theories where **the** cosmological behaviour is decoupled from **the** small-scale behaviour 2
. **The** dark energy **effective** action for models like **K**-**mouflage** does not carry new infor- mation which cannot be extracted from **the** original non-linear Lagrangian. In that respect, **the** purpose **of** our paper is twofold. First we show that **the** complete **K**-**mouflage** **theory** can be defined not only by its Lagrangian but also by two functions **of** **the** cosmological scale factor. Given these two functions, it is straightforward to reconstruct **the** original La- grangian, to derive **the** cosmological background evolution and to deduce **the** **effective** dark energy **effective** **theory** at any order. This reconstruction can be easily used at second order in **the** **effective** **theory**, which is enough to analyse all **the** linear observables **of** **the** models and eventually to compare them with data. Secondly, **the** reconstruction mapping does not require any knowledge **of** **the** initial conditions in **the** early Universe and only requires **the**

En savoir plus
many models (for example **of** **the** late time universe) **the** equations **of** scalar (or even vector) fields can also be written using fluid variables such as density, pressure and anisotropic stress. This adds up to **the** need for a general framework to classify and describe fluid interactions in cosmological perturbation **theory**.
To simplify **the** process **of** model testing, a useful strategy is to search in **the** data for specific features shared by classes **of** models. In this work we develop a framework, exclusively based on symmetry arguments, that describes th e dynamics **of** cosmological perturbations at large scales in multi-component fluids. We use **the** **Effective** **Field** **Theory** (EFT) **of** Fluids [20–22] to describe **the** propagation **of** gapless sound waves, i.e phonons, in continuous media at low energies (or equivalently large distances). **The** power **of** **the** **effective** **field** **theory** is that given **the** low-energy degrees **of** freedom and **the** symmetries that characterize them, **the** form **of** **the** action is completely determined, with strong relations between its various terms. This framework is then able to capture at once several microscopic models that share **the** same degrees **of** freedom and symmetry at large distances.

En savoir plus
Abstract
We develop an approach to compute observables beyond **the** linear regime **of** dark matter perturbations for general dark energy and modified gravity models. We do so by combining **the** **Effective** **Field** **Theory** **of** Dark Energy and **Effective** **Field** **Theory** **of** Large-Scale Structure approaches. In particular, we parametrize **the** linear and nonlinear effects **of** dark energy on dark matter clustering in terms **of** **the** Lagrangian terms introduced in a companion paper [ 1 ], focusing on Horndeski theories and assuming **the** quasi-static approximation. **The** Euler equation for dark matter is sourced, via **the** Newtonian potential, by new nonlinear vertices due to modified gravity and, as in **the** pure dark matter case, by **the** effects **of** short-scale physics in **the** form **of** **the** divergence **of** an **effective** stress tensor. **The** **effective** fluid introduces a counterterm in **the** solution to **the** matter continuity and Euler equations, which allows a controlled expansion **of** clustering statistics on mildly nonlinear scales. We use this setup to compute **the** one-loop dark-matter power spectrum.

En savoir plus
That chiral symmetry could play an important role in nuclear physics was recognized already in early 1970’s. It was implicit in considerations **of** pion-mediated nuclear potentials, but **the** first realization **of** its potential impact in nuclear physics was in nuclear response functions to **the** electroweak external potential. There was no **effective** **field** **theory** then but just phenomenological Lagrangians built with identified hadronic degrees **of** freedom considered to be relevant to **the** kinematic regime concerned. Both **the** nuclear potentials and response functions were then calculated only – and by necessity – at **the** tree order. It was in calculating **the** EW response functions that **the** soft-pion theorems, applicable at **the** tree order with **the** Lagrangian, were applied to pionic exchange currents. Given that **the** pion-exchange represented dominant contribution, with heavier meson degrees **of** freedom suppressed by their heavy mass, **the** soft-pion contribution with constraints from **the** current algebras were calculated reliably parameter-free. This represented **the** first indication that chiral symmetry could figure significantly in nuclear processes [21]. **The** further development in this line **of** reasoning led to **the** prediction that **the** M 1 matrix element and **the** weak axial- charge matrix element should receive an important contribution from **the** soft-pion theorems. It was recognized on **the** ground **of** **the** soft-pion theorems that **the** axial-charge transitions can have an extremely clean meson-exchange effects [22]. Indeed **the** nuclear EFT so formulated led to high precision calculations **of** electroweak processes in light nuclei, a brief summary **of** which is given in [23].

En savoir plus
In this paper, we showed that **the** **effective** **field** **theory** **of** **the** new state S, combined with **the** standard model, leads to non-trivial signatures at **the** level **of** **the** LHC observables. In section 4 , we concentrated on **the** decay **of** S and showed that there are necessarily decays into other electroweak final states, with non-trivial relations between **the** branching ratios among **the** final states. Importantly, **the** branching-ratio relations and sum rules we derived in that section will be tested in future runs **of** **the** collider. In section 5 we asked a related question: given **the** **effective** **field** **theory** and **the** rate to diphotons observed so far, how can observables, such as ratios **of** rates that survive VBF cuts to inclusive rates, tell us about **the** coupling **of** S to non-electroweak states, such as quarks. We showed that **the** VBF ratio is a discriminator between gluon-fusion production and, for example, quark anti-quark produc- tion. This is particularly relevant, given that in section 2 we showed that current LHC data supports production through either gluon fusion or heavy quark annihilation. Similarly, in section 6 we showed that additional constraints on **the** coupling **of** **the** resonance to non- electroweak states are found when considering simultaneously **the** total width along with **the** VBF ratio. In summary, we have provided a variety **of** simple relations directly among observables at **the** LHC which, in light **of** **the** low energy **effective** **field** **theory**, may have profound implications for understanding **the** nature **of** **the** excess as more data accumulates.

En savoir plus
F-91191 Gif-sur-Yvette, C´ edex, France
(Dated: February 8, 2017)
We consider **K**-**mouflage** models, which are **K**-essence theories coupled to matter. We analyze their quantum properties and in particular **the** quantum corrections to **the** classical Lagrangian. We setup **the** renormalization program for these models and show that, contrary to renormalizable **field** theories where renormalization by infinite counterterms can be performed in one step, **K**-**mouflage** theories involve a recursive construction whereby each set **of** counterterms introduces new divergent quantum contributions which in turn must be subtracted by new counterterms. This tower **of** counterterms can be in principle constructed step by step by recursion and allows one to calculate **the** finite renormalized action **of** **the** model. In particular, it can be checked that **the** classical action is not renormalized and that **the** finite corrections to **the** renormalized action contain only higher-derivative operators. We concentrate then on **the** regime where calculability is ensured, i.e., when **the** corrections to **the** classical action are negligible. We establish an operational criterion for classicality and show that this is satisfied in cosmological and astrophysical situations for (healthy) **K**-**mouflage** models which pass **the** Solar System tests. These results rely on perturbation **theory** around a background and are only valid when **the** background configuration is quantum stable. We analyze **the** quantum stability **of** astrophysical and cosmological backgrounds and find that models that pass **the** Solar System tests are quantum stable. We then consider **the** possible embedding **of** **the** **K**-**mouflage** models in an Ultra-Violet completion. We find that **the** healthy models which pass **the** Solar System tests all violate **the** positivity constraint which would follow from **the** unitarity **of** **the** putative UV completion, implying that these healthy **K**-**mouflage** theories have no UV completion. We then analyze their behavior at high energy, and we find that **the** classicality criterion is satisfied in **the** vicinity **of** a high-energy collision, implying that **the** classical **K**-**mouflage** **theory** can be applied in this context. Moreover, **the** classical description becomes more accurate as **the** energy increases, in a way compatible with **the** classicalization concept.

En savoir plus
∗ Institut für Theoretische Physik II, Ruhr-Universität Bochum, Bochum, Germany † Department **of** Physics and Technology, University **of** Bergen, Bergen, Norway
∗∗ Department **of** High Energy Physics, Saint-Petersburg State University, Saint-Petersburg, Russia
Abstract. We argue how it is possible to apply **the** general scheme **of** **the** **effective** scattering **theory** (EST) to **the** description **of** **the** hadronic processes. **The** results **of** **the** numerical tests **of** sum rules for πN spectrum parameters that follow from **the** bootstrap system allow us to claim **the** consistency

En savoir plus
i and c τ
0
j and depend on properties such as target element, WIMP mass, WIMP spin, WIMP velocity, and nuclear recoil energy. We evaluate **the** A ττ ij 0 without integrating over **the** dark matter velocity distribution to avoid introducing more variables. Amplitudes are summed over **the** isotopes for a given element according to their natural abundances. Finding **the** eigenvectors **of** this matrix will give **the** “principal components" **of** **the** interaction space. We expect that three **of** **the** four eigenvalues should be small, since **the** matrix for a single isotope is an outer product and therefore should have a single nonzero eigenvalue. **The** vector with **the** largest eigenvalue corresponds to **the** maximal ampli- tude for scattering in **the** interference space under consid- eration, while **the** three small eigenvalues correspond to local extrema in **the** scattering amplitude which tend to suppress **the** event rate. To be maximally sensitive to **the** parameter space for a given interference case, we would like to choose target elements whose constructive interfer- ence eigenvectors span **the** space **of** interactions.

En savoir plus
In a seminal pair **of** papers from 1967, Barker and Henderson combined **the** approach **of** Zwanzig with **the** Percus-Yevick results for hard spheres to obtain **the** first true microscopic **theory** **of** liquids, embedding **the** ideas **of** van der Waals within **the** framework **of** statistical mechanics [ 10 , 11 ] (reviewed in [ 12 ]). In addition to providing a correct pertur- bative treatment **of** interparticle attractions, they also devised **the** first prescription for mapping a softly repulsive refer- ence system (required to treat, e.g., Lennard-Jones particles) onto a system **of** hard spheres with an **effective**, temperature- dependent diameter. **The** **theory** worked very well for a variety **of** model systems, accurately reproducing data for **the** thermodynamics and structure obtained from Monte Carlo simulation. Although there nowadays exist more elaborate ap- proaches to **the** thermodynamics, namely, **the** self-consistent Ornstein-Zernike approximation **of** Høye and Stell [ 13 , 14 ] and **the** heirarchical reference **theory** **of** Reatto and Parola [ 15 ], these “beyond mean-**field**” approximations are not easy to implement and only yield significant differences from **the** Barker-Henderson **theory** in **the** vicinity **of** **the** critical point.

En savoir plus
We now discuss why we restrict to this action and some ways to extend it.
1.1 **The** gravitational action
While trying to extend **the** NRGR formalism to dark energy/scalar **field** models we im- mediately encounter an obstruction. It is well known that, to pass Solar System tests, modified gravity theories display screening mechanisms that make **the** scalar interac- tions weaker in high density environments. For instance, most theories belonging to **the** Galileon/Horndeski [ 37 – 39 ] and “beyond Horndeski” [ 40 – 44 ] classes have a rich structure **of** non-linear terms in their Lagrangians that become more important close to **the** sources, thereby screening **the** effects **of** **the** scalar fluctuations [ 45 , 46 ]. While it is legitimate to neglect such non-linearities on **the** largest cosmological scales, they are expected to play a major role in **the** vicinity **of** **the** binaries, causing a breakdown **of** **the** perturbative expan- sion that we use in this paper.

En savoir plus
1. Introduction
Relativistic Heavy Ion Collider (RHIC) in Brookhaven National Laboratory provides a testing ground for QCD. Collisions **of** heavy ions at relativistic speed create quark gluon plasma (QGP) which is **the** high temperature, high density phase **of** **the** QCD phase diagram. QGP behaves in a surprising way in which its evolution can be modelled as a nearly ideal ﬂuid [1]. Therefore, hydrodynamics provides a useful framework to study **the** collective motion and its ﬂuctuations **of** QGP. One **of** **the** simplest models is **the** Bjorken ﬂow [2]. **The** Bjorken ﬂow describes a static ﬂuid in a Boost invariant background which agrees well with experimental measurements.

En savoir plus
intermediate state without **the** need to include them explicitly, provided **the** **effective** Lagrangian has **the** right dynamics to generate these resonances.
5. Perspectives
**The** general framework we presented above to study **the** structure **of** relativistic compound systems in light-front dynamics in a nonperturbative way relies on three main advances: i) **the** con- struction **of** a covariant formulation **of** light-front dynamics [ 2 , 3 ] in order to control any violation **of** rotational invariance; ii) **the** development **of** an appropriate renormalization scheme — **the** so- called Fock sector dependent renormalization scheme — to deal with **the** truncation **of** **the** Fock expansion [ 4 ]; iii) **the** use **of** an appropriate regularization scheme — **the** so-called Taylor-Lagrange regularization scheme — very well adapted to systematic calculations in light-front dynamics [ 11 ]. These advances should enable us to have a predictive framework order by order in **the** Fock expansion. We shall complete in **the** future this description by considering physical systems involv- ing spontaneous symmetry breaking. It is known that these systems can be described in light-front dynamics by **the** consideration **of** zero-mode contributions, in **the** λ φ 4 **theory** in 1 + 1 dimension for instance [ 15 ]. Their full calculation in 3 + 1 dimensions within **the** general framework presented above remains to be done.

En savoir plus
bands [6]. Their approach allowed to confirm **the** anoma- lous Hall effect predicted by Karplus and Luttinger [5] and to express this effect in terms **of** Berry curvature. Following this approach, we derive our corrected equa- tions up to **the** second order in external constant force for a two-band system using perturbation **theory**. We con- sider **the** case **of** geodesic trajectory **of** **the** wavepacket, corresponding to **the** evolution **of** **the** **effective** **field** on **the** equator **of** **the** Bloch sphere. We show that in this configuration, all first-order and most **of** **the** second-order corrections to **the** semiclassical equations **of** motion are zero, except **the** particular correction due to **the** differ- ence **of** **the** metric on **the** equator and at **the** equilibrium deviation angle **of** **the** spin.

En savoir plus
3.1 Wilsonian treatment **of** divergences
Potentials that go to infinity faster than 1/r 2 at **the** origin are called singular [36] and generically
arise in dark sectors with spinning dm and/or with some strong dynamics. **The** occurrence **of** unphysical behavior originating from **the** infinitely large energies **of** such potentials are analogous to **the** infinities **of** quantum **field** **theory** (qft). These inconsistencies arise when one extrapolates a long-range potential to arbitrarily short distances where ultraviolet physics should be taken into account. In fact, **the** Schr¨odinger equation can be renormalized by adopting **the** Wilsonian renormalization group (rg) methods **of** qft [37]: **the** singular potential is regulated at a short distance a and augmented with a series **of** local operators that parametrize **the** unknown uv physics,

En savoir plus
In all these **effective** models approaches, one must dis- tinguish **the** two steps: first, an **effective** Hamiltonian is derived; then, because it is still an interacting quantum problem, one needs to resort to an efficient technique to study it. Although it is a bosonic model, **the** presence **of** positive off-diagonal terms prohibits quantum Monte Carlo calculations. Possible alternatives are mean-**field** analysis [ 12 ] which main drawback is to overestimate **the** tendency to form plateaux and also needs a careful numerical analy- sis on finite clusters. Given **the** various small amplitudes, we prefer not to make any further assumption, and we provide exact diagonalizations (ED) **of** these **effective** models on finite lattices.

En savoir plus
Simply put, scientific realism is **the** stance that takes our best sci- entific theories to offer approximately true descriptions **of** **the** world. **The** history **of** science shows, however, that many past theories have proven to make radically false claims about unobservable entities and structures when these theories are assessed relative to their succes- sors. This suggests that our current best theories might be in **the** same situation. **The** most popular response to this problem is a po- sition called ‘selective realism’: even though our best theories do not get everything right, they still contain parts that are likely to remain (approximately) true [30, 36, 50]. Williams [48] and J. Fraser [19] have recently defended this position in **the** context **of** QFT: they argue that Wilsonian RG methods provide ‘local’ (i.e., restricted to QFT) tools to distinguish essential parts in current EFTs that are likely to with- stand future **theory** change and give (approximately) true descriptions **of** **the** world. In particular, RG methods give selective realists some confidence in **the** claim that **the** low-energy content **of** **the** presently most successful EFTs is largely independent **of** **the** high-energy con- tent **of** future theories and is therefore likely to remain unaffected by **the** discovery **of** new high-energy physics.

En savoir plus
(|∂ z f | 2 + g(z)|f| 2 )dz.
These norms are equivalent for all continuous conformal metrics and we denote **the** space simply by H 1 ( ˆ C ).
Finally we define H −1 ( ˆ C ) as **the** dual space and denote **the** dual pairing by hX, fi.
**The** LQFT measure will be defined as a measure on H −1 ( ˆ C ). It will be constructed using **the** Gaussian Free **Field** (GFF) on ˆ C . As is well known **the** GFF in such a setup is only defined modulo a constant. For LQFT it is important to include this constant as an integration variable. In general **the** GFF is a Gaussian random **field** whose covariance is **the** Green function **of** **the** Laplace operator. In our setup **the** Laplace operator is given by ∆ g = 4g(z) −1 ∂ ¯ z ∂ z . Some care is needed here since ∆ g is not invertible. Indeed, −∆ g is a non-negative self-

En savoir plus
Initially implemented for inflation in [ 4 , 5 ], a convenient way to describe dark energy and modified gravity models characterized by a single scalar degree **of** freedom and to connect them to observational predictions in terms **of** a minimal number **of** parameters is **the** **Effective** **Field** **Theory** **of** Dark Energy (EFTofDE) [ 6 – 10 ] (see [ 11 – 13 ] for reviews); see also [ 14 – 17 ] for analogous approaches in dark energy. In **the** EFTofDE approach, one assumes that **the** time-diffeomorphism invariance **of** **the** gravitational sector is broken by **the** dark-energy **field**. In **the** so-called unitary gauge, **the** gravitational action can be constructed as **the** sum **of** all possible operators in terms **of** **the** metric, invariant under time-dependent spatial diffeomorphisms and ordered in **the** number **of** perturbations and derivatives. Physical principles such as locality, causality, stability, and unitarity can be imposed at **the** level **of** **the** Lagrangian, so that **the** predicted signatures are physically acceptable.

En savoir plus
Institut de Physique Th´ eorique, CEA Saclay, Universit´ e Paris-Saclay, 91191 Gif-sur-Yvette, France
We present in detail an **Effective** **Field** **Theory** (EFT) formulation for **the** essential case **of** spinning objects as **the** components **of** inspiralling compact binaries. We review its implemen- tation, carried out in a series **of** works in recent years, which leveled **the** high post-Newtonian (PN) accuracy in **the** spinning sector to that, recently attained in **the** non-spinning sector. We note a public package, “EFTofPNG”, that we recently created for high precision computation in **the** EFT **of** PN Gravity, which covers all sectors, and includes an observables pipeline.

En savoir plus