Asymptotic freedom, dimensional transmutation, and an infrared conformal fixed point for the δ-function potential in one-dimensional relativistic quantum mechanics

We consider the Schrödinger equation for a relativistic point particle in an external one-dimensional δ-function potential. Using dimensional regularization, we investigate both bound and scattering states, and we obtain results that are consistent with the abstract mathematical theory of self-adjoint extensions of the pseudodifferential operator H=p2+m2−−−−−−−√. Interestingly, this relatively simple system is asymptotically free. In the massless limit, it undergoes dimensional transmutation and it possesses an infrared conformal fixed point. Thus it can be used to illustrate nontrivial concepts of quantum field theory in the simpler framework of relativistic quantum mechanics.

Atomization Energies of LnX Molecules (Ln = Sm, Eu, and Yb; X = Cl, Br, and I)

The gas phase equilibria Ba + LnX = BaX + Ln (Ln = Sm, Eu, Yb; X = Cl, Br, I) were investigated by Knudsen effusion mass spectrometry using a low energy of ionizing electrons to avoid fragmentation processes. The BaX molecules were used as references with well-established bond energies. The atomization enthalpies ΔatH0° of the LnX molecules were determined to be 427 ± 9 (SmCl), 409 ± 9 (EuCl), 366 ± 9 (YbCl), 360 ± 10 (SmBr), 356 ± 13 (EuBr), 316 ± 9 (YbBr), 317 ± 10 (SmI), 293 ± 10 (EuI), and 283 ± 10 (YbI) kJ·mol−1.

Accurate computations of the structures and binding energies of the imidazole ... benzene and pyrrole ... benzene complexes

Using explicitly-correlated coupled-cluster theory with single and double excitations, the intermolecular distances and interaction energies of the T-shaped imidazole⋯⋯benzene and pyrrole⋯⋯benzene complexes have been computed in a large augmented correlation-consistent quadruple-zeta basis set, adding also corrections for connected triple excitations and remaining basis-set-superposition errors. The results of these computations are used to assess other methods such as Møller–Plesset perturbation theory (MP2), spin-component-scaled MP2 theory, dispersion-weighted MP2 theory, interference-corrected explicitly-correlated MP2 theory, dispersion-corrected double-hybrid density-functional theory (DFT), DFT-based symmetry-adapted perturbation theory, the random-phase approximation, explicitly-correlated ring-coupled-cluster-doubles theory, and double-hybrid DFT with a correlation energy computed in the random-phase approximation.

Measurement of Higgs boson production in the diphoton decay channel in pp collisions at center-of-mass energies of 7 and 8 TeV with the ATLAS detector

A measurement of the production processes of the recently discovered Higgs boson is performed in the two-photon final state using 4.5  fb −1 of proton-proton collisions data at s √ =7  TeV and 20.3  fb −1 at s √ =8  TeV collected by the ATLAS detector at the Large Hadron Collider. The number of observed Higgs boson decays to diphotons divided by the corresponding Standard Model prediction, called the signal strength, is found to be μ=1.17±0.27 at the value of the Higgs boson mass measured by ATLAS, m H =125.4  GeV . The analysis is optimized to measure the signal strengths for individual Higgs boson production processes at this value of m H . They are found to be μ ggF =1.32±0.38 , μ VBF =0.8±0.7 , μ WH =1.0±1.6 , μ ZH =0.1 +3.7 −0.1 , and μ tt ¯ H =1.6 +2.7 −1.8 , for Higgs boson production through gluon fusion, vector-boson fusion, and in association with a W or Z boson or a top-quark pair, respectively. Compared with the previously published ATLAS analysis, the results reported here also benefit from a new energy calibration procedure for photons and the subsequent reduction of the systematic uncertainty on the diphoton mass resolution. No significant deviations from the predictions of the Standard Model are found.

Measurement of the Higgs boson mass from the H→γγ and H→ZZ ∗ →4ℓ collisions at center-of-mass energies of 7 and 8 TeV with the ATLAS detector

An improved measurement of the mass of the Higgs boson is derived from a combined fit to the reconstructed invariant mass spectra of the decay channels H→γγ and H→ZZ ∗ →4ℓ . The analysis uses the pp collision data sample recorded by the ATLAS experiment at the CERN Large Hadron Collider at center-of-mass energies of 7 TeV and 8 TeV, corresponding to an integrated luminosity of 25  fb −1 . The measured value of the Higgs boson mass is m H =125.36±0.37(stat)±0.18(syst)  GeV . This result is based on improved energy-scale calibrations for photons, electrons, and muons as well as other analysis improvements, and supersedes the previous result from ATLAS. Upper limits on the total width of the Higgs boson are derived from fits to the invariant mass spectra of the H→γγ and H→ZZ ∗ →4ℓ decay channels.

Microscopic study of vorticities in relativistic chiral fermions

It is usually believed that unlike the external magnetic field which one can set directly, vorticity is a property of the flow of particles, which is indirectly controlled by external fields and initial conditions. Using the curved-space technics it is shown that the influence of the vorticity on the relativistic chiral fermions can indeed be controlled directly.

The bottom-quark mass from non-relativistic sum rules at NNNLO

We determine the mass of the bottom quark from high moments of the bbproduction cross section in e+e−annihilation, which are dominated by the threshold region. On the theory side next-to-next-to-next-to-leading order (NNNLO) calculations both for the resonances and the continuum cross section are used for the first time. We find mPSb(2GeV) =4.532+0.013−0.039GeVfor the potential-subtracted mass and mMSb(mMSb) =4.193+0.022−0.035GeVfor the MSbottom-quark mass.

Solution of the relativistic Schrödinger equation for the δ ′ -Function potential in one dimension using cutoff regularization

We study the relativistic version of the Schrödinger equation for a point particle in one dimension with the potential of the first derivative of the delta function. The momentum cutoff regularization is used to study the bound state and scattering states. The initial calculations show that the reciprocal of the bare coupling constant is ultraviolet divergent, and the resultant expression cannot be renormalized in the usual sense, where the divergent terms can just be omitted. Therefore, a general procedure has been developed to derive different physical properties of the system. The procedure is used first in the nonrelativistic case for the purpose of clarification and comparisons. For the relativistic case, the results show that this system behaves exactly like the delta function potential, which means that this system also shares features with quantum filed theories, like being asymptotically free. In addition, in the massless limit, it undergoes dimensional transmutation, and it possesses an infrared conformal fixed point. The comparison of the solution with the relativistic delta function potential solution shows evidence of universality.

Fate of accidental symmetries of the relativistic hydrogen atom in a spherical cavity

The non-relativistic hydrogen atom enjoys an accidental SO(4) symmetry, that enlarges the rotational SO(3) symmetry, by extending the angular momentum algebra with the Runge–Lenz vector. In the relativistic hydrogen atom the accidental symmetry is partially lifted. Due to the Johnson–Lippmann operator, which commutes with the Dirac Hamiltonian, some degeneracy remains. When the non-relativistic hydrogen atom is put in a spherical cavity of radius R with perfectly reflecting Robin boundary conditions, characterized by a self-adjoint extension parameter γ, in general the accidental SO(4) symmetry is lifted. However, for R=(l+1)(l+2)a (where a is the Bohr radius and l is the orbital angular momentum) some degeneracy remains when γ=∞ or γ = 2/R. In the relativistic case, we consider the most general spherically and parity invariant boundary condition, which is characterized by a self-adjoint extension parameter. In this case, the remnant accidental symmetry is always lifted in a finite volume. We also investigate the accidental symmetry in the context of the Pauli equation, which sheds light on the proper non-relativistic treatment including spin. In that case, again some degeneracy remains for specific values of R and γ.

From quantum to classical dynamics: The relativistic O ( N ) model in the framework of the real-time functional renormalization group

We investigate the transition from unitary to dissipative dynamics in the relativistic O(N) vector model with the λ(φ2)2 interaction using the nonperturbative functional renormalization group in the real-time formalism. In thermal equilibrium, the theory is characterized by two scales, the interaction range for coherent scattering of particles and the mean free path determined by the rate of incoherent collisions with excitations in the thermal medium. Their competition determines the renormalization group flow and the effective dynamics of the model. Here we quantify the dynamic properties of the model in terms of the scale-dependent dynamic critical exponent z in the limit of large temperatures and in 2≤d≤4 spatial dimensions. We contrast our results to the behavior expected at vanishing temperature and address the question of the appropriate dynamic universality class for the given microscopic theory.