Self-motion perception influences number processing: evidence from a parity task

We investigated the role of horizontal body motion on the processing of numbers. We hypothesized that leftward self-motion leads to shifts in spatial attention and therefore facilitates the processing of small numbers, and vice versa, we expected that rightward self-motion facilitates the processing of large numbers. Participants were displaced by means of a motion platform during a parity judgment task. We found a systematic influence of self-motion direction on number processing, suggesting that the processing of numbers is intertwined with the processing of self-motion perception. The results differed from known spatial numerical compatibility effects in that self-motion exerted a differential influence on inner and outer numbers of the given interval. The results highlight the involvement of sensory body motion information in higher-order spatial cognition.

NLL QCD contribution of the electromagnetic dipole operator to B -> Xs gamma gamma with a massive strange quark

We calculate the O(αs) corrections to the double differential decay width dΓ77/(ds1ds2) for the process B¯→Xsγγ, originating from diagrams involving the electromagnetic dipole operator O7. The kinematical variables s1 and s2 are defined as si=(pb−qi)2/m2b, where pb, q1, q2 are the momenta of the b quark and two photons. We introduce a nonzero mass ms for the strange quark to regulate configurations where the gluon or one of the photons become collinear with the strange quark and retain terms which are logarithmic in ms, while discarding terms which go to zero in the limit ms→0. When combining virtual and bremsstrahlung corrections, the infrared and collinear singularities induced by soft and/or collinear gluons drop out. By our cuts the photons do not become soft, but one of them can become collinear with the strange quark. This implies that in the final result a single logarithm of ms survives. In principle, the configurations with collinear photon emission could be treated using fragmentation functions. In a related work we find that similar results can be obtained when simply interpreting ms appearing in the final result as a constituent mass. We do so in the present paper and vary ms between 400 and 600 MeV in the numerics. This work extends a previous paper by us, where only the leading power terms with respect to the (normalized) hadronic mass s3=(pb−q1−q2)2/m2b were taken into account in the underlying triple differential decay width dΓ77/(ds1ds2ds3).

The block numerical range of analytic operator functions

We introduce the block numerical range Wn(L) of an operator function L with respect to a decomposition H = H1⊕. . .⊕Hn of the underlying Hilbert space. Our main results include the spectral inclusion property and estimates of the norm of the resolvent for analytic L . They generalise, and improve, the corresponding results for the numerical range (which is the case n = 1) since the block numerical range is contained in, and may be much smaller than, the usual numerical range. We show that refinements of the decomposition entail inclusions between the corresponding block numerical ranges and that the block numerical range of the operator matrix function L contains those of its principal subminors. For the special case of operator polynomials, we investigate the boundedness of Wn(L) and we prove a Perron-Frobenius type result for the block numerical radius of monic operator polynomials with coefficients that are positive in Hilbert lattice sense.

On the similarity of Sturm-Liouville operators with non-Hermitian boundary conditions to self-adjoint and normal operators

We consider one-dimensional Schrödinger-type operators in a bounded interval with non-self-adjoint Robin-type boundary conditions. It is well known that such operators are generically conjugate to normal operators via a similarity transformation. Motivated by recent interests in quasi-Hermitian Hamiltonians in quantum mechanics, we study properties of the transformations and similar operators in detail. In the case of parity and time reversal boundary conditions, we establish closed integral-type formulae for the similarity transformations, derive a non-local self-adjoint operator similar to the Schrödinger operator and also find the associated “charge conjugation” operator, which plays the role of fundamental symmetry in a Krein-space reformulation of the problem.

Measurement of the parity-violating asymmetry parameter αb and the helicity amplitudes for the decay Λ 0 b →J/ψ⁰ with the ATLAS detector

A measurement of the parity-violating decay asymmetry parameter, αb , and the helicity amplitudes for the decay Λ 0 b →J/ψ(μ + μ − )Λ 0 (pπ − ) is reported. The analysis is based on 1400 Λ 0 b and Λ ¯ 0 b baryons selected in 4.6  fb −1 of proton–proton collision data with a center-of-mass energy of 7 TeV recorded by the ATLAS experiment at the LHC. By combining the Λ 0 b and Λ ¯ 0 b samples under the assumption of CP conservation, the value of α b is measured to be 0.30±0.16(stat)±0.06(syst) . This measurement provides a test of theoretical models based on perturbative QCD or heavy-quark effective theory.

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.

On the CFT operator spectrum at large global charge

We calculate the anomalous dimensions of operators with large global charge J in certain strongly coupled conformal field theories in three dimensions, such as the O(2) model and the supersymmetric fixed point with a single chiral superfield and a W = Φ3 superpotential. Working in a 1/J expansion, we find that the large-J sector of both examples is controlled by a conformally invariant effective Lagrangian for a Goldstone boson of the global symmetry. For both these theories, we find that the lowest state with charge J is always a scalar operator whose dimension ΔJ satisfies the sum rule J2ΔJ−(J22+J4+316)ΔJ−1−(J22+J4+316)ΔJ+1=0.04067 up to corrections that vanish at large J . The spectrum of low-lying excited states is also calculable explcitly: for example, the second-lowest primary operator has spin two and dimension ΔJ+3√. In the supersymmetric case, the dimensions of all half-integer-spin operators lie above the dimensions of the integer-spin operators by a gap of order J+12. The propagation speeds of the Goldstone waves and heavy fermions are 12√ and ±12 times the speed of light, respectively. These values, including the negative one, are necessary for the consistent realization of the superconformal symmetry at large J.