12 research outputs found
Low Energy Theorems For Nucleon-Nucleon Scattering
Low energy theorems are derived for the coefficients of the effective range
expansion in s-wave nucleon-nucleon scattering valid to leading order in an
expansion in which both and (where is the scattering length)
are treated as small mass scales. Comparisons with phase shift data, however,
reveal a pattern of gross violations of the theorems for all coefficients in
both the and channels. Analogous theorems are developed for the
energy dependence parameter which describes mixing.
These theorems are also violated. These failures strongly suggest that the
physical value of is too large for the chiral expansion to be valid in
this context. Comparisons of with phenomenological scales known to
arise in the two-nucleon problem support this conjecture.Comment: 12 pages, 1 figure, 1 table; appendix added to discuss behavior in
chiral limit; minor revisions including revised figure reference to recent
work adde
Producing the Deuteron in Stars: Anthropic Limits on Fundamental Constants
Stellar nucleosynthesis proceeds via the deuteron (D), but only a small
change in the fundamental constants of nature is required to unbind it. Here,
we investigate the effect of altering the binding energy of the deuteron on
proton burning in stars. We find that the most definitive boundary in parameter
space that divides probably life-permitting universes from probably
life-prohibiting ones is between a bound and unbound deuteron. Due to neutrino
losses, a ball of gas will undergo rapid cooling or stabilization by electron
degeneracy pressure before it can form a stable, nuclear reaction-sustaining
star. We also consider a less-bound deuteron, which changes the energetics of
the and reactions. The transition to endothermic and
reactions, and the resulting beta-decay instability of the deuteron, do not
seem to present catastrophic problems for life.Comment: 19 pages, 5 figures. Accepted to JCAP. Revised to match the published
version; corrected to better take into account free neutron
The Coulomb interaction in Helium-3: Interplay of strong short-range and weak long-range potentials
Quantum chromodynamics and the electroweak theory at low energies are
prominent instances of the combination of a short-range and a long-range
interaction. For the description of light nuclei, the large nucleon-nucleon
scattering lengths produced by the strong interaction, and the reduction of the
weak interaction to the Coulomb potential, play a crucial role. Helium-3 is the
first bound nucleus comprised of more than one proton in which this combination
of forces can be studied.
We demonstrate a proper renormalization of Helium-3 using the pionless
effective field theory as the formal representation of the nuclear regime as
strongly interacting fermions. The theory is found consistent at leading and
next-to-leading order without isospin-symmetry-breaking 3-nucleon interactions
and a non-perturbative treatment of the Coulomb interaction. The conclusion
highlights the significance of the regularization method since a comparison to
previous work is contradictory if the difference in those methods is not
considered.
With a perturbative Coulomb interaction, as suggested by dimensional
analysis, we find the Helium-3 system properly renormalized, too.
For both treatments, renormalization-scheme independence of the effective
field theory is demonstrated by regulating the potential and a variation of the
associated cutoff.Comment: accepted version; additional figure; additional discussion of renorm.
and limit cycl
Two-nucleon S-wave interactions at the flavor-symmetric point with : a first lattice QCD calculation with the stochastic Laplacian Heaviside method
We report on the first application of the stochastic Laplacian Heaviside
method for computing multi-particle interactions with lattice QCD to the
two-nucleon system. Like the Laplacian Heaviside method, this method allows for
the construction of interpolating operators which can be used to construct a
positive definite set of two-nucleon correlation functions, unlike nearly all
other applications of lattice QCD to two nucleons in the literature. It also
allows for a variational analysis in which optimal linear combinations of the
interpolating operators are formed that couple predominantly to the eigenstates
of the system. Utilizing such methods has become of paramount importance in
order to help resolve the discrepancy in the literature on whether two nucleons
in either isospin channel form a bound state at pion masses heavier than
physical, with the discrepancy persisting even in the -flavor symmetric
point with all quark masses near the physical strange quark mass. This is the
first in a series of papers aimed at resolving this discrepancy. In the present
work, we employ the stochastic Laplacian Heaviside method without a hexaquark
operator in the basis at a lattice spacing of ~fm, lattice volume
of ~fm and pion mass MeV. With this setup, the
observed spectrum of two-nucleon energy levels strongly disfavors the presence
of a bound state in either the deuteron or dineutron channel.Comment: v2: version to be published in Phys. Rev. C.; v1: 13 pages plus
figures and appendice
Low-energy scattering and effective interaction of two baryons at m(pion) ~ 450 MeV from lattice quantum chromodynamics
The interactions between two-octet baryons are studied at low energies using lattice quantum chromodynamics (LQCD) with larger-than-physical quark masses corresponding to a pion mass of ~450 MeV and a kaon mass of ~ 596 MeV. The two-baryon systems that are analyzed range from strangeness S=0 to -4 and include the spin-singlet and triplet NN, ΣN (I=3/2), and ΞΞ states, the spin-singlet ΣΣ (I=2) and ΞΣ (I=3/2) states, and the spin-triplet ΞN (I=0) state. The corresponding s-wave scattering phase shifts, low-energy scattering parameters, and binding energies when applicable are extracted using Lüscher's formalism. While the results are consistent with most of the systems being bound at this pion mass, the interactions in the spin-triplet ΣN and ΞΞ channels are found to be repulsive and do not support bound states. Using results from previous studies of these systems at a larger pion mass, an extrapolation of the binding energies to the physical point is performed and is compared with available experimental values and phenomenological predictions. The low-energy coefficients in pionless effective field theory (EFT) relevant for two-baryon interactions, including those responsible for SU(3) flavor-symmetry breaking, are constrained. The SU(3) flavor symmetry is observed to hold approximately at the chosen values of the quark masses, as well as the SU(6) spin-flavor symmetry, predicted at large Nc. A remnant of an accidental SU(16) symmetry found previously at a larger pion mass is further observed. The SU(6)-symmetric EFT constrained by these LQCD calculations is used to make predictions for two-baryon systems for which the low-energy scattering parameters could not be determined with LQCD directly in this study, and to constrain the coefficients of all leading SU(3) flavor-symmetric interactions, demonstrating the predictive power of two-baryon EFTs matched to LQCD
Chiral perturbation theory for heavy hadrons and chiral effective field theory for heavy hadronic molecules
Chiral symmetry and its spontaneous breaking play an important role both in
the light hadron and heavy hadron systems. In this work, we shall review the
investigations on the chiral corrections to the properties of the heavy mesons
and baryons within the framework of the chiral perturbation theory (PT).
We will also review the scatterings of the light pseudoscalar mesons and heavy
hadrons. Moreover, the modern nuclear force was built upon the chiral effective
field theory (EFT). In the past decades many new hadron states were
observed experimentally. A large group of these states are near-threshold
resonances, such as the charged charmoniumlike and states,
bottomoniumlike states, hidden-charm pentaquark and states
and the doubly charmed state etc. They are very good candidates of the
loosely bound molecular states composed of a pair of charmed hadrons. The same
chiral dynamics not only governs the nuclei and forms the deuteron, but also
dictates the above shallow bound states or resonances. We will perform an
extensive review on the progress on the heavy hadronic molecular states within
the framework of EFT.Comment: A Review on hadronic molecules in EFT frameworks with 168 pages and
67 figure
Towards grounding nuclear physics in QCD
Exascale computing could soon enable a predictive theory of nuclear structure
and reactions rooted in the Standard Model, with quantifiable and
systematically improvable uncertainties. Such a predictive theory will help
exploit experiments that use nucleons and nuclei as laboratories for testing
the Standard Model and its limitations. Examples include direct dark matter
detection, neutrinoless double beta decay, and searches for permanent electric
dipole moments of the neutron and atoms. It will also help connect QCD to the
properties of cold neutron stars and hot supernova cores. We discuss how a
quantitative bridge between QCD and the properties of nuclei and nuclear matter
will require a synthesis of lattice QCD (especially as applied to two- and
three-nucleon interactions), effective field theory, and ab initio methods for
solving the nuclear many-body problem. While there are significant challenges
that must be addressed in developing this triad of theoretical tools, the rapid
advance of computing is accelerating progress. In particular, we focus this
review on the anticipated advances from lattice QCD and how these advances will
impact few-body effective theories of nuclear physics by providing critical
input, such as constraints on unknown low-energy constants of the effective
(field) theories. We also review particular challenges that must be overcome
for the successful application of lattice QCD for low-energy nuclear physics.
We describe progress in developing few-body effective (field) theories of
nuclear physics, with an emphasis on HOBET, a non-relativistic effective theory
of nuclear physics, which is less common in the literature. We use the examples
of neutrinoless double beta decay and the nuclear-matter equation of state to
illustrate how the coupling of lattice QCD to effective theory might impact our
understanding of symmetries and exotic astrophysical environments.Comment: v2: updated manuscript based upon community feedback and referee
comments. Also, substantially re-written section on two-nucleon lattice QCD
controversy. 53.5 pages plus a "few more" references; v1: Contribution to:
The tower of effective (field) theories and the emergence of nuclear
phenomena; 47 pages plus a "few" reference