Pseudoscalar Case Research Articles

Systematizing the effective theory of self-interacting dark matter

If dark matter has strong self-interactions, future astrophysical and cosmological observations, together with a clearer understanding of baryonic feedback effects, might be used to extract the velocity dependence of the dark matter scattering rate. To interpret such data, we should understand what predictions for this quantity are made by various models of the underlying particle nature of dark matter. In this paper, we systematically compute this function for fermionic dark matter with light bosonic mediators of vector, scalar, axial vector, and pseudoscalar type. We do this by matching to the nonrelativistic effective theory of self-interacting dark matter and then computing the spin-averaged viscosity cross section nonperturbatively by solving the Schrödinger equation, thus accounting for any possible Sommerfeld enhancement of the low-velocity cross section. In the pseudoscalar case, this requires a coupled-channel analysis of different angular momentum modes. We find, contrary to some earlier analyses, that nonrelativistic effects only provide a significant enhancement for the cases of light scalar and vector mediators. Scattering from light pseudoscalar and axial vector mediators is well described by tree-level quantum field theory.

Dynamical evidence for a fifth force explanation of the ATOMKI nuclear anomalies

Recent anomalies in $^8$Be and $^4$He nuclear decays can be explained by postulating a fifth force mediated by a new boson $X$. The distributions of both transitions are consistent with the same $X$ mass, 17 MeV, providing kinematic evidence for a single new particle explanation. In this work, we examine whether the new results also provide dynamical evidence for a new particle explanation, that is, whether the observed decay rates of both anomalies can be described by a single hypothesis for the $X$ boson's interactions. We consider the observed $^8$Be and $^4$He excited nuclei, as well as a $^{12}$C excited nucleus; together these span the possible $J^P$ quantum numbers up to spin 1. For each transition, we determine whether scalar, pseudoscalar, vector, or axial vector $X$ particles can mediate the decay, and we construct the leading operators in a nuclear physics effective field theory that describes them. Assuming parity conservation, the scalar case is excluded and the pseudoscalar case is highly disfavored. Remarkably, however, the protophobic vector gauge boson, first proposed to explain only the $^8$Be anomaly, also explains the $^4$He anomaly within experimental uncertainties. We predict signal rates for other closely related nuclear measurements, which, if confirmed, will provide overwhelming evidence that a fifth force has been discovered.

First Look at Heavy–Light Mesons with a Dressed Quark–Gluon Vertex

Following up on earlier work, we investigate possible effects of a dressed quark-gluon vertex in heavy-light mesons. In particular, we study corrections to the popular rainbow-ladder truncation of the Dyson-Schwinger-Bethe-Salpeter equation system. We adopt a simple interaction kernel which reduces the resulting set of coupled integral equations to a set of coupled algebraic equations, which are solved numerically. In this way, we extend previous studies to quark-antiquark systems with unequal current-quark masses, at first for the pseudoscalar case, and investigate the resulting set of problems and solutions. We attempt to find patterns in - as well as to quantify corrections to - the rainbow-ladder truncation. In addition, we open this approach to phenomenological predictions of the heavy quark symmetry.

OPE of the pseudoscalar gluonium correlator in massless QCD to three-loop order

In this paper analytical results are presented for higher order corrections to coefficient functions of the operator product expansion (OPE) for the correlator of two pseudoscalar gluonium operators $ {{\mathop{O}\limits^{\sim}}_1}={G^{{\mu v}}}\;{{\mathop{G}\limits^{\sim}}_{{\mu v}}} $ . The Wilson coefficient in front of the scalar gluon condensate operator $ {O_1}=-\frac{1}{4}{G^{{\mu v}}}{G_{{^{{\mu v}}}}} $ is given at three-loop accuracy. The leading coefficient C 0 in front of the unity operator O 0 = 1 has been calculated up to three-loop order some time ago [1] but has been checked independently in this work. It is interesting to see that the coefficient C 1 in the pseudoscalar case is finite, whereas contact terms appear in C 0 in this case and in both coefficients C 0 and C 1 in the cases of the scalar gluonium correlator and the energy momentum tensor correlator [2]. For the corresponding Renormalization Group invariant Wilson coefficients which are also constructed the results are partially extended to four-loop accuracy. All results are given in the $ \overline{\mathrm{MS}}-\mathrm{scheme} $ at zero temperature.

Production of scalar and pseudo-scalar Higgs bosons to next-to-next-to-leading order at hadron colliders

We consider the production of intermediate-mass CP-even and CP-odd Higgs bosons in proton-proton and proton-anti-proton collisions. We extend the recently published results for the complete next-to-next-to-leading order calculation for a scalar Higgs boson to the pseudo-scalar case and present details of the calculation that might be useful for similar future investigations. The result is based on an expansion in the limit of a heavy top quark mass and a subsequent matching to the expression obtained in the limit of infinite energy. For a Higgs boson mass of 120 GeV the deviation from the infinite-top quark mass result is small. For 300 GeV, however, the next-to-next-to-leading order corrections for a scalar Higgs boson exceed the effective-theory result by about 9% which increases to 22% in the pseudo-scalar case. Thus in this mass range the effect on the total cross section amounts to about 2% and 6%, respectively, which may be relevant in future precision studies.

Bound states and fermiophobic unparticle oblique corrections to the photon

We study the effects of fermiophobic scalar/pseudoscalar oblique corrections on bound state energy levels in muonic atoms. To make the treatment sufficiently general, while including ordinary scalar and axionlike pseudoscalar fields as special cases, we consider unparticle scalar/pseudoscalar operators with couplings predominantly to photons. We derive the relevant vacuum polarization functions and comment on the functional forms of the unparticle Uehling potentials for various scaling dimensions in the point nucleus and finite nucleus approximations. It is estimated that for an infrared fixed point near the scale of electroweak-symmetry breaking, in the low TeV range, and natural values for the model parameters, the energy shifts in the low-lying muonic-lead transitions are typically of the order of a few times 0.1 eV to a few times 0.01 eV. The energy level structures of the unparticle Uehling shifts are inferred using general methods for the scalar and pseudoscalar cases and it is shown that the two cases contribute to the energy shifts with the same sign. It is shown that this conclusion is not changed even when scale invariance is broken and is in fact relatively insensitive to the scale at which it is broken. It is pointed out nevertheless that the estimated magnitude of the unparticle Uehling shift (based on some natural values for the model parameters) is a factor of 1000--10000 below the discrepancy in QED/nuclear theory and precision muonic-lead spectroscopy from about two decades ago. We briefly comment on scenarios where the unparticle induced energy shift, if it exists, may be experimentally measurable. One possibility in this direction is if the UV sector, from which the unparticle sector arises, has a large number of fermions. Comments are also made on the possibility of further studying muonic atoms, as a probe for beyond-standard-model physics, in the context of forthcoming experiments, such as those probing lepton flavor violation through coherent muon-electron conversions. For completeness we explore some of the astrophysical and cosmological consequences of a fermiophobic scalar/pseudoscalar unparticle sector. In the fermiophobic context we also estimate a minimum value for the conformal invariance breaking scale.

Next-to-leading log resummation of scalar and pseudoscalar Higgs boson differential cross sections at the CERN LHC and Fermilab Tevatron

The region of small transverse momentum in $q\overline{q}$- and $gg$-initiated processes must be studied in the framework of resummation to account for the large, logarithmically enhanced contributions to physical observables. In this paper, we will calculate the fixed order next-to-leading order perturbative total and differential cross sections for both a Standard Model scalar Higgs boson and the Minimal Supersymmetric Standard Model's pseudoscalar Higgs boson in the Heavy Quark Effective Theory where the mass of the top quark is taken to be infinite. Resummation coefficients ${B}_{g}^{(2)},{C}_{gg}^{(2)}$ for the total cross-section resummation for the pseudoscalar case are given, as well as ${\overline{C}}_{gg}^{(1)}$ for the differential cross section.

Model solutions of regularized relativistic transport equations.

We present numerical solutions of recently proposed relativistic transport equations for fluctuating hadronic fields with simplified model Lagrangians containing a spin-1/2 nucleon and a light scalar or pseudoscalar meson. We introduce and implement a method for regularizing tadpoles and vector loops which is consistent with the previously proposed regularization of the scalar loops. The resulting solutions in vacuum are well behaved, exhibiting the expected differences between the scalar and pseudoscalar cases without apparent pathologies.

The Z 0 → Hγ decay in two-Higgs-doublet models

We have computed the Z 0 → Hγ decay width, where H can be either a scalar or pseudoscalar Higgs particle, in two Higgs doublet models. For the scalar Higgs we compare the result with standard model and show that there exists a domain of parameters such that the width is enhanced by one or two orders of magnitude. This requires a small charged Higgs mass ( M h < M w) as well as one large scalar boson mass ( M S1 ⪢ M S2). For the pseudoscalar case a comparison with Z → π 0γ is performed. Despite the phase space suppression the pseudoscalar Higgs decay mode can be much larger since it does not suffer from form factor suppression. In all calculations we respect the recent LEP limits and low energy constraints on Higgs masses.

Quantum-chromodynamic corrections to meson-photon transition form factors

We calculate corrections to the hard-scattering amplitude for meson-photon transition form factors using dimensional regularization. Special attention is paid to the pseudoscalar case in which there is an ambiguity associated with ${\ensuremath{\gamma}}_{5}$. We resolve this ambiguity by appealing to axial-vector Ward identities and check the answer by using a four-dimensional regularization.

Non-relativistic approximations to the pion production operator in 4He(p, n π+) 4He

Various non-relativistic pion production operators are applied in the study of the 4He(p, nπ +) 4He process. We compare their predictions with fully covariant calculations of the external emission graphs both for pseudovector and pseudoscalar coupling. It is found that the non-relativistic pion production operators cannot reproduce the relativistic results quantitatively, in particular for the pseudoscalar case. The simple static pion production operator gives agreement with the relativistic pseudovector results to within a factor three or four. Adding recoil terms to this static operator has a significant effect on the cross section but does not improve the agreement with the relativistic results. The implications of PCAC and the soft-pion theorem for the relativistic calculation are studied. The uncertainty in the cross section in the soft-pion approach is found to be considerably smaller than the difference between pseudovector and pseudoscalar results or between the relativistic pseudovector result and its non-relativistic approximations.

Behaviour of interacting fields on the light cone. The pseudoscalar case

In order to extend some results obtained in a previous paper, we consider a pseudoscalar boson field coupled with a fermion field. By means of general methods, developed along the lines of the Heisenberg philosophy, we study the leading singularities on the light cone of the commutators and the anticommutators. Our results indicate that the behaviour of the fermion field is not consistent with the assumption of a positive-definite metric.

Die darstellungen der starken kopplung und das resonanzproblem der meson-nucleon-streuung

This paper deals with the completion of the strong-coupling method in meson field theory. By means of a canonical and non-linear transformation of variables the original meson field is split into a free meson part and a self field part of the nucleon. The transformation is defined so that the interaction between the compound nucleon system thus arising and the free mesons vanishes in the case of infinitely strong coupling. It is shown that there exists a family of transformations satisfying the conditions. A system of equations for certain transformation functions is stated as the consequence of the conditions. The solutions of the field-splitting problem are investigated. The general scheme for a strong-coupling approximation method based on this field splitting is derived, and the problem of calculating the pion-nucleon resonance scattering from the strong coupling theory is treated on this basis. A special approximation is made for calculations near the resonance. Numerical results obtained from such a calculation are discussed. For the sake of simplicity the symmetric scalar fixed-source meson theory is used. But the principle of the method will be the same in the more essential but more complicated symmetric pseudoscalar case. Thus the present considerations will serve to guide an analogous investigation using the symmetric pseudoscalar theory.

The two-body problem in the extreme relativistic limit

In view of the composite model for elementary particles the two-body problem is studied in the extreme relativistic limit. Spinless particle-antiparticle bound states are investigated for a single massless self-interacting Weyl field. High momenta are suppressed in a Lorentz invariant manner by introducing a heavy auxiliary boson. A Bethe-Salpeter equation is set up in the ladder approximation. The consequences of the continuity equation are studied in the same approximation and are shown to be fulfilled automatically only for scalar bound states. A new method is presented for solving the Bethe-Salpeter equation. A spectral ansatz is made for the wave function which leads to a one-dimensional integral equation for the weight function when the rest mass of the bound state is neglected. This integral equation is solved in the Fredholm approximation for a somewhat modified cut-off prescription in the scalar case. With the same restriction, the eigenvalue is found also in the pseudoscalar case. It is shown that the method of solution can be extended to any order in the rest mass of the bound state.

Non-adiabatic treatment of the scattering of K+-mesons by nucleons

The problem of the K+-nucoleon scattering is treated with the method of Tamm-Dankoff in the two-meson approximation, both with scalar and pesudovector coupling. In both cases it turns out that the most important phase at low energy is T=1, which corresponds, to an attractive potential. In the scalar case this phase does not lead to a resonance; in the pseudoscalar case there is, however, a resonant state whose position, is strongly dependent on the momentum cut-offK. At the end of the work there is a brief discussion of the results obtained, in relation to the few experimental data so far available.

Some Notes on Multiple-Boson Processes

Methods of calculation with nonlinear functions of quantized boson fields are developed during the discussion of two problems involving multiple boson processes. In the first of these a simple treatment is given of the multiple radiation of photons by classical current distributions, a special case of which, in effect, is the infrared catastrophe. In the second illustration, generalizations of the scalar and pseudoscalar meson theories are considered in which the interaction hamiltonian depends exponentially on the meson field. In the pseudoscalar case such hamiltonians are closely related to the familiar form of pseudovector coupling. Assuming the over-all coupling of the nucleon and meson fields to be weak, calculations are made of the nuclear forces, and of the multiple production of mesons in meson-nucleon and in nucleon-nucleon collisions. In the latter events statistical independence of meson emissions is found to prevail.

On the Use of -Formalism of the Meson Field for Nuclear Interactions

Following a method due to Harish-Chandra, a correspondence between the Proca and the ?-formalisms of the meson field theory is developed. An important feature of the method is that one can at any stage of calculations pass over from one formalism to the other. No explicit representation of the ?-matrices is required nor need one know the exact relationship between the elements of the wave function ? and the Proca field quantities U? and G??. This introduces considerable simplification in the introduction of nuclear interaction as compared with earlier treatments where one has to choose a special explicit representation of the ??'s and identify the various elements of the matrix ? with the components of U? and G??. The nuclear interaction is, in fact, here introduced very simply in an elegant way. The quantization is performed for the vector, scalar and pseudoscalar cases assuming in all cases both charge and dipole types of couplings. As an illustration of the method we calculate the scattering of positively charged mesons by protons. The spur calculations, so tedious in the earlier works, are now replaced by simple relations which are easily handled, and the results are obtained with about as much labour as is used in Proca's case with the additional advantage that both the longitudinal and the transverse parts of the meson field can here be treated together.

Bremsstrahlung in High Energy Nucleon-Nucleon Collisions

Field-theoretic calculations are made of the electromagnetic radiation accompanying a proton-neutron collision. The nucleons are treated non-relativistically, and it is assumed that their scattering is produced either by a scalar meson field with scalar coupling or a pseudoscalar field with pseudoscalar coupling. The resulting energy spectrum for the photons has the form $\frac{{(\frac{1}{2}{E}_{0}\ensuremath{-}ck)}^{\frac{1}{2}}\mathrm{dk}}{k}$ for the scalar field and ${(\frac{1}{2}{E}_{0}\ensuremath{-}ck)}^{\frac{1}{2}}\mathrm{kdk}$ for the pseudoscalar field. The ratio of the intensity at 90\ifmmode^\circ\else\textdegree\fi{} to 0\ifmmode^\circ\else\textdegree\fi{} (in the CM system) is about 100 for the scalar theory and about 1 for the pseudoscalar case for incident energies of about 200 Mev. Integrated cross sections are obtained for both theories. The yield decreases with energy for the scalar field and increases for the pseudoscalar field.

Solutions of Equations for Particles of Spin Zero or One When No Field Is Present

Belinfante's four-component spinor form of the equations investigated by Kemmer for particles of spin zero and one are obtained in general coordinate systems. These equations are then solved when no external field is present by means of two simple spinors which satisfy Dirac equations for particles of spin one-half. The results previously obtained for the vector case hold for the pseudo-scalar case with one additional condition which says that the spins must be oppositely oriented. The pseudo-vector and scalar cases have similar conditions. In these cases the results differ from the previous two in that if one particle of spin one-half satisfies a Dirac equation with a positive mass term then the other satisfies one with a negative mass term.