347 research outputs found
The renormalized Hamiltonian truncation method in the large expansion
Hamiltonian Truncation Methods are a useful numerical tool to study strongly
coupled QFTs. In this work we present a new method to compute the exact
corrections, at any order, in the Hamiltonian Truncation approach presented by
Rychkov et al. in Refs. [1-3]. The method is general but as an example we
calculate the exact and some of the contributions for the
theory in two dimensions. The coefficients of the local expansion calculated in
Ref. [1] are shown to be given by phase space integrals. In addition we find
new approximations to speed up the numerical calculations and implement them to
compute the lowest energy levels at strong coupling. A simple diagrammatic
representation of the corrections and various tests are also introduced.Comment: JHEP version, typos fixed in Appendix and eq. (23
High-Precision Calculations in Strongly Coupled Quantum Field Theory with Next-to-Leading-Order Renormalized Hamiltonian Truncation
Hamiltonian Truncation (a.k.a. Truncated Spectrum Approach) is an efficient
numerical technique to solve strongly coupled QFTs in d=2 spacetime dimensions.
Further theoretical developments are needed to increase its accuracy and the
range of applicability. With this goal in mind, here we present a new variant
of Hamiltonian Truncation which exhibits smaller dependence on the UV cutoff
than other existing implementations, and yields more accurate spectra. The key
idea for achieving this consists in integrating out exactly a certain class of
high energy states, which corresponds to performing renormalization at the
cubic order in the interaction strength. We test the new method on the strongly
coupled two-dimensional quartic scalar theory. Our work will also be useful for
the future goal of extending Hamiltonian Truncation to higher dimensions d >=
3.Comment: 8 pages, 4 figures; v2: published versio
NLO Renormalization in the Hamiltonian Truncation
Hamiltonian Truncation (a.k.a. Truncated Spectrum Approach) is a numerical
technique for solving strongly coupled QFTs, in which the full Hilbert space is
truncated to a finite-dimensional low-energy subspace. The accuracy of the
method is limited only by the available computational resources. The
renormalization program improves the accuracy by carefully integrating out the
high-energy states, instead of truncating them away. In this paper we develop
the most accurate ever variant of Hamiltonian Truncation, which implements
renormalization at the cubic order in the interaction strength. The novel idea
is to interpret the renormalization procedure as a result of integrating out
exactly a certain class of high-energy "tail states". We demonstrate the power
of the method with high-accuracy computations in the strongly coupled
two-dimensional quartic scalar theory, and benchmark it against other existing
approaches. Our work will also be useful for the future goal of extending
Hamiltonian Truncation to higher spacetime dimensions.Comment: 28pp + appendices, detailed version of arXiv:1706.0612
One-loop non-renormalization results in EFTs
In Effective Field Theories (EFTs) with higher-dimensional operators many
anomalous dimensions vanish at the one-loop level for no apparent reason. With
the use of supersymmetry, and a classification of the operators according to
their embedding in super-operators, we are able to show why many of these
anomalous dimensions are zero. The key observation is that one-loop
contributions from superpartners trivially vanish in many cases under
consideration, making supersymmetry a powerful tool even for non-supersymmetric
models. We show this in detail in a simple U(1) model with a scalar and
fermions, and explain how to extend this to SM EFTs and the QCD Chiral
Langrangian. This provides an understanding of why most "current-current"
operators do not renormalize "loop" operators at the one-loop level, and allows
to find the few exceptions to this ubiquitous rule.Comment: Corrections made in Sec. 3.2 and Fig.
Scaling and tuning of EW and Higgs observables
We study deformations of the SM via higher dimensional operators. In
particular, we explicitly calculate the one-loop anomalous dimension matrix for
13 bosonic dimension-6 operators relevant for electroweak and Higgs physics.
These scaling equations allow us to derive RG-induced bounds, stronger than the
direct constraints, on a universal shift of the Higgs couplings and some
anomalous triple gauge couplings by assuming no tuning at the scale of new
physics, i.e. by requiring that their individual contributions to the running
of other severely constrained observables, like the electroweak oblique
parameters or , do not exceed their
experimental direct bounds. We also study operators involving the Higgs and
gluon fields.Comment: v2: 41 pages, 12 tables, 4 figures. Plots of the RG-induced bounds
from S and T added, presentation of our approach in sections 2 and 4
improved, a few typos fixed, references added, conclusions and analysis
unchanged. Version to appear in JHE
Renormalization of dimension-six operators relevant for the Higgs decays
The discovery of the Higgs boson has opened a new window to test the SM
through the measurements of its couplings. Of particular interest is the
measured Higgs coupling to photons which arises in the SM at the one-loop
level, and can then be significantly affected by new physics. We calculate the
one-loop renormalization of the dimension-six operators relevant for
, which can be potentially important since
it could, in principle, give log-enhanced contributions from operator mixing.
We find however that there is no mixing from any current-current operator that
could lead to this log-enhanced effect. We show how the right choice of
operator basis can make this calculation simple. We then conclude that
can only be affected by RG mixing from
operators whose Wilson coefficients are expected to be of one-loop size, among
them fermion dipole-moment operators which we have also included.Comment: 21 pages. Improved version with h -> gamma Z results added and
structure of anomalous-dimension matrix determined further. Conclusions
unchange
Higgs Inflation as a Mirage
We discuss a simple unitarization of Higgs inflation that is genuinely weakly
coupled up to Planckian energies. A large non-minimal coupling between the
Higgs and the Ricci curvature is induced dynamically at intermediate energies,
as a simple ratio of mass scales. Despite not being dominated by the Higgs
field, inflationary dynamics simulates the `Higgs inflation' one would get by
blind extrapolation of the low-energy effective Lagrangian, at least
qualitatively. Hence, Higgs inflation arises as an approximate `mirage' picture
of the true dynamics. We further speculate on the generality of this phenomenon
and show that, if Higgs-inflation arises as an effective description, the
details of the UV completion are necessary to extract robust quantitative
predictions.Comment: 21 pages, 2 figure
Bridging Positivity and S-matrix Bootstrap Bounds
The main objective of this work is to isolate Effective Field Theory
scattering amplitudes in the space of non-perturbative two-to-two amplitudes,
using the S-matrix Bootstrap. We do so by introducing the notion of Effective
Field Theory cutoff in the S-matrix Bootstrap approach. We introduce a number
of novel numerical techniques and improvements both for the primal and the
linearized dual approach. We perform a detailed comparison of the full
unitarity bounds with those obtained using positivity and linearized unitarity.
In most cases, the S-matrix Bootstrap bounds are stronger. Moreover, we discuss
the notion of Spin Zero and UV dominance along the boundary of the allowed
amplitude space by introducing suitable observables. Finally, we show that this
construction also leads to novel bounds on operators of dimension less or equal
than six.Comment: 40 pages + appendice
Higgs mass in Noncommutative Geometry
In the noncommutative geometry approach to the standard model, an extra
scalar field - initially suggested by particle physicist to stabilize the
electroweak vacuum - makes the computation of the Higgs mass compatible with
the 126 GeV experimental value. We give a brief account on how to generate this
field from the Majorana mass of the neutrino, following the principles of
noncommutative geometry.Comment: Proceedings of the Corfou Workshop on noncommutative field theory and
gravity, september 201
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