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Thomas D. Cohen

Publications and source records attributed to Thomas D. Cohen.

At least 127 records · Page 7Linked to original sources
arXiv2001

The extraction of the axial coupling from finite volume systems: The long and short of it

Due to a pion-pole contribution, the nucleon axial current matrix elements can be visualized in position space as becoming delocalized as the chiral limit is approached, with one-third of the current at distance of order the inverse pion mass. However, this delocalization effect will not cause calculations of the axial coupling in a finite system with standard boundary conditions (periodic for boson fields, antiperiodic for fermions) to have large finite volume effects. This is seen by calculating axial coupling using a nonstandard current with axial quantum numbers. The matrix elements of this new current lacks a pion pole and is not delocalized; however, its zero-momentum matrix element is identical to that of the standard axial current both for infinite and finite volumes.

hep-lat↗
arXiv2001

Phases of QCD with nonvanishing isopin density

The propagation of low-momentum baryons through QCD matter at low isospin density is studied using chiral perturbation theory. When the isospin chemical potential exceeds a critical value, the dispersion relation for the lowest nucleon mode becomes anomalous near zero momentum---increasing momentum yields decreasing energy---so that the momentum for the lowest energy state, p_min, becomes nonzero. This can be interpreted as a new phase of QCD, with p_min serving as the order parameter and the kinetic mass (defined as the inverse of the second derivative of the energy with respect to the momentum at p_min) serving as the susceptibility. A lowest-order chiral-perturbation-theory calculation yields a critical isospin chemical potential of 285 MeV. Since this is small compared to the chiral-symmetry-breaking scale, corrections to it are likely to be modest.

hep-ph↗
arXiv2001

Model-Independent Predictions for Low Energy Isoscalar Heavy Baryon Observables in the Combined Heavy Quark and Large $N_c$ Expansion

Model-independent predictions for excitation energies, semileptonic form factors and electromagnetic decay rates of isoscalar heavy baryons and their low energy excited states are discussed in terms of the combined heavy quark and large $N_c$ expansion. At leading order, the observables are completely determined in terms of the known excitation energy of the first excited state of $Λ_c$. At next-to-leading order in the combined expansion all heavy baryon observables can be expressed in a model-independent way in terms of two experimentally measurable quantities. We list predictions at leading and next-to-leading order.

hep-ph↗
arXiv2001

Excited Heavy Baryons and Their Symmetries III: Phenomenology

Phenomenological applications of an effective theory of low-lying excited states of charm and bottom isoscalar baryons are discussed at leading and next-to-leading order in the combined heavy quark and large $N_c$ expansion. The combined expansion is formulated in terms of the counting parameter $λ\sim 1/m_Q, 1/N_c$; the combined expansion is in powers of $λ^{1/2}$. We work up to next-to-leading order. We obtain model-independent predictions for the excitation energies, the semileptonic form factors and electromagnetic decay rates. The spin-averaged mass of the doublet of the first orbitally excited sate of $Λ_b$ is predicted to be approximately $5920 MeV$. It is shown that in the combined limit at leading and next-to-leading order there is only one independent form factor describing $Λ_b \to Λ_c \ell \barν$; similarly, $Λ_b \to Λ_{c}^{*} \ell \barν$ and $Λ_b \to Λ_{c1} \ell \barν$ decays are described by a single independent form factor. These form factors are calculated at leading and next-to-leading order in the combined expansion. The electromagnetic decay rates of the first excited states of $Λ_c$ and $Λ_b$ are determined at leading and next-to leading order. The ratio of radiative decay rates $Γ(Λ_{c}^{*} \to Λ_c γ) / Γ(Λ_{b1} \to Λ_b γ)$ is predicted to be approximately 0.2, greatly different from the heavy quark effective theory value of unity.

hep-ph↗
arXiv2001

Excited Heavy Baryons and Their Symmetries II: Effective Theory

We develop an effective theory for heavy baryons and their excited states. The approach is based on the contracted O(8) symmetry recently shown to emerge from QCD for these states in the combined large N_c and heavy quark limits. The effective theory is based on perturbations about this limit; a power counting scheme is developed in which the small parameter is lambda^{1/2} where lambda ~ 1/N_c, Lambda /m_Q (with Lambda being a typical strong interaction scale). We derive the effective Hamiltonian for strong interactions at next-to-leading order. The next-to-leading order effective Hamiltonian depends on only two parameters beyond the known masses of the nucleon and heavy meson. We also show that the effective operators for certain electroweak transitions can be obtained with no unknown parameters at next-to-leading order.

hep-ph↗
arXiv2001

Spontaneous Parity Violation in QCD At Finite Temperature: On the Inapplicability of the Vafa-Witten Theorem

The generalization of the Vafa-Witten theorem ruling out parity violation to QCD at finite temperature is considered. It is shown that this generalization of the theorem rules out Lorentz-invariant parity violating operators from spontaneously acquiring vacuum expectation values. However, it does not rule out Lorentz-noninvariant parity-violating operators from acquiring expectation values. Other situations where the theorem is inapplicable are also discussed.

hep-th↗
arXiv2000

Parity Violation in Polarized-Gamma Proton Compton Scattering

Polarized beam gamma p Compton scattering provides a theoretically clean way to extract the isovector parity violating pion-nucleon coupling constant $h_{πNN}^{(1)}$. This channel is more tractable experimentally than the recently proposed extraction of $h_{πNN}^{(1)}$ from the Bedaque-Savage process --- polarized target gamma p compton scattering. The leading parity violating effect is calculated using Heavy Baryon Chiral Perturbation Theory. The size of the asymmetry is estimated to be ~ 4 10^{-8} for 120 MeV photon energy.

nucl-th↗
arXiv2000

Excited Heavy Baryons and Their Symmetries I: Formalism

This is the first of two papers to study a new emergent symmetry which connects orbitally excited heavy baryons to the ground states in the combined heavy quark and large $N_c$ limit. The existence of this symmetry is shown in a model-independent way, and different possible realizations of the symmetry are discussed. It is also proved that this emergent symmetry commutes with the large $N_c$ spin-flavor symmetry.

hep-ph↗
arXiv2000

Quantum Coins, Dice and Children: Probability and Quantum Statistics

We discuss counterintuitive aspects of probabilities for systems of identical particles obeying quantum statistics. Quantum coins and children (two level systems) and quantum dice (many level systems) are used as examples. It is emphasized that, even in the absence of interactions, (anti)symmetrizations of multi-particle wavefunctions destroy statistical independences and often lead to dramatic departures from our intuitive expectations.

quant-ph↗
arXiv1999

The Predictive Power of Effective Field Theory in NN Scattering: ^3S_1-^3D_1 Mixing at Next-to Next-to Leading Order

The convergence of the Q expansion in the ^3S_1-^3D_1 mixing angle is investigated through the renormalization condition used to fit the free paramteter encountered at NNLO. Although the NNLO calculation describes the data well at momenta much less than 50 MeV, a variation in the renormalization condition results in 100% expected uncertainties at momenta as low as 100 MeV. This uncertainty can be traced to the presence of large cancelations between terms entering at NNLO, which are found to be several times larger than the terms entering at NLO. This implies a fundamental lack of predictive power at this order int he Q expansion of ε_1. Given the small empirical size, this lack of predictive power is easily understood in terms of simple power counting arguments.

nucl-th↗
arXiv1999

Looking For Disoriented Chiral Condensates From Pion Distributions

We suggest two methods for the detection of the formation of disoriented chiral condensates in heavy ion collisions. We show that the variance in the number of charged pions (in a suitable range of momentum space) provides a signature for the observation of a disoriented chiral condensate. The signal should be observable even if multiple domains of D$χ$C form provided the average number of pions per domain is significantly larger than unity. The variance of the number charged pions alone provides a signal which can be used even if the number of neutral pions cannot be measured in a given detector. On the other hand, the probability distribution in $R$, the proportion of neutral pions to all pions emitted in heavy ion collisions in certain kinematic regions, has been suggested as a signal of a disoriented chiral condensate. Here we note that the signature can be greatly enhanced by making suitable cuts in the data. In particular, we consider reducing the data set such that the $k$ pions with lowest $p_T$ are all neutral. We find that, given such cuts, $ $ can be substantially different from 1/3. For example, for a single D$χ$C domain without contamination due to incoherently emitted pions, $ $ is 3/5 given the pion with lowest $p_T$ is neutral, and 5/7 given the two pions with lowest $p_T$ are both neutral, {\it etc.}. The effects of multi-domain D$χ$C formation and noise due to incoherent pion emission can be systematically incorporated. Potential applications to experiments and their limitations are briefly discussed.

nucl-th↗
arXiv1999

The pion photoproduction in the Δ(1232) region

We investigate the pion photoproduction in the Δ(1232) region in the framework of an effective Lagrangian including pions, nulceon and Δ(1232). We work to third order in a small scale expansion with both $m_π$ and $M_Δ-M_N$ treated as light scales. We note that in the $Δ$ region, straightward power counting breaks as the amplitudes become very large, to deal with this problem, we suggest that the appropriate way to compare theoretical calculations with experimental data is via weighted integrals of the amplitudes through the $Δ$ region.

nucl-th↗
arXiv1999

Enhanced Signatures for Disoriented Chiral Condensates

The probability distribution in $R$, the proportion of neutral pions to all pions emitted in heavy ion collisions in certain kinematic regions, has been suggested as a signal of a disoriented chiral condensate (D$χ$C). Here we note that the signature can be greatly enhanced by making suitable cuts in the data. In particular, we consider reducing the data set such that the $k$ pions with lowest $p_T$ are all neutral. We find that, given such cuts, $ $ can be substantially different from 1/3. For example, for a single D$χ$C domain without contamination due to incoherently emitted pions, $ $ is 3/5 given the pion with lowest $p_T$ is neutral, and 5/7 given the two pions with lowest $p_T$ are both neutral, etc.. The effects of multi-domain D$χ$C formation and noise due to incoherent pion emission can be systematically incorporated. Potential applications to experiments and their limitations are briefly discussed.

nucl-th↗
arXiv1999

Perturbative Pions and the Effective Range Expansion

In this talk the $Q$ counting scheme to implement effective field theory is discussed. It is pointed out that there are two small mass scales in the problem $m_π$ and $1/a$ with $1/a \ll m_π$. It is argued that while the expansion based on $1/a$ being small compared to the underlying short distance scales works well, the chiral expansion may not. The coefficients of the effective range expansion are sensitive to the chiral physics and are very poorly described in $Q$ counting at lowest nontrivial order. A ``shape function'' is introduced which again is sensitive to pionic physics and insensitive to fitting procedures. It is also poorly described in $Q$ counting.

nucl-th↗
arXiv1999

Signatures of Disoriented Chiral Condensates from Charged Pions

We show that the variance in the number of charged pions (in a suitable range of momentum space) provides a signature for the observation of a disoriented chiral condensate (D$χ$C). The signal should be observable even if multiple domains of D$χ$C form provided the average number of pions per domain is significantly large than unity. The variance of the number charged pions alone provides a signal which can be used even if the number of neutral pions cannot be measured in a given detector. If the neutrals can be measured, however, the fluctuations in the total number of pions provides a signature which distinguishes disoriented chiral condensates from other hypothetical sources of coherent states of pions.

nucl-th↗
arXiv1999

Testing Low Energy Theorems in Nucleon-Nucleon Scattering

Low energy theorems have been derived for the coefficients of the effective range expansion in s-wave nucleon-nucleon scattering valid to leading nontrivial order in an expansion based $Q$ counting, a scheme in which both $m_π$ and $1/a$ (where $a$ is the scattering length) are treated as small mass scales. Previous tests of these theorems based on coefficients extracted from scattering data indicate a pattern of gross violations which suggested serious problems for the perturbative treatment of pions implicit in $Q$ counting. We discuss the possibility that uncertainties associated with extracting the coefficients from the scattering data make such tests invalid. Here we show that errors in the s-wave phase shift extractions are sufficiently small to test direct test predictions from $Q$ counting at next to leading order. In particular we show that there exist low energy theorems for the sum of all terms in the effective range expansion beyond the first two which allow for precise tests. These low energy theorems fail badly which suggests that pionic aspects of $Q$ counting are not under control.

nucl-th↗