{J}^{(*)}\ell^{+}\ell^{-}\) decay, for which the zero is highly insensitive to the K-resonances in the LEET parametrization.

CP-violating asymmetries inB0decays toK+K−KS(L)0andKS0KS0KS(L)0

Decay rates and time-dependent and direct CP asymmetries in the decays $B^0\to K^+K^-K_{S(L)}$ and $K_S K_S K_{S(L)}$ are studied. Resonant and nonresonant contributions to the three-body decays are carefully investigated. Nonresonant effects on 2-body and 3-body matrix elements are constrained by QCD counting rules. The predicted branching ratios are consistent with the data within the theoretical and experimental errors, though the theoretical central values are somewhat smaller than the experimental ones. Owing to the presence of color-allowed tree amplitudes in $B^0\to K^+K^-K_{S(L)}$, this penguin-dominated mode is subject to a significant tree pollution and the deviation of the mixing-induced \CP asymmetry from that measured in $B\to J/\psi K_S$, namely, $\Delta \sin 2\beta_{K^+K^-K_{S(L)}}\equiv \sin 2\beta_{K^+K^-K_{S(L)}}-\sin 2 \beta_{J/\psi K_S}$, can be as large as O(0.10). In contrast, the $K_SK_SK_{S(L)}$ modes appear theoretically very clean in our picture with negligible $\Delta\sin 2\beta_{K_SK_SK_{S(L)}}$. Direct CP asymmetries in $K^+K^-K_{S(L)}$ and $K_S K_S K_{S(L)}$ modes are found to be very small.

Selection rules forJPCexotic hybrid meson decay in largeNc

The coupling of a neutral hybrid {1,3,5...}^-+ exotic particle (or current) to two neutral (hybrid) meson particles with the same J^PC and J=0 is proved to be sub-leading to the usual large-N_c QCD counting. The coupling of the same exotic particle to certain two - (hybrid) meson currents with the same J^PC and J=0 is also sub-leading. The decay of a {1,3,5...}^-+ hybrid to eta pi^0, eta' pi^0, eta' eta, eta(1295) pi^0, pi(1300)^0 pi0, eta(1440) pi^0, a_0(980)^0 sigma or f_0(980) sigma is sub-leading, assuming that these final state particles are (hybrid) mesons in the limit of large N_c.

Evidence for factorization in three-body $\overline B\to D^{(*)}\,K^-\,K^0$ decays

Motivated by experimental results on $\overline B\to D^{(*)}K^{-}K^{0}$ , we use a factorization approach to study these decays. Two mechanisms concerning kaon pair production arise: current-produced (from vacuum) and transition (from the B meson). The kaon pair in the $\overline B {}^0\to D^{(*)+}K^{-}K^0$ decays can be produced only by the vector current (current-produced), whose matrix element can be extracted from $e^+e^{-}\to K\overline K$ processes via isospin relations. The decay rates obtained this way are in good agreement with experiment. The B–→ D(*)0K– K0 decays involve both current-produced and transition processes. By using QCD counting rules and the measured B–→ D(*)0 K– K0 decay rates, the measured decay spectra can be understood. PACS: 13.25.Hw – 14.40.Nd

Three-body baryonic $\overline B\to \Lambda \bar p \pi$ decays and such

We study decay rates and spectra of anti-B --> Lambda anti-p pi, Sigma0 anti-p pi, Sigma- anti-n pi, Xi0 anti-Sigma+ pi, Xi- anti-Sigma0 pi and Xi- anti-Lambda pi modes under a factorization approach. The baryon pairs are produced through vector, axial vector, scalar and pseudoscalar operators. Previous predictions, including ours, are an order of magnitude too small compared to experiment. By incorporating QCD counting rules and studying the asymptotic behavior, we find an earlier relation between the pseudoscalar and axial vector form factors to be too restrictive. Instead, the pseudoscalar and scalar form factors are related asymptotically. Following this approach, the measured Lambda anti-p pi rate (~4.0x10^{-6}) and spectrum can be understood, and Lambda should be dominantly left-hand polarized, while we expect Br(Sigma0 anti-p pi)~1.6x10^{-6}. These results and other predictions can be checked soon.

Evidence for factorization in three-bodyB¯→D(*)K−K0decays

Motivated by recent experimental results, we use a factorization approach to study the three-body B --> D(*) K- K0 decay modes. Two mechanisms are proposed for kaon pair production: current-produced (from vacuum) and transition (from B meson). The Bbar0 --> D(*)+ K- K0 decay is governed solely by the current-produced mechanism. As the kaon pair can be produced only by the vector current, the matrix element can be extracted from e+ e- --> K Kbar processes via isospin relations. The decay rates obtained this way are in good agreement with experiment. Both current-produced and transition processes contribute to B- --> D(*)0 K- K0 decays. By using QCD counting rules and the measured B- --> D(*)0 K- K0 decay rates, the measured decay spectra can be understood.

Charmless three-body baryonicBdecays

Motivated by recent data on $\stackrel{\ensuremath{\rightarrow}}{B}p\overline{p}K$ decay, we study various charmless three-body baryonic B decay modes, including $\ensuremath{\Lambda}\overline{p}\ensuremath{\pi},$ ${\ensuremath{\Sigma}}^{0}\overline{p}\ensuremath{\pi},$ $p\overline{p}\ensuremath{\pi},$ $p\overline{p}{K}^{0},$ in a factorization approach. These modes have rates of order ${10}^{\ensuremath{-}6}.$ There are two mechanisms for the production of baryon pairs: current produced and transition. The behavior of decay spectra from these baryon production mechanisms can be understood by using QCD counting rules. Predictions on rates and decay spectra can be checked in the near future.

K ∗±(892) Production in π −N interactions at 200 GeV/c

K ∗±(892) production is studied in the reaction π −N → K S 0K S 0 + X where X includes up to five observed charged particles. An excess of K ∗− over K ∗+ is observed for Feynman- x > 0.1. The ratio of K ∗+ to K ∗− decreases with x as predicted by QCD counting rules. K S 0 and K ∗ production are compared to recent D and D ∗ data from other experiments.