High energy physics and algebraic geometry
Superstring theory is applied to construction of the Minimal Supersymmetric Standard Model.
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| Дата: | 2009 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
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Інститут математики НАН України
2009
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | High energy physics and algebraic geometry / Yu.M. Malyuta, T.V. Obikhod // Збірник праць Інституту математики НАН України. — 2009. — Т. 6, № 2. — С. 499-504. — Бібліогр.: 6 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859807969078673408 |
|---|---|
| author | Malyuta, Yu.M. Obikhod, T.V. |
| author_facet | Malyuta, Yu.M. Obikhod, T.V. |
| citation_txt | High energy physics and algebraic geometry / Yu.M. Malyuta, T.V. Obikhod // Збірник праць Інституту математики НАН України. — 2009. — Т. 6, № 2. — С. 499-504. — Бібліогр.: 6 назв. — англ. |
| collection | DSpace DC |
| description | Superstring theory is applied to construction of the Minimal Supersymmetric Standard Model.
|
| first_indexed | 2025-12-07T15:17:30Z |
| format | Article |
| fulltext |
Çáiðíèê ïðàöüIí-òó ìàòåìàòèêè ÍÀÍ Óêðà¨íè2009, ò.6, �2, 499-504539.12Yu. M. MalyutaInstitute for Nu
lear Resear
h National A
ademy of S
ien
es ofUkraine 03068 Kiev, UkraineE-mail: obikhod�kinr.kiev.uaT. V. ObikhodInstitute for Nu
lear Resear
h National A
ademy of S
ien
es ofUkraine 03068 Kiev, UkraineE-mail: obikhod�kinr.kiev.uaHigh energy physi
s and algebrai
geometry
Superstring theory is applied to construction of the Minimal Supersym-
metric Standard Model.
Keywords: Superstring theory, Calabi-Yau fourfold, Superpotential, Mass
spectrum of superpartners
1. Introduction
The purpose of the present work is to derive the Minimal Su-
persymmetric Standard Model [1] from superstring theory [2]. It
is performed by choosing superstring compactification in the form
of elliptically fibred Calabi-Yau fourfold. Such approach allows
to determine the gauge group, matter content, superpotential and
mass spectrum of superpartners.
These predictions are important from experimental point of
view as they are connected with searches for new physics at the
LHC.
c© Yu. M. Malyuta, T. V. Obikhod, 2009
500 Yu.M. Malyuta and T.V. Obikhod
2. Superstring compactification
We consider superstring compactification on the Calabi-Yau
fourfold F represented as the elliptic fibration
(1)
E −−−−→ F
y
B
where the base B is the Fano variety of dimension three and the
fiber ε is the elliptic curve.
Singular elliptic fibers [3] and their classification in terms of Lie
groups are shown in Figure 1.
3. Matter content
The Fano variety B [4] contains two del Pezzo surfaces S and S
′
.
The surface S intersects the surface S
′
transversely along complex
curves Σ
(u)
H , Σ
(d)
H , Σ
(1)
M , Σ
(2)
M shown in Table 1 and in Figure 2. The
fibration (1) restricted to these curves has sections
1 × 5H , 1 × 5H , 3 × 10M , 3 × 5M
presented in Table 1 and in Figure 2. These sections determine
the matter content of the MSSM.
4. Superpotential
The gauge invariant MSSM superpotential takes the form
(2) WSU(5) = λdij · 5H × 5
(i)
M × 10
(j)
M + λuij · 5H × 10
(i)
M × 10
(j)
M +
+ λia · 5H × 5
(i)
M ×N
(a)
R + µ · 5H × 5H
where 5H and 5H are Higgs multiplets, 5
(i)
M and 10
(j)
M are multiplets
of quark and lepton superpartners, λdij , λ
u
ij , λia, µ are Yukawa
coupling constants.
High Energy Physics and Algebraic Geometry 501
Figure 10
5. Mass spectrum of superpartners
The analysis of Yukawa coupling constants, based on observa-
tional hints and theoretical considerations, allows to restrict the
502 Yu.M. Malyuta and T.V. Obikhod
Figure 11
parameter space in (2) to five free parameters. Using this re-
stricted parameter set it is possible to calculate the mass spec-
trum of superpartners by application of the computer program
SOFTSUSY [5]. This MSSM spectrum is displayed in Figure 3.
High Energy Physics and Algebraic Geometry 503
6. Comparison with experiment
Comparison of the predicted spectrum with experimental data
obtained at the LEP and TEVATRON [6] (see Table 2) shows, that
the calculated masses exceed the lower limits on masses reached
at colliders.
New searches for superpartners and measurements of their mas-
ses should be realized at the LHC.
References
[1] Allanach B. C. et al., Mass spectrum in R-parity violating minimal super-
gravity and benchmark points, arXiv: hep-ph/0609263.
[2] Vafa C. et al., Stringy reflections on LHC,
http://www.claymath.org/workshops/lhc/.
[3] Perevalov E., Skarke H., Enhanced gauge symmetry in Type II and F-
theory compactifications, arXiv: hep-th/9704129.
[4] Klemm A., Lian B., Roan S-S., Yau S-T., Calabi-Yau fourfolds for M- and
F-theory compactifications, arXiv: hep-th/9701023.
[5] Allanach B. C., SOFTSUSY2.0: a program for calculating supersymmet-
ric spectra, arXiv: hep-ph/0104145.
504 Yu.M. Malyuta and T.V. Obikhod
Figure 12
[6] Schmitt M., Supersymmetry, Part II (Experiment), Phys. Lett. B592
(2004) 1014.
|
| id | nasplib_isofts_kiev_ua-123456789-6329 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-2910 |
| language | English |
| last_indexed | 2025-12-07T15:17:30Z |
| publishDate | 2009 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Malyuta, Yu.M. Obikhod, T.V. 2010-02-23T14:51:14Z 2010-02-23T14:51:14Z 2009 High energy physics and algebraic geometry / Yu.M. Malyuta, T.V. Obikhod // Збірник праць Інституту математики НАН України. — 2009. — Т. 6, № 2. — С. 499-504. — Бібліогр.: 6 назв. — англ. 1815-2910 https://nasplib.isofts.kiev.ua/handle/123456789/6329 539.12 Superstring theory is applied to construction of the Minimal Supersymmetric Standard Model. en Інститут математики НАН України Геометрія, топологія та їх застосування High energy physics and algebraic geometry Article published earlier |
| spellingShingle | High energy physics and algebraic geometry Malyuta, Yu.M. Obikhod, T.V. Геометрія, топологія та їх застосування |
| title | High energy physics and algebraic geometry |
| title_full | High energy physics and algebraic geometry |
| title_fullStr | High energy physics and algebraic geometry |
| title_full_unstemmed | High energy physics and algebraic geometry |
| title_short | High energy physics and algebraic geometry |
| title_sort | high energy physics and algebraic geometry |
| topic | Геометрія, топологія та їх застосування |
| topic_facet | Геометрія, топологія та їх застосування |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/6329 |
| work_keys_str_mv | AT malyutayum highenergyphysicsandalgebraicgeometry AT obikhodtv highenergyphysicsandalgebraicgeometry |