S.M. Roy

Exact integral equation for pion-pion scattering involving only physical region partial waves

Abstract We derive an exact relation for ππ scattering which yields the real parts of the ππ partial wave amplitudes al(I)(s) in the region 4m2π ⩽ s ⩽ 60m2π, is given i) the I = 0 and the I = 2 S wave scattering lengths and ii) the 1m al(I)(s) for 4m2π ⩽ s ⩽ ∞, where s denotes the centre-of-mass energy, l the angular momentum and I the isotopic spin. It also provides i) a system of integral equations to determine the al(I)(s) for 4m2π ⩽ s ⩽ 16m2π, 162π ⩽ s ⩽ ∞, and ii) necessary and sufficient conditions for crossing symmetry expressed in terms of the physical region partial wave amplitudes only.

HIGH ENERGY THEOREMS FOR STRONG INTERACTIONS AND THEIR COMPARISON WITH EXPERIMENTAL DATA.

We review the high energy theorems for strong interaction scattering amplitudes based on analyticity in the domain derived from axiomatic field theory, crossing and unitarity, and compare them with experimental data.

Exponentially Enhanced Quantum Metrology

We show that when a suitable entanglement-generating unitary operator depending on a parameter is applied on N qubits in parallel, a precision of the order of 2(-N) in estimating the parameter may be achieved. This exponentially improves the precision achievable in classical and in quantum nonentangling strategies.

Physical pion-pion partial-wave equations based on three channel crossing symmetry

We present a set of closed systems of partial-wave equations for pion-pion scattering valid for −28 mπ2 ⩽ s ⩽ 125.31 mπ2. These equations give the real part of a given partial-wave amplitude in terms of scattering lengths and a convergent series of integrals over the physical values of the absorptive parts of all partial waves. Our equations are extensions of relations previously derived from fixed-t dispersion relations. The new equations are rigorous consequences of axiomatic analyticity and three channel crossing symmetry. As an application, the effect of the f0-meson on the I = O S-wave is evaluated.

Semi-relativistic stability and critical mass of a system of spinless bosons in gravitational interaction

Abstract The N particle hamiltonian Σ i=1 N ( p i 2 +m 2 ) 1 2 −Σ i Gm 2 /r ij implies a critical mass M cr a bosonic analogue of the Chandrasekhar limit, beyond which there must be relativistic collapse. We prove that M cr ⩾4(3√3 Gm ) −1 ∼ 0.77( Gm ) −1 , consistent with the bound M cr Gm ) −1 obtained by one of us (A.M.). Comparison with the Kaup-Ruffini-Bonazzola statistical curved space Klein-Gordon equation result M cr ≈0.633 ( Gm ) −1 raises interesting questions.

UPPER BOUNDS ON THE ELASTIC DIFFERENTIAL CROSS SECTION.

Abstract We derive improved axiomatic upper bounds on the elastic unpolarized differential cross section, dσ dΩ , at high energies for the scattering of particles with arbitrary spin. We prove that dσ dω ⩽ s→∞ σ el 4φ {(L+1) 2 [P L (cos θ)] 2 +sin 2 θ[P L′ (cos θ)] 2 } with L= 1 2 S t o In s σ el ), where s and t are, respectively, the squares of the c.m. energy and the c.m. momentum transfer; θ is the c.m. scattering angle. Further t o , is the mass of the lowest mass state that couples to the crossed t-channel (being equal to twice the pion mass for ππ and πN scattering). This result has the following important consequences: 1. (i) for forward scattering, dσ dt t=0 ⩽ s→∞ σ el 4t 0 In s σ el 2 2. (ii) for fixed θ ≠ 0, π, dσ dω (s;cosθ) ⩽ s→∞ 1 4φ 2 s t 0 σ el sin θ In s σ el and 3. (iii) for fixed negative t, dσ dω (s,t) ⩽ s→∞ 1 8φ t 0 s −t σ el In s σ el We also give an upper bound on differential cross section involving the diffraction peak width but not having an explicit ln s dependence.

The "Herbst Hamiltonian" and the mass of boson stars

Abstract We present new accurate lower bounds on the ground state of the Hamiltonian p 2 +m 2 − α r . From these, we obtain a lower bound on the maximum mass of a boson star in the semirelativistic framework, and we compare it to a variational upper bound. We get 0.846 ( Gm ) −1 M max Gm ) −1 , where G is Newtons constant and m the boson mass.

Bounds on polarization in πN scattering from isotopic spin invariance

Abstract Isotopic spin bounds on the polarization in π − p→ π o n scattering in terms of the polarizations in π + p→ π + p and π − p→ π − p scattering and the unpolarized differential cross-sections for π + p→ π + p, π − p→ π − p, and π − p→ π o n scattering are derived, and compared with recent experimental data. Similar bounds on the P , R and A parameters for elastic scattering are also given.

Exploring the Origin of Nearly Degenerate Doublet Bands in Ag 106

The lifetimes of the excited levels for the two nearly degenerate bands of

Multipartite separability inequalities exponentially stronger than local reality inequalities.

^{106}\mathrm{Ag}