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TOI-396 is an F6V star ($V\approx6.4$) orbited by three transiting planets. The orbital periods of the two innermost planets are close to the 5:3 commensurability ($P_b \sim3.6$ d and $P_c \sim6.0$ d). To measure the masses of the three planets, refine their radii, and investigate whether planets b and c are in MMR, we carried out HARPS RV observations and retrieved photometric data from TESS. We extracted the RVs via a skew-normal fit onto the HARPS CCFs and performed an MCMC joint analysis of the Doppler measurements and transit photometry, while employing the breakpoint method to remove stellar activity from the RV time series. We also performed a thorough TTV dynamical analysis of the system. Our analysis confirms that the three planets have similar sizes: $R_b=2.004_{-0.047}^{+0.045}R_{\oplus}$; $R_c=1.979_{-0.051}^{+0.054}R_{\oplus}$; $R_d=2.001_{-0.064}^{+0.063}R_{\oplus}$. For the first time, we determine RV masses for TOI-396b and d: $M_b=3.55_{-0.96}^{+0.94}M_{\oplus}$ ($\rho_b=2.44_{-0.68}^{+0.69}$ g cm$^{-3}$) and $M_d=7.1\pm1.6M_{\oplus}$ ($\rho_d=4.9_{-1.1}^{+1.2}$ g cm$^{-3}$). Our results suggest a quite unusual system architecture, with the outermost planet being the densest. The Doppler reflex motion induced by TOI-396c remains undetected in our RV time series, likely due to the proximity of $P_c$ to the star's rotation period ($P_{\mathrm{rot}}=6.7\pm1.3$ d). We also discovered that TOI-396b and c display significant TTVs. While the TTV dynamical analysis returns a formally precise mass for TOI-396c ($M_{c,\mathrm{dyn}}=2.24^{+0.13}_{-0.67}M_{\oplus}$), the result might not be accurate owing to the poor sampling of the TTV phase. We also conclude that TOI-396b and c are close to-, but out of- the 5:3 MMR. Our numerical simulation suggests TTV semi-amplitudes of up to 5 hours over a temporal baseline of $\sim$5.2 years., Comment: 24 pages (6 in the Appendix), 15 Figures (2 in the Appendix), 10 Tables (5 in the Appendix). Accepted for publication in A&A

We study the equation of state (EoS) of a neutron star (NS) accounting for new advances. In the low energy density, $n\leq 0.1 n_s$, with $n_s$ the saturation density, we use a new pure neutron matter EoS that is regulator independent and expressed directly in terms of experimental nucleon-nucleon scattering data. In the highest-density domain our EoS's are matched with pQCD to $\mathcal{O}(\alpha_s^3)$. First principles of causality, thermodynamic consistency and stability are invoked to transit between these two extreme density regimes. The EoS's are further constrained by the new measurements from PREX-II and CREX on the symmetry energy ($S_0$) and its slope ($L$). In addition, we also take into consideration the recent experimental measurements of masses and radii of different NSs and tidal deformabilities. A band of allowed EoS's is then obtained. Interestingly, the resulting values within the band for $S_0$ and $L$ are restricted with remarkably narrower intervals than the input values, with $32.9\leq S_0 \leq 39.5~\text{MeV}$ and $ 37.3 \leq L\leq 69.0~\text{MeV}$ at the 68\% CL. The band of EoS's constructed also allows possible phase transitions (PTs) for NS masses above 2.1~$M_\odot$ at 68\% CL for $n>2.5n_s$. We find both long and short coexistence regions during the PT, corresponding to first and second order PTs, respectively. We also generate the band of EoS's when excluding the astrophysical observables. This is of interest to test General Relativity and modified theories of gravity. Our band of EoS's for NSs can be also used to study other NS properties and dark matter capture in NS., Comment: 13 pages, 8 figures

We report on the precise radial velocity follow-up of TOI-544 (HD 290498), a bright K star (V=10.8), which hosts a small transiting planet recently discovered by the Transiting Exoplanet Survey Satellite (TESS). We collected 122 high-resolution HARPS and HARPS-N spectra to spectroscopically confirm the transiting planet and measure its mass. The nearly 3-year baseline of our follow-up allowed us to unveil the presence of an additional, non-transiting, longer-period companion planet. We derived a radius and mass for the inner planet, TOI-544b, of 2.018 $\pm$ 0.076 R$_{\oplus}$ and 2.89 $\pm$ 0.48 M$_{\oplus}$ respectively, which gives a bulk density of $1.93^{+0.30}_{-0.25}$ g cm$^{-3}$. TOI-544c has a minimum mass of 21.5 $\pm$ 2.0 M$_{\oplus}$ and orbital period of 50.1 $\pm$ 0.2 days. The low density of planet-b implies that it has either an Earth-like rocky core with a hydrogen atmosphere, or a composition which harbours a significant fraction of water. The composition interpretation is degenerate depending on the specific choice of planet interior models used. Additionally, TOI-544b has an orbital period of 1.55 days and equilibrium temperature of 999 $\pm$ 14 K, placing it within the predicted location of the radius valley, where few planets are expected. TOI-544b is a top target for future atmospheric observations, for example with JWST, which would enable better constraints of the planet composition., Comment: Accepted in MNRAS, 06 December 2023

The MUSE experiment at Paul Scherrer Institute will perform the first measurement of low-energy muon-proton elastic scattering (muon lab momenta 115-210 MeV) with the aim of determining the proton charge radius. We study the prospects for the proton radius extraction using the theoretical framework of Dispersively Improved Chiral Effective Field Theory (DI$\chi$EFT). It connects the proton radii with the finite-$Q^2$ behavior of the form factors through complex analyticity and enables the use of data up to $Q^2 \sim$ 0.1 GeV$^2$ for radius extraction. We quantify the sensitivity of the $\mu p$ cross section to the proton charge radius, the theoretical uncertainty of the cross section predictions, and the size of two-photon exchange corrections. We find that the optimal kinematics for radius extraction at MUSE is at momenta 210 MeV and $Q^2 \sim$ 0.05-0.08 GeV$^2$. We compare the performance of electron and muon scattering in the same kinematics. As a byproduct, we obtain explicit predictions for the $\mu p$ and $ep$ cross sections at MUSE as functions of the assumed value of the proton radius., Comment: 12 pages, 12 figures

TOI-1055 is a Sun-like star known to host a transiting Neptune-sized planet on a 17.5-day orbit (TOI-1055 b). Radial velocity (RV) analyses carried out by two independent groups using nearly the same set of HARPS spectra have provided measurements of planetary masses that differ by $\sim$ 2$\sigma$. Our aim in this work is to solve the inconsistency in the published planetary masses by significantly extending the set of HARPS RV measurements and employing a new analysis tool that is able to account and correct for stellar activity. Our further aim was to improve the precision on measurements of the planetary radius by observing two transits of the planet with the CHEOPS space telescope. We fit a skew normal (SN) function to each cross correlation function extracted from the HARPS spectra to obtain RV measurements and hyperparameters to be used for the detrending. We evaluated the correlation changes of the hyperparameters along the RV time series using the breakpoint technique. We performed a joint photometric and RV analysis using a Markov chain Monte Carlo (MCMC) scheme to simultaneously detrend the light curves and the RV time series. We firmly detected the Keplerian signal of TOI-1055 b, deriving a planetary mass of $M_b=20.4_{-2.5}^{+2.6} M_{\oplus}$ ($\sim$12%). This value is in agreement with one of the two estimates in the literature, but it is significantly more precise. Thanks to the TESS transit light curves combined with exquisite CHEOPS photometry, we also derived a planetary radius of $R_b=3.490_{-0.064}^{+0.070} R_{\oplus}$ ($\sim$1.9%). Our mass and radius measurements imply a mean density of $\rho_b=2.65_{-0.35}^{+0.37}$ g cm$^{-3}$ ($\sim$14%). We further inferred the planetary structure and found that TOI-1055 b is very likely to host a substantial gas envelope with a mass of $0.41^{+0.34}_{-0.20}$ M$_\oplus$ and a thickness of $1.05^{+0.30}_{-0.29}$ R$_\oplus$., Comment: 13 pages, 6 figures, 5 tables. Accepted for publication in A&A

Infinite nuclear matter is studied by resuming the series of ladder diagrams based on the results developed by us in Ann. Phys. 437, 168741 (2022). The master formula for the energy density is explicitly solved for the case of contact interactions, within a pionless description of the nucleon-nucleon interactions. Renormalized results are obtained which are directly expressed in terms of the nucleon-nucleon phase shifts and mixing angles in partial-wave amplitudes up to an including $G$ waves, with convergence reached under the inclusion of higher partial waves. The energy per particle, density and sound velocity resulting from the ladder series are given for symmetric and neutron matter. This resummation of the ladder diagrams provides a rigorous result that may be used as low-density reference for other parameterizations of $\bar{\cal{E}}$ for higher densities., Comment: 29 pages, 9 figures

The pion-nucleon sigma term is a quantity involved in many important aspects of particle and nuclear physics. In this review I show its origin and how it is connected to important questions as the origin of mass of the ordinary matter, studies of dark matter detection and nucleosynthesis. I mention the most common methods used to obtain the sigma term, and comment on the extracted values. As it is shown, the accepted value of the sigma term has been moving from relatively low ($\sim 40$ MeV) to larger ones ($\sim 60$ MeV) until today, where this controversy still persist., Comment: Invited review for European Physical Journal Special Topics (REVTeX version). 34 pages, 5 figures. Accepted for publication on 10 May 2021

Background: The transverse densities $\rho_{1, 2}(b)$ describe the distributions of electric charge and magnetic moment at fixed light-front time and connect the nucleon's elastic form factors with its partonic structure. The dispersive representation of the form factors $F_{1, 2}(t)$ expresses the densities in terms of exchanges of hadronic states in the $t$-channel and permits their analysis using hadronic physics methods. Purpose: Compute the densities at peripheral distances $b = \mathcal{O}(M_\pi^{-1})$, where they are generated predominantly by the two-pion states in the dispersive representation. Quantify the uncertainties. Methods: Dispersively improved chiral effective field theory (DI$\chi$EFT) is used to calculate the isovector spectral functions $\textrm{Im}\, F_{1, 2}(t)$ on the two-pion cut. The method includes $\pi\pi$ interactions ($\rho$ resonance) through elastic unitarity and provides realistic spectral functions up to $t \approx$ 1 GeV$^2$. Higher-mass states are parametrized by effective poles and constrained by sum rules (charges, radii, superconvergence relations). The densities $\rho_{1, 2}(b)$ are obtained from their dispersive representation. Uncertainties are quantified by varying the spectral functions. The method respects analyticity and ensures the correct $b \rightarrow \infty$ asymptotic behavior of the densities. Results: Accurate densities are obtained at all distances $b \gtrsim 0.5$ fm, with correct behavior down to $b \rightarrow 0$. The region of distances is quantified where transverse nucleon structure is governed by the two-pion state. The light-front current distributions in the polarized nucleon are computed and discussed. Conclusions: Peripheral nucleon structure can be computed from first principles using DI$\chi$EFT. The method can be extended to generalized parton distributions and other nucleon form factors., Comment: 20 pages, 12 figures, 1 table

This paper will review the origins, development, and examples of new versions of Micro-Pattern Gas Detectors. The goal for MPGD development was the creation of detectors that could cost-effectively cover large areas while offering excellent position and timing resolution, and the ability to operate at high incident particle rates. The early MPGD developments culminated in the formation of the RD51 collaboration which has become the critical organization for the promotion of MPGDs and all aspects of their production, characterization, simulation, and uses in an expanding array of experimental configurations. For the Snowmass 2021 study, a number of Letters of Interest were received that illustrate ongoing developments and expansion of the use of MPGDs. In this paper, we highlight high precision timing, high rate application, trigger capability expansion of the SRS readout system, and a structure designed for low ion backflow., Comment: Contribution to Snowmass 2021

This article describes the setup and performance of the near and far detectors in the Double Chooz experiment. The electron antineutrinos of the Chooz nuclear power plant were measured in two identically designed detectors with different average baselines of about 400 m and 1050 m from the two reactor cores. Over many years of data taking the neutrino signals were extracted from interactions in the detectors with the goal of measuring a fundamental parameter in the context of neutrino oscillation, the mixing angle {\theta}13. The central part of the Double Chooz detectors was a main detector comprising four cylindrical volumes filled with organic liquids. From the inside towards the outside there were volumes containing gadolinium-loaded scintillator, gadolinium-free scintillator, a buffer oil and, optically separated, another liquid scintillator acting as veto system. Above this main detector an additional outer veto system using plastic scintillator strips was installed. The technologies developed in Double Chooz were inspiration for several other antineutrino detectors in the field. The detector design allowed implementation of efficient background rejection techniques including use of pulse shape information provided by the data acquisition system. The Double Chooz detectors featured remarkable stability, in particular for the detected photons, as well as high radiopurity of the detector components., Comment: 49 pages, 29 figures

We present the discovery and characterisation of two transiting planets observed by \textit{TESS} in the light curves of the young and bright (V=9.67) star HD73583 (TOI-560). We perform an intensive spectroscopic and photometric space- and ground-based follow-up in order to confirm and characterise the system. We found that HD73583 is a young ($\sim 500$~Myr) active star with a rotational period of $12.08 \pm 0.11 $\,d, and a mass and radius of $ 0.73 \pm 0.02 M_\odot$ and $0.65 \pm 0.02 R_\odot$, respectively. HD73583 b ($P_b=6.3980420 _{ - 0.0000062 }^{+0.0000067}$ d) has a mass and radius of $10.2 _{-3.1}^{+3.4} M_\oplus$ and$2.79 \pm 0.10 R_\oplus$, respectively, that gives a density of $2.58 _{-0.81}^{ 0.95} {\rm g\,cm^{-3}}$. HD73583 c ($P_c= 18.87974 _{-0.00074 }^{+0.00086}$) has a mass and radius of $9.7_{-1.7} ^ {+1.8} M_\oplus$ and $2.39_{-0.09}^{+0.10} R_\oplus$, respectively, this translates to a density of $3.88 _{-0.80}^{+0.91} {\rm g\,cm^{-3}}$. Both planets are consistent with worlds made of a solid core surrounded by a volatile envelope. Because of their youth and host star brightness, they both are excellent candidates to perform transmission spectroscopy studies. We expect ongoing atmospheric mass-loss for both planets caused by stellar irradiation. We estimate that the detection of evaporating signatures on H and He would be challenging, but doable with present and future instruments., Comment: Accepted for publication in MNRAS

We consider a spin-balanced degenerate gas of spin-1/2 fermions whose dynamics is governed by low-energy $P$-wave interactions, characterized by the scattering volume $a_1$ and effective momentum $r_1$. The energy per particle $\bar{\cal{E}}$ in the many-body system is calculated by resumming the ladder diagrams comprising both particle-particle and hole-hole intermediate states, following the novel advances recently developed by us in Ann.Phys. 437,168741(2022). This allows to obtain a renormalized result for $\bar{\cal{E}}$ within generic cutoff regularization schemes, with $\bar{\cal{E}}$ directly expressed in terms of the scattering parameters $a_1$ and $r_1$, once the cut off is sent to infinity. The whole set of possible values of $a_1$ and $r_1$ is explored for the first time in the literature looking for minima in the energy per particle with $\bar{\cal{E}}$ given as described. They are actually found, but a further inspection reveals that the associated scattering parameters give rise to resonance poles in the complex momentum-plane with positive imaginary part, which is at odds with the Hermiticity of the Hamiltonian. We also determine that these conflictive poles, with a pole-position momentum that is smaller in absolute value than the Fermi momentum of the system, clearly impact the calculation of $\bar{\cal{E}}$. As a result, we conclude that unpolarized spin-1/2 fermionic normal matter interacting in $P$-wave is not stable. We also study three universal parameters around the unitary limit. Finally, the whole set of values for the parameters $a_1$, $r_1$ is characterized according to whether they give rise to unallowed poles and, if so, by attending to their pole positions relative to the Fermi momentum of the system explored., Comment: Version that matches the published one. 15 pages, 8 figures, 2 tables

We resum the ladder diagrams for the calculation of the energy density $\cal{E}$ of a spin 1/2 fermion many-body system in terms of arbitrary vacuum two-body scattering amplitudes. The partial-wave decomposition of the in-medium two-body scattering amplitudes is developed, and the expression for calculating $\cal{E}$ in a partial-wave amplitude expansion is also given. The case of contact interactions is completely solved and is shown to provide renormalized results, expressed directly in terms of scattering data parameters, within cutoff regularization in a wide class of schemes. $S$- and $P$-wave interactions are considered up to including the first three-terms in the effective-range expansion, paying special attention to the parametric region around the unitary limit., Comment: 58 pages, 16 figures, 2 table. New version to match the accepted manuscript in Annals of Physics. Pole content and pairing is further discussed

We extract the proton magnetic radius from the high-precision electron-proton elastic scattering cross section data. Our theoretical framework combines dispersion analysis and chiral effective field theory and implements the dynamics governing the shape of the low-$Q^2$ form factors. It allows us to use data up to $Q^2\sim$ 0.5 GeV$^2$ for constraining the radii and overcomes the difficulties of empirical fits and $Q^2 \rightarrow 0$ extrapolation. We obtain a magnetic radius $r_M^p$ = 0.850 $\pm$0.001 (fit 68%) $\pm$0.010 (theory full range) fm, significantly different from earlier results obtained from the same data, and close to the extracted electric radius $r_E^p$ = 0.842 $\pm$0.002 (fit) $\pm$0.010 (theory) fm., Comment: 5 pages, 2 figures

We extract the proton charge radius from the elastic form factor (FF) data using a novel theoretical framework combining chiral effective field theory and dispersion analysis. Complex analyticity in the momentum transfer correlates the behavior of the spacelike FF at finite $Q^2$ with the derivative at $Q^2 = 0$. The FF calculated in the predictive theory contains the radius as a free parameter. We determine its value by comparing the predictions with a descriptive global fit of the spacelike FF data, taking into account the theoretical and experimental uncertainties. Our method allows us to use the finite-$Q^2$ FF data for constraining the radius (up to $Q^2\sim$ 0.5 GeV$^2$ and larger) and avoids the difficulties arising in methods relying on the $Q^2 \rightarrow 0$ extrapolation. We obtain a radius of 0.844(7) fm, consistent with the high-precision muonic hydrogen results., Comment: 8 pages, 5 figures

Baryon masses and nucleon \sigma-terms are studied with the effective theory that combines the chiral and 1/Nc expansions for three flavors. In particular the connection between the deviation of the Gell-Mann-Okubo relation and the \sigma-term corresponding to the scalar density associated with the hypercharge is emphasized. The latter is at lowest order related to a mass combination whose low value has given rise to a \sigma- term puzzle. It is shown that while the nucleon \sigma-terms have a well behaved low energy expansion, that mass combination is affected by large higher order corrections non-analytic in quark masses. Adding to the analysis lattice QCD baryon masses, it is found that {\sigma}{\pi}N=69(10) MeV and {\sigma}s has natural magnitude within its relative large uncertainty., Comment: 8 pages, 1 table, 1 figure

We present a theoretical parametrization of the nucleon electromagnetic form factors (FFs) based on a combination of chiral effective field theory and dispersion analysis. The isovector spectral functions on the two-pion cut are computed using elastic unitarity, chiral pion-nucleon amplitudes, and timelike pion FF data. Higher-mass isovector and isoscalar t-channel states are described by effective poles, whose strength is fixed by sum rules (charges, radii). Excellent agreement with the spacelike proton and neutron FF data is achieved up to Q^2 \sim 1 GeV^2. Our parametrization provides proper analyticity and theoretical uncertainty estimates and can be used for low-Q^2 FF studies and proton radius extraction., Comment: 5 pages, 3 figures, 2 tables

We study the nucleon electromagnetic form factors (EM FFs) using a recently developed method combining Chiral Effective Field Theory ($\chi$EFT) and dispersion analysis. The spectral functions on the two-pion cut at $t > 4 M_\pi^2$ are constructed using the elastic unitarity relation and an $N/D$ representation. $\chi$EFT is used to calculate the real functions $J_\pm^1 (t) = f_\pm^1(t)/F_\pi(t)$ (ratios of the complex $\pi\pi \rightarrow N \bar N$ partial-wave amplitudes and the timelike pion FF), which are free of $\pi\pi$ rescattering. Rescattering effects are included through the empirical timelike pion FF $|F_\pi(t)|^2$. The method allows us to compute the isovector EM spectral functions up to $t \sim 1$ GeV$^2$ with controlled accuracy (LO, NLO, and partial N2LO). With the spectral functions we calculate the isovector nucleon EM FFs and their derivatives at $t = 0$ (EM radii, moments) using subtracted dispersion relations. We predict the values of higher FF derivatives with minimal uncertainties and explain their collective behavior. We estimate the individual proton and neutron FFs by adding an empirical parametrization of the isoscalar sector. Excellent agreement with the present low-$Q^2$ FF data is achieved up to $\sim$0.5 GeV$^2$ for $G_E$, and up to $\sim$0.2 GeV$^2$ for $G_M$. Our results can be used to guide the analysis of low-$Q^2$ elastic scattering data and the extraction of the proton charge radius., Comment: 14 pages, 10 figures, 6 tables

We propose a method for calculating the nucleon form factors (FFs) of $G$-parity-even operators by combining Chiral Effective Field Theory ($\chi$EFT) and dispersion analysis. The FFs are expressed as dispersive integrals over the two-pion cut at $t > 4 M_\pi^2$. The spectral functions are obtained from the elastic unitarity condition and expressed as products of the complex $\pi\pi \rightarrow N\bar N$ partial-wave amplitudes and the timelike pion FF. $\chi$EFT is used to calculate the ratio of the partial-wave amplitudes and the pion FF, which is real and free of $\pi\pi$ rescattering in the $t$-channel ($N/D$ method). The rescattering effects are then incorporated by multiplying with the squared modulus of the empirical pion FF. The procedure results in a marked improvement compared to conventional $\chi$EFT calculations of the spectral functions. We apply the method to the nucleon scalar FF and compute the scalar spectral function, the scalar radius, the $t$-dependent FF, and the Cheng-Dashen discrepancy. Higher-order chiral corrections are estimated through the $\pi N$ low-energy constants. Results are in excellent agreement with dispersion-theoretical calculations. We elaborate several other interesting aspects of our method. The results show proper scaling behavior in the large-$N_c$ limit of QCD because the $\chi$EFT calculation includes $N$ and $\Delta$ intermediate states. The squared modulus of the timelike pion FF required by our method can be extracted from Lattice QCD calculations of vacuum correlation functions of the operator at large Euclidean distances. Our method can be applied to the nucleon FFs of other operators of interest, such as the isovector-vector current, the energy-momentum tensor, and twist-2 QCD operators (moments of generalized parton distributions)., Comment: 17 pages and 11 figures

The baryon electromagnetic form factors are expressed in terms of two-dimensional densities describing the distribution of charge and magnetization in transverse space at fixed light-front time. We calculate the transverse densities of the spin-1/2 flavor-octet baryons at peripheral distances b = O(M_\pi^{-1}) using methods of relativistic chiral effective field theory (\chi EFT) and dispersion analysis. The densities are represented as dispersive integrals over the imaginary parts of the form factors in the timelike region (spectral functions). The isovector spectral functions on the two-pion cut t > 4 M_\pi^2 are calculated using relativistic \chi EFT including octet and decuplet baryons. The \chi EFT calculations are extended into the \rho meson mass region using an N/D method that incorporates the pion electromagnetic form factor data. The isoscalar spectral functions are modeled by vector meson poles. We compute the peripheral charge and magnetization densities in the octet baryon states, estimate the uncertainties, and determine the quark flavor decomposition. The approach can be extended to baryon form factors of other operators and the moments of generalized parton distributions., Comment: 23 pages, 12 figures, 3 tables. Typos corrected and discussion about the anomalous thresholds added. Matches the journal version

We stress, on theoretical and phenomenological grounds, the importance of the $\Delta(1232)$-resonance in a chiral effective field theory approach applied to the study of $\pi N$ scattering. We show how its inclusion as a dynamical degree of freedom allow us to obtain reliably valuable information from $\pi N$ scattering data., Comment: Contribution to NSTAR 2013, May 27-30, 2013, Peniscola (Spain); 4 pages

The pion-nucleon sigma term ($\sigma_{\pi N}$) is an observable of fundamental importance because embodies information about the internal scalar structure of the nucleon. Nowadays this quantity has triggered renewed interest because it is a key input for a reliable estimation of the dark matter-nucleon spin independent elastic scattering cross section. In this proceeding we present how this quantity can be reliably extracted by employing only experimental information with the use covariant baryon chiral perturbation theory. We also contrast our extraction with updated phenomenology related to $\sigma_{\pi N}$ and show how this phenomenology favours a relatively large value of $\sigma_{\pi N}$. Finally, we extract a value of $\sigma_{\pi N}=59(7)$ MeV from modern partial wave analyses data., Comment: PROCEEDINGS to Xth "Quark Confinement and the Hadron Spectrum"- 8 Pag,, 4 Tables, 2 Figures. TUM Campus Garching, Munich, Germany: October 8-12, 2012. Version 2: 2 references added

We present a novel analysis of the $\pi N$ scattering amplitude in covariant baryon chiral perturbation theory up to ${\cal O}(p^3)$ within the extended-on-mass-shell renormalization scheme and including the $\Delta(1232)$ explicitly in the $\delta$-counting. We take the hadronic phase shifts provided by partial wave analyses as basic experimental information to fix the low-energy constants. Subsequently, we study in detail the various observables and low-energy theorems related to the $\pi N$ scattering amplitude. In particular, we discuss the results and chiral expansion of the phase shifts, the threshold coefficients, the Goldberger-Treiman relation, the pion-nucleon sigma term and the extrapolation onto the subthreshold region. The chiral representation of the amplitude in the theory with the $\Delta$ presents a good convergence from very low energies in the subthreshold region up to energies well above threshold, leading also to a phenomenological description perfectly consistent with the one reported by the respective partial wave analyses and independent determinations. We conclude that a model-independent and systematic framework to analyze $\pi N$-scattering observables using directly experimental data shall be possible in covariant baryon chiral perturbation theory., Comment: 64 pages, 19 figures, 18 tables