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Spin Effects in the Sommerfeld–Gamow–Sakharov Factor
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It is shown that production of low-mass e + e - -pairs in ultraperipheral nuclear collisions is enhanced due to the Sommerfeld–Gamow–Sakharov (SGS) factor. This effect is especially strong near the threshold of creation of unbound e + e - -pairs with low masses in the two-photon fusion. Coulomb attraction of the non-relativistic components of such pairs may lead to the increased intensity of 511 keV photons. It can be recorded at the NICA collider and has some astrophysical implications. The analogous effect can be observed at LHC in dilepton production.
The formation and decay of dark matter (DM) bound states deplete the thermal relic density during the chemical decoupling process, allowing for larger DM masses. While so far the bound state formation (BSF) has been described via the emission of an on-shell mediator, we point out that this particular process does not have to be the dominant one in general. If the mediator is coupled in a direct way to any relativistic species present in the early Universe, we demonstrate that BSF can much more efficiently occur through particle scattering. Consequently, DM can be heavier than previously expected.
We show that the presence of nearby Coulombic resonances at finite energy could lead to the enhancement of the dark matter annihilation cross section at specific non-zero velocities correlated with the mass splitting between the dark matter pair and that of the resonance. If one of these resonant velocities approximately matches the velocity of dark matter in our local neighbourhood, we would see this enhancement in existing indirect-detection measurements, such as the measurements of the continuum photon spectrum made by HESS and Fermi-LAT. We explore this effect in the context of pure Higgsino and Wino dark matter with a variable splitting between charged and neutral components, controlled by the Wilson coefficient of a higher-dimension operator. For electroweak WIMPs a relevant and appreciable enhancement from Coulomb resonances requires tuning the charged-neutral splitting to be of order the Coulomb binding energies. This leads to strong exclusions of Higgsino dark matter with charged-neutral splittings in the narrow ranges (2, 2.5) and (8.5, 10.5) MeV. In contrast, by decreasing the charged-neutral splitting for the thermal Wino, we can move the Yukawa resonance away from the thermal relic mass, decreasing the indirect-detection signal to a level that is compatible with HESS measurements in the window (25, 35) MeV.
Thermal pair annihilation of heavy particles, such as dark matter or its co-annihilation partners, can be strongly influenced by attractive interactions. We investigate the case that pair annihilation proceeds through a velocity-suppressed p-wave operator, in the presence of an SU(3) gauge force. Making use of a non-relativistic effective theory, the thermal average of the pair-annihilation rate is estimated both through a resummed perturbative computation and through lattice simulation, in the range M/T∼10...30. Bound states contribute to the annihilation process and enhancement factors of up to ∼100 can be found.
A model based on the analytic approach to QCD, involving a summation of threshold singularities and taking into account the nonperturbative character of the light quark masses, is applied to find hadronic contributions to different physical quantities. It is shown that the suggested model allows us to describe well such objects as the hadronic contribution to the anomalous magnetic moment of the muon, the ratio of hadronic to leptonic τ-decay widths in the vector channel, the Adler D-function, the smeared RΔ-function, and the hadronic contribution to the evolution of the fine structure constant.
A novel quasi-potential relativistic equation for two scalar particles of arbitrary masses is presented. The derivation is
demonstrated in detail. For the electromagnetic interaction, the equation has the form of the one-particle Schrödinger equation.
The interaction is introduced by the minimal substitution. The exact solutions are considered in several limits: non-relativistic,
equal masses, one particle at rest and ultrarelativistic. The problem of interaction retardation is discussed.
The interpretation of the narrow boson resonances at 3.1 and 3.7 GeV as charmed quark-antiquark bound states implies the existence of other states. Some of these should be copiously produced in the radiative decays of the 3.7-GeV resonance. We estimate the masses and decay rates of these states and emphasize the importance of γ-ray spectroscopy.
In a recent Letter we reported on some work which led us to suggest the possibility of narrow spikes in the e+e- annihilation cross section into hadrons. In this paper, we discuss the theoretical infrastructure of this work more thoroughly, and improve and extend the calculations and experimental predictions. We examine a colored quark-gluon model of hadronic matter, with color an exact SU(3) gauge symmetry. In addition to the light quarks that make up ordinary hadrons, a heavy quark, such as the charmed c, is included. The narrow resonances recently discovered by the MIT-BNL and SLAC-LBL groups are interpreted as cc̅ bound states (orthocharmonium). In this energy range, the effective coupling has become small according to asymptotic freedom, and many aspects of the bound-state structure can be calculated. The existence of 0-(paracharmonium) states is predicted, and decay widths and mass splittings are estimated. The total e+e- cross section into hadrons is predicted to scale asymptotically, with an approach to scaling from above that can be calculated over a large energy range.
The new relativistic Coulomb-like threshold resummation S-factor in quantum chromodynamics is obtained. The consideration is given within the framework of quasipotential approach in quantum field theory which is formulated in relativistic configuration representation for two particles of unequal masses.
Assuming that two incoming annihilating particles interact by a generally massive attractive vector potential,we find, by taking the non-relativistic limit of the field theory ladder diagrams, that the complete annihilation amplitude A is equal to: the convolution of a solution of the Schroedinger equation (including the vector potential) with the Fourier transform of the bare (i.e. ignoring the attraction) annihilation amplitude A0. The main novelty is that A0 is completely arbitrary. In particular for a massless vector potential we find for the l-partial-wave cross-section the Sommerfeld enhancement 2pi/(l!)^2 (alpha/ v)^{2l+1} (v relative velocity), e.g. for the P wave the enhancement 2pi(alpha/ v)^3. Comment: published version, it contains also the material of 0903.0317
We propose a comprehensive theory of dark matter that explains the recent proliferation of unexpected observations in high-energy astrophysics. Cosmic ray spectra from ATIC and PAMELA require a WIMP with mass M_chi ~ 500 - 800 GeV that annihilates into leptons at a level well above that expected from a thermal relic. Signals from WMAP and EGRET reinforce this interpretation. Taken together, we argue these facts imply the presence of a GeV-scale new force in the dark sector. The long range allows a Sommerfeld enhancement to boost the annihilation cross section as required, without altering the weak scale annihilation cross section during dark matter freezeout in the early universe. If the dark matter annihilates into the new force carrier, phi, its low mass can force it to decay dominantly into leptons. If the force carrier is a non-Abelian gauge boson, the dark matter is part of a multiplet of states, and splittings between these states are naturally generated with size alpha m_phi ~ MeV, leading to the eXciting dark matter (XDM) scenario previously proposed to explain the positron annihilation in the galactic center observed by the INTEGRAL satellite. Somewhat smaller splittings would also be expected, providing a natural source for the parameters of the inelastic dark matter (iDM) explanation for the DAMA annual modulation signal. Since the Sommerfeld enhancement is most significant at low velocities, early dark matter halos at redshift ~10 potentially produce observable effects on the ionization history of the universe, and substructure is more detectable than with a conventional WIMP. Moreover, the low velocity dispersion of dwarf galaxies and Milky Way subhalos can greatly increase the substructure annihilation signal.
In processes involving Coulomb-type initial- and final-state interactions, the Gamow factor has been traditionally used to take into account these additional interactions. The Gamow factor needs to be modified when the magnitude of the effective coupling constant increases or when the velocity increases. For the production of a pair of particles under their mutual Coulomb-type interaction, we obtain the modification of the Gamow factor in terms of the overlap of the Feynman amplitude with the relativistic wave function of the two particles. As a first example, we study the modification of the Gamow factor for the production of two bosons. The modification is substantial when the coupling constant is large. Comment: 13 pages, in LaTex
In the production or annihilation of a pair of fermions, the initial-state or final-state interactions often lead to significant effects on the reaction cross sections. For Coulomb-type interactions, the Gamow factor has been traditionally used to take into account these effects. However the Gamow factor needs to be modified when the magnitude of the coupling constant or the relative velocity of two particles increases. We obtain the relativistic generalization of the Gamow factor in terms of the overlap of the Feynman amplitude with the relativistic wave function of two fermions with an attractive Coulomb-type interaction. An explicit form of the corrective factor is presented for the spin-singlet S-wave state. While the corrective factor approaches the Gamow factor in the non-relativistic limit, we found that the Gamow factor significantly over-estimates the effects when the coupling constant or the velocity is large. Comment: 16 pages, 4 figures in LaTex
The method of analytic perturbation theory, which avoids the problem of ghost-pole type singularities and gives a self-consistent description of both spacelike and timelike regions, is applied to describe the "light" Adler function corresponding to the non-strange vector channel of the inclusive decay of the lepton. The role of threshold effects is investigated. The behavior of the quark-antiquark system near threshold is described by using a new relativistic resummation factor. It is shown that the method proposed leads to good agreement with the ``experimental'' Adler function down to the lowest energy scale. Comment: 13 pages, one ps figure, REVTeX
A relativistic Coulomb-like resummation factor in quantum chromodynamics is suggested, based on the solution of the quasipotential equation.
A new resummation of the S-factor of a composite system of two relativistic spin-1/2 particles of arbitrary masses interacting via a Coulomb-like chromodynamical potential is presented. The analysis is performed in the framework of a relativistic quasipotential approach based on the Hamiltonian formulation of the covariant quantum field theory in the relativistic configuration representation. The pseudoscalar, vector, and pseudovector systems are considered, and the behavior of the S-factor near the threshold and in the relativistic limit is investigated in detail. The spin dependence of the S-factors is discussed as well. It is argued that at the threshold the contribution of spins significantly reduces the Sommerfeld effect, while at ultrarelativistic velocities their role diminishes and the S-factor becomes basically the same as for the spinless systems. A connection between the new and previously obtained S-factors for spinless particles of arbitrary masses and for relativistic spinor particles of equal masses is established.
We propose that perturbation theory in a gauge field theory of quarks and gluons can be used to calculate physical mass-shell processes, provided that both the data and the theory are smeared over a suitable energy range. This procedure is explored in detail for the process of electron-positron annihilation into hadrons. We show that a smearing range of 3 GeV2 in the squared center-of-mass energy should be adequate to allow the use of lowest-order perturbation theory. The smeared data are compared with theory for a variety of models. It appears to be difficult to fit the present data with theory, unless there is a new charged lepton or quark with mass in the region 2 to 3 GeV.
We calculate the Coulomb effects on the cross section for {ital e}{sup +}{ital e}â»â{ital W}{sup +}{ital W}â» taking into account the instability of the {ital W} bosons. We carefully explain the consequences of instability throughout the energy range which will be accessible at CERN LEP 2. We present a formula which allows these effects to be easily implemented.
The relativistic S-matrix formalism of Feynman is applied to the bound-state problem for two interacting Fermi-Dirac particles. The bound state is described by a wave function depending on separate times for each of the two particles. Two alternative integral equations for this wave function are derived with kernels in the form of an expansion in powers of g2, the dimensionless coupling constant for the interaction. Each term in these expansions gives Lorentz-invariant equations. The validity and physical significance of these equations is discussed. In extreme nonrelativistic approximation and to lowest order in g2 they reduce to the appropriate Schrödinger equation. One of these integral equations is applied to the deuteron ground state using scalar mesons of mass mu with scalar coupling. For neutral mesons the Lorentz-invariant interaction is transformed into the sum of the instantaneous Yukawa interaction and a retarded correction term. The value obtained for g2 differs only by a fraction proportional to (muM)2 from that obtained by using a phenomenological Yukawa potential. For a purely charged meson theory a correction term is obtained by a direct solution of the relativistic integral equation using only the first term in the expansion of the kernel. This correction is due to the fact that a nucleon can emit, or absorb, positive and negative mesons only alternately. The constant g2 is increased by a fraction of 1.1(muM) or 15 percent.
It is shown that the assumption about the existence of the Mandelstam ; representation leads to the requirement that the system should be described by a ; potential that is a superposition of Yukawa potentials with energy dependent ; intensities. (auth)
The quasipotential type equation for the relativistic scattering amplitude is obtained with the help of a special kind of perturbation theory.
Übersicht: Der I. Teil bildet eine systematische Einleitung zu der Behandlung des kontinuierlichen Röntgenspektrums im II. Teil. Der I. Teil geht nur in der Methode, nicht in den Resultaten über die Arbeiten von Gordon, Mott, Temple hinaus. Der II. Teil setzt, im Gegensatz zu Arbeiten von Oppenheimer und Sugiura den Endzustand des gebremsten Elektrons als ebene, durch Beugung modifizierte Welle an. Polarisation und Intensität im kontinuierlichen Spektrum werden nach der Methode der Matrixelemente berechnet. Um die azimutale Verteilung der Intensität, insbesondere die Voreilung des Maximums zu erhalten, muß die Rechenmethode verfeinert werden durch Berücksichtigung der Retardierung. Die Resultate werden mit Messungen von Kulenkampff verglichen.
We obtain a new relativistic Coulomb-like resummation factor (L-factor) for an arbitrary orbital moment ℓ ≥ 0. We work within
the fully covariant quasipotential approach in quantum field theory formulated in the relativistic configuration representation
in the case of two interacting relativistic particles with arbitrary masses.
Keywordsquantum field theory–relativistic configuration representation–Coulomb-like quasipotential
Es wird der Versuch gemacht, die Prozesse der -Ausstrahlung auf Grund der Wellenmechanik nher zu untersuchen und den experimentell festgestellten Znsammenhang zwischen Zerfallskonstante und Energie der -Partikel theoretisch zu erhalten.
A quasi-optical approach in the quantum field theory is developed.
It is shown that in order to describe the bound states in quantum field theory it is possible to construct a local potential
which is a superposition of Yukawa potentials with energy-dependent intensities.
Si dimostra che per descrivere gli stati legati nella teoria quantistica dei campi é possibile costruire un potenziale local
che é una sovrappsizione di potenziali di Yukawa aventi intensita che dipendono dall’energia.
The expansion in matrix elements of unitary representations of the Lorentz groups is applied in the relativistic quasi-potential
scattering theory. A relativistic analogue of the three-dimensional configuration space is found. The formalism developed
is very close to the nonrelativistic one. It allows us to hope that in the framework of this approach, an adequate relativistic
generalization of Regge's ideas can be found.
Si applica lo sviluppo in elementi di matrice delle rappresentazioni unitarie dei gruppi di Lorentz alla teoria dello scattering
di quasi potenziali relativistici. Si trova un analogo relativistico dello spazio delle configurazioni tridimensionale. Il
formalismo sviluppato è molto simile a quello non relativistico. Ciò permette di sperare che nel quadro di questa approssimazione
si possa trovare un'adeguata generalizzazione delle idee di Regge.
Разложение по матричным элементам унитарных представлений групп Лорентца применяется в релятивистской квазипотенциальной теории
рассеяния. Получен пелятивистский аналог трехмерного конфигурационного пространства. Развитый формализм очень близок к нерелятивистскому
формализму. Это позволяет нам надеяться, что в рамках этого подхода может быть найдено адекватное релятивистское обобщение
идей Редже.
An explicitly relativistically invariant three-dimensional formulation of the quasipotential method of Logunov and Tavkhelidze for the system of two particles with arbitrary spins and masses is given. This formalism is used to consider the matrix elements of local operators between bound states (the form factors of the bound system). The transformation law of the three-dimensional wavefunctions in the transition from the center of mass system to an arbitrary reference frame is obtained.
We point out that thermal relic abundance of the dark matter is strongly altered by a non-perturbative effect called the Sommerfeld enhancement, when constituent particles of the dark matter are non-singlet under the SU(2)L gauge interaction and much heavier than the weak gauge bosons. Typical candidates for such dark matter particles are the heavy wino- and higgsino-like neutralinos. We investigate the non-perturbative effect on the relic abundance of dark matter for the wino-like neutralino as an example. We show that its thermal abundance is reduced by 50% compared to the perturbative result. The wino-like neutralino mass consistent with the observed dark matter abundance turns out to be 2.7 TeV≲m≲3.0 TeV.
The Sommerfeld factor for arbitrary partial wave processes is derived in the non-relativistic limit. The s-wave and p-wave numerical results are presented for the case of Yukawa interactions. An approximate analytic expression is also found for the Sommerfeld factor of Yukawa interactions with arbitrary partial waves, which is exact in the Coulomb limit. It is demonstrated that this result is accurate to within 10% for some common scenarios. The non s-wave Sommerfeld effect is determined to be significant, and can allow higher partial waves to dominate cross sections. Comment: 20 pages, 6 figures
Two-loop contributions to the electromagnetic form factors are calculated in the kinematic regime close to the fermion-antifermion threshold. The results are presented in an expansion in the velocity fi of the fermions in the c.m. frame up to next-to-next-to leading order in fi. The existence of a new Coulomb singularity logarithmic in fi, which is closely related to the O(ff 2 ln ff) corrections known from positronium decays, is demonstrated. It is shown that due to this Coulomb singularity O(ff 2 ) relativistic corrections to the non-relativistic cross section of heavy fermion-antifermion pair production in e + e Gamma annihilation cannot be determined by means of conventional multi-loop perturbation theory. 1 Introduction In view of future experiments (NLC, B-factory, ø-charm factory) where heavy quark-antiquark pairs will be produced in the kinematic region close to the threshold and a large amount of data can be expected, it is a very attractive idea that an extracti...
Seminar Dedicated to the Memory of I
- K A Milton
- Preprint No
- V S Fadin
- V A Khoze
- A D Martin
- A Chapovsky
- J.-H Yoon
- Ch.-Yi Wong
- J.-H Yoon
- Ch.-Yi Wong