Effective gauge theory and the effect of heavy quarks in Higgs boson decays

A general framework is given for evaluating the contributions of as yet undiscovered heavy quarks to the gluonic decay rate of the Weinberg-Salam type Higgs boson. Since the Yukawa coupling of the Higgs boson to a quark pair is proportional to the quark mass, loop graphs involving heavy quarks have a non-vanishing effect on the gluonic decay width of the Higgs boson. This effect of heavy quarks with massesM _j(j=t,...) much greater than the Higgs boson massm _H is calculated in an effective gauge theory. The effects of two different kinds of large logarithms, lnM _j ² /μ m _h ² /μ ² are separated and summed up by the renormalization group method. It is found that the higher order QCD corrections are large and that the gluonic contribution to the hadronic decay width is significant if there are more than three generations. The Higgs decay width can therefore be used to probe the number of generations of heavy quarks.     

Perturbative QCD and the exclusive decay of heavy quarkonium into a photon and two mesons

We consider the radiative decays of the ³S₁ ground state Q$\text{Q}$ into a real photon and two light pseudoscalar or vector mesons. For sufficiently large mass of the heavy quark Q, the decay, e.g. ? → γππ, can be calculated in perturbative QCD, provided that the photon does not carry away a predominant fraction of the available energy. We present differential and integrated Dalitz plot distributions and, for quarkonium states produced with transverse polarization in e⁺e^? annihilation, angular distributions of the orientation of the decay triangle relative to the beam direction.     

Jet-like distributions from the weak decay of heavy quarks

We consider the production and weak decay of a pair of heavy quarks (mesons) ine ⁺ e ^? experiments and study their effect on the various jet distributions. The relative magnitudes of the two-quark-jet and three-quark-jet final states, in the decay of a heavy quark are estimated in the framework of an SU(2) _L ×U(1) model. We find that the three quark configuration dominates over the two quark configuration. For the quark jets resulting from the weak decay of the heavy quarks, we calculate the jet distributions in Sphericity, Spherocity and Thrust for the process \(e^ + e^ - \to Q\bar Q \to 6\) quarks. These distributions are compared with the corresponding quantities from the non-perturbative process \(e^ + e^ - \to q\bar q\) and the QCD process \(e^ + e^ - \to q\bar qg\) . We find that the weak decay of heavy quarks is the dominant mechanism for jet broadening ine ⁺ e ^? experiments, in the intermediate energy region relevant for PETRA and PEP.     

Semileptonic decays of heavy quarks in quantum chromodynamics

We investigate the semileptonic decays of heavy quarks in the leading non-trivial order in quantum chromodynamics. Effects of gluon corrections and the initial quark Fermi motion on the semileptonic rates and decay distributions are calculated. The resulting lepton energy spectrum for the charm semileptonic decay is compared with data to extract the mass of the charm quark. This is combined with the semileptonic branching ratio to predict the charm-quark lifetime. We find the lepton energy spectrum very stable with respect to gluon corrections. Expected spectra from the semileptonic decays of bottom and top quarks are presented. We also study the semileptonic decay process Q → q?v_? + G, involving the emission of a single hard non-collinear gluon. This process should be observable with a branching ratio of a few percent in the decays of top (and heavier) quarks.     

Generalized on-shell renormalization of heavy quarks

A generalized on-shell (GOS) renormalization scheme of QCD is developed to evaluate the renormalization of heavy quark wave functions and currents. All large logarithms arising from the physical range of quark masses and momentum transferq ² can be absorbed into wave function and vertex renormalization. Our results are more general than those of the heavy quark effective theory and agree with the latter only at zero recoil. The proposed GOS scheme is very suitable for the /m _Q expansion. As an application we discuss the renormalization of the flavour changing currentsb-c, t-b andt-c.Supported by Bundesministerium für Forschung und Technologie (BMFT)     

Calculable observables in quantum chromodynamics: (II). Heavy quark production

It is argued that the color-averaged inclusive cross section dσ/d³p for the production of a heavy quark of given momentum p and given flavor is infrared-singularity free and therefore calculable in perturbative QCD if it is evaluated away from heavy quark thresholds and if the typical reaction energy Q is such that α_s(Q)ln[Q/m(Q)] is small, α_s and m being the strong coupling constant and the heavy quark mass respectively. An interpretation of this cross section is proposed in terms of heavy flavor hadronic production.     

Weak radiative decay Λ b →Λγ in the heavy quark effective theory

The weak radiative decay Λ _b →Λγ is studied in the heavy quark effective theory treatings-quark as heavy. This rare decay is induced by the short distance electromagnetic penguins. Including corrections of the order of (1/m _Q), we obtain the transition matrix element and the corresponding decay width. The Isgur-Wise function is evaluated in the largeN _c limit and the branching ratio obtained is 1.48×10⁻⁵.     

Non-leptonic weak decay rate of explicitly flavored heavy mesons

It is argued quantitatively that a large difference between the D⁰ and D⁺ lifetimes is mainly due to non-perturbative long-distance effects. The total non-leptonic weak decay rates are related to the soft limit of short-distance processes. Scaling laws for the decay rates of heavy mesons with respect to mass are inferred from the QCD analysis of the soft limit of fragmentation. It is found that the decay rates are not determined by the disconnected spectator diagrams alone even in the limit of the heavy quark mass M going to infinity (< M_W), since the leading term after the QCD correction scales like M⁵ exp √clog M. Some numerical discussion is made for the decay of B mesons and T mesons.     

The QCD sum rule approach for the semileptonic decay of the D or B meson into a light meson and leptons

We use the method of QCD sum rules to treat the semileptonic weak decay of the D or B meson into a light meson and leptons. To obtain the transition form factors, we adopt the two-point Green’s function in the presence of an external vector or axial-vector field. We find that this method can be related approximately to the traditional three-point Green’s function in the heavy quark limit (m _Q → ∞). Unlike some existing QCD sum rule calculations, our results indicate that the form factors have simple dipole or monopole behavior. We obtain results on the various form factors of the semileptonic decay of D and B mesons into a light meson and investigate various decay processes such as B?⁰ → π ⁺ τ _^?ν?_τ and B?⁰ → ρ ⁺ τ^～ν?_τ. The method allows us to take into account nonperturbative strong interaction effects, thereby providing a more reliable determination of the Cabibbo-Kobayashi-Maskawa matrix elements from the experimental data.     

Baryon wave functions and nucleon decay

We apply to nucleon decay the knowledge about the short-distance structure of baryon wave functions gleaned from QCD form factor calculations nd the $\text{J}\text{gY →}\text{p}\text{?}\text{p}$ decay rate. We review the uncertainties arising when current algebra and PCAC are used to relate $\text{N}\text{→}\text{?}\text{+}$ meson decay rates to 〈0|qqq|N〉 matrix elements. We show that the relevant matrix elements are not directly related to those of the leading twist operators “measured” in conventional high momentum transfer physics, but argue for an indirect based on models that fit both form factor and $\text{J}\text{Ψ}$ decay data. We use these inputs to calculate the p → e⁺π⁰ decay rate in minimal SU(5) and other grand unified theories (GUTs) for a specified value of the heavy vector boson mass m_X. Our results combined with the recent experimental lower limit on this mode indicate that m_X > 2 × 10¹⁵ GeV in the minimal SU(5) GUT, and we derive analogous bounds for supersymmetric GUTs. Our calculated lifetime for a given value of m_X is considerably shorter than previous estimates made using non-relativistic SU(6) or the bag model, a difference traceable to the different normalizations of 2 and 3 quark wave functions at short distances.     

On the Standard Model prediction for \mathcal{B}(B_{s,d} \to \mu^{+} \mu^{-})

The decay B _s →μ ⁺ μ ^? is one of the milestones of the flavor program at the LHC. We reappraise its Standard Model prediction. First, by analyzing the theoretical rate in the light of its main parametric dependence, we highlight the importance of a complete evaluation of higher-order electroweak corrections, at present known only in the large-m _t limit, and leaving sizable dependence on the definition of electroweak parameters. Using insights from a complete calculation of such corrections for $K\to\pi\nu\bar{\nu}We present O(?? _s ) results on the decays of polarized W ^± and Z bosons into massive quark pairs. The NLO QCD corrections to the polarized decay functions are given up to the second order in the quark mass expansion. We find a surprisingly strong dependence of the NLO polarized decay functions on finite quark mass effects even at the relatively large mass scale of the W ^± and Z bosons. As a main application we consider the decay t??b+W ⁺ involving the helicity fractions ?? _mm of the W ⁺ boson followed by the polarized decay $W^{+}(\uparrow)\to q_{1}\bar{q}_{2}$ for which we determine the O(?? _s ) polar angle decay distribution. We also discuss NLO polarization effects in the production/decay process $e^{+}e^{-}\to Z(\uparrow)\to q\bar{q}$ .     

A CP violating mixing matrix compatible with neutral flavour conservation and spontaneous CP violation

A specific ansatz for the Yukawa couplings of a four-generation SU(2)_L×U(1) model with two Higgs doublets is discussed which leads to neutral flavour conservation, spontaneous CP violation and to a genuinely complex mixing matrix. W exchange conserves CP in the limit m_t′ = m_t only. The decay rate for t→b is reduced by factor two compared to the standard model wit three generations. The phenomenological implications for K⁰−K̄⁰ and B⁰−B̄⁰ are investigated.     

Bound states of light and heavy quarks in hot hadronic matter

The correlators of currents \(\bar q\) Q,γ _v γ ₅ Q,q andQ being correspondingly light and heavy quark fields, in hot hadronic matter are investigated by means of finite temperature QCD sum rules. AtT? 100 MeV the modification of the effective spectrum parameters takes place, similar to that found earlier in the correlators of light quark currents. AtT?150 MeV the form of the spectrum is obtained, which indicates an appearance in hadronic matter of quasifree quarks with nonzero mass being fixed by the value of the quark condensate 〈 \(\bar q\) q〉 (T).     

A model for chiral symmetry breaking in QCD

A recently proposed model for dynamical breaking of chiral symmetry in QCD is extended and developed for the calculation of pion and chiral symmetry breaking parameters. The pion is explicitly realized as a massless Goldstone boson and as a bound state of the constituent quarks. We compute, in the limit of exact chiral symmetry, M_Q, the constituent quark mass $\text{?}{}_{\mathrm{\pi }}$ the pion decay coupling, $\text{〈}\text{u}\text{u〉}$, the constituent quark loop density, μ_π²/m_q, the ratio of the Goldstone boson mass squared to the bare quark mass, and 〈r²〉_π, the pion electromagnetic charge radius squared.     

A string-breaking model of heavy meson decays

Within QCD, heavy quarkonia are viewed as a quark antiquark pair bound by a narrow chromoelectric flux tube. This flux can create light quark antiquark pairs accounting for the decay into mesons with heavy quantum numbers. This model is shown to be as consistent with current data on charmonium decays intoD-meson pairs and upsilon decay to \(B\bar B\) , as is the physically less appealing³ P ₀ model.     

Bounds on a top quark with charged Higgs decay

If the top quark decays to a charged Higgs boson t→bH⁺, semileptonic decay signatures are suppressed and the mass bounds set by the UA1 top search are evaded. However the charged Higgs decay mode H⁺→τ⁺ν_τ gives a missing-ϱ_T signature; depending on the decay branching fraction and using the UA1 limits on new physics contributions to missing-ϱ_T, we set bounds on the top mass in this scenario. We also evaluate the feasibility of seeking visible-τ-jet signals for top at a pp̄ collider.     

Spin-dependent parton distributions in polarized deep inelastic lepton nucleon scattering

We analyze the recently measured first moment Г ^p (Q ²) of the structure functiong ₁ ^p (x,Q ²) obtained in deep inelastic scattering of polarized electrons from polarized protons. It is shown that the recent experimental result Г ^p (〈Q ²〉?10 GeV²)? 0.113 implies a polarized strange quark sea whose total polarization Δs(μ²)??0.22 is comparable to Δμ(μ²)?0.74 and Δd(μ²)??0.50 already at a typically hadronic scale μ=0(1 GeV). Most remarkably, the total polarization due to quark distributions Δμ(μ²)+Δd(μ²)+Δs(μ²) practically vanishes which implies that the spin of the proton is carried by the gluons, ΔG(μ²), and/or the angular momentum of the partons. This surprising conjecture can be experimentally tested with heavy quark production in longitudinally polarized lepton-nucleon scattering. In particular the (real) photon-gluon fusion process γg→Q \(\bar Q\) provides a rather unique measure of ΔG(x,Q ²).     

Radiative leptonic decays of heavy mesons in heavy quark limit

We study the radiative leptonic decays of heavy mesons within the covariant light-front model. Using this model, both the form factors F_V and F_A have the same form when the heavy quark limit is taken. In addition, the relation between the form factor F_V and the decay constant of a heavy meson F_H is obtained. The hadronic parameter β can be determined by the parameters appearing in the wave function of the heavy meson. We find that the value of β is not only quite smaller than the one in the non-relativistic case, but also insensitive to the value of the light quark mass m_q. These results mean that the relativistic effects are very important in this work. We also obtain that the branching ratio of B→lν_lγ is about (1.40–1.67)×10^-6, in agreement with the general estimates in the literature. PACS 12.39.Hg; 13.40.Gp     

Mass corrections to the tau decay rate

In this note radiative corrections to the total hadronic decay rate of the τ-lepton are studied employing perturbative QCD and the operator product expansion. We calculate quadratic quark mass corrections to the decay rate rationR _τ to the order0(α _s ² m²) and find that they contribute appreciably to the Cabbibo supressed decay modes of the τ-lepton. We also discuss corrections of mass dimensionD=4, where we emphasize the need of a suitable choice of the renormalization scale of the quark and gluon condensates.     

Comment on resummation of mass distribution for jets initiated by massive quarks

We compute in the heavy quark effective theory the soft coefficient D₂ entering the resummation of next-to-next-to-leading threshold logarithms for jets initiated by a quark with a small mass compared to the hard scale of the process. We find complete agreement with a previous computation in full QCD. Contrary to our previous guess, this coefficient turns out to be different from that one entering heavy flavor decay or heavy flavor fragmentation.