arXiv subjects

Thomas D. Cohen

Publications and source records attributed to Thomas D. Cohen.

At least 55 records · Page 3Linked to original sources

arXiv2013

Multi-channel S-matrices from energy levels in finite boxes

We show that for a generic quantum mechanical system with more than one open scattering channel, it is not possible to fully reconstruct the theory's S-matrix from spectral information obtained in large finite volumes with periodic boundary conditions. Physically distinct S-matrices can have identical finite-volume spectra for large finite boxes of arbitrary sizes. If the theory is not time-reversal symmetric, there exists an uncountably infinite set of distinct S-matrices with the same spectra. If the theory respects time-reversal symmetry there exists a discrete set of S-matrices with identical energy levels for finite boxes. We illustrate the issue for simple quantum mechanical systems in 1+1 dimensions.

hep-lat↗

arXiv2012

Baryons and Low-Density Baryonic Matter in 1+1 Dimensional Large N_c QCD with Heavy Quarks

This paper studies baryons and baryonic matter in the combined large N_c and heavy quark mass limits of QCD in 1+1 dimension. In this non-relativistic limit, baryons are composed of N_c quarks that interact, at leading order in N_c, through a color Coulomb potential. Using variational techniques, very accurate calculations of single baryon masses and interaction energies of low-density baryon crystal are performed. These results are used to cross-check a general numerical approach applicable for arbitrary quark masses and baryon densities recently proposed by Bringoltz, which is based on a lattice in a finite box with periodic boundary conditions. The Bringoltz method differs from a previous approach of Salcedo, et al. in its treatment of a finite box effect - namely gauge configurations that wind around the box. One might expect these effects to be small for large enough boxes, in which the baryon density approaches zero to high accuracy at the edges. However, the effects of these windings appear to be quite large even in such boxes. The large mass infinite volume calculations performed here are consistent with the results of numerical calculations using the Bringoltz method. The calculation of the baryon crystal interaction energy requires the assumption that at low-densities the ground state is composed of individual baryons, each in a color-singlet state and orthogonal to each other. This assumption is plausible but ad hoc in that one can construct configurations in which the entire state is color-singlet but cannot be broken into individual color-singlet baryons. The interaction energy of low-density baryon crystals calculated with the assumption is consistent with numerical results based on Bringoltz's approach suggesting that the assumption is justified. This further supports a similar assumption that was made in 3+1 dimensions, where no alternative means of calculation exist.

nucl-th↗

arXiv2012

Alternate 1/N_c Expansions and SU(3) Breaking from Baryon Lattice Results

A combined expansion in the number of QCD colors 1/N_c and SU(3) flavor breaking parameter epsilon has long been known to provide an excellent accounting for the mass spectrum of the lightest spin-1/2, 3/2 baryons when the quarks are taken to transform under the fundamental SU(N_c) representation, and in the final step N_c \to 3 and epsilon is set to its physical value ~0.3. Subsequent work shows that placing quarks in the two-index antisymmetric SU(N_c) representation leads to quantitatively equally successful mass relations. Recent lattice simulations allow for varying the value of epsilon and confirm the robustness of the original 1/N_c relations. In this paper we show that the same conclusion holds for the antisymmetric quarks, and demonstrate that the mass relations also hold under alternate prescriptions for identifying physical baryons with particular members of the large N_c multiplets.

hep-ph↗

arXiv2012

Model-independent form factor relations at large $N_c$

In this paper a model-independent relation which holds for the long distance part of the Fourier transform of the electromagnetic form factors of the nucleon in the large $N_c$ and chiral limits is demonstrated. This relation was previously conjectured based on the fact that it emerged in {\it all} semiclassical chiral models independent of the details of the model. Here we show that the result is, in fact, model independent by deriving it directly in large $N_c$ chiral perturbation theory which is known to capture the long distance behavior of the form factors. The relation is valid when the large $N_c$ limit is formally taken before the chiral limit. A new relation is derived for the case where the chiral limit is taken prior to the large $N_c$ limit.

hep-ph↗

arXiv2012

The total nucleon-nucleon cross section at large N_c

It is shown that at sufficiently large $N_c$ for incident momenta which are much larger than the QCD, the total nucleon-nucleon cross section is independent of incident momentum and given by $σ^{\rm total}=2 π\log^2(N_c) / (m^2_π)$. This result is valid in the extreme large $N_c$ regime of $\log(N_c) \gg 1$ and has corrections of relative order $\log (\log(N_c))/\log(N_c)$. A possible connection of this result to the Froissart-Martin bound is discussed.

hep-ph↗

arXiv2012

Total nucleon-nucleon cross sections in large N(c) QCD

We use contracted spin-flavor symmetry which emerges in the large Nc limit of QCD to obtain relations between proton-proton and proton-neutron total cross sections for both polarized and unpolarized scattering. The formalism used is valid in the semi-classical regime in which the relative momentum of the incident nucleons is much larger than the inverse size of the nucleon, provided that certain technical assumptions are met. The relations should be phenomenologically useful provided that Nc=3 is sufficiently large so that the large Nc results have at least semi-quantitative predictive power. The relations are model-independent in the sense that they depend on properties of large Nc QCD only and not on any particular model-dependent details of the nucleon-nucleon interaction. We compare these model-independent results to experimental data. We find the relation for spin-unpolarized scattering works well empirically. For the case of polarized scattering, the data is consistent with the relations but the cross sections are too small to make sharp predictions.

nucl-th↗

arXiv2011

Does the empirical meson spectrum support the Hagedorn conjecture?

It has long been conjectured that strong interactions give rise to a Hagedorn spectrum and theoretical arguments have been presented in support of Hagedorn spectrum in large $N_c$ QCD. This paper discusses the extent to which the meson spectrum should be viewed as evidence for a Hagedorn spectrum and argues that data do not provide a strong evidence for the Hagedorn conjecture. The conclusion is based on three reasons. It is shown that "realistic" quark models have a spectrum in which the number of mesons up to 2.3 GeV grows with mass in a very similar way to the spectrum of physical mesons up to 2.3 GeV. However, these models can be shown not to have Hagedorn spectra. It is also shown that the available data are insufficient to determine the Hagedorn temperature. The data can be described with comparable accuracy by various functional forms of the prefactor that yield radically different Hagedorn temperatures. An analysis of the behavior of the spectrum for the various parity-spin-charge conjugation-isospin channels also appears to be inconsistent with what one expects if the data were in the regime dominated by exponential behavior.

hep-ph↗

arXiv2011

Conference Discussion of the Nuclear Force

Discussion of the nuclear force, lead by a round table consisting of T. Cohen, E. Epelbaum, R. Machleidt, and F. Gross (chair). After an invited talk by Machleidt, published elsewhere in these proceedings, brief remarks are made by Epelbaum, Cohen, and Gross, followed by discussion from the floor moderated by the chair. The chair asked the round table and the participants to focus on the following issues: (i) What does each approach (chiral effective field theory, large Nc, and relativistic phenomenology) contribute to our knowledge of the nuclear force? Do we need them all? Is any one transcendent? (ii) How important for applications (few body, nuclear structure, EMC effect, for example) are precise fits to the NN data below 350 MeV? How precise do these fits have to be? (iii) Can we learn anything about nonperturbative QCD from these studies of the nuclear force? The discussion presented here is based on a video recording made at the conference and transcribed afterward.

nucl-th↗

arXiv2011

The Hagedorn spectrum and large $N_c$ QCD in 2+1 and 3+1 dimensions

We show that a Hagedorn spectrum (i.e., spectrum where the number of hadrons grows exponentially with the mass) emerges automatically in large $N_c$ QCD in 2+1 and 3+1 dimensions. The approach is based on the study of Euclidean space correlation functions for composite operators constructed from quark and gluon fields and exploits the fact that the short time behavior of the correlators is known in QCD. The demonstration relies on one critical assumption: that perturbation theory accurately describes the trace of the logarithm of a matrix of point-to-point correlation functions in the regime where the perturbative corrections to the asymptotically free value are small.

hep-th↗

arXiv2011

On Chiral Symmetry Restoration at Finite Density in Large N_c QCD

At large N_c, cold nuclear matter is expected to form a crystal and thus spontaneously break translational symmetry. The description of chiral symmetry breaking and translational symmetry breaking can become intertwined. Here, the focus is on aspects of chiral symmetry breaking and its possible restoration that are by construction independent of the nature of translational symmetry breaking---namely spatial averages of chiral order parameters. A system will be considered to be chirally restored provided all spatially-averaged chiral order parameters are zero. A critical question is whether chiral restoration in this sense is possible for phases in which chiral order parameters are locally non-zero but whose spatial averages all vanish. We show that this is not possible unless all chirally-invariant observables are spatially uniform. This result is first derived for Skyrme-type models, which are based on a nonlinear sigma model and by construction break chiral symmetry on a point-by-point basis. A no-go theorem for chiral restoration (in the average sense) for all models of this type is obtained by showing that in these models there exist chirally symmetric order parameters which cannot be spatially uniform. Next we show that the no-go theorem applies to large N_c QCD in any phase which has a non-zero but spatially varying chiral condensate. The theorem is demonstrated by showing that in a putative chirally-restored phase, the field configuration can be reduced to that of a nonlinear sigma model.

nucl-th↗

arXiv2011

Baryons and baryonic matter in the large Nc and heavy quark limits

This paper explores properties of baryons and finite density baryonic matter in an artificial world in which Nc, the number of colors, is large and the quarks of all species are degenerate and much larger than Λ_QCD. It has long been known that in large Nc QCD, baryons composed entirely of heavy quarks are accurately described in the mean-field approximation. However, the detailed properties of baryons in the combined large Nc and heavy quark limits have not been fully explored. Here some basic properties of baryons are computed using a variational approach. At leading order in both the large Nc and heavy quark expansions the baryon mass is computed explicitly as is the baryon form factor. Baryonic matter, the analog of nuclear matter in this artificial world, should also be well described in the mean-field approximation. In the special case where all baryons have an identical spin flavor structure, it is shown that in the formal heavy quark and large Nc limit interactions between baryons are strictly repulsive at low densities. The energy per baryon is computed in this limit and found to be exponentially small. It is shown that when the restriction to baryons with an identical spin-flavor structure is dropped, a phase of baryonic matter exists with a density of 2Nf times that for the restricted case but with the same energy (where Nf is the number of degenerate flavors). It is shown that this phase is at least metastable.

nucl-th↗

arXiv2010

QCD and the Hagedorn spectrum

It is shown that large Nc QCD must have a Hagedorn spectrum (i.e. a spectrum of hadron which grows exponentially with the hadrons mass) provided that certain technical assumptions concerning the applicability of perturbation theory to a certain class of correlation functions apply. The basic argument exploits the interplay of confinement and asymptotic freedom.

hep-th↗

arXiv2010

The chiral condensate in holographic models of QCD

Bottom-up holographic models of QCD, inspired by the AdS/CFT correspondence, have shown a remarkable degree of phenomenological success. However, they rely on a number of bold assumptions. We investigate the reliability of one of the key assumptions, which involves matching the parameters of these models to QCD at high 4D momentum $q^2$ and renormalization scale $μ^2$. We show that this leads to phenomenological and theoretical inconsistencies for scale-dependent quantities such as $\bra \bar{q}q\ket$

hep-ph↗

arXiv2009

Baryons in QCD_{AS} at Large N_c: A Roundabout Approach

QCD_{AS}, a variant of large N_c QCD in which quarks transform under the color two-index antisymmetric representation, reduces to standard QCD at N_c = 3 and provides an alternative to the usual large N_c extrapolation that uses fundamental representation quarks. Previous strong plausibility arguments assert that the QCD_{AS} baryon mass scales as N_c^2; however, the complicated combinatoric problem associated with quarks carrying two color indices impeded a complete demonstration. We develop a diagrammatic technique to solve this problem. The key ingredient is the introduction of an effective multi-gluon vertex: a "traffic circle" or "roundabout" diagram. We show that arbitrarily complicated diagrams can be reduced to simple ones with the same leading N_c scaling using this device, and that the leading contribution to baryon mass does, in fact, scale as N_c^2.

hep-ph↗

arXiv2009

Hadrons and Chiral Symmetry

These lectures discuss the question of whether a key feature is seen in hadron spectroscopy--the near degeneracy of hadrons with different parity and/or spin. It has been conjectured that this is due to an effective restoration of chiral symmetry. The conjecture is that while these states are, of course, in the symmetry-broken (Nambu-Goldstone) phase, as one goes higher in the spectrum the states become progressively less sensitive to the dynamics of chiral symmetry breaking. These lectures discuss the current status of this conjecture. The motivations for the conjecture are discussed, as is evidence--both theoretical and experimental--in its favor. Possible alternative explanations for the data are also discussed.

hep-ph↗

arXiv2009

Color Superconductivity at Large N: A New Hope

At zero density, the `t Hooft large N_c limit often provides some very useful qualitative insights into the non-perturbative physics of QCD. However, it is known that at high densities the `t Hooft large N_c world looks very different from the N_c=3 world, which is believed to be in a color superconducting phase at high densities. At large N_c, on the other hand, the DGR instability causes a chiral-density wave phase to dominate over the color superconducting phase. There is an alternative large N_c limit, with the quarks transforming in the two-index antisymmetric representation of the gauge group, which at N_c=3 reduces to QCD but looks quite different at large N_c. We show that in this alternative large N_c limit, the DGR instability does not occur, so that it may be plausible that the ground state of high-density quark matter is a color superconductor even when N_c is large. This revives the hope that a large N_c approximation might be useful for getting some insights into the high-density phenomenology of QCD.

hep-ph↗

arXiv2009

All you need is N: Baryon spectroscopy in two large N limits

The generalization of QCD to many colors is not unique; each distinct choice corresponds to a distinct 1/N_c expansion. The familiar 't Hooft N_c -> \infty limit places quarks in the fundamental representation of SU(N_c), while an alternative approach places quarks in its two-index antisymmetric representation. At N_c=3 these two 1/N_c expansions coincide. We compare their predictions for certain observables in baryon spectroscopy, particularly mass combinations organized according to SU(3) flavor breaking. Each large N_c limit generates an emergent spin-flavor symmetry that leads to the vanishing of particular linear combinations of baryon masses at specific orders in the expansions. Experimental evidence shows that these relations hold at the expected orders regardless of which large N_c limit one uses, suggesting the validity of either limit in the study of baryons. We also consider a hybrid large N_c limit in which one flavor is taken to transform in the two-index antisymmetric representation and the rest of the flavors are in the fundamental representation. While this hybrid large N_c limit is theoretically attractive, we show that for a wide class of observables it faces some phenomenological difficulties.

hep-ph↗

arXiv2009

To what systems does the Bohigas conjecture apply?

We test the applicability of the Bohigas conjecture to systems whose Hamiltonian is not written as a closed form analytic expression. A class of such Hamiltonians is created and appear to violate the conjecture. Numerical methods are employed to find the spectra of a two-dimensional, classically chaotic "billiard" system whose Hamiltonian is in this class. We find that the spectral fluctuations are not in agreement with the conjecture.

quant-ph↗