Evidence for a fourth quark from weak interaction-the GIM mechanism

Transcription

1 Evience for a fourth quark from weak interaction-the GIM mechanism Haris Ðapo November

2 Outline 1 Motivation 2 Before charm 3 Charm 4 After charm 5 Conclusions

3 hat o we want to achieve?

4 Electroweak Lagrangian Lepton part L l = e lγ λ l A λ g 2 2 νγλ (1 γ 5 )l + λ g 2 lγ λ (1 γ 5 )ν λ 2 g [ νγ λ (1 γ 5 )ν 4 cosθ lγ ] λ (1 4 sin 2 θ γ 5 )l Zλ 0

5 Electroweak Lagrangian Lepton part L l = e lγ λ l A λ g 2 2 νγλ (1 γ 5 )l + λ g 2 lγ λ (1 γ 5 )ν λ 2 g [ νγ λ (1 γ 5 )ν 4 cosθ lγ ] λ (1 4 sin 2 θ γ 5 )l Zλ 0 Quark part L q = 2 3 e Pγ λ P A λ 1 3 e Nγ λ N A λ g 2 Pγ λ (1 γ 5 )U N + λ 2 g 2 N U γ λ (1 γ 5 )P λ 2 g [ 4 cosθ Pγ λ (1 8 3 sin2 θ γ 5 )P Nγ λ (1 4 ] 3 sin2 θ γ 5 )N Zλ 0 P = ( ū c t ) ; N = ( s b )

6 History Fermi theory of β-ecay in 1934 Fermi propose the theory of β-ecay his Lagrangian ha only the vector current L = 1 G ] F [ p γ λ n ē γ λ ν e + n γ λ p ν e γ λ e 2 2 G F = GeV

7 History Fermi theory of β-ecay in 1934 Fermi propose the theory of β-ecay his Lagrangian ha only the vector current L = 1 G ] F [ p γ λ n ē γ λ ν e + n γ λ p ν e γ λ e 2 2 G F = GeV Parity violation parity violation was suggeste in 1956 by Lee an Young axial current was ae to the Lagrangian so we got the V-A law L = 1 G ] F [ p γ λ (1 1.25γ 5 )n ēγ λ (1 γ 5 )ν e + H.c. 2 2

8 History Three quarks Gell-Mann in 61 invente eightfol way, an in 64 presente the quark moel with there quarks (u,, s) Cabbibo 63: quark is not an eigenstate of the weak interaction c = cosθ c + s sin θ c, θ c 13 o

9 History Three quarks Gell-Mann in 61 invente eightfol way, an in 64 presente the quark moel with there quarks (u,, s) Cabbibo 63: quark is not an eigenstate of the weak interaction c = cosθ c + s sin θ c, θ c 13 o Lagrangian L = 1 G ( ) F j λ j λ + j λ j λ 2 2 j λ = ē γ λ (1 γ 5 )ν e + µ γ λ (1 γ 5 )ν µ + c γ λ (1 γ 5 )u

10 Vector bosons Charge vector bosons Fermi type theory fails for higher energies; ω 300 GeV V A law is not renormalizable an new an more severe ivergencies appear at each higher orer from Yukawa s meson theory we take the iea of intermeiate bosons weak interaction is now meiate by ±

11 Vector bosons Charge vector bosons Fermi type theory fails for higher energies; ω 300 GeV V A law is not renormalizable an new an more severe ivergencies appear at each higher orer from Yukawa s meson theory we take the iea of intermeiate bosons weak interaction is now meiate by ± ith vector bosons L q = g 2 2ū γλ (1 γ 5 ) c + λ g 2 c γ λ (1 γ 5 )u λ 2 g/2 2 = m G 1/2 F 2 1/4

12 Vector bosons Charge vector bosons Fermi type theory fails for higher energies; ω 300 GeV V A law is not renormalizable an new an more severe ivergencies appear at each higher orer from Yukawa s meson theory we take the iea of intermeiate bosons weak interaction is now meiate by ± ith vector bosons L q = g 2 2ū γλ (1 γ 5 ) c + λ g 2 c γ λ (1 γ 5 )u λ 2 g/2 2 = m G 1/2 F 2 1/4 To complete the moel one also nees a neutral boson Z 0.

13 Glashow, Iliopoulos, Maiani paper GIM 1970, 6th most cite paper [3522] a new moel of quarks with not three but four quarks new quantum number for the fourth quark name charm which is preserve by strong interaction

14 Glashow, Iliopoulos, Maiani paper GIM 1970, 6th most cite paper [3522] a new moel of quarks with not three but four quarks new quantum number for the fourth quark name charm which is preserve by strong interaction

15 Mass ifference KL 0 K S 0 KS 0 = ( s + s )/ 2, KL 0 = ( s s )/ 2 τ S s; τ L 10 8 s KS 0 ecays into two pions, K L 0 ecay into three pions m = m L m S MeV(exp)

16 Mass ifference s K 0 L K 0 S K 0 S = ( s + s )/ 2, K 0 L = ( s s )/ 2 τ S s; τ L 10 8 s KS 0 ecays into two pions, K L 0 ecay into three pions m = m L m S MeV(exp) u ū s K 0 K 0 s s K 0 u u K 0 m G2 F 4π 2 m2 w cos 2 θ c sin 2 θ c f 2 K m K 10 8 MeV

17 Mass ifference s K 0 L K 0 S K 0 S = ( s + s )/ 2, K 0 L = ( s s )/ 2 τ S s; τ L 10 8 s KS 0 ecays into two pions, K L 0 ecay into three pions m = m L m S MeV(exp) u ū s K 0 K 0 s s K 0 u u K 0 m G2 F 4π 2 m2 w cos 2 θ c sin 2 θ c f 2 K m K 10 8 MeV incluing higher orer terms leas to ivergencies

18 eak current weak haron current J H µ = q C H γ µ (1 + γ 5 )q where q is a quark column vector (c, u,, s) an C H is C H = U U is the rotation matrix [ ] sin θ cos θ U = cos θ sin θ

19 Mass ifference u s u s K 0 K 0 K 0 K 0 s ū s c c s c s K 0 K 0 K 0 K 0 s ū s c s s K 0 u u K 0 K 0 u c K 0 s s s s K 0 c u K 0 K 0 c c K 0 s s m G2 F 4π 2 m2 c cos 2 θ c sin 2 θ c f 2 K m K MeV

20 Another example Neutral current strangeness changing neutral weak interactions o not occur neutral ecay K 0 L µ+ µ branching ratio only analogous ecay K + µ + ν µ is fully allowe

21 Another example Neutral current strangeness changing neutral weak interactions o not occur neutral ecay K 0 L µ+ µ branching ratio only analogous ecay K + µ + ν µ is fully allowe u ν µ K s µ + KL 0 7 Z 0 s µ + µ

22 Secon orer even if first orer amplitue is zero there is the secon orer contribution cosθc µ u s sin θc + µ +

23 Secon orer even if first orer amplitue is zero there is the secon orer contribution cosθc µ u s + µ + sin θc sinθc µ c s µ + cosθc if all of the quark masses where egenerate than there woul be no strangeness changing neutral current effect in any orer since these two graphs woul cancel exactly

24 Experimental suggestions Phenomenon for the iscovery of charm "irect" lepton prouction large number of strange particles narrow peaks in mass spectra of harons apparent strangeness violation short tracks, inicative of particles with lifetimes s narrow peaks in e + e or µ + µ mass spectra approach of the (e + e harons)/(e + e µ + µ ) ratio to 3 1/3

25 SU(4) Consequences four quarks make SU(4) SU(3) is a subgroup of SU(4) Figure: left: 20-plet with SU(3) octet, right:20-plet with SU(3) ecuplet.

26 Cabibbo-Kobayashi-Maskava CKM 75 τ was iscovere an a thir generation was neee GIM moel was mae for 4 quarks but can be easily extene to 6 quarks U is now a 3 3 matrix with 8 real inepenent parameters so we nee three Cabibbo-like angles an one CP-violating phase

27 Cabibbo-Kobayashi-Maskava CKM 75 τ was iscovere an a thir generation was neee GIM moel was mae for 4 quarks but can be easily extene to 6 quarks U is now a 3 3 matrix with 8 real inepenent parameters so we nee three Cabibbo-like angles an one CP-violating phase U = c 1 s 1 c 3 s 1 s 3 s 1 c 2 c 1 c 2 c 3 s 2 s 3 e iδ c 1 c 2 s 3 + s 2 c 3 e iδ s 1 s 2 c 1 s 2 c 3 + c 2 s 3 e iδ c 1 s 2 s 3 c 2 s 3 e iδ where c i (s i ) = cos θ i (sin θ i ) with i = 1, 2, 3

28 CKM toay ( ) ( ) 10 3 ( ) 10 3 ( ) square of elements of this matrix represent probability of a transition from one quark to another quark mixing between t an ( an s) is very small

29 The beginning is the en. Summary from Fermi type interaction to stanar moel gauge theories of electroweak interaction became viable GIM mechanism le to the introuction of a family concept GIM was a clear preiction of an entirely new funamental particle

30 The beginning is the en. Summary from Fermi type interaction to stanar moel gauge theories of electroweak interaction became viable GIM mechanism le to the introuction of a family concept GIM was a clear preiction of an entirely new funamental particle Conclusion matter is inee compose of 6 quark an 6 leptons all particles are necessary to explain the experimental situation the "real" evelopment was not so straight forwar, only in hinsight it becomes clear

31 Literature Literature S.L.Glashow, J. Iliopulos, an L. Maiani, Phy. Rev. D2, 1285, (1970) E.D. Commins, an P.H. Bucksbaum, eak interaction of leptons an quarks Cambrige University Press Thank you for your attention!