p461 - particles vii1 glashow-weinberg-salam model em and weak forces mix…or just ew force. before...

P461 - particles VII 1

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 W1,2,3 g T weak isospin U(1) B g’ Y leptonic hypercharge

• Interaction Lagrangian is

• convert to physical fields. Neutrals mix (B,W3Z, 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)

)arg.(2/3 echelecQYT

2int

YBgWTgL

g

ganglemixingweak

BWZ

BWA

WW

WW

WW

tan

sincos

cossin3

3


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??)

GeVmH

HWHZH

production

100%20)(

)()(


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 l l bb

ZH bb

H WW l l

D0+CDF

Limits 1.4-8 times SM (2007)


• Look at EM and 2 weak “currents”

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

• weak neutral current

emWEM

WEM

WWEM

JeAQAgL

AY

TgL

YBgWTgL

sin

)2

(sin

2cossin

3

33

QYT

egg WW

2/

sincos

3

WF

W

F

WF

W

cc

GeV

G

e

G

gM

G

M

g

WTWTgL

sin

3.37

2

sin/

228 4/54/52

2

W

WZ

F

Z

W

NCW

WW

NC

MM

G

M

g

JZg

QTZg

L

cos28

cos/

cos)sin(

cos

2

22

23


W and Z couplings

• EW model has left-handed doublets right handed singlets

• W couplings to left-handed component and always essentially the same

• Z to left-handed doublet Z to right-handed singlet

• redefine as Vector and Axial parts of V-A

]00[

10

0,12

1

3

3

3

QT

QTe

QTe

R

R

L

e

gletdoubletgTgW sin0;213

]sin[cossin

23W

WW

QTe

Z

)sin(""

)sin(""2

23

WzR

WzL

Qgg

QTgg

3

23 sin2

Tggc

QTggc

RLA

WRLV

Z

e

e

22AV cc


Z decays/vertices

bb

sscc

dduueeZ ee

3

1

3

201

2

1

2

1

2

1

2

13

Q

T

37.29.50.26.

2

1

2

1

2

1

2

1

34.19.2

108.

22VA

A

V

cc

c

c

Color factor of 3 for quarks

21.0sin

sin2

2

3

23

W

RLA

WRLV

Tggc

QTggc


Z Branching Fraction

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

•

)70(.70.03.7

29.*3*237.*3*3

)15(.15.03.7

37.*3

)20(.21.03.7

50.*3

)034(.036.3.7

26.37.*3*329.*3*250.*326.*3

26.

allZ

qqZallZ

bbZ

allZ

Z

allZ

eeZ


Neutrino Physics

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

• 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

MeVm

MeVm

eVme

18

2.0

3

)(10

10232

242

inactiveorxeVm

orxeVm

x

ex

W

Z

e

e

e

e

e

e n

p

n,p,e

n,p,e

charge

neutral

ee

e

ee

pn

pen

ee

ee

pp

ee

ee


Neutrino Cross Sections

• Use Fermi Golden Rule

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

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

22

22

4

)(

cmecm

ee

ee

pG

ppp

dppdppspacephase

CCee

spacephaseMRate 2||2

WWW

MEMMq

222

11

2

2

82 WM

gG


Neutrino Cross Sections II

• Look in center-of-momentum frame

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

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

sGpGps

pEEEppp

pEMs

etottote

tottot

2222

222

4)2(

20

mEG

EmpmEmEs

mEEEpp

eee

etottot

2

222

222

2000)(

)(

e

p

m

m

e

p


Neutral Currents

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

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

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

pp

ee

)sin3

16sin

3

4

3

1(

)sin3

16sin41(

422

422

WWee

WWee

EmG

EmG


Neutrino Oscillations

• Different eigenstates for weak and 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)

• assume that at t=0 100% muon-type

massweak e :,,,,: 321

cossin

sincos

21

21

e

sin)0(cos)0(

0)0(1)0(

21

tt

tt e


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

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

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

p

mpEet i

itiE

2)0()(

2

2,12,12,1 1c

cE

Lcm

eet tiEtiE

4sin2sin1

sincos)(

4222

222221

p

E

c

Lt

2

)(sin21)cos(

2sincossin2

12212

tEEtEE


Neutrino Oscillations III

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

• 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)

22

42222

)(1)(

4sin2sin1)(

tt

cE

Lcmt

e


Neutrino Oscillations IV


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


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.

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

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

)(

)(

,,,, nppnRate

penrate

ee

e

production

e

e

e

2

1

#

#


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

• 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

ee eK003.0


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

80$ active.


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 vii1 glashow-weinberg-salam model em and weak forces mix…or just ew force. before...

Documents

z slide

p461 particles vii4

p461 particles vii5

target mass slide

z exchange

massive w z bosons mass

vector slide

weak currents