, a C++ library for Yukawa decomposition in models

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• 作者：Nuno Cardoso^a ; ^b ; ^{nuno.cardoso@tecnico.ulisboa.pt" class="auth_mail" title="E-mail the corresponding author} ; David Emmanuel-Costa^b ; ^{david.costa@tecnico.ulisboa.pt" class="auth_mail" title="E-mail the corresponding author} ; Nuno Gonç ; alves^c ; ^{nunogon@deec.uc.pt" class="auth_mail" title="E-mail the corresponding author} ; C. Simõ ; es^d ; ^{csimoes@ulg.ac.be" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Special orthogonal groups ; Grand Unified Theory
• 刊名：Computer Physics Communications
• 出版年：2016
• 出版时间：June 2016
• 年：2016
• 卷：203
• 期：Complete
• 页码：178-200
• 全文大小：1270 K

文摘

We present in this paper the class="imgLazyJSB inlineImage" height="17" width="39" alt="Full-size image (33 K)" title="Full-size image (33 K)" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0010465516000308-fx5.jpg"> library, which calculates an analytic decomposition of the Yukawa interactions invariant under class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0010465516000308&_mathId=si31.gif&_user=111111111&_pii=S0010465516000308&_rdoc=1&_issn=00104655&md5=b87f475f165033ed844471927481b819">class="imgLazyJSB inlineImage" height="15" width="53" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0010465516000308-si31.gif">class="mathContainer hidden">class="mathCode">$\mathrm{SO}\left(2N\right)$ in terms of an class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0010465516000308&_mathId=si33.gif&_user=111111111&_pii=S0010465516000308&_rdoc=1&_issn=00104655&md5=b53087f50c16fb3b0ef8a2ac1d4fed38">class="imgLazyJSB inlineImage" height="15" width="45" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0010465516000308-si33.gif">class="mathContainer hidden">class="mathCode">$\mathrm{SU}\left(N\right)$ basis. We make use of the oscillator expansion formalism, where the class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0010465516000308&_mathId=si31.gif&_user=111111111&_pii=S0010465516000308&_rdoc=1&_issn=00104655&md5=b87f475f165033ed844471927481b819">class="imgLazyJSB inlineImage" height="15" width="53" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0010465516000308-si31.gif">class="mathContainer hidden">class="mathCode">$\mathrm{SO}\left(2N\right)$ spinor representations are expressed in terms of creation and annihilation operators of a Grassmann algebra acting on a vacuum state. These noncommutative operators and their products are simulated in class="imgLazyJSB inlineImage" height="17" width="39" alt="Full-size image (33 K)" title="Full-size image (33 K)" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0010465516000308-fx6.jpg"> through the implementation of doubly-linked-list data structures. These data structures were determinant to achieve a higher performance in the simplification of large products of creation and annihilation operators. We illustrate the use of our library with complete examples of how to decompose Yukawa terms invariant under class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0010465516000308&_mathId=si31.gif&_user=111111111&_pii=S0010465516000308&_rdoc=1&_issn=00104655&md5=b87f475f165033ed844471927481b819">class="imgLazyJSB inlineImage" height="15" width="53" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0010465516000308-si31.gif">class="mathContainer hidden">class="mathCode">$\mathrm{SO}\left(2N\right)$ in terms of class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0010465516000308&_mathId=si33.gif&_user=111111111&_pii=S0010465516000308&_rdoc=1&_issn=00104655&md5=b53087f50c16fb3b0ef8a2ac1d4fed38">class="imgLazyJSB inlineImage" height="15" width="45" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0010465516000308-si33.gif">class="mathContainer hidden">class="mathCode">$\mathrm{SU}\left(N\right)$ degrees of freedom for class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0010465516000308&_mathId=si37.gif&_user=111111111&_pii=S0010465516000308&_rdoc=1&_issn=00104655&md5=7dfc03714e0455f4bf19bca7b9e70e49" title="Click to view the MathML source">N=2class="mathContainer hidden">class="mathCode">$N=2$ and 5. We further demonstrate, with an example for class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0010465516000308&_mathId=si5.gif&_user=111111111&_pii=S0010465516000308&_rdoc=1&_issn=00104655&md5=030fb9e70d1703aa8f0f2fe40982c278">class="imgLazyJSB inlineImage" height="15" width="41" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0010465516000308-si5.gif">class="mathContainer hidden">class="mathCode">$\mathrm{SO}\left(4\right)$, that higher dimensional field-operator terms can also be processed with our library. Finally, we describe the functions available in class="imgLazyJSB inlineImage" height="17" width="39" alt="Full-size image (33 K)" title="Full-size image (33 K)" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0010465516000308-fx7.jpg"> that are made to simplify the writing of spinors and their interactions specifically for class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0010465516000308&_mathId=si9.gif&_user=111111111&_pii=S0010465516000308&_rdoc=1&_issn=00104655&md5=6096bb2f0079afb1f9d7f3dd61a62676">class="imgLazyJSB inlineImage" height="15" width="49" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0010465516000308-si9.gif">class="mathContainer hidden">class="mathCode">$\mathrm{SO}\left(10\right)$ models.

Program summary

Program title: SOSpin

Catalogue identifier: AEZM_v1_0

Program summary URL:class="interref" data-locatorType="url" data-locatorKey="http://cpc.cs.qub.ac.uk/summaries/AEZM_v1_0.html">http://cpc.cs.qub.ac.uk/summaries/AEZM_v1_0.html

Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland

Licensing provisions: GNU General Public License, version 3

No. of lines in distributed program, including test data, etc.: 25623

No. of bytes in distributed program, including test data, etc.: 200391

Distribution format: tar.gz

Programming language: C++.

Computer: PC, Apple.

Operating system: UNIX (Linux, Mac OS X 11).

RAM: >20 MB depending on the number of processes required

Classification: 4.2, 11.1, 11.6.

External routines: In order to make further simplifications on the expressions obtained the library calls the Symbolic Manipulation System FORM program [1].

Nature of problem:   The decomposition of an Yukawa interaction invariant under SO(class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0010465516000308&_mathId=si40.gif&_user=111111111&_pii=S0010465516000308&_rdoc=1&_issn=00104655&md5=81691840a2d0eb049fcbd766ad54362e" title="Click to view the MathML source">2Nclass="mathContainer hidden">class="mathCode">$2N$) in terms of SU (class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0010465516000308&_mathId=si41.gif&_user=111111111&_pii=S0010465516000308&_rdoc=1&_issn=00104655&md5=c77a0d228ee90ae29a2c26dedf15015a" title="Click to view the MathML source">Nclass="mathContainer hidden">class="mathCode">$N$) fields.

Solution method:   We make use of the oscillator expansion formalism, where the SO(class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0010465516000308&_mathId=si40.gif&_user=111111111&_pii=S0010465516000308&_rdoc=1&_issn=00104655&md5=81691840a2d0eb049fcbd766ad54362e" title="Click to view the MathML source">2Nclass="mathContainer hidden">class="mathCode">$2N$) spinor representations are expressed in terms of creation and annihilation operators of a Grassmann algebra acting on a vacuum state.

Running time: It depends on the input expressions, it can take a few seconds or more for very large representations (because of memory exhaustion).

References:

class="listitem" id="list_l000005">

class="label">[1]

J. Kuipers, T. Ueda, J. A. M. Vermaseren and J. Vollinga, “FORM version 4.0”, Comput. Phys. Commun. class="boldFont">184 (2013) 1453.

class="label">[2]

class="interref" data-locatorType="url" data-locatorKey="http://sospin.hepforge.org">http://sospin.hepforge.org