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, Volume:
100, Issue:
9
Journal Article
Peer reviewed
Open access
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.
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.
•Recommendation system is new era of research to predict things to end user.•Content-based and collaborative filtering are two main building block of recommendation system.•Recommendation system ...suffers from cold-start, sparsity and shilling attack problems.•Different online and offline dimensions are available to evaluate recommendation system.•Recommending crops, pesticides, fertilizer in agriculture based on soil properties can help farmers to gain profit.
With the new era of the Internet, we have a large amount of data available in the form of ratings, reviews, graphs, images, etc. However, still, people face difficulty in finding useful information or knowledge from those data. To address these challenges, recommendation systems come into the picture by providing useful content to the user based on users’ history and similarity among users. Content-based and collaborative filtering are two major building blocks of recommendation systems. Recommendation systems have been applied into numbers of a domain such as recommending movies, music, course, literature, items, people, links, location, healthcare, agriculture. In the agriculture domain, appropriate crops to cultivate and selecting applicable pesticides based on land quality and types of crops are interesting factors to consider for a country like India. Initially, we review different types of recommendation systems along with its application area. Subsequently, we explore various parameters to evaluate recommendation systems followed by open issues and research challenges. We further study the work carried out by existing researchers in the said domain. As part of our contribution through this research, we have selected the Agriculture domain and proposed our algorithm for recommending crops based on various parameters. As an outcome of our contribution, a crop is recommended to farmers based on his land. Also, the system recommends a list of lands for a given crop. Using statistical analysis, we achieve accuracy from 93% to 97%.
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.
The mortality and morbidity after aneurysmal subarachnoid hemorrhage has improved because of better diagnosis, early treatment to secure the aneurysm, and better management of disease-specific ...complications. With these improvements in care, it is not clear if the previously identified independent predictors of a negative outcome have changed. The aim of this study was to identify the independent predictors of an unfavorable outcome (Glasgow Outcome Score 1, 2, and 3) in aneurysmal subarachnoid hemorrhage patients.
Univariate and multivariate analysis of prospectively collected data on patients presenting with an aneurysmal subarachnoid hemorrhage was performed. Outcome was assessed at discharge. Data were collected from 14 centers in the United Kingdom over a period of 4 years (September 2011-2015).
The median age (interquartile range) at presentation of 3341 patients with aneurysmal subarachnoid hemorrhage was 55 (18) years. Most patients were female (n=2288 68.5%), presented in good grade (2397 70%; World Federation of Neurological Surgeons grade 1 and 2), and were treated by endovascular coiling (n=2600; 75%). The independent predictors of an unfavorable outcome (95% confidence interval CI) were increasing age (odds ratio OR, 1.04; 95% CI, 1.03-1.05;
<0.001), World Federation of Neurological Surgeons grade (OR, 2.06; 95% CI, 1.91-2.22;
<0.001), preoperative rebleeding (OR, 7.41; 95% CI, 4.48-12.30;
<0.001), need for cerebrospinal fluid diversion (OR, 3.25; 95% CI, 2.58-4.09;
<0.001), and delayed cerebral ischemia (OR, 2.21; 95% CI, 1.72-2.83;
<0.001).
These data suggest that potentially modifiable risk factors of preoperative rebleeding and delayed cerebral ischemia are associated with unfavorable outcomes. Understanding the reasons why patients requiring cerebrospinal fluid diversion have 3.25-fold higher adjusted odds of a poor outcome at discharge needs to be studied.
The performance of a photovoltaic (PV) array is affected by temperature, solar insolation, shading, and array configuration. Often, the PV arrays get shadowed, completely or partially, by the passing ...clouds, neighboring buildings and towers, trees, and utility and telephone poles. The situation is of particular interest in case of large PV installations such as those used in distributed power generation schemes. Under partially shaded conditions, the PV characteristics get more complex with multiple peaks. Yet, it is very important to understand and predict them in order to extract the maximum possible power. This paper presents a MATLAB-based modeling and simulation scheme suitable for studying the I-V and P-V characteristics of a PV array under a nonuniform insolation due to partial shading. It can also be used for developing and evaluating new maximum power point tracking techniques, especially for partially shaded conditions. The proposed models conveniently interface with the models of power electronic converters, which is a very useful feature. It can also be used as a tool to study the effects of shading patterns on PV panels having different configurations. It is observed that, for a given number of PV modules, the array configuration (how many modules in series and how many in parallel) significantly affects the maximum available power under partially shaded conditions. This is another aspect to which the developed tool can be applied. The model has been experimentally validated and the usefulness of this research is highlighted with the help of several illustrations. The MATLAB code of the developed model is freely available for download.
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.
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