arXiv subjects

H. -W. Hammer

Publications and source records attributed to H. -W. Hammer.

At least 163 records · Page 9Linked to original sources

arXiv2002

Quasiparticle Properties in Effective Field Theory

The quasiparticle concept is an important tool for the description of many-body systems. We study the quasiparticle properties for dilute Fermi systems with short-ranged, repulsive interactions using effective field theory. We calculate the proper self-energy contributions at order (K_f/Lambda)^3, where Lambda is the short-distance scale that sets the size of the effective range parameters and K_f the Fermi momentum. The quasiparticle energy, width, and effective mass to order O(K_f/Lambda)^3 are derived from the calculated self-energy.

nucl-th↗

arXiv2002

What Do We Know About the Strange Magnetic Radius?

We analyze the q^2-dependence of the strange magnetic form factor, \GMS(q^2), using heavy baryon chiral perturbation theory (HBChPT) and dispersion relations. We find that in HBChPT a significant cancellation occurs between the O(p^2) and O(p^3) loop contributions. Consequently, the slope of \GMS at the origin displays an enhanced sensitivity to an unknown O(p^3) low-energy constant. Using dispersion theory, we estimate the magnitude of this constant, show that it may have a natural size, and conclude that the low-q^2 behavior of \GMS could be dominated by nonperturbative physics. We also discuss the implications for the interpretation of parity-violating electron scattering measurements used to measure \GMS(q^2).

hep-ph↗

arXiv2002

The Dilute Bose-Einstein Condensate with Large Scattering Length

We study a dilute Bose gas of atoms whose scattering length a is large compared to the range of their interaction. We calculate the energy density of the homogeneous Bose-Einstein condensate to second order in the low-density expansion, expressing it in terms of a and a second parameter Lambda_* that determines the low-energy observables in the 3-body sector. The second-order correction to the energy density has a small imaginary part that reflects the instability due to 3-body recombination. In the case of a trapped Bose-Einstein condensate with large negative scattering length, we calculate the coefficient of the 3-body mean-field term in the energy density in terms of a and Lambda_*. It can be very large if there is an Efimov state near threshold.

cond-mat↗

arXiv2001

The Hypertriton in Effective Field Theory

Doublet Lambda d scattering and the hypertriton are studied in the framework of an effective field theory for large scattering lengths. As in the triton case, consistent renormalization requires a one-parameter three-body force at leading order whose renormalization group evolution is governed by a limit cycle. Constraining unknown parameters from symmetry considerations and the measured binding energy of the hypertriton, we calculate the low-energy phase shifts for doublet Lambda d scattering. For the low-energy parameters, we find a_{Lambda d}=(16.8^{+4.4}_{-2.4}) fm and r_{Lambda d}=(2.3 +/- 0.3) fm, where the errors are due to the uncertainty in the hypertriton binding energy. Since the hypertriton is extremely shallow, low-energy three-body observables in this channel are very insensitive to the exact values of the Lambda N low-energy parameters.

nucl-th↗

arXiv2001

Are Occupation Numbers Observable?

The question of whether occupation numbers and momentum distributions of nucleons in nuclei are observables is considered from an effective field theory perspective. Field redefinitions lead to variations that imply the answer is negative, as illustrated in the interacting Fermi gas at low density. Implications for the interpretation of (e,e'p) experiments with nuclei are discussed.

nucl-th↗

arXiv2001

Three-body recombination into deep bound states in a Bose gas with large scattering length

An effective field theory for the three-body system with large scattering length a is applied to three-body recombination into deep bound states in a Bose gas. The recombination constant αis calculated to first order in the short-distance interactions that allow the recombination. For a < 0, the dimensionless combination m α/(\hbar a^4) is a periodic function of \ln |a| that exhibits resonances at values of a that differ by multiplicative factors of 22.7. This dramatic behavior should be observable near a Feshbach resonance when a becomes large and negative.

cond-mat↗

arXiv2001

Nucleon Form Factors in the Space- and Timelike Regions

Dispersion relations provide a powerful tool to describe the electromagnetic form factors of the nucleon both in the spacelike and timelike regions with constraints from unitarity and perturbative QCD. We give a brief introduction into dispersion theory for nucleon form factors and present results from a recent form factor analysis. Particular emphasis is given to the form factors in the timelike region. Furthermore, some recent results for the spacelike form factors at low momentum transfer from a ChPT calculation by Kubis and Meissner are discussed.

hep-ph↗

arXiv2001

Range Corrections to Doublet S-Wave Neutron-Deuteron Scattering

We calculate the range corrections to S-wave neutron-deuteron scattering in the doublet channel (S=1/2) to first order in r/a where a is the scattering length and r the effective range. Ultraviolet divergences appearing at this order can be absorbed into a redefinition of the leading order three-body force. The corrections to the elastic scattering amplitude below the deuteron breakup threshold are computed. Inclusion of the range corrections gives good agreement with measured scattering data and potential model calculations.

nucl-th↗

arXiv2000

Field Redefinitions at Finite Density

The apparent dependence of nuclear matter observables on off-shell properties of the two-nucleon potential is re-examined in the context of the effective field theory (EFT) approach. Finite density (thermodynamic) observables are invariant under field redefinitions, which extends the well-known theorem about the invariance of S-matrix elements. Simple examples demonstrate how field redefinitions can shift contributions between purely off-shell two-body interactions and many-body forces, leaving both scattering and finite-density observables unchanged. If only the transformed two-body potentials are kept, however, the nuclear matter binding curves will depend on the off-shell part (generating ``Coester bands''). The correspondence between field redefinitions and unitary transformations, which have traditionally been used to generate ``phase-equivalent'' nucleon-nucleon potentials, is also demonstrated.

nucl-th↗

arXiv2000

Nonuniversal Effects in the Homogeneous Bose Gas

Effective field theory predicts that the leading nonuniversal effects in the homogeneous Bose gas arise from the effective range for S-wave scattering and from an effective three-body contact interaction. We calculate the leading nonuniversal contributions to the energy density and condensate fraction and compare the predictions with results from diffusion Monte Carlo calculations by Giorgini, Boronat, and Casulleras. We give a crude determination of the strength of the three-body contact interaction for various model potentials. Accurate determinations could be obtained from diffusion Monte Carlo calculations of the energy density with higher statistics.

cond-mat.stat-mech↗

arXiv2000

A renormalized equation for the three-body system with short-range interactions

We study the three-body system with short-range interactions characterized by an unnaturally large two-body scattering length. We show that the off-shell scattering amplitude is cutoff independent up to power corrections. This allows us to derive an exact renormalization group equation for the three-body force. We also obtain a renormalized equation for the off-shell scattering amplitude. This equation is invariant under discrete scale transformations. The periodicity of the spectrum of bound states originally observed by Efimov is a consequence of this symmetry. The functional dependence of the three-body scattering length on the two-body scattering length can be obtained analytically using the asymptotic solution to the integral equation. An analogous formula for the three-body recombination coefficient is also obtained.

nucl-th↗

arXiv2000

Effective Field Theory for Dilute Fermi Systems

The virtues of an effective field theory (EFT) approach to many-body problems are illustrated by deriving the expansion for the energy of an homogeneous, interacting Fermi gas at low density and zero temperature. A renormalization scheme based on dimensional regularization with minimal subtraction leads to a more transparent power-counting procedure and diagrammatic expansion than conventional many-body approaches. Coefficients of terms in the expansion with logarithms of the Fermi momentum are determined by the renormalization properties of the EFT that describes few-body scattering. Lessons for an EFT treatment of nuclear matter are discussed.

nucl-th↗

arXiv2000

Three-body recombination in Bose gases with large scattering length

An effective field theory for the three-body system with large scattering length is applied to three-body recombination to a weakly-bound s-wave state in a Bose gas. Our model independent analysis demonstrates that the three-body recombination constant alpha is not universal, but can take any value between zero and 67.9 \hbar a^4/m, where a is the scattering length. Other low-energy three-body observables can be predicted in terms of a and alpha. Near a Feshbach resonance, alpha should oscillate between those limits as the magnetic field B approaches the point where a -> infinity. In any interval of B over which a increases by a factor of 22.7, alpha should have a zero.

cond-mat↗

arXiv2000

Effective Theory of the Triton

We apply the effective field theory approach to the three-nucleon system. In particular, we consider S=1/2 neutron-deuteron scattering and the triton. We show that in this channel a unique nonperturbative renormalization takes place which requires the introduction of a single three-body force at leading order. With one fitted parameter we find a good description of low-energy data. Invariance under the renormalization group explains some universal features of the three-nucleon system ---such as the Thomas and Efimov effects and the Phillips line--- and the origin of SU(4) symmetry in nuclei.

nucl-th↗

arXiv1999

Spectral Content of Isoscalar Nucleon Form Factors

The nucleon strange vector and isoscalar electromagnetic form factors are studied using a spectral decomposition. The K\bar{K} contribution to the electric and magnetic radii as well as the magnetic moment is evaluated to all orders in the strong interaction using an analytic continuation of experimental KN scattering amplitudes and bounds from unitarity. The relationship between non-resonant and resonant K\bar{K} contributions to the form factors is demonstrated, and values for the vector and tensor ϕN\bar{N} couplings are derived. The K\bar{K} spectral functions are used to evaluate the credibility of model calculations for the strange quark vector current form factors.

hep-ph↗

arXiv1999

Rare Pionium Decays and Pion Polarizability

We calculate the decay of pionium atoms into two photons. The pion polarizability gives rise to a 10% correction to the corresponding decay width for pointlike pions. This opens the possibility to obtain the difference between the electric and magnetic polarizability of the charged pion from a future measurement of the branching fraction of pionium into two photons. For such an experiment the ππ-scattering lengths would have to be known to better than 5% precision. We also comment on the contribution of the axial anomaly to the decay of pionium into γπ^0.

hep-ph↗

arXiv1999

Effective Theory for Neutron-Deuteron Scattering and the Triton

We apply the effective field theory approach to the three-nucleon system. In particular, we consider neutron-deuteron scattering and the triton. Precise predictions for S=3/2 scattering are obtained in a straightforward way. In the S=1/2 channel, however, a unique nonperturbative renormalization takes place which requires the introduction of a three-body force at leading order. We also show that invariance under the renormalization group explains some universal features of the three-nucleon system.

nucl-th↗

arXiv1999

K\bar{K}-Continuum and Isoscalar Nucleon Form Factors

We analyse the isoscalar vector current form factors of the nucleon using dispersion relations. In addition to the usual vector meson poles, we account for the K\bar{K}-continuum contribution by drawing upon a recent analytic continuation of KN scattering amplitudes. For the Pauli form factor all strength in the ϕregion is already given by the continuum contribution, whereas for the Dirac form factor additional strength in the ϕregion is required. The pertinent implications for the leading strangeness moments are demonstrated as well. We derive a reasonable range for the leading moments which is free of assumptions about the asymptotic behavior of the form factors. We also determine the \phiNN coupling constants from the form factor fits and directly from the K\bar{K} -> N\bar{N} partial waves and compare the resulting values.

hep-ph↗