Search

We present the Standard Model Effective Field Theories (SMEFT) from purely on-shell arguments. Starting from a few basic assumptions such as Poincar\'e invariance and locality, we classify all the renormalisable and non-renormalisable interactions at the lowest order in the couplings. From these building blocks, we review how locality and unitarity enforce Lie algebra structures to appear in the S-matrix elements together with relations among couplings (and hypercharges). Furthermore, we give a fully on-shell algorithm to compute any higher-point tree-level amplitude (or form factor) in generic EFTs, bypassing BCFW-like recursion relations which are known to be problematic when non-renormalisable interactions are involved. Finally, using known amplitudes techniques we compute the mixing matrix of SMEFT irrelevant interactions up to mass dimension 8, to linear order in the effective interactions., Comment: 39 + 14 pages; v3:matched published version, typos corrected

Topological phases in non-Hermitian systems have become fascinating subjects recently. In this paper, we attempt to classify topological phases in 1D interacting non-Hermitian systems. We begin with the non-Hermitian generalization of the Su-Schrieffer-Heeger (SSH) model and discuss its many-body topological Berry phase, which is well defined for all interacting quasi-Hermitian systems (non-Hermitian systems that have real energy spectrum). We then demonstrate that the classification of topological phases for quasi-Hermitian systems is exactly the same as their Hermitian counterparts. Finally, we construct the fixed point partition function for generic 1D interacting non-Hermitian local systems and find that the fixed point partition function still has a one-to-one correspondence to their Hermitian counterparts. Thus, we conclude that the classification of topological phases for generic 1D interacting non-Hermitian systems is still exactly the same as Hermitian systems., 15 pages, 5 figures

We revisit $$ T\overline{T} $$ T T ¯ deformations of d = 2 theories with fermions with a view toward the quantization. As a simple illustration, we compute the deformed Dirac bracket for a Majorana doublet and confirm the known eigenvalue flows perturbatively. We mostly consider those $$ T\overline{T} $$ T T ¯ theories that can be reconstructed from string-like theories upon integrating out the worldsheet metric. After a quick overview of how this works when we add NSR-like or GS-like fermions, we obtain a known non-supersymmetric $$ T\overline{T} $$ T T ¯ deformation of a $$ \mathcal{N} $$ N = (1, 1) theory from the latter, based on the Noether energy-momentum. This world- sheet reconstruction implies that the latter is actually a supersymmetric subsector of a d = 3 GS-like model, implying hidden supercharges, which we do construct explicitly. This brings us to ask about different $$ T\overline{T} $$ T T ¯ deformations, such as manifestly supersymmetric $$ T\overline{T} $$ T T ¯ and also more generally via the symmetric energy-momentum. We show that, for theories with fermions, such choices often lead us to doubling of degrees of freedom, with potential unitarity issues. We show that the extra sector develops a divergent gap in the “small deformation” limit and decouples in the infrared, although it remains uncertain in what sense these can be considered a deformation.

Applying quantum processors to model a high-dimensional function approximator is a typical method in quantum machine learning with potential advantage. It is conjectured that the unitarity of quantum circuits provides possible regularization to avoid overfitting. However, it is not clear how the regularization interplays with the expressibility under the limitation of current Noisy-Intermediate Scale Quantum devices. In this article, we perform simulations and theoretical analysis of the quantum circuit learning problem with hardware-efficient ansatz. Thorough numerical simulations show that the expressibility and generalization error scaling of the ansatz saturate when the circuit depth increases, implying the automatic regularization to avoid the overfitting issue in the quantum circuit learning scenario. This observation is supported by the theory on PAC learnability, which proves that VC dimension is upper bounded due to the locality and unitarity of the hardware-efficient ansatz. Our study provides supporting evidence for automatic regularization by unitarity to suppress overfitting and guidelines for possible performance improvement under hardware constraints.

We study the observability of new interactions which modify Higgs-pair production via vector-boson fusion processes at the LHC and at future proton-proton colliders. In an effective-Lagrangian approach, we explore in particular the effect of the operator $h^2 W_{\mu\nu}^a W^{a,\mu\nu}$, which describes the interaction of the Higgs boson with transverse vector-boson polarization modes. By tagging highly boosted Higgs bosons in the final state, we determine projected bounds for the coefficient of this operator at the LHC and at a future 27 TeV or 100 TeV collider. Taking into account unitarity constraints, we estimate the new-physics discovery potential of Higgs pair production in this channel., Comment: 27 pages, 11 figures, 14 tables, added references

We consider the theory of spinor fields written in polar form, that is the form in which the spinor components are given in terms of a module times a complex unitary phase respecting Lorentz covariance. In this formalism, spinors can be treated in their most general mathematical form, without the need to restrict them to plane waves. As a consequence, calculations of scattering amplitudes can be performed by employing the most general fermion propagator, and not only the free propagator usually employed in QFT. In this article, we use these quantities to perform calculations in two notable processes, the electron-positron and Compton scatterings. We show that although the methodology differs from the one used in QFT, the final results in the two examples turn out to give no correction as predicted by QFT., Comment: 7 pages

We propose a novel representation of differential scattering cross-sections that locally realises the direct cancellation of infrared singularities exhibited by its so-called real-emission and virtual degrees of freedom. We take advantage of the Loop-Tree Duality representation of each individual forward-scattering diagram and we prove that the ensuing expression is locally free of infrared divergences, applies at any perturbative order and for any process without initial-state collinear singularities. Divergences for loop momenta with large magnitudes are regulated using local ultraviolet counterterms that reproduce the usual Lagrangian renormalisation procedure of quantum field theories. Our representation is especially suited for a numerical implementation and we demonstrate its practical potential by computing fully numerically and without any IR counterterm the next-to-leading order accurate differential cross-section for the process e+e− → dd¯¯¯. We also show first results beyond next-to-leading order by computing interference terms part of the N4LO-accurate inclusive cross-section of a 1 → 2 + X scalar scattering process., Journal of High Energy Physics, 2021 (4), ISSN:1126-6708, ISSN:1029-8479

In this paper, we explore the open string amplitude's dual role as a space-time S-matrix and a 1D CFT correlation function. We pursue this correspondence in two directions. First, beginning with a general disk integrand dressed with a Koba-Nielsen factor, we demonstrate that exchange symmetry for the factorization residue of the amplitude forces the integrand to be expandable on SL(2,R) conformal blocks. Furthermore, positivity constraints associated with unitarity imply the SL(2,R) blocks must come in linear combinations for which the Virasoro block emerges at the "kink" in the space of solutions. In other words, Virasoro symmetry arises at the boundary of consistent factorization. Next, we consider the low energy EFT description, where unitarity manifests as the EFThedron in which the couplings must live. The existence of a worldsheet description implies, through the Koba-Nielsen factor, monodromy relations which impose algebraic identities amongst the EFT couplings. We demonstrate at finite derivative order that the intersection of the "monodromy plane" and the EFThedron carves out a tiny island for the couplings, which continues to shrink as the derivative order is increased. At the eighth derivative order, on a three-dimensional monodromy plane, the intersection fixes the width of this island to around 1.5$\%$ (of $\zeta(3)$) and 0.2$\%$ (of $\zeta(5)$) with respect to the super string answer. This leads us to conjecture that the four-point open superstring amplitude can be completely determined by the geometry of the intersection of the monodromy plane and the EFThedron., Comment: 13 figures

In a recent paper [1], three-particle interactions without invariance under Lorentz boosts were constrained by demanding that they yield tree-level four-particle scattering amplitudes with singularities as dictated by unitarity and locality. In this brief note, we show how to obtain an independent verification and consistency check of these boostless bootstrap results using BCFW momentum shifts. We point out that the constructibility criterion, related to the behaviour of the deformed amplitude at infinite BCFW parameter z, is not strictly necessary to obtain non-trivial constraints for the three-particle interactions., Comment: 5 pages + references Revised version with an additional assumption

We explore the entanglement evolution of boundary intervals in eternal Janus black holes that can be embedded consistently into string theory in the low-energy limit. By studying the geodesics we show that there is a transition in the entanglement characteristic around the Page time, which manifests the unitarity of the evolution. We reproduce and reinterpret these bulk results from two different lower-dimensional perspectives: first as an interface CFT in the usual AdS/CFT correspondence and second as an effective gravity theory in one lower dimension coupled to a radiation background. In the limit where the number of interface degrees of freedom becomes large, we obtain an effective theory on appropriate branes that replace the deep interior region in the bulk, coined the shadow region. In this effective theory, we also identify the island of the radiation entanglement wedge and verify the newly proposed quantum extremization method. Our model clarifies that double holography with gravity in two higher dimensions can be realized in a concrete and consistent way and that the occurrence of islands is natural in one higher dimension. Furthermore, our model reveals that there can be a transitional behavior of the Page curve before the Page time, which is related to the emergence of new matter degrees of freedom on the branes., 1+49 pages, 13 figures, v2: refs added, typos fixed, v3: version accepted to JHEP

We calculate the rates of radiative $\beta^- \to \alpha^- + \gamma$ decays for $(\alpha, \beta) = (e, \mu)$, $(e, \tau)$ and $(\mu, \tau)$ by taking the {\it unitary} gauge in the $(3+n)$ active-sterile neutrino mixing scheme, and make it clear that constraints on the unitarity of the $3\times 3$ Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix $U$ extracted from $\beta^- \to \alpha^- + \gamma$ decays in the {\it minimal unitarity violation} scheme differ from those obtained in the canonical seesaw mechanism with $n$ heavy Majorana neutrinos by a factor $5/3$. In such a natural seesaw case we show that the rates of $\beta^- \to \alpha^- + \gamma$ can be used to cleanly and strongly constrain the effective apex of a unitarity polygon, and compare its geometry with the geometry of its three sub-triangles formed by two vectors $U^{}_{\alpha i} U^*_{\beta i}$ and $U^{}_{\alpha j} U^*_{\beta j}$ (for $i \neq j$) in the complex plane. We find that the areas of such sub-triangles can be described in terms of the Jarlskog-like invariants of CP violation ${\cal J}^{ij}_{\alpha\beta}$, and their small differences signify slight unitarity violation of the PMNS matrix $U$., Comment: 26 pages, 5 figures, and the version accepted for publication in EPJC

In the Next-to-Minimal Supersymmetric Standard Model with the inverse seesaw mechanism to generate neutrino masses, the lightest sneutrino may act as a feasible dark matter candidate in vast parameter space. In this case, the smallness of the leptonic unitarity violation and the recent XENON-1T experiment can limit the dark matter physics. In particular, they set upper bounds of the neutrino Yukawa couplings $\lambda_\nu$ and $Y_\nu$. We study such effects by encoding the constraints in a likelihood function and carrying out elaborated scans over the parameter space of the theory with the Nested Sampling algorithm. We show that these constraints are complementary to each other in limiting the theory, and in some cases, they are very strict. We also study the impact of the future LZ experiment on the theory., Comment: The version to be published in JHEP

The "Cabibbo Angle Anomaly" (CAA) originates from the disagreement between the CKM elements $V_{ud}$ and $V_{us}$ extracted from superallowed beta and kaon decays, respectively, once compared via CKM unitarity. It points towards new physics with a significance of up to $4\,\sigma$, depending on the theoretical input used, and can be explained through modified $W$ couplings to leptons. In this context, vector-like leptons (VLLs) are prime candidates for a corresponding UV completion since they can affect $W\ell\nu$ couplings at tree-level, such that this modification can have the dominant phenomenological impact. In order to consistently asses the agreement with the data, a global fit is necessary which we perform for gauge-invariant dimension-6 operators and all patterns obtained for the six possible representations (under the SM gauge group) of VLLs. We find that even in the lepton flavour universal case, including the measurements of the CKM elements $V_{us}$ and $V_{ud}$ into the electroweak fit has a relevant impact, shifting the best fit point significantly. Concerning the VLLs we discuss the bounds from charged lepton flavour violating processes and observe that a single representation cannot describe experimental data significantly better than the SM hypothesis. However, allowing for several representations of VLLs at the same time, we find that the simple scenario in which $N$ couples to electrons via the Higgs and $\Sigma_1$ couples to muons not only explains the CAA but also improves the rest of the electroweak fit in such a way that its best fit point is preferred by more than $4\,\sigma$ with respect to the SM., Comment: Version accepted for publication in JHEP, 34 pages, 9 figures, 7 tables, typos corrected

It is almost universally believed that in quantum theory the two following statements hold: 1) all transformations are achieved by a unitary interaction followed by a von Neumann measurement; 2) all mixed states are marginals of pure entangled states. I name this doctrine the dogma of purification ontology. The source of the dogma is the original von Neumann axiomatisation of the theory, which largely relies on the Schroedinger equation as a postulate, which holds in a nonrelativistic context, and whose operator version holds only in free quantum field theory, but no longer in the interacting theory. In the present paper I prove that both ontologies of unitarity and state purity are unfalsifiable, even in principle, and therefore axiomatically spurious. I propose instead a minimal four-postulate axiomatisation: 1) associate a Hilbert space HA to each system A; 2) compose two systems by the tensor product rule HAB = HAxHB; 3) associate a transformation from system A to B to a quantum operation, i.e. to a completely positive trace-non-increasing map between the trace-class operators of A and B; 4) (Born rule) evaluate all joint probabilities through that of a special type of quantum operation: the state preparation. I then conclude that quantum paradoxes-such as the Schroedinger-cat's, and, most relevantly, the information paradox-are originated only by the dogma of purification ontology, and they are no longer paradoxes of the theory in the minimal formulation. For the same reason, most interpretations of the theory (e.g. many-world, relational, Darwinism, transactional, von Neumann-Wigner, time-symmetric, ...) interpret the same dogma, not the strict theory stripped of the spurious postulates., Comment: To be published on Foundations of Physics

An important task at future colliders is the measurement of the triple Higgs coupling. Depending on its size relative to the Standard Model (SM) value, certain collider options result in a higher experimental accuracy. Within the framework of Two Higgs Doublet Models (2HDM) types I and II we investigate the allowed ranges for all triple Higgs couplings involving at least one light, SM-like Higgs boson. We take into account theoretical constraints (unitarity, stability), experimental constraints from direct Higgs-boson searches, measurements of the SM-like Higgs-boson properties, flavor observables and electroweak precision data. We find that the SM-type triple Higgs coupling w.r.t. its SM value, λhhh/λSM, can range between ∼−0.5 and ∼1.5. Depending on which value is realized, the HL-LHC can compete with, or is clearly inferior to the ILC. We find the coupling λhhH between ∼−1.5 and ∼1.5. Triple Higgs couplings involving two heavy Higgs bosons, λhHH, λhAA and λhH+H− can reach values up to O(10), roughly independent of the 2HDM type. This can lead to potentially strongly enhanced production of two Higgs-bosons at the HL-LHC or high-energy e+e− colliders., The present work has received financial support from the ‘Spanish Agencia Estatal de Investigación” (AEI) and the EU “Fondo Europeo de Desarrollo Regional” (FEDER) through the project FPA2016-78022-P and from the grant IFT Centro de Excelencia Severo Ochoa SEV-2016-0597. The work of S.H. was also supported in part by the MEINCOP Spain under contract FPA2016-78022-P and in part by the “Spanish Red Consolider MultiDark” FPA2017-90566-REDC. This work has also received partial funding/support from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 674896. The work of F.A. was also supported by the Spanish Ministry of Science and Innovation via a FPU grant with code FPU18/06634., Funded by SCOAP3.

We argue that nonperturbative CFT correlation functions admit a Mellin amplitude representation. Perturbative Mellin representation readily follows. We discuss the main properties of nonperturbative CFT Mellin amplitudes: subtractions, analyticity, unitarity, Polyakov conditions and polynomial boundedness at infinity. Mellin amplitudes are particularly simple for large N CFTs and 2D rational CFTs. We discuss these examples to illustrate our general discussion. We consider subtracted dispersion relations for Mellin amplitudes and use them to derive bootstrap bounds on CFTs. We combine crossing, dispersion relations and Polyakov conditions to write down a set of extremal functionals that act on the OPE data. We check these functionals using the known 3d Ising model OPE data and other known bootstrap constraints. We then apply them to holographic theories., The erroneous claims regarding the consistency of certain AdS EFTs are corrected

We argue that resonances terminate, i.e. at certain mass/temperature they “melt”, converting into a kind of a quark-gluon soup. We predict a finite spectrum of glueball/oddball resonances lying on the pomeron/odderon trajectories. A simple model for Regge trajectories with threshold and asymptotic behaviour required by analyticity and unitarity is used.

Due to a recent more precise evaluation of $V_{ud}$ and $V_{us}$, the unitarity condition of the first row in the Cabibbo-Kobayashi-Maskawa (CKM) matrix: $|V_{ud}|^2 + |V_{us}|^2 + |V_{ub}|^2 = 0.99798 \pm 0.00038$ now stands at a deviation more than $4\sigma$ from unity. Furthermore, a mild excess in the overall Higgs signal strength appears at about $2\sigma$ above the standard model (SM) prediction, as well as the long-lasting discrepancy in the forward-backward asymmetry ${\cal A}_{\rm FB}^b$ in $Z\to b\bar b$ at LEP. Motivated from the above three anomalies we investigate an extension of the SM with vector-like quarks (VLQs) associated with the down-quark sector, with the goal of alleviating the tension among these datasets. We perform global fits of the model under the constraints coming from the unitarity condition of the first row of the CKM matrix, the $Z$-pole observables ${\cal A}_{\rm FB}^b$, $R_b$ and $\Gamma_{\rm had}$, Electro-Weak precision observables $\Delta S$ and $\Delta T$, $B$-meson observables $B_d^0$-$\overline{B}_d^0$ mixing, $B^+ \to \pi^+ \ell^+ \ell^-$ and $B^0 \to \mu^+ \mu^-$, and direct searches for VLQs at the Large Hadron Collider (LHC). Our results suggest that adding VLQs to the SM provides better agreement than the SM., Comment: 30 pages, 3 figures, version published in JHEP

We compute all master integrals for massless three-loop four-particle scattering amplitudes required for processes like di-jet or di-photon production at the LHC. We present our result in terms of a Laurent expansion of the integrals in the dimensional regulator up to 8$^{\text{th}}$ power, with coefficients expressed in terms of harmonic polylogarithms. As a basis of master integrals we choose integrals with integrands that only have logarithmic poles - called $d$log forms. This choice greatly facilitates the subsequent computation via the method of differential equations. We detail how this basis is obtained via an improved algorithm originally developed by one of the authors. We provide a public implementation of this algorithm. We explain how the algorithm is naturally applied in the context of unitarity. In addition, we classify our $d$log forms according to their soft and collinear properties., 5 figures, 533 integrals

We consider modifications of the Higgs potential due to new physics at high energy scales. These upset delicate cancellations predicted by the Standard Model for processes involving Higgs bosons and longitudinal gauge bosons, and lead to a breakdown of the theory at high energies. We focus on modifications of the Higgs trilinear coupling and use the violation of tree-level unitarity as an estimate of the scale where the theory breaks down. We obtain a completely model-independent bound of ~ 13 TeV for an order-1 modification of the trilinear. We argue that this bound can be saturated only in fine-tuned models, and the scale of new physics is likely to be much lower. The most stringent bounds are obtained from amplitudes involving multiparticle states that are not conventional scattering states. Our results show that a future determination of the Higgs cubic coupling can point to a well-defined scale of new physics that can be targeted and explored at future colliders., 28 pages, 3 figures, added discussion. Final published version in JHEP

We study a three Higgs doublet model where one doublet is inert and the other two doublets are active. Flavor changing neutral currents are avoided at tree-level by imposing a softly broken $Z'_2$ symmetry and we consider type I and type II Yukawa structures. The lightest inert scalar is a viable Dark Matter (DM) candidate. A numerical scan of the free parameters is performed taking into account theoretical constraints such as positivity of the scalar potential and unitarity of $2 \rightarrow 2$ scattering amplitudes. The model is further constrained by experimental results such as $B$ physics lower limits on charged Higgs masses, Electroweak Precision Observables, LEP II, LHC Higgs measurements, Planck measurement of the DM relic abundance and WIMP direct searches by the LUX and XENON1T experiments. The model predictions for mono-jet, mono Z and mono Higgs final states are studied and tested against current LHC data and we find the model to be allowed. We also discuss the effects of abandoning the "dark democracy" assumption common in studies of inert models. Projected sensitivities of direct detection experiments will leave only a tiny window in the DM mass versus coupling plane that is compliant with relic density bounds., Matches version to appear in JHEP. Significant modifications were made including a discussion of lifting the dark democracy assumption of the quartic couplings

We investigate Dirac fermion transport through opposite quantum Hall edge channels in armchair graphene nanoribbons where a magnetic quantum dot (MQD) is placed between the edges. The resulting conductance shows distinguished resonant features according to the angle Φ between the valley isospins at the opposite edges. Particularly, for Φ = 0, the conductance exhibits a behavior characteristic of dissipative resonances when the edge—dot distance is sufficiently small even though the unitarity of the whole system is conserved. As the edge—dot distance increases, a crossover behavior emerges between two distinct regimes: largely perturbed and unperturbed MQD. Resonant energy converges to a specific energy corresponding to the eigenenergy of the localized states in the unperturbed MQD. For sufficiently weak couplings, a fine splitting of the conductance resonances is observed, of which splitting energy is several μeV. The finding of these finely split localized states in the MQD allows us to better elucidate related electronic and transport properties in graphene.

We employ the curvature expansion of the quantum effective action for gravity-matter systems to construct graviton-mediated scattering amplitudes for non-minimally coupled scalar fields in a Minkowski background. By design, the formalism parameterises all quantum corrections to these processes and is manifestly gauge-invariant. The conditions resulting from UV-finiteness, unitarity, and causality are analysed in detail and it is shown by explicit construction that the quantum effective action provides sufficient room to meet these structural requirements without introducing non-localities or higher-spin degrees of freedom. Our framework provides a bottom-up approach to all quantum gravity programs seeking for the quantisation of gravity within the framework of quantum field theory. Its scope is illustrated by specific examples, including effective field theory, Stelle gravity, infinite derivative gravity, and Asymptotic Safety.

We revisit, advancing a useful approximation, a recently formulated QFT treatment that successfully overcomes any troubles with infinities for non-renormalizable QFTs [J. Phys. Comm. 2 115029 (2018)]. Such methodology was able to successfully deal, in non-relativistic fashion, with Newton’s gravitation potential [Annals of Physics 412, 168013 (2020)]. Our present approximation to the QFT method of [J. Phys. Comm. 2 115029 (2018)] is based on the Einstein’s Lagrangian (EG) elaborated by Gupta [1], save for a different constraint’s selection. This choice allows one to avoid the lack of unitarity for the S matrix that impaired the proceedings of Gupta and Feynman. Moreover, we are able to simplify the handling of such constraint by eliminating the need to involve ghosts for guarantying unitarity. Our approximation consists in setting the graviton field φ μν =γ μνφ , where γ μν is a constant tensor and φ a scalar (graviton) field. The ensuing approximate approach is non-renormalizable, an inconvenience that we are able to overcome in [J. Phys. Comm. 2 115029 (2018)]., Facultad de Ciencias Exactas

We apply on-shell methods to the bottom-up construction of electroweak amplitudes, allowing for both renormalizable and non-renormalizable interactions. We use the little-group covariant massive-spinor formalism, and flesh out some of its details along the way. Thanks to the compact form of the resulting amplitudes, many of their properties, and in particular the constraints of perturbative unitarity, are easily seen in this formalism. Our approach is purely bottom-up, assuming just the standard-model electroweak spectrum as well as the conservation of electric charge and fermion number. The most general massive three-point amplitudes consistent with these symmetries are derived and studied in detail, as the primary building blocks for the construction of scattering amplitudes. We employ a simple argument, based on tree-level unitarity of four-point amplitudes, to identify the three-point amplitudes that are non-renormalizable at tree level. This bottom-up analysis remarkably reproduces many low-energy relations implied by electroweak symmetry through the standard-model Higgs mechanism and beyond it. We then discuss four-point amplitudes. The gluing of three-point amplitudes into four-point amplitudes in the massive spinor helicity formalism is clarified. As an example, we work out the $\psi^c \psi Zh$ amplitude, including also the non-factorizable part. The latter is an all-order expression in the effective-field-theory expansion. Further constraints on the couplings are obtained by requiring perturbative unitarity. In the $\psi^c \psi Zh$ example, one for instance obtains the renormalizable-level relations between vector and fermion masses and gauge and Yukawa couplings. We supplement our bottom-up derivations with a matching of three- and four-point amplitude coefficients onto the standard-model effective field theory (SMEFT) in the broken electroweak phase., Comment: 55 pages, 2 figures, references added, journal version

We study the gravity-mediated scattering of scalar fields based on a parameterisation of the Lorentzian quantum effective action. We demonstrate that the interplay of infinite towers of spin zero and spin two poles at imaginary squared momentum leads to scattering amplitudes that are compatible with unitarity bounds, causal, and scale-free at trans-Planckian energy. Our construction avoids introducing non-localities or the massive higher-spin particles that are characteristic in string theory., v2: various small improvements/clarifications, version accepted for publication

We present a proof of perturbative unitarity for $\mathcal{N}=4$ SYM, following from the geometry of the amplituhedron. This proof is valid for amplitudes of arbitrary multiplicity $n$, loop order $L$ and MHV degree $k$., version accepted to JHEP

In this work we study the phenomenological constraints on the parameter space of scalars carrying colour quantum numbers. In particular we constrain the Manohar-Wise model based on the addition of a SU(2) doublet and SU(3) octet to the minimal Higgs model. The fits are performed using the open-source package HEPfit . We include both theoretical constraints, such as unitarity and perturbativity, and experimental constraints, like the ones coming from flavour and electroweak observables. For the first time we combine all these results and we are able to constrain the parameters of the potential, the Yukawa couplings and the masses of the scalars.

The authors acknowledge the financial support of the funding agencies: Agence Nationale de la Recherche (contract ANR-15-CE31-0020), Centre National de la Recherche Scientifique (CNRS), Commission Europeenne (FEDER fund and Marie Curie Program), Institut Universitaire de France (IUF), LabEx UnivEarthS (ANR-10-LABX-0023 and ANR-18-IDEX-0001), Paris Ile-de-France Region, France; Shota Rustaveli National Science Foundation of Georgia (SRNSFG, FR-18-1268), Georgia; Deutsche Forschungsgemeinschaft (DFG), Germany; The General Secretariat of Research and Technology (GSRT), Greece; Istituto Nazionale di Fisica Nucleare (INFN), Ministero dell'Universita e della Ricerca (MIUR), PRIN 2017 program (Grant NAT-NET 2017W4HA7S) Italy; Ministry of Higher Education Scientific Research and Professional Training, ICTP through Grant AF-13, Morocco; Nederlandse organisatie voor Wetenschappelijk Onderzoek (NWO), the Netherlands; The National Science Centre, Poland (2015/18/E/ST2/00758); National Authority for Scientific Research (ANCS), Romania; Ministerio de Ciencia, Innovacion, Investigacion y Universidades (MCIU): Programa Estatal de Generacion de Conocimiento (refs. PGC2018-096663-B-C41, -A-C42, -B-C43, -B-C44) (MCIU/FEDER), Severo Ochoa Centre of Excellence and MultiDark Consolider (MCIU), Junta de Andalucia (ref. SOMM17/6104/UGR), Generalitat Valenciana: Grisolia (ref. GRISOLIA/2018/119) and GenT (ref. CIDEGENT/2018/034 and CIDEGENT/2019/043) programs, La Caixa Foundation (ref. LCF/BQ/IN17/11620019), EU: MSC program (ref. 713673), Spain., The next generation of water Cherenkov neutrino telescopes in the Mediterranean Sea are under construction offshore France (KM3NeT/ORCA) and Sicily (KM3NeT/ARCA). The KM3NeT/ORCA detector features an energy detection threshold which allows to collect atmospheric neutrinos to study flavour oscillation. This paper reports the KM3NeT/ORCA sensitivity to this phenomenon. The event reconstruction, selection and classification are described. The sensitivity to determine the neutrino mass ordering was evaluated and found to be 4.4 sigma if the true ordering is normal and 2.3 sigma if inverted, after 3 years of data taking. The precision to measure Delta m(32)(2) and theta(23) were also estimated and found to be 85.10(-6) eV(2) and ((+1.9)(-3.1))degrees for normal neutrino mass ordering and, 75.10(-6) eV(2) and ((+2.0)(-7.0))degrees for inverted ordering. Finally, a unitarity test of the leptonic mixing matrix by measuring the rate of tau neutrinos is described. Three years of data taking were found to be sufficient to exclude (nu)over-left-right-arrow tau event rate variations larger than 20% at 3 sigma level., French National Research Agency (ANR) ANR-15-CE31-0020 Centre National de la Recherche Scientifique (CNRS) Commission Europeenne (FEDER fund), France Institut Universitaire de France (IUF), France LabEx UnivEarthS, France ANR-10-LABX-0023 ANR-18-IDEX-0001 Paris Ile-de-France Region, France, Shota Rustaveli National Science Foundation of Georgia (SRNSFG), Georgia FR-18-1268, German Research Foundation (DFG), The General Secretariat of Research and Technology (GSRT), Greece, Istituto Nazionale di Fisica Nucleare (INFN), Ministry of Education, Universities and Research (MIUR), PRIN 2017 program, Italy NAT-NET 2017W4HA7S, Ministry of Higher Education Scientific Research and Professional Training, ICTP, Morocco AF-13, Netherlands Organization for Scientific Research (NWO) Netherlands Government, The National Science Centre, Poland 2015/18/E/ST2/00758, National Authority for Scientific Research (ANCS), Romania, Ministerio de Ciencia, Innovacion, Investigacion y Universidades (MCIU): Programa Estatal de Generacion de Conocimiento, Spain PGC2018-096663-B-C41 PGC2018-096663-A-C42 PGC2018-096663-B-C43 PGC2018-096663-B-C44 Generalitat Valenciana: Grisolia program, Spain GRISOLIA/2018/119 La Caixa Foundation LCF/BQ/IN17/11620019, EU: MSC program, Spain 713673, Commission Europeenne (Marie Curie Program), France, Generalitat Valenciana: GenT programs, Spain CIDEGENT/2018/034 CIDEGENT/2019/043, Ministerio de Ciencia, Innovacion, Investigacion y Universidades (MCIU): Severo Ochoa Centre of Excellence, Ministerio de Ciencia, Innovacion, Investigacion y Universidades (MCIU): MultiDark Consolider (MCIU), Junta de Andalucia European Commission SOMM17/6104/UGR

We revisit the relation between the anomalies in four and six dimensions and the Chern-Simons couplings one dimension below. While the dimensional reduction of chiral theories is well-understood, the question which three and five-dimensional theories can come from a general circle reduction, and are hence liftable, is more subtle. We argue that existence of an anomaly cancellation mechanism is a necessary condition for liftability. In addition, the anomaly cancellation and the CS couplings in six and five dimensions respectively determine the central charges of string-like BPS objects that cannot be consistently decoupled from gravity, a.k.a. supergravity strings. Following the completeness conjecture and requiring that their worldsheet theory is unitary imposes bounds on the admissible theories. We argue that for the anomaly-free six-dimensional theories it is more advantageous to study the unitarity constraints obtained after reduction to five dimensions. In general these are slightly more stringent and can be cast in a more geometric form, highly reminiscent of the Kodaira positivity condition (KPC). Indeed, for the F-theoretic models which have an underlying Calabi-Yau threefold these can be directly compared. The unitarity constraints (UC) are in general weaker than KPC, and maybe useful in understanding the consistent models without F-theoretic realisation. We catalogue the cases when UC is more restrictive than KPC, hinting at more refined hidden structure in elliptic Calabi-Yau threefolds with certain singularity structure., 47 pages

We compute the semi-classical potential arising from a generic theory of cubic gravity, a higher derivative theory of spin-2 particles, in the framework of modern amplitude techniques. We show that there are several interesting aspects of the potential, including some non-dispersive terms that lead to black hole solutions (include quantum corrections) that agree with those derived in Einsteinian cubic gravity (ECG). We show that these non-dispersive terms could be obtained from theories that include the Gauss-Bonnet cubic invariant $G_3$. In addition, we derive the one-loop scattering amplitudes using both unitarity cuts and via the leading singularity, showing that the classical effects of higher derivative gravity can be easily obtained directly from the leading singularity with far less computational cost., Updated to reflect published version

Journal of high energy physics 2019(12), 26 (1-57) (2019). doi:10.1007/JHEP12(2019)026, Among the unitarity cuts of 4-loop massless propagators two kinds are currently fully known: the 2-particle cuts with 3 loops corresponding to form-factors, and the 5-particle phase-space integrals. In this paper we calculate master integrals for the remaining ones: 3-particle cuts with 2 loops, and 4-particle cuts with 1 loop. The 4-particle cuts are calculated by solving dimensional recurrence relations. The 3-particle cuts are integrated directly using 1→3 amplitudes with 2 loops, which we also re-derive here up to transcendentality weight 7. The results are verified both numerically, and by showing consistency with previously known integrals using Cutkosky rules. We provide the analytic results in the space-time dimension 4 − 2ε as series in ε with coefficients being multiple zeta values up to weight 12. In the supplementary material we also provide dimensional recurrence matrices and SummerTime files suitable for numerical evaluation of the series in arbitrary dimensions with any precision., Published by SISSA, [Trieste]

We compute the four-momentum radiated during the scattering of two spinless bodies, at leading order in the Newton's contant $G$ and at all orders in the velocities, using the Effective Field Theory worldline approach. Following \cite{Mougiakakos:2021ckm}, we derive the conserved stress-energy tensor linearly coupled to gravity generated by localized sources, at leading and next-to-leading order in $G$, and from that the classical probability amplitude of graviton emission. The total emitted momentum is obtained by phase-space integration of the graviton momentum weighted by the modulo squared of the radiation amplitude. We recast this as a two-loop integral that we solve using techniques borrowed from particle physics, such as reverse unitarity, reduction to master integrals by integration-by-parts identities and canonical differential equations. The emitted momentum agrees with recent results obtained by other methods. Our approach provides an alternative way of directly computing radiated observables in the post-Minkowskian expansion without going through the classical limit of scattering amplitudes., Comment: 41 pages, corrected typos

Low-energy effective field theories containing a light scalar field are used extensively in cosmology, but often there is a tension between embedding such theories in a healthy UV completion and achieving a phenomenologically viable screening mechanism in the IR. Here, we identify the range of interaction couplings which allow for a smooth resummation of classical non-linearities (necessary for kinetic/Vainshtein-type screening), and compare this with the range allowed by unitarity, causality and locality in the underlying UV theory. The latter region is identified using positivity bounds on the $2\to2$ scattering amplitude, and in particular by considering scattering about a non-trivial background for the scalar we are able to place constraints on interactions at all orders in the field (beyond quartic order). We identify two classes of theories can both exhibit screening and satisfy existing positivity bounds, namely scalar-tensor theories of $P(X)$ or quartic Horndeski type in which the leading interaction contains an odd power of $X$. Finally, for the quartic DBI Galileon (equivalent to a disformally coupled scalar in the Einstein frame), the analogous resummation can be performed near two-body systems and imposing positivity constraints introduces a non-perturbative ambiguity in the screened scalar profile. These results will guide future searches for UV complete models which exhibit screening of fifth forces in the IR., 34+12 pages, 6 figures

We present a determination of the ratio of kaon and pion leptonic decay constants in isosymmetric QCD (ISOQCD), ${f}_{K}/{f}_{\ensuremath{\pi}}$, making use of the gauge ensembles produced by the Extended Twisted Mass Collaboration with ${N}_{f}=2+1+1$ flavors of Wilson-clover twisted-mass quarks, including configurations close to the physical point for all dynamical flavors. The simulations are carried out at three values of the lattice spacing ranging from $\ensuremath{\sim}0.068$ to $\ensuremath{\sim}0.092\text{ }\text{ }\mathrm{fm}$ with linear lattice size up to $L\ensuremath{\sim}5.5\text{ }\text{ }\mathrm{fm}$. The scale is set by the particle data group (PDG) value of the pion decay constant, ${f}_{\ensuremath{\pi}}^{\text{ISO}\mathrm{QCD}}=130.4(2)\text{ }\text{ }\mathrm{MeV}$, at the ISOQCD pion point, ${M}_{\ensuremath{\pi}}^{\text{ISO}\mathrm{QCD}}=135.0(2)\text{ }\text{ }\mathrm{MeV}$, obtaining for the gradient-flow scales the values ${w}_{0}=0.17383(63)\text{ }\text{ }\mathrm{fm}$, $\sqrt{{t}_{0}}=0.14436(61)\text{ }\text{ }\mathrm{fm}$ and ${t}_{0}/{w}_{0}=\phantom{\rule{0ex}{0ex}}0.11969(62)\text{ }\text{ }\mathrm{fm}$. The data are analyzed within the framework of SU(2) chiral perturbation theory without resorting to the use of renormalized quark masses. At the ISOQCD kaon point ${M}_{K}^{\text{ISO}\mathrm{QCD}}=494.2(4)\text{ }\text{ }\mathrm{MeV}$ we get $({f}_{K}/{f}_{\ensuremath{\pi}}{)}^{\text{ISO}\mathrm{QCD}}=1.1995(44)$, where the error includes both statistical and systematic uncertainties. Implications for the Cabibbo-Kobayashi-Maskawa matrix element $|{V}_{us}|$ and for the first-row Cabibbo-Kobayashi-Maskawa unitarity are discussed.

It was recently found that, when linearised in the absence of matter, 58 cases of the general gravitational theory with quadratic curvature and torsion are (i) free from ghosts and tachyons and (ii) power-counting renormalisable. We inspect the nonlinear Hamiltonian structure of the eight cases whose primary constraints do not depend on the curvature tensor. We confirm the particle spectra and unitarity of all these theories in the linear regime. We uncover qualitative dynamical changes in the nonlinear regimes of all eight cases, suggesting at least a broken gauge symmetry, and possibly the activation of negative kinetic energy spin-parity sectors and acausal behaviour. Two of the cases propagate a pair of massless modes at the linear level, and were interesting as candidate theories of gravity. However, we identify these modes with vector excitations, rather than the tensor polarisations of the graviton. Moreover, we show that these theories do not support a viable cosmological background., Comment: 20 pages, 0 figures

We prove spectral optical identities in quantum field theories of physical particles (defined by the Feynman $i\epsilon $ prescription) and purely virtual particles (defined by the fakeon prescription). The identities are derived by means of purely algebraic operations and hold for every (multi)threshold separately and for arbitrary frequencies. Their major significance is that they offer a deeper understanding on the problem of unitarity in quantum field theory. In particular, they apply to "skeleton" diagrams, before integrating on the space components of the loop momenta and the phase spaces. In turn, the skeleton diagrams obey a spectral optical theorem, which gives the usual optical theorem for amplitudes, once the integrals on the space components of the loop momenta and the phase spaces are restored. The fakeon prescription/projection is implemented by dropping the thresholds that involve fakeon frequencies. We give examples at one loop (bubble, triangle, box, pentagon and hexagon), two loops (triangle with "diagonal", box with diagonal) and arbitrarily many loops. We also derive formulas for the loop integrals with fakeons and relate them to the known formulas for the loop integrals with physical particles., Comment: 49 pages, 6 figures; v2: JHEP

We examine an intriguing possibility that a single field is responsible for both inflation and dark matter, focussing on the minimal set-up where inflation is driven by a scalar coupling to curvature. We study in detail the reheating process in this framework, which amounts mainly to particle production in a quartic potential, and distinguish thermal and non-thermal dark matter options. In the non-thermal case, the reheating is impeded by backreaction and rescattering, making this possibility unrealistic. On the other hand, thermalized dark matter is viable, yet the unitarity bound forces the inflaton mass into a narrow window close to half the Higgs mass., Comment: 16 pages, 4 figures

The canonical type-I seesaw model with three heavy Majorana neutrinos is one of the most natural extensions of the standard model (SM) to accommodate tiny Majorana masses of three ordinary neutrinos. At low-energy scales, Majorana neutrino masses and unitarity violation of lepton flavor mixing have been extensively discussed in the literature, which are respectively generated by the unique dimension-five Weinberg operator and one dimension-six operator in the seesaw effective field theory (SEFT) with the tree-level matching. In this work, we clarify that a self-consistent calculation of radiative decays of charged leptons $\beta^- \to \alpha^- + \gamma$ requires the SEFT with one-loop matching, where new six-dimensional operators emerge and make important contributions. For the first time, the Wilson coefficients of all the relevant six-dimensional operators are computed by carrying out the one-loop matching between the effective theory and full seesaw model, and applied to calculate the total rates of radiative decays of charged leptons., Comment: 20 pages, 3 figures, matches the version published in PLB

Made available in DSpace on 2022-04-29T08:32:27Z (GMT). No. of bitstreams: 0 Previous issue date: 2021-08-20 We use the S-matrix bootstrap to carve out the space of unitary, crossing symmetric and supersymmetric graviton scattering amplitudes in ten dimensions. We focus on the leading Wilson coefficient α controlling the leading correction to maximal supergravity. The negative region α

We present a comprehensive analysis of the $\ensuremath{\gamma}W$ interference radiative correction to the neutron $\ensuremath{\beta}$-decay matrix element. Within a dispersion relations approach, we compute the axial-vector part of the $\ensuremath{\gamma}W$ box amplitude ${\ensuremath{\square}}_{A}^{\ensuremath{\gamma}W}$ in terms of the isoscalar part of the ${F}_{3}^{\ensuremath{\gamma}W}$ interference structure function. Using the latest available phenomenology for ${F}_{3}^{\ensuremath{\gamma}W}$ from the nucleon elastic, resonance, deep-inelastic, and Regge regions, we find the real part of the box correction to be ${\ensuremath{\square}}_{A}^{\ensuremath{\gamma}W}=3.90(9)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$. This improved correction gives a theoretical estimate of the CKM matrix element $|{V}_{ud}{|}^{2}=0.94805(26)$, which represents a $4\ensuremath{\sigma}$ violation of unitarity.

The Fermi constant GF is extremely well measured through the muon lifetime, defining one of the key fundamental parameters in the standard model (SM). Therefore, to search for physics beyond the SM (BSM) via GF, the constraining power is determined by the precision of the second-best independent determination of GF. The best alternative extractions of GF proceed either via the global electroweak (EW) fit or from superallowed β decays in combination with the Cabibbo angle measured in kaon, τ, or D decays. Both variants display some tension with GF from muon decay, albeit in opposite directions, reflecting the known tensions within the EW fit and hints for the apparent violation of Cabibbo-Kobayashi-Maskawa unitarity, respectively. We investigate how BSM physics could bring the three determinations of GF into agreement using SM effective field theory and comment on future perspectives.

We present a Monte Carlo approach to soft-gluon resummation at subleading color which can be used to improve existing parton shower algorithms. At the single-emission level, soft-collinear enhancements of the splitting functions are explicitly linked to quadratic Casimir operators, while wide angle single-soft enhancements are connected to nontrivial color correlators. We focus on a numerically stable implementation of color matrix element corrections to all orders and approximate the virtual corrections by requiring unitarity at the single-emission level. We provide a proof-of-concept implementation to compute nonglobal event shapes at lepton colliders., Comment: 11 pages, 3 figures, 1 table, revised claimed accuracy in response to arXiv:2003.06399, version accepted for publication in Phys. Rev. D

We study the AdS/BCFT duality between two-dimensional conformal field theories with two boundaries and three-dimensional anti-de Sitter space with two Karch-Randall branes. We compute the entanglement entropy of a bipartition of the BCFT, on both the gravity side and the field theory side. At finite temperature this entanglement entropy characterizes the communication between two braneworld black holes, coupled to each other through a common bath. We find a Page curve consistent with unitarity. The gravitational result, computed using double-holographically realized quantum extremal surfaces, matches the conformal field theory calculation. At zero temperature, we obtain an interesting extension of the AdS$_3$/BCFT$_2$ correspondence. For a central charge $c$, we find a gap $(\frac{c}{16},\frac{c}{12})$ in the spectrum of the scaling dimension $\Delta_{\text{bcc}}$ of the boundary condition changing operator (which interpolates mismatched boundary conditions on the two boundaries of the BCFT). Depending on the value of $\Delta_{\text{bcc}}$, the gravitational dual is either a defect global AdS$_3$ geometry or a single sided black hole, and in both cases there are two Karch-Randall branes., Comment: 43 pages, 9 figures, published version in JHEP

We study conformal twist field four-point functions on a $\mathbb Z_N$ orbifold. We examine in detail the case $N=3$ and analyze theories obtained by replicated $N$-times a minimal model with central charge $c, 39 pages, 5 figures, 2 tables. Typos corrected. Final version published in JHEP

Unitarity cut method has been proved to be very useful in the computation of one-loop integrals. In this paper, we generalize the method to the situation where the powers of propagators in the denominator are larger than one in general. We show how to use the trick of differentiation over masses to translate the problem to the integrals where all powers are just one. Then by using the unitarity cut method, we can find the wanted reduction coefficients of all basis except the tadpole. Using this method, we calculate the reduction of scalar bubble, scalar triangle, scalar box and scalar pentagon with general power of propagators., 31 pages

In this work we explicitly show that the perturbative unitarity of analytic infinite derivative (AID) scalar field theories can be achieved using a modified prescription for computing scattering amplitudes. The crux of the new prescription is the analytic continuation of a result obtained in the Euclidean signature to the Minkowski external momenta. We intensively elaborate an example of a non-local $\phi^4$ model for various infinite derivative operators. General UV properties of amplitudes in non-local theories are discussed., Comment: 16 pages, 7 figures; revision matching the published version

The pre-asymptotic analysis of the multichannel scattering problem for particles with an arbitrary spin and short-range interactions has been presented. The complete operator-valued dependence of the scattered differential flux on the distance to the target exactly consistent with the unitarity condition has been obtained., 8 pages

Sum rules in effective field theories, predicated upon causality, place restrictions on scattering amplitudes mediated by effective contact interactions. Through unitarity of the $S$-matrix, these imply that the size of higher dimensional corrections to transition amplitudes between different states is bounded by the strength of their contributions to elastic forward scattering processes. This places fundamental limits on the extent to which hypothetical symmetries can be broken by effective interactions. All analysis is for dimension $8$ operators in the forward limit. Included is a thorough derivation of all positivity bounds for a chiral fermion in $SU(2)$ and $SU(3)$ global symmetry representations resembling those of the Standard Model, general bounds on flavour violation, new bounds for interactions between particles of different spin, inclusion of loops of dimension $6$ operators and illustration of the resulting strengthening of positivity bounds over tree-level expectations, a catalogue of supersymmetric effective interactions up to mass dimension $8$ and $4$ legs and the demonstration that supersymmetry unifies the positivity theorems as well as the new bounds., ~50 pages v2: Improved discussion and use of discrete symmetries, some corrections and clarifications, some other minor improvements. v3: Corrected sign error in isospin projectors and resulting bounds (no qualitative changes to the extent investigated), minor improvements in exposition and typing errors corrected

We analyze the validity of BCFW recursion relations for currents of n - 2 gluons and two massive quarks, where one of the quarks is off shell and the remaining particles are on shell. These currents are gauge-dependent and can be used as ingredients in the unitarity-based approach to computing one-loop amplitudes. The validity of BCFW recursion relations is well known to depend on the so-called boundary behavior of the currents as the momentum shift parameter goes to infinity. With off-shell currents, a new potential problem arises, namely unphysical poles that depend on the choice of gauge. We identify conditions under which boundary terms are absent and unphysical poles are avoided, so that there is a natural recursion relation. In particular, we are able to choose a gauge in which we construct a valid shift for currents with at least n - 3 gluons of the same helicity. We derive an analytic formula in the case where all gluons have the same helicity. As by-products, we prove the vanishing boundary behavior of general off-shell objects in Feynman gauge, and we find a compact generalization of Berends-Giele gluon currents with a generic reference spinor., 30 pages, 8 figures; v2 minor corrections, journal version