Stringy approach to the Minimal Supersymmetric Standard Model

Superstring theory is applied to construct the Minimal Supersymmetric Standard Model. The mass spectrum, partial widths and production cross sections of superpartners are calculated. This approach gives concrete predictions for superpartner searches at the LHC.

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Datum:	2010
Hauptverfasser:	Malyuta, Yu.M., Obikhod, T.V.
Format:	Artikel
Sprache:	English
Veröffentlicht:	Національний науковий центр «Харківський фізико-технічний інститут» НАН України 2010
Schriftenreihe:	Вопросы атомной науки и техники
Schlagworte:	Ядерная физика и элементарные частицы
Online Zugang:	http://dspace.nbuv.gov.ua/handle/123456789/111067
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spelling	irk-123456789-1110672017-01-09T03:02:23Z Stringy approach to the Minimal Supersymmetric Standard Model Malyuta, Yu.M. Obikhod, T.V. Ядерная физика и элементарные частицы Superstring theory is applied to construct the Minimal Supersymmetric Standard Model. The mass spectrum, partial widths and production cross sections of superpartners are calculated. This approach gives concrete predictions for superpartner searches at the LHC. Теорію суперструн застосовано для побудови Мінімальної суперсиметричної стандартної моделі. Виконано обчислення спектра масс, парціальних ширин і перерізів народження суперпартнерів. Цей підхід дає конкретні передбачення для пошуку суперпартнерів на LHC. Теория суперструн применена для построения Минимальной суперсимметричной стандартной модели. Проведены вычисления спектра масс, парциальных ширин и сечений рождения суперпартнеров. Этот подход дает конкретные предсказания для поиска суперпартнеров на LHC. 2010 Article Stringy approach to the Minimal Supersymmetric Standard Model / Yu.M. Malyuta, T.V. Obikhod // Вопросы атомной науки и техники. — 2011. — № 3. — С. 10-13. — Бібліогр.: 11 назв. — англ. 1562-6016 PACS: 11.25.-w, 12.60.Jv, 02.10.Ws http://dspace.nbuv.gov.ua/handle/123456789/111067 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
language	English
topic	Ядерная физика и элементарные частицы Ядерная физика и элементарные частицы
spellingShingle	Ядерная физика и элементарные частицы Ядерная физика и элементарные частицы Malyuta, Yu.M. Obikhod, T.V. Stringy approach to the Minimal Supersymmetric Standard Model Вопросы атомной науки и техники
description	Superstring theory is applied to construct the Minimal Supersymmetric Standard Model. The mass spectrum, partial widths and production cross sections of superpartners are calculated. This approach gives concrete predictions for superpartner searches at the LHC.
format	Article
author	Malyuta, Yu.M. Obikhod, T.V.
author_facet	Malyuta, Yu.M. Obikhod, T.V.
author_sort	Malyuta, Yu.M.
title	Stringy approach to the Minimal Supersymmetric Standard Model
title_short	Stringy approach to the Minimal Supersymmetric Standard Model
title_full	Stringy approach to the Minimal Supersymmetric Standard Model
title_fullStr	Stringy approach to the Minimal Supersymmetric Standard Model
title_full_unstemmed	Stringy approach to the Minimal Supersymmetric Standard Model
title_sort	stringy approach to the minimal supersymmetric standard model
publisher	Національний науковий центр «Харківський фізико-технічний інститут» НАН України
publishDate	2010
topic_facet	Ядерная физика и элементарные частицы
url	http://dspace.nbuv.gov.ua/handle/123456789/111067
citation_txt	Stringy approach to the Minimal Supersymmetric Standard Model / Yu.M. Malyuta, T.V. Obikhod // Вопросы атомной науки и техники. — 2011. — № 3. — С. 10-13. — Бібліогр.: 11 назв. — англ.
series	Вопросы атомной науки и техники
work_keys_str_mv	AT malyutayum stringyapproachtotheminimalsupersymmetricstandardmodel AT obikhodtv stringyapproachtotheminimalsupersymmetricstandardmodel
first_indexed	2025-07-08T01:34:24Z
last_indexed	2025-07-08T01:34:24Z
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fulltext	STRINGY APPROACH TO THE MINIMAL SUPERSYMMETRIC STANDARD MODEL Yu.M. Malyuta, T.V. Obikhod ∗ Institute for Nuclear Research National Academy of Sciences of Ukraine, 03068, Kiev, Ukraine (Received March 10, 2010) Superstring theory is applied to construct the Minimal Supersymmetric Standard Model. The mass spectrum, partial widths and production cross sections of superpartners are calculated. This approach gives concrete predictions for superpartner searches at the LHC. PACS: 11.25.-w, 12.60.Jv, 02.10.Ws 1. INTRODUCTION The purpose of the present work is to construct the Minimal Supersymmetric Standard Model [1] from superstring theory [2]. This aim is achieved by using the notion of derived category [3]. Such approach al- lows to determine the mass spectrum, partial widths and production cross sections of superpartners. These predictions are important from experimen- tal point of view as they are connected with searches for new physics at the LHC. 2. DERIVED CATEGORY Derived categories are the mathematical foundation of superstring theory. We consider the derived cate- gory of distinguished triangles over the abelian cate- gory of McKay quivers [3]. Objects of this category are distinguished triangles (numbers a, b, c and a ′ , b ′ , c ′ denote orbifold charges [4] characterizing McKay quivers); morphisms of this category are morphisms of distinguished triangles. In this approach D-branes are described by quivers Q : and open superstrings are described by Exti(Q, Q ′ ) groups determined by the diagram [3] : 3. PARTICLE CONTENT It was shown in [5] that the moduli space of the open superstring has the form Ext0(Q, Q ′ ) = C aa ′ +bb ′ +cc ′ , Ext1(Q, Q ′ ) = C 3ab ′ +3bc ′ +3ca ′ . (1) Substituting in (1) orbifold charges a = b = c = a′ = b′ = c′ = 4 ∗Corresponding author E-mail address: obikhod@kinr.kiev.ua 10 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY, 2011, N3. Series: Nuclear Physics Investigations (55), p.10-13. and using the Langlands hypothesis [6], we obtain the realization of (1) in terms of SU(5) multiplets 3× (24 + 5H + 5H + 5M + 5M + 10M + 10M ) . This result determines the particle content of the MSSM. 4. SUPERPOTENTIAL The gauge invariant MSSM superpotential takes the form WSU(5) = λd ij · 5H × 5(i) M × 10(j) M + +λu ij · 5H × 10(i) M × 10(j) M + µ · 5H × 5H , (2) where 5H and 5H are Higgs multiplets, 5(i) M and 10(j) M are multiplets of quark and lepton superpartners, λd ij , λu ij are Yukawa coupling constants and µ is the Higgs mixing parameter. 5. MASS SPECTRUM The analysis of Yukawa coupling constants, based on observational hints and theoretical considerations, al- lows to restrict the parameter space in (2) to five free parameters [7]: M0 = 0.01 GeV , M1/2 = 600 GeV , A0 = 0 , tanβ = 35 , sgn(µ) = +1 . (3) Using this restricted parameter set it is possible to calculate the mass spectrum of superpartners by ap- plication of the computer program SOFTSUSY [8]. This MSSM spectrum is shown in Table 1. Table 1. Mass spectrum of superpartners GeV GeV GeV ũR 1187 g̃ 1354 ũL 1232 ν̃e 391 χ̃0 1 249 d̃R 1182 ẽR 224 χ̃0 2 471 d̃L 1235 ẽL 398 χ̃0 3 727 c̃R 1187 χ̃0 4 738 c̃L 1232 ν̃µ 391 χ̃±1 470 s̃R 1182 µ̃R 224 χ̃±2 738 s̃L 1235 µ̃L 398 t̃1 958 h0 116 t̃2 1155 ν̃τ 379 A0 671 b̃1 1095 τ̃1 127 H0 671 b̃2 1148 τ̃2 408 H± 676 6. PARTIAL WIDTHS Using the parameter set (3) it is possible to calcu- late partial widths of superpartners by application of the computer program SDECAY [9]. These partial widths are shown in Tables 2, 3, 4, 5. Table 2. Partial widths of superpartners channel BR channel BR ν̃e χ̃0 1νe 1.000 ẽL χ̃0 1e 1.000 ν̃µ χ̃0 1νµ 1.000 µ̃L χ̃0 1µ 1.000 ν̃τ χ̃0 1ντ 0.072 τ̃1W + 0.928 τ̃2 χ̃0 1τ 0.107 τ̃1Z 0.527 τ̃1h 0 0.365 ũR χ̃0 1u 0.997 χ̃0 4u 0.002 ũL χ̃0 1u 0.013 χ̃+ 1 d 0.646 χ̃0 2u 0.320 χ̃+ 2 d 0.012 χ̃0 4u 0.008 d̃R χ̃0 1d 0.997 χ̃0 4d 0.002 d̃L χ̃0 1d 0.016 χ̃−1 u 0.628 χ̃0 2d 0.317 χ̃−2 u 0.027 χ̃0 4d 0.011 c̃R χ̃0 1c 0.997 χ̃0 4c 0.002 c̃L χ̃0 1c 0.013 χ̃+ 1 s 0.646 χ̃0 2c 0.320 χ̃0 2s 0.012 χ̃0 4c 0.008 s̃R χ̃0 1s 0.997 χ̃0 4s 0.002 s̃L χ̃0 1s 0.016 χ̃−1 c 0.628 χ̃0 2s 0.317 χ̃−2 c 0.027 χ̃0 4s 0.011 t̃1 χ̃0 1t 0.216 χ̃0 4t 0.032 χ̃0 2t 0.105 χ̃+ 1 b 0.249 χ̃0 3t 0.171 χ̃+ 2 b 0.227 Table 3. Partial widths of superpartners channel BR channel BR t̃2 χ̃0 1t 0.025 χ̃+ 1 b 0.247 χ̃0 2t 0.111 χ̃+ 2 b 0.165 χ̃0 3t 0.114 t̃1h 0 0.045 χ̃0 4t 0.213 t̃1Z 0.080 b̃1 χ̃0 1b 0.055 χ̃−1 t 0.390 χ̃0 2b 0.220 χ̃−2 t 0.183 χ̃0 3b 0.063 t̃1W − 0.047 χ̃0 4b 0.041 b̃2 χ̃0 1b 0.023 χ̃−1 t 0.161 χ̃0 2b 0.091 χ̃−2 t 0.425 χ̃0 3b 0.079 t̃1W − 0.125 χ̃0 4b 0.095 g̃ d̃Ld∗ 0.019 c̃Lc∗ 0.020 d̃∗Ld 0.019 c̃∗Lc 0.020 d̃Rd∗ 0.038 c̃Rc∗ 0.036 d̃∗Rd 0.038 c̃∗Rc 0.036 ũLu∗ 0.020 b̃1b ∗ 0.078 ũ∗Lu 0.020 b̃∗1b 0.078 ũRu∗ 0.036 b̃2b ∗ 0.054 ũ∗Ru 0.036 b̃∗2b 0.054 s̃Ls∗ 0.019 t̃1t ∗ 0.097 s̃∗Ls 0.019 t̃∗1t 0.097 s̃Rs∗ 0.038 t̃2t ∗ 0.043 s̃∗Rs 0.038 t̃∗2t 0.043 11 Table 4. Partial widths of superpartners channel BR channel BR A0 bb∗ 0.858 τ̃−1 τ̃+ 2 0.004 τ+τ− 0.130 τ̃+ 1 τ̃−2 0.004 tt∗ 0.002 H0 bb∗ 0.859 τ̃−1 τ̃+ 1 0.003 τ+τ− 0.130 τ̃−1 τ̃+ 2 0.002 tt∗ 0.002 τ̃+ 1 τ̃−2 0.002 H+ cb∗ 0.001 tb∗ 0.818 τ+ντ 0.169 τ̃+ 1 ν̃τ 0.010 χ̃0 1 ẽ−Re+ 0.032 µ̃+ Rµ− 0.032 ẽ+ Re− 0.032 τ̃−1 τ+ 0.436 µ̃−Rµ+ 0.032 τ̃+ 1 τ− 0.436 χ̃0 2 χ̃0 1Z 0.001 τ̃−2 τ+ 0.037 χ̃0 1h 0 0.010 τ̃+ 2 τ− 0.037 ẽ−Le+ 0.056 ν̃eν ∗ e 0.064 ẽ+ Le− 0.056 ν̃∗e νe 0.064 µ̃−Lµ+ 0.056 ν̃µν∗µ 0.064 µ̃+ Lµ− 0.056 ν̃∗µνµ 0.064 τ̃−1 τ+ 0.135 ν̃τν∗τ 0.081 τ̃+ 1 τ− 0.135 ν̃∗τ ντ 0.081 χ̃0 3 χ̃0 1Z 0.080 χ̃0 2h 0 0.007 χ̃0 2Z 0.193 τ̃−1 τ+ 0.088 χ̃+ 1 W− 0.211 τ̃+ 1 τ− 0.088 χ̃−1 W+ 0.211 τ̃−2 τ+ 0.051 χ̃0 1h 0 0.016 τ̃+ 2 τ− 0.051 7. CROSS SECTIONS Using the parameter set (3) it is possible to calculate production cross sections of superpartners by appli- cation of the computer program PYTHIA [10]. These cross sections at center-of-mass energy √ s = 14 TeV are shown in Table 6. Table 5. Partial widths of superpartners channel BR channel BR χ̃0 4 χ̃0 1Z 0.016 µ̃−Rµ+ 0.001 χ̃0 2Z 0.009 µ̃+ Rµ− 0.001 χ̃+ 1 W− 0.208 τ̃−1 τ+ 0.061 χ̃−1 W+ 0.208 τ̃+ 1 τ− 0.061 χ̃0 1h 0 0.069 τ̃−2 τ+ 0.058 χ̃0 2h 0 0.171 τ̃+ 2 τ− 0.058 ẽ−Le+ 0.005 ν̃eν ∗ e 0.009 ẽ+ Le− 0.005 ν̃∗e νe 0.009 ẽ−Re+ 0.001 ν̃µν∗µ 0.009 ẽ+ Re− 0.001 ν̃∗µνµ 0.009 µ̃−Lµ+ 0.005 ν̃τν∗τ 0.010 µ̃+ Lµ− 0.005 ν̃∗τ ντ 0.010 χ̃+ 1 ν̃ee + 0.135 µ̃+ Lνµ 0.108 ν̃µµ+ 0.135 τ̃+ 1 ντ 0.261 ν̃ττ+ 0.176 τ̃+ 2 ντ 0.067 ẽ+ Lνe 0.108 χ̃0 1W + 0.010 χ̃+ 2 ν̃ee + 0.009 τ̃+ 2 ντ 0.051 ν̃µµ+ 0.009 χ̃+ 1 Z 0.206 ν̃ττ+ 0.105 χ̃0 1W + 0.079 ẽ+ Lνe 0.020 χ̃0 2W + 0.214 µ̃+ Lνµ 0.020 χ̃+ 1 h0 0.183 τ̃+ 1 ντ 0.104 Table 6. Cross sections of superpartners channel cross section gg → g̃g̃ σg̃g̃ = 0.307 pb gu → g̃ũ σg̃ũ = 0.891 pb du → d̃ũ σd̃ũ = 0.466 pb uu → χ̃+ 1 χ̃−1 σ χ̃+ 1 χ̃−1 = 0.157 pb du → χ̃+ 1 χ̃0 2 σ χ̃+ 1 χ̃0 2 = 0.208 pb Table 7. Lower limits on masses reached at colliders particle Condition Lower limit (GeV) Source χ̃±1 gaugino Mν̃ > 200 GeV 103 LEP 2 Mν̃ > Mχ̃± 85 LEP 2 any Mν̃ 45 Z width Higgsino M2 < 1 TeV 99 LEP 2 GMSB 150 D0 isolated photons RPV LLE worst case 87 LEP 2 LQD m0 > 500 GeV 88 LEP 2 χ̃0 1 indirect any tanβ, Mν̃ > 500 GeV 39 LEP 2 any tanβ, any m0 36 LEP 2 any tanβ, any m0, SUGRA Higgs 59 LEP 2 combined GMSB 93 LEP 2 combined RPV LLE worst case 23 LEP 2 ẽR eχ̃0 1 ∆M > 10 GeV 99 LEP 2 combined µ̃R µχ̃0 1 ∆M > 10 GeV 95 LEP 2 combined τ̃R τχ̃0 1 Mχ̃0 1 < 20 GeV 80 LEP 2 combined ν̃ 43 Z width µ̃R, τ̃R stable 86 LEP 2 combined t̃1 cχ̃0 1 any θmix, ∆M > 10 GeV 95 LEP 2 combined any θmix, Mχ̃0 1 ∼ 1 2 Mt̃ 115 CDF any θmix, and any ∆M 59 ALEPH blν̃ any θmix, ∆M > 7 GeV 96 LEP 2 combined g̃ any Mq̃ 195 CDF jets+ET q̃ Mq̃ = Mg̃ 300 CDF jets+ET 12 8. COMPARISON WITH EXPERIMENTS Comparison of the predicted MSSM spectrum with experimental data obtained at the LEP and TEVA- TRON [11] (see Table 7) shows, that the calculated masses exceed the lower limits on masses reached at colliders. New searches for superpartners will be made at the LHC. References 1. H.E. Haber. Introductory low-energy supersym- metry // arXiv: hep-ph/9306207. 2. C. Vafa, et al. Stringy reflections on LHC // http://www.claymath.org/workshops/lhc/. 3. P.S. Aspinwall. D-branes on Calabi-Yau mani- folds // arXiv: hep-th/0403166. 4. M.R. Douglas, B. Fiol and C. Römelsberger. The spectrum of BPS branes on a noncompact Calabi- Yau // JHEP. 2005, 09, p.1-57. 5. S. Katz, T. Pantev, and E. Sharpe. D-branes, orbifolds, and Ext groups // Nucl. Phys. 2003, B673, p.263-300. 6. W. Schmid. Homogeneous complex manifolds and representations of semisimple Lie groups // Proc. Natl. Acad. Sci. USA. 1968, 69, p.56-59. 7. J.J. Heckman, and C. Vafa. F-theory, GUTs, and the weak scale // arXiv:0809.1098 [hep-th]. 8. B.C. Allanach. SOFTSUSY2.0: a program for calculating supersymmetric spectra // Comput. Phys. Commun. 2002, 143, p.305-331. 9. M. Muhlleitner, A. Djouadi, and Y. Mambrini. SDECAY: a fortran code for the decays of the supersymmetric particles in the MSSM // Com- put. Phys. Commun. 2005, 168, p.46-70. 10. T. Sjöstrand, S. Mrenna and P. Skands. PYTHIA 6.4 Physics and Manual // JHEP. 2006, 05, p.1- 26. 11. M. Schmitt. Supersymmetry, Part II (Experi- ment) // Phys. Lett. 2004, B592, p.1014-1023. СТРУННЫЙ ПОДХОД К МИНИМАЛЬНОЙ СУПЕРСИММЕТРИЧНОЙ СТАНДАРТНОЙ МОДЕЛИ Ю.М. Малюта, Т.В. Обиход Теория суперструн применена для построения Минимальной суперсимметричной стандартной модели. Проведены вычисления спектра масс, парциальных ширин и сечений рождения суперпартнеров. Этот подход дает конкретные предсказания для поиска суперпартнеров на LHC. СТРУННИЙ ПIДХIД ДО МIНIМАЛЬНОЇ СУПЕРСИМЕТРИЧНОЇ СТАНДАРТНОЇ МОДЕЛI Ю.М. Малюта, Т.В. Обiход Теорiю суперструн застосовано для побудови Мiнiмальної суперсиметричної стандартної моделi. Вико- нано обчислення спектра масс, парцiальних ширин i перерiзiв народження суперпартнерiв. Цей пiдхiд дає конкретнi передбачення для пошуку суперпартнерiв на LHC. 13

Stringy approach to the Minimal Supersymmetric Standard Model

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