scholarly journals Analytic continuation of the harmonic sums for the 3-loop anomalous dimensions

2005 ◽  
Vol 614 (1-2) ◽  
pp. 53-61 ◽  
Author(s):  
Johannes Blümlein ◽  
Sven-Olaf Moch
Keyword(s):  
Analytic Continuation ◽  
Anomalous Dimensions

scholarly journals Renormalization Group evolution from on-shell SMEFT

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Minyuan Jiang ◽  
Teng Ma ◽  
Jing Shu
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Standard Model ◽  
Effective Field Theory ◽  
Effective Field ◽  
High Dimensional ◽  
Anomalous Dimensions ◽  
The Standard Model ◽  
Group Evolution

Abstract We describe the on-shell method to derive the Renormalization Group (RG) evolution of Wilson coefficients of high dimensional operators at one loop, which is a necessary part in the on-shell construction of the Standard Model Effective Field Theory (SMEFT), and exceptionally efficient based on the amplitude basis in hand. The UV divergence is obtained by firstly calculating the coefficients of scalar bubble integrals by unitary cuts, then subtracting the IR divergence in the massless bubbles, which can be easily read from the collinear factors we obtained for the Standard Model fields. Examples of deriving the anomalous dimensions at dimension six are presented in a pedagogical manner. We also give the results of contributions from the dimension-8 H4D4 operators to the running of V+V−H2 operators, as well as the running of B+B−H2D2n from H4D2n+4 for general n.

scholarly journals The low-energy effective theory of axions and ALPs

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Martin Bauer ◽  
Matthias Neubert ◽  
Sophie Renner ◽  
Marvin Schnubel ◽  
Andrea Thamm
Keyword(s):  
High Energy ◽  
New Physics ◽  
Mass Scale ◽  
Low Energy ◽  
Effective Theory ◽  
Loop Order ◽  
Flavor Changing ◽  
Effective Lagrangian ◽  
Anomalous Dimensions ◽  
Pseudoscalar Mesons

Abstract Axions and axion-like particles (ALPs) are well-motivated low-energy relics of high-energy extensions of the Standard Model, which interact with the known particles through higher-dimensional operators suppressed by the mass scale Λ of the new-physics sector. Starting from the most general dimension-5 interactions, we discuss in detail the evolution of the ALP couplings from the new-physics scale to energies at and below the scale of electroweak symmetry breaking. We derive the relevant anomalous dimensions at two-loop order in gauge couplings and one-loop order in Yukawa interactions, carefully considering the treatment of a redundant operator involving an ALP coupling to the Higgs current. We account for one-loop (and partially two-loop) matching contributions at the weak scale, including in particular flavor-changing effects. The relations between different equivalent forms of the effective Lagrangian are discussed in detail. We also construct the effective chiral Lagrangian for an ALP interacting with photons and light pseudoscalar mesons, pointing out important differences with the corresponding Lagrangian for the QCD axion.

scholarly journals Toward massless and massive event shapes in the large-β0 limit

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
N. G. Gracia ◽  
V. Mateu
Keyword(s):  
Top Quark ◽  
Matrix Elements ◽  
Position Space ◽  
Positive Real ◽  
Full Agreement ◽  
Anomalous Dimensions ◽  
Fixed Order ◽  
Principal Value ◽  
Contour Deformation ◽  
Perturbative Corrections

Abstract We present results for SCET and bHQET matching coefficients and jet functions in the large-β0 limit. Our computations exactly predict all terms of the form $$ {\alpha}_s^{n+1}{n}_f^n $$ α s n + 1 n f n for any n ≥ 0, and we find full agreement with the coefficients computed in the full theory up to $$ \mathcal{O}\left({\alpha}_s^4\right) $$ O α s 4 . We obtain all-order closed expressions for the cusp and non-cusp anomalous dimensions (which turn out to be unambiguous) as well as matrix elements (with ambiguities) in this limit, which can be easily expanded to arbitrarily high powers of αs using recursive algorithms to obtain the corresponding fixed-order coefficients. Examining the poles laying on the positive real axis of the Borel-transform variable u we quantify the perturbative convergence of a series and estimate the size of non-perturbative corrections. We find a so far unknown u = 1/2 renormalon in the bHQET hard factor Hm that affects the normalization of the peak differential cross section for boosted top quark pair production. For ambiguous series the so-called Borel sum is defined with the principal value prescription. Furthermore, one can assign an ambiguity based on the arbitrariness of avoiding the poles by contour deformation into the positive or negative imaginary half-plane. Finally, we compute the relation between the pole mass and four low-scale short distance masses in the large-β0 approximation (MSR, RS and two versions of the jet mass), work out their μ- and R-evolution in this limit, and study how their implementation improves the convergence of the position-space bHQET jet function, whose three-loop coefficient in full QCD is numerically estimated.

scholarly journals Anomalous dimensions for ϕn in scale invariant d=3 theory

2020 ◽  
Vol 102 (8) ◽  
Author(s):  
I. Jack ◽  
D. R. T. Jones
Keyword(s):  
Scale Invariant ◽  
Anomalous Dimensions

scholarly journals CONFORMAL HOUSE

2010 ◽  
Vol 25 (24) ◽  
pp. 4603-4621 ◽  
Author(s):  
THOMAS A. RYTTOV ◽  
FRANCESCO SANNINO
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Gauge Group ◽  
Gauge Theories ◽  
Simultaneous Presence ◽  
Consistency Check ◽  
Effective Lagrangian ◽  
Anomalous Dimensions ◽  
Mass Terms

We investigate the gauge dynamics of nonsupersymmetric SU (N) gauge theories featuring the simultaneous presence of fermionic matter transforming according to two distinct representations of the underlying gauge group. We bound the regions of flavors and colors which can yield a physical infrared fixed point. As a consistency check we recover the previously investigated bounds of the conformal windows when restricting to a single matter representation. The earlier conformal windows can be imagined to be part now of the new conformal house. We predict the nonperturbative anomalous dimensions at the infrared fixed points. We further investigate the effects of adding mass terms to the condensates on the conformal house chiral dynamics and construct the simplest instanton induced effective Lagrangian terms.

Erratum to: “ -Factorization and small-x anomalous dimensions”

2001 ◽  
Vol 607 (1-2) ◽  
pp. 431-432 ◽  
Author(s):  
G. Camici ◽  
M. Ciafaloni
Keyword(s):  
Anomalous Dimensions ◽  
Small X

scholarly journals Spectral Inclusion and Analytic Continuation

1999 ◽  
Vol 31 (6) ◽  
pp. 722-728 ◽  
Author(s):  
A. Atzmon ◽  
A. Eremenko ◽  
M. Sodin
Keyword(s):  
Analytic Continuation ◽  
Spectral Inclusion
Sign in / Sign up

Export Citation Format

Share Document