Fri·Oct 2, 2020Friday·October 2, 2020

1. 01*

   Effective Field Theory for jet substructure in heavy ion collisions

   Varun Vaidya🇺🇸

   I develop an Effective Field Theory (EFT) framework to compute jet substructure observables for heavy ion collision experiments. As an illustration, I consider dijet events that accompany the formation of a weakly coupled Quark Gluon Plasma(QGP) medium in a heavy ion collision and look at an observable insensitive to jet selection bias: the simultaneous measurement of jet mass along with the transverse momentum imbalance between the jets that are groomed to remove soft radiation. Treating the jet as an open quantum system, I write down a factorization formula within the SCET(Soft Collinear Effective Theory) framework in the forward scattering regime. The physics of the medium is encoded in a universal soft field correlator while the jet-medium interaction is captured by a medium induced jet function. The factorization formula leads to a Lindblad type equation for the evolution of the reduced density matrix of the jet in the Markovian approximation. The solution for this equation allows a resummation of large logarithms that arise due to the final state measurements imposed while simultaneously summing over multiple incoherent interactions of the jet with the medium.

   hep-phhep-thnucl-thJHEP(2021)·34 citations
2. 02*

   Towards a Quantum Computing Algorithm for Helicity Amplitudes and Parton Showers

   Khadeejah Bepari🇬🇧 · Sarah Malik🇬🇧 · Michael Spannowsky🇬🇧 · Simon Williams🇬🇧

   The interpretation of measurements of high-energy particle collisions relies heavily on the performance of full event generators. By far the largest amount of time to predict the kinematics of multi-particle final states is dedicated to the calculation of the hard process and the subsequent parton shower step. With the continuous improvement of quantum devices, dedicated algorithms are needed to exploit the potential quantum computers can provide. We propose general and extendable algorithms for quantum gate computers to facilitate calculations of helicity amplitudes and the parton shower process. The helicity amplitude calculation exploits the equivalence between spinors and qubits and the unique features of a quantum computer to compute the helicities of each particle involved simultaneously, thus fully utilising the quantum nature of the computation. This advantage over classical computers is further exploited by the simultaneous computation of s and t-channel amplitudes for a 2$\to$2 process. The parton shower algorithm simulates collinear emission for a two-step, discrete parton shower. In contrast to classical implementations, the quantum algorithm constructs a wavefunction with a superposition of all shower histories for the whole parton shower process, thus removing the need to explicitly keep track of individual shower histories. Both algorithms utilise the quantum computer's ability to remain in a quantum state throughout the computation and represent a first step towards a quantum computing algorithm to describe the full collision event at the LHC.

   hep-phhep-exquant-phPRD(2021)·54 citations
3. 03*

   Next-to-soft corrections for Drell-Yan and Higgs boson rapidity distributions beyond N${}^3$LO

   A.H. Ajjath · Pooja Mukherjee🇮🇳 · V. Ravindran🇮🇳 · Aparna Sankar🇮🇳 · Surabhi Tiwari🇮🇳

   We present a formalism that sums up both soft-virtual (SV) and next to SV (NSV) contributions to all orders in perturbative QCD for the rapidity distribution of any colorless particle produced in hadron colliders. We have exploited the factorization properties and the renormalisation group (RG) invariance of the differential cross-section to achieve this. Using the state-of-the-art multiloop and multileg results, we determine the complete NSV contributions to third order in strong coupling constant for the rapidity distributions for a pair of leptons in Drell-Yan and also for Higgs boson in gluon fusion as well as bottom quark annihilation. Using the integral representation of our all order $z$ space result, we show how the NSV contributions can be resummed in two-dimensional Mellin space.

   hep-phPRD(2021)·36 citations
4. 04*

   Quark and Lepton Mass and Mixing with non-universal $Z^{\prime }$ from a 5d Standard Model with gauged $SO(3)$

   Francisco J. de Anda🇲🇽 · Stephen F. King🇬🇧

   We propose a theory of quark and lepton mass and mixing with non-universal $Z^{\prime }$ couplings based on a 5d Standard Model with quarks and leptons transforming as triplets under a new gauged $SO(3)$ isospin. In the 4d effective theory, the $SO(3)$ isospin is broken to $U(1{)}^{\prime }$, through a $S^1/({\mathbb{Z}}_2\times {\mathbb{Z}}_2^{\prime })$ orbifold, then subsequently dynamically broken, resulting in a massive $Z^{\prime }$. Quarks and leptons in the 5d bulk appear as massless modes, with zero Yukawa couplings to the Higgs on the brane, and zero couplings to $Z^{\prime }$, at leading order, due to the $U(1{)}^{\prime }$ symmetry. However, after the $U(1{)}^{\prime }$ breaking, both Yukawa couplings and non-universal $Z^{\prime }$ couplings are generated by heavy Kaluza-Klein exchanges. Hierarchical quark and lepton masses result from a hierarchy of 5d Dirac fermion masses. Neutrino mass and mixing arises from a novel type Ib seesaw mechanism, mediated by Kaluza-Klein Dirac neutrinos. The non-universal $Z^{\prime }$ couplings may contribute to semi-leptonic $B$ decay ratios which violate $\mu -e$ universality. In this model such couplings are related to the corresponding quark and lepton effective Yukawa couplings.

   hep-phJHEP(2021)·3 citations
5. 05*

   Reading the Lattice QCD Form Factors of the ${\Lambda }_b\to {\Lambda }_c$ Transition Using a C-Code

   Bradley Smith🇺🇸 · Ahmed Rashed🇺🇸

   The ${\Lambda }_b\to {\Lambda }_c{\ell }^{-}{\bar{\nu }}_{\ell }$ process has been discussed in the literatures as a probe for new physics. This process receives contributions in new physics models from scalar, vector, and tensor hadronic currents. The form factors of these currents can be obtained from the quark model or the lattice QCD. In this work, we present a c-code to read the scalar, vector, and tensor lattice QCD form factors. A Mathematica code was used in Ref. \cite{Datta:2017aue} to read the form factors. Our c-code is much faster than the Mathematica code where the ratio of the wall clock time for the c-code compared to the Mathematica code is 1:64.2 per data point.

   hep-phhep-lat0 citations
6. 06*

   Performance studies of Time-of-Flight detectors at LHC

   Karel Černý🇨🇿 · Marek Taševský🇨🇿 · Tomáš Sýkora🇨🇿 · Radek Žlebčík🇨🇿

   We present results of a toy model study of performance of the Time-of-Flight detectors integrated into forward proton detectors. The goal of the ToF device is to suppress effects of additional soft processes (so called pile-up) accompanying the hard-scale central diffractive event, characterized by two tagged leading protons, one on each side from the interaction point. The method of mitigation of the pile-up effects exemplified in this study is based on measuring a difference between arrival times of these leading protons at the forward proton detectors and hence estimate the z-coordinate of the production vertex. We evaluate effects of the the pile-up background by studying in detail its components, and estimate the performance of the ToF method as a function of the time and spatial resolution of the ToF device and of the number of pile-up interactions per bunch crossing. We also propose a new observable with a potential to efficiently separate central diffractive signal from the harsh pile-up environment.

   hep-phhep-exJINST(2021)·21 citations
7. 07*

   Completeness and Complementarity for $\mu \to e\gamma$, $\mu \to 3e$ and $\mu \to e$ conversion

   Sacha Davidson🇫🇷

   Lepton Flavour Violation(LFV) is New Physics that must occur, but is stringently constrained by experiments searching for mu to e flavour change, such as $\mu \to e\gamma$, $\mu \to 3e$ and $\mu \to e$ conversion. However, in an Effective Field Theory(EFT) parametrisation, there are many more $\mu \leftrightarrow e$ operators than restrictive constraints, so determining operator coefficients from data is a remote dream. It is nonetheless interesting to learn about New Physics from data, so this manuscript introduces "observable-vectors" in the space of operator coefficients, which identify at any scale the combination of coefficients probed by the observable. These vectors have at least partpermil overlap with most of the coefficients, and are used to study whether $\mu \to e\gamma$, $\mu \to 3e$ and $\mu \to e$ conversion give complementary information about New Physics. The appendix gives updated sensitivities of these processes, (and a subset of LFV tau decays), to operator coefficients at the weak scale in the SMEFT and in the EFT below mW.

   hep-phJHEP(2021)·49 citations
8. 08*

   Leptonic CP Violation and its Origin

   Ivan Esteban🇪🇸

   This PhD thesis deals with the current experimental hint for large CP violation in the leptonic sector. We first quantify its global statistical significance, by combining the results from relevant neutrino oscillation experiments. As the hint is indirect, other new physics apart from three massive neutrinos could be present, masking the results as direct leptonic CP violation has not yet been conclusively observed. Thus, we move on to checking the robustness of the hint against the framework in which the experimental data is interpreted; in other words, its physical origin. To that purpose, we confront with data the scenario that is less bounded by other experiments: neutral current Non-Standard Interactions (NSI) among neutrinos and matter. In the end, CP violation induced by neutrino masses and leptonic mixing is found to be quite robust, due to the large amount of neutrino flavour transition data collected along three decades. Nevertheless, the next generation LBL accelerator experiments are aimed at precision measurements that could be more severely affected. Luckily, in the last years the COHERENT experiment has provided independent constraints on NSI. In the final chapter of the thesis, the data from the COHERENT experiment is analysed and integrated into the global analyses from previous chapters. These first results could be greatly improved by increasing the statistics of the signal and/or by performing measurements with different nuclei sensitive to different NSI models. For that, the European Spallation Source is an ideal future facility, whose prospects for bounding NSI are also explored. In summary, this thesis takes a global approach to rigorously assess whether cutting-edge leptonic flavour measurements are pointing towards a new strong violation of a symmetry of Nature.

   hep-ph6 citations
9. 09*

   Prompt photon production in proton collisions as a probe of parton scattering in high energy limit

   Krzysztof Golec-Biernat🇵🇱 · Leszek Motyka🇵🇱 · Tomasz Stebel🇵🇱

   We study the prompt photon hadroproduction at the LHC with the $k_T$-factorization approach and the $q{g}^{\ast }\to q\gamma$ and $g^{\ast }{g}^{\ast }\to q\bar{q}\gamma$ partonic channels, using three unintegrated gluon distributions which depend on gluon transverse momentum. They represent three different theoretical schemes which are usually considered in the $k_T$-factorization approach, known under the acronyms: KMR, CCFM and GBW gluon distributions. We find sensitivity of the calculated prompt photon transverse momentum distribution to the gluon transverse momentum distribution. The predictions obtained with the three approaches are compared to data, that allows to differentiate between them. We also discuss the significance of the two partonic channels, confronted with the expectations which are based on the applicability of the $k_T$-factorization scheme in the high energy approximation.

   hep-phPRD(2021)·18 citations
10. 10*

    Confronting lattice parton distributions with global QCD analysis

    J. Bringewatt🇺🇸 · N. Sato🇺🇸 · W. Melnitchouk🇺🇸 · Jian-Wei Qiu🇺🇸 · F. Steffens🇩🇪 · M. Constantinou🇺🇸

    We present the first Monte Carlo based global QCD analysis of spin-averaged and spin-dependent parton distribution functions (PDFs) that includes nucleon isovector matrix elements in coordinate space from lattice QCD. We investigate the degree of universality of the extracted PDFs when the lattice and experimental data are treated under the same conditions within the Bayesian likelihood analysis. For the unpolarized sector, we find rather weak constraints from the current lattice data on the phenomenological PDFs, and difficulties in describing the lattice matrix elements at large spatial distances. In contrast, for the polarized PDFs we find good agreement between experiment and lattice data, with the latter providing significant constraints on the spin-dependent isovector quark and antiquark distributions.

    hep-phhep-latnucl-thPRD(2021)·69 citations
11. 11*

    Phenomenology of ${\tau }^{-}\to {\pi }^{-}{\nu }_{\tau }\gamma$ using LCSR

    Anshika Bansal🇮🇳 · Namit Mahajan🇮🇳

    We present the study of radiative tau decay (${\tau }^{-}\to {\pi }^{-}{\nu }_{\tau }\gamma$), computing the structure dependent contribution using Light Cone Sum Rules. This decay includes the same form factors as the radiative pion decay with the crucial difference that the momentum transfer squared, $t$, between the pion-photon system is positive, which makes these form factors timelike and also as $t$ can now take values upto $m_{\tau }^2$ , it can produce real hadronic resonances. The analytical form for these form factors has been calculated using light cone sum rules method and the invariant mass-spectrum in the $\pi -\gamma$ system and the decay width are presented. The structure dependent parameter, $\gamma$, the ratio of the axial to vector form factor is found to be in good agreement with the experimental determination.

    hep-phhep-exPRD(2021)·2 citations
12. 12*

    Nuclear parton distribution functions with uncertainties in a general mass variable flavor number scheme

    Hamzeh Khanpour🇮🇷 · Maryam Soleymaninia🇮🇷 · S. Atashbar Tehrani🇮🇷 · Hubert Spiesberger🇩🇪 · Vadim Guzey🇷🇺

    In this article we obtain a new set of nuclear parton distribution functions (nuclear PDFs) at next-to-leading order and next-to-next-to-leading order accuracy in perturbative QCD. The common nuclear deep-inelastic scattering (DIS) data analyzed in our study are complemented by the available charged-current neutrino DIS data with nuclear targets and data from Drell-Yan cross-section measurements for several nuclear targets. In addition, the most recent DIS data from the Jefferson Lab CLAS and Hall C experiments are also added to our data sample. For these specific datasets, we consider the impact of target mass corrections and higher twist effects which are expected to be important in the region of large $x$ and intermediate-to-low $Q^2$. Our analysis is based on a publicly available open-source tool {\tt APFEL}, which has been modified to be applicable for our analysis of nuclear PDFs. Heavy quark contributions to nuclear DIS are considered within the framework of the {\tt FONLL} general-mass variable-flavor-number scheme. The most recent {\tt CT18} PDFs are used as baseline proton PDFs. The uncertainties of nuclear PDFs are determined using the standard Hessian approach. The results of our global QCD analysis are compared with existing nuclear PDF sets and with the fitted cross-sections, for which our set of nuclear PDFs provides a very good description.

    hep-phhep-exnucl-thPRD(2021)·50 citations
13. 13*

    The Electro-Weak Phase Transition at Colliders: Confronting Theoretical Uncertainties and Complementary Channels

    Andreas Papaefstathiou🇺🇸 · Graham White🇯🇵

    We explore and contrast the capabilities of future colliders to probe the nature of the electro-weak phase transition. We focus on the real singlet scalar field extension of the Standard Model, representing the most minimal, yet most elusive, framework that can enable a strong first-order electro-weak phase transition. By taking into account the theoretical uncertainties and employing the powerful complementarity between gauge and Higgs boson pair channels in the searches for new scalar particles, we find that a 100 TeV proton collider has the potential to confirm or falsify a strong first-order transition. Our results hint towards this occurring relatively early in its lifetime. Furthermore, by extrapolating down to 27 TeV, we find that a lower-energy collider may also probe a large fraction of the parameter space, if not all. Such early discoveries would allow for precise measurements of the new phenomena to be obtained at future colliders and would pave the way to definitively verify whether this is indeed the physical remnant of a scalar field that catalyses a strong first-order transition.

    hep-phhep-exJHEP(2021)·48 citations
14. 14*

    Direct Detection of Atomic Dark Matter in White Dwarfs

    David Curtin🇨🇦 · Jack Setford🇨🇦

    Dark matter could have a dissipative asymmetric subcomponent in the form of atomic dark matter (aDM). This arises in many scenarios of dark complexity, and is a prediction of neutral naturalness, such as the Mirror Twin Higgs model. We show for the first time how White Dwarf cooling provides strong bounds on aDM. In the presence of a small kinetic mixing between the dark and SM photon, stars are expected to accumulate atomic dark matter in their cores, which then radiates away energy in the form of dark photons. In the case of white dwarfs, this energy loss can have a detectable impact on their cooling rate. We use measurements of the white dwarf luminosity function to tightly constrain the kinetic mixing parameter between the dark and visible photons, across many orders of magnitude in DM mass, down to values of $ϵ\sim 10^{-12}$. Using this method we can constrain scenarios in which aDM constitutes fractions as small as $10^{-3}$ of the total dark matter density. Our methods are highly complementary to other methods of probing aDM, especially in scenarios where the aDM is arranged in a dark disk, which can make direct detection extremely difficult but actually slightly enhances our cooling constraints.

    hep-phastro-ph.SRJHEP(2021)·34 citations
15. 15*

    Displaced Vertex signatures of a pseudo-Goldstone sterile neutrino

    Stéphane Lavignac🇫🇷 · Anibal D. Medina🇦🇷

    Low-scale models of neutrino mass generation often feature sterile neutrinos with masses in the GeV-TeV range, which can be produced at colliders through their mixing with the Standard Model neutrinos. We consider an alternative scenario in which the sterile neutrino is produced in the decay of a heavier particle, such that its production cross section does not depend on the active-sterile neutrino mixing angles. The mixing angles can be accessed through the decays of the sterile neutrino, provided that they lead to observable displaced vertices. We present an explicit realization of this scenario in which the sterile neutrino is the supersymmetric partner of a pseudo-Nambu-Goldstone boson, and is produced in the decays of higgsino-like neutralinos and charginos. The model predicts the active-sterile neutrino mixing angles in terms of a small number of parameters. We show that a sterile neutrino with a mass between a few 10 GeV and 200 GeV can lead to observable displaced vertices at the LHC, and outline a strategy for reconstructing experimentally its mixing angles.

    hep-phhep-exJHEP(2021)·5 citations
16. 16*

    Light tetraquark states with the exotic quantum number $J^{PC}=3^{-+}$

    Niu Su🇨🇳 · Rui-Rui Dong🇨🇳 · Hua-Xing Chen🇨🇳 · Wei Chen🇨🇳 · Er-Liang Cui🇨🇳

    We apply the method of QCD sum rules to study the $sq\bar{s}\bar{q}$ tetraquark states with the exotic quantum number $J^{PC}=3^{-+}$, and extract mass of the lowest-lying state to be $2.33_{-0.16}^{+0.19}$ GeV. To construct the relevant tetraquark currents we need to explicitly add the covariant derivative operator. Our systematical analysis on their relevant interpolating currents indicates that: a) this state well decays into the $P$-wave $\rho \varphi /\omega \varphi$ channel but not into the $\rho f_2(1525)/\omega f_2(1525)/\varphi f_2(1270)$ channels, and b) it well decays into the $K^{\ast }(892){\bar{K}}_2^{\ast }(1430)$ channel but not into the $P$-wave $K^{\ast }(892){\bar{K}}^{\ast }(892)$ channel.

    hep-phhep-exPRD(2021)·4 citations
17. 17*

    Bridging the gap: spectral distortions meet gravitational waves

    Thomas Kite🇬🇧 · Andrea Ravenni🇬🇧 · Subodh P. Patil🇳🇱 · Jens Chluba🇬🇧

    Gravitational waves (GWs) have the potential to probe the entirety of cosmological history due to their nearly perfect decoupling from the thermal bath and any intervening matter after emission. In recent years, GW cosmology has evolved from merely being an exciting prospect to an actively pursued avenue for discovery, and the early results are very promising. As we highlight in this paper, spectral distortions (SDs) of the cosmic microwave background (CMB) uniquely probe GWs over six decades in frequency, bridging the gap between astrophysical high- and cosmological low-frequency measurements. This means SDs will not only complement other GW observations, but will be the sole probe of physical processes at certain scales. To illustrate this point, we explore the constraining power of various proposed SD missions on a number of phenomenological scenarios: early-universe phase transitions (PTs), GW production via the dynamics of SU(2) and ultra-light U(1) axions, and cosmic string (CS) network collapse. We highlight how some regions of parameter space were already excluded with data from COBE/FIRAS, taken over two decades ago. To facilitate the implementation of SD constraints in arbitrary models we provide GW2SD. This tool calculates the window function, which easily maps a GW spectrum to a SD amplitude, thus opening another portal for GW cosmology with SDs, with wide reaching implications for particle physics phenomenology.

    ↳ astro-ph.COgr-qchep-phhep-thMNRAS(2021)·63 citations
18. 18*

    Review of the $\mathbf{\Lambda }$(1405): A curious case of a strange-ness resonance

    Maxim Mai🇺🇸

    During its long-lasting history, the $\Lambda (1405)$ has become a benchmark for our understanding of the $\mathrm{SU}(3)$ hadron dynamics. Starting with its theoretical prediction and later experimental verification, until the most recent debates on the existence of the second broad pole, it emerged as a fruitful research area sparking many theoretical and experimental developments. This review intends to provide the reader with the current status of research on the $\Lambda (1405)$-resonance, reflecting on historical, experimental and theoretical developments. A common database for experimental results and a comparison of most recent theoretical approaches will be provided in the last two parts of this manuscript.

    ↳ nucl-thhep-lathep-phnucl-exEur.Phys.J.ST(2021)·107 citations
19. 19*

    A new branch of inflationary speed limits

    Dayshon Mathis🇺🇸 · Alexandros Mousatov🇺🇸 · George Panagopoulos🇺🇸 · Eva Silverstein🇺🇸

    We present a new mechanism for inflation which exhibits a speed limit on scalar motion, generating accelerated expansion even on a steep potential. This arises from explicitly integrating out the short modes of additional fields coupled to the inflaton $\varphi$ via a dimension six operator, yielding an expression for the effective action which includes a nontrivial (logarithmic) function of $(\partial \varphi {)}^2$. The speed limit appears at the branch cut of this logarithm arising in a large flavor expansion, similarly to the square root branch cut in DBI inflation arising in a large color expansion. Finally, we describe observational constraints on the parameters of this model.

    ↳ hep-thastro-ph.COhep-phJHEP(2021)·4 citations
20. 20*

    Apparent convergence of Padé approximants for the crossover line in finite density QCD

    Attila Pásztor🇭🇺 · Zsolt Szép🇭🇺 · Gergely Markó🇩🇪

    We propose a novel Bayesian method to analytically continue observables to real baryochemical potential ${\mu }_B$ in finite density QCD. Taylor coefficients at ${\mu }_B=0$ and data at imaginary chemical potential ${\mu }_B^I$ are treated on equal footing. We consider two different constructions for the Padé approximants, the classical multipoint Padé approximation and a mixed approximation that is a slight generalization of a recent idea in Padé approximation theory. Approximants with spurious poles are excluded from the analysis. As an application, we perform a joint analysis of the available continuum extrapolated lattice data for both pseudocritical temperature $T_c$ at ${\mu }_B^I$ from the Wuppertal-Budapest Collaboration and Taylor coefficients ${\kappa }_2$ and ${\kappa }_4$ from the HotQCD Collaboration. An apparent convergence of $[p/p]$ and $[p/p+1]$ sequences of rational functions is observed with increasing $p.$ We present our extrapolation up to ${\mu }_B\approx 600$ MeV.

    ↳ hep-lathep-phnucl-thPRD(2021)·25 citations
21. 21*

    ET sensitivity to the anisotropic Stochastic Gravitational Wave Background

    Giorgio Mentasti🇮🇹 · Marco Peloso🇮🇹

    We study the sensitivity of a pair of Einstein Telescopes (ET) (hypothetically located at the two sites currently under consideration for ET) to the anisotropies of the Stochastic Gravitational Wave Background (SGWB). We focus on the $\ell =0,2,4$ multipoles of an expansion of the SGWB in spherical harmonics, since the sensitivity to other multipoles is suppressed due to the fact that this pair of detector operates in a regime for which the product between the observed frequency and the distance between the two sites is much smaller than one. In this regime, the interferometer overlap functions for the anisotropic signal acquire very simple analytic expressions. These expressions can also be applied to any other pairs of interferometers (each one of arbitrary opening angle between its two arms) operating in this regime. Once the measurements at the vertices of the two sites are optimally combined, the sensitivity to the multipoles of the SGWB depends only on the latitude of the two sites, on the difference of their longitude, but not on the orientation of their arms.

    ↳ astro-ph.COgr-qchep-phhep-thJCAP(2021)·51 citations
22. 22*

    Light charged fermions in quantum gravity

    Gustavo P. de Brito🇩🇰 · Astrid Eichhorn🇩🇰 · Marc Schiffer🇩🇪

    We study the impact of quantum gravity on a system of chiral fermions that are charged under an Abelian gauge group. Under the impact of quantum gravity, a finite value of the gauge coupling could be generated and in turn drive four-fermion interactions to criticality. We find indications that the gravity-gauge-fermion interplay protects the lightness of fermions for a large enough number of fermions. On the other hand, for a smaller number of fermions, chiral symmetry may be broken, which would be in tension with the observation of light fermions.

    ↳ hep-thgr-qchep-phPLB(2021)·49 citations

* Reconstructed cohort: no mailing for this day survives in the archive. Papers are grouped by their submission times and arXiv's announcement cut-off, assuming announcement without delay; positions follow identifier order. Validated at ~91% exact-day agreement against the archived era.