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Title: Extending the Universal One-Loop Effective Action: heavy-light coefficients

Abstract

The Universal One-Loop Effective Action (UOLEA) is a general expression for the effective action obtained by evaluating in a model-independent way the one-loop expansion of a functional path integral. It can also be used to match UV theories to their low-energy EFTs more efficiently by avoiding redundant steps in the application of functional methods, simplifying the process of obtaining Wilson coefficients of operators up to dimension six. In addition to loops involving only heavy fields, matching may require the inclusion of loops containing both heavy and light particles. Here we use the recently-developed covariant diagram technique to extend the UOLEA to include heavy-light terms which retain the same universal structure as the previously-derived heavy-only terms. As an example of its application, we integrate out a heavy singlet scalar with a linear coupling to a light doublet Higgs. The extension presented here is a first step towards completing the UOLEA to incorporate all possible structures encountered in a covariant derivative expansion of the one-loop path integral.

Authors:
 [1];  [2];  [3];  [1]
  1. Univ. of Michigan, Ann Arbor, MI (United States). Dept. of Physics and Michigan Center for Theoretical Physics (MCTP)
  2. King's College London (United Kingdom). Theoretical Particle Physics and Cosmology Group and Physics Dept.
  3. Univ. of Cambridge (United Kingdom). Dept. of Applied Mathematics and Theoretical Physics and Cavendish Lab.
Publication Date:
Research Org.:
Univ. of Michigan, Ann Arbor, MI (United States)
Sponsoring Org.:
USDOE Office of Science (SC); Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Univ. of Cambridge-Gonville and Caius College, Cambridge (United Kingdom); Science and Technology Facilities Council (STFC) (United Kingdom)
OSTI Identifier:
1425648
Grant/Contract Number:  
SC0007859; ST/L000326/1
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Volume: 2017; Journal Issue: 8; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Phenomenology of Field Theories in Higher Dimensions

Citation Formats

Ellis, Sebastian A. R., Quevillon, Jérémie, You, Tevong, and Zhang, Zhengkang. Extending the Universal One-Loop Effective Action: heavy-light coefficients. United States: N. p., 2017. Web. doi:10.1007/JHEP08(2017)054.
Ellis, Sebastian A. R., Quevillon, Jérémie, You, Tevong, & Zhang, Zhengkang. Extending the Universal One-Loop Effective Action: heavy-light coefficients. United States. https://doi.org/10.1007/JHEP08(2017)054
Ellis, Sebastian A. R., Quevillon, Jérémie, You, Tevong, and Zhang, Zhengkang. 2017. "Extending the Universal One-Loop Effective Action: heavy-light coefficients". United States. https://doi.org/10.1007/JHEP08(2017)054. https://www.osti.gov/servlets/purl/1425648.
@article{osti_1425648,
title = {Extending the Universal One-Loop Effective Action: heavy-light coefficients},
author = {Ellis, Sebastian A. R. and Quevillon, Jérémie and You, Tevong and Zhang, Zhengkang},
abstractNote = {The Universal One-Loop Effective Action (UOLEA) is a general expression for the effective action obtained by evaluating in a model-independent way the one-loop expansion of a functional path integral. It can also be used to match UV theories to their low-energy EFTs more efficiently by avoiding redundant steps in the application of functional methods, simplifying the process of obtaining Wilson coefficients of operators up to dimension six. In addition to loops involving only heavy fields, matching may require the inclusion of loops containing both heavy and light particles. Here we use the recently-developed covariant diagram technique to extend the UOLEA to include heavy-light terms which retain the same universal structure as the previously-derived heavy-only terms. As an example of its application, we integrate out a heavy singlet scalar with a linear coupling to a light doublet Higgs. The extension presented here is a first step towards completing the UOLEA to incorporate all possible structures encountered in a covariant derivative expansion of the one-loop path integral.},
doi = {10.1007/JHEP08(2017)054},
url = {https://www.osti.gov/biblio/1425648}, journal = {Journal of High Energy Physics (Online)},
issn = {1029-8479},
number = 8,
volume = 2017,
place = {United States},
year = {Wed Aug 16 00:00:00 EDT 2017},
month = {Wed Aug 16 00:00:00 EDT 2017}
}

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Works referenced in this record:

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font-size:0.75rem;"><br/> <span class="type">preprint</span>, <span class="date" data-date="2016-01-01">January 2016</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#557B2D;"> Henning, Brian; Lu, Xiaochuan; Murayama, Hitoshi</span> </li> <li> arXiv</li> <li> <span class="text-muted related-url"><a href="https://doi.org/10.48550/arxiv.1604.01019" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.48550/arxiv.1604.01019<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.48550/arxiv.1811.08878" target="_blank" rel="noopener noreferrer" class="name">Complete One-Loop Matching for a Singlet Scalar in the Standard Model EFT<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">text</span>, <span class="date" data-date="2018-01-01">January 2018</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#557B2D;"> Jiang, Minyuan; Craig, Nathaniel; Li, Ying-Ying</span> </li> <li> arXiv</li> <li> <span class="text-muted related-url"><a href="https://doi.org/10.48550/arxiv.1811.08878" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.48550/arxiv.1811.08878<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> </div> <div class="pagination-container small"> <a class="pure-button prev page" href="#" rel="prev"><span class="fa fa-angle-left"></span><span class="sr-only">Previous</span></a><ul class="pagination d-inline-block" style="padding-left:.2em;"></ul><a class="pure-button next page" href="#" rel="next"><span class="fa fa-angle-right"></span><span class="sr-only">Next</span></a> </div> </div> </div> <div class="col-sm-3 order-sm-3"> <ul class="nav nav-stacked"> <li class="active"><a href="" class="reference-type-filter tab-nav" data-filter="type" data-pattern="*"><span class="fa fa-angle-right"></span> All Cited By</a></li> <li class="small" style="margin-left:.75em; 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margin-top:0px;">Similar records in OSTI.GOV collections:</p> <aside> <ul class="item-list" itemscope itemtype="http://schema.org/ItemList" style="padding-left:0; list-style-type: none;"> <li> <div class="article item document" itemprop="itemListElement" itemscope itemtype="http://schema.org/WebPage"><meta itemprop="position" content="0" /><div class="item-info"> <h2 class="title" itemprop="name headline"><a href="/biblio/1325311" itemprop="url">Mixed heavy–light matching in the Universal One-Loop Effective Action</a></h2> <div class="metadata"> <small class="text-muted" style="text-transform:uppercase;display:block;line-height:2.5em;">Journal Article</small><span class="authors"> <span class="author">Ellis, Sebastian</span>; <span class="author">Quevillon, Jérémie</span>; <span class="author">You, Tevong</span>; <span class="author">...</span> <span class="text-muted pubdata"> - Physics Letters. B</span> </span></div> <div class="abstract">Recently, a general result for evaluating the path integral at one loop was obtained in the form of the Universal One-Loop Effective Action. It may be used to derive effective field theory operators of dimensions up to six, by evaluating the traces of matrices in this expression, with the mass dependence encapsulated in the universal coefficients. In this study we show that it can account for loops of mixed heavy–light particles in the matching procedure. Our prescription for computing these mixed contributions to the Wilson coefficients is conceptually simple. Moreover it has the advantage of maintaining the universal structure of<a href='#' onclick='$(this).hide().next().show().next().show();return false;' style='margin-left:10px;'>more »</a><span style='display:none;'> the effective action, which we illustrate using the example of integrating out a heavy electroweak triplet scalar coupling to a light Higgs doublet. Finally we also identify new structures that were previously neglected in the universal results.</span><a href='#' onclick='$(this).hide().prev().hide().prev().show();return false;' style='margin-left:10px;display:none;'>« less</a></div><div class="metadata-links small clearfix text-muted" style="margin-top:15px;"> <span class="fa fa-book text-muted" aria-hidden="true"></span> Cited by 60<div class="pure-menu pure-menu-horizontal pull-right" style="width:unset;"> <ul class="pure-menu-list"> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc doi-link " href="https://doi.org/10.1016/j.physletb.2016.09.016" target="_blank" rel="noopener" title="Link to document DOI" data-ostiid="1325311" data-product-type="Journal Article" data-product-subtype="PA" >https://doi.org/10.1016/j.physletb.2016.09.016</a></span></li> </ul> </div> </div> </div> <div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemprop="itemListElement" itemscope itemtype="http://schema.org/WebPage"><meta itemprop="position" content="2" /><div class="item-info"> <h2 class="title" itemprop="name headline"><a href="/biblio/1435097" itemprop="url">One-loop matching and running with covariant derivative expansion</a></h2> <div class="metadata"> <small class="text-muted" style="text-transform:uppercase;display:block;line-height:2.5em;">Journal Article</small><span class="authors"> <span class="author">Henning, Brian</span>; <span class="author">Lu, Xiaochuan</span>; <span class="author">Murayama, Hitoshi</span><span class="text-muted pubdata"> - Journal of High Energy Physics (Online)</span> </span></div> <div class="abstract">We develop tools for performing effective field theory (EFT) calculations in a manifestly gauge-covariant fashion. We clarify how functional methods account for one-loop diagrams resulting from the exchange of both heavy and light fields, as some confusion has recently arisen in the literature. To efficiently evaluate functional traces containing these “mixed” one-loop terms, we develop a new covariant derivative expansion (CDE) technique that is capable of evaluating a much wider class of traces than previous methods. The technique is detailed in an appendix, so that it can be read independently from the rest of this work. We review the well-known<a href='#' onclick='$(this).hide().next().show().next().show();return false;' style='margin-left:10px;'>more »</a><span style='display:none;'> matching procedure to one-loop order with functional methods. What we add to this story is showing how to isolate one-loop terms coming from diagrams involving only heavy propagators from diagrams with mixed heavy and light propagators. This is done using a non-local effective action, which physically connects to the notion of “integrating out” heavy fields. Lastly, we show how to use a CDE to do running analyses in EFTs, i.e. to obtain the anomalous dimension matrix. We demonstrate the methodologies by several explicit example calculations.</span><a href='#' onclick='$(this).hide().prev().hide().prev().show();return false;' style='margin-left:10px;display:none;'>« less</a></div><div class="metadata-links small clearfix text-muted" style="margin-top:15px;"> <span class="fa fa-book text-muted" aria-hidden="true"></span> Cited by 54<div class="pure-menu pure-menu-horizontal pull-right" style="width:unset;"> <ul class="pure-menu-list"> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc doi-link " href="https://doi.org/10.1007/JHEP01(2018)123" target="_blank" rel="noopener" title="Link to document DOI" data-ostiid="1435097" data-product-type="Journal Article" data-product-subtype="AM" >https://doi.org/10.1007/JHEP01(2018)123</a></span></li> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc fulltext-link " href="/servlets/purl/1435097" title="Link to document media" target="_blank" rel="noopener" data-ostiid="1435097" data-product-type="Journal Article" data-product-subtype="AM" >Full Text Available</a></span></li> </ul> </div> </div> </div> <div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemprop="itemListElement" itemscope itemtype="http://schema.org/WebPage"><meta itemprop="position" content="3" /><div class="item-info"> <h2 class="title" itemprop="name headline"><a href="/biblio/1768128" itemprop="url">The fermionic universal one-loop effective action</a></h2> <div class="metadata"> <small class="text-muted" style="text-transform:uppercase;display:block;line-height:2.5em;">Journal Article</small><span class="authors"> <span class="author">Ellis, Sebastian</span>; <span class="author">Quevillon, Jérémie</span>; <span class="author">Vuong, Pham</span>; <span class="author">...</span> <span class="text-muted pubdata"> - Journal of High Energy Physics (Online)</span> </span></div> <div class="abstract">Recent development of path integral matching techniques based on the covariant derivative expansion has made manifest a universal structure of one-loop effective Lagrangians. The universal terms can be computed once and for all to serve as a reference for one-loop matching calculations and to ease their automation. Here we present the fermionic universal one-loop effective action (UOLEA), resulting from integrating out heavy fermions (Dirac or Majorana) with scalar, pseudo-scalar, vector and axial-vector couplings. We also clarify the relation of the new terms computed here to terms previously computed in the literature and those that remain to complete the UOLEA. Our<a href='#' onclick='$(this).hide().next().show().next().show();return false;' style='margin-left:10px;'>more »</a><span style='display:none;'> results can be readily used to efficiently obtain analytical expressions for effective operators arising from heavy fermion loops.</span><a href='#' onclick='$(this).hide().prev().hide().prev().show();return false;' style='margin-left:10px;display:none;'>« less</a></div><div class="metadata-links small clearfix text-muted" style="margin-top:15px;"> <div class="pure-menu pure-menu-horizontal pull-right" style="width:unset;"> <ul class="pure-menu-list"> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc doi-link " href="https://doi.org/10.1007/jhep11(2020)078" target="_blank" rel="noopener" title="Link to document DOI" data-ostiid="1768128" data-product-type="Journal Article" data-product-subtype="AM" >https://doi.org/10.1007/jhep11(2020)078</a></span></li> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc fulltext-link " href="/servlets/purl/1768128" title="Link to document media" target="_blank" rel="noopener" data-ostiid="1768128" data-product-type="Journal Article" data-product-subtype="AM" >Full Text Available</a></span></li> </ul> </div> </div> </div> <div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemprop="itemListElement" itemscope itemtype="http://schema.org/WebPage"><meta itemprop="position" content="4" /><div class="item-info"> <h2 class="title" itemprop="name headline"><a href="/biblio/1389267" itemprop="url">Covariant diagrams for one-loop matching</a></h2> <div class="metadata"> <small class="text-muted" style="text-transform:uppercase;display:block;line-height:2.5em;">Journal Article</small><span class="authors"> <span class="author">Zhang, Zhengkang</span><span class="text-muted pubdata"> - Journal of High Energy Physics (Online)</span> </span></div> <div class="abstract">Here, we present a diagrammatic formulation of recently-revived covariant functional approaches to one-loop matching from an ultraviolet (UV) theory to a low-energy effective field theory. Various terms following from a covariant derivative expansion (CDE) are represented by diagrams which, unlike conventional Feynman diagrams, involve gauge-covariant quantities and are thus dubbed "covariant diagrams." The use of covariant diagrams helps organize and simplify one-loop matching calculations, which we illustrate with examples. Of particular interest is the derivation of UV model-independent universal results, which reduce matching calculations of specific UV models to applications of master formulas. We also show how such derivation can<a href='#' onclick='$(this).hide().next().show().next().show();return false;' style='margin-left:10px;'>more »</a><span style='display:none;'> be done in a more concise manner than the previous literature, and discuss how additional structures that are not directly captured by existing universal results, including mixed heavy-light loops, open covariant derivatives, and mixed statistics, can be easily accounted for.</span><a href='#' onclick='$(this).hide().prev().hide().prev().show();return false;' style='margin-left:10px;display:none;'>« less</a></div><div class="metadata-links small clearfix text-muted" style="margin-top:15px;"> <span class="fa fa-book text-muted" aria-hidden="true"></span> Cited by 54<div class="pure-menu pure-menu-horizontal pull-right" style="width:unset;"> <ul class="pure-menu-list"> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc doi-link " href="https://doi.org/10.1007/JHEP05(2017)152" target="_blank" rel="noopener" title="Link to document DOI" data-ostiid="1389267" data-product-type="Journal Article" data-product-subtype="AM" >https://doi.org/10.1007/JHEP05(2017)152</a></span></li> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc fulltext-link " href="/servlets/purl/1389267" title="Link to document media" target="_blank" rel="noopener" data-ostiid="1389267" data-product-type="Journal Article" data-product-subtype="AM" >Full Text Available</a></span></li> </ul> </div> </div> </div> <div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemprop="itemListElement" itemscope itemtype="http://schema.org/WebPage"><meta itemprop="position" content="5" /><div class="item-info"> <h2 class="title" itemprop="name headline"><a href="/biblio/1415951" itemprop="url">How to use the Standard Model effective field theory</a></h2> <div class="metadata"> <small class="text-muted" style="text-transform:uppercase;display:block;line-height:2.5em;">Journal Article</small><span class="authors"> <span class="author">Henning, Brian</span>; <span class="author">Lu, Xiaochuan</span>; <span class="author">Murayama, Hitoshi</span><span class="text-muted pubdata"> - Journal of High Energy Physics (Online)</span> </span></div> <div class="abstract">Here, we present a practical three-step procedure of using the Standard Model effective field theory (SM EFT) to connect ultraviolet (UV) models of new physics with weak scale precision observables. With this procedure, one can interpret precision measurements as constraints on a given UV model. We give a detailed explanation for calculating the effective action up to one-loop order in a manifestly gauge covariant fashion. This covariant derivative expansion method dramatically simplifies the process of matching a UV model with the SM EFT, and also makes available a universal formalism that is easy to use for a variety of UV<a href='#' onclick='$(this).hide().next().show().next().show();return false;' style='margin-left:10px;'>more »</a><span style='display:none;'> models. A few general aspects of RG running effects and choosing operator bases are discussed. Finally, we provide mapping results between the bosonic sector of the SM EFT and a complete set of precision electroweak and Higgs observables to which present and near future experiments are sensitive. Many results and tools which should prove useful to those wishing to use the SM EFT are detailed in several appendices.</span><a href='#' onclick='$(this).hide().prev().hide().prev().show();return false;' style='margin-left:10px;display:none;'>« less</a></div><div class="metadata-links small clearfix text-muted" style="margin-top:15px;"> <span class="fa fa-book text-muted" aria-hidden="true"></span> Cited by 175<div class="pure-menu pure-menu-horizontal pull-right" style="width:unset;"> <ul class="pure-menu-list"> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc doi-link " href="https://doi.org/10.1007/JHEP01(2016)023" target="_blank" rel="noopener" title="Link to document DOI" data-ostiid="1415951" data-product-type="Journal Article" data-product-subtype="AM" >https://doi.org/10.1007/JHEP01(2016)023</a></span></li> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc fulltext-link " href="/servlets/purl/1415951" title="Link to document media" target="_blank" rel="noopener" data-ostiid="1415951" data-product-type="Journal Article" data-product-subtype="AM" >Full Text Available</a></span></li> </ul> </div> </div> </div> <div class="clearfix"></div> </div> </li> </ul> </aside> </div> </section> </div> <div class="col-sm-3 order-sm-3"> <ul class="nav nav-stacked"> <li class="active"><a class="tab-nav disabled" data-tab="related" style="color: #636c72 !important; opacity: 1;"><span class="fa fa-angle-right"></span> Similar Records</a></li> </ul> </div> </div> </section> </div></div> </div> </div> </section> <footer class="" style="background-color:#f9f9f9; /* padding-top: 0.5rem; */"> <div class="footer-minor"> <div class="container"> <hr class="footer-separator" /> <div class="text-center" style="margin-top:1.25rem;"> <div class="pure-menu pure-menu-horizontal"> <ul class="pure-menu-list" id="footer-org-menu"> <li class="pure-menu-item d-block d-inline-small"> <a href="https://energy.gov" target="_blank" rel="noopener noreferrer"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" class="sprite sprite-footer-us-doe-min" alt="U.S. Department of Energy" /> </a> </li> <li class="pure-menu-item d-block d-inline-small"> <a href="https://www.energy.gov/science/office-science" target="_blank" rel="noopener noreferrer"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" class="sprite sprite-footer-office-of-science-min" alt="Office of Science" /> </a> </li> <li class="pure-menu-item d-block d-inline-small"> <a href="/"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" class="sprite sprite-footer-osti-min" alt="Office of Scientific and Technical Information" /> </a> </li> </ul> </div> </div> <div class="text-center small" style="margin-top:0.5em;margin-bottom:2.0rem;"> <div class="pure-menu pure-menu-horizontal"> <ul class="pure-menu-list"> <li class="pure-menu-item"><a href="/disclaim" class="pure-menu-link"><span class="fa fa-institution"></span> Website Policies <span class="d-none d-sm-inline" style="color:#737373;">/ Important Links</span></a></li> <li class="pure-menu-item"><a href="/contact" class="pure-menu-link"><span class="fa fa-comments-o"></span> Contact Us</a></li> <li class="d-block d-md-none mb-1"></li> <li class="pure-menu-item"><a href="https://doe.responsibledisclosure.com/hc/en-us" target="_blank" class="pure-menu-link">Vulnerability Disclosure Program</a></li> <li class="d-block d-lg-none mb-1"></li> <li class="pure-menu-item"><a href="https://www.facebook.com/ostigov" target="_blank" rel="noopener noreferrer" class="pure-menu-link social"><span class="fa fa-facebook"></span><span class="sr-only">Facebook</span></a></li> <li class="pure-menu-item"><a href="https://twitter.com/OSTIgov" target="_blank" rel="noopener noreferrer" class="pure-menu-link social"><span class="fa fa-twitter"></span><span class="sr-only">Twitter</span></a></li> <li class="pure-menu-item"><a href="https://www.youtube.com/user/ostigov" target="_blank" rel="noopener noreferrer" class="pure-menu-link social"><span class="fa fa-youtube-play"></span><span class="sr-only">YouTube</span></a></li> </ul> </div> </div> </div> </div> </footer> <link href="/css/ostigov.fonts.240327.0425.css" rel="stylesheet"> <script src="/js/ostigov.240327.0425.js"></script><noscript></noscript> <script defer src="/js/ostigov.biblio.240327.0425.js"></script><noscript></noscript> <script async type="text/javascript" src="/js/Universal-Federated-Analytics-Min.js?agency=DOE" id="_fed_an_ua_tag"></script><noscript></noscript> </body> <!-- OSTI.GOV v.240327.0425 --> </html>