Index Motivation Lightest Supersymmetric Particle 3 body Stop decay Conclusions 3 B ODY S TOP DECAY WITH G RAVITINO /G OLDSTINO IN THE FINAL STATE Bryan Larios J. Lorenzo Diaz Cruz bryanlarios@gmail.com ldiaz@gmail.com Facultad de Ciencias F´ ısico M´ atematico BUAP XXIX Reuni´ on Anual de Part´ ıculas y Campos Bryan Larios 3 body Stop decay with gravitino/goldstino in the f.s.
Index Motivation Lightest Supersymmetric Particle 3 body Stop decay Conclusions Outline Motivation: Dark Matter (DM) and Supersymmetry (SUSY), Gravitino Lightest Supersymmetric Particle (LSP) and Dark Matter, The Next Lightest Supersymmetric Particle (NLSP), 3 body Stop decay, With Gravitino With Goldstino Conclusions. Bryan Larios 3 body Stop decay with gravitino/goldstino in the f.s.
Index Galaxy Rotation Curve Motivation New Physics: LHC and the Cosmos Lightest Supersymmetric Particle A little bit about Supersymmetry 3 body Stop decay The MSSM particle content Conclusions Dark Matter F T = ma √ G N M v = r Bryan Larios 3 body Stop decay with gravitino/goldstino in the f.s.
Index Galaxy Rotation Curve Motivation New Physics: LHC and the Cosmos Lightest Supersymmetric Particle A little bit about Supersymmetry 3 body Stop decay The MSSM particle content Conclusions New Physics: LHC and the Cosmos After 30-40 years of Standard Model success (apart from ν hints) something new should happen or else..., LHC is expected to find Physics Beyond the SM (BSM), At the same time, astro/cosmo phenomena also suggest BSM physics may be needed, SUSY is one of the best motivated theories BSM. Bryan Larios 3 body Stop decay with gravitino/goldstino in the f.s.
Index Galaxy Rotation Curve Motivation New Physics: LHC and the Cosmos Lightest Supersymmetric Particle A little bit about Supersymmetry 3 body Stop decay The MSSM particle content Conclusions Supersymmetry is a symmetry that relates Boson fields degree of freedom with Fermion Fields degree of freedom. ∣ Fermions ⟩ = ˆ Q ∣ Bosons ⟩ ∣ Bosons ⟩ = ˆ Q ∣ Fermions ⟩ There are a lot of SUSY models. We will use the Minimal Supersymmetric Standard Model MSSM (4D) with N = 1 . Bryan Larios 3 body Stop decay with gravitino/goldstino in the f.s.
Index Galaxy Rotation Curve Motivation New Physics: LHC and the Cosmos Lightest Supersymmetric Particle A little bit about Supersymmetry 3 body Stop decay The MSSM particle content Conclusions The MSSM particle content SM Superpartners W ± ,Z,γ SM Wino, Zino, Photino Bosons gluon gluino Higgs bosons Higgsinos SM quarks squarks Fermions leptons sleptons neutrinos sneutrinos The particles in the SM are distinguished from their superparthers from R-Parity. With R-Parity being preserved the (LSP) cannot decay. Bryan Larios 3 body Stop decay with gravitino/goldstino in the f.s.
Index Gravitino ˜ Motivation Ψ µ as LSP in SUGRA models NLSP phenomenology with ˜ Lightest Supersymmetric Particle Ψ µ as LSP Gravitino ( ˜ 3 body Stop decay Ψ µ ) interactions, Conclusions What is the LSP? The lightest Supersymmetric (LSP) particle is suppose to be stable and electrically neutral and to interact weakly with the particles of the SM. These are exactly the characteristic required for DM. One option is: Gravitino ( ˜ Ψ µ ), there are other ones (Neutralino, Sneutrino). Bryan Larios 3 body Stop decay with gravitino/goldstino in the f.s.
Index Gravitino ˜ Motivation Ψ µ as LSP in SUGRA models NLSP phenomenology with ˜ Lightest Supersymmetric Particle Ψ µ as LSP Gravitino ( ˜ 3 body Stop decay Ψ µ ) interactions, Conclusions Gravitino ˜ Ψ µ as LSP in SUGRA models One of the candidates for dark matter in Supergravity (local Supersymmetry) is the gravitino. However, the exact relation is uncertain. Gravitino is a very weakly interacting particle, with coupling ≃ 1 / M Pl = 0 . 83 × 10 − 19 GeV − 1 (in Supergravity). Practically undetectable. (Except for its gravitational effect.) The next lightest SUSY particle (NLSP) could be long lived. We have many possibilities for the NLSP: neutralino, stau, stop, sneutrino. Each with its own distinct phenomenology. Bryan Larios 3 body Stop decay with gravitino/goldstino in the f.s.
Index Gravitino ˜ Motivation Ψ µ as LSP in SUGRA models NLSP phenomenology with ˜ Lightest Supersymmetric Particle Ψ µ as LSP Gravitino ( ˜ 3 body Stop decay Ψ µ ) interactions, Conclusions NLSP phenomenology with ˜ Ψ µ as LSP To determine viability of each scenario one need to: Identify Gravitino-MSSM interactions, Define the models (CMSSM, NUHM), Calculate NLSP lifetime, Check consistency with low-energy and collider constraints, Verify implications for cosmology. Bryan Larios 3 body Stop decay with gravitino/goldstino in the f.s.
Index Gravitino ˜ Motivation Ψ µ as LSP in SUGRA models NLSP phenomenology with ˜ Lightest Supersymmetric Particle Ψ µ as LSP Gravitino ( ˜ 3 body Stop decay Ψ µ ) interactions, Conclusions Gravitino ( ˜ Ψ µ ) interactions All interactions can be derived from SUGRA lagrangian (Wess-Bagger), Most relevant terms are: Coupling with chiral superfields: 1 ˜ i ˜ D ∗ ν φ ∗ Ψ µ γ ν γ µ χ i L 1 = − √ R + h.c. ( L → R ) (1) 2 M Coupling with vector superfields: i ¯ ˜ Ψ µ [ γ ν ,γ ρ ] γ µ λ a F a L 2 = (2) νρ 8 M Bryan Larios 3 body Stop decay with gravitino/goldstino in the f.s.
Index Feynman Diagrams Motivation Amplitudes Lightest Supersymmetric Particle Goldstino Approximation 3 body Stop decay Numerical Results Conclusions 3 body Stop decay To determine viability of the scenario (NLSP) with ˜ Ψ µ as LSP, we need to calculate NLSP life time. τ = 1 (3) Γ Bryan Larios 3 body Stop decay with gravitino/goldstino in the f.s.
Index Feynman Diagrams Motivation Amplitudes Lightest Supersymmetric Particle Goldstino Approximation 3 body Stop decay Numerical Results Conclusions The expression for the decay width is (After integration): m 2 d Γ ˜ t 1 256 π 3 ∣ M ∣ 2 dxdy = Let’s focus on the amplitude for the moment Bryan Larios 3 body Stop decay with gravitino/goldstino in the f.s.
Index Feynman Diagrams Motivation Amplitudes Lightest Supersymmetric Particle Goldstino Approximation 3 body Stop decay Numerical Results Conclusions The expression for the decay width is (After integration): m 2 d Γ ˜ t 1 256 π 3 ∣ M ∣ 2 dxdy = Let’s focus on the amplitude for the moment Bryan Larios 3 body Stop decay with gravitino/goldstino in the f.s.
Index Feynman Diagrams Motivation Amplitudes Lightest Supersymmetric Particle Goldstino Approximation 3 body Stop decay Numerical Results Conclusions The expression for the decay width is (After integration): m 2 d Γ ˜ t 1 256 π 3 ∣ M ∣ 2 dxdy = Let’s focus on the amplitude for the moment (Squaring and summing over final polarizations). Bryan Larios 3 body Stop decay with gravitino/goldstino in the f.s.
Index Feynman Diagrams Motivation Amplitudes Lightest Supersymmetric Particle Goldstino Approximation 3 body Stop decay Numerical Results Conclusions t 1 → b + W + ˜ ˜ Ψ µ We are considering the ˜ t as NLSP. In what follows we need to consider the following Feynman diagrams: Where V i ∀ i = 1 ,..., 6 are the interactions vertex. Bryan Larios 3 body Stop decay with gravitino/goldstino in the f.s.
Index Feynman Diagrams Motivation Amplitudes Lightest Supersymmetric Particle Goldstino Approximation 3 body Stop decay Numerical Results Conclusions 3 body Stop decay We can write the squared amplitude from the last 3 Feynman diagram. ∣ M ∣ 2 =∣ M t ∣ 2 + ∣ M ˜ b ∣ 2 + ∣ M χ + ∣ 2 + 2 Re (M † b + M † t M χ + + M † t M ˜ b M χ + ) (4) ˜ In order to keep control of ∣M∣ 2 we shall write the chargino amplitude as M χ = M 1 χ + M 2 χ . (Because the huge vertex functions in the process.) Bryan Larios 3 body Stop decay with gravitino/goldstino in the f.s.
Index Feynman Diagrams Motivation Amplitudes Lightest Supersymmetric Particle Goldstino Approximation 3 body Stop decay Numerical Results Conclusions The amplitudes are: M t = C t P t ( q 1 ) Ψ µ p µ ( A t + B t γ 5 )( / q 1 + m t ) γ ρ ǫ ρ ( k ) P L u ( p 2 ) b i ( q 2 ) Ψ µ q µ 2 ( a i P l + b i P R ) p ρ ǫ ρ ( k ) P L u ( p 2 ) M ˜ b i = C ˜ b i P ˜ i ( q 3 ) Ψ µ γ ρ ǫ ρ ( k ) γ µ ( V i + Λ i 5 )( q 3 + m χ )( S i + P i 5 ) u ( p 2 ) M 1 χ + i = C χ + i P χ + i Ψ µ p ρµ ( T i + Q i 5 ) ǫ ρ ( k )( q 3 + m χ )( S i + P i 5 ) u ( p 2 ) M 2 χ + i = C χ + i P χ + Basically we shall have to compute 4 squared amplitudes and 6 interferences in [4]. � Bryan Larios 3 body Stop decay with gravitino/goldstino in the f.s.
Index Feynman Diagrams Motivation Amplitudes Lightest Supersymmetric Particle Goldstino Approximation 3 body Stop decay Numerical Results Conclusions Squared amplitudes can be written as: ψ a ∣ P ψ a ( q a ) ∣ 2 W ψ a ψ a ∣ M ψ a ∣ 2 = C 2 (5) where ψ a = ( t, ˜ b j ,χ + k ) , and the functions W ψ a ψ a are : W ψ a ψ a = w 1 ψ a + m ψ a w 2 ψ a + m 2 ψ a w 3 ψ a (6) w iψ a ∀ i = 1 , 2 , 3 , 4 are functions of the scalar products of the momenta p,p 1 ,p 2 ,k . Bryan Larios 3 body Stop decay with gravitino/goldstino in the f.s.
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