Abdus Salam & Physics Beyond the Standard Model

Transcription

1 Abdus Salam & Physics Beyond the Standard Model Qaisar Shafi Bartol Research Institute Department of Physics and Astronomy University of Delaware Abdus Salam Memorial Meeting, Singapore. January / 36

2 (1964) 2 / 36

3 (1993) 3 / 36

4 BCSPIN : Bangladesh, China, SriLanka, Pakistan, India, Nepal; Salam present in the first school in 1989; also King of Nepal. BC(V)SPIN / Asian American Advanced Study Institute Held in Nepal, India, China, Vietnam, Mexico (2014). Supported by ICTP, NSF (USA), China, Mexico, Univ. of Delaware, Mitchell Foundation (Texas A& M),... 4 / 36

5 5 / 36

6 (2007) 6 / 36

7 (2007) 7 / 36

8 Physics Beyond the Standard Model Neutrino Physics: SM + Gravity suggests m ν 10 5 ev, which disagrees with neutrino data; Dark Matter: SM offers no plausible DM candidate; Origin of matter in the universe: Electric Charge Quantization: Unexplained in the SM; CMB Isotropy / Anisotropy, Origin of Structure require ideas beyond Hot Big Bang Cosmology (which comes from SM + General Relativity.) Strong CP Problem. 8 / 36

9 Quark-Lepton Unification, lepton number as 4th color, electric charge quantization, neutrino mass,... (with JCP); Baryon number violation (with JCP); Superfields & R- symmetry (with John Strathdee); Kaluza-Klein Theories (JS, Randjbar-Daemi,...). 9 / 36

10 Sky is the Limit Matter Multiplets in Grand Unification Pati-Salam SU(4) c SU(2) L SU(2) R : (4, 2, 1) + (4, 1, 2) ( ) u u u νe = 16 chiral fields; d d d l L,R SM neutrinos have non-zero masses. Georgi-Glashow SU(5): chiral fields; Massless neutrinos Fritzsch-Minkowski, Georgi SO(10): 16 plet SU(5) (ν R ) 10 / 36

11 b-τ YU in SU(4) SU(2) L SU(2) R (422) m 16, m Hi, M i, A 0, tan β, sign(µ) m 16 Universal soft SUSY breaking (SSB) sfermion mass m Hd,H u Universal SSB MSSM Higgs masses. M i SSB gaugino masses. M 1 = 3 5 M M 3 A 0 Universal SSB trilinear interaction tan β = vu v d µ SUSY bilinear Higgs parameter µ > 0 11 / 36

12 Random scans for the following parameter range (NUHM2): 0 m TeV, 0 M 2 5 TeV, 0 M 3 5 TeV, 3 A 0 /m 16 3, 0 m Hd 20 TeV, 0 m Hu 20 TeV 2 tan β 60, µ > 0, m t = GeV. 12 / 36

13 Point 1 Point 2 Point 3 m M M M A tan β µ m h m H m A m H ± m χ 0 1,2 424, , , 762 m χ 0 3,4 1845, , , 4032 m ± 810, , , 4023 χ 1,2 m g mũl,r 2239, , , 3118 m t1,2 1084, , , 3768 m dl,r 2240, , , 3025 m b1,2 1721, , , 3808 m ν m ν mẽl,r 1265, , , 1407 m τ1,2 719, , , 3156 σ SI (pb) σ SD (pb) Ω CDM h EW HS / 36

14 Point 1 Point 2 Point 3 Point 4 Point 5 m M M M m Hd, m Hu 11720, , , , , 5478 tan β A 0 /m m t µ (g 2) µ m h m H m A m H ± m χ 0 1,2 641, , , , , 2441 m χ 0 3,4 4973, , , , , m ± 1697, , , , , χ 1,2 m g mũl,r 12743, , , , , m t1,2 689, , , , , 5263 m dl,r 12743, , , , , m b1,2 6234, , , , , 7047 m ν m ν mẽl,r 12846, , , , , m τ1,2 9129, , , , , σ SI (pb) σ SD (pb) Ω CDM h R / 36

15 Those Guys from Harvard 15 / 36

16 Those Guys from Harvard 16 / 36

17 The Biggest Hoax in Physics? Inflationary Cosmology Successful Primordial Inflation should: Explain flatness, isotropy; Provide origin of δt T ; Offer testable predictions for n s, r, dn s /d ln k; Recover Hot Big Bang Cosmology; Explain the observed baryon asymmetry; Offer plausible CDM candidate; Physics Beyond the SM? 17 / 36

18 Inflation can be defined as: Cosmic Inflation d 1 < 0, dt ah a& & > 0, a decreasing comoving horizon an accelerated expansion P < ρ / 3, a negative pressure repulsive gravity Consider a scalar field φ drives inflation ρφ 1 = & φ 2 +V ( φ ) V, 2 a( t) Slow rolling scalar field acts as an inflaton Ht e inflation 18 / 36

19 Cosmic Inflation Tiny patch ~10-28 cm > 1 cm after 60 e-foldings (time constant ~10-38 sec) Inflation over radiation dominated universe (hot big bang) Quantum fluctuations of inflation field give rise to nearly scale invariant, adiabatic, Gaussian density perturbations Seed for forming large scale structure 19 / 36

20 k Solution to the Flatness Problem 1 = Ω 2 ( ah ) 2N Ω f 1 = Ωi 1 e 0, where N = H Δt 50 Solution to the Horizon Problem Image courtesy of W. Kinney 20 / 36

21 Slow-roll Inflation Inflation is driven by some potential V (φ): Slow-roll parameters: ɛ = m2 p 2 ( V V ) 2, ( ) η = m 2 V p V. The spectral index n s and the tensor to scalar ratio r are given by n s 1 d ln 2 R d ln k, r 2 h, 2 R where 2 h and 2 R are the spectra of primordial gravity waves and curvature perturbation respectively. Assuming slow-roll approximation (i.e. (ɛ, η ) 1), the spectral index n s and the tensor to scalar ratio r are given by n s 1 6ɛ + 2η, r 16ɛ. 21 / 36

22 The tensor to scalar ratio r can be related to the energy scale of inflation via V (φ 0 ) 1/4 = r 1/4 GeV. The amplitude of the curvature perturbation is given by ( 2 R = 1 V/m 4 ) p 24π 2 ɛ = (WMAP7 normalization). φ=φ 0 The spectrum of the tensor perturbation is given by ( ) 2 h = 2 V 3 π 2 m 4 P φ=φ 0. The number of e-folds after the comoving scale l 0 = 2 π/k 0 has crossed the horizon is given by N 0 = 1 φ0 ( V ) m 2 p φ e V dφ. Inflation ends when max[ɛ(φ e ), η(φ e ) ] = / 36

23 R. Symmetry and Inflation [Dvali, Shafi, Schaefer; Copeland, Liddle, Lyth, Stewart, Wands 94] [Lazarides, Schaefer, Shafi 97][Senoguz, Shafi 04; Linde, Riotto 97] Attractive scenario in which inflation can be associated with symmetry breaking G H Simplest inflation model is based on W = κ S (Φ Φ M 2 ) S = gauge singlet superfield, (Φ, Φ) belong to suitable representation of G Need Φ, Φ pair in order to preserve SUSY while breaking G H at scale M TeV, SUSY breaking scale. R-symmetry Φ Φ Φ Φ, S e iα S, W e iα W W is a unique renormalizable superpotential 23 / 36

24 Tree Level Potential V F = κ 2 (M 2 Φ 2 ) 2 + 2κ 2 S 2 Φ 2 SUSY vacua Φ = Φ = M, S = 0 S M V Κ 2 M M 1 24 / 36

25 Tree level + radiative corrections + minimal Kähler potential yield: n s = 1 1 N δt/t proportional to M 2 /M 2 p, where M denotes the gauge symmetry breaking scale. Thus we expect M M GUT for this simple model. Since observations suggest that n s lie close to 0.97, there are at least two ways to realize this slightly lower value: (1) include soft SUSY breaking terms, especially a linear term in S; (2) employ non-minimal Kähler potential. r 0.02 in these models 25 / 36

26 Electric Charge Quantization: Monopoles & Inflation Magnetic Monopoles in Unified Theories Any unified theory with electric charge quantization predicts the existence of topologically stable ( thooft-polyakov ) magnetic monopoles. Their mass is about an order of magnitude larger than the associated symmetry breaking scale. Examples: 1 SU(5) SM (3-2-1) Lightest monopole carries one unit of Dirac magnetic charge even though there exist fractionally charged quarks; 2 SU(4) c SU(2) L SU(2) R (Pati-Salam) Electric charge is quantized with the smallest permissible charge being ±(e/6); Lightest monopole carries two units of Dirac magnetic charge; 26 / 36

27 Electric Charge Quantization: Monopoles & Inflation Examples: Magnetic Monopoles in Unified Theories 3 SO(10) Two sets of monopoles: First breaking produces monopoles with a single unit of Dirac charge. Second breaking yields monopoles with two Dirac units. 4 E 6 breaking to the SM can yield lighter monopoles carrying three units of Dirac charge. The discovery of primordial magnetic monopoles would have far-reaching implications for high energy physics & cosmology. 27 / 36

28 Tree Level Gauge Singlet Higgs Inflation [Kallosh and Linde, 07; Rehman, Shafi and Wickman, 08] Consider the following Higgs Potential: V (φ) = V 0 [1 ( φ M ) 2 ] 2 (tree level) Here φ is a gauge singlet field. V Φ Below vev BV inflation Above vev AV inflation WMAP/Planck data favors BV inflation (r 0.1). M Φ 28 / 36

29 Higgs Potential: n s vs. r for Higgs potential, superimposed on Planck and Planck+BKP 68% and 95% CL regions taken from arxiv: The dashed portions are for φ > v. N is taken as 50 (left curves) and 60 (right curves). 29 / 36

30 Coleman Weinberg Potential: n s vs. r for Coleman Weinberg potential, superimposed on Planck and Planck+BKP 68% and 95% CL regions taken from arxiv: The dashed portions are for φ > v. N is taken as 50 (left curves) and 60 (right curves). 30 / 36

31 Primordial Monopoles Let s consider how much dilution of the monopoles is necessary. M I GeV corresponds to monopole masses of order M M GeV. For these intermediate mass monopoles the MACRO experiment has put an upper bound on the flux of cm 2 s 1 sr 1. For monopole mass GeV, this bound corresponds to a monopole number per comoving volume of Y M n M /s There is also a stronger but indirect bound on the flux of (M M /10 17 GeV)10 16 cm 2 s 1 sr 1 obtained by considering the evolution of the seed Galactic magnetic field. At production, the monopole number density n M is of order Hx, 3 which gets diluted to Hxe 3 3Nx, where N x is the number of e-folds after φ = φ x. Using Y M H3 xe 3Nx, s where s = (2π 2 g S /45)T 3 r, we find that sufficient dilution requires N x ln(h x /T r ) Thus, for T r 10 9 GeV, N x 30 yields a monopole flux close to the observable level. 31 / 36

32 Proton Decay Coleman-Weinberg Potential Higgs Potential M X 2 V 1/4 0 (GeV) τ(p π 0 e + ) (years) M X V 1/4 0 (GeV) τ(p π 0 e + ) (years) Table: Superheavy gauge bosons masses and corresponding proton lifetimes with α G = 1 35 in the CW and Higgs models. Note that since the lifetime depends only on M X, the results shown here apply equally well to the BV and AV branches in each model. 32 / 36

33 Diphoton Resonance: New Physics, at last? 33 / 36

34 34 / 36

35 Acknowledgements Grateful thanks to many collaborators, including: Gia Dvali, George Lazerides, Ilia Gogoladze, Nefer Senoguz, Steve King, Mansoor Rehman, Shabbar Raza, Cem Salih Un, Fariha Nasir, Adeel Ajaib, / 36