Package-X, a Mathematica package for the analytic computation of one-loop integrals dimensionally regulated near 4 spacetime dimensions is described. Package-X computes arbitrarily high rank tensor ...integrals with up to three propagators, and gives compact expressions of UV divergent, IR divergent, and finite parts for any kinematic configuration involving real-valued external invariants and internal masses. Output expressions can be readily evaluated numerically and manipulated symbolically with built-in Mathematica functions. Emphasis is on evaluation speed, on readability of results, and especially on user-friendliness. Also included is a routine to compute traces of products of Dirac matrices, and a collection of projectors to facilitate the computation of fermion form factors at one-loop. The package is intended to be used both as a research tool and as an educational tool.
Program title: Package-X
Catalogue identifier: AEXT_v1_0
Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEXT_v1_0.html
Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland
Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html
No. of lines in distributed program, including test data, etc.: 63912
No. of bytes in distributed program, including test data, etc.: 1224562
Distribution format: tar.gz
Programming language: Mathematica (Wolfram Language).
Computer: Any, which supports Mathematica.
Operating system: Windows, Mac OS X, Linux (or any system supporting Mathematica 8.0 or higher).
RAM: 10 MB, depending on size of computation
Classification: 4.4, 11.1.
Nature of problem: Analytic calculation of one-loop integrals in relativistic quantum field theory for arbitrarily high-rank tensor integrals and any kinematic configuration of real-valued external invariants and internal masses.
Solution method: Passarino–Veltman reduction formula, Denner–Dittmaier reduction formulae, and two new reduction algorithms described in the manuscript.
Restrictions: One-loop integrals are limited to those involving no more than three propagator factors.
Unusual features: Includes rudimentary routines for tensor algebraic operations and for performing traces over Dirac gamma matrices.
Running time: 5 ms to 10 s for integrals typically occurring in practical computations; longer for higher rank tensor integrals.
This article summarizes new features and enhancements of the first major update of Package-X. Package-X 2.0 can now generate analytic expressions for arbitrarily high rank dimensionally regulated ...tensor integrals with up to four distinct propagators, each with arbitrary integer weight, near an arbitrary even number of spacetime dimensions, giving UV divergent, IR divergent, and finite parts at (almost) any real-valued kinematic point. Additionally, it can generate multivariable Taylor series expansions of these integrals around any non-singular kinematic point to arbitrary order. All special functions and abbreviations output by Package-X 2.0 support Mathematica’s arbitrary precision evaluation capabilities to deal with issues of numerical stability. Finally, tensor algebraic routines of Package-X have been polished and extended to support open fermion chains both on and off shell. The documentation (equivalent to over 100 printed pages) is accessed through Mathematica’s Wolfram Documentation Center and contains information on all Package-X symbols, with over 300 basic usage examples, 3 project-scale tutorials, and instructions on linking to FeynCalc and LoopTools.
Program title: Package-X
Program files doi:http://dx.doi.org/10.17632/yfkwrd4d5t.1
Licensing provisions: CC by 4.0
Programming language: Mathematica (Wolfram Language)
Journal reference of previous version: H. H. Patel, Comput. Phys. Commun 197, 276 (2015)
Does the new version supersede the previous version?: Yes
Summary of revisions: Extension to four point one-loop integrals with higher powers of denominator factors, separate extraction of UV and IR divergent parts, testing for power IR divergences, construction of Taylor series expansions of one-loop integrals, numerical evaluation with arbitrary precision arithmetic, manipulation of fermion chains, improved tensor algebraic routines, and much expanded documentation.
Nature of problem: Analytic calculation of one-loop integrals in relativistic quantum field theory.
Solution method: Passarino–Veltman reduction formula, Denner–Dittmaier reduction formulae, and additional algorithms described in the manuscript.
Restrictions: One-loop integrals are limited to those involving no more than four denominator factors.
Majoron at two loops Heeck, Julian; Patel, Hiren H.
Physical review. D,
11/2019, Letnik:
100, Številka:
9
Journal Article
Recenzirano
Odprti dostop
We present singlet-Majoron couplings to Standard Model particles through two loops at leading order in the seesaw expansion, including couplings to gauge bosons as well as flavor-changing quark ...interactions. We discuss and compare the relevant phenomenological constraints on Majoron production as well as decaying Majoron dark matter. A comparison with standard seesaw observables in low-scale settings highlights the importance of searches for lepton-flavor-violating two-body decays ℓ → ℓ ′ + Majoron in both the muon and the tau sectors.
Comments on axions, domain walls, and cosmic strings Dine, Michael; Fernandez, Nicolas; Ghalsasi, Akshay ...
Journal of cosmology and astroparticle physics,
11/2021, Letnik:
2021, Številka:
11
Journal Article
Recenzirano
Odprti dostop
Abstract
Axions have for some time been considered a plausible candidate for dark matter. They can be produced through misalignment, but it has been argued that when inflation occurs before a ...Peccei-Quinn transition, appreciable production can result from cosmic strings. This has been the subject of extensive simulations. But there are reasons to be skeptical about the possible role of axion strings. We review and elaborate on these questions, and argue that parametrically strings are already accounted for by the assumption of random misalignment angles. We review and elaborate on these questions, and provide several qualitative arguments that parametrically strings are already accounted for by the assumption of random misalignment angles. The arguments are base on considerations of the collective modes of the string solutions, on computations of axion radiation in particular models, and reviews of simulations.
We present the first complete two loop calculation of the electron EDM in the complex two-Higgs doublet model. We confirm gauge independence by demonstrating analytic cancellation of the gauge ...parameter ξ in the background field gauge and the 't Hooft Rξ gauge. We also investigate the behavior of the electron EDM near the decoupling limit and determine the short- and long-distance contributions by matching onto an effective field theory. Compared with earlier studies of the electron EDM in the complex two-Higgs doublet model, we note disagreements in several places and provide diagnoses where possible. We also provide expressions for EDMs of light quarks.
We analyze the universal radiative correction ΔRV to neutron and superallowed nuclear β decay by expressing the hadronic γW-box contribution in terms of a dispersion relation, which we identify as an ...integral over the first Nachtmann moment of the γW interference structure function F3(0). By connecting the needed input to existing data on neutrino and antineutrino scattering, we obtain an updated value of ΔRV=0.02467(22), wherein the hadronic uncertainty is reduced. Assuming other standard model theoretical calculations and experimental measurements remain unchanged, we obtain an updated value of |Vud|=0.97370(14), raising tension with the first row Cabibbo-Kobayashi-Maskawa unitarity constraint. We comment on ways current and future experiments can provide input to our dispersive analysis.
We analyze the conventional perturbative treatment of sphaleron-induced baryon number washout relevant for electroweak baryogenesis and show that it is not gauge-independent due to the failure of ...consistently implementing the Nielsen identities order-byorder in perturbation theory. We provide a gauge-independent criterion for baryon number preservation in place of the conventional (gauge-dependent) criterion needed for successful electroweak baryogenesis. We also review the arguments leading to the preservation criterion and analyze several sources of theoretical uncertainties in obtaining a numerical bound. In various beyond the standard model scenarios, a realistic perturbative treatment will likely require knowledge of the complete two-loop finite temperature effective potential and the one-loop sphaleron rate.
We study the dynamics of electroweak symmetry breaking in an extension of the Standard Model where the Higgs sector is augmented by the addition of a real (Y = 0) isospin triplet. We show that this ...scenario exhibits a novel, two-step electroweak phase transition, wherein the first step provides the strongly first-order transition as required for electroweak baryogenesis, followed by a second step to the Standard Model Higgs phase that also admits a cold dark matter candidate. We analyze the constraints on this scenario from recent results obtained at the Large Hadron Collider for the Higgs diphoton decay channel. We argue that this two-step scenario can be generalized to extensions of the Standard Model with additional higher-dimensional scalar multiplets that may yield realistic baryogenesis dynamics.
In a series of two papers, we make a comparative analysis of the performance of conventional perturbation theory to analyze electroweak phase transition in the real triplet extension of the Standard ...Model (ΣSM). In Part I (this paper), we derive and present the high−T dimensionally reduced effective theory that is suitable for numerical simulation on the lattice. In Part II, we will present results of the numerical simulation and benchmark the performance of conventional perturbation theory. Under the assumption that Σ is heavy, the resulting effective theory takes the same form as that derived from the minimal Standard Model. By recasting the existing nonperturbative results, we map out the phase diagram of the model in the plane of triplet mass MΣ and Higgs portal coupling a2. Contrary to conventional perturbation theory, we find regions of parameter space in which the phase transition may be first order, second order, or crossover. We comment on prospects for prospective future colliders to probe the region where the electroweak phase transition is first order by a precise measurement of the h→γγ partial width.
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