A Simple-Minded Unitarity Constraint and an Application to Unparticles

Unitarity, a powerful constraint on new physics, has not always been properly accounted for in the context of hidden sectors. Feng, Rajaraman and Tu have suggested that large (pb to nb) multi-photon or multi-lepton sugnals could be generated at the LHC through the three-point functions of a conformally-invariant hidden sector (an "unparticle" sector.) Because of the conformal invariance, the kinematic distributions are calculable. However, the cross-sections for many such processes grow rapidly with energy, and at some high scale, to preserve unitarity, conformal invariance must break down. Requiring that conformal invariance not be broken, and that no signals be already observed at the Tevatron, we obtain a strong unitarity bound on multi-photon events at the (10 TeV) LHC. For the model of Feng et al., even with extremely conservative assumptions, cross-sections must be below 25 fb, and for operator dimension near 2, well below 1 fb. In more general models, four-photon signals could still reach cross-sections of a few pb, though bounds below 200 fb are more typical. Our methods apply to a wide variety of other processes and settings

Analysis of the stellar population in the central area of the HII region Sh 2-284

There is a lack of state-of-the-art information on very young open clusters, with implications for determining the structure of the Galaxy. Our main objective is to study the timing and location of the star formation processes which yielded the generation of the giant HII region Sh 2-284. The analysis is based on UBVRcIc CCD measurements and JHKs photometry in the central part of the HII region, where the cluster Dolidze 25 is located.The determination of cluster distance, reddening and age is carried out through comparison with ZAMS, post-MS and PMS isochrones. Reference lines for metallicity Z=0.004 are used, in agreement with spectroscopic metallicity determination published for several cluster members. The results are: E(B-V)=0.78+-0.02, M=12.8+-0.2, LogAge(yr)=6.51+-0.07. A PMS member sequence is proposed, coeval within the errors with the post-MS cluster age (LogAge(yr)=6.7+-0.2). The mass function for this PMS population in the mass range above 1.3-3.5 Msun is well fitted by a Salpeter mass function.The presence of a different star generation in the cluster with a distinctly older age, around 40 Myr, is suggested. The NIR results indicate a large number of sources with H-Ks excess, practically distinct from the optical PMS candidate members. The distance determined for the cluster is distinctly lower than previously published values. This result originates in the consistent use of low metallicity models for ZAMS fitting, applying published metallicity values for the cluster.Comment: gzipped tar file: 1 aa.cls, 1 tex file, 1 bbl file, 13 figures. Accepted in Astronomy & Astrophysics (9.11.2009

Harmonic mappings and conformal minimal immersions of Riemann surfaces into RN

We prove that for any open Riemann surface N, natural number N ≥ 3, non-constant harmonic map h:N→R N−2 and holomorphic 2-form H on N , there exists a weakly complete harmonic map X=(Xj)j=1,…,\scN:N→R\scN with Hopf differential H and (Xj)j=3,…,\scN=h. In particular, there exists a complete conformal minimal immersion Y=(Yj)j=1,…,\scN:N→R\scN such that (Yj)j=3,…,\scN=h . As some consequences of these results (1) there exist complete full non-decomposable minimal surfaces with arbitrary conformal structure and whose generalized Gauss map is non-degenerate and fails to intersect N hyperplanes of CP\scN−1 in general position. (2) There exist complete non-proper embedded minimal surfaces in R\scN, ∀\scN>3.Ministerio de Ciencia y Tecnología MTM2007-61775Ministerio de Ciencia y Tecnología MTM2007-64504Junta de Andalucía P09-FQM-508

Complete minimal surfaces and harmonic functions

We prove that for any open Riemann surface N and any non constant harmonic function h : N → R, there exists a complete conformal minimal immersion X : N → R3 whose third coordinate function coincides with h. As a consequence, completeminimal surfaceswith arbitrary conformal structure andwhose Gauss map misses two points are constructed.Ministerio de Educación y Ciencia MTM2007-61775Ministerio de Educación y Ciencia MTM2007-64504Junta de Andalucía P06-FQM-01642

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

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

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