Unification Paradigm

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2 Unfcaton Paradgm GUT m D=10 Unfcaton of strong, weak and electromagnetc nteractons wthn Grand Unfed Theores s the new step n unfcaton of all forces of Nature Creaton of a unfed theory of everythng based on strng paradgm seems to be possble

3 What s SUSY? Supersymmetry s a boson-fermon symmetry that s amed to unfy all forces n Nature ncludng gravty wthn a snge framework t 7 e 9 y 1 fermon >= Q boson >= fermon > n Q s boson > c s s r y e h p jp a e p l j c [b, b] = 0, { f,rsf t} = 0 {Q t, Q } = # ( $ ) P r a F p n e c n e Modern vews on supersymmetry n partcle physcs d v e are based on N strng o paradgm, though low energy manfestatons of SUSY can be found (?) at modern collders and n non-accelerator experments

4 Motvaton of SUSY n Partcle Physcs Unfcaton wth Gravty Unfcaton of gauge couplngs Soluton Q boson of the >= herarchy fermonproblem > Q fermon >= boson > Dark matter n the Unverse Superstrngs spn spn 3/ spn 1 spn 1/ spn 0 Unfcaton of matter (fermons) wth forces (bosons) naturally arses from an attempt to unfy gravty wth the other nteractons j j { Q, Q } = $ (% ) P & { $, $ } = ( % ) P # # = ( x) local coordnate transf. & (super)gravty Local supersymmetry = general relatvty

5 Motvaton of SUSY n Unfcaton of gauge couplngs Partcle Physcs Low Energy Hgh Energy n SU (3) SU () U (1) G (or G + symm) c L Y 3 1 GUT gluons W, Z photon gauge bosons quarks leptons fermons g g g g GUT Q = ( ) = (dstance) Runnng of the strong couplng

6 # 1 ( M ) = ± 0.07 Z sn = ± MS ( M ) = ± s RG Equatons Z Motvaton of SUSY d dt b1 0 4 / 3 1/10 # $ # $ # $ # $ SM : b = b = % / 3 + NFam 4 / 3 + NHggs 1/ 6 # b $ # % 11 $ # 4 / 3$ # 0 $ & 3 ' & ' & ' & ' Input Output = b, = / 4 = g /16, t=log(q / ) Unfcaton of the Couplng Constants n the SM and n the MSSM b1 0 3/10 # $ # $ # $ # $ MSSM : b = b = % 6 + NFam + NHggs 1/ # b $ # % 9$ # $ # 0 $ & 3 ' & ' & ' & ' M M SUSY GUT -1 GUT = = 3.4± 0.9± GeV 15.8± 0.3± GeV = 6.3± 1.9 ± 1.0 SUSY yelds unfcaton

7 Motvaton of SUSY Soluton of the Herarchy Problem m H v 10 GeV 16 m V 10 GeV Destructon of the herarchy by radatve correctons m H m Cancellaton of quadratc terms SUSY may also explan the orgn of the herarchy due to radatve mechansm m = bosons fermons m

8 Motvaton of SUSY Dark Matter n the Unverse The flat rotaton curves of spral galaxes provde the most drect evdence for the exstence of large amount of the dark matter. Spral galaxes consst of a central bulge and a very thn dsc, and surrounded by an approxmately sphercal halo of dark matter SUSY provdes a canddate for the Dark matter a stable neutral partcle

9 Cosmologcal Constrants New precse cosmologcal data h = vacuum 1 73% 3± 4% DarkMatter Baryon 4% Dark Matter n the Unverse: = crt Supernova Ia exploson CMBR thermal fluctuatons (recent news from WMAP ) Hot DM (not favoured by galaxy formaton) Cold DM (rotaton curves of Galaxes) SUSY

10 Lorentz Algebra [ P, P ] = 0, [ P, M ] = ( g P $ g P ), SUSY Algebra [ Q, P ] = [ Q, P ] = 0, ( Super) Alg ebra # # # 1 1 # = $ # # = & $ # [ Q, M ] ( ) Q, [ Q, M ] Q ( ), j j = j { Q, Q } = % ( $ ) P,,,, = 1,;, j = 1,,..., N. Superalgebra [ M, M ] = ( g M $ g M $ g M + g M ), # # # # # j { Q, Q } # ( $ ) P The only possble graded Le algebra that mxes nteger and half-nteger spns and changes statstcs Grassmannan parameters Q Superspace x # x,, Supertranslaton x $ x + # % #, $ + #, $ + #, = 1, % = % & # $ % % Q = & + # $ % % = 0, = 0 SUSY Generators Q Q = 0, = 0

11 Quantum States Quantum states: Vacuum = E, > Q E, >= 0 [ Q, P ] = [ Q, P ] = 0 State Energy helcty Expresson # of states vacuum 1-partcle -partcle E, > Q E, >= E, + 1/ > Q Q E, >= E, + 1 > j 1 ( N ) 1 = N ( N ) N ( N 1) = N-partcle Q...,, / 1Q QN E >= E + N > N Total # of states: ( N ) N N 1 N 1 k = = bosons + k = 0 ( N ) N = 1 fermons

12 Chral multplet Vector multplet SUSY Multplets N = 1, =0 helcty # of states N = 1, =1/ helcty # of states -1/ 0 1/ / 1/ Members of a supermultplet are called superpartners scalar spnor (, ) (, A ) spnor vector N=4 SUSY YM helcty -1 1/ 0 1/ 1 λ = -1 # of states N=8 SUGRA helcty - 3/ 1 1/ 0 1/ 1 3/ λ = - # of states N 4S spn N 4 N 8 For renormalzable theores (YM) For (super)gravty

13 Smplest (N=1) SUSY Multplets Bosons and Fermons come n pars (, ) (, A ) (g, g) Spn 0 Spn 1/ Spn 1/ Spn 1 Spn 3/ Spn

14 SUSY Transformaton N=1 SUSY Chral supermultplet: spn=0 spn=1/ A = #, # = $ % A + F, F = $ % # parameter of SUSY transformaton (spnor) Auxlary feld (unphyscal d.o.f. needed to close SYSY algebra ) SUSY multplets Superfled n Superspace $ ( y, ) = A( y) + ( y) + F( y) superfeld = A( x) + # % A( x) + A( x) + ( x) & / % ( x) # + F( x) =, = = ( y = x + ) Expanson over grassmannan parameter component felds

15 Gauge superfeld Gauge superfelds + V ( x,, ) = C( x) + ( x) % ( x) + M ( x) % M ( x) %# v ( x) + [ $ ( x) + # & ( x)] % [ $ ( x) + # & ( x)] + [ D( x) + C( x)] 1 1 Gauge transformaton C $ C + A + A $ % M $ M % F v v A A * $ % & ( % ) # $ # D $ D * V V + + Wess-Zumno gauge C = = M = 0 physcal felds W Feld strength tensor 1 V = 4 D e D e Covarant dervatves W = & + D & F + D D D $ = $ + # $ $ = % % # $ $ V # $ ( ) % % $ $ % #

16 How to wrte SUSY 1 st step Lagrangans Take your favorte Lagrangan wrtten n terms of felds nd step Replace Feld (,, A ) # Superfeld ( $, V ) 3 rd step Acton = 4 d x L x ( ) Replace d x d 4 4 L( x,, ) Grassmannan ntegraton n superspace % % d# = 0, # d# = $

17 Superfeld Lagrangans Acton = 4 d x L d x d 4 4 L Grassmannan ntegraton n superspace d 0, Matter felds L = d d # # + d ( # + m # # + y # # # ) + h. c.] j j 3 jk j k $ $ % % # = # d# = $ Gauge felds Superpotental L d # W W d # W W D F F $% D $ = ' + ' = & & Gauge transformaton e #g$, + + e g$+, V V + ($ # $ + ) Gauge nvarant nteracton + + gv e

18 Gauge Invarant SUSY Lagrangan L SUSY YM = 1 4 d Tr(W # W # ) d Tr(W # W # ) + d d $a(e gv ) b a $ b + d W($ ) + d W($) SUSY YM 1 a a a a 1 a a 4 # L = % F F % D + D D a a a a a a ( A gv T A ) ( A gv T A ) $ # ( $ gv T $ ) + & % & % % & % a a a a a a $ $ % D ga T A % ga T + g T A + F F & W & W & W & W + + % $ $ % $ $ & A & A & A& A & A & A 1 1 F F j j j W D = ga T A, F = # V= D D + F F a a 1 a a A j