Gravitino Dark Matter in D3/D7 µ-split supersymmetry

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1 Gravitino Dark Matter in D3/D7 µ-split supersymmetry Department of Physics, Indian Institute of Technology Roorkee, INDIA Based on: Nucl.Phys. B 867 (013) 636 (with Aalok Misra), Nucl.Phys. B 855 (01) 439 (with Aalok Misra) Indian Strings Meeting-01, Puri

2 Outline To realize the signatures of µ-split supersymmetry in large volume local D3/D7 set up. Light fermions,heavy scalars(squarks/sleptons) except one light Higgs. Long lived gluinos- a distinguished feature of µ-split supersymmetry. LSP- Gravitino- a viable dark matter candidate even in the presence of non zero R-parity violating couplings- Next(Lightest Supersymmetric Particle) decays, annihilation cross section as well as relic density of LSP.

3 L(arge) V(olume) S(cenario) set up: a brief discussion Type IIB compactified on the orientifold of a Swiss-Cheese Calabi-Yau (expressible as a degree-18 hypersurface in WCP 4 [1, 1, 1, 6, 9]) in the large volume limit in presence of a mobile space-time filling D3-brane (position moduli z 1, and D7-brane(s)(Wilson line moduli a I, I = 1,, 3, 4) wrapping the big divisor, with the inclusion of (non-) perturbative α -corrections to the Kähler potential and ED3-instanton superpotential Analogous to intersecting-brane world scenarios wherein bifundamental leptons and quarks are obtained from open strings stretched between four stacks of D7-branes (Blumenhagen et al, 001), in the LVS setup, however, one considers four stacks of D7-branes (the QCD stack of 3 corresponding to U(3), the EW stack of corresponding to U() and two single corresponding to U(1) Y and the EW singlets (like intersecting brane world models)) wrapping Σ B but with different choices of magnetic (non-abelian) two-form fluxes turned on, on the two-cycles which are non-trivial in the Homology of Σ B.

4 Continued... To obtain, bifundamental leptons and quarks from the superpartners of the adjoint Wilson line moduli, consider, e.g., only two stacks (of D7-branes) consisting of i + j D7-branes wrapping Σ B. By turning on different two-form fluxes on, i and j D7 branes stacks, the original U(i + j) gauge group is broken down to U(i) U(j) and all four-dimensional fields, in particular the Wilson line moduli a I (=1,...,h 0,1 (Σ B )) and their fermionic superpartners χi that are valued in the adj(i + j) ( to begin with, decompose) and yield (adj(i), 1) (i, j) bifundamentals as follows: (ī, j) (1, adj(j)) Including a space time filling D3-brane and D7- brane, N = 1 chiral co-ordinates get modified (in particular) T α = 3i (ρ α 1 κ αbcc b B c ) κ α + 3i 4(τ τ) κ αbcg b (G c Ḡ c ) +3iκ 4 µ 7l δαc B I J α a I ā J + 3i 4 δb ατq f + 3i µ 3l (ω α ) i j zi ( z j i zã( Pã) j l zl ).

5 Continued... The YM couplings are defined in terms of the divisor volumes through the gauge kinetic functions as: 1 g j=su(3) or SU() ) ( = Re(T B )+ln (P (Σ S ) D3 ΣB +ln P (Σ S ) ) D3 ΣB +O(Fj ), After constructing four local appropriate( involutively-odd harmonic ) distribution one-forms that are in coker H (0,1), (CY 3) i H (0,1), (ΣΛ ) supported on a (almost) slag (localized around the location of the mobile D3-brane in the Calabi-Yau): z 1 V 1 36, z V 1 36, z 3 V 1 6, we see that there is the possibility that: Vol(Σ B ) + C I Ja I ā J + h.c. V 1 18 i.e due to the possible competing contributions to the gauge kinetic function (and hence to the gauge coupling) coming from the D7-brane Wilson line moduli as compared to the volume of the big divisor, we are able to reproduce g YM O(1) by wrapping D7-branes around big divisor and a 1,,3,4 can be shown to be stabilized at V 9, V 1 3, V 13 18, V 11 9 for the mobile D3-brane position moduli stabilized along the aforementioned (nearly) slag.

6 Continued... Amongst the effective Yukawa couplings (O(Z i ) coefficient in e K D I D J W χ I L χj R KZi Z i K Aj Ā j K Ak Ā k ) calculated in the context of N = 1 gauged supergravity action; one can show Y ˆeff (EW) O(1) Y ˆeff (string), henceafter we show that Yˆ eff z 1 a 1 a 3 z i corresponds respectively to masses of first generation SM like- leptons and Yˆ eff z 1 a a 4 z i corresponds to masses of first generation SM- like quarks. Therefore, fermionic superpartners of a 1 and a 3 get identified with first generation leptons: e L and e R, and the fermionic superpartners of a and a 4 get identified with the first generation quarks: u L and u R. The soft SUSY parameters are obtained via expansion of Kähler potential and superpotential around the stabilized VEV of position moduli as well as wilson line moduli.

7 Multiple D7-branes Assuming that complex structure moduli z ã=1,...,h,1 (CY3) are stabilized at very small values, define a modified intersection matrix in the a I z i moduli: C IJ = C I J, I = I, J = J; C IJ = µ 3 (πα ) (ω α ) i j, I = i, J = j; C IJ = 0, I = I, J = j, etc.. Before fluxes are turned on, the bifundamental Wilson line super-moduli A I can be valued in the adjoint of U(7). However, turning on different -form fluxes on the world volume of D7-branes, U(7) is broken down to U(3) U() U(1) U(1). Considering an ansatz to write a I and z i in terms of A I, we show that in the large volume limit, C A I Ā J C a I ā J, C Z i Z j C zi zj. Therefore, we assume that C Λ ΣTr ( ) M Λ M Σ is invariant under moduli transformations in the (A I, Z i )/(a I, z i )-subspace of the open-string moduli space implying that C I Ja I ā J + µ 3 (α ) (ω B ) i j zi z j for multiple D7-branes, in a basis that diagonalizes g MI at stabilized values M J of the open string moduli, is replaced by C I J Tr(M I M J ).

8 Mass scales of SM as well soft SUSY parameters Quark mass Lepton mass Gravitino mass m 3 M q O(5)MeV M l O(1)MeV V ns 1 Gaugino mass M g V 3 m 3 Neutralino mass M χ 0 V 3 m 3 3 D3-brane position moduli m Zi V 59 7 m 3 (Higgs) mass Wilson line moduli mass mãi V 1 m 3 I = 1,, 3, 4 A-terms A pqr n s V m 3 {p, q, r} {à I, Z i } Physical µ-terms ˆµ Zi Z j (Higgsino mass) V m 3 Physical ˆµB-terms (ˆµB) Z1 Z V m 3

9 Phenomenological implications of L(arge) V(olume) S(cenario) set up: signatures of µ split SUSY By diagonalizing the Higgs mass matrix, it has been shown that one can generate light Higgs of the order 15GeV mass and other Higgs and higgsino mass parameter to be heavy at EW scale. (M.D, A.Misra(01)) Life time of gluino calculated via two body and three body decay of gluino decay into Neutralino/Goldstino comes out to be long, thus satisfying one of the important phenomenological feature of µ split SUSY.(M.D, A.Misra(01)) After calculating the masses of various SM and their superpartners, it appears that gravitino is the Lightest Supersymmetric Particle (LSP) which for V 10 5,NLSP=slepton/squark or neutralino, motivates the query: can we have Gravitino DM in gravity mediation scenarios?

10 Gravitino LSP: the possible Dark matter candidate in µ-split SUSY Decays of LSP are in general driven by trilinear R-parity violating interactions, W R parityviolating = i,j,k λ ijk L i L j E c k + λ ijk L iq j D c k + u dλ ijk Uc i Dc j Dc k The production of gravitino depends on thermal as well as non thermal production mechanism of gravitino i.e Ω total 3/ = Ωth 3/ + ΩNLSP 3/. Ignoring the thermal production, we consider that most of the gravitino s are produced by non thermal decays of Co-(NLSP) s with an argument that they do not spoil the bounds given by Big-Bang Nucleosynthesis.

11 Life time estimates of various N(LSP) decay channels (M.D, A.Misra(01)) Particle decay Decay Modes Life Time Remarks W 0 ψ µ W + W s Respect Neutralino/Gaugino B ψ µ Z/γ s BBN q decays W ψµ uū s constarint B Z ψ µ uū s Slepton decays l l G V 10 8 s l/ q l/qψµ s RPV Neutralino decay χ 0 3 u de 10 1 s does not effect gravitino abundance ψ µ νγ, νz 10 1 s Life time Gravitino decays ψ µ hν e s greater ψ µ l i l j ek c 10 1 s than age ψ µ l i q j dk c 10 0 s of ψ µ ui cd j cd k c s Universe Gluino decays g χ o nq I q J 10 5 s stable g χ 0 3 g 10 s (from g ψ µ q I q J 10 4 s collider point g ψ µ g s of view)

12 Relic abundance of gravitino If gravitino(lsp) produced by decay of Co-NLSP s is to account for all the gravitinos, the relic abundance of gravitino is given as Ω Gh = Ω χ 0h m 3 3 m χ 0 3 Evaluation of Relic density depends sensitively on the annihilation cross section (σv Møl ) of such particles. To get the idea of same, we have calculated annihilation cross-section of all important channels: χ 0 3 χ0 3 hh, χ0 3 χ0 3 ZZ, χ0 3 χ0 3 ff in case of neutralino annihilation and ( l a l b ZZ, l a l b Zh, l a l b hh, l a l b γγ, l a l b γh, l a l b ll) in case of slepton annihilation. for m 3 V m pl, m χ 0 3 V 3 m 3 (NLSP), Ω G = Ω la m 3 m la and V 1 m 3, from sleptons m la for V 10 5 and from Neutralino (NLSP), Ω G = Ω χ 0 m 3 3 m 0.16 (in accordance with WMAP data χ 0 3 and other experimental predictions) (M.D, A.Misra(01)).

13 To summarize, we conclude that the gravitino qualifies as a potential dark matter candidate in Large volume µ split SUSY scenario.

14 Thanks for your kind attention!

15 L(arge) V(olume) S(cenario)-set up The Swiss Cheese Calabi Yau variety that is being used, is an algebraic variety in WCP 4 [1, 1, 1, 6, 9] given as: x x18 + x x3 4 + x 5 18ψ 5 i=1 x i 3φx1 6x6 x6 3 = 0 The Big divisor Σ B : x 5 = 0 and the Small divisor Σ S : x 4 = 0; ( ) V = 1 9 τ 3 B τ 3 S In L(arge) V(olume) S(cenarios) limit, divisor volumes are stabilized at τ S lnv and τ B V 3.