Radiative QCD backgrounds to exclusive $H\to b\bar{b}$ production: radiation from the screening gluon

Central exclusive Higgs boson production, pp→p ⊕ H ⊕ p, at the LHC can provide an important complementary contribution to the comprehensive study of the Higgs sector in a remarkably clean topology. The \(b\bar{b}\) Higgs decay mode is especially attractive, and for certain BSM scenarios may even become the discovery channel. Obvious requirements for the success of such exclusive measurements are strongly suppressed and controllable backgrounds. One potential source of background comes from additional gluon radiation which leads to a three-jet \(b\bar{b}g\) final state. We perform an explicit calculation of the subprocesses \(gg\to q\bar{q}g\), gg→ggg in the case of ‘internal’ gluon radiation from the spectator, t-channel screening gluon, when the two incoming active t-channel gluons form a color octet. We find that the overall contribution of this source of background is orders of magnitude lower than that caused by the main irreducible background resulting from the \(gg^{\mathrm{PP}}\to b\bar{b}\) subprocess. Therefore, this background contribution can be safely neglected.     

Possible violation of the δS=δQ selection rule in leptonic decays of σ+-hyperons

We have found a possible example of the rare decayσ ⁺ →nΜ ⁺ Ν, which violatesδS=δQ. The positive decay track of theσ ⁺ comes to rest in the hydrogen bubble chamber and decays into ane ⁺. This track has all the characteristics of a stoppingΜ ⁺. The decay neutron fortuitously scatters twice, producing two recoil protons. The only other possible interpretation of the event isσ ⁺→nγ(π ⁺ →Μ ⁺ Ν), where theπ ⁺ →Μ ⁺ Ν decay produces no deflection (θ<0.1 rad) and no significant change in curvature. Using thep-wave radiative decay predictions ofBarshay et al. we calculate that the integrated branching ratio for such “accidental” events isγ(σ ⁺ →nγ(π ⁺ →Μ _stop ⁺ Ν))/γ(σ ⁺ →nπ ⁺)=1.6×10^?6. Most of the contribution to this “accidental” branching ratio comes from radiative decays where theπ ⁺ mesons have ranges less than 1 mm (p _π<20 MeV/c). If one excludes thoseΜ's with ranges less than 1.2 cm the above “accidental” branching ratio becomes 5.5×10^?7. With this figure we estimate that we should have seen 6.5×10^?2 events of this type thusfar in our experiment. The neutron momentum does not help in deciding between the two hypotheses. We therefore assign a confidence level of 7% for the radiative hypothesis. For the leptonic hypothesis we obtain an estimate of the branching ratio,γ(σ ⁺ →nΜ ⁺ Ν)/γ(σ ⁺ →nπ ⁺)=5×10^?5. If one further accepts theσ ⁺ →nπ ⁺ Ν event reported byBarbaro-Galtieri et al. and theσ ⁺ →ne ⁺ Ν event reported byNauenberg et al., one obtains theδS=?δQ leptonic branching ratio [γ(σ ⁺ →nΜ ⁺ Ν)+γ(σ ⁺ →ne ⁺ Ν)]/γ(σ ⁺ →nπ ⁺)=(4±3)×10^?5.     

Simple models of the contribution of intermediate stage gluons to J/ψ suppression at the CERN SPS

We construct three simple scenarios of the time dependence of density of intermediate stage gluons in nuclear collisions in the CERN SPS energy range. Gluons with energy of about 0.6–1.0 GeV are assumed to be produced in nucleon-nucleon collisions in a Glauber type model. The rate of gluon production is given by the parameter n _g/nn equal to the average number of gluons produced per nucleon-nucleon collision. The value of this parameter determines the behaviour of the gas of gluons. The number of gluons increases due to gluon branching and processes like g+g → g+g+g and decreases due to the hadronization. Gluons are assumed to be able to dissociate J/ψ in g+J/ψ collisions, the dissociation cross-section σ _gγ is taken as a free parameter. In the first scenario, the energy density of the gas of gluons never reaches the critical energy density ε _c ≈ 0.7 GeV/fm³ and gluons rapidly hadronize. In the second scenario, the critical energy density is reached but the system of gluons is unable to reach thermalization. In the third scenario gluons reach thermalization and the thermalized system suppresses J/ψ by the Matsui-Satz mechanism. The third scenario under the assumption of a small value of σ _gψ is able to describe qualitatively the data on J/ψ suppression in Pb?Pb interactions obtained by the NA50 Collaboration. Other scenarios have problems with getting the rather abrupt onset of J/ψ suppression.     

Calculation of HELAS amplitudes for QCD processes using graphics processing unit (GPU)

We use a graphics processing unit (GPU) for fast calculations of helicity amplitudes of quark and gluon scattering processes in massless QCD. New HEGET (HELAS Evaluation with GPU Enhanced Technology) codes for gluon self-interactions are introduced, and a C++ program to convert the MadGraph generated FORTRAN codes into HEGET codes in CUDA (a C-platform for general purpose computing on GPU) is created. Because of the proliferation of the number of Feynman diagrams and the number of independent color amplitudes, the maximum number of final state jets we can evaluate on a GPU is limited to 4 for pure gluon processes (gg→4g), or 5 for processes with one or more quark lines such as $q\overline{q}\rightarrow 5g$ and qq→qq+3g. Compared with the usual CPU-based programs, we obtain 60–100 times better performance on the GPU, except for 5-jet production processes and the gg→4g processes for which the GPU gain over the CPU is about 20.     

Effect of FCNC mediated <Emphasis Type="Italic">Z</Emphasis> boson on lepton flavor violating decays

We study the three body lepton flavor violating (LFV) decays μ ^?→e ^? e ⁺ e ^?, \(\tau^{-} \to l_{i}^{-} l_{j}^{+} l_{j}^{-}\) and the semileptonic decay τ→μφ in the flavor changing neutral current (FCNC) mediated Z boson model. We also calculate the branching ratios for LFV leptonic B decays, B _d,s →μe, B _d,s →τe, B _d,s →τμ and the conversion of muon to electron in Ti nucleus. The new physics parameter space is constrained by using the experimental limits on μ ^?→e ^? e ⁺ e ^? and τ ^?→μ ^? μ ⁺ μ ^?. We find that the branching ratios for τ→eee and τ→μφ processes could be as large as \({\sim}{\mathcal{O}}(10^{-8})\) and \(\mathrm{Br}(B_{d,s} \to \tau \mu,~ \tau e) \sim {\mathcal{O}}(10^{-10})\). For other LFV B decays the branching ratios are found to be too small to be observed in the near future.     

Master integrals for double real radiation emission in heavy-to-light quark decay

We evaluate analytically the master integrals for double real radiation emission in the \(b \rightarrow u W^*\) decay, where b and u are a massive and massless quark, respectively, while \(W^{*}\) is an off-shell charged weak boson. Since the W boson can subsequently decay in a lepton anti-neutrino pair, the results of the present paper constitute a further step toward a fully analytic computation of differential distributions for the semileptonic decay of a b quark at NNLO in QCD. The latter partonic process plays a crucial role in the study of inclusive semileptonic charmless decays of B mesons. Our results are expressed in terms of multiple polylogarithms of maximum weight four.     

Penguin decays of B meson

The theory of loop induced rare B decays is reviewed. Both electromagnetic penguin processes and gluon mediated penguin processes are discussed. After consideringb→sy andb→se ⁺ e ^? decays, purely hadronic modes likeB→K? are estimated. Constraints on the Higgs sector of SUSY theory fromb→sy is discussed. CP violation in charged B Decays is reviewed.     

Winkelverteilungen elastisch an Edelgas-Atomstrahlen gestreuter Elektronen; Spinpolarisation eines an Argon gestreuten 40 eV-Elektronenstrahls

Various non-leptonic decay modes of baryons are calculated in a simple quark model. Form factors for various matrix elements are taken both from experiment and the quark model. Additionally theK→2π andK→3π decay modes are computed in the same model. The theory has theΔ I=1/2 rule and static SU⁶ built-in. A relation between the∑ ⁺→N ⁺ π ⁺ decay, not calculable in the model, and theK→3π decay is given via an effective six quark interaction. Agreement with experiment is order of magnitude for the baryonic decays and worse for theK decays.     

Limits on the scalar-leptoquark and scalar-gluon masses from the parameters <Emphasis Type="Italic">S</Emphasis>, <Emphasis Type="Italic">T</Emphasis>, and <Emphasis Type="Italic">U</Emphasis> in the minimal model based on four-color symmetry

The contributions to the parameters S, T, and U of radiative corrections from the doublets of scalar leptoquarks and scalar gluons are analyzed within the minimal model based on four-color symmetry of the Pati-Salam type. It is shown that current experimental data on the parameters S, T, and U admit the existence of relatively light scalar leptoquarks and scalar gluons (of mass lower than 1 TeV), the best fit to experimental data being attained at mass values not greater than 400 GeV. In particular, the existence of scalar leptoquarks of mass below 300 GeV is found to be compatible with data on the parameters S, T, and U at χ² < 3.1 (3.2) for m_H = 115 (300) GeV as against χ _SM ² = 3.5 (5.0) in the Standard Model. The mass of the lightest scalar gluon is then predicted to be less than 850 (720) GeV. It is emphasized that the aforementioned doublets of scalar leptoquarks and scalar gluons can play a significant role in processes involving a t quark at LHC.     

Angular distributions in the decays of the triplet <Emphasis Type="Italic">D</Emphasis><Subscript>2</Subscript> state of charmonium directly produced in polarized proton–antiproton collisions

Using the helicity formalism, we calculate the combined angular distribution function of the two gamma photons and the electron in the cascade process \({\bar{p}p}\to{}^{3}{D}_{2}\to\chi_{J}+\gamma_{1}\to(\psi +\gamma_{2})+\gamma_{1}\to({e}^{+}+{e}^{-})+\gamma_{1}+\gamma_{2}\) (J=0,1,2), when \({\bar{p}}\) and p are arbitrarily polarized. We also present the partially integrated angular distribution functions in six different cases. Our results show that by measuring the two-particle angular distribution of γ ₁ and γ ₂ and that of γ ₁ and e ^?, one can determine the relative magnitudes as well as the relative phases of all the helicity amplitudes in the two radiative decay processes ³ D ₂→χ _J +γ ₁ and χ _J →ψ+γ ₂.     

Asymptotics of Self-similar Solutions to Coagulation Equations with Product Kernel

We consider mass-conserving self-similar solutions for Smoluchowski’s coagulation equation with kernel K(ξ,η)=(ξη) ^λ with λ∈(0,1/2). It is known that such self-similar solutions g(x) satisfy that x ^?1+2λ g(x) is bounded above and below as x→0. In this paper we describe in detail via formal asymptotics the qualitative behavior of a suitably rescaled function h(x)=h _λ x ^?1+2λ g(x) in the limit λ→0. It turns out that \(h \sim 1+ C x^{\lambda/2} \cos(\sqrt{\lambda} \log x)\) as x→0. As x becomes larger h develops peaks of height 1/λ that are separated by large regions where h is small. Finally, h converges to zero exponentially fast as x→∞. Our analysis is based on different approximations of a nonlocal operator, that reduces the original equation in certain regimes to a system of ODE.     

Polarized angular distributions in the decays of the singlet D2 state of charmonium originating from $\bar{p}p$ collisions

Using the helicity formalism, we calculate the combined angular distribution function of the neutral pion (π ⁰) and the polarized electron (e ^?) and photon (γ) produced in the triple cascade process \(\bar{p}+p\rightarrow{}^{1}D_{2}\rightarrow{}^{1}P_{1}+\gamma\rightarrow(\psi +\pi^{0})+\gamma \rightarrow(e^{-}+e^{+})+\pi^{0}+\gamma\), when \(\bar{p}\) and p are unpolarized. We also present the partially integrated angular distribution functions in three different cases where the combined angular distribution function of the three particles is integrated over the direction of one of the particles. Our results show that by measuring the two-particle angular distribution of the electron and the photon with the polarization of either particle, one can determine the relative magnitudes as well as the relative phases of all the angular-momentum helicity amplitudes in the two decay processes ¹ D ₂→¹ P ₁+γ and ¹ P ₁→ψ+π ⁰.     

High-pressure phases of Weyl semimetals NbP,NbAs, TaP,and TaAs

In this study, we used the crystal structure search method and first-principles calculations to systematically explore the highpressure phase diagrams of the TaAs family(NbP, NbAs, TaP, and TaAs). Our calculation results show that NbAs and TaAs have similar phase diagrams, the same structural phase transition sequence I4_1 md→P6 m2→P2_1/c→Pm3 m, and slightly different transition pressures. The phase transition sequence of NbP and TaP differs somewhat from that of NbAs and TaAs, in which new structures emerge, such as the Cmcm structure in NbP and the Pmmn structure in TaP. Interestingly, we found that in the electronic structure of the high-pressure phase P6 m2-NbAs, there are coexistingWeyl points and triple degenerate points, similar to those found in high-pressure P6 m2-TaAs.     

Elastic Deuteron Scattering on the <Superscript>12</Superscript>C Nucleus within a Three-Body Model

The formalism developed earlier for elastic pd scattering on the basis of Glauber theory with allowance for a total spin dependence is modified by replacing pN amplitudes by amplitudes for N¹²C scattering and is applied to elastic deuteron scattering on the ¹²C nucleus. The amplitudes for elastic N¹²C scattering are obtained within the optical model. Respective numerical calculations performed at the kinetic deuteron-beam energy of 270 MeV lead to results that agree well with data on the differential cross section for d¹²C scattering into the forward hemisphere, but the calculated spin observable A _y ^d agrees with experimental data only qualitatively.     

Account of energy losses of hard gluons in processes of <Emphasis Type="Italic">J</Emphasis>/ψ-meson production in proton–nucleus collisions

Processes of production of cc?-states in proton–nucleus collisions are considered. The model is proposed taking into account energy losses of hard gluons in inelastic interactions of hadron states with nucleus nucleons. Results of performed calculations on the A-dependence of inclusive spectra of pA → J/ψX processes are presented together with FNAL E866 experimental data.     

General expressions for extra-dimensional tree amplitudes and all-plus 1-loop integrands in $$\mathcal {}$$-cut representation

In this paper, we give the general expressions for a special series of tree amplitudes of the Yang–Mills theory. This series of amplitudes have two adjacent massless spin-1 particles with extra-dimensional momenta and any number of positive helicity gluons. With special helicity choices, we use the spinor helicity formalism to express these n-point amplitudes in compact forms, and find a clever way to use the BCFW recursion relations to prove the results. Then these amplitudes are used to form the complete 1-loop all-plus integrand with any number of gluons, expressed in the \(\mathcal {Q}\)-cut representation.     

Polarization of phosphorescence transitions and probabilities of intramolecular nonradiative deactivation of the lowest triplet state of aromatic molecules

This study continues the experimental testing of the validity of the inductive resonance theory of dipole-dipole energy transfer from the T ₁→S ₀ transition dipole to stretching vibrations of intramolecular CH bonds of naphthalene and its hydroxy derivatives. To this end, in the series of compounds under study, the range of variation of the geometrical parameter [Φ(CH)]² of the Förster theory, which accounts for the mutual orientation of the energy donor and acceptor, is estimated. Preliminarily, the angles between the transition dipole moments of the radiative and absorptive electronic transitions (T ₁→S ₀ and S ₀→S ₁; T ₁→S ₀ and S ₀→S ₂; S ₁→S ₀ and S ₀ →S ₁; and S ₁→S ₀ and S ₀→S ₂) are measured at 77 K by the method of polarization photoselection. From the polarization measurements, the angles between the phosphorescence transition dipole moment and the plane of a molecule are determined. It was found that, upon passage from naphthalene to its β derivatives, the orientation of the dipole moment of the radiative T ₁→S ₀ transition relative to the plane of a molecule markedly changes, with the in-plane component of the dipole moment being increased by an order of magnitude. The experimentally determined rate constants of nonradiative deactivation of the T ₁ state averaged over the CH groups of the naphthalene ring system, k _nr(CH), are compared with the rate constants [Φ(CH)]² of the inductive resonance energy transfer from the dipole of the T ₁→S ₀ transition to the dipole of the CH vibrations polarized in the plane of a molecule, calculated with regard to the orientational factor [Φ(CH)]². This comparison showed that, in the series of compounds under study, a change in the orientation of the dipole moment of the radiative T ₁→S ₀ transition relative to the plane of a molecule does not affect the rate of the nonradiative T ₁?S ₀ transition. This inference is confirmed by the absence of a correlation between the rate constants k _dd(CH) calculated by us (with regard to [Φ(CH)]²) and the well-known rate constants k _nr(CH) of individual sublevels of the T ₁ state measured at T≤1.35 K for a number of organic molecules. The possible sources of discrepancy between the experimental data that k _nr(CH) is independent of [Φ(CH)]² and the predictions of the theory are considered. A conclusion is made that the electronic-vibrational energy transfer between electric dipoles is the most probable mechanism of the T ₁?S ₀ transitions, but the rate constant of the dipole-dipole energy transfer upon interaction of the electronic and vibrational dipoles in a molecule does not depend on their orientations.     

Asymptocic Freedom of Gluons in Hamiltonian Dynamics

We derive asymptotic freedom of gluons in terms of the renormalized SU(3) Yang–Mills Hamiltonian in the Fock space. Namely, we use the renormalization group procedure for effective particles to calculate the three-gluon interaction term in the front-form Yang–Mills Hamiltonian using a perturbative expansion in powers of g up to third order. The resulting three-gluon vertex is a function of the scale parameter s that has an interpretation of the size of effective gluons. The corresponding Hamiltonian running coupling constant exhibits asymptotic freedom, and the corresponding Hamiltonian \({\beta}\) -function coincides with the one obtained in an earlier calculation using a different generator.     

On the Production of <Emphasis Type="Italic">J</Emphasis>/ψ-Mesons in Pion–Nucleus Collisions

The processes of J/ψ-mesons production in pion–nucleus collisions are considered. For the determination of the inclusive spectra πA → J/ψX, the model was used which takes into account the energy losses of hard gluons in the interactions of hadron states with the nucleus nucleons. The results of calculations are presented together with the experimental data of NA3 Collaboration on π^–Pt¹⁹⁵ → J/ψX spectra at the incident pions energies of 150 and 280 GeV.