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T. D. Cohen

Publications and source records attributed to T. D. Cohen.

At least 19 recordsLinked to original sources
arXiv2024

Large $N_c$ QCD phase diagram at $μ_B = 0$

Lattice studies suggest that at zero baryon chemical potential and increasing temperature there are three characteristic regimes in QCD that are connected by smooth analytical crossovers: a hadron gas regime at T < T_ch ~ 155 MeV, an intermediate regime, called stringy fluid, at T_ch < T < ~ 3 T_ch, and a quark-gluon plasma regime at higher temperatures. These regimes have been interpreted to reflect different approximate symmetries and effective degrees of freedom. In the hadron gas the effective degrees of freedom are hadrons and the approximate chiral symmetry of QCD is spontaneously broken. The intermediate regime has been interpreted as lacking spontaneous chiral symmetry breaking along with the emergence of new approximate symmetry, chiral spin symmetry, that is not a symmetry of the Dirac Lagrangian, but is a symmetry of the confining part of the QCD Lagrangian. While the high temperature regime is the usual quark-gluon plasma which is often considered to reflect "deconfinement" in some way. This paper explores the behavior of these regimes of QCD as the number of colors in the theory, N_c, gets large. In the large N_c limit the theory is center-symmetric and notions of confinement and deconfinement are unambiguous. The energy density is O(N_c^0) in the meson gas, O(N_c^1) in the intermediate regime and O(N_c^2) in the quark-gluon plasma regime. In the large N_c limit these regimes may become distinct phases separated by first order phase transitions. The intermediate phase has the peculiar feature that glueballs should exist and have properties that are unchanged from what is seen in the vacuum (up to 1/N_c corrections), while the ordinary dilute gas of mesons with broken chiral symmetry disappears and approximate chiral spin symmetry should emerge.

hep-ph↗
arXiv2024

On interpretation of fluctuations of conserved charges at high T

Fluctuations of conserved charges calculated on the lattice which can be measured experimentally, are well reproduced by a hadron resonanse gas model at temperatures below T_{ch} ~ 155 MeV and radically deviate from the hadron resonance gas predictions above the chiral restoration crossover. This behavior is typically interpreted as an indication of deconfinement in the quark-gluon plasma regime. We present an argument that this interpretation may be too simple. The argument is based on the scaling of quantities with the number of colors: demonstration of deconfinement and QGP requires observable that is sensitive to N_c^2 gluons while the conserved charges are sensitive only to quarks and above T_{ch} scale as N_c^1. The latter scaling is consistent with the existence of an intermediate regime characterized by restored chiral symmetry and by approximate chiral spin symmetry which is a symmetry of confining interaction. In this regime the energy density, pressure and entropy density scale as N_c^1. In the large N_c limit this regime might become a distinct phase separated from the hadron gas and from QGP by phase transitions. A natural observable that associates with deconfinement and is directly sensitive to deconfined N_c^2-1 gluons is the Polyakov loop; in the N_c=3 world it remains very close to 0 at temperatures well above chiral crossover, reaches the value 0.5 around 3T_{ch} and the value close to 1 at temperatures ~1 GeV.

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arXiv2016

Issues and Opportunities in Exotic Hadrons

The last few years have been witness to a proliferation of new results concerning heavy exotic hadrons. Experimentally, many new signals have been discovered that could be pointing towards the existence of tetraquarks, pentaquarks, and other exotic configurations of quarks and gluons. Theoretically, advances in lattice field theory techniques place us at the cusp of understanding complex coupled-channel phenomena, modelling grows more sophisticated, and effective field theories are being applied to an ever greater range of situations. It is thus an opportune time to evaluate the status of the field. In the following, a series of high priority experimental and theoretical issues concerning heavy exotic hadrons is presented.

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arXiv2014

QCD and strongly coupled gauge theories: challenges and perspectives

We highlight the progress, current status, and open challenges of QCD-driven physics, in theory and in experiment. We discuss how the strong interaction is intimately connected to a broad sweep of physical problems, in settings ranging from astrophysics and cosmology to strongly-coupled, complex systems in particle and condensed-matter physics, as well as to searches for physics beyond the Standard Model. We also discuss how success in describing the strong interaction impacts other fields, and, in turn, how such subjects can impact studies of the strong interaction. In the course of the work we offer a perspective on the many research streams which flow into and out of QCD, as well as a vision for future developments.

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arXiv2009

Tests of Universality of Baryon Form Factors in Holographic QCD

We describe a new exact relation for large $N_c$ QCD for the long-distance behavior of baryon form factors in the chiral limit, satisfied by all 4D semi-classical chiral soliton models. We use this relation to test the consistency of the structure of two different holographic models of baryons.

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arXiv2002

The large-N(c) nuclear potential puzzle

An analysis of the baryon-baryon potential from the point of view of large-N(c) QCD is performed. A comparison is made between the N(c)-scaling behavior directly obtained from an analysis at the quark-gluon level to the N(c)-scaling of the potential for a generic hadronic field theory in which it arises via meson exchanges and for which the parameters of the theory are given by their canonical large-N(c) scaling behavior. The purpose of this comparison is to use large-N(c) consistency to test the widespread view that the interaction between nuclei arises from QCD through the exchange of mesons. Although at the one- and two-meson exchange level the scaling rules for the potential derived from the hadronic theory matches the quark-gluon level prediction, at the three- and higher-meson exchange level a generic hadronic theory yields a potential which scales with N(c) faster than that of the quark-gluon theory.

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arXiv2002

Does one observe chiral symmetry restoration in baryon spectrum?

It has recently been suggested that the parity doublet structure seen in the spectrum of highly excited baryons may be due to effective chiral symmetry restoration for these states. We review the recent developments in this field. We demonstrate with a simple quantum-mechanical example that it is a very natural property of quantum systems that a symmetry breaking effect which is important for the low-lying spectrum of the system, can become unimportant for the highly-lying states; the highly lying states reveal a multiplet structure of nearly degenerate states. Using the well established concepts of quark-hadron duality, asymptotic freedom in QCD and validity of the operator product expansion in QCD we show that the spectral densities obtained with the local currents that are connected to each other via chiral transformations, very high in the spectrum must coincide. Hence effects of spontaneous breaking of chiral symmetry in QCD vacuum that are crucially important for the low-lying spectra, become irrelevant for the highly-lying states. Then to the extent that identifiable hadronic resonances still exist in the continuum spectrum at high excitations this implies that the highly excited hadrons must fall into multiplets associated with the representations of the chiral group. We demonstrate that this is indeed the case for meson spectra in the large $N_c$ limit. All possible parity-chiral multiplets are classified for baryons and it is demonstrated that the existing data on highly excited $N$ and $Δ$ states at masses of 2 GeV and higher is consistent with approximate chiral symmetry restoration. However new experimental studies are needed to achieve any definitive conclusions.

hep-ph↗
arXiv2001

Chiral multiplets versus parity doublets in highly excited baryons

It has recently been suggested that the parity doublet structure seen in the spectrum of highly excited baryons may be due to effective chiral restoration for these states. We argue how the idea of chiral symmetry restoration high in the spectrum is consistent with the concept of quark-hadron duality. If chiral symmetry is effectively restored for highly-lying states, then the baryons should fall into representations of $SU(2)_L\times SU(2)_R$ that are compatible with the given parity of the states - the parity-chiral multiplets. We classify all possible parity-chiral multiplets: (i) $(1/2,0)\oplus(0, 1/2)$ that contain parity doublet for nucleon spectrum;(ii) $(3/2,0) \oplus (0, 3/2)$ consists of the parity doublet for delta spectrum; (iii) $(1/2,1) \oplus (1, 1/2)$ contains one parity doublet in the nucleon spectrum and one parity doublet in the delta spectrum of the same spin that are degenerate in mass. Here we show that the available spectroscopic data for nonstrange baryons in the $\sim$ 2 GeV range is consistent with all possibilities, but the approximate degeneracy of parity doublets in nucleon and delta spectra support the latter possibility with excited baryons approximately falling into $(1/2,1) \oplus (1, 1/2)$ representation of $SU(2)_L\timesSU(2)_R$ with approximate degeneracy between positive and negative parity $N$ and $Δ$ resonances of the same spin.

hep-ph↗
arXiv1999

Deuteron electromagnetic properties and the viability of effective field theory methods in the two-nucleon system

The central tenet of effective theory is that the details of short-distance physics will not have a significant impact on low-energy observables. Here we perform an analysis of electron-deuteron scattering at low momentum transfers which is based on effective field theory. We show that in our approach the deuteron electromagnetic form factors $F_C$ and $F_M$ indeed are largely insensitive to the short-range $NN$ potential at momenta $Q$ up to about 700 MeV. We also find that the effective field theory approach to deuteron electromagnetic structure provides a systematic justification for many features which have been seen in potential model calculations of the same quantities.

nucl-th↗
arXiv1997

Regularization and renormalization in effective field theories of the nucleon-nucleon interaction

Some form of nonperturbative regularization is necessary if effective field theory treatments of the NN interaction are to yield finite answers. We discuss various regularization schemes used in the literature. Two of these methods involve formally iterating the divergent interaction and then regularizing and renormalizing the resultant amplitude. Either a (sharp or smooth) cutoff can be introduced, or dimensional regularization can be applied. We show that these two methods yield different results after renormalization. Furthermore, if a cutoff is used, the NN phase shift data cannot be reproduced if the cutoff is taken to infinity. We also argue that the assumptions which allow the use of dimensional regularization in perturbative EFT calculations are violated in this problem. Another possibility is to introduce a regulator into the potential before iteration and then keep the cutoff parameter finite. We argue that this does not lead to a systematically-improvable NN interaction.

nucl-th↗
arXiv1997

The potential of effective field theory in NN scattering

We study an effective field theory of interacting nucleons at distances much greater than the pion's Compton wavelength. In this regime the NN potential is conjectured to be the sum of a delta function and its derivatives. The question we address is whether this sum can be consistently truncated at a given order in the derivative expansion, and systematically improved by going to higher orders. Regularizing the Lippmann-Schwinger equation using a cutoff we find that the cutoff can be taken to infinity only if the effective range is negative. A positive effective range---which occurs in nature---requires that the cutoff be kept finite and below the scale of the physics which has been integrated out, i.e. O(m_π). Comparison of cutoff schemes and dimensional regularization reveals that the physical scattering amplitude is sensitive to the choice of regulator. Moreover, we show that the presence of some regulator scale, a feature absent in dimensional regularization, is essential if the effective field theory of NN scattering is to be useful. We also show that one can define a procedure where finite cutoff dependence in the scattering amplitude is removed order by order in the effective potential. However, the characteristic momentum in the problem is given by the cutoff, and not by the external momentum. It follows that in the presence of a finite cutoff there is no small parameter in the effective potential, and consequently no systematic truncation of the derivative expansion can be made. We conclude that there is no effective field theory of NN scattering with nucleons alone.

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arXiv1996

Short-range interactions in an effective field theory approach for nucleon-nucleon scattering

We investigate in detail the effect of making the range of the ``contact'' interaction used in effective field theory (EFT) calculations of NN scattering finite. This is done in both an effective field theory with explicit pions, and one where the pions have been integrated out. In both cases we calculate NN scattering in the ${}^1 S_0$ channel using potentials which are second-order in the EFT expansion. The contact interactions present in the EFT Lagrangian are made finite by use of a square-well regulator. We find that there is an optimal radius for this regulator, at which second-order corrections to the EFT are identically zero; for radii near optimal these second-order corrections are small. The cutoff EFTs which result from this procedure appear to be valid for momenta up to about 100 MeV/c. We also find that the radius of the square well cannot be reduced to zero if the theory is to reproduce both the experimental scattering length and effective range. Indeed, we show that, if the NN potential is the sum of a one-pion exchange piece and a short-range interaction, then the short-range piece must extend out beyond 1.1 fm, regardless of its particular form.

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arXiv1996

The $p p \to p pπ^0$ Reaction near Threshold: A Chiral Power Counting Approach

We use power-counting arguments as an organizing principle to apply chiral perturbation theory, including an explicit $Δ$, to the $p p \rightarrow p p π^0$ reaction near threshold. There are two lowest-order leading mechanisms expected to contribute to the amplitude with similar magnitudes: an impulse term, and a $Δ$-excitation mechanism. We examine formally sub-leading but potentially large mechanisms, including pion-rescattering and short-ranged contributions. We show that the pion-rescattering contribution is enhanced by off-shell effects and has a sign opposite to that of a recent estimate based on a PCAC pion interpolating field. Our result is that the impulse term interferes destructively with the pion rescattering and $Δ$-excitation terms. In addition, we have modeled the short-ranged interaction using $σ$ and $ω$ exchange mechanisms. A recoil correction to the impulse approximation is small. The total amplitude obtained including all of these processes is found to yield cross sections substantially smaller than the measured ones.

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arXiv1995

QCD Sum Rules and Applications to Nuclear Physics

Applications of QCD sum-rule methods to the physics of nuclei are reviewed, with an emphasis on calculations of baryon self-energies in infinite nuclear matter. The sum-rule approach relates spectral properties of hadrons propagating in the finite-density medium, such as optical potentials for quasinucleons, to matrix elements of QCD composite operators (condensates). The vacuum formalism for QCD sum rules is generalized to finite density, and the strategy and implementation of the approach is discussed. Predictions for baryon self-energies are compared to those suggested by relativistic nuclear physics phenomenology. Sum rules for vector mesons in dense nuclear matter are also considered.

hep-ph↗
arXiv1994

Model Independent Extraction of $|V_{\rm bc}|$ Without Heavy Quark Symmetry

A new method to extract $|V_{\rm bc}|$ is proposed based on a sum--rule for semileptonic decays of the $B$ meson. The method relies on much weaker assumptions than previous approaches which are based on heavy--quark symmetry. This sum--rule only relies on the assumption that the virtual $c \overline{c}$ pair content of the $B$ meson can be neglected. The extraction of the CKM matrix element also requires that the sum--rule saturates in the kinematically accessible region.

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