- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Nonholomorphic impact on t−b−τ Yukawa unification in minimal gauge mediated supersymmetry breaking

Ali Çiçi1,2,*, Büşra Niş3,†, and Cem Salih Ün3,‡

  • 1Orhaneli Türkan-Sait Y𝚤lmaz High School, TR16980 Bursa, Türkiye
  • 2Department of Physics, Faculty of Engineering and Natural Sciences, Bursa Technical University, TR16310, Bursa, Türkiye
  • 3Department of Physics, Bursa Uludağ University, TR16059 Bursa, Türkiye

  • *Contact author: ali.cici@cern.ch
  • †Contact author: busranis@uludag.edu.tr
  • ‡Contact author: cemsalihun@uludag.edu.tr
PDF

Phys. Rev. D 114, 035043 – Published 28 August, 2026

DOI: https://doi.org/10.1103/5lq8-wn6g

Abstract

We study and explore the low scale implications of Yukawa unification (YU) in the minimal gauge mediated supersymmetry breaking models. We also assume nonzero nonholomorphic terms, with which the YU solutions can be accommodated in the cases with μ>0. These results can be considered a direct effect from the nonholomorphic terms, but they also lead to testable low scale implications compatible with YU. We observe abundant solutions consistent with the Higgs boson mass. This constraint leads to heavy strongly interacting supersymmetric particles, while the electroweak sector can be relatively light and can be probed by several experiments. We find that the chargino can be lighter than 1 TeV and it is degenerate with the lightest neutralino in most of these solutions. Consistent solutions in this region can accommodate charginos as light as about 120 GeV, and they will likely be tested soon by the analyses over the compressed spectra. These solutions are also subjected in the lifetime analyses. Our analyses identify such light charginos as decaying in about 10−2  ns. Probing such points may need a slight improvement in the sensitivity of current analyses, and one can expect them to be tested very soon. In the same region, the stau is found to be another light supersymmetric particle, and some of the solutions can be inconsistently lighter. We find that it can weigh as light as about 600 GeV consistently, and it can be tested over its lifetime. We summarize and also exemplify our findings with five benchmark scenarios. Furthermore, the benchmark solutions also reveal that the solutions can be tested in heavy Higgs boson searches, which shape the whole Higgs boson spectrum in models.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (90)

  1. A. Cici, B. Nis, and C. S. Un, Circular future of Yukawa unification in supersymmetric Pati-Salam model: Stop on neutralino, arXiv:2603.25825.
  2. CMS Collaboration, Search for long-lived particles decaying to jets with displaced vertices in proton-proton collisions at s=13  TeV, Phys. Rev. D 104, 052011 (2021).
  3. CMS Collaboration, Search for long-lived particles using displaced vertices and missing transverse momentum in proton-proton collisions at s=13  TeV, Phys. Rev. D 109, 112005 (2024).
  4. ATLAS Collaboration, Search for long-lived charged particles using large specific ionisation loss and time of flight in 140  fb−1 of pp collisions at s=13  TeV with the ATLAS detector, J. High Energy Phys. 07 (2025) 140.
  5. ATLAS Collaboration, Search for long-lived charginos and τ-sleptons using final states with a disappearing track in pp collisions at s=13  TeV with the ATLAS detector, J. High Energy Phys. 07 (2026) 152.
  6. G. F. Giudice and R. Rattazzi, Theories with gauge mediated supersymmetry breaking, Phys. Rep. 322, 419 (1999).
  7. P. Meade, N. Seiberg, and D. Shih, General gauge mediation, Prog. Theor. Phys. Suppl. 177, 143 (2009).
  8. S. Dimopoulos, S. D. Thomas, and J. D. Wells, Sparticle spectroscopy and electroweak symmetry breaking with gauge mediated supersymmetry breaking, Nucl. Phys. B488, 39 (1997).
  9. U. Ellwanger and C. Hugonie, Constraints from charge and color breaking minima in the (M+1)SSM, Phys. Lett. B 457, 299 (1999).
  10. ATLAS Collaboration, Observation of a new particle in the search for the standard model Higgs boson with the ATLAS detector at the LHC, Phys. Lett. B 716, 1 (2012).
  11. CMS Collaboration, Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC, Phys. Lett. B 716, 30 (2012).
  12. CMS Collaboration, Observation of a new boson with mass near 125 GeV in pp collisions at s=7 and 8 TeV, J. High Energy Phys. 06 (2013) 081.
  13. M. A. Ajaib, I. Gogoladze, F. Nasir, and Q. Shafi, Revisiting mGMSB in light of a 125 GeV Higgs, Phys. Lett. B 713, 462 (2012).
  14. J. Bagger, E. Poppitz, and L. Randall, Destabilizing divergences in supergravity theories at two loops, Nucl. Phys. B455, 59 (1995).
  15. S. P. Martin, Dimensionless supersymmetry breaking couplings, flat directions, and the origin of intermediate mass scales, Phys. Rev. D 61, 035004 (2000).
  16. U. Chattopadhyay, D. Das, and S. Mukherjee, Exploring non-holomorphic soft terms in the framework of gauge mediated supersymmetry breaking, J. High Energy Phys. 01 (2018) 158.
  17. M. I. Ali, M. Chakraborti, U. Chattopadhyay, and S. Mukherjee, Muon and electron (g−2) anomalies with non-holomorphic interactions in MSSM, Eur. Phys. J. C 83, 60 (2023).
  18. S. Chakraborty and T. S. Roy, Radiatively generated source of flavor universal scalar soft masses, Phys. Rev. D 100, 035020 (2019).
  19. C. S. Ün, c. H. Tany𝚤ld𝚤z𝚤, S. Kerman, and L. Solmaz, Generalized soft breaking leverage for the MSSM, Phys. Rev. D 91, 105033 (2015).
  20. M. Rehman and S. Heinemeyer, Nonholomorphic soft-term contributions to the Higgs-boson masses in the Feynman diagrammatic approach, Phys. Rev. D 107, 095033 (2023).
  21. C. S. Un, Low fine-tuning with heavy higgsinos in Yukawa unified SUSY GUTs, Turk. J. Phys. 48, 1 (2024).
  22. S. Israr, M. E. Gómez, and M. Rehman, Nonholomorphic higgsino mass term effects on muon g−2 and dark matter relic density in flavor symmetry-based minimal supersymmetric standard model, Particles 8, 30 (2025).
  23. S. Israr and M. Rehman, Higgs decay to Zγ in the minimal supersymmetric standard model and its nonholomorphic extension, Eur. Phys. J. Plus 140, 397 (2025).
  24. M. Rehman and S. Heinemeyer, Toward a refined understanding of nonholomorphic soft SUSY-breaking effects on the Higgs boson mass spectra, Phys. Rev. D 111, 115027 (2025).
  25. B. Nis and C. S. Un, Non-holomorphic contributions in GMSB with adjoint messengers, Eur. Phys. J. C 86, 235 (2026).
  26. S. P. Martin and M. T. Vaughn, Regularization dependence of running couplings in softly broken supersymmetry, Phys. Lett. B 318, 331 (1993).
  27. I. Gogoladze, A. Mustafayev, Q. Shafi, and C. S. Un, Yukawa unification and sparticle spectroscopy in gauge mediation models, Phys. Rev. D 91, 096005 (2015).
  28. B. de Wit, M. T. Grisaru, and M. Rocek, Nonholomorphic corrections to the one loop N=2 superYang-Mills action, Phys. Lett. B 374, 297 (1996).
  29. D. Bellisai, F. Fucito, M. Matone, and G. Travaglini, Nonholomorphic terms in N=2 SUSY Wilsonian actions and the renormalization group equation, Phys. Rev. D 56, 5218 (1997).
  30. M. Henningson, Extended superspace, higher derivatives and SL(2,Z) duality, Nucl. Phys. B458, 445 (1996).
  31. F. Gonzalez-Rey and M. Rocek, Nonholomorphic N=2 terms in N=4 SYM: One loop calculation in N=2 superspace, Phys. Lett. B 434, 303 (1998).
  32. E. I. Buchbinder, I. L. Buchbinder, and S. M. Kuzenko, Nonholomorphic effective potential in N=4 SU(N) SYM, Phys. Lett. B 446, 216 (1999).
  33. I. Antoniadis, E. Dudas, D. M. Ghilencea, and P. Tziveloglou, MSSM with dimension-five operators (MSSM5), Nucl. Phys. B808, 155 (2009).
  34. N. Arkani-Hamed and R. Rattazzi, Exact results for nonholomorphic masses in softly broken supersymmetric gauge theories, Phys. Lett. B 454, 290 (1999).
  35. I. Gogoladze, R. Khalid, S. Raza, and Q. Shafi, t−b−τ Yukawa unification for μ<0 with a sub-TeV sparticle spectrum, J. High Energy Phys. 12 (2010) 055.
  36. L. J. Hall, R. Rattazzi, and U. Sarid, The top quark mass in supersymmetric SO(10) unification, Phys. Rev. D 50, 7048 (1994).
  37. R. Aliberti et al., The anomalous magnetic moment of the muon in the standard model: An update, Phys. Rep. 1143, 1 (2025).
  38. Muon g−2 Collaboration, Measurement of the positive muon anomalous magnetic moment to 127 ppb, Phys. Rev. Lett. 135, 101802 (2025).
  39. D. A. Demir and C. S. Ün, Stop on top: SUSY parameter regions, fine-tuning constraints, Phys. Rev. D 90, 095015 (2014).
  40. M. Rehman and S. Heinemeyer, Lepton flavor violation in nonholomorphic soft SUSY-breaking scenarios: Experimental limits and excesses, Eur. Phys. J. C 85, 638 (2025).
  41. M. Rehman, Rabish, and S. Ajmal, Impact of nonholomorphic soft SUSY-breaking terms on two-body gluino decays in the MSSM, Eur. Phys. J. Plus 140, 987 (2025).
  42. T. Moroi, The muon anomalous magnetic dipole moment in the minimal supersymmetric standard model, Phys. Rev. D 53, 6565 (1996).
  43. S. P. Martin and J. D. Wells, Muon anomalous magnetic dipole moment in supersymmetric theories, Phys. Rev. D 64, 035003 (2001).
  44. G. F. Giudice, P. Paradisi, A. Strumia, and A. Strumia, Correlation between the Higgs decay rate to two photons and the muon g−2, J. High Energy Phys. 10 (2012) 186.
  45. H. Fargnoli, C. Gnendiger, S. Paßehr, D. Stöckinger, and H. Stöckinger-Kim, Two-loop corrections to the muon magnetic moment from fermion/sfermion loops in the MSSM: Detailed results, J. High Energy Phys. 02 (2014) 070.
  46. H. Baer, S. Kraml, S. Sekmen, and H. Summy, Dark matter allowed scenarios for Yukawa-unified SO(10) SUSY GUTs, J. High Energy Phys. 03 (2008) 056.
  47. G. Belanger, F. Boudjema, A. Pukhov, and R. K. Singh, Constraining the MSSM with universal gaugino masses and implication for searches at the LHC, J. High Energy Phys. 11 (2009) 026.
  48. W. Porod, spheno, a program for calculating supersymmetric spectra, SUSY particle decays and SUSY particle production at e+e− colliders, Comput. Phys. Commun. 153, 275 (2003).
  49. M. D. Goodsell, K. Nickel, and F. Staub, Two-loop Higgs mass calculations in supersymmetric models beyond the MSSM with sarah and spheno, Eur. Phys. J. C 75, 32 (2015).
  50. F. Staub, sarah, arXiv:0806.0538.
  51. F. Staub, Introduction to sarah and related tools, Proc. Sci. CORFU2015 (2016) 027 [arXiv:1509.07061].
  52. J. Hisano, H. Murayama, and T. Yanagida, Nucleon decay in the minimal supersymmetric SU(5) grand unification, Nucl. Phys. B402, 46 (1993).
  53. Y. Yamada, SUSY and GUT threshold effects in SUSY SU(5) models, Z. Phys. C 60, 83 (1993).
  54. J. L. Chkareuli and I. G. Gogoladze, Unification picture in minimal supersymmetric SU(5) model with string remnants, Phys. Rev. D 58, 055011 (1998).
  55. Particle Data Group, Review of particle physics, Chin. Phys. C 38, 090001 (2014).
  56. ATLAS Collaboration, Search for squarks and gluinos in final states with one isolated lepton, jets, and missing transverse momentum at s=13 with the ATLAS detector, Eur. Phys. J. C 81, 600 (2021).
  57. ATLAS Collaboration, Search for squarks and gluinos in final states with jets and missing transverse momentum using 139  fb−1 of s=13  TeV pp collision data with the ATLAS detector, J. High Energy Phys. 02 (2021) 143.
  58. ATLAS Collaboration, SUSY summary plots March 2022, Report No. ATL-PHYS-PUB-2022-013.
  59. Belle-II Collaboration, Measurement of the photon-energy spectrum in inclusive B→Xsγ decays identified using hadronic decays of the recoil B meson in 2019–2021 Belle II data, Report No. BELLE2-CONF-PH-2022-018, 2022, arXiv:2210.10220.
  60. CMS Collaboration, Combination of the ATLAS, CMS and LHCb results on the B(s)0→μ+μ− decays, Report No. CMS-PAS-BPH-20-003, 2020.
  61. ALEPH Collaboration, Search for charginos nearly mass degenerate with the lightest neutralino in e+e− collisions at center-of-mass energies up to 209-GeV, Phys. Lett. B 533, 223 (2002).
  62. LEP Working Group for Higgs boson searches, ALEPH, DELPHI, L3, and OPAL Collaborations, Search for the standard model Higgs boson at LEP, Phys. Lett. B 565, 61 (2003).
  63. ALEPH, DELPHI, L3, OPAL, and LEP Electroweak Collaborations, Electroweak measurements in electron-positron collisions at W-boson-pair energies at LEP, Phys. Rep. 532, 119 (2013).
  64. CMS Collaboration, A search for decays of the Higgs boson to invisible particles in events with a top-antitop quark pair or a vector boson in proton-proton collisions at s=13  TeV, Eur. Phys. J. C 83, 933 (2023).
  65. H. E. Haber and D. O’Neil, Basis-independent methods for the two-Higgs-doublet model III: The CP-conserving limit, custodial symmetry, and the oblique parameters S, T, U, Phys. Rev. D 83, 055017 (2011).
  66. Particle Data Group, Review of particle physics, Phys. Rev. D 110, 030001 (2024).
  67. B. C. Allanach, A. Djouadi, J. L. Kneur, W. Porod, and P. Slavich, Precise determination of the neutral Higgs boson masses in the MSSM, J. High Energy Phys. 09 (2004) 044.
  68. H. Bahl, S. Heinemeyer, W. Hollik, and G. Weiglein, Theoretical uncertainties in the MSSM Higgs boson mass calculation, Eur. Phys. J. C 80, 497 (2020).
  69. E. Bagnaschi, J. Pardo Vega, and P. Slavich, Improved determination of the Higgs mass in the MSSM with heavy superpartners, Eur. Phys. J. C 77, 334 (2017).
  70. P. Athron, J.-h. Park, T. Steudtner, D. Stöckinger, and A. Voigt, Precise Higgs mass calculations in (non-)minimal supersymmetry at both high and low scales, J. High Energy Phys. 01 (2017) 079.
  71. P. Drechsel, R. Gröber, S. Heinemeyer, M. M. Muhlleitner, H. Rzehak, and G. Weiglein, Higgs-boson masses and mixing matrices in the NMSSM: Analysis of on-shell calculations, Eur. Phys. J. C 77, 366 (2017).
  72. H. Bahl, I. Sobolev, and G. Weiglein, The light MSSM Higgs boson mass for large tanβ and complex input parameters, Eur. Phys. J. C 80, 1063 (2020).
  73. S. R. Choudhury and N. Gaur, Dileptonic decay of B(s) meson in SUSY models with large tan Beta, Phys. Lett. B 451, 86 (1999).
  74. K. S. Babu and C. F. Kolda, Higgs mediated B0→μ+μ− in minimal supersymmetry, Phys. Rev. Lett. 84, 228 (2000).
  75. FCC Collaboration, Future circular collider feasibility study report: Volume 1, physics, experiments, detectors, Eur. Phys. J. C 85, 1468 (2025).
  76. FCC Collaboration, Future circular collider feasibility study report: Volume 2, accelerators, technical infrastructure and safety, Eur. Phys. J. Special Topics 234, 5713 (2025).
  77. FCC Collaboration, Future circular collider feasibility study report: Volume 3 civil engineering, implementation and sustainability, Eur. Phys. J. Special Topics 234, 33 (2025).
  78. CMS Collaboration, Search for supersymmetry in final states with disappearing tracks in proton-proton collisions at s=13  TeV, Phys. Rev. D 109, 072007 (2024).
  79. ATLAS Collaboration, Search for pairs of muons with small displacements in pp collisions at s=13  TeV with the ATLAS detector, Report No. ATLAS-CONF-2023-018.
  80. ATLAS Collaboration, Search for heavy Higgs bosons decaying into two tau leptons with the ATLAS detector using pp collisions at s=13  TeV, Phys. Rev. Lett. 125, 051801 (2020).
  81. CMS Collaboration, Searches for additional Higgs bosons and for vector leptoquarks in ττ final states in proton-proton collisions at s=13  TeV, J. High Energy Phys. 07 (2023) 073.
  82. T. Moroi, H. Murayama, and M. Yamaguchi, Cosmological constraints on the light stable gravitino, Phys. Lett. B 303, 289 (1993).
  83. L. Roszkowski, S. Trojanowski, and K. Turzyński, Neutralino and gravitino dark matter with low reheating temperature, J. High Energy Phys. 11 (2014) 146.
  84. J. Pradler and F. D. Steffen, Thermal gravitino production and collider tests of leptogenesis, Phys. Rev. D 75, 023509 (2007).
  85. G. Georgilas and V. C. Spanos, Gravitino freeze-in dark matter with an additional scalar field, arXiv:2606.03448.
  86. V. S. Rychkov and A. Strumia, Thermal production of gravitinos, Phys. Rev. D 75, 075011 (2007).
  87. M. Viel, J. Lesgourgues, M. G. Haehnelt, S. Matarrese, and A. Riotto, Constraining warm dark matter candidates including sterile neutrinos and light gravitinos with WMAP and the Lyman-alpha forest, Phys. Rev. D 71, 063534 (2005).
  88. J. L. Feng, M. Kamionkowski, and S. K. Lee, Light gravitinos at colliders and implications for cosmology, Phys. Rev. D 82, 015012 (2010).
  89. M. Deshpande, J. Hamann, D. Sengupta, M. White, A. G. Williams, and Y. Y. Y. Wong, Revisiting cosmological constraints on supersymmetric SuperWIMPs, Eur. Phys. J. C 84, 667 (2024).
  90. M. Nemevšek and Y. Zhang, Dark matter dilution mechanism through the lens of large-scale structure, Phys. Rev. Lett. 130, 121002 (2023).

Outline

Information

Phys. Rev. D 114, 035043– Published 28 August, 2026
  • Received 12 May 2026
  • Accepted 11 August 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation