Glashow-Weinberg-Salam Model

• EM and weak forces mix…or just EW force. Before mixing Bosons are massless: • Group Boson Coupling Quantum No. SU(2) L W 1,2,3 g T weak isospin U(1) B g’ Y leptonic hypercharge

T



Y

/ 2 

Q

(

elec

.

ch

arg

e

)

L

int 

g T

  

W



g



YB

• convert to physical fields. Neutrals mix (B,W3  Z, photon). W,Z acquire mass. Force photon mass=0. Higgs Boson introduced to break mass symmetry (A is same field as in EM….4 vector)

A

 sin 

W W

3  cos 

W B Z

 cos 

W W

3  sin 

W B



W



weak mixing angle

 tan 

W

P461 - particles VII 

g



g

1

Higgs Boson

• breaking electroweak symmetry gives: massive W+Z Bosons mass=0 photon 1 or more scalar particles (Higgs) minimal SUSY, 2 charged and 3 neutral • Higgs couples to mass and simplistically decays to the most massive available particles • “easy” to produce in conjunction with heavy objects (helps to discover??)  (

HZ

)   (

HW

 (

H

)

production

)  20 %

m H

 100

GeV

P461 - particles VII 2

Standard Model Higgs Boson

• Branching fraction depends on mass • Use ZH,WH for m<135 GeV • Use WW for m> 135 GeV • Current limits use 1-2 fb -1 • D0: 12 Higgs decay channels + 20 analyses combined

WH



l

 

bb ZH



ZH



H

 

bb WW

 P461 - particles VII D0+CDF Limits 1.4-8 times SM (2007) 3

• Look at EM and 2 weak “currents”

L EM



g

sin 

W T

3

W

3 

g

 cos 

W YB

 2

L EM



g

sin  (

T

3 

Y

)

A



g

 cos 

W



g

sin 

W



e L EM



g

sin 

W W A Q

2 

eA



J



em T

3 

Y

/ 2 

Q

• charged current. Compare to mu/beta decay (have measured weak force, eg. weak mixing only “new” free parameter)

L cc



g



T

 

W

  

T

 

W

  

g

2 8

M W

2 

G F

2 

M W

 2 5 / 4

g G F



e

/ sin 

W

2 5 / 4

G F

 37 .

3

GeV

sin 

W

• weak neutral current

L NC g

2 

g

cos 

W

/ cos 2 

W

8

M Z

2 

Z

(

T

3

G F

2  sin 

M Z

2 

W Q



M

cos ) 

W



W g

cos 

W Z

 

J NC

P461 - particles VII 4

W and Z couplings

right handed singlets   

e e

  [    

R R L T

3

T

3

T

3     2

Q

  0 0

Q Q

   1 0 ] 1 , 0 • W couplings to left-handed component and always essentially the same

gW

 

T

3   1 2

g doublet

;  0 sin

glet

Z to right-handed singlet

g R

 " (

T

 "

g z

" ( 

Q

sin 2 

W

) 

W Z

 sin 

W e

cos 

W

[

T

3 

Q

sin 2 

W

] • redefine as Vector and Axial parts of V-A Z

e



c V c A



g L



g L



g R



g R



T

3  2

Q

sin 2 

W



T

3

c

2

V



c

2

A e

 P461 - particles VII 5

Z



Z decays/vertices

e



e

     

e



e

   

u u c c

       

d d s s b b T

3

Q

  1 2 1

c V

 .

08

c A c

2

A

 2

c V

 1 2 .

26  1 2 0  1  2 1 2 .

50   1 2 2 3   1 2 1 3 .

19  .

34  1 2 .

29  1 2 .

37 Color factor of 3 for quarks

c V



g L



g R



T

3

c A



g L

sin 2 

W

 

g R



T

3 0 .

21  2

Q

sin 2 

W

P461 - particles VII 6

Z Branching Fraction

• Can use couplings to get branching modes • PDG measured values in () •

Z Z

 

ee all

 .

26 3 * .

26  3 * .

50  2 * 3 * .

29  3 * 3 * .

37  .

26 7 .

3  .

036 (.

034 )

Z Z Z Z Z Z

   

all b b

  

all q q all

 3 * .

50  0 .

21 7 .

3 (.

20 )   3 * .

37  0 .

15 7 .

3 3 * 3 * .

37  2 (.

15 * 3 * .

29 ) 7 .

3  0 .

70 (.

70 ) P461 - particles VII 7

Neutrino Physics

• Three “active” neutrino flavors (from Z width measurements). Mass limit from beta decay

m



e m

    3

eV

0 .

2

MeV

 2

m ex



m

2 

x

 10  4

eV

2  10  3

eV

2

x

 

or



x

  (

or inactive

)

m

   18

MeV

• Probably have non-zero masses as they oscillate (right-handed neutrinos? messes up electroweak • Only have weak interactions and can be either charged or neutral currents

e

charge 

e



e

neutral 

e

W p n n,p,e

e

Z n,p,e P461 - particles VII  

e n e

 

n

 

e

  

p p



e e

 

e

 

e

 

e e e p

   

e e e p

 

e

  

e

8

Neutrino Cross Sections

• Use Fermi Golden Rule

Rate

 2   |

M

| 2 

phase space

• M (matrix element) has weak interaction physics…W, Z exchange ~ constant at modest neutrino energies. Same G factor as beta decay

G



g

2 2 8

M W

2

q

2  1 2

M W

 1 2

M W E

 

M W

• cross section depends on phase space and spin terms. Look at phase space first for charged current. Momentum conservation integrates out one particle 

e e



e



e

(

CC

)

phase space



p e

2

dp e p

 2

dp



p cm



p e



p

    4

G

2  2

p cm

P461 - particles VII 9

Neutrino Cross Sections II

• Look in center-of-momentum frame

s



p e

 

M

 2  

p

 2

E tot

 

p tot

2

p tot

 0 

s

 ( 2

p

) 2

E tot



E

 

E e

 2

p

  4

G

2 

p

2 

G

2

s

 • s is an invariant and can also determine in the lab frame

p tot



s



E

 2

p

 

E

  2

m e E



E tot



m e

2 

E

 

p

 2 

m e

 2

m e E

  

G

2 2 

mE

 • cross section grows with phase space (either neutrino energy or target mass)   ( ( 

p

) 

e

) 

m p m e

 2000 P461 - particles VII 10

Neutral Currents

• The detection of some reactions proved that neutral current (and the Z) exist     

e



p

      

e



p

• the cross section depends on the different couplings at each vertex and measure the weak mixing angle  

e



G

2

m e



E

  

e



G

2

m e



E

 ( 1  4 sin 2 

W

 16 sin 3 4 

W

) ( 1 3  4 3 sin 2 

W

 16 3 sin 4 

W

) • about 40% of the charged current cross section. due to Z-e-e coupling compared to W-e-nu coupling P461 - particles VII 11

Neutrino Oscillations

• Different eigenstates for weak and mass

weak

: 

e

,   ,     1 ,  2 ,  3 :

mass

• can mix with a CKM-like 3x3 matrix with (probably) different angles and phases then quarks. The neutrino lifetime is ~infinite and so mix due to having mass and mass differences (like KL and KS) • example. Assume just 2 generations (1 angle)     1 cos    2 sin  

e

   1 sin    2 cos  • assume that at t=0 100% muon-type   (

t

 0 )  1 

e

(

t

 0 )  0   1 (

t

 0 )  cos   2 (

t

 0 )  sin  P461 - particles VII 12

Neutrino Oscillations II

• Can now look at the time evolution • from the Scrod. Eq. And assuming that the energy is much larger than the mass  1 , 2 (

t

)   1 , 2 ( 0 )

e iE

1 , 2

t E i



p



m i

2 2

p

 

c

 1 • probability of e/mu type vs time (or length L the neutrino has traveled) is then   (

t

) 2  cos 2 

e iE

1

t

 sin 2 

e iE

2

t

2  1  sin 2 2  sin 2 

m

2

Lc

4 4

E



c

• where we now put back in the missing constants and used 2 trig identities

t



L E c p

2 sin  cos   sin 2  cos(

E

2 

E

1 )

t

 1  2 sin 2 (

E

2 

E

1 )

t

2 P461 - particles VII 13

Neutrino Oscillations III

• Oscillation depends on mixing angle and mass difference (but need non-zero mass or no time propagation)   (

t

) 2  1  sin 2 2  sin 2 

m

2

Lc

4 4

E



c



e

(

t

) 2  1    (

t

) 2 • so some muon-type neutrinos are converted to electron type. Rate depends on neutrino energy and distance neutrino travels L/E • go to 3 neutrino types and will have terms with more than one mixing angle. Plus neutrinos can oscillate into either of the other two (or to a fourth “sterile” type of neutrino which has different couplings to the W/Z than the known 3 types) P461 - particles VII 14

Neutrino Oscillations IV

P461 - particles VII 15

Neutrino Oscillations V

With three generations of neutrinos the change of one neutrino type into another depends on many terms You can understand the terms by measuring at different energies and lengths There is another effect (interactions in matter) which we will skip that comes into play Oscillations can also violate CP – be different if neutrino or antineutrino beam P461 - particles VII 16

Detecting Neutrino Oscillations

• Disappearance: flux reduction larger L/E • Solar Neutrinos. Measure rate for both electron neutrinos and all neutrinos (using neutral current). Low energies (few MeV) cause experimental thresholds for some techniques. Compare to solar models.

Rate

(

rate

(  

e

,  ,  

e



pn n



e

   

e

,  , 

p

) 

p



n

) • Atmospheric neutrinos. Measure rate as a function of energy and length (from angle)      

e



e

  # 

e

#    1 2

production

• also electron or muon neutrinos produced at reactors or accelerators. Compare flux near production to far away L/E >> 1 P461 - particles VII 17

Detecting Neutrino Oscillations

• Appearance: start with one flavor detect another • Ideal. Tag nu production by detecting the lepton. Then detect neutrino interaction. Poor rates (considered pi/K beams and muon storage rings) • • Real. Tau neutrino very difficult to detect sources of pure electon neutrinos (reactors) are below muon/tau threshold  use mostly muon neutrino beam  

e

  0 .

003

K

   

e

  

e

• can measure neutrino energy in detector (if above 1 GeV. Below hurt by Fermi gas effects). Can usually separate electron from muon events with a very good ~100% active detector P461 - particles VII 18

Nova detector will be mostly liquid scintillator (like BNL neutrino experiment of the 1980s. Greater than 80$ active.

P461 - particles VII 19

High Priority Items in Particle Physics

• Quark Mixing and CP violation • Neutrino Mixing and maybe CP violation • are Quark and Neutrino mixing related?

• Source of Electro-Weak symmetry breaking (Higgs?) • Precision measurements of current parameters (top,W,Z mass)(g-2) • what is dark matter? dark energy?

• Searches for New Phenomena – Supersymmetry, Extra Dimensions, Leptoquarks, new quarks/leptons/bosons, compositeness, why spin ½ vs spin 1 • some NP can explain other questions (source of CP, dark matter, etc) P461 - particles VII 20