素粒子物理学2 素粒子物理学序論B 2010年度講義第10回

素粒子物理学2 素粒子物理学序論B 2010年度講義第10回

L = ν(i / m ν )ν + l(i / m l )l + 1 2 ( µχ µ χ µ 2 χ 2 ) 1 4 F i µνf iµν + m 2 W W +µ W µ + 1 4 G µνg µν + m2 Z 2 Z µz µ + ea µ ( lγ µ l) g 2 [ W µ + ( νγ µ P L l)+c.c. ] ḡz µ [ νγ µ (s νl P L + s νr P R )ν + lγ µ (s ll P L + s lr P R )l ] 2aχ + χ2 ( + g 2 W 4 +µ W + µ + ḡ2 2 Z µz µ) m l a χ( ll) m ν a χ( νν),

ḡ 2 g 2 2 v = gm W = e sin θ W m W 4 v = gm Z cos θ W = H 2e sin(2θ W ) m Z V µ V ν 2 H h f Y f = v m f f f

ḡ 2 g 2 2 v = gm W = e sin θ W m W 4 v = gm Z cos θ W = H 2e sin(2θ W ) m Z V µ V ν 2 H h f Y f = v m f f f

σ s W - W + W - W + γ Z e - e + e - e + W - W + ν e - e +

σ s W - W + W - W + γ Z e - e + e - e + W - W + ν e - e +

σ s W - W + W - W + γ Z e - e + e - e + W - W + ν e - e +

σ s W - W + W - W + γ Z e - e + e - e + W - W + ν W - W + H e - e + e - e +

σ s W - W + W - W + γ e - e + W - W + Z e - e + W - W + ν H e - e + e - e +

σ s W - W + W - W + γ e - e + W - W + Z e - e + W - W + ν H e - e + e - e +

M = ig 8m 2 W (u νµ γ µ (1 γ 5 )u µ )(u e γ µ (1 γ 5 )u νe )

where s, t are the Mandelstam variables [the c.m. energy s is the square of the sum of the momenta of the initial or final states, while t is the square of the difference between the momenta of one initial and one final state]. In fact, this contribution is coming from longitudinal W bosons which, at high energy, are equivalent to the would be Goldstone bosons as discussed in 1.1.3. One can then use the potential of eq. (1.58) which gives the interactions of the Goldstone bosons and write in a very simple way the three individual amplitudes for the scattering of longitudinal W bosons [ A(w + w w + w )= 2 M ( ) H 2 M 2 2 ( ) ] + H 1 M 2 2 + H 1 (1.150) v 2 v s MH 2 v t MH 2 which after some manipulations, can be cast into the result of eq. (1.149) given previously. W + W W H W + H Figure 1.15: Some Feynman diagrams for the scattering of W bosons at high energy. These amplitudes will lead to cross sections σ(w + W W + W ) σ(w + w w + w ) which could violate their unitarity bounds. To see this explicitly, we first decompose the scattering amplitude A into partial waves a l of orbital angular momentum l A =16π (2l +1)P l (cos θ) a l (1.151) l=0 where P l are the Legendre polynomials and θ the scattering angle. Since for a 2 2 process, the cross section is given by dσ/dω = A 2 /(64π 2 s) with dω =2πdcos θ, one obtains σ = 8π s = 16π s l=0 l =0 (2l +1)(2l +1)a l a l 1 1 dcosθp l (cos θ)p l (cos θ) (2l +1) a l 2 (1.152) l=0 where the orthogonality property of the Legendre polynomials, dcosθp l P l = δ ll, has been used. The optical theorem tells us also that the cross section is proportional to the imaginary part of the amplitude in the forward direction, and one has the identity σ = 1 s Im [ A(θ =0)] = 16π s (2l +1) a l 2 (1.153) l=0

ヒッグス質量に対する理論的制限 WW散乱断面積 GF m2h m2h m2h s A(W W W W ) = [2 + ln(1 + 2 ] 2 s mh s mh 8 2π mh 1 TeV ヒッグスの自己結合定数 v= V = µ φ φ + λ φ φ 2 2 Triviality 1 1 3 Q2 = ln 2 2 λ(v) λ(q) 4π v λ(q) = µ2 /λ λ(v) 1 Q2 3 4π 2 λ(v) ln( v 2 ) 真空の安定性 λ>0が必要 11

実験からの制約 R0(+R.,+S#&-T+'&55 "#$%&'($)&*+,&-&'()(-+./+)0(+1)&$%&-%+2.%(* 80.70 experimental errors 90% CL: LEP2/Tevatron (today) Tevatron/LHC MW [GeV] 80.60 不確定性原理の範囲内でvirtualな 3//(4)5+,-(%64)6.$5+./++12+76&+-&%6&)67( 4.--(4)6.$5 ILC/GigaZ USY ( light S 中間状態が可能 ;9+).+)0(+<6==5+'&55+!%* # % ) & "#$%!') 4&$+8(+-(*&)(%9+:6)0+'! MSSM' 80.50 80.40 80.30 heav 114 MH = SM MH = GeV SM MSSM both models ev 400 G 80.20 量子補正 SY y SU Heinemeyer, Hollik, Stockinger, Weber, Weiglein 08 160 165 170 175 180 185 mt [GeV] ') 65+-.#=0*>+?+)0( 7&4##'+(@,(4)&)6.$ 量子補正には直接観測されない ヒッグスボソン 粒子 7&*#(./+)0(+<6==5+/6(*% の影響も含まれる!,-.86$=+)0(+A;1B '(40&$65'+C$(:+,0>5645DE ヒッグス以外の種々の精密測定からヒッグスの質量を!"##$%&'()&*&+,-'(.&/&#,00 予測可能 F-(4656.$+'(&5#-('($)+! GCHE+/8IJ,-.K(4)6.$L+"')MJNOCJE+P(QN! 12

600 500 M H [GeV/c 2 ] 400 300 200 EW Precision Triviality 100 EW vacuum is absolute minimum 0 3 5 7 9 11 13 15 17 19 log 10! [GeV]

! [fb] 10 5 10 4 qq! qqh SM Higgs production gg! h LHC q V V q q V H 10 3 q H q V q qq! Wh 10 2 bb! h qb! qth TeV4LHC Higgs working group gg,qq! tth qq! Zh 100 200 300 400 500 m h [GeV] g g Q H g g H Q Q

1 2m H spin,color dlip S = (2π) 4 δ 4 (q p 1 p 2 ) M 2 dlip S d 3 p 1 (2π) 3 2E 1 d 3 p 2 (2π) 3 2E 2 Γ(H VV)= G µm 3 H 16 2π δ V 1 4x (1 4x +12x 2 ), x = M 2 V M 2 H Γ Born (H f f) = G µn c 4 2π M H m 2 f β3 f

1 2m H spin,color dlip S = (2π) 4 δ 4 (q p 1 p 2 ) M 2 dlip S d 3 p 1 (2π) 3 2E 1 d 3 p 2 (2π) 3 2E 2 Γ(H VV)= G µm 3 H 16 2π δ V 1 4x (1 4x +12x 2 ), x = M 2 V M 2 H Γ Born (H f f) = G µn c 4 2π M H m 2 f β3 f

100 Higgs Width [GeV] 10 1 0.1 0.01 m H m 3 H 0.001 0 100 200 300 400 Higgs Mass [GeV/c 2 ] 500

!"

100m

100m

10 5! [fb] 10 4 10 3 10 2 gg! h qq! qqh qq! Wh bb! h gg,qq! tth qb! qth TeV4LHC Higgs working group SM Higgs production LHC qq! Zh 100 200 300 400 500 m h [GeV]

LHCでのヒッグス探索能力 必要な統計量 ルミノシティ(fb-1) S/ B ルミノシティ!"# 1,2年目 a few fb-1 / yr 2,3,4年目 a few x 10 fb-1 /yr 予想は非常に難しい 標準理論ヒッグスの質量 図はLHC実験の1つATLAS実験単独での結果予想 実験グループはもう1つ CMS ある 非常に軽くなければ数年で発見可能 24

ヒッグス発見後にやること ゲージ対称性により ゲージボソンの質量は本来ゼロ カイラル対称性により フェルミオンの質量は本来ゼロ 標準理論では 素性の違う2種類の粒子に質量を与える メカニズムが一つ 省エネだが若干 かなり 怪しい ヒッグスセクターには原理がない 結合定数 質量 の関係を確認することが最重要 結果次第では発見された ヒッグスは標準理論の枠外 25