arXiv subjects

Loyal Durand

Publications and source records attributed to Loyal Durand.

49 records · Page 3Linked to original sources

arXiv2001

Effective field theory and the quark model, II. Structure of loop corrections

We analyze the structure of meson loop corrections to the O($m_s$) expressions for the baryon masses and magnetic moments in heavy-baryon chiral perturbation theory (HBChPT), and show in detail how the bulk of the corrections are absorbed into redefinitions of the unknown parameters of the O($m_s$) chiral expansion. To effect this analysis, we use the three-flavor-index representation of the effective baryon fields and HBChPT developed in a preceding paper, and a decomposition of the corrections in terms of effective one-, two-, and three-quark operators. The results show why the loop corrections have so little effect on fits to the masses and moments, and do not seriously disrupt the Gell-Mann--Okubo relations for the masses and the Okubo relation for the moments even though individual loops can be quite large. We also examine the momentum structure of the residual loop corrections, and comment on limits on their validity in HBChPT. The structural analysis can be generalized straightforwardly to other problems in HBChPT using the three-flavor-index representation of the effective baryon fields, and provides a fairly simple way to determine what parts of the loop corrections are actually significant in a given setting.

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arXiv2001

Effective field theory and the quark model

We analyze the connections between the quark model (QM) and the description of hadrons in the low-momentum limit of heavy-baryon effective field theory in QCD. By using a three-flavor-index representation for the effective baryon fields, we show that the ``nonrelativistic'' constituent QM for baryon masses and moments is completely equivalent through O(m_s) to a parametrization of the relativistic field theory in a general spin--flavor basis. The flavor and spin variables can be identified with those of effective valence quarks. Conversely, the spin-flavor description clarifies the structure and dynamical interpretation of the chiral expansion in effective field theory, and provides a direct connection between the field theory and the semirelativistic models for hadrons used in successful dynamical calculations. This allows dynamical information to be incorporated directly into the chiral expansion. We find, for example, that the striking success of the additive QM for baryon magnetic moments is a consequence of the relative smallness of the non-additive spin-dependent corrections.

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arXiv1998

Baryon masses in a loop expansion with form factor

We show that the average multiplet masses in the baryon octet and decuplet can be fitted with an average error of only $0.5\pm 0.3$ MeV in a meson loop expansion with chiral SU(6) couplings, with the hadrons treated as composite particles using a baryon-meson form factor. The form factor suppresses unphysical short distance effects and leads to a controllable expansion. We find, in contrast to the results of standard chiral perturbation theory, that pion loops are as important as kaon or eta loops as would be expected when only intermediate- and long-distance contributions are retained. We also find that the contributions of decuplet intermediate states are important in the calculation of the masses, and those states must be included explicitly in a consistent theory. These results agree with those of our recent loop-expansion analysis of the baryon magnetic moments. We show, finally, that the parts of the loop contributions that change the tree-level structure of the baryon masses are small, but largely account for the violations of the baryon mass sum rules which hold at tree level.

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arXiv1998

Understanding the success of nonrelativistic potential models for relativistic quark-antiquark bound states

We investigate the connection between relativistic potential models for quark-antiquark bound states and the nonrelativistic models that have been used successfully to fit and predict the spectra of relativistic systems. We use Martin's operator inequality \sqrt{p^2+m^2} <= (p^2+M^2+m^2)/2M to motivate the approximation of the relativistic kinetic energy terms in the spinless Salpeter equation by expressions of the nonrelativistic form M+ε+p^2/2M for each quark. To investigate the validity of the resulting approximation numerically, we generate energy spectra for q\bar{q} mesons composed of two light or two heavy quarks using the spinless Salpeter equation with the linear-plus-Coulomb potential, and then fit the lowest few states of each type using the effective Schrödinger description with the same potential. We find good fits to the lowest four calculated c\bar{c} and the lowest three s\bar{s} states either taking M fixed at the value M_q=\sqrt{ +m_q^2}, or allowing M_q to vary in the fit. The energies of the lowest few c\bar{s} states are then predicted with similar accuracy. The reasons for the success of the nonrelativistic approximation are identified, and explain the success of Martin's nonrelativistic predictions for the spectra of relativistic light-heavy mesons. However, we note that the agreement between the nonrelativistic and relativistic wave functions is not good, a point of potential concern for the calculation of transition matrix elements.

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arXiv1998

Baryon Magnetic Moments in a QCD-based Quark Model with loop corrections

We study meson loop corrections to the baryon magnetic moments starting from a QCD-based quark model derived earlier in a quenched approximation to QCD. The model reproduces the standard quark model with extra corrections for the binding of the quarks. The loop corrections are necessary to remove the quenching. Our calculations use heavy baryon perturbation theory with chiral baryon-meson couplings and a form factor characterizing the structure of baryons as composite particles. The form factor reflects soft wave function effects with characteristic momenta $\approx 400$ MeV, well below the usual chiral cutoff of $\approx 1$ GeV. The resulting model involves only three parameters, the quark moments $μ_u$ and $μ_s$ and a parameter $λ$ that sets the momentum scale in the wavefunctions. We find that this approach substantially improves the agreement between the theoretical and experimental values of the octet baryon magnetic moments, with an average difference between the theoretical and experimental moments of 0.05$μ_N$. An extension to the decuplet states using the same input predicts a moment of 1.97 $μ_N$ for the $Ω^-$ hyperon, in excellent agreement with the measured moment of $2.02\pm0.05 μ_N$.

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arXiv1998

Perturbative reliability of the Higgs-boson coupling in the standard electroweak model

We apply Pade summation to the β(λ) function for the quartic Higgs coupling λin the standard electroweak model. We use the βfunction calculated to five loops in the minimal subtraction scheme to demonstrate the improvement resulting from the summation, and then apply the method to the more physical on-mass-shell renormalization scheme where βis known to three loops. We conclude that the OMS βfunction and the running coupling λ(μ) are reliably known over the range of energies and Higgs-boson masses of current interest.

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arXiv1997

Chiral perturbation theory analysis of the baryon magnetic moments revisited

We reexamine critically the chiral expansion for the baryon magnetic moments including the contributions from loops which involve intermediate octet and decuplet baryons. We find that, contrary to some claims, the nonanalytic loop contributions of orders $m_s^{1/2}$ and $m_s ln m_s$ are of the same general size because of large coupling factors for the latter, and that the decuplet contributions are as large as the octet contributions and must be included in a consistent calculation. There is no clear evidence of the convergence of the chiral series. The adequacy of the theory will not be established until dynamical models are able to calculate the contributions from the counterterms that largely hide the loop effects in fits to the data.

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arXiv1996

Baryon moments in a QCD-based model

We have analyzed the theory of the baryon magnetic moments in the approximate) QCD setting suggested by Brambilla et al. By modifying their derivation of the $qqq$ interaction and wave equation for baryons, we derived expressions for the baryon moments in terms of the underlying quark moments, including the first corrections associated with the binding of the quarks in baryons. The results, which hold in the ``quenched approximation'' in which the contributions of virtual quark pairs are neglected, fail to describe the measured moments, with typical errors on the order of 7%. We conclude from our analysis that the quenched approximation is at fault, and that the baryon moments give a sensitive test of that standard approximation in the lattice and analytic approaches to QCD.

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arXiv1995

The Goldstone boson equivalence theorem with fermions

The calculation of the leading electroweak corrections to physical transition matrix elements in powers of $M_H^2/v^2$ can be greatly simplified in the limit $M_H^2\gg M_W^2,\, M_Z^2$ through the use of the Goldstone boson equivalence theorem. This theorem allows the vector bosons $W^\pm$ and $Z$ to be replaced by the associated scalar Goldstone bosons $w^\pm$, $z$ which appear in the symmetry breaking sector of the Standard Model in the limit of vanishing gauge couplings. In the present paper, we extend the equivalence theorem systematically to include the Yukawa interactions between the fermions and the Higgs and Goldstone bosons of the Standard Model. The corresponding Lagrangian ${\cal L}_{EQT}$ is given, and is formally renormalized to all orders. The renormalization conditions are formulated both to make connection with physical observables and to satisfy the requirements underlying the equivalence theorem. As an application of this framework, we calculate the dominant radiative corrections to fermionic Higgs decays at one loop including the virtual effects of a heavy top quark. We apply the result to the decays $H\rightarrow t\bar{t}$ and $H\rightarrow b\bar{b}$, and find that the equivalence theorem results including fermions are quite accurate numerically for Higgs-boson masses $M_H> 400\,(350)$ GeV, respectively, even for $m_t=175$ GeV.

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arXiv1994

Two-loop ${\rm O}\left(G_F^2M_H^4\right)$ corrections to the fermionic decay rates of the Higgs boson

We calculate the dominant ${\rm O}\left(G_F^2M_H^4\right)$ two-loop electroweak corrections to the fermi\-onic decay widths of a heavy Higgs boson in the Standard Model. Use of the Goldstone-boson equivalence theorem reduces the problem to one involving only the physical Higgs boson $H$ and the Goldstone bosons $w^\pm$ and $z$ of the unbroken theory. The two-loop corrections are opposite in sign to the one-loop electroweak corrections, exceed the one-loop corrections in magnitude for $M_H>1114\ {\rm GeV}$, and increase in relative magnitude as $M_H^2$ for larger values of $M_H$. We conclude that the perturbation expansion in powers of $G_FM_H^2$ breaks down for $M_H\approx 1100\ {\rm GeV}$. We discuss briefly the QCD and the complete one-loop electroweak corrections to $H\rightarrow b\bar{b}, \,t\bar{t}$, and comment on the validity of the equivalence theorem. Finally we note how a very heavy Higgs boson could be described in a phenomenological manner.

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arXiv1993

New perturbative upper bound on M_H from fermionic Higgs decays at two loops

We present the dominant two-loop ${\rm O}\left(G_F^2M_H^4\right)$ electroweak corrections to the fermi\-onic decay widths of a high-mass Higgs boson in the Standard Model. The corrections are negative and quite significant, and are larger in magnitude than the one-loop electroweak corrections for $M_H\gsim 400\ {\rm GeV}$. This indicates the onset of a breakdown of perturbation theory in the Higgs sector of the Standard Model at this surprisingly low value of the Higgs-boson mass.

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arXiv1993

Two-loop renormalization constants and high energy $2\rightarrow 2$ scattering amplitudes in the Higgs sector of the standard model

We calculate the complete matrix of two-body scattering amplitudes for the scattering of longitudinally polarized gauge bosons $W_L^\pm$, $Z_L$ and Higgs bosons to two loops in the high-energy, heavy-Higgs limit $\sqrt{s}\gg M_H\gg M_W$. Use of the Goldstone boson equivalence theorem reduces the problem to one involving only the scalar fields $w^\pm$, $z$ (the Goldstone bosons of the original theory) and the Higgs boson. Renormalization of the scattering amplitudes requires the calculation of the self-energy functions $Π_i^0(M_i^2)$, the renormalization constants $Z_i$, and the bare quartic Higgs coupling $λ_0$ to two loops. The results will be useful in other calculations. To facilitate the calculations, we introduce a powerful new technique for evaluating integrals over Feynman parameters in dimensional regularization which is based on a Barnes' type representation of the binomial expansion. We also collect some useful integrals which extend the tables given by Devoto and Duke.

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arXiv1993

Two-loop unitarity constraints on the Higgs boson coupling

We use the results of Maher {\em et al.\/} (preceding paper) to construct the matrix of $j=0$ partial-wave two-body and $2\rightarrow3$ scattering amplitudes for the scattering of longitudinally polarized gauge bosons $W_L^\pm$, $Z_L$ and Higgs bosons $H$ correct to two loops in the high-energy, heavy-Higgs limit $\sqrt{s}\gg M_H\gg M_W$. We show explicitly that the energy dependence of the $2\rightarrow2$ amplitudes can be completely absorbed into a running quartic Higgs coupling $λ_s= λ_s(s,M_H^2)$ and factors which involve small anomalous dimensions and remain near unity. After diagonalizing the matrix of partial-wave amplitudes, we use an Argand-diagram analysis to show that the elastic scattering amplitudes are approximately unitary and weakly interacting for $λ_s\alt2.3$, but that three-loop corrections are necessary to restore unitarity for larger values of $λ_s$. That is, the interactions in the Higgs sector of the standard model are effectively strong with respect to the perturbative expansion for $λ_s\agt2.3$. The bound $λ_s\alt2.3$ for a weakly interacting theory translates to a physical Higgs mass $M_H\alt380$ GeV if the bound is to hold for energies up to a few TeV, or $M_H\leq155$ GeV in perturbatively unified theories with mass scales of order $10^{16}$ GeV.

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