scholarly journals Loops and trees in generic EFTs

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Nathaniel Craig ◽  
Minyuan Jiang ◽  
Ying-Ying Li ◽  
Dave Sutherland
Keyword(s):  
Standard Model ◽  
High Energy ◽  
Tree Level ◽  
Energy Limit ◽  
High Energy Limit ◽  
Functional Methods ◽  
Weakly Coupled ◽  
The Standard Model ◽  
Helicity Amplitudes ◽  
The Impact

Abstract We consider aspects of tree and one-loop behavior in a generic 4d EFT of massless scalars, fermions, and vectors, with a particular eye to the high-energy limit of the Standard Model EFT at operator dimensions 6 and 8. First, we classify the possible Lorentz structures of operators and the subset of these that can arise at tree-level in a weakly coupled UV completion, extending the tree/loop classification through dimension 8 using functional methods. Second, we investigate how operators contribute to tree and one-loop helicity amplitudes, exploring the impact of non-renormalization theorems through dimension 8. We further observe that many dimension 6 contributions to helicity amplitudes, including rational parts, vanish exactly at one-loop level. This suggests the impact of helicity selection rules extends beyond one loop in non-supersymmetric EFTs.

scholarly journals Sum rules in the standard model effective field theory from helicity amplitudes

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Jiayin Gu ◽  
Lian-Tao Wang
Keyword(s):  
Field Theory ◽  
Standard Model ◽  
Effective Field Theory ◽  
Sum Rules ◽  
High Energy ◽  
Effective Field ◽  
Low Energy ◽  
Tree Level ◽  
The Standard Model ◽  
Helicity Amplitudes

Abstract The dispersion relation of an elastic 4-point amplitude in the forward direction leads to a sum rule that connects the low energy amplitude to the high energy observables. We perform a classification of these sum rules based on massless helicity amplitudes. With this classification, we are able to systematically write down the sum rules for the dimension-6 operators of the Standard Model Effective Field Theory (SMEFT), some of which are absent in previous literatures. These sum rules offer distinct insights on the relations between the operator coefficients in the EFT and the properties of the full theory that generates them. Their applicability goes beyond tree level, and in some cases can be used as a practical method of computing the one loop contributions to low energy observables. They also provide an interesting perspective for understanding the custodial symmetries of the SM Higgs and fermion sectors.

scholarly journals High Energy Rho Meson Leptoproduction §

2014 ◽  
Vol 1 (1) ◽  
pp. 33-35
Author(s):  
Adrien Besse ◽  
Lech Szymanowski ◽  
Samuel Wallon
Keyword(s):  
Cross Sections ◽  
Scattering Amplitude ◽  
Good Description ◽  
High Energy ◽  
Energy Limit ◽  
Rho Meson ◽  
Forward Limit ◽  
Helicity Amplitudes ◽  
Impact Parameter Space ◽  
The Impact

We investigate the longitudinal and transverse polarized cross-sections of the leptoproduction of the ρ meson in the high energy limit. Our model is based on the computation of the impact factor γ*(λγ)→ ρ (λρ) using the twist expansion in the forward limit which is expressed in the impact parameter space. This treatment involves in the final stage the twist 2 and twist 3 distribution amplitudes (DAs) of the ρ meson and the dipole scattering amplitude. Taking models that exist for the DAs and for the dipole cross-section. We get a phenomenological model for the helicity amplitudes. We compare our predictions with HERA data and get a fairly good description for large enough virtualities of the photon. PACS number(s): 13.60.Le, 12.39.St, 12.38.Bx.

scholarly journals Virtual next-to-leading corrections to the impact factors in the high-energy limit

1998 ◽  
Vol 57 (7) ◽  
pp. 4069-4079 ◽  
Author(s):  
Vittorio Del Duca ◽  
Carl R. Schmidt
Keyword(s):  
High Energy ◽  
Impact Factors ◽  
Energy Limit ◽  
High Energy Limit ◽  
The Impact

scholarly journals High Energy Scattering of Non-Critical Strings

1997 ◽  
Vol 12 (06) ◽  
pp. 1253-1263 ◽  
Author(s):  
Kenichiro Aoki ◽  
Eric D'Hoker
Keyword(s):  
Central Charge ◽  
String Tension ◽  
High Energy ◽  
Tree Level ◽  
Energy Limit ◽  
Electrostatic Problem ◽  
High Energy Limit ◽  
On Line ◽  
High Energy Scattering ◽  
Branch Cuts

We summarize recent work, in which we consider scattering amplitudes of non-critical strings in the limit where the energy of all external states is large compared to the string tension. We show that the high energy limit is dominated by a saddle point that can be mapped onto an electrostatic equilibrium configuration of an assembly of charges associated with the external states, together with a density of charges arising from the Liouville field. The Liouville charges accumulate on line segments, which produce quadratic branch cuts on the worldsheet. The electrostatic problem is solved for string tree level in terms of hyperelliptic integrals and is given explicitly for the 3- and 4-point functions. For generic values of the central charge, the high energy limit behaves in a string-like fashion, with exponential energy dependence.

scholarly journals Beyond the standard Higgs after the 125 GeV Higgs discovery

2015 ◽  
Vol 373 (2032) ◽  
pp. 20140042 ◽  
Author(s):  
C. Grojean
Keyword(s):  
Standard Model ◽  
Degrees Of Freedom ◽  
Planck Scale ◽  
High Energy ◽  
Weakly Coupled ◽  
The Standard Model ◽  
Very High Energy ◽  
The Universe ◽  
Large Quantum ◽  
Organizing Principles

An elementary, weakly coupled and solitary Higgs boson allows one to extend the validity of the Standard Model up to very high energy, maybe as high as the Planck scale. Nonetheless, this scenario fails to fill the universe with dark matter and does not explain the matter–antimatter asymmetry. However, amending the Standard Model tends to destabilize the weak scale by large quantum corrections to the Higgs potential. New degrees of freedom, new forces, new organizing principles are required to provide a consistent and natural description of physics beyond the standard Higgs.

scholarly journals Unitarity violation and the geometry of Higgs EFTs

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Timothy Cohen ◽  
Nathaniel Craig ◽  
Xiaochuan Lu ◽  
Dave Sutherland
Keyword(s):  
Standard Model ◽  
Higgs Field ◽  
Higgs Sector ◽  
High Energy ◽  
Effective Field ◽  
Energy Limit ◽  
Geometric Invariants ◽  
Energy Behavior ◽  
The Standard Model ◽  
Derivatives Of

Abstract We derive the scale of unitarity violation from the geometry of Effective Field Theory (EFT) extensions of the Standard Model Higgs sector. The high-energy behavior of amplitudes with more than four scalar legs depends on derivatives of geometric invariants with respect to the physical Higgs field h, such that higher-point amplitudes begin to reconstruct the scalar manifold away from our vacuum. In theories whose low-energy limit can be described by the Higgs EFT (HEFT) but not the Standard Model EFT (SMEFT), non-analyticities in the vicinity of our vacuum limit the radius of convergence of geometric invariants, leading to unitarity violation at energies below 4πv. Our results unify approaches to the HEFT/SMEFT dichotomy based on unitarity, analyticity, and geometry, and more broadly illustrate the sense in which observables probe the geometry of an EFT. Along the way, we provide novel basis-independent results for Goldstone/Higgs boson scattering amplitudes expressed in terms of geometric covariant quantities.

scholarly journals Towards the renormalisation of the Standard Model effective field theory to dimension eight: Bosonic interactions I

2021 ◽  
Vol 11 (3) ◽  
Author(s):  
Mikael Chala ◽  
Guilherme Guedes ◽  
Maria Ramos ◽  
Jose Santiago
Keyword(s):  
Standard Model ◽  
Effective Field Theory ◽  
New Physics ◽  
Effective Field ◽  
Tree Level ◽  
Electroweak Phase Transition ◽  
Anomalous Dimensions ◽  
Weakly Coupled ◽  
The Standard Model ◽  
The One

We compute the one-loop renormalisation group running of the bosonic Standard Model effective operators to order v^4/\Lambda^4v4/Λ4, with v\sim 246v∼246 GeV being the electroweak scale and \LambdaΛ the unknown new physics threshold. We concentrate on the effects triggered by pairs of the leading dimension-six interactions, namely those that can arise at tree level in weakly-coupled ultraviolet completions of the Standard Model. We highlight some interesting consequences, including the interplay between positivity bounds and the form of the anomalous dimensions; the non-renormalisation of the SS and UU parameters; or the importance of radiative corrections to the Higgs potential for the electroweak phase transition. As a byproduct of this work, we provide a complete Green basis of operators involving only the Higgs and derivatives at dimension-eight, comprising 13 redundant interactions.

scholarly journals Planck Neutrinos as Ultra High Energy Cosmic Rays

2020 ◽  
Vol 29 (1) ◽  
pp. 40-46
Author(s):  
Dmitri L. Khokhlov
Keyword(s):  
Black Holes ◽  
Cosmic Rays ◽  
Standard Model ◽  
Active Galactic Nuclei ◽  
Planck Scale ◽  
Galactic Nuclei ◽  
High Energy ◽  
Ultra High Energy ◽  
High Energy Cosmic Rays ◽  
The Standard Model

AbstractThe studied conjecture is that ultra high energy cosmic rays (UHECRs) are hypothetical Planck neutrinos arising in the decay of the protons falling onto the gravastar. The proton is assumed to decay at the Planck scale into positron and four Planck neutrinos. The supermassive black holes inside active galactic nuclei, while interpreted as gravastars, are considered as UHECR sources. The scattering of the Planck neutrinos by the proton at the Planck scale is considered. The Planck neutrinos contribution to the CR events may explain the CR spectrum from 5 × 1018 eV to 1020 eV. The muon number in the Planck neutrinos-initiated shower is estimated to be larger by a factor of 3/2 in comparison with the standard model that is consistent with the observational data.

scholarly journals Effective operator bases for beyond Standard Model scenarios: an EFT compendium for discoveries

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Upalaparna Banerjee ◽  
Joydeep Chakrabortty ◽  
Suraj Prakash ◽  
Shakeel Ur Rahaman ◽  
Michael Spannowsky
Keyword(s):  
Standard Model ◽  
High Energy ◽  
Beyond The Standard Model ◽  
Minimal Extension ◽  
Effective Operator ◽  
Abelian Gauge ◽  
Gauge Symmetries ◽  
Higher Dimensional ◽  
The Standard Model ◽  
Mass Dimension

Abstract It is not only conceivable but likely that the spectrum of physics beyond the Standard Model (SM) is non-degenerate. The lightest non-SM particle may reside close enough to the electroweak scale that it can be kinematically probed at high-energy experiments and on account of this, it must be included as an infrared (IR) degree of freedom (DOF) along with the SM ones. The rest of the non-SM particles are heavy enough to be directly experimentally inaccessible and can be integrated out. Now, to capture the effects of the complete theory, one must take into account the higher dimensional operators constituted of the SM DOFs and the minimal extension. This construction, BSMEFT, is in the same spirit as SMEFT but now with extra IR DOFs. Constructing a BSMEFT is in general the first step after establishing experimental evidence for a new particle. We have investigated three different scenarios where the SM is extended by additional (i) uncolored, (ii) colored particles, and (iii) abelian gauge symmetries. For each such scenario, we have included the most-anticipated and phenomenologically motivated models to demonstrate the concept of BSMEFT. In this paper, we have provided the full EFT Lagrangian for each such model up to mass dimension 6. We have also identified the CP, baryon (B), and lepton (L) number violating effective operators.

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