Pseudo-Dirac Bino as Dark Matter and Signatures of D-Type G

Transcription

1 and Signatures of D-Type Gauge Mediation Ken Hsieh Michigan State Univeristy KH, Ph. D. Thesis (2007) ArXiv: [hep-ph] Other works with M. Luty and Y. Cai (to appear) MSU HEP Seminar November 6, 2007 and Signatures of D-Type G

2 1 Standard Model Supersymmetry and its Breaking The Little Hierarchy Problem Fine-tuning of Dark Matter 2 Collider Signatures of 3 and Signatures of D-Type G

3 Standard Model Supersymmetry and its Breaking The Little Hierarchy Problem Fine-tuning of Dark Matter INTRODUCTION: STANDARD MODEL AND BEYOND and Signatures of D-Type G

4 Standard Model Supersymmetry and its Breaking The Little Hierarchy Problem Fine-tuning of Dark Matter The Standard Model and the Hierarchy Problem The Standard Model is enormously successful in describing the strong and electroweak forces through spontaneous symmetry breaking. SU(3) }{{ C } SU(2) L U(1) Y SU(3) }{{}}{{ C } U(1) }{{ em } strong electroweak strong electromagnetic W ±, Z }{{} weak and Signatures of D-Type G

5 Standard Model Supersymmetry and its Breaking The Little Hierarchy Problem Fine-tuning of Dark Matter The Standard Model and the Hierarchy Problem The Standard Model is enormously successful in describing the strong and electroweak forces through spontaneous symmetry breaking. SU(3) }{{ C } SU(2) L U(1) Y SU(3) }{{}}{{ C } U(1) }{{ em } strong electroweak strong electromagnetic But the Higgs boson is still missing, and δm 2 H y 2 t Λ 2 /(16π 2 ) W ±, Z }{{} weak requires a spectacular fine-tuning if Λ M GUT GeV, of one part in 10 28! and Signatures of D-Type G

6 Paths Beyond the Standard Model Standard Model Supersymmetry and its Breaking The Little Hierarchy Problem Fine-tuning of Dark Matter If the Higgs particle exists (and there is no guarantee of this), the solution to the hierarchy problem requires that we have a low cutoff scale and/or tame the Higgs mass and its radiative corrections with new symmetries. Treat Higgs as a composite (technicolor) Treat Higgs as a pseudo-goldstone boson (little Higgs, twin Higgs, etc.) Explain the apparent largeness of M Planck (extra dimensions) Relate scalar masses to fermion masses (supersymmetry) and Signatures of D-Type G

7 Supersymmetry Standard Model Supersymmetry and its Breaking The Little Hierarchy Problem Fine-tuning of Dark Matter Supersymmetry relates fermions to bosons, and doubles the particle content of the Standard Model. Q L Leptons Quarks H u H d Higgs bosons B µ, W µ, G µ Gauge bosons Q L S-leptons S-quarks H u Hd Higgsinos λ 1 ( b), λ 2 ( w), λ 3 ( g) Gauginos and Signatures of D-Type G

8 Why We Study SUSY Standard Model Supersymmetry and its Breaking The Little Hierarchy Problem Fine-tuning of Dark Matter Quadratic Corrections No More! }{{} y 2 t 16π 2 Λ 2 + y 2 t 16π 2 Λ 2 and Signatures of D-Type G

9 Why We Study SUSY Standard Model Supersymmetry and its Breaking The Little Hierarchy Problem Fine-tuning of Dark Matter Quadratic Corrections No More! y t 2 Λ 2 16π 2 Dark matter through R-parity. }{{} + y 2 t 16π 2 Λ 2 Dynamical electroweak symmetry breaking. mh 2 < 0 at weak scale automatically. Gauge coupling unification extendable to GUT. SUSY can be seen at colliders! and Signatures of D-Type G

10 Supersymmetric Interactions Standard Model Supersymmetry and its Breaking The Little Hierarchy Problem Fine-tuning of Dark Matter We can supersymmetrize the existing Yukawa and gauge interactions. (Possible B- and L-violating interactions forbidden through U(1) R.) and Signatures of D-Type G

11 SUSY-Breaking Standard Model Supersymmetry and its Breaking The Little Hierarchy Problem Fine-tuning of Dark Matter SUSY must be broken softly, in such a way that the hierarchy problem is still solved. L soft = m 2 L Q 2 + m 2 L L 2 + m 2 Ũ Ũc 2 + m 2 D D c 2 + m 2 Ẽ Ẽ c 2 + m 2 H u H u 2 + m 2 H d H d 2 + B µ µ(h u H d + h.c.) M 1λ 1 λ M 2λ 2 λ M 3λ 3 λ 3 + h.c. + y t A t Q H u ũ c + y b A b Q H d d c + y τ A τ L H d ẽ c + h.c.. These soft terms have the renormalization group equations: β(m i ) β(g 2 i )M i (16π 2 )β(m 2 f ) y 2 m 2 q g 2 i M 2 i (16π 2 )β(a) ya g i M i. This gives a dynamical origin of m 2 H u < 0 at low scales! and Signatures of D-Type G

12 Standard Model Supersymmetry and its Breaking The Little Hierarchy Problem Fine-tuning of Dark Matter The Need of SUSY-Breaking Theories Why Study Models of SUSY-Breaking? MSSM contains roughly 120 free parameters; most reside in the SUSY-breaking sector. Systematic studies of large parameter space is forbiddingly difficult need an organizing principle. Many of the free parameters, such as phases and off-diagonal elements in mass matrices, are tightly constrained by current experiments. We need a further theoretical guide to constraint them. Models of SUSY-breaking may point to preferred region of parameter space. and Signatures of D-Type G

13 The Little Hierarchy Problem Standard Model Supersymmetry and its Breaking The Little Hierarchy Problem Fine-tuning of Dark Matter Experiment (LEP2): m h > 114 GeV Theory (MSSM): m 2 h = m2 Z cos2 2β and Signatures of D-Type G

14 The Little Hierarchy Problem Standard Model Supersymmetry and its Breaking The Little Hierarchy Problem Fine-tuning of Dark Matter Experiment (LEP2): m h > 114 GeV Theory (MSSM): mh 2 = m2 Z cos2 2β + 3 mt 4 8π 2 v 2 Big A t are hard to come by... ( ln m2 t m 2 t + A2 t m 2 t 1 12 A 4 t m 4 t Only logarithmic m t dependence large m t are needed! ) and Signatures of D-Type G

15 The Little Hierarchy Problem Standard Model Supersymmetry and its Breaking The Little Hierarchy Problem Fine-tuning of Dark Matter Experiment (LEP2): m h > 114 GeV Theory (MSSM): mh 2 = m2 Z cos2 2β + 3 mt 4 8π 2 v 2 Big A t are hard to come by... ( ln m2 t m 2 t + A2 t m 2 t 1 12 A 4 t m 4 t Only logarithmic m t dependence large m t are needed! Large stop masses feed into soft mass-squared term... δmhu 2 = 3y t 2 8π 2 (m2 t L + m 2 t R + A 2 t ) log Λ2 m 2 t ( δ ln MZ 2 δ ln mhu 2 (Λ) = 6y t 2 m + m 2 t 2 t + A 2 ) L R t 8π 2 MZ 2 ln Λ M Z This is fine-tuning of 1 part in 100, and grows very rapidly with increasing m h. ) and Signatures of D-Type G

16 Dark Matter of the MSSM Standard Model Supersymmetry and its Breaking The Little Hierarchy Problem Fine-tuning of Dark Matter The lightest neutralino is an eigenvector of the mass matrix T B M 1 0 g Y g 2 v Y2 d v u B L W g 0 M v d g 2 2 v u H d g W Y g 2 v 2 d 2 v d 0 µ H d. g H Y2 u v u g 2 2 v u µ 0 H u The higgsino- and wino-dominated limits give small relic density due to co-annihilation with nearly degenerate charged wino and Higgsinos. The bino-dominated limit gives a large relic density because it self-annihilation is p-wave suppressed. (The leading s-wave contribution is chirality suppressed.) Root of the problem is the Majorana nature of χ 0 1. and Signatures of D-Type G

17 Fine-tuning of LSP Dark Matter Standard Model Supersymmetry and its Breaking The Little Hierarchy Problem Fine-tuning of Dark Matter To be consistent WMAP with observations, we can arrange for Enhanced co-annihilation (for example, with τ). Delicate mixture of B, W and H. s-channel resonance ( B B A f f ). But these involve a fine-tuning of the MSSM spectra, requiring two independent masses to be nearly degenerate to a few percent. and Signatures of D-Type G

18 Standard Model Supersymmetry and its Breaking The Little Hierarchy Problem Fine-tuning of Dark Matter LSP Dark Matter - a Qualitative Look Battaglia, M.; 2006 Mitchell Symposium; April 10-14, and Signatures of D-Type G

19 Collider Signatures of DIRAC GAUGINOS AND D-TYPE SUSY-BREAKING and Signatures of D-Type G

20 Mini- Collider Signatures of Dirac gauginos as a possible solution to the little hierarchy problem. Model building with D-type SUSY-breaking: issues and constraints. Pseudo-Dirac bino as dark matter: relic density and direct detection. Collider signatures of D-type models: suppression of same-sign di-lepton signals. and Signatures of D-Type G

21 Fine-Tuning Revisited Collider Signatures of ( mh 2 = 3 m 4 8π 2 t ln m2 t v 2 mt 2 m 2 Hu = 3y 2 t 8π 2 ( m 2 t A2 t + A2 t 1 A 4 m 2 t t 12 m 4 t ) ln Λ 2 m 2 t ) prefers large m t and A t, prefers small m t and A t. Even with large A t terms, large t masses are inevitable because of ( RGEs. Squark Mass = Slepton Mass g 3 2 g1 2 ( m t 1 TeV ). ) ( ) 10 + Exp. bound: m l > 100 GeV Generically, independent of LEP bound on the Higgs mass, MSSM is inevitably fine-tuned! and Signatures of D-Type G

22 Dirac Gauginos Collider Signatures of Dirac gaugino masses are supersoft. They do not ruin the cancellation of quadratic corrections, and they do not enter the radiative corrections of other soft terms. Nelson, Weiner, and Fox [hep-ph/ ] With Dirac gauginos we have a chance of making s-quarks (in particular the s-tops) light without having s-leptons violating LEP bounds. The modified RGEs (starting at 2-loop order) naturally give compact and inverted spectra, with sleptons heavier than squarks! (Dirac Gauginos)+(Inverted Spectra)=(Lots of Collider Projects)! The (almost) Dirac bino as lightest superpartner is a more natural dark matter than the Majorana bino. and Signatures of D-Type G

23 Super-soft SUSY-Breaking Collider Signatures of L MSSM = M 2 (λ 1λ 1 + λ 1 λ 1 ) g YY q ( q λ 1 q + qλ 1 q ) β( m 2 q) ( ) g Y 2 M 2 16π 2 λ + O g 4 Y (16π 2 ) 2 L DGMSB = M(λ 1 ξ 1 + λ 1 ξ 1 ) g YY q ( q λ 1 q + qλ 1 q ). ( ) β( m q) 2 g 4 = 0+O Y (16π 2 ) 2 The β-functions now vanish at one-loop order, and may lead to compact spectra! and Signatures of D-Type G

24 Review Gauge-Mediated SUSY Breaking Collider Signatures of The pictorial idea The messenger threshold L = [ ( M }{{} SUSY + }{{} F θ 2 ) P P] θ 2 + h.c. Breaking and Signatures of D-Type G

25 Review Gauge-Mediated SUSY Breaking Collider Signatures of The pictorial idea The messenger threshold L = [ ( M }{{} SUSY + }{{} F θ 2 ) P P] θ 2 + h.c. Breaking { M 2 boson = M2 ± F M 2 fermion = M2 and Signatures of D-Type G

26 Collider Signatures of Gauge-Mediated SUSY Breaking Spectrum The messengers in loops will generate scalar and gaugino masses. ( m λ (M) g 2 F ) 16π 2 M ( m 2 f (M) g 4 F ) 2 (16π) 2 M Gauge interactions are flavor-blind, and there is freedom to align the flavor basis of the scalar with the fermion flavor basis. The flavor-changing neutral currents induced by the superpartners are thus suppressed. and Signatures of D-Type G

27 Collider Signatures of Consider a gauged U(1) X symmetry with a collection of matter content Σ i with charge U i that is spontaneously broken by Σ + and Σ, with U + = U = 1 and σ + σ GeV. D X = σ + 2 σ 2 0. The messengers carry both SM charges and U(1) X charge of ± 1 2 : P ± and P. The messenger scale is chosen to be near M GUT. ] L = [M ± P P ± + y Σ P ± P ± + h.c. θ 2 In addition, the scalar components of the messengers receive SUSY-breaking masses D X. and Signatures of D-Type G

28 Dirac Gaugino Collider Signatures of Dirac particles need more degrees of freedom. Ξ = (η, ξ) is the chiral adjoint, consisting of the gaugino partner and the s-gaugino. Coupling between Ξ to the messengers generates Dirac gaugino masses. [ ] L = h PΞP θ 2 m λ hg D 16π 2 M U(1) R forbids the generation of Majorana masses. and Signatures of D-Type G

29 The S-gaugino Collider Signatures of The s-gaugino, η, is the scalar partner of the gaugino partner ξ in the super-multiplet Ξ. Like the Dirac gaugino, masses are generated at one-loop V η = mη η B η(η 2 + η 2 ) + O(η 3 ), mη 2 B η h2 D X m 2 16π 2 M 2. Since mη 2 B η, stability of V η is extremely important! Note that η is heavier than the Dirac gaugino masses by 4π. and Signatures of D-Type G

30 Collider Signatures of Model-building Issues and Further Constraints The gauge-kinetic mixing between U(1) X and U(1) Y can be dangerous even with a unification group. The mixing gives un-acceptably large MSSM soft masses. The MSSM scalar masses are determined once the interactions of hidden and messenger sectors are specified. We have to ensure that it arises at two-loops, as with the case of GMSB. The effective operator of Dirac gaugino masses also give a tadpole to the s-gaugino that consequently gives rise to a contribution to S. This constraints the s-gauginos to be heavier than 1 TeV. and Signatures of D-Type G

31 Collider Signatures of In the MSSM, the self-annihilation of Majorana bino is p-wave suppressed. (The s-wave contribution is suppressed by fermion masses.) dσ dω m2 f m 4 f With D-type SUSY-Breaking, there is no longer such suppressions. In the pure Dirac bino limit, we have dσ dω M2 1 m 4 f and Signatures of D-Type G

32 Collider Signatures of Dark Matter in the Pure-Dirac Bino Limit The relic density Ωh 2 of Majorana and pure-dirac bino ((Ωh 2 ) exp 0.12). and Signatures of D-Type G

33 Collider Signatures of We now have the expanded mass matrix: ξ 1 λ 1 L ξ 2 λ 1 H d H u 0 M ξ 1 M g Y g 2 v Y2 d v u λ M g 0 0 M v d g ξ v u 0 g λ 2. Y g 2 v d v d 0 µ H d g 0 Y2 v u 0 g 2 2 v u µ 0 H u T We take the limit of M 1 M 2, µ: L ( ) T ( ξ1 g 2 v uv d Y B M 1 0 2µ M 1 ) ( ) ξ1 B χ 0 1,2 = 1 2 (λ 1 ξ 1 ), M χ 0 = M 1,2 1 g Y 2vuv d 4µ. and Signatures of D-Type G

34 Pure- vs. Pseudo-Dirac Bino Collider Signatures of We started out with a pure Dirac bino, where there is no p-wave suppression in the relic density. However, because of EWSB, the two states of the pure Dirac bino split into two nearly-degenerate Majorana states. We might expect the self-annihilation of the lightest state to be again p-wave suppressed. However, there are co-annihilation effects: χ 0 1 χ0 2 f f. The total relic density of dark matter depends on the abundance of χ 0 2 when χ0 1 freezes out. This is sensitive to the mass splitting. and Signatures of D-Type G

35 Collider Signatures of The relic density Ωh 2 of Majorana and pseudo-dirac bino for = 0.01, 0.02, 0.05, 0.10, and ((Ωh 2 ) exp 0.12). and Signatures of D-Type G

36 Direct Detection of Dark Matter Collider Signatures of Cryogenic Dark Matter Search (CDMS) is an underground lab located at Soudan, MN. CDMS experiment aims to measure the recoil energy imparted to detector nuclei through neutralino-nucleon collisions by employing sensitive phonon detection equipment coupled to arrays of cryogenic germanium and silicon crystals. Pictures from and Signatures of D-Type G

37 Results from CDMS II Collider Signatures of Spin-independent DM-nucleon cross-section. (astro-ph/ ) and Signatures of D-Type G

38 Results from CDMS II Collider Signatures of Spin-dependent bounds from CDMS II. (astro-ph/ ) and Signatures of D-Type G

39 Direct Detection of Dark Matter Collider Signatures of Dirac particles are generally ruled out as dark matter by direct detection bounds. (For example, the KK neutrino.) Because of electroweak breaking, the pseudo-dirac bino composes of two nearly-degenerate Majorana particles, with splitting of the order a few GeV. Direct-detection experiments involve elastic scattering with momentum exchange of the order of 10s of kevs, and are sensitive only to the lightest Majorana state. The lightest state χ 0 1 has diluted interactions compared to the MSSM bino, and as such it is consistent with current direct detection bounds (σ s dep N ] cm [ 2 ). ] L g Y Y Q [λ 1 Q Q χ 0 + h.c. g Y Y 1 +χ 0 2 Q 2 Q Q + h.c.. and Signatures of D-Type G

40 The Inverted MSSM Spectrum Collider Signatures of For the moment, let us assume that the MSSM sfermion soft masses arise at two-loop order, and have a common value at M GUT, as in msugra. (That is, the MSSM matter content are embedded in a representation of a unifying gauge group.) The RGEs of the s-fermions arise at two loops, with a positive sign! β MSSM (m 2 Q) = g 2 16π 2 M2 λ, β DGMSB (m 2 Q ) = + g 4 (16π 2 ) 2 m2 η. This gives a negative contribution when evolved to lower scale, and squarks are lighter than sleptons! and Signatures of D-Type G

41 Collider Signatures Collider Signatures of Lack of same-sign di-muon event Dirac nature of gauginos suppresses same-sign lepton events. (The botto Yukawa coupling may still generate such events). Inverted Spectrum Cascade decays now proceed with three-body decays of gluino and winos. Singly Produced SU(3)-Adjoint The s-gauginos are even under matter-parity. The loop-induced production channel gg η is similar to gg h. This leads to possible bump in the cross-section. and Signatures of D-Type G

42 Collider Signatures of Same-Sign Di-Lepton Events in the MSSM In MSSM, the Majorana gluino can decay to either a quark or an anti-quark, We also typically have the ordered spectrum g > q > w > l > b. and Signatures of D-Type G

43 Collider Signatures of Same-Sign Di-Lepton Events in the MSSM Majorana nature of the gauginos and the order of the spectrum leads to same sign di-lepton events. and Signatures of D-Type G

44 Inverted Spectra + Dirac Gauginos Collider Signatures of With a Dirac gluino, particle is different from anti-particle. While one decays to fermion, the other decays to anti-fermion. There may still be same-sign di-lepton signals involving Higgsino, but these are suppressed by the bottom Yukawa coupling. In DGMSB, typical spectra have the order: l > q > g > w > b. Such pattern of superpartner masses require three-body decays of the g and w. and Signatures of D-Type G

45 Collider Signatures of Opposite-Sign Di-Lepton Events in the MSSM In DGMSB, an almost conserved (broken only by y b ) U(1) R charge suppresses same-sign di-lepton events. and Signatures of D-Type G

46 Singly-Produced S-gaugino Collider Signatures of In MSSM, matter parity (R-parity) distinguishes SM matter content (R-even) and superpartners (R-odd), and superpartner states must be produced in pairs at colliders. In this case, the gaugino partner ξ is the super-partner, and thus odd under R-parity. The s-gaugino is then R-even and can be produced singly at the LHC! The production diagram involves a loop (analogous to Higgs production from two gluons), but strong couplings may enhance this production rate. There may be a resonance! and Signatures of D-Type G

47 While SM has worked spectacularly, naturalness drives for a more fundamental theory and new physics at 1 TeV. Supersymmetry is the leading candidate of such new physics. Within the minimal framework (MSSM) with generic SUSY-breaking pattern, there are fine-tuning problems in the Higgs sector (little hierarchy problem) requiring fine-tuning of order parts in a few hundred, and in the dark matter sector. Dirac gaugino may be a solution to the little-hierarchy problem, and it comes with potentially many new, interesting experimental signatures. The main feature of D-type models, the Dirac gauginos, can lead to a more natural candidate of dark matter, and also have unique signatures at colliders in the suppression of same-sign di-lepton events. and Signatures of D-Type G