Gauge-Higgs Nobuhito Maru

Transcription

1 Gauge-Higgs Nobuhio Maru (Chuo Universiy wih N. Okada (KEK Gauge-Higgs unificaion a CERN LHC PRD (008 /8/008 Theory workshop@icrr

2 PLAN Inroducion Calculaion of Ampliudes Summary

3 Inroducion One of he problems in in he Sandard Model: Gauge Hierarchy Problem Quanum correcions o Higgs mass is sensiive o he cuoff scale of he heory = Higgs + W,Z,γ + Top δ m H Λ 6 π Too large!! (Naural cuoff scale is Planck scale or GUT scale

4 Problem: We have NO symmery forbidding he scalar mass SUSY φ ψ Mass erm is is forbidden by by chiral symmery

5 Problem: We have NO symmery forbidding he scalar mass SUSY φ ψ Idenified wih Higgs in in he SM GHU Mass erm is is forbidden by by chiral symmery A A 5 μ Higher dimensional Lorenz invariance Mass erm is is forbidden by by he gauge symmery Higher dimensional gauge symmery

6 A 5 Indeed, he (local mass erm is forbidden by he gauge symmery for he 5 h componen of he gauge field ( ( A A + ε x, y + i ε x, y, A In oher words, no local couner erm is is allowed No quadraic divergence, finie regardless of he nonrenormalizabiliy m A 5 6 π R

7 D-dim QED on Haanaka, Inami Inami & Lim Lim (998 (998 5D Non-Abelian gauge heory on Gersdorff, Irges Irges & Quiros Quiros (00 (00 6D Non-Abelian gauge heory on Anoniadis, Benakli Benakli & Quiros Quiros (00 (00 6D Scalar QED on Lim, Lim, N.M. N.M. & Hasegawa (006 (006 5D QED on Explici calculaions of Higgs mass N.M. N.M. & Yamashia (006, Hosoani, N.M., N.M., Takenaga & Yamashia (007 (007 GHU has opened up a new avenue o solve he gauge hierarchy problem

8 How can we es he gauge-higgs unificaion by experimens?? In his alk, we focus on collider signaures, in paricular LHC signaure In he gauge-higgs unificaion, : : New srucure in in he Higgs secor : Coupling of new paricles o Higgs boson conrolled by higher dimensional gauge invariance Deviaions from he SM predicions & Collider signaures specific o GHU are expeced!!

9 Calculaion of Ampliudes

10 Higgs boson search: LHC is a pp collider s = 4 TeV Gluon fusion is he dominan Higgs producion process

11 Discovery Mode In In his work, we we are ineresed in in he case mh mh < 50 GeV H γ is is he primary discovery mode

12 Discovery Mode We calculae KK KK op loop conribuion o o gg gg -> -> H -> -> γ in in a 5D SU(3 gauge-higgs unificaion on on S^/Z S^/Z

13 Lagrangian L ( MN M = Tr FMN F + iψγ DM Ψ MN M N N M 5 M N M M 5 M M M ( ψ, ψ, ψ 3 T M Γ = [, ](, 0,,,3, F = F F ig A A M N = D a a a ( : : Gell-Mann marices D = ig A A = A λ λ Ψ= ( μ 5 γ, iγ A Boundary condiions: μ (+,+ only has massless mode ( +, + + ψ R(, ( ψ R( ( ψ ( ++, ++,,,, ++, ψl = ++, ++,,, A5 =,, ++,, Ψ= ψl ++, +,,, ++, ++, ++,, ψ, + +, + 3L 3R

14 Lagrangian L ( MN M = Tr FMN F + iψγ DM Ψ MN M N N M 5 M N M M 5 M M M ( ψ, ψ, ψ 3 T M Γ = [, ](, 0,,,3, F = F F ig A A M N = D a a a ( : : Gell-Mann marices D = ig A A = A λ λ Ψ= ( μ 5 γ, iγ A Boundary condiions: μ ( +, + + ψ R(, ( ψ R( ( ψ ( ++, ++,,,, ++, ψl = ++, ++,,, A5 =,, ++,, Ψ= ψl ++, +,,, ++, ++, ++,, ψ, + +, + 3L 3R SU(3 SU( x U(

15 Lagrangian L ( MN M = Tr FMN F + iψγ DM Ψ MN M N N M 5 M N M M 5 M M M ( ψ, ψ, ψ 3 T M Γ = [, ](, 0,,,3, F = F F ig A A M N = D a a a ( : : Gell-Mann marices D = ig A A = A λ λ Ψ= ( μ 5 γ, iγ A Boundary condiions: μ ( +, + + ψ R(, ( ψ R( ( ψ ( ++, ++,,,, ++, ψl = ++, ++,,, A5 =,, ++,, Ψ= ψl ++, +,,, ++, ++, ++,, ψ, + +, + 3L 3R Higgs is is idenified wih 0 mode of A5 A5 (KK (KK modes modes of of A5 A5are absorbed ino ino KK KK gauge gauge bosons

16 Lagrangian L ( MN M = Tr FMN F + iψγ DM Ψ MN M N N M 5 M N M M 5 M M M ( ψ, ψ, ψ 3 T M Γ = [, ](, 0,,,3, F = F F ig A A M N = D a a a ( : : Gell-Mann marices D = ig A A = A λ λ Ψ= ( μ 5 γ, iγ A Boundary condiions: μ ( +, + + ψ R(, ( ψ R( ( ψ ( ++, ++,,,, ++, ψl = ++, ++,,, A5 =,, ++,, Ψ= ψl ++, +,,, ++, ++, ++,, ψ, + +, + 3L 3R Chiral fermions are easily obained

17 we obain 4D effecive Lagrangian of fermion ( n n n n μ i ( ψ, ψ, ψ3 γ μ ψ n= ψ 3 ( L 4D fermion = ψ B 3 μ + Wμ + Wμ 0 3 ψ g B + ( ψ, ψ, ψ W W + 0 γ ψ 3 ψ n n n 3 μ μ n 3 μ μ ( Bμ mn 0 0 ψ ( ψ, ψ, ψ3 0 mn m ψ 0 m m n ψ 3 μ μ g μ + μ g μ μ + ilγ L + b ( iγ m b + ( γ LbW + bγ LW + ( γ L + bγ Lb W 3 μ μ μ μ μ 3g ( μ L b μ Lb b μ + γ + γ γ Rb B μ 6 n g L 5 R 5 mn g m R π R 5 ( γ, ( + γ, =, =, = ( = 3 gv M W

18 4D effecive Lagrangian in erms of mass eigenbasis ( n ψ ( n ψ 0 0 ψ n n μ = i ( ψ, ψ, ψ 3 γ μ ψ n= ψ = 0 ψ ψ 3 0 ψ 3 ψ 3 B 3 μ + + Wμ + Wμ Wμ 3 ( n ψ 3 3 g Wμ Bμ Wμ B μ μ + ( ψ, ψ, ψ 3 Wμ + γ ψ ψ 3 Wμ Bμ Wμ B μ W μ ( 4D ( ( L fermion mn 0 0 ψ ( ψ, ψ, ψ 3 0 mn + m 0 ψ 0 0 m m n ψ 3 g + g + ilγ + b ( iγ m b + ( γ LbW + bγ LW + ( γ L + bγ Lb W + μ μ μ μ μ μ 3 μ L μ μ μ μ 3g ( μ L b μ Lb μ γ + γ bγ Rb Bμ 6 n g5 L γ5, R + γ5, mn =, g =, m= gv = M R π R W

19 Essenial Poin for calculaion m ( n m m R v + n = + m ( n m m R v n = + KK specrum: Mass spliing Top Yukawa: Sign flipping

20 Higgs-glue-glue effecive coupling L eff = ( C Yukawa Loop Group funcion facor hg G KK aμν a glue μν ( + m αsf 4m m h S 4 h m α F m m = + + n= v 8πm n 8 = v πm ( ( ( ( 4 F x = x + x sin x ( x 3 mα S αs ( mr n m + πv n= m 6 v m π n= n R Finie!! Each ±mode conribuion is is log divergen, bu heir sum is is finie Subracive Opposie sign o o he SM case m α SF( 4m mh α C = + v 8π m π v SM S glue This cancellaion holds rue in in arbirary dimension (N.M., (N.M., MPLA3 MPLA3 (008 (

21 Higgs-γ-γ effecive coupling L eff = C ( KK γ hf μν F μν ( m αemf 4m m h 4 em 4 h m α F m m + 4 = + n= v 8πm 3 n= v 8πm 3 + mα em 4αem ( mr n m Finie!! 9πv n= m m 9πv n= n R + We neglec here KK KK W-boson loops : : KK KKop :: KK KK W = mop^ :: mw^ ~ 4 :: : : fermion wih large dim. rep. is is inroduced o o ge op mass Cacciapaglia, Csaki Csaki & Park, Park, JHEP0603 (006 ( Mf Mf = MW MW Mf Mf = MW MW (ex. 5^*, 4^*, 7-dim rep. exra vecor-like quarks & is is KK KK modes inroduced and enhance he Higgs coupling by by # of of exra quarks

22 Raio of gg -> H -> γγ mh = 0 GeV n = n = 3 4% = TeV periodic ani-periodic SM n = 5 s KK mass

23 UED Addiive /R = 500 GeV /R = 750 GeV /R = TeV SM /R =.5 TeV,.5 TeV Periello, JHEP05 (00 003

24 Lile Higgs SM Subracive symmery breaking scale Han, Logan, McElrah &Wang, PLB563 (003 9

25 SUSY SM A = A μ an β Djouadi, PLB435 (998 0

26 Similar ype of of deviaions from he SM are also seen in in : : SUSY model Djouadi, PLB453 (998 ( : : Lile Higgs model Han, Han, Logan, Logan, McElrah & Wang, Wang, PLB563 (003 ( Common feaure among GHU, SUSY & LH is is ha he quadraic divergence in in mh^ is is canceled This can be seen diagrammaically as follows h Top h h New paricles h Sar wih Higgs self-energy diagram wih a relaive minus sign

27 Similar ype of of deviaions from he SM are also seen in in : : SUSY model Djouadi, PLB453 (998 ( : : Lile Higgs model Han, Han, Logan, Logan, McElrah & Wang, Wang, PLB563 (003 ( Common feaure among GHU, SUSY & LH is is ha he quadraic divergence in in mh^ is is canceled This can be seen diagrammaically as follows <h> Top h <h> New paricles h Replace one of he Higgs by is VEV

28 Similar ype of of deviaions from he SM are also seen in in : : SUSY model Djouadi, PLB453 (998 ( : : Lile Higgs model Han, Han, Logan, Logan, McElrah & Wang, Wang, PLB563 (003 ( Common feaure among GHU, SUSY & LH is is ha he quadraic divergence in in mh^ is is canceled This can be seen diagrammaically as follows <h> Top h <h> New paricles h Aaching gluon lines gluon fusion diagram wih a relaive minus sign

29 Summary We have calculaed calculable ampliudes for gg -> H -> γγ@lhc Clear qualiaive deviaions from he SM & UED predicions Connecion o he cancellaion of quadraic divergence of Higgs mass For scenarios solving he gauge hierarchy problem, he ampliude for gg -> -> H -> -> γγ is is suppressed c.f. GHU, Lile Higgs, SUSY, ec