Universal physics of two neutrons with one flavored meson

. The meson-neutron scattering length can become infinitely large in an unphysical region of the quark mass when extrapolated from strangeness to charm in the so-called zero coupling limit. Using a low-energy cluster effective field theory, we demonstrate that the Efimov effect is manifest in the three-body system when the meson-neutron scattering length is extrapolated to the unitary limit of the two-body interaction. We thereby discuss the consequence of universal physics in the physical

K^{-}nn

and

D^{0}nn

systems.

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Universal physics of the few-body system of two neutrons and one flavored meson

Udit Raha, Yuki Kamiya, Shung-Ichi Ando +1 more

We investigate the $s$ -wave three-body system of two neutrons and one flavored meson with total spin-isospin $J=0,I=3/2$ . The meson-neutron scattering length can become infinitely large when extrapolated to an unphysical region of the quark mass between strangeness and charm in the so-called zero coupling limit. Using a low-energy cluster effective field theory, we demonstrate that the Efimov effect is formally manifest in the three-body system when the meson-neutron scattering length approaches the unitary limit of the two-body interaction. We thereby discuss the consequence of remnant universal physics in the physical ${K}^{\ensuremath{-}}nn$ and ${D}^{0}nn$ systems.We investigate the $s$-wave three-body system of two neutrons and one flavored meson with total spin-isospin $J=0,I=3/2$. The meson-neutron scattering length can become infinitely large when extrapolated to an unphysical region of the quark mass between strangeness and charm in the so-called zero coupling limit. Using a low-energy cluster effective field theory, we demonstrate that the Efimov effect is formally manifest in the three-body system when the meson-neutron scattering length approaches the unitary limit of the two-body interaction. We thereby discuss the consequence of remnant universal physics in the physical ${K}^{\ensuremath{-}}nn$ and ${D}^{0}nn$ systems.

arXiv:1708.03369Physical Review CSep 12, 20186 citations

Efimov Effect in Pionless Effective Field Theory and its Application to Hadronic Molecules

Erik Wilbring

In the past years various new hadronic states were discovered in the charm and bottom meson sector by experiments like Belle, BES and Babar. Many of these states fit into the conventional charmonium or bottomonium spectrum, but a growing number of them does not. Especially, the charged ones which can definitely be no conventional hadrons motivate the term exotic hadrons to classify particles which are neither conventional baryons nor conventional mesons. Their substructure is not yet clear due to the often poor experimental knowledge and there are many different interpretations for these exotic particles. One very popular idea is the hadronic molecule interpretation which states that two ordinary hadrons can form a loosely bound pair similar to the deuteron made of a proton and a neutron. However, in the latter system it is known that after adding a third nucleon there appears a three particle bound state, the triton. The emergence of such a three-body state can be explained by the Efimov effect as a low-energy universality phenomenon. The question which will be answered in this work is if there exists also an Efimov effect in systems of hadronic molecules which scatter off a third meson or baryon. Since the number of candidate systems is large (and still growing due to ongoing experiments) it is useful to find a general expression that tells us if the Efimov effect is present. Moreover, this expression should only depend on the basic particle properties like mass, spin and isospin. Such a relation will be derived in this work for a generic three particle system that can be described in a pionless effective field theory. It will then be applied to a set of possible hadronic molecule systems in order to check if the Efimov effect occurs. The thesis is organized as follows: after an introduction of quantum chromodynamics and a review of the classification of hadrons we continue with a summary, firstly, of experimental observations concerning exotic hadrons, secondly, of the idea of effective field theories and thirdly, of basic scattering theory. In chapter 2 the three identical boson system will be discussed in order to explain the Efimov effect more quantitatively. With this knowledge it is possible to derive the mentioned general expression regarding the existence of Efimov physics in a generic three particle system. After the detailed derivation in chapter 3 (using the information given in the appendices) the results will be applied to scattering processes where known hadronic molecules as well as hypothetical ones are involved. This is done in order to either search for the Efimov effect or - for the hypothetical molecular states - to predict under which conditions an Efimov trimer is expected. For system without Efimov effect we will calculate in chapter 5 for a selected example S-wave observables of the in this case elastic scattering process. The thesis is completed by a summary of the results and an outlook on further work that can be done based on this work.In the past years various new hadronic states were discovered in the charm and bottom meson sector by experiments like Belle, BES and Babar. Many of these states fit into the conventional charmonium or bottomonium spectrum, but a growing number of them does not. Especially, the charged ones which can definitely be no conventional hadrons motivate the term exotic hadrons to classify particles which are neither conventional baryons nor conventional mesons. Their substructure is not yet clear due to the often poor experimental knowledge and there are many different interpretations for these exotic particles. One very popular idea is the hadronic molecule interpretation which states that two ordinary hadrons can form a loosely bound pair similar to the deuteron made of a proton and a neutron. However, in the latter system it is known that after adding a third nucleon there appears a three particle bound state, the triton. The emergence of such a three-body state can be explained by the Efimov effect as a low-energy universality phenomenon. The question which will be answered in this work is if there exists also an Efimov effect in systems of hadronic molecules which scatter off a third meson or baryon. Since the number of candidate systems is large (and still growing due to ongoing experiments) it is useful to find a general expression that tells us if the Efimov effect is present. Moreover, this expression should only depend on the basic particle properties like mass, spin and isospin. Such a relation will be derived in this work for a generic three particle system that can be described in a pionless effective field theory. It will then be applied to a set of possible hadronic molecule systems in order to check if the Efimov effect occurs. The thesis is organized as follows: after an introduction of quantum chromodynamics and a review of the classification of hadrons we continue with a summary, firstly, of experimental observations concerning exotic hadrons, secondly, of the idea of effective field theories and thirdly, of basic scattering theory. In chapter 2 the three identical boson system will be discussed in order to explain the Efimov effect more quantitatively. With this knowledge it is possible to derive the mentioned general expression regarding the existence of Efimov physics in a generic three particle system. After the detailed derivation in chapter 3 (using the information given in the appendices) the results will be applied to scattering processes where known hadronic molecules as well as hypothetical ones are involved. This is done in order to either search for the Efimov effect or - for the hypothetical molecular states - to predict under which conditions an Efimov trimer is expected. For system without Efimov effect we will calculate in chapter 5 for a selected example S-wave observables of the in this case elastic scattering process. The thesis is completed by a summary of the results and an outlook on further work that can be done based on this work.

Jan 21, 20161 citation

Universal physics of three bosons with isospin

Tetsuo Hyodo, Tetsuo Hatsuda, Yusuke Nishida

We show that there exist two types of universal phenomena for three-boson systems with isospin degrees of freedom. In the isospin symmetric limit, there is only one universal three-boson bound state with the total isospin one, whose binding energy is proportional to that of the two-boson bound state. With large isospin symmetry breaking, the standard Efimov states of three identical bosons appear at low energies. Both phenomena can be realized by three pions with the pion mass appropriately tuned in lattice QCD simulations, or by spin-one bosons in cold atom experiments. Implication to the in-medium softening of multi-pion states is also discussed.We show that there exist two types of universal phenomena for three-boson systems with isospin degrees of freedom. In the isospin symmetric limit, there is only one universal three-boson bound state with the total isospin one, whose binding energy is proportional to that of the two-boson bound state. With large isospin symmetry breaking, the standard Efimov states of three identical bosons appear at low energies. Both phenomena can be realized by three pions with the pion mass appropriately tuned in lattice QCD simulations, or by spin-one bosons in cold atom experiments. Implication to the in-medium softening of multi-pion states is also discussed.

arXiv:1311.6289Physical Review CMar 7, 201413 citations

Super Efimov effect for mass-imbalanced systems

Sergej Moroz, Yusuke Nishida

We study two species of particles in two dimensions interacting by isotropic short-range potentials with the interspecies potential fine-tuned to a $p$ -wave resonance. Their universal low-energy physics can be extracted by analyzing a properly constructed low-energy effective field theory with the renormalization group method. Consequently, a three-body system consisting of two particles of one species and one of the other is shown to exhibit the super Efimov effect, the emergence of an infinite tower of three-body bound states with orbital angular momentum $\ensuremath{\ell}=\ifmmode\pm\else\textpm\fi{}1$ whose binding energies obey a doubly exponential scaling, when the two particles are heavier than the other by a mass ratio greater than 4.034 04 for identical bosons and 2.414 21 for identical fermions. With increasing the mass ratio, the super Efimov spectrum becomes denser which would make its experimental observation easier. We also point out that the Born-Oppenheimer approximation is incapable of reproducing the super Efimov effect, the universal low-energy asymptotic scaling of the spectrum.We study two species of particles in two dimensions interacting by isotropic short-range potentials with the interspecies potential fine-tuned to a $p$-wave resonance. Their universal low-energy physics can be extracted by analyzing a properly constructed low-energy effective field theory with the renormalization group method. Consequently, a three-body system consisting of two particles of one species and one of the other is shown to exhibit the super Efimov effect, the emergence of an infinite tower of three-body bound states with orbital angular momentum $\ensuremath{\ell}=\ifmmode\pm\else\textpm\fi{}1$ whose binding energies obey a doubly exponential scaling, when the two particles are heavier than the other by a mass ratio greater than 4.034 04 for identical bosons and 2.414 21 for identical fermions. With increasing the mass ratio, the super Efimov spectrum becomes denser which would make its experimental observation easier. We also point out that the Born-Oppenheimer approximation is incapable of reproducing the super Efimov effect, the universal low-energy asymptotic scaling of the spectrum.

arXiv:1407.7664Physical Review ADec 22, 201423 citations

Some aspects of universality in Efimov physics

M. Gattobigio, Alejandro Kievsky

The Efimov effect is the appearance of an infinite tower of bound states, E n 3 , that accumulate in a geometrical way at zero energy in systems of three-identical bosons having an infinite large two-body scattering length a . In the zero-range limit the geometrical factor is E n +1 3 / E n 3 = e −2π/ s 0 with s 0 ≈ 1.00624 an universal number. The Efimov effect is the signature of the discrete scale invariance (DSI) present in these systems close to the unitary limit (1/ a = 0). The DSI constrains also the spectrum in N > 3 systems. In this contribution the two-level tree structure observed in bosons systems with N ≥ 4 will be discussed using potential models.The Efimov effect is the appearance of an infinite tower of bound states, E n 3 , that accumulate in a geometrical way at zero energy in systems of three-identical bosons having an infinite large two-body scattering length a . In the zero-range limit the geometrical factor is E n +1 3 / E n 3 = e −2π/ s 0 with s 0 ≈ 1.00624 an universal number. The Efimov effect is the signature of the discrete scale invariance (DSI) present in these systems close to the unitary limit (1/ a = 0). The DSI constrains also the spectrum in N > 3 systems. In this contribution the two-level tree structure observed in bosons systems with N ≥ 4 will be discussed using potential models.

Journal of Physics Conference SeriesJul 7, 20141 citation

Unitarity potentials and neutron matter at the unitary limit

Huan Dong, L.-W. Siu, T.T.S. Kuo +1 more

We study the equation of state of neutron matter using a family of unitarity potentials, all of which are constructed to have infinite ${}^{1}{S}_{0}$ scattering lengths ${a}_{s}$ . For such a system, a quantity of much interest is the ratio $\ensuremath{\xi}={E}_{0}/{E}_{0}^{\mathrm{free}}$, where ${E}_{0}$ is the true ground-state energy of the system and ${E}_{0}^{\mathrm{free}}$ is that for the noninteracting system. In the limit of ${a}_{s}\ensuremath{\rightarrow}\ifmmode\pm\else\textpm\fi{}\ensuremath{\infty}$, often referred to as the unitary limit, this ratio is expected to approach a universal constant, namely $\ensuremath{\xi}~0.44(1)$. In the present work we calculate this ratio $\ensuremath{\xi}$ using a family of hard-core square-well potentials whose ${a}_{s}$ can be exactly obtained, thus enabling us to have many potentials of different ranges and strengths, all with infinite ${a}_{s}$ . We have also calculated $\ensuremath{\xi}$ using a unitarity CDBonn potential obtained by slightly scaling its meson parameters. The ratios $\ensuremath{\xi}$ given by these different unitarity potentials are all close to each other and also remarkably close to 0.44, suggesting that the above ratio $\ensuremath{\xi}$ is indifferent to the details of the underlying interactions as long as they have infinite scattering length. A sum-rule and scaling constraint for the renormalized low-momentum interaction in neutron matter at the unitary limit is studied. The importance of pairing in our all-order ring diagram and model-space HF calculations of neutron matter is discussed.We study the equation of state of neutron matter using a family of unitarity potentials, all of which are constructed to have infinite ${}^{1}{S}_{0}$ scattering lengths ${a}_{s}$. For such a system, a quantity of much interest is the ratio $\ensuremath{\xi}={E}_{0}/{E}_{0}^{\mathrm{free}}$, where ${E}_{0}$ is the true ground-state energy of the system and ${E}_{0}^{\mathrm{free}}$ is that for the noninteracting system. In the limit of ${a}_{s}\ensuremath{\rightarrow}\ifmmode\pm\else\textpm\fi{}\ensuremath{\infty}$, often referred to as the unitary limit, this ratio is expected to approach a universal constant, namely $\ensuremath{\xi}~0.44(1)$. In the present work we calculate this ratio $\ensuremath{\xi}$ using a family of hard-core square-well potentials whose ${a}_{s}$ can be exactly obtained, thus enabling us to have many potentials of different ranges and strengths, all with infinite ${a}_{s}$. We have also calculated $\ensuremath{\xi}$ using a unitarity CDBonn potential obtained by slightly scaling its meson parameters. The ratios $\ensuremath{\xi}$ given by these different unitarity potentials are all close to each other and also remarkably close to 0.44, suggesting that the above ratio $\ensuremath{\xi}$ is indifferent to the details of the underlying interactions as long as they have infinite scattering length. A sum-rule and scaling constraint for the renormalized low-momentum interaction in neutron matter at the unitary limit is studied. The importance of pairing in our all-order ring diagram and model-space HF calculations of neutron matter is discussed.

arXiv:0912.0273Physical Review CMar 15, 201012 citations

We investigate the

s

-wave three-body system of two neutrons and one flavored meson with total spin-isospin

J=0,I=3/2

K^{-}nn

and

D^{0}nn

systems.

We investigate the

s

-wave three-body system of two neutrons and one flavored meson with total spin-isospin

J=0,I=3/2

. The meson-neutron scattering length can become infinitely large when extrapolated to an unphysical region of the quark mass between strangeness and charm in the so-called zero coupling limit. Using a low-energy cluster effective field theory, we demonstrate that the Efimov effect is formally manifest in the three-body system when the meson-neutron scattering length approaches the unitary limit of the two-body interaction. We thereby discuss the consequence of remnant universal physics in the physical ${K}^{\ensuremath{-}}nn$ and

{D}^{0}nn

systems.

We study two species of particles in two dimensions interacting by isotropic short-range potentials with the interspecies potential fine-tuned to a

p

-wave resonance. Their universal low-energy physics can be extracted by analyzing a properly constructed low-energy effective field theory with the renormalization group method. Consequently, a three-body system consisting of two particles of one species and one of the other is shown to exhibit the super Efimov effect, the emergence of an infinite tower of three-body bound states with orbital angular momentum $\ensuremath{\ell}=\ifmmode\pm\else\textpm\fi{}1$ whose binding energies obey a doubly exponential scaling, when the two particles are heavier than the other by a mass ratio greater than 4.034 04 for identical bosons and 2.414 21 for identical fermions. With increasing the mass ratio, the super Efimov spectrum becomes denser which would make its experimental observation easier. We also point out that the Born-Oppenheimer approximation is incapable of reproducing the super Efimov effect, the universal low-energy asymptotic scaling of the spectrum.

We study the equation of state of neutron matter using a family of unitarity potentials, all of which are constructed to have infinite

{}^{1}{S}_{0}

scattering lengths

{a}_{s}

. For such a system, a quantity of much interest is the ratio $\ensuremath{\xi}={E}_{0}/{E}_{0}^{\mathrm{free}}$, where

{E}_{0}

is the true ground-state energy of the system and

{E}_{0}^{\mathrm{free}}

is that for the noninteracting system. In the limit of ${a}_{s}\ensuremath{\rightarrow}\ifmmode\pm\else\textpm\fi{}\ensuremath{\infty}$, often referred to as the unitary limit, this ratio is expected to approach a universal constant, namely $\ensuremath{\xi}~0.44(1)$. In the present work we calculate this ratio $\ensuremath{\xi}$ using a family of hard-core square-well potentials whose

{a}_{s}

can be exactly obtained, thus enabling us to have many potentials of different ranges and strengths, all with infinite

{a}_{s}

. We have also calculated $\ensuremath{\xi}$ using a unitarity CDBonn potential obtained by slightly scaling its meson parameters. The ratios $\ensuremath{\xi}$ given by these different unitarity potentials are all close to each other and also remarkably close to 0.44, suggesting that the above ratio $\ensuremath{\xi}$ is indifferent to the details of the underlying interactions as long as they have infinite scattering length. A sum-rule and scaling constraint for the renormalized low-momentum interaction in neutron matter at the unitary limit is studied. The importance of pairing in our all-order ring diagram and model-space HF calculations of neutron matter is discussed.