Yukawa and Gauge-Yukawa Unification
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1 Miami 2010, Florida Bartol Research Institute Department Physics and Astronomy University of Delaware, USA in collaboration with Ilia Gogoladze, Rizwan Khalid, Shabbar Raza, Adeel Ajaib, Tong Li and Kai Wang.
2 Low Scale ( TeV) Supersymmetry (SUSY): Arguably the most compelling extension of the Standard Model; Resolves the gauge hierarchy problem; Provides cold dark matter candidate (LSP); Implements radiative electroweak symmetry breaking; Predicts new particles accessible at the LHC, and thereby enables unification of the SM gauge couplings; Α 1 1 MSSM Α 1 1 SM Αi Α 2 1 Α 3 1 Αi Α 2 1 Α Log 10 GeV Log 10 GeV
3 Supersymmetric SO(10): Fermion families reside in 16 i (i=1,2,3) predicts right handed neutrino non-zero neutrino masses; (Cf: SU(5) with families in 10 i + 5 i ) Yukawa couplings provide masses to SM fermions. They include 16 i 16 j 10, 16 i 16 j 126, etc yields t b τ unification Y t = Y b = Y τ = Y ν In the old days it was used to predict the top quark mass! 1 1 B. Ananthanarayan, George Lazarides, Q. Shafi (1991);
4 Nowadays, one employs t b τ unification to make predictions, such as sparticle masses, which can be tested at the LHC/Tevatron (Baer et al.); t b τ unification can also be realized in SU(4) c SU(2) L SU(2) R, a maximal subgroup of SO(10);
5 CMSSM (msugra): Unbroken Z 2 matter parity stable LSP, typically neutralino; Universal soft susy breaking parameters m 0, m 1/2, A 0, tanβ, sign(µ) Alexander Belyaev, Pramana 72: ,2009.
6 Supersymmetric SO(10)(Baer et al.) 1 m 16, m 10, M D, M 1/2, A 0, tan β, sign(µ) m 16 Universal soft SUSY breaking sfermion mass m 10 Universal soft SUSY breaking MSSM Higgs mass M D The Higgs mass splitting M 2 H u,d = m M2 D m 1/2 Universal SSB gaugino mass A 0 Universal SSB trilinear interaction tan β = vu v d µ SUSY bilinear Higgs parameter 1 H. Baer, S. Kraml, S. Sekmen and H. Summy, JHEP 0803, 056 (2008)
7 Random scans were performed over the parameter space m 16 : 0 20 TeV (1 20 TeV), m 10 /m 16 : ( ), m 1/2 : 0 5 TeV (0 1 TeV), A 0 /m ( ), M D /m 16 : ( ), tan β : (46 53). Quantify Yukawa unification by R = max(yt,y b,y τ ) min(y t,y b,y τ )
8 Constraints m χ ± 1 (chargino mass) GeV, m h (lightest Higgs mass) GeV, m τ (stau mass) 86 GeV, m g (gluino mass) 220 GeV, BR(B s µ + µ ) < , 0.53 < BR(B u τν τ )MSSM BR(B u τν τ )SM < 2.03 (2σ), BR(b sγ) (2σ), Ω CDM h 2 = (5σ), α µ (3σ).
9
10 SUSY and t b τ Yukawa coupling unification yt yb yτ yi log 10 (Q/GeV)
11 Radiative contributions to the bottom quark mass from the gluino and chargino loop δy b g 3 2 µm g tan β + y 2 12π 2 m 2 b t µa t tan β π 2 m 2 t
12 H. Baer, S. Kraml, S. Sekmen and H. Summy, JHEP 0803, 056 (2008)
13 parameter Pt. A Pt. D m m 1/ A m tan β M D f t f b f τ µ m g m ul m t m b m el m ± χ m χ m χ m A m h σ [fb] % ( g g) % ( χ ± 1 χ± 2 ) % ( t 1 t 1 ) Lightest colored sparticle is gluino; But Ωh 2 >> 1!! DM: Axions, Axinos.
14 Yukawa Unification and Neutralino DM in SU(4) c SU(2) L SU(2) R (4-2-2) I.G, R. Khalid and Q. Shafi, Phys. Rev. D 79, (2009). SM fermions: ψ i = (4, 2, 1) and ψ c i = ( 4, 1, 2) MSSM Higgs: H = (1, 2, 2) Third family Yukawa coupling ψ ψ c H yields Y t = Y b = Y τ = Y ν Asymptotic relation between the three MSSM gaugino masses M 1 = 3 5 M M 3 One additional parameter compared to the SO(10) model (from gaugino non-universality)
15 We performed random scans for the following parameter range 0 m TeV, 0 M 2 1 TeV, 0 M 3 1 TeV, 3 A 0 /m 16 0, 0 M D /m , 0 m 10 /m , 40 tan β 58, µ > 0, m t = GeV.
16 Constraints m χ ± 1 (chargino mass) GeV, m h (lightest Higgs mass) GeV, m τ (stau mass) 86 GeV, m g (gluino mass) 220 GeV, BR(B s µ + µ ) < , 0.53 < BR(B u τν τ )MSSM BR(B u τν τ )SM < 2.03 (2σ), BR(b sγ) (2σ), Ω CDM h 2 = (5σ), α µ (3σ).
17
18 Points in green satisfy all experimental constraints. Red points represent R 1.1, but do not satisfy g-2.
19 Point 1 Point 2 Point 3 m M M tan β M D /m m 10/m A 0/m m h m H m A m H ± ± m χ 887, , ,3750 1,2 0 m χ 283, , ,712 1,2 0 m χ 13879, , ,3785 3,4 m g mũl,r 14126, , ,12841 m t1,2 5337, , ,5310 m dl,r 14126, , ,13249 m b1,2 5237, , ,5146 m ν m ν mẽl,r 13988, , ,13500 m τ1,2 6412, , ,9559 µ Ω LSP h R
20 Yukawa unification with relative sign gauginos Yukawa unification prefers µm 3 < 0 Dominant contributions to the bottom quark mass from the gluino and chargino loop δy b g 3 2 µm g tan β + y 2 12π 2 m 2 b t µa t tan β π 2 m 2 t Dominant contribution to the muon anomalous magnetic moment for large tan β case is αµ SUSY µm 2 tan β/ m 4 In model with left-right symmetry, M 2 and M 3 are free parameters We can have µ < 0, M 2 < 0, M 3 > 0 or µ > 0, M 2 > 0, M 3 < 0
21 We performed random scans for the following parameter range 0 m 0, M Hu, M Hd 20 TeV, 2 TeV M 2 2 TeV, 2 M 3 2 TeV, 3 A 0 /m 16 3, 45 tan β 55, µ > 0, µ < 0, m t = GeV.
22 Green points satisfy all constraints. Points in red represent R 1.1
23 Red points satisfy all constraints and R 1.1
24 Dark matter indirect detection Red points satisfy all constraints and R 1.1
25 Dark matter direct detection Red points satisfy all constraints and R 1.1
26 Point 1 Point 2 Point 3 Point 4 Point 5 m M M M tan β A 0 /m m Hu m Hd m h m H m A m H ± m χ 0 1,2 280,341 43, ,242 56, ,782 m χ 0 3,4 352, , , , ,1216 m ± χ 342, , , , ,1217 1,2 m g mũl,r 1771, , , , ,1697 m t1,2 1053, , , , ,1248 m d L,R 1773, , , , ,1730 m b1,2 954, , , , ,1245 m ν m ν mẽl,r 1393, , , , ,1763 m τ1,2 500, , , , ,1554 σ SI (pb) σ SD (pb) Ω CDM h R g 3 /g 1 (M GUT )
27 Yukawa Unification & NLSP gluino search at Hadron Colliders Yukawa unification predicts light gluino, heavy scalars and is compatible with gluino-bino coannihilation with gluino as NLSP. Conventional gluino searches with small SM background g g jets + χ ± 1 χ± 1 jets + l ± l ± + E T. For NLSP gluino these channels are absent and we consider the parameter space region with dominant contributions from gluino three body decay b b χ 0 1 pp, p p g g b bb b + E T.
28 Potential SM backgrounds considered b bb b, b bb bz b bb bν ν, jjb bz jjb bν ν We choose two benchmark points from previously described models M g (GeV) M χ 0 1 (GeV) M b 1 (GeV) Br( g b b χ 0 1 ) Model A (µ > 0) % Model B(µ < 0) % For Tevatron, we employ the following event selection cuts p j T > 15 GeV, η j < 1.0, R jj > 0.4 and b tagging efficiency 50% and E T > 30 GeV cut for χ 0 1.
29 The production cross section for the two points for Tevatron Tevatron Model A Model B b bb b b bb bz jjb bz S/ B basic cuts and 3b tagging E T > 30 GeV (A)/11(B)
30 The production cross section for the two points for LHC 7 TeV LHC Model A Model B b bb b b bb bz jjb bz basic cuts and 3b tagging E T > 40 GeV
31 SO(10) Gray points are consistent with REWSB and χ 0 1 LSP. Green, blue and red points are subsets of gray points with R 1.2, 1.1, 1.02 respectively. µ>0,m 2 >0,M 3 >0
32 µ<0,m 2 <0,M 3 >0 Gray points are consistent with REWSB and χ 0 1 LSP. Green, blue and red points are subsets of gray points with R 1.2, 1.1, 1.02 respectively. µ>0,m 2 >0,M 3 <0
33 Gauge-Yukawa Unification in from Orbifold Compactification Example: I. Gogoladze, Y. Mimura and S. Nandi, Phys. Lett. B 562, 307 (2003); I. Gogoladze, Y. Mimura, S. Nandi and K. Tobe, Phys. Lett. B 575, 66 (2003); T. Kobayashi, S. Raby and R. J. Zhang, Nucl. Phys. B 704, 3 (2005). I. Gogoladze, R. Khalid, S. Raza, Q. Shafi: To appear soon.
34
35 GY = max(g 1,g 2,g 3,y t,y b,y τ ) min(g 1,g 2,g 3,y t,y b,y τ )
36 µ<0,m 2 <0,M 3 >0 Gray points are consistent with REWSB and χ 0 1 LSP. Green points are consistent with all bounds except Ωh 2. Blue points consistent with all bounds. µ>0,m 2 >0,M 3 <0
37 µ<0,m 2 <0,M 3 >0 δy b µa t = For µ < 0, A 0 > 0, and for µ > 0, A 0 < 0 µ>0,m 2 >0,M 3 <0
38 µ<0,m 2 <0,M 3 >0 Gray points are consistent with REWSB and χ 0 1 LSP. Blue points are consistent with all bounds. Red points have gauge-yukawa unification to within 10% µ>0,m 2 >0,M 3 <0
39 Summary - Yukawa Unification In supersymmetric and L-R symmetric SU(4) c SU(2) L SU(2) R model with gravity mediated supersymmetry breaking, t b τ Yukawa coupling unification is consistent with neutralino dark matter abundance and with all constraints from collider experiments (except (g 2) µ )for same sign gauginos. For µm 3 < 0 we can have Yukawa unification satisfying all current constraints. The model with same sign gauginos predicts a very characteristic sparticle spectrum: very heavy sfermions (> 5 TeV ) but relatively light gluinos ( 300 GeV). With relative sign gauginos, Yukawa unification can be achieved with relatively light sparticle spectrum O(600) GeV. NLSP gluino can be tested at the LHC/Tevatron.
40 NLSP gluino search at Tevatron and 7 TeV LHC through multi-b jets g g b bb b χ 0 1 χ0 1. With 10 fb 1 luminosity one can reach 5σ at Tevatron after selection cuts. At 7 TeV LHC the signal is at least one order of magnitude larger than leading backgrounds.
41 Summary - Gauge-Yukawa Unification Bino-Higgsino dark matter (Good for direct and indirect searches) By varying m t within 1σ of its central value, we can find bino-gluino and stau coannihilation regions and the A resonance solution. m χ 0 1 (GeV) m χ 0 2,3 (GeV) 384, , , ,2050 m g (GeV) m τ (GeV) m A (GeV) N 11, N , , , ,0.00 N 13, N , , , ,0.00 σ SI (cm 2 ) σ SD (cm 2 ) χ 0 1 = N 11 B + N 12 W + N13 H1 + N 14 H2
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