Search

In the context of $f(R)$ gravity, as well as other extended theories of gravity, the correct counting of globally well-defined dynamical modes has recently drawn a vivid interest. In this communication we present a consistent approach shedding light on such issues for both so-called degenerate and non-degenerate $f(R)$ models embedded in maximally-symmetric backgrounds. We find that the linearised spectrum of degenerate models on these backgrounds is empty, lacking both the graviton and scalaron modes which appear in generic non-degenerate models. Our work generalises previous results in the literature applicable only to the specific (degenerate) model $f(R)=\alpha R^2$; in fact, we find that the same pathologies discovered therein emerge for all choices of $f(R)$ belonging to the wide class of degenerate models., Comment: 14 pages, 1 figure

Constant-curvature solutions lie at the very core of gravitational physics, with Schwarzschild and (Anti)-de Sitter being two of the most paradigmatic examples. Although such kind of solutions are very well-known in General Relativity, that is not the case for theories of gravity beyond the Einsteinian paradigm. In this article, we provide a systematic overview on $f(R)$ models allowing for constant-curvature solutions, as well as of the constant-curvature solutions themselves. We conclude that the vast majority of these $f(R)$ models suffer, in general, from several shortcomings rendering their viability extremely limited, when not ruled out by physical evidence. Among these deficiencies are instabilities (including previously unforeseen strong-coupling problems) and issues limiting the predictive power of the models. Furthermore, we will also show that most $f(R)$-exclusive constant-curvature solutions also exhibit a variety of unphysical properties., Comment: 20 pages, 1 table, no figures

We present the contributions to the imaginary part of the $W^+W^-$ elastic scattering from top and bottom quark one-loop diagrams. The computation is performed within the context of HEFT, where we compare them with the boson-loop corrections. We argue that the often neglected (top and bottom) fermion contributions may in fact be relevant., Comment: 4 pages, 4 figures, contribution to the proceedings of QCD22 - 25th International Conference in Quantum Chromodynamics (4-7/07/2022, Montpellier - France)

In this work we interpret the Einstein-Hilbert (EH) Lagrangian of gravitation as the first term of a low-energy effective theory similar to those considered in the chiral Lagrangian approach to low-energy hadron physics or the electroweak chiral Lagragians describing the symmetry breaking sector of the Standard Model (SM). Starting from the one-loop computation of the elastic graviton-graviton scattering amplitude by Dunbar and Norridge, we unitarize the IR regularized partial waves by using the Inverse Amplitude Method (IAM). This method enlarges the regime of applicability of the perturbative results to higher energies of the order of the Plank scale $M_P$ and allows for the possibility of poles in the second Riemann which have the natural interpretation of dynamical resonances. In this work we look for these possible resonances for the $++++$ and $ -- -$ helicity channels and the $J=0$, $2$ and $4$ partial waves., Comment: 7 pages, 3 figures, Contribution to the proceedings of the XVth Quark Confinement and the Hadron Spectrum (CONF15). Aug. 1 - 6, 2022. Stavanger, Norway

Some effective field theories exhibit dynamical resonances that, when properly included, mitigate their bad behaviour at high energies. Unitarization of the partial wave amplitudes is the preferred method to unveil such resonances. Interpreting the Einstein-Hilbert theory in the spirit of effective Lagrangians, we implement the Inverse Amplitude Method and unitarize the one-loop level graviton-graviton scattering in pure gravity. Due to the presence of infrared divergences, the analysis requires a careful treatment of the infrared region and the introduction of infrared regulators, carefully selected in order to fulfil perturbative unitarity. No evidence of any graviball is found, in contradiction with a recent study., Comment: 12 pages, 5 figures

We study the one-loop corrections to Vector Boson Scattering (in particular $W^+W^-$ elastic scattering) within the framework of effective theories. Re-scattering via intermediate electroweak would-be-Goldstone bosons dominate at high energies, as the corresponding loop diagrams with these intermediate bosons scale like $\mathcal{O}(s^2/v^4)$ in the chiral effective counting. In the present article, we focus our attention on fermion-loop corrections which scale like $\mathcal{O}(M_{\rm Fer}^2 s/v^4)$ in the Higgs Effective Field Theory (HEFT). Although this dependency is formally suppressed for $s\to\infty$ with respect to that from boson loops, the large top mass can lead to a numerical competition between fermion and boson loops at intermediate energies of the order of a few TeV. For the study of these fermion effects we have calculated the imaginary part induced by loops of top and bottom quarks in $W^+ W^-\to W^+W^-$ elastic scattering and compared it to the loop contributions from purely bosonic loops. We have examined the dependence of both amplitudes on the effective couplings, allowing an $\mathcal{O}(10 \%)$ deviation from the SM. In some cases, boson loops dominate over top and bottom corrections, as expected. However, we find that there are regions in the space of effective parameters that yield a significant -- and even dominant -- imaginary contribution from fermion loops. In addition to our conclusions for the general HEFT, we also provide analyses particularized to some benchmark points in the $SO(5)/SO(4)$ Minimal Composite Higgs Model., Comment: 35 pages, 31 figures

Gravitational collapse is still poorly understood in the context of $f(R)$ theories of gravity, since the Oppenheimer-Snyder model is incompatible with their junction conditions. In this work, we will present a systematic approach to the problem. Starting with a thorough analysis of how the Oppenheimer-Snyder construction should be generalised to fit within metric $f(R)$ gravity, we shall subsequently proceed to explore the existence of novel exterior solutions compatible with physically viable interiors. Our formalism has allowed us to show that some paradigmatic vacuum metrics cannot represent spacetime outside a collapsing dust star in metric $f(R)$ gravity. Moreover, using the junction conditions, we have found a novel vacuole solution of a large class of $f(R)$ models, whose exterior spacetime is documented here for the first time in the literature as well. Finally, we also report the previously unnoticed fact that the Oppenheimer-Snyder model of gravitational collapse is incompatible with the Palatini formulation of $f(R)$ gravity., Comment: 18 pages, 0 figures; minor typos corrected, version published in Phys. Rev. D 105 084060

We test the assumption that fermion-loop corrections to high energy $W^+W^-$ scattering are negligible when compared to the boson-loop ones. Indeed, we find that, if the couplings of the interactions deviate from their Standard Model values, fermion-loop corrections can in fact become as important or even greater than boson-loop corrections for some particular regions of the parameter space, and both types of loops should be taken into account. Some preliminary results are shown., Comment: 5 pages, 7 jpg figures; proceedings of the International Conference in Quantum Chromodynamics: QCD20 - 35 years later} (QCD 20), 27-30 October 2020, Montpellier, France. arXiv admin note: substantial text overlap with arXiv:2012.12242

We calculate fermion-loop corrections to high energy $W^+W^-$ scattering in the context of a Strongly Interacting Electroweak Symmetry Breaking Sector (EWSBS) using Higgs Effective Field Theory(HEFT). We test the assumption that these corrections are negligible when compared to the boson-loop ones, as it is commonly taken for granted in the literature. While this is correct inmost cases, we find that, for some particular regions of the parameter space, fermion-loops can be important: deviations in the couplings of the HEFT from their Standard Model values may lead to fermion-loop corrections as relevant as the boson-loop ones., Comment: 6 pages, 3 figures. Talk given at the 40th International Conference on High Energy Physics - ICHEP2020 (28 July - 6 August, 2020, virtual meeting, Prague, Czech Republic

This article presents a number of technical tools and results that may be instrumental to discern the nature of the Higgs particle. In scenarios where an additional strongly interacting sector is present in the electroweak theory resulting in a composite Higgs and longitudinal components of the massive gauge bosons, unitarity, analyticity and related techniques will be crucial to understand the properties of such a sector. The situation today may be reminiscent of the pre-QCD days: a strongly interacting theory governs the short-distances, but we have only access to long-distance experiment involving Nambu-Goldstone or pseudo Nambu-Goldstone bosons. Like in those days we can only rely on symmetry and general properties of field theory. Luckily, unlike in the pre-QCD days, we have now a much clearer idea of what we may be after. After presenting a classification of the various types of effective theories, we establish the criteria as to under which conditions different representations are possible and their equivalence. We discuss in detail the implications of analyticity, causality and unitarity; describe various unitarization methods and establish the properties of dynamically generated resonances and form factors. The relation to effective Lagrangians with explicit resonances is explained in the context of beyond the Standard Model (BSM) physics and the Higgs effective field theory (HEFT). We discuss how various BSM models may be reduced to the HEFT as well as implications from holography and lattice studies in establishing BSM phenomenology. The methods presented are then applied to various processes relevant to disentangle the existence and nature of an extended electroweak symmetry breaking sector visible in $VV$ fusion: two-Higgs production, vector resonances, $\gamma\gamma$ physics and top-antitop production.

Higgs Effective Field Theory (HEFT) is deployed to study elastic vector-boson scattering at the high LHC energies. The interaction is strong over most of the parameter space, with the minimal Standard Model being a remarkable exception. One-loop HEFT complemented with dispersion relations and the Equivalence Theorem leads to two different unitarization methods which produce analytical amplitudes corresponding to different approximate solutions to the dispersion relations: the Inverse Amplitude method (IAM) and the N/D method. The partial waves obtained can show poles in the second Riemann sheet whose natural interpretation is that of dynamical resonances with masses and widths depending on the starting HEFT parameters. Different unitarizations yield qualitatively, and in many cases quantitatively, very similar results. The amplitudes obtained provide realistic resonant and nonresonant cross sections to be compared with and to be used for a proper interpretation of the LHC data., Comment: 4 pages, 3 plots, for the proceedings of the EPS-HEP2019 Conference- 10-17 July, 2019 Ghent, Belgium

In this work we study the chiral phase transition as observed by an accelerating observer taking into account the Unruh effect. We use Chiral Perturbation Theory at leading order and the large $N$ limit ($N$ being the number of pions) as an effective description of low-energy QCD, and the Thermalization Theorem to compute the relevant partition function for the accelerating observer. As a result, we obtain that chiral symmetry is restored for uniformly accelerated observers with acceleration $a$ larger than the critical value $a_c=4\pi f_\pi$, with $f_\pi$ being the pion decay constant.

The possibility of chiral symmetry restoration by acceleration is considered. The Thermalization Theorem formalism and the large $N$ limit (with $N$ being the number of pions) are employed to solve the lowest-order approximation to QCD at low energies in Rindler spacetime. It is shown that chiral symmetry is restored for accelerations higher than the critical value $a_c=4\pi f_\pi$, with $f_\pi$ being the pion decay constant. The results are completely analogous to those obtained in the inertial, finite-temperature case, evincing the ontic character of the Unruh effect.

We study the production of vector resonances at the LHC via $WZ$ scattering processes and explore the sensitivities to these resonances for the expected future LHC luminosities. The electroweak chiral Lagrangian and the Inverse Amplitude Method (IAM) are used for analyzing a dynamically generated vector resonance, whose origin would be the (hypothetically strong) self interactions of the longitudinal gauge bosons, $W_L$ and $Z_L$. We implement the unitarized scattering amplitudes into a single model, the IAM-MC, that has been adapted to MadGraph~5. It is written in terms of the electroweak chiral Lagrangian and an additional effective Proca Lagrangian for the vector resonances, so that it reproduces the resonant behavior of the IAM and allows us to perform a realistic study of signal versus background at the LHC. We focus on the $pp\to WZjj$ channel, discussing first on the potential of the hadronic and semileptonic channels of the final $WZ$, and next exploring in more detail the clearest signals. These are provided by the leptonic decays of the gauge bosons, leading to a final state with $l^+_1l^-_1l^+_2\nu jj$, $l=e,\mu$, having a very distinctive signature, and showing clearly the emergence of the resonances with masses in the range of $1.5$-$2.5\,{\rm TeV}$, which we have explored., Comment: 8 pages, 5 figures, contributed to the XIII Quark Confinement and the Hadron Spectrum - Confinement2018, 31 July - 6 August 2018, Maynooth University, Ireland

Higgs Effective Field Theory can be used to study vector-boson elastic scattering at the high energies relevant for the LHC. For most of the parameter space, the scattering is strongly interacting, with the minimal Standard Model being a remarkable exception. From its one-loop treatment complemented with dispersion relations and the Equivalence Theorem, we derive two different unitarization methods which produce analytical amplitudes corresponding to different approximate solutions to the dispersion relations: the Inverse Amplitude method (IAM) and the N/D method. The partial waves obtained can show poles in the second Riemann sheet whose natural interpretation is that of dynamical resonances with masses and widths a function of the starting HEFT parameters. We compare the different unitarizations and we find that they are qualitatively, and in many cases quantitatively, very similar. However, for different reason it is more interesting to use one of the two methods depending on the particular channel for WW, ZZ, WZ, Zh, Wh or hh scattering. In this note we briefly describe the possible I and J channels for these reactions and give the unitarization method of choice in each case. The amplitudes obtained provide realistic resonant and nonresonant cross sections to be compared with and to be used for a proper interpretation of the LHC data., Comment: Proceedings of the Sixth Annual Large Hadron Collider Physics conference LHCP 2018. June 3rd - 9th 2018. 5 pages, 1 figure

We present a study of the production of vector resonances at the LHC via $W^+Z$ vector boson scattering and explore the sensitivities to these resonances for expected LHC luminosities. We work in the framework of the electroweak chiral Lagrangian, where these resonances can be generated dynamically by unitarizing the scattering amplitudes. We implement all these features into a model adapted for MonteCarlo, the IAM-MC, that allows us to give predictions for the sensitivity to these resonances and to the relevant parameters involved for $pp \to W^+Zjj$, $pp\to \ell_1^+\ell_1^-\ell_2^+\nu jj$, and $pp \to JJjj$., Comment: 4 pages, 2 figures (7 plots), Proceedings of the Moriond 2018 EW session

We examine the production of Wh and Zh pairs at the LHC in the context of a Strongly Interacting Symmetry Breaking Sector of the Standard Model. Our description is based on a non-linear Higgs Effective Theory, including only the Standard Model particles. We focus on its scalar sector (Higgs boson h and electroweak Goldstones associated to $W_L^\pm$ and $Z_L$), which is expected to give the strongest beyond Standard Model rescattering effects. The range of the effective theory is extended with dispersion-relation based unitarization, and compared to the alternative extension with explicit axial-vector resonances. We estimate the Wh and Zh production cross-section, where an intermediate axial-vector resonance is generated for certain values of the chiral couplings. We exemplify our analysis with a benchmark axial-vector with $M_A=3$ TeV. Interestingly enough, these different approaches provide essentially the same prediction. Finally we discuss the sensitivity of ATLAS and CMS to such resonances., Comment: 28 pages, 7 eps figures

We estimate production cross sections for 2-body resonances of the Electroweak Symmetry Breaking sector (in $W_LW_L$ and $Z_LZ_L$ rescattering) from $\gamma\gamma$ scattering. We employ unitarized Higgs Effective Field Theory amplitudes previously computed coupling the two photon channel to the EWSBS. We work in the Effective Photon Approximation and examine both $e^-e^+$ collisions at energies of order 1-2 TeV (as relevant for future lepton machines) and $pp$ collisions at LHC energies. Dynamically generating a spin-0 resonance around 1.5 TeV (by appropriately choosing the parameters of the effective theory) we find that the differential cross section per unit $s$, $p_t^2$ is of order 0.01 fbarn/TeV$^4$ at the LHC. Injecting a spin-2 resonance around 2 TeV we find an additional factor 100 suppression for $p_t$ up to 200 GeV. The very small cross sections put these $\gamma\gamma$ processes, though very clean, out of reach of immediate future searches., Comment: 36 pages, 20 plots

We report computations of the production cross-section of longitudinal electroweak and Higgs boson pairs within Effective Field Theory for the Electroweak sector (including the Higgs). We have recently reported theoretical studies of gauge boson-gauge boson and Higgs-Higgs resonance production with various quantum numbers. We are now focusing on gauge boson-Higgs boson two-body axial-vector resonances and show a typical cross section. At last, we point out that photon-photon production has also been studied (in $e^-e^+$ as well as pp machines), as this is a very clean process allowing access to scalar and tensor resonances., Comment: 3 pages, 4 eps figures; to appear in the proceedings of the European Physical Society Conference on High Energy Physics (EPS-HEP 2017), Venice, Italy 5-12 July 2017

In this work we consider the spontaneous symmetry breaking of the electroweak $SU(2)_L\times U(1)_Y$ gauge group into $U(1)_{em}$ taken place in the Standard Model of particle physics as seen from the point of view of an accelerating observer. According to the Unruh effect that observer detects the Minkowski vacuum as a thermal bath at a temperature proportional to the proper acceleration $a$. Then we show that (in a certain large $N$ limit) when the acceleration is bigger than the critical value $a_c = 4 \pi v$ (where $v$ is the Higgs vacuum expectation value), the electroweak $SU(2)_L\times U(1)_Y$ gauge symmetry is restored and all elementary particles become massless. In addition, even observers with $a

Due to the gap between the known 100 GeV scale and new physics if any, it is natural to employ an effective one-loop Lagrangian (HEFT) for the particles of the Electroweak Symmetry Breaking Sector (W_L, Z_L and h). To describe any new particles and resonances that may be found at the LHC we employ its unitarized amplitudes, valid even in the presence of new strong interactions. We have assessed the systematics by comparing several such methods, and find that they give qualitatively similar results and succesfully produce unitary amplitudes in the nonperturbative regime. We are thus in a position to describe new physics in the 0.5 TeV-3 TeV (region of validity of our approximations: the effective theory and the equivalence theorem to substitute W_L, Z_L by the Goldstone bosons of electroweak symmetry breaking). We have also computed the coupling of the EWSBS to the top-antitop and two-photon channels to describe resonances that decay through them or to study their photon-photon production, for example. The approach is universal and useful for many BSM theories at low energy., Comment: Contribution to the EPS conference on High Energy Physics, Venice, Italy, 5th-12th July 2017. 4+1 pages, 7 plots

In the present work we study the production of vector resonances at the LHC by means of the vector boson scattering $WZ \to WZ$ and explore the sensitivities to these resonances for the expected future LHC luminosities. We are assuming that these vector resonances are generated dynamically from the self interactions of the longitudinal gauge bosons, $W_L$ and $Z_L$, and work under the framework of the electroweak chiral Lagrangian to describe in a model independent way the supposedly strong dynamics of these modes. The properties of the vector resonances, mass, width and couplings to the $W$ and $Z$ gauge bosons are derived from the inverse amplitude method approach. We implement all these features into a single model, the IAM-MC, adapted for MonteCarlo, built in a Lagrangian language in terms of the electroweak chiral Lagrangian and a chiral Lagrangian for the vector resonances, which mimics the resonant behavior of the IAM and provides unitary amplitudes. The model has been implemented in MadGraph, allowing us to perform a realistic study of the signal versus background events at the LHC. In particular, we have focused our study on the $pp\to WZjj$ type of events, discussing first on the potential of the hadronic and semileptonic channels of the final $WZ$, and next exploring in more detail the clearest signals. These are provided by the leptonic decays of the gauge bosons, leading to a final state with $\ell_1^+\ell_1^-\ell_2^+\nu jj$, $\ell=e,\mu$, having a very distinctive signature, and showing clearly the emergence of the resonances with masses in the range of 1.5-2.5 TeV, which we have explored., Comment: Revised version accepted for publication in JHEP. Enlarged analysis. References added. 44 pages, 23 figures, 3 tables

In this work we consider the ontological status of the Unruh effect. Is it just a formal mathematical result? Or the temperature detected by an accelerating observer can lead to real physical effects such as phase transition. In order to clarify this issue we use the Thermalization Theorem to explore the possibility of having a restoration of the symmetry in a system with spontaneous symmetry breaking of an internal continuous symmetry as seen by an accelerating observer. We conclude that the Unruh effect is an ontic effect, rather than an epistemic one, giving rise, in the particular example considered here, to a phase transition (symmetry restoration) in the region close to the accelerating observer horizon., Comment: Presented at the Fourth International Conference on the Nature and Ontology of Spacetime, dedicated to the 100th anniversary of the publication of General Relativity, 30 May - 2 June 2016, Golden Sands, Varna, Bulgaria (Minkowski Institute Press, Montreal 2017)

This Report summarizes the results of the activities of the LHC Higgs Cross Section Working Group in the period 2014-2016. The main goal of the working group was to present the state-of-the-art of Higgs physics at the LHC, integrating all new results that have appeared in the last few years. The first part compiles the most up-to-date predictions of Higgs boson production cross sections and decay branching ratios, parton distribution functions, and off-shell Higgs boson production and interference effects. The second part discusses the recent progress in Higgs effective field theory predictions, followed by the third part on pseudo-observables, simplified template cross section and fiducial cross section measurements, which give the baseline framework for Higgs boson property measurements. The fourth part deals with the beyond the Standard Model predictions of various benchmark scenarios of Minimal Supersymmetric Standard Model, extended scalar sector, Next-to-Minimal Supersymmetric Standard Model and exotic Higgs boson decays. This report follows three previous working-group reports: Handbook of LHC Higgs Cross Sections: 1. Inclusive Observables (CERN-2011-002), Handbook of LHC Higgs Cross Sections: 2. Differential Distributions (CERN-2012-002), and Handbook of LHC Higgs Cross Sections: 3. Higgs properties (CERN-2013-004). The current report serves as the baseline reference for Higgs physics in LHC Run 2 and beyond., Comment: 869 pages, 295 figures, 248 tables and 1645 citations. Working Group web page: https://twiki.cern.ch/twiki/bin/view/LHCPhysics/LHCHXSWG

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 figures

By using a Non-linear Electroweak Chiral Lagrangian, including the Higgs, coupled to heavy quarks, and the Equivalence Theorem, we compute (in the regime $M_t^2/v^2\ll\sqrt{s}M_t/v^2\ll s/v^2$) the one-loop amplitudes $W^+W^-\to t\bar t$, $ZZ\to t\bar t$ and $hh\to t\bar t$ (to NLO in the effective theory). We calculate the scalar partial-wave helicity amplitudes which allow us to check unitarity at the perturbative level in both $M_t/v$ and $s/v$. As with growing energy perturbative unitarity deteriorates, we also introduce a new unitarization method with the right analytical behavior on the complex $s$-plane and that can support poles on the second Riemann sheet to describe resonances in terms of the Lagrangian couplings. Thus we have achieved a consistent phenomenological description of any resonant $t\bar t$ production that may be enhanced by a possible strongly interacting Electroweak Symmetry Breaking Sector., Comment: 13 pages, 12 figures

Tantalizing LHC hints suggest that resonances of the Electroweak Symmetry Breaking Sector might exist at the TeV scale. We recall a few key meson-meson resonances in the GeV region that could have high-energy analogues which we compare, as well as the corresponding unitarized effective theories describing them. While detailed dynamics may be different, the constraints of unitarity, causality and global-symmetry breaking, incorporated in the Inverse Amplitude Method, allow to carry some intuition over to the largely unmeasured higher energy domain. If the 2 TeV ATLAS excess advances one such new resonance, this could indicate an anomalous q qbar W coupling., Comment: Proceedings of the Bled miniworkshop "Exploring hadron resonances", July 5th-11th 2015. 8 pages, 10 plots

If new resonances of the electroweak symmetry breaking sector (longitudinal-gauge and Higgs) bosons are found in the 1-3 TeV region, the right tool to assess their properties and confront experimental data in a largely model-independent yet simple manner is Unitarized Effective Theory. Its ingredients are: 1) custodial symmetry and the Equivalence Theorem, that allow to approximate W_L and Z_L by an isospin-triplet of Goldstone bosons omega^a in the 1-TeV region. 2) The effective coupling of a generic, approximately massless scalar-isoscalar h to those Goldstone bosons, and the chiral Lagrangian describing them, valid up to about 3 TeV. 3) The Inverse Amplitude or other unitarization techniques that allow to extend the reach of perturbation theory to the first resonance in each partial wave. We highlight some of the parameter space that can give rise to 2-TeV resonances, for example a simultaneous scalar-isoscalar and a vector-isovector ones (motivated by the ATLAS excess) and also the potential importance of coupled-channel dynamics between hh and omega omega., Comment: 6 pages, 12 plots

The LHC is now exploring the 1-3 TeV scale where resonances of the Electroweak Symmetry Breaking Sector might exist. If so, Unitarized Effective Theory can be used to describe the data with all the constraints of unitarity, causality and global-symmetry breaking, and to find the resonance positions in the complex s-plane. From any resonances found, one can infer the parameters of the universal Effective Lagrangian, and those may be used to inform higher-energy theories (UV completions) that can be matched to it. We exemplify with two-body resonances in the coupled channels hh and W_L W_L- Z_L Z_L employing the Equivalence Theorem and comment on the apparent excess in the ATLAS dijet data at 2 TeV., Comment: Contribution to the proceedings of the XVIIIth workshop "What Comes Beyond the Standard Models?", Bled, Slovenia, July 11th-19th 2015. 12 graphs, 10 pages

We are exploring a generic strongly-interacting Electroweak Symmetry Breaking Sector (EWSBS) with the low-energy effectie field theory for the four experimentally known particles ($W_L^\pm$, $Z_L$, $h$) and its dispersion-relation based unitary extension. In this contribution we provide simple estimates for the production cross section of pairs of the EWSBS bosons and their resonances at proton-proton colliders as well as in a future $e^-e^+$ (or potentially a $\mu^-\mu^+$) collider with a typical few-TeV energy. We examine the simplest production mechanisms, tree-level production through a $W$ (dominant when quantum numbers allow) and the simple effective boson approximation (in which the electroweak bosons are considered as collinear partons of the colliding fermions). We exemplify with custodial isovector and isotensor resonances at 2 TeV, the energy currently being discussed because of a slight excess in the ATLAS 2-jet data. We find it hard, though not unthinkable, to ascribe this excess to one of these $W_LW_L$ rescattering resonances. An isovector resonance could be produced at a rate smaller than, but close to earlier CMS exclusion bounds, depending on the parameters of the effective theory. The $ZZ$ excess is then problematic and requires additional physics (such as an additional scalar resonance). The isotensor one (that would describe all charge combinations) has a smaller cross section., Comment: 15 pages, 8 figures

We point out that in the early universe, for temperatures in the approximate interval 175-80 MeV (after the quark-gluon plasma), pions carried a large share of the entropy and supported the largest inhomogeneities. Thus, we examine the production of entropy in a pion gas, particularizing to inhomogeneities of the temperature, for which we benefit from the known thermal conductivity. We finally put that entropy produced in relaxing such thermal inhomogeneities in the broad context of this relatively unexplored phase of early-universe cosmology., Comment: 10 pages, 10 figures

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 figures

The apparent finding of a 125 GeV light Higgs boson would close the minimal Standard Model (SM), that is weakly interacting. This is an exceptional feature not generally true if new physics exists beyond the mass gap found at the LHC up to 700 GeV. Any such new physics would induce departures from the SM in the low-energy dynamics for the minimal electroweak symmetry-breaking sector (EWSBS), with three Goldstone bosons (related to longitudinal W and Z bosons) and one light Higgs-like scalar. With no new particle content, for most of the parameter space, the scattering is actually strongly interacting (with the SM a remarkable exception). We therefore explore various unitarization methods, that have already be applied to the tree-level WL WL amplitude; we find and study a natural second sigma-like scalar pole there. Of note is its appearance due to either elastic or coupled-channel dynamics, especially since the later is largely unconstrained by current LHC data and could be large., Comment: 7 pages, 10 figures. Proceedings of the XIth Quark Confinement and the Hadron Spectrum, 8-12 September, 2014, Saint-Petersburg, Russia

In these proceedings we provide a brief summary of the findings of a previous article where we have studied the photon-photon scattering into longitudinal weak bosons within the context of the electroweak chiral Lagrangian with a light Higgs, a low-energy effective field theory including a Higgs-like scalar singlet and where the electroweak would-be Goldstone bosons are non-linearly realized. We consider the relevant Lagrangian up to next-to-leading order in the chiral counting, which is explained in some detail here. We find that these amplitudes are ultraviolet finite and the relevant combinations of next-to-leading parameters ($c_\gamma$ and $a_1-a_2+a_3$) do not get renormalized. We propose the joined analysis of $\gamma\gamma$-scattering and other photon related observables ($\Gamma(h\to\gamma\gamma)$, $S$--parameter and the $\gamma^*\to W^+_LW^-_L$ and $\gamma^*\to h\gamma$ electromagnetic form-factors) in order to separate and determine each chiral parameter. Moreover, the correlations between observables provided by the NLO computations would lead to more stringent bounds on the new physics that is parametrized by means of this effective Lagrangian. We also show an explicit computation of the $\gamma\gamma$--scattering up to next-to-leading order in the $SO(5)/SO(4)$ minimally composite Higgs model., Comment: 7 pages, 8 eps figures. Proceedings of the 37th International Conference on High Energy Physics (ICHEP 2014), Valencia (Spain), 2nd-9th July 2014

Recently, a new boson h has been discovered at the LHC which, so far, is compatible with the properties of the SM Higgs. However, the SM is not the most general low-energy dynamics for the minimal electroweak symmetry breaking sector with three Goldstone bosons and one light scalar. By using non-linear effective Lagrangian for these four particles we study different processes at one-loop precision, identifying the counterterms needed to cancel the divergences. Then we apply the IAM unitarization method on the partial waves, both to make more realistic predictions which could be tested at the LHC and to discuss the limitations of the one-loop computations. The studied processes are the elastic scattering amplitude for both the longitudinal components of the gauge bosons V = W, Z and the hh -> hh, as well as the inelastic VV -> hh., Comment: 3 pages, 3 figures, ICHEP2014 Proceedings

In these proceedings we discuss our recent work on $\gamma\gamma\to W^+_L W^-_L$ and $\gamma\gamma\to Z_L Z_L$ within the framework of Electroweak Chiral Lagrangians with a light Higgs. These observables are good candidates to provide indications of physics beyond the Standard Model and can complement other analyses and global fits. Making use of the equivalence theorem, we have performed the computation up to the next-to-leading order in the chiral expansion, i.e., including one-loop corrections and the full set of possible counterterms allowed at that order in the low-energy effective field theory. The one-loop amplitudes turn out to have a extremely simple structure and they are ultraviolet finite. Thus, the relevant combinations of higher order chiral couplings $c_\gamma^r$ and $(a_1^r-a_2^r+a_3^r)$ do not run. We also identify an additional set of observables that depend on these same parameters, which can be use to complement the $\gamma\gamma$ analysis through a global fit., Comment: 6 pages. Proceedings of the Second Annual Conference on Large Hadron Collider Physics - LCHP 2014, Columbia University, New York, U.S.A (June 2-7, 2014)