Abstract
The strongly coupled heterotic M-theory vacuum for both the observable and hidden sectors of the B − L MSSM theory is reviewed, including a discussion of the “bundle” constraints that both the observable sector SU(4) vector bundle and the hidden sector bundle induced from a single line bundle must satisfy. Gaugino condensation is then introduced within this context, and the hidden sector bundles that exhibit gaugino condensation are presented. The condensation scale is computed, singling out one line bundle whose associated condensation scale is low enough to be compatible with the energy scales available at the LHC. The corresponding region of Kähler moduli space where all bundle constraints are satisfied is presented. The generic form of the moduli dependent F-terms due to a gaugino superpotential — which spontaneously break N = 1 supersymmetry in this sector — is presented and then given explicitly for the unique line bundle associated with the low condensation scale. The moduli-dependent coefficients for each of the gaugino and scalar field soft supersymmetry breaking terms are computed leading to a low-energy effective Lagrangian for the observable sector matter fields. We then show that at a large number of points in Kähler moduli space that satisfy all “bundle” constraints, these coefficients are initial conditions for the renormalization group equations which, at low energy, lead to completely realistic physics satisfying all phenomenological constraints. Finally, we show that a substantial number of these initial points also satisfy a final constraint arising from the quadratic Higgs-Higgs conjugate soft supersymmetry breaking term.
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References
P. Hořava and E. Witten, Heterotic and type-I string dynamics from eleven-dimensions, Nucl. Phys. B 460 (1996) 506 [hep-th/9510209] [INSPIRE].
P. Hořava and E. Witten, Eleven-dimensional supergravity on a manifold with boundary, Nucl. Phys. B 475 (1996) 94 [hep-th/9603142] [INSPIRE].
A. Lukas, B. A. Ovrut, K. S. Stelle and D. Waldram, The Universe as a domain wall, Phys. Rev. D 59 (1999) 086001 [hep-th/9803235] [INSPIRE].
A. Lukas, B. A. Ovrut, K. S. Stelle and D. Waldram, Heterotic M-theory in five-dimensions, Nucl. Phys. B 552 (1999) 246 [hep-th/9806051] [INSPIRE].
A. Lukas, B. A. Ovrut and D. Waldram, On the four-dimensional effective action of strongly coupled heterotic string theory, Nucl. Phys. B 532 (1998) 43 [hep-th/9710208] [INSPIRE].
T. Banks and M. Dine, Couplings and scales in strongly coupled heterotic string theory, Nucl. Phys. B 479 (1996) 173 [hep-th/9605136] [INSPIRE].
R. Donagi, B. A. Ovrut, T. Pantev and D. Waldram, Nonperturbative vacua in heterotic M-theory, Class. Quant. Grav. 17 (2000) 1049 [INSPIRE].
V. Braun, Y.-H. He, B. A. Ovrut and T. Pantev, The Exact MSSM spectrum from string theory, JHEP 05 (2006) 043 [hep-th/0512177] [INSPIRE].
V. Braun, Y.-H. He, B. A. Ovrut and T. Pantev, A Standard model from the E8 × E8 heterotic superstring, JHEP 06 (2005) 039 [hep-th/0502155] [INSPIRE].
V. Braun, Y.-H. He, B. A. Ovrut and T. Pantev, A Heterotic standard model, Phys. Lett. B 618 (2005) 252 [hep-th/0501070] [INSPIRE].
V. Bouchard and R. Donagi, An SU(5) heterotic standard model, Phys. Lett. B 633 (2006) 783 [hep-th/0512149] [INSPIRE].
L. B. Anderson, J. Gray, Y.-H. He and A. Lukas, Exploring Positive Monad Bundles And A New Heterotic Standard Model, JHEP 02 (2010) 054 [arXiv:0911.1569] [INSPIRE].
V. Braun, P. Candelas, R. Davies and R. Donagi, The MSSM Spectrum from (0,2)-Deformations of the Heterotic Standard Embedding, JHEP 05 (2012) 127 [arXiv:1112.1097] [INSPIRE].
L. B. Anderson, J. Gray, A. Lukas and E. Palti, Two Hundred Heterotic Standard Models on Smooth Calabi-Yau Threefolds, Phys. Rev. D 84 (2011) 106005 [arXiv:1106.4804] [INSPIRE].
L. B. Anderson, J. Gray, A. Lukas and E. Palti, Heterotic Line Bundle Standard Models, JHEP 06 (2012) 113 [arXiv:1202.1757] [INSPIRE].
L. B. Anderson, A. Constantin, J. Gray, A. Lukas and E. Palti, A Comprehensive Scan for Heterotic SU(5) GUT models, JHEP 01 (2014) 047 [arXiv:1307.4787] [INSPIRE].
S. Groot Nibbelink, O. Loukas, F. Ruehle and P. K. S. Vaudrevange, Infinite number of MSSMs from heterotic line bundles?, Phys. Rev. D 92 (2015) 046002 [arXiv:1506.00879] [INSPIRE].
S. Groot Nibbelink, O. Loukas and F. Ruehle, (MS)SM-like models on smooth Calabi-Yau manifolds from all three heterotic string theories, Fortsch. Phys. 63 (2015) 609 [arXiv:1507.07559] [INSPIRE].
A. P. Braun, C. R. Brodie and A. Lukas, Heterotic Line Bundle Models on Elliptically Fibered Calabi-Yau Three-folds, JHEP 04 (2018) 087 [arXiv:1706.07688] [INSPIRE].
C. Schoen, On fiber products of rational elliptic surfaces with section, Math. Z. 197 (1988) 177.
V. Braun, B. A. Ovrut, T. Pantev and R. Reinbacher, Elliptic Calabi-Yau threefolds with Z(3) x Z(3) Wilson lines, JHEP 12 (2004) 062 [hep-th/0410055] [INSPIRE].
V. Braun, Y.-H. He, B. A. Ovrut and T. Pantev, Vector bundle extensions, sheaf cohomology, and the heterotic standard model, Adv. Theor. Math. Phys. 10 (2006) 525 [hep-th/0505041] [INSPIRE].
B. A. Ovrut, A. Purves and S. Spinner, A statistical analysis of the minimal SUSY B-L theory, Mod. Phys. Lett. A 30 (2015) 1550085 [arXiv:1412.6103] [INSPIRE].
B. A. Ovrut, A. Purves and S. Spinner, The minimal SUSY B − L model: from the unification scale to the LHC, JHEP 06 (2015) 182 [arXiv:1503.01473] [INSPIRE].
L. L. Everett, P. Fileviez Perez and S. Spinner, The Right Side of TeV Scale Spontaneous R-Parity Violation, Phys. Rev. D 80 (2009) 055007 [arXiv:0906.4095] [INSPIRE].
D. K. Ghosh, G. Senjanović and Y. Zhang, Naturally Light Sterile Neutrinos from Theory of R-parity, Phys. Lett. B 698 (2011) 420 [arXiv:1010.3968] [INSPIRE].
V. Barger, P. Fileviez Perez and S. Spinner, Three Layers of Neutrinos, Phys. Lett. B 696 (2011) 509 [arXiv:1010.4023] [INSPIRE].
B. Mukhopadhyaya, S. Roy and F. Vissani, Correlation between neutrino oscillations and collider signals of supersymmetry in an R-parity violating model, Phys. Lett. B 443 (1998) 191 [hep-ph/9808265] [INSPIRE].
E. J. Chun and J. S. Lee, Implication of Super-Kamiokande data on R-parity violation, Phys. Rev. D 60 (1999) 075006 [hep-ph/9811201] [INSPIRE].
E. J. Chun and S. K. Kang, One loop corrected neutrino masses and mixing in supersymmetric standard model without R-parity, Phys. Rev. D 61 (2000) 075012 [hep-ph/9909429] [INSPIRE].
M. Hirsch, M. A. Diaz, W. Porod, J. C. Romao and J. W. F. Valle, Neutrino masses and mixings from supersymmetry with bilinear R parity violation: A Theory for solar and atmospheric neutrino oscillations, Phys. Rev. D 62 (2000) 113008 [Erratum ibid. 65 (2002) 119901] [hep-ph/0004115] [INSPIRE].
P. Fileviez Perez and S. Spinner, The Minimal Theory for R-parity Violation at the LHC, JHEP 04 (2012) 118 [arXiv:1201.5923] [INSPIRE].
P. Fileviez Perez and S. Spinner, Supersymmetry at the LHC and The Theory of R-parity, Phys. Lett. B 728 (2014) 489 [arXiv:1308.0524] [INSPIRE].
G. Gamberini, G. Ridolfi and F. Zwirner, On Radiative Gauge Symmetry Breaking in the Minimal Supersymmetric Model, Nucl. Phys. B 331 (1990) 331 [INSPIRE].
Particle Data Group collaboration, Review of Particle Physics, Chin. Phys. C 38 (2014) 090001 [INSPIRE].
S. Dumitru, C. HERWIG and B. A. Ovrut, R-parity Violating Decays of Bino Neutralino LSPs at the LHC, JHEP 12 (2019) 042 [arXiv:1906.03174] [INSPIRE].
S. Dumitru, B. A. Ovrut and A. Purves, The R-parity Violating Decays of Charginos and Neutralinos in the B-L MSSM, JHEP 02 (2019) 124 [arXiv:1810.11035] [INSPIRE].
S. Dumitru, B. A. Ovrut and A. Purves, R-parity Violating Decays of Wino Chargino and Wino Neutralino LSPs and NLSPs at the LHC, JHEP 06 (2019) 100 [arXiv:1811.05581] [INSPIRE].
P. Fileviez Perez and S. Spinner, Spontaneous R-Parity Breaking in SUSY Models, Phys. Rev. D 80 (2009) 015004 [arXiv:0904.2213] [INSPIRE].
Z. Marshall, B. A. Ovrut, A. Purves and S. Spinner, Spontaneous R-Parity Breaking, Stop LSP Decays and the Neutrino Mass Hierarchy, Phys. Lett. B 732 (2014) 325 [arXiv:1401.7989] [INSPIRE].
V. Barger, P. Fileviez Perez and S. Spinner, Minimal gauged U(1)(B-L) model with spontaneous R-parity violation, Phys. Rev. Lett. 102 (2009) 181802 [arXiv:0812.3661] [INSPIRE].
V. Braun, Y.-H. He and B. A. Ovrut, Stability of the minimal heterotic standard model bundle, JHEP 06 (2006) 032 [hep-th/0602073] [INSPIRE].
V. Braun, Y.-H. He and B. A. Ovrut, Supersymmetric Hidden Sectors for Heterotic Standard Models, JHEP 09 (2013) 008 [arXiv:1301.6767] [INSPIRE].
A. Ashmore, S. Dumitru and B. A. Ovrut, Line Bundle Hidden Sectors for Strongly Coupled Heterotic Standard Models, arXiv:2003.05455 [INSPIRE].
M. Dine, R. Rohm, N. Seiberg and E. Witten, Gluino Condensation in Superstring Models, Phys. Lett. B 156 (1985) 55 [INSPIRE].
P. Hořava, Gluino condensation in strongly coupled heterotic string theory, Phys. Rev. D 54 (1996) 7561 [hep-th/9608019] [INSPIRE].
T. R. Taylor, Dilaton, gaugino condensation and supersymmetry breaking, Phys. Lett. B 252 (1990) 59 [INSPIRE].
A. Lukas, B. A. Ovrut and D. Waldram, Gaugino condensation in M-theory on S1 /Z(2), Phys. Rev. D 57 (1998) 7529 [hep-th/9711197] [INSPIRE].
A. Lukas, B. A. Ovrut and D. Waldram, Five-branes and supersymmetry breaking in M-theory, JHEP 04 (1999) 009 [hep-th/9901017] [INSPIRE].
I. Antoniadis and M. Quirós, On the M-theory description of gaugino condensation, Phys. Lett. B 416 (1998) 327 [hep-th/9707208] [INSPIRE].
E. Dudas, Supersymmetry breaking in the effective Hořava-Witten supergravity and quantization rules, Phys. Lett. B 416 (1998) 309 [hep-th/9709043] [INSPIRE].
H. P. Nilles, M. Olechowski and M. Yamaguchi, Supersymmetry breakdown at a hidden wall, Nucl. Phys. B 530 (1998) 43 [hep-th/9801030] [INSPIRE].
R. Minasian, M. Petrini and E. E. Svanes, On Heterotic Vacua with Fermionic Expectation Values, Fortsch. Phys. 65 (2017) 1700010 [arXiv:1702.01156] [INSPIRE].
V. S. Kaplunovsky and J. Louis, Model independent analysis of soft terms in effective supergravity and in string theory, Phys. Lett. B 306 (1993) 269 [hep-th/9303040] [INSPIRE].
K. Choi, H. B. Kim and C. Munoz, Four-dimensional effective supergravity and soft terms in M-theory, Phys. Rev. D 57 (1998) 7521 [hep-th/9711158] [INSPIRE].
S. K. Soni and H. A. Weldon, Analysis of the Supersymmetry Breaking Induced by N = 1 Supergravity Theories, Phys. Lett. B 126 (1983) 215 [INSPIRE].
J. Louis and Y. Nir, Some phenomenological implications of string loop effects, Nucl. Phys. B 447 (1995) 18 [hep-ph/9411429] [INSPIRE].
A. Brignole, L. E. Ibáñez and C. Muñoz, Soft supersymmetry breaking terms from supergravity and superstring models, Adv. Ser. Direct. High Energy Phys. 18 (1998) 125 [hep-ph/9707209] [INSPIRE].
L. Randall and R. Sundrum, Out of this world supersymmetry breaking, Nucl. Phys. B 557 (1999) 79 [hep-th/9810155] [INSPIRE].
G. F. Giudice, M. A. Luty, H. Murayama and R. Rattazzi, Gaugino mass without singlets, JHEP 12 (1998) 027 [hep-ph/9810442] [INSPIRE].
J. A. Bagger, T. Moroi and E. Poppitz, Anomaly mediation in supergravity theories, JHEP 04 (2000) 009 [hep-th/9911029] [INSPIRE].
P. Binetruy, M. K. Gaillard and B. D. Nelson, One loop soft supersymmetry breaking terms in superstring effective theories, Nucl. Phys. B 604 (2001) 32 [hep-ph/0011081] [INSPIRE].
K. Choi, A. Falkowski, H. P. Nilles, M. Olechowski and S. Pokorski, Stability of flux compactifications and the pattern of supersymmetry breaking, JHEP 11 (2004) 076 [hep-th/0411066] [INSPIRE].
K. Choi, A. Falkowski, H. P. Nilles and M. Olechowski, Soft supersymmetry breaking in KKLT flux compactification, Nucl. Phys. B 718 (2005) 113 [hep-th/0503216] [INSPIRE].
K. Uhlenbeck and S. T. Yau, On the existence of hermitian-yang-mills connections in stable vector bundles, Commun. Pure Appl. Math. 39 (1986) S257.
S. K. Donaldson, Anti self-dual yang-mills connections over complex algebraic surfaces and stable vector bundles, Proc. Lond. Math. Soc. s3-50 (1985) 1.
B. A. Ovrut, Vacuum Constraints for Realistic Strongly Coupled Heterotic M-Theories, Symmetry 10 (2018) 723 [arXiv:1811.08892] [INSPIRE].
M. Dine, N. Seiberg and E. Witten, Fayet-Iliopoulos Terms in String Theory, Nucl. Phys. B 289 (1987) 589 [INSPIRE].
A. Lukas and K. S. Stelle, Heterotic anomaly cancellation in five-dimensions, JHEP 01 (2000) 010 [hep-th/9911156] [INSPIRE].
R. Blumenhagen, G. Honecker and T. Weigand, Loop-corrected compactifications of the heterotic string with line bundles, JHEP 06 (2005) 020 [hep-th/0504232] [INSPIRE].
R. Blumenhagen, S. Moster and T. Weigand, Heterotic GUT and standard model vacua from simply connected Calabi-Yau manifolds, Nucl. Phys. B 751 (2006) 186 [hep-th/0603015] [INSPIRE].
J. Gray and A. Lukas, Gauge five-brane moduli in four-dimensional heterotic models, Phys. Rev. D 70 (2004) 086003 [hep-th/0309096] [INSPIRE].
M. Brandle and A. Lukas, Five-branes in heterotic brane world theories, Phys. Rev. D 65 (2002) 064024 [hep-th/0109173] [INSPIRE].
A. Lukas, B. A. Ovrut and D. Waldram, Nonstandard embedding and five-branes in heterotic M-theory, Phys. Rev. D 59 (1999) 106005 [hep-th/9808101] [INSPIRE].
R. Deen, B. A. Ovrut and A. Purves, The minimal SUSY B − L model: simultaneous Wilson lines and string thresholds, JHEP 07 (2016) 043 [arXiv:1604.08588] [INSPIRE].
B. A. Ovrut, A. Purves and S. Spinner, Wilson Lines and a Canonical Basis of SU(4) Heterotic Standard Models, JHEP 11 (2012) 026 [arXiv:1203.1325] [INSPIRE].
B. A. Ovrut, T. Pantev and J. Park, Small instanton transitions in heterotic M-theory, JHEP 05 (2000) 045 [hep-th/0001133] [INSPIRE].
M. Brandle, Aspects of branes in (heterotic) M-theory, Ph.D. thesis, Humboldt University, Berlin (2003).
L. B. Anderson, J. Gray, A. Lukas and B. Ovrut, Stabilizing the Complex Structure in Heterotic Calabi-Yau Vacua, JHEP 02 (2011) 088 [arXiv:1010.0255] [INSPIRE].
L. B. Anderson, J. Gray, A. Lukas and B. Ovrut, Stabilizing All Geometric Moduli in Heterotic Calabi-Yau Vacua, Phys. Rev. D 83 (2011) 106011 [arXiv:1102.0011] [INSPIRE].
L. B. Anderson, J. Gray, A. Lukas and B. Ovrut, The Atiyah Class and Complex Structure Stabilization in Heterotic Calabi-Yau Compactifications, JHEP 10 (2011) 032 [arXiv:1107.5076] [INSPIRE].
F. Paccetti Correia and M. G. Schmidt, Moduli stabilization in heterotic M-theory, Nucl. Phys. B 797 (2008) 243 [arXiv:0708.3805] [INSPIRE].
N. Yamatsu, Finite-Dimensional Lie Algebras and Their Representations for Unified Model Building, arXiv:1511.08771 [INSPIRE].
M. Headrick and T. Wiseman, Numerical Ricci-flat metrics on K 3, Class. Quant. Grav. 22 (2005) 4931 [hep-th/0506129] [INSPIRE].
M. R. Douglas, R. L. Karp, S. Lukic and R. Reinbacher, Numerical Calabi-Yau metrics, J. Math. Phys. 49 (2008) 032302 [hep-th/0612075] [INSPIRE].
V. Braun, T. Brelidze, M. R. Douglas and B. A. Ovrut, Calabi-Yau Metrics for Quotients and Complete Intersections, JHEP 05 (2008) 080 [arXiv:0712.3563] [INSPIRE].
M. Headrick and A. Nassar, Energy functionals for Calabi-Yau metrics, Adv. Theor. Math. Phys. 17 (2013) 867 [arXiv:0908.2635] [INSPIRE].
M. R. Douglas, R. L. Karp, S. Lukic and R. Reinbacher, Numerical solution to the hermitian Yang-Mills equation on the Fermat quintic, JHEP 12 (2007) 083 [hep-th/0606261] [INSPIRE].
L. B. Anderson, V. Braun and B. A. Ovrut, Numerical Hermitian Yang-Mills Connections and Kähler Cone Substructure, JHEP 01 (2012) 014 [arXiv:1103.3041] [INSPIRE].
L. B. Anderson, V. Braun, R. L. Karp and B. A. Ovrut, Numerical Hermitian Yang-Mills Connections and Vector Bundle Stability in Heterotic Theories, JHEP 06 (2010) 107 [arXiv:1004.4399] [INSPIRE].
W. Cui and J. Gray, Numerical Metrics, Curvature Expansions and Calabi-Yau Manifolds, JHEP 05 (2020) 044 [arXiv:1912.11068] [INSPIRE].
L. B. Anderson, M. Gerdes, J. Gray, S. Krippendorf, N. Raghuram and F. Ruehle, Moduli-dependent Calabi-Yau and SU(3)-structure metrics from Machine Learning, JHEP 05 (2021) 013 [arXiv:2012.04656] [INSPIRE].
M. R. Douglas, S. Lakshminarasimhan and Y. Qi, Numerical Calabi-Yau metrics from holomorphic networks, arXiv:2012.04797 [INSPIRE].
J. Keller and S. Lukic, Numerical Weil-Petersson metrics on moduli spaces of Calabi-Yau manifolds, J. Geom. Phys. 92 (2015) 252 [arXiv:0907.1387] [INSPIRE].
V. Braun, T. Brelidze, M. R. Douglas and B. A. Ovrut, Eigenvalues and Eigenfunctions of the Scalar Laplace Operator on Calabi-Yau Manifolds, JHEP 07 (2008) 120 [arXiv:0805.3689] [INSPIRE].
A. Ashmore, Eigenvalues and eigenforms on Calabi-Yau threefolds, arXiv:2011.13929 [INSPIRE].
R. Deen, B. A. Ovrut and A. Purves, Supersymmetric Sneutrino-Higgs Inflation, Phys. Lett. B 762 (2016) 441 [arXiv:1606.00431] [INSPIRE].
S. P. Martin, A Supersymmetry primer, Adv. Ser. Direct. High Energy Phys. 18 (1998) 1 [hep-ph/9709356] [INSPIRE].
ATLAS and CMS collaborations, Studies of rare top quark processes: tZq, tγq, \( t\overline{t}t\overline{t} \) flavour changing neutral currents, PoS LHCP2019 (2019) 106 [INSPIRE].
ATLAS collaboration, Search for flavour-changing neutral currents in processes with one top quark and a photon using 81 fb−1 of pp collisions at \( \sqrt{s} \) = 13 TeV with the ATLAS experiment, Phys. Lett. B 800 (2020) 135082 [arXiv:1908.08461] [INSPIRE].
ATLAS collaboration, Sensitivity of searches for the flavour-changing neutral current decay t → qZ using the upgraded ATLAS experiment at the High Luminosity LHC, ATL-PHYS-PUB-2019-001 [INSPIRE].
ATLAS collaboration, Search for flavour-changing neutral currents tZ interactions in pp collisions at \( \sqrt{s} \) = 13 TeV with ATLAS, in 11th International Workshop on Top Quark Physics, (2018) [arXiv:1812.01363] [INSPIRE].
ATLAS collaboration, Search for flavour-changing neutral current top-quark decays t → qZ in proton-proton collisions at \( \sqrt{s} \) = 13 TeV with the ATLAS detector, JHEP 07 (2018) 176 [arXiv:1803.09923] [INSPIRE].
M. Ambroso and B. Ovrut, The B-L/Electroweak Hierarchy in Heterotic String and M-theory, JHEP 10 (2009) 011 [arXiv:0904.4509] [INSPIRE].
M. Ambroso and B. A. Ovrut, The B-L/Electroweak Hierarchy in Smooth Heterotic Compactifications, Int. J. Mod. Phys. A 25 (2010) 2631 [arXiv:0910.1129] [INSPIRE].
M. Ambroso and B. A. Ovrut, The Mass Spectra, Hierarchy and Cosmology of B-L MSSM Heterotic Compactifications, Int. J. Mod. Phys. A 26 (2011) 1569 [arXiv:1005.5392] [INSPIRE].
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Ashmore, A., Dumitru, S. & Ovrut, B.A. Explicit soft supersymmetry breaking in the heterotic M-theory B − L MSSM. J. High Energ. Phys. 2021, 33 (2021). https://doi.org/10.1007/JHEP08(2021)033
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DOI: https://doi.org/10.1007/JHEP08(2021)033