ON THE RENTAL PRICE OF CAPITAL AND THE PROFIT RATE: THE PERILS AND PITFALLS OF TOTAL FACTOR PRODUCTIVITY GROWTH

This paper considers the implications of the conceptual difference between the rental price of capital, embedded in the neoclassical cost identity (output equals the cost of labour plus the cost of capital), and used in growth accounting studies; and the profit rate, which can be derived from the national income and product accounts (NIPA). The neoclassical identity is a "virtual" identity in that it depends on a series of assumptions (constant returns to scale and perfectly competitive factor markets). The income side of the NIPA also provides an accounting identity for output as the sum of the wage bill plus the surplus. This identity, however, is a "real" one, in the sense that it does not depend on any assumptions and thus it holds always. It is shown that because the neoclassical cost identity and the income accounting identity according to the NIPA are formally equivalent expressions, estimations of aggregate production functions and growth accounting studies are tautologies. Likewise, the test of the hypothesis of competitive markets using Hall's (1988) framework gives rise to a null hypothesis that cannot be rejected statistically.

Comparing omnidirectional reflection from periodic and quasiperiodic one-dimensional photonic crystals

We determine the range of thicknesses and refractive indices for which omnidirectional reflection from quasiperiodic multilayers occurs. By resorting to the notion of area under the transmittance curve, we assess in a systematic way the performance of the different quasiperiodic Fibonacci multilayers.Comment: 5 pages, 4 color figures. Comments welcome

Possible new resonance from WLWLW_L W_L-hhhh interchannel coupling

We propose and theoretically study a possible new resonance caused by strong coupling between the Higgs-Higgs and the W_L W_L (Z_L Z_L) scattering channels, without regard to the intensity of the elastic interaction in either channel at low energy (that could be weak as in the Standard Model). We expose this channel-coupling resonance from unitarity and dispersion relations encoded in the Inverse Amplitude Method, applied to the Electroweak Chiral Lagrangian with a scalar Higgs.Comment: 4 pages, 7 figure

One-loop WLWLW_L W_L and ZLZLZ_L Z_L scattering from the Electroweak Chiral Lagrangian with a light Higgs-like scalar

By including the recently discovered Higgs-like scalar $\varphi$ in the Electroweak Chiral Lagrangian, and using the Equivalence Theorem, we carry out the complete one-loop computation of the elastic scattering amplitude for the longitudinal components of the gauge bosons $V=W, Z$ at high energy. We also compute $\varphi\varphi \rightarrow \varphi\varphi$ and the inelastic process $VV\rightarrow \varphi\varphi$, and identify the counterterms needed to cancel the divergences, namely the well known $a_4$ and $a_5$ chiral parameters plus three additional ones only superficially treated in the literature because of their dimension 8. Finally we compute all the partial waves and discuss the limitations of the one-loop computation due to only approximate unitarity.Comment: 28 pages, 19 plots, 9 Feynman-diagram sets This version revised and accepted in JHE

Unitarity, analyticity, dispersion relations and resonances in strongly interacting WLWLW_L W_L, ZLZLZ_L Z_L and hhhh scattering

If the Electroweak Symmetry Breaking Sector turns out to be strongly interacting, the actively investigated effective theory for longitudinal gauge bosons plus Higgs can be efficiently extended to cover the regime of saturation of unitarity (where the perturbative expansion breaks down). This is achieved by dispersion relations, whose subtraction constants and left cut contribution can be approximately obtained in different ways giving rise to different unitarization procedures. We illustrate the ideas with the Inverse Amplitude Method, one version of the N/D method and another improved version of the K-matrix. In the three cases we get partial waves which are unitary, analytical with the proper left and right cuts and in some cases poles in the second Riemann sheet that can be understood as dynamically generated resonances. In addition they reproduce at Next to Leading Order (NLO) the perturbative expansion for the five partial waves not vanishing (up to J=2) and they are renormalization scale ($\mu$) independent. Also the unitarization formalisms are extended to the coupled channel case. Then we apply the results to the elastic scattering amplitude for the longitudinal components of the gauge bosons $V=W, Z$ at high energy. We also compute $h h \rightarrow h h$ and the inelastic process $VV\rightarrow h h$ which are coupled to the elastic $VV$ channel for custodial isospin $I=0$. We numerically compare the three methods for various values of the low-energy couplings and explain the reasons for the differences found in the $I=J=1$ partial wave. Then we study the resonances appearing in the different elastic and coupled channels in terms of the effective Lagrangian parameters.Comment: 45 pages, 28 figure

Coupling WW, ZZ unitarized amplitudes to γγ\gamma\gamma in the TeV region

We define and calculate helicity partial-wave amplitudes for processes linking the Electroweak Symmetry Breaking Sector (EWSBS) to $\gamma\gamma$, employing (to NLO) the Higgs-EFT (HEFT) extension of the Standard Model and the Equivalence Theorem, while neglecting all particle masses. The resulting amplitudes can be useful in the energy regime ($500\,{\rm GeV}-3\,{\rm TeV}$). We also deal with their unitarization so that resonances of the EWSBS can simultaneously be described in the $\gamma\gamma$ initial or final states. Our resulting amplitudes satisfy unitarity, perturbatively in $\alpha$, but for all $s$ values. In this way we improve on the HEFT that fails as interactions become stronger with growing $s$ and provide a natural framework for the decay of dynamically generated resonances into $WW$, $ZZ$ and $\gamma\gamma$ pairs.Comment: 23 pages, 9 figure