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Probing the Supersymmetric Grand Unified Theories at the Future Proton-Proton Colliders and Hyper-Kamiokande Experiment Tianjun Li Institute of Theoretical Physics, Chinese Academy of Sciences Interdisciplinary Center for Theoretical Study, University of Science and Technology of China, Peng Huanwu Center for Fundamental Theory, June 9, 2023 Tianjun Li ITP-CAS The Nature The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful. If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living. Jules H. Poincare Tianjun Li ITP-CAS The Standard Model The particle physics Standard Model (SM) is a model that describes the elementary particles in the nature and the fundamental interactions between them. Tianjun Li ITP-CAS Fundamental Interactions Interactions Gravity Strong Weak Hypercharge Invariant Diffeomorphism Gauge Gauge Gauge Tianjun Li Symmetry SU(3)C SU(2)L U(1)Y ITP-CAS Fields Graviton Gluon W ±, W 0 B0 Spin 2 1 1 1 Elementary Particles I Three families of SM fermions:  Quarks : Q1 =  U U U D D D , (U U U)R , (D D D)R . L  Leptons : L1 = ν E  , L I One Higgs doublet Breaking SU(2)L × U(1)Y down to the U(1)EM .  H = Tianjun Li H0 H−  ITP-CAS . ER . The convincing evidence for new physics beyond the SM: I Dark energy I Dark matter I Neutrino masses and mixings I Baryon asymmetry I Inflation The SM is incomplete! Tianjun Li ITP-CAS Major Theoretical Problems in the SM I Fine-tuning problems Cosmological constant problem, gauge hierarchy problem, strong CP probelm, and the SM fermion mass hierarchies. I Aesthetic problems: Interaction unification, fermion unification, charge quantization, gauge coupling unification. I Stability problem. The aesthetic problems can be solved in the Grand Unified Theories (GUTs) if the SM gauge couplings are unified. Tianjun Li ITP-CAS Gauge Hierarchy Problem −L = λf Hf f + λS |H|2 |S|2 . |λf |2 2 2 ∆mH = − 2 ΛUV + 8π Tianjun Li λS 2 . Λ 16π 2 UV ITP-CAS Gauge Hierarchy Problem Tianjun Li ITP-CAS Supersymmetry I A supersymmetry is a space-time symmetry, which turns a bosonic state into a fermionic state, and vice versa. Q|Bosoni = |Fermioni, Q|Fermioni = |Bosoni. I Algebra: supersymmetry generator Q is a fermionic operator with spin-1/2. {Q, Q † } = P µ , {Q, Q} = {Q † , Q † } = 0, [P µ , Q] = [P µ , Q † ] = 0. I Each supermultiplet contains an equal number of fermion and boson degrees of freedom. Tianjun Li ITP-CAS The Supersymmetry Standard Model I Four-dimesional N = 1 supersymmetry: Kähler potential, superpotential, gauge kinetic function. I A chiral SM fermion has a complex scalar partner. I Gauge bosons and Higgs fields have a spin 1/2 partner. I Graviton has a spin 3/2 partner. Tianjun Li ITP-CAS The Minimal Supersymmetry Standard Model (MSSM) I Two Higgs doublets Hu and Hd : holomorphic superpotential and anomaly cancellation. I Unlike the SM, proton can decay at the renormalizable level in the SSMs. To forbid the proton decay operaors, we introduce a Z2 R symmetry: R = (−1)3B−L+2s . I The SM particle are even while the supersymmetric particles are odd. I Dark matter: neutralino, sneutrino, gravitino, etc. Tianjun Li ITP-CAS Names squarks quarks sleptons leptons Higgs Higgsinos Q u d L e Hu Hd spin 0 (e uL deL ) eR∗ u deR∗ (e ν e eL ) ∗ e eR + (Hu Hu0 ) (Hd0 Hd− ) spin 1/2 SU(3)C , SU(2)L , U(1)Y (uL dL ) uR† dR† (ν eL ) eR† e+ H e 0) (H u u e0 H e −) (H d d ( 3, 2 , 61 ) ( 3, 1, − 23 ) ( 3, 1, 31 ) ( 1, 2 , − 12 ) ( 1, 1, 1) ( 1, 2 , + 12 ) ( 1, 2 , − 12 ) Table : Chiral supermultiplets in the Minimal Supersymmetric Standard Model. The spin-0 fields are complex scalars, and the spin-1/2 fields are left-handed two-component Weyl fermions. Tianjun Li ITP-CAS Names gluino, gluon Winos, W bosons Bino, B boson spin 1/2 ge f± W f0 W e0 B spin 1 g ± W W0 B0 SU(3)C , SU(2)L , U(1)Y ( 8, 1 , 0) ( 1, 3 , 0) ( 1, 1 , 0) Table : Gauge supermultiplets in the Minimal Supersymmetric Standard Model. Neutralinos: neutral Higgsinos, Wino and Bino. Chargino: charged Higgsinos and Wino. Tianjun Li ITP-CAS Gauge Coupling Unification for the SM and MSSM Tianjun Li ITP-CAS The Supersymmetric Standard Models I A natural solution to the gauge hierarchy problem in the SM. I Gauge coupling unification can be achieved. I The Lightest Supersymmetric Particle (LSP) such as the LSP neutralino etc can be a dark matter candidate. I The electroweak gauge symmetry can be broken radiatively due to the large top quark Yukawa coupling. I Generating baryon asymmetry via the electroweak baryogenesis. I Electroweak precision: R parity. Tianjun Li ITP-CAS Problems in the MSSM I µ problem: µHu Hd I Little hierarchy problem I CP violation and EDMs I FCNC I Dimension-5 proton decays Tianjun Li ITP-CAS Supersymmetry Breakings and Mediations I The supersymmetry breaking is broken in the hidden sector via F -term and/or D-term. I The supersymmetry breaking mediations: gravity mediation, gauge mediation, and anomaly mediation, etc. Tianjun Li ITP-CAS The Grand Unified Theories I The Unification Conjecture: all the fundamental interactions have the same origin!!! I Gauge coupling unification in the SSMs strongly suggests the GUTs. Tianjun Li ITP-CAS The Road to the Unification I The First Unification by Newton The Celestial and Terretrial Gravity are the same! I The Second Unification by James C. Maxwell: The Electricity and Magnetism are different manifestations of the same phenomenon! I The Kaluza-Klein Theory The unification of gravity and U(1)EM ! I The Third Unification by Glashow, Salam, and Weinberg The Electroweak Theory for the Weak and Electromagnetic Interaction. I What is/are the next unification(s)? Grand Unified Theory (GUT) and/or String Theory. Tianjun Li ITP-CAS The Grand Unified Theories: SU(5) and SO(10) I Gauge interaction unification. I In SO(10) model, one family of the SM fermion forms a spinor 16 representation. I Yukawa coupling unification. I Charge quantization. I Weak mixing angle at weak scale MZ . I Neutrino masses and mixings by seesaw mechanism. I Prediction: dimension-six proton decay via heavy gauge boson exchange. Tianjun Li ITP-CAS Problems I Gauge symmetry breaking I Doublet-triplet splitting problem I Proton decay problem I Fermion mass problem The wrong prediction on the fermion mass ratios: me /mµ = md /ms . Tianjun Li ITP-CAS String Models I Calabi-Yau compactification of heterotic string theory I Orbifold compactification of heterotic string theory Grand Unified Theory (GUT) can be realized naturally through the elegant E8 breaking chain: E8 ⊃ E6 ⊃ SO(10) ⊃ SU(5) I D-brane models on Type II orientifolds N stacks of D-branes gives us U(N) gauge symmetry: Pati-Salam Models I Free fermionic string model builing Realistic models with clean particle spectra can only be constructed at the Kac-Moody level one: the Standard-like models, Pati-Salam models, and flipped SU(5) models. Tianjun Li ITP-CAS F-Theory Model Building I The models are constructed locally, and then the gravity should decoupled, i.e., MGUT /MPl is a small number. I The SU(5) and SO(10) gauge symmetries can be broken by the U(1)Y and U(1)X /U(1)B−L fluxes. I Gauge mediated supersymmetry breaking can be realized via instanton effects. Gravity mediated supersymmetry breaking predicts the gaugino mass relation. I All the SM fermion Yuakwa couplings can be generated in the SU(5) and SO(10) models. I The doublet-triplet splitting problem, proton decay problem, µ problem as well as the SM fermion masses and mixing problem can be solved. Tianjun Li ITP-CAS Supersymmetry I The most promising new physics beyond the Standard Model. I Gauge coupling unification strongly suggests the Grand Unified Theories (GUTs), and the SUSY GUTs can be constructed from superstring theory. Supersymmetry is a bridge between the low energy phenomenology and high-energy fundamental physics. Tianjun Li ITP-CAS Particle Physics Paradigm String Theory → String Models → GUTs → SSMs → SM Tianjun Li ITP-CAS The Predictions of the GUTs: Proton Decays I The dimension-6 proton decay via superheavy (Xµ , Yµ ) gauge boson exchanges  SU(5) = SU(3)C (X µ , Y µ ) (Xµ , Yµ ) SU(2)L  . I The dimension-5 proton decay via colored Higgsino exchanges in the supersymmetric GUTs. . Tianjun Li ITP-CAS The Dimension-Six Proton Decay via (Xµ , Yµ ) Exchanges Tianjun Li ITP-CAS The Proton Decay in the Supersymmetric GUTs Tianjun Li ITP-CAS Proton Decays 1 I The current bounds from Super-Kamiokande (SK) τp→e + π0 ≥ 1.6 × 1034 yrs , τp→ν̄K + ≥ 5.9 × 1033 yrs . I The expected bounds from Hyper-Kamiokande (HK) τp→e + π0 ≥ 1.0 × 1035 yrs , τp→ν̄K + ≥ 2.5 × 1034 yrs . 1 K. Abe et al. [Super-Kamiokande], Phys. Rev. D 95, no.1, 012004 (2017) [arXiv:1610.03597 [hep-ex]]; M. Yokoyama [Hyper-Kamiokande Proto Collaboration], arXiv:1705.00306 [hep-ex]; K. Abe et al. [Hyper-Kamiokande], [arXiv:1805.04163 [physics.ins-det]]. Tianjun Li ITP-CAS The LHC Supersymmetry Search Contraints I The first two-generation squark mass low bounds are around 1.6 (1.75) TeV. I The gluino mass low bound is around 2.25 (2.46) TeV. I The stop and sbottom mass low bounds are around 1.16 (1.3) and 1.35 (1.45) TeV, respectively. The SSMs are fine-tuned!!! Tianjun Li ITP-CAS Supersymmetry at the Current and Future Colliders I The wrong impression is that supersymmetry was excluded at the LHC? I Can we rule out supersymmetry at the LHC, VLHC, FCChh and SppC? No! No!! No!!! I Points: supersymmetry breaking soft mass scale can be pushed to be much higher than 1 TeV, while gauge coupling unification can still be realized due to the logarithmic RGE running and threshold corrections around the GUT scale. I Conclusion: supersymmetry will defintely not die in the near future!!! Tianjun Li ITP-CAS Natural Supersymmetry The interesting question: can we rule out the natural supersymmetry at the FCChh and SppC? Or can we solve the supersymmetry electroweak fine-tuning problem naturally? Tianjun Li ITP-CAS Fine-Tuning Definition I Fine-tuning Definition 2 : the quantitative measure ∆EENZ−BG FT for fine-tuning is the maximum of the logarithmic derivative of MZ with respect to all the fundamental parameters ai at the GUT scale ∆EENZ−BG = Max{∆GUT }, i FT ∆GUT = i ∂ln(MZ ) . ∂ln(aiGUT ) 2 J. R. Ellis, K. Enqvist, D. V. Nanopoulos and F. Zwirner, Mod. Phys. Lett. A 1, 57 (1986); R. Barbieri and G. F. Giudice, Nucl. Phys. B 306, 63 (1988). Tianjun Li ITP-CAS Question: Super-Natural Supersymmetry Can we propose a supersymmetry scenario whose the EENZ-BG fine-tuning measure is automatically 1 or order 1 (O(1))? Fundamental physics principles: simplicity and naturalness. Tianjun Li ITP-CAS Super-Natural Supersymmetry 3 I Fine-Tuning Definition: ∆FT = Max{∆GUT }, i ∆GUT = i ∂ln(MZ ) . ∂ln(aiGUT ) I Natural Solution: MZn  = fn MZ M∗  M∗n . ∂ln(MZn ) M∗n ∂MZn 1 ' ' fn ' O(1) . n n n ∂ln(M∗ ) MZ ∂M∗ fn I For no-scale supergravity and M-theory on S 1 /Z2 , we have M∗ = M1/2 and M∗ = M3/2 , respectively. 3 T. Leggett, T. Li, J. A. Maxin, D. V. Nanopoulos and J. W. Walker, arXiv:1403.3099 [hep-ph]; Phys. Lett. B 740, 66 (2015) [arXiv:1408.4459 [hep-ph]]; G. Du, T. Li, D. V. Nanopoulos and S. Raza, Phys. Rev. D 92, no. 2, 025038 (2015) [arXiv:1502.06893 [hep-ph]]; T. Li, S. Raza and X. C. Wang, Phys. Rev. D 93, no. 11, 115014 (2016) [arXiv:1510.06851 [hep-ph]]. Tianjun Li ITP-CAS The Interesting Questions? I The SUSY electroweak fine-tuning problem can be solved by the super-natural supersymmetry. I Can we probe supersymmetry at the future pp colliders? No? I Can we probe the supersymmetric GUTs at the future pp colliders? Yes!!! 4 4 W. Ahmed, T. Li, S. Raza and F. Z. Xu, [arXiv:2007.15059 [hep-ph]]. Tianjun Li ITP-CAS Future Colliders I Lepton colliders: CEPC, CLIC, FCCee , and ILC. I Hadron colliders: HL-LHC, HE-LHC, FCChh , SppC, and VLHC. To probe the new physics beyond the SM, we do need future proton-proton colliders. Tianjun Li ITP-CAS Future Proton-Proton Colliders I Question: what is the concrete scientific goal for the future pp colliders? I Question: what is the center-of-mass energy needed for this scientific goal? Tianjun Li ITP-CAS The Scientific Goal for the Future PP Colliders I Supersymmetry cannot be the scientific goal since the sparticles can be very heavy and then we cannot probe supersymmetry. I The supersymmetric GUTs with grand desert hypothesis can be the scientific goal 5 . 5 Waqas Ahmed, TL, Shabbar Raza and Fang-Zhou Xu, Phys. Lett. B 819, 136378 (2021) [arXiv:2007.15059 [hep-ph]]; in preparation. Tianjun Li ITP-CAS The Proof I Grand desert hypothesis: no new physics between the sparticle mass scale and the GUT scale. I For the GUTs with the GUT scale MGUT ≤ 1.2 × 1016 GeV, we can probe the dimension-six proton decay via heavy gauge boson exchange at the Hyper-Kamiokande experiment. I For the GUTs with MGUT ≥ 1.2 × 1016 GeV, we can probe the gluino and/or squarks at the future pp colliders. I Providing the “Concrete Scienctific Goal” for the future pp colliders and Hyper-Kamiokande experiment. Tianjun Li ITP-CAS The First Part of the Proof For the GUTs with the GUT scale MGUT ≤ 1.2 × 1016 GeV, we can probe the dimension-six proton decay via heavy gauge boson exchange at the Hyper-Kamiokande experiment. Tianjun Li ITP-CAS The GUTs with MGUT ≤ 1.2 × 1016 GeV I The proton lifetime from the dimension-six proton decay p → e + π 0 via heavy gauge boson exchange is 35 τp ' 1.0 × 10  ×  × 2.5 AR 2 MGUT 1.0 × 1016 GeV  × 0.04 αGUT 2 4 years . I At the future Hyper-Kamiokande experiment with 186 kt water, we can probe the GUTs with proton lifetime via dimension-6 proton decay at least above 1.0 × 1035 years 6 . The original Hyper-Kamiokande experimental proposal has 1,000 kt water, therefore, we can probe the GUTs with proton lifetime via dimension-6 proton decay at least above 5.37634 × 1035 years. 6 K. Abe et al. [Hyper-Kamiokande], [arXiv:1805.04163 [physics.ins-det]]. Tianjun Li ITP-CAS The GUTs with MGUT ≤ 1.2 × 1016 GeV I For the original Hyper-Kamiokande experimental proposal, we can probe the GUTs with GUT scale up to 1.46726 × 1016 GeV. I Therefore, we can probe the GUTs with GUT scale up to 1.2 × 1016 GeV. Tianjun Li ITP-CAS The GUTs with MGUT ≥ 1.2 × 1016 GeV I Gravity mediated supersymmetry breaking. I Anomaly mediated supersymmetry breaking. I Gauge mediated supersymmetry breaking. Tianjun Li ITP-CAS The Supersymmetry Searches at the Future pp Colliders I For the 100 TeV pp Colliders such as FCChh and SppC, gluino g̃ via heavy flavor decay, gluino via light flavor decay, and the first-two generation squarks q̃ can be discovered for their masses up to about 11 TeV, 17 TeV, and 14 TeV, respectively. If the gluino and first-two generation squark masses are similar, they can be probed up to 20 TeV. I To probe the gluino g̃ via heavy flavor decay with mass around 15 TeV, we need the 160 TeV pp collider such as the VLHC. Tianjun Li ITP-CAS Gravity Mediated Supersymmetry Breaking Tianjun Li ITP-CAS Gravity Mediated Supersymmetry Breaking Tianjun Li ITP-CAS Gravity Mediated Supersymmetry Breaking Tianjun Li ITP-CAS Anomaly and Gauge Mediated Supersymmetry Breakings For anomaly and gauge mediated supersymmetry breakings, the GUTs with MGUT ≥ 1.0 × 1016 GeV are well within the reaches of the future 100 TeV pp colliders such as the FCChh and SppC. Tianjun Li ITP-CAS Summary I Supersymmetry is a bridge between the low energy phenomenology and high-energy fundamental physics, and thus is the promising new physics beyond the SM. I Gauge coupling unification in the supersymmetric SM strongly implies the GUTs. I With the grand desert hypothesis, we show that the supersymmetric GUTs can be probed at the future pp colliders and Hyper-Kamiokande experiment. Tianjun Li ITP-CAS Thank You Very Much for Your Attention! Tianjun Li ITP-CAS