arXiv subjects

Thomas D. Cohen

Publications and source records attributed to Thomas D. Cohen.

At least 37 records · Page 2Linked to original sources

arXiv2019

Does chiral perturbation theory rule out QCD-based solutions to the strong CP problem?

The conventional view is that a solution of the strong CP problem lies beyond QCD. A strong argument supporting this view is that the chiral expansion shows that observables depend on theta (unless a quark mass is zero); this eliminates the possibility that theta is physically irrelevant and appears to necessitate an explanation beyond the standard model. However, scenarios that solve the strong CP problem exist that are consistent with known chiral behavior; in these, QCD becomes nonviable as a theory for nonzero theta. Such scenarios appear to be compatible with lattice studies of the topological susceptibility.

hep-ph↗

arXiv2018

Model-Independent Bounds on $R(J/ψ)$

We present a model-independent bound on $R(J/ψ) \! \equiv \! \mathcal{BR} (B_c^+ \rightarrow J/ψ\, τ^+ν_τ)/ \mathcal{BR} (B_c^+ \rightarrow J/ψ\, μ^+ν_μ)$. This bound is constructed by constraining the form factors through a combination of dispersive relations, heavy-quark relations at zero-recoil, and the limited existing determinations from lattice QCD. The resulting 95\% confidence-level bound, $0.20\leq R(J/ψ)\leq0.39$, agrees with the recent LHCb result at $1.3 \, σ$, and rules out some previously suggested model form factors.

hep-ph↗

arXiv2018

Tests of the Standard Model in $B \to D\ell ν_\ell$, $B \to D^* \ell ν_\ell$ and $B_c \to J/ψ\, \ell ν_\ell$

A number of recent experimental measurements suggest the possibility of a breakdown of lepton ($\ell$) universality in exclusive $b \to c \ell ν_\ell$ semileptonic meson decays. We analyze the full differential decay rates for several such processes, and show how to extract combinations of the underlying helicity amplitudes that are completely independent of $m_\ell$. Ratios of these combinations for different $\ell$ (as well as some combinations for a single value of $\ell$) therefore equal unity in the Standard Model and provide stringent tests of lepton universality. Furthermore, the extractions assume the form of weighted integrals over the differential decay rates and therefore are useful even in situations where data in some regions of allowed phase space may be sparse.

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arXiv2016

On the nature of an emergent symmetry in QCD

Remarkable symmetry properties appear to arise in lattice calculations of correlation functions in which the lowest-lying eigenmodes of the Dirac operator in quark propagators are removed by hand. The Banks-Casher relation ties the chiral condensate to the density of low lying modes; thus, it is plausible that removal of such modes could lead to a regime where spontaneous chiral symmetry breaking does not occur. Surprising, a pattern of identical correlation functions was observed that is larger than can be explained by a restoration of chiral symmetry. This suggests that a larger symmetry---one that is not present in the QCD lagrangian---emerges when these modes are removed. Previously it was argued that this emergent symmetry was SU(4). However, when the low-lying modes are removed, the correlation functions of sources in the SU(4) 15-plet of spin-1 mesons appear to coincide with the correlation function of the SU(4) singlet. A natural explanation for this is an emergent symmetry larger than SU(4). In this work, it is shown that there exists no continuous symmetry whose generators in the field theory are spatial integrals of local operators that can account for the full pattern of identical correlation functions unless the apparent coincidence of the singlet channel with the 15-plet is accidental.

hep-lat↗

arXiv2015

Low Energy Effective Theory of QCD at High Isospin Chemical Potential

The goal of this paper is to arrive at a low energy effective theory of QCD with two massless flavors of quarks at very high isospin density and zero baryon density. In a seminal paper by Son and Stephanov in the year 2001, it was conjectured that the low energy dynamics of QCD with two light flavors at asymptotically high isospin density was described by that of a pure Yang-Mills effective Lagrangian. Since the existence of a first order deconfinement phase transition with increasing temperature is a feature of every pure SU(N) Yang-Mills theory with N greater than or equal to 3, the regime considered in this paper is also expected to exhibit a first order deconfinement phase transition with increasing temperature. However, the low energy constants(LEC) of this pure Yang-Mills theory have not been calculated till date. We calculate the LEC s for this effective theory which in turn enables us to calculate the critical temperature of the deconfinement transition as a function of the isospin chemical potential $μ_I$.The scaling of the critical temperature as a function of the isospin chemical potential that we find in this paper can be compared with future lattice calculations at finite isospin density.

hep-ph↗

arXiv2015

Deconfinement Transition at High Isospin Chemical Potential and Low Temperature

We consider QCD with two degenerate flavors of light quarks(up and down) at asymptotically high isospin chemical potential with zero baryon chemical potential and calculate for the first time a quantitative expression for the critical temperature of the deconfinement transition in this regime. At high isospin chemical potential and sufficiently low temperatures this theory becomes equivalent to a pure Yang-Mills theory and accordingly has a first order deconfinement phase transition. Although this was conjectured in a seminal paper by Son and Stephanov in the year 2001, the critical temperature of this deconfinement phase transition was not computed. This paper computes the energy scale associated with this transition as a function of the isospin chemical potential by relating the parameters of the equivalent Yang-Mills theory to those of the underlying theory. We also relate the equation of state in one strongly interacting regime of QCD namely at finite isospin density to that in pure Yang-Mills, with the latter being amenable to straightforward numerical calculation. Our results for the critical temperature of deconfinement transition can be compared with future lattice calculations.

hep-ph↗

arXiv2015

Nucleon-Antinucleon Annhiliation at Large Nc

Nucleon-antinucleon annihilation in the large $N_c$ limit of QCD in the Witten regime of fixed velocity is considered with a focus on the spin and isospin dependence of the annihilation cross-section. In general, time-reversal and isospin invariance restricts the annihilation cross-section to depend on 6 independent energy-dependent terms. At large $N_c$, a spin-flavor symmetry emerges in the theory that acts to further restrict the dependence of the annihilation cross-section to three of these terms; the other terms amount to $1/N_c$ corrections. Assuming dominance of the leading order terms, several identities are derived that relate annihilation in different spin-isospin channels. A key prediction is that for unpolarized nucleons in Witten kinematics, the proton-antiproton annihilation cross-section should be equal to the proton-antineutron annihilation cross-section up to corrections of relative order $1/N_c$. Unpolarized nucleon-antinucleon annihilation data appears to be consistent with this expectation.

hep-ph↗

arXiv2015

Center symmetry and Hagedorn spectrum

This paper explores the conjecture that large Nc gauge theories have a Hagedorn spectrum, if, and only if, they are confining and posses an explicit or emergent center symmetry. Evidence in support of this conjecture is presented. Many classes of large Nc gauge theories are considered. In all cases, we find that theories for which there exists a strong plausibility argument for a Hagedorn spectrum at large Nc are also believed to be confining and possess either an explicit center symmetric or have a strong plausibility argument for the existence of an emergent center symmetry at large Nc . Conversely, all theories we considered which are believed not to have a Hagedorn spectrum at large Nc, either were known not to be confining or else were believed to lack an emergent center symmetry. This is consistent with expectations based on the conjecture.

hep-th↗

arXiv2015

Finite Isospin Chiral Perturbation Theory in a Magnetic Field

The phase diagram of finite isospin, zero temperature QCD with the pions coupled to photons in a uniform external magnetic field is explored in the low field, small isospin density regime for which chiral perturbation theory is a valid description. For realistic pion masses, the system behaves as a type-II superconductor: a uniform superconducting state is formed at low-enough magnetic fields, a vortex state for intermediate magnetic fields and finally a normal state for large magnetic fields. In each these phases (including the vortex phase), the $π^{0}$ remains uncondensed just as in the zero-external field problem. The critical magnetic field where the phase transition from the uniform superconducting state to a vortex state occurs was found numerically.

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arXiv2014

Center symmetry and area laws

SU($N_c$) gauge theories containing matter fields may be invariant under transformations of some subgroup of the $\mathbb{Z}_{N_c}$ center; the maximum such subgroup is $\mathbb{Z}_{p}$, with $p$ depending on $N_c$ and the representations of the various matter fields in the theory. Confining SU($N_c$) gauge theories in either 3+1 or 2+1 space-time dimensions and with matter fields in any representation have string tensions for representation $R$ given by $σ_R =σ_f \, \, \frac{p_R (p-p_R) \, \, g\left (p_R (p-p_R) \right )}{(p-1) \, \, g(p -1 )} $ with $p_R={n_R \, \rm mod}(p)$, where $σ_f $ is the string tension for the fundamental representation, $g$ is a positive finite function and $n_R$ is the n-ality of $R$. This implies that a necessary condition for a theory in this class to have an area law is invariance of the theory under a nontrivial subgroup of the center. Significantly, these results depend on $p$ regardless of the value of $N_c$.

hep-th↗

arXiv2014

Large Nc gauge theory with quarks in high representations

This paper explores a novel tractable regime for ultraviolet-complete quantum field theories -- the large Nc limit of non-abelian gauge theories with quarks in high dimensional representations (scaling with Nc faster than Nc^2 ), such as quarks with 'a' fundamental indices with a greater than or equal to 3. A smooth and nontrivial Nc limit can be obtained if g^2 Nc^(a-1) is held fixed instead of the standard t Hooft coupling g^2 Nc as Nc goes to infinity where g is the gauge coupling. SU(Nc) gauge theories in 3+1 dimensions are not asymptotically free at large Nc when they contain quarks in representations whose dimensions scale faster than Nc^2 and hence are not ultraviolet complete. However, in lower space-time dimensions (2+1, 1+1), for any Nc, renormalization group flow for such theories always has a stable ultraviolet fixed point at g = 0; the theory is thus ultraviolet complete. For the case of massless quarks, the theory has an infrared fixed point. For massive quarks, the theory is confining. The confining scale is parametrically of the order Nc^((2-a)/(4-d)) and is driven to zero at large Nc for theories with a > 2 and d < 4 where d is the space time dimension.

hep-th↗

arXiv2014

New critical point for QCD in a magnetic field

We provide a general argument for the possible existence of a new critical point associated with a deconfinement phase transition in QCD at finite temperature $T$ and in a magnetic field $B$ with zero chemical potential. This is the first example of a QCD critical point in a physical external parameter region that can be studied using lattice QCD simulations without suffering from a sign problem.

hep-ph↗

arXiv2014

Are There Tetraquarks at Large $N_c$ in QCD(F)?

Weinberg recently pointed out a flaw in the standard argument that large $N_c$ QCD with color-fundamental quarks [QCD(F)] cannot yield narrow tetraquark states. In particular, he observed that the argument does not rule out narrow tetraquarks associated with the leading-order connected diagrams; such tetraquarks would have a width scaling as $N_c^{-1}$. It is shown here, however, that while the standard analysis of tetraquarks does not rule them out, a more thorough analysis rules out quantum-number exotic tetraquarks associated with the leading-order connected diagrams. This analysis is based entirely on conventional assumptions used in large $N_c$ physics applied to the analytic properties of meson-meson scattering. Our result implies that one of three possibilities must be true: i) quantum-number exotic tetraquarks do not exist at large $N_c$; ii) quantum-number exotic tetraquarks exist, but are associated with subleading connected diagrams and have anomalously small widths that scale as $N_c^{-2}$ or smaller; or iii) the conventional assumptions used in large $N_c$ analysis are inadequate.

hep-ph↗

arXiv2014

Quantum-Number Exotic Tetraquarks at Large $N_c$ in QCD(AS)

It is shown that the large $N_c$ limit of QCD with quarks in the two-index antisymmetric color representation [QCD(AS)] has narrow tetraquark states with exotic flavor quantum numbers. They decay into mesons with a width that is parametrically $O(1/N_c^2)$. Tetraquarks with non-exotic quantum numbers mix at leading order with mesons of the same overall quantum numbers. QCD(AS) at $N_c=3$ corresponds to ordinary QCD; its large $N_c$ limit represents an alternative starting point for a $1/N_c$ expansion to the standard one with quarks in the fundamental color representation.

hep-ph↗

arXiv2013

The inelastic vs. total nucleon-nucleon cross section at large $N_c$

In this paper, the implication of the extreme large $N_c$ limit for nucleon-nucleon cross section is examined. Starting from the $N_c$ scaling of the S-matrix elements, a relation between the total inelastic and total cross sections is derived for the regime in which the momenta are much larger than the QCD scale. A conceptual complication arise from the fact that there is a tower of baryons, such as the $Δ$, with mass splittings from the nucleon which go to zero at large $N_c$. Since these baryons are stable at large $N_c$, the meaning of elasticity must be modified. Processes which only transform nucleons to these baryons are considered elastic; processes in which at least one additional meson is produced are considered inelastic. It is shown that in the extreme large $N_c$ limit, the total inelastic cross section is exactly one eighth of the total cross section. In contrast, in the physical world of $N_c=3$ the total cross section for high-energy nucleon-nucleon scattering is dominated by inelastic processes.

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arXiv2013

Density of Saturated Nuclear Matter at Large $N_{c}$ and Heavy Quark Mass Limits

We exhibit the existence of stable, saturated nuclear matter in the large $N_{c}$ and heavy quark mass limits of QCD. In this limit, baryons (with the same spin flavor structure) interact at leading order in $N_{c}$ via a repulsive interaction due to the Pauli exclusion principle and at subleading order in $1/N_c$ via the exchange of glueballs. Assuming that the lightest glueball is a scalar, which implies that the subleading baryon interaction is attractive, we find that nuclear matter saturates since the subleading attractive interaction is longer ranged than the leading order repulsive one. We find that the saturated matter is in the form of a crystal with either a face-centered cubic or a hexagonal-close-packed symmetry with baryon densities of $\mathcal{O}((\, \tildeα_{s} m_q (\ln (N_{c}m_{q}Λ_{\textrm{QCD}}^{-1}))^{-1})^3 )$. Remarkably, the leading order expression for the density of saturated nuclear matter is independent of the lighest glueball mass and scalar-glueball-baryon coupling in the extreme large $N_{c}$ limit or heavy quark limit (or both), which we define precisely in this work.

nucl-th↗

arXiv2013

Nucleon-nucleon scattering matrix and its Nc scaling

This paper focuses on the scaling of the S-matrix for elastic nucleon-nucleon scattering at large Nc. It is argued that the logarithm of a typical S-matrix element is proportional to Nc in the regime where the large Nc limit is taken with momentum of the incident nucleons proportional Nc. The suggested scaling was previously derived within the framework of potential scattering models for purely elastic scattering in which the parameters scale the same way as in large Nc QCD. A variety of heuristic arguments strongly suggest that the same scaling holds in the realistic case where both elastic and inelastic scattering are possible.

nucl-th↗

arXiv2013

Mean-field theory of baryonic matter for QCD in the large $N_{c}$ and heavy quark mass limits

We discuss theoretical issues pertaining to baryonic matter in the combined heavy-quark and large $N_c$ limits of QCD. Witten's classic argument that baryons and interacting systems of baryons can be described in a mean-field approximation with each of the quarks moving in an average potential due to the remaining quarks is heuristic. It is important to justify this heuristic description for the case of baryonic matter since systems of interacting baryons are intrinsically more complicated than single baryons due to the possibility of hidden color states---states in which the subsystems making up the entire baryon crystal are not color-singlet nucleons but rather colorful states coupled together to make a color-singlet state. In this work, we provide a formal justification of this heuristic prescription. In order to do this, we start by taking the heavy quark limit, thus effectively reducing the problem to a many-body quantum mechanical system. This problem can be formulated in terms of integrals over coherent states, which for this problem are simple Slater determinants. We show that for the many-body problem, the support region for these integrals becomes narrow at large $N_c$, yielding an energy which is well-approximated by a single coherent state---that is a mean-field description. Corrections to the energy are of relative order $1/N_c$. While hidden color states are present in the exact state of the heavy quark system, they only influence the interaction energy at sub-leading order in $1/N_{c}$.

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