Wednesday, Nov. 29, 2006PHYS 3446, Fall 2006 Jae Yu 1 PHYS 3446 – Lecture #22 Wednesday, Nov. 29, 2006 Dr. Jae Yu 1. The Standard Model Symmetry Breaking.

Wednesday, Nov. 29, 2006 PHYS 3446, Fall 2006Jae Yu

1

PHYS 3446 – Lecture #22Wednesday, Nov. 29, 2006

Dr. Jae Yu

1. The Standard Model Symmetry Breaking and the Higgs particleHiggs Search StrategyNeutrino OscillationsIssues in the Standard Model

2. Feynmann Diagrams


2

Spontaneous Symmetry BreakingWhile the collection of ground states does preserve the symmetry in L, the Feynman formalism allows to work with only one of the ground states through the local gauge symmetry Causes the symmetry to break.This is called “spontaneous” symmetry breaking, because symmetry breaking is not externally caused.

The true symmetry of the system is hidden by an arbitrary choice of a particular ground state. This is the case of discrete symmetry w/ 2 ground states.


3

EW Potential and Symmetry Breaking

4222

4

1

2

1

Symmetric about this axis

Not symmetric about this axis


4

The Higgs Mechanism• Recovery from a spontaneously broken electroweak

symmetry gives masses to gauge fields (W and Z) and produce a massive scalar boson– The gauge vector bosons become massive (W and Z) – The massive scalar boson produced through this

spontaneous EW symmetry breaking is the Higgs particle• In SM, the Higgs boson is a ramification of the

mechanism that gives masses to weak vector bosons, leptons and quarks

The Higg

s

Mechan

ism


5

Higgs Production Processes at Hadron Colliders

Gluon fusion: Hgg

WW, ZZ Fusion: HZZWW ,

Higgs-strahlung off W,Z: HZWZWqq , , **

Higgs Bremsstrahlung off top: Httggqq ,


6

Hadron Collider SM Higgs Production

LHC

Tevatron

We use WHe+bb channel for search for Higgs at Tevatron


7

SM Higgs Branching Ratio

140GeV/c2 We use WHe+bb channel for search for Higgs


8

How do we find the Higgs particle?• Look for WHl++b b-bar• Use the finite lifetime of mesons containing b-quarks

within a particle jets.

b vertex

SiliconDetectors

Beampipe

1”


9LEP EWWG: http://www.cern.ch/LEPEWWG 114.4<MH<199GeV

What do we know as of Winter 06?

http://www.cern.ch/LEPEWWG


10

How do we make a Neutrino Beam?

• Use large number of protons on target to produce many secondary hadrons (, K, D, etc) and focus as many of them as possible

• Let and K decay in-flight for beam in the decay pipe– +K

• Let the beam go through shield and dirt to filter out and the remaining hadrons, except for – Dominated by

p

Good target

Good beam focusing

Long decay region

Sufficient dump


11

How can we select sign of neutrinos?• Neutrinos are electrically neutral• Need to select the charge of the secondary hadrons

from the proton interaction on target• Sets of Dipoles are used to select desired charges of

the secondary hadrons

di-poles


12

How can there be wrong sign of neutrinos in a sign selected beam?

• Interaction of correct sign secondary hadrons with beamline elements, including dump and shields– Act as if a fixed target is hit by hadron beam

• Back-scatter of unused protons into the beamline

• CP violating neutrino oscillations


13

4. QCD Factorization Theorem

Non-perturbative, infra-red part

k k’

W+(W-)

p,

} EHadP

q=k-k’

q, (q)

xP

Partonic hard scatter

=f*p

f

p

Factor the whole interaction into two independent parts!!

Allow QCD perturbation theory to work and physical observables calculable.


14

How is sin2W measured?

• Cross section ratios between NC and CC proportional to sin2W

• Llewellyn Smith Formula:

• Define experimental variable to distinguish NC and CC• Compare the measured ratio with MC prediction

)(CC

)(CC

W4

W22

)(CC

)(NC)(

σ

σ1θsin

95

θsin21

ρσ

σR

WEMweak QIcoupling 2)3( sin)3(weakIcoupling


15

Charged Current Events

Neutral Current Events

How Can Events be Separated?

x-view

y-view

x-view

y-viewNothing is coming in!!!

Nothing is coming in!!!

Nothing is going out!!!

Event Length


16

Neutrino Oscillation• First suggestion of neutrino mixing by B. Pontecorvo at the

K0, K0-bar mixing in 1957• Solar neutrino deficit in 1969 by Ray Davis in Homestake

Mine in SD. Called MSW effect• Caused by the two different eigenstates for mass and weak• Neutrinos change their flavor as they travel Neutrino

flavor mixing• SM based on massless neutrinos• SM inconsistent• Oscillation probability depends on

– Distance between the source and the observation point– Energy of the neutrinos– Difference in square of the masses


17

Neutrino Oscillation Formalism• Two neutrino mixing case:

sin cos 1 2

where and are weak eigenstates, while and are mass eigenstates, and is the mixing angle that give the extent of mass eigenstate mixture, analogous to Cabbio angle

e

1 2

e

OR

cos sin

sin cos

1

2

cos sin e 1 2


18

Oscillation Probability• Substituting the energies in the wave functions:

E

tmiE

mpitt 2expcossin2exp22

121

where and .22

21

2 mmm pE

• Since the ’s move at the speed of light, t=x/c, where x is the distance to the source of .

• The probability for with energy E oscillates to e at the distance L from the source becomes

E

LmP e

222 27.1

sin2sin


19

Sources for Oscillation Experiments• Natural Sources

– Solar neutrinos– Atmospheric neutrinos

• Manmade Sources– Nuclear Reactor– Accelerator


20

Oscillation Detectors• The most important factor is the energy of neutrinos

and its products from interactions• Good particle ID is crucial• Detectors using natural sources

– Deep under ground to minimize cosmic ray background– Use Cerenkov light from secondary interactions of

neutrinos• e + e e+X: electron gives out Čerenkov light• CC interactions, resulting in muons with Čerenkov light

• Detectors using accelerator made neutrinos– Look very much like normal neutrino detectors

• Need to increase statistics


21

Atmospheric Neutrinos & Their Flux• Neutrinos resulting from the atmospheric

interactions of cosmic ray particles– He, p, etc + N ,K, etc

•

• e+e+

– This reaction gives 2 and 1 e

• Expected flux ratio between and e is 2 to 1• Give a predicted ratio of

2

1

N

Ne


22

SNO Experiment Results

0.35


23

Importance of the Zenith Angle• The Zenith angle represents the different distance the neutrinos

traveled through the earth• The dependence to the angle is a direct proof of the oscillation

probability

E

LmP e

222 27.1

sin2sin


24

Super-K Atmospheric Neutrino Results


25

Accelerator Based Experiments• Mostly from accelerators• Far better control for the beam than natural or

reactor sources• Long and Short baseline experiments

– Long baseline: Detectors located far away from the source, assisted by a similar detector at a very short distance (eg. MINOS: 370km, K2K: 250km, etc)

• Compare kinematic quantities measured at the near detector with the far detector, taking into account angular dispersion

– Short baseline: Detectors located at a close distance to the source

• Need to know flux well


26

Long Baseline Experiment Concept (K2K)

Compare kinematic distributions between near and far detectors


27

Different Neutrino Oscillation Strategies


28

Exclusion Plotse appearance

e appearance

disappearance


29

Future: Neutrino Factory• Spin-off of a muon collider research

– One a hot, summer day at BNL, the idea of neutrino storage ring popped up

• Future facility using muon storage ring, providing well understood neutrino beam ( and e) at about 106 times higher intensity


30

What do we know now?• We clearly know neutrinos oscillate Neutrinos have

masses• It seems that there are three allowed regions of

parameters (sin22 and m2) that the current data seem to point– LSND ~1eV2; Super-K ~ 10-3 eV2, Solar (LMA) ~ 10-5 eV2

– There are at least three flavors participating in oscillation– Sin2223 ~ 1 at 90% confidence level– |m32

2| ~ 2x10-3 eV2

– m212 ~ 2x10-3 eV2 (If LMA confirmed)

– Sin2212 ~ 0.87 at 90% confidence level (if LMA confirmed)– Sin2213 < O(0.1)


31

What do we not know?• Does 3-flavor mixing provide the right framework?

– For CP–violating oscillation, additional neutrino flavors, neutrino decay, etc?

• How many flavors of neutrinos do we have?• Is sin2213 0 or small?

• What is the sign of m32?– What are the configuration of neutrino masses?– What are the actual masses of neutrinos mass eigenstates?

• What are the matter effects?• Is sin2223 = 1?


32

Issues in SM• Why are the masses of quarks, leptons and vector bosons the

way they are?• Why are there three families of fundamental particles?• What gives the particle their masses?• Do the neutrinos have mass?• Why is the universe dominated by particles?

– What happened to anti-particles?• What are the dark matter and dark energy?• Are quarks and leptons the “real” fundamental particles?• Other there other particles that we don’t know of?• Why are there only four forces?• How is the universe created?• Where are we from?


33

Feynman Rules• The rules for any process are: • Draw all possible diagrams

– Different time-orderings of a given process are represented by the same diagram.

• Given the initial momentum and energy, define how momentum and energy flow for each line in the diagram. – Where each diagram has a closed loop, there is an arbitrary momentum

and energy flow around the loop and we must integrate over all possible choices for these quantities.

– Each intermediate line in the diagram contributes a factor to the amplitude of 1/(E2-p2c2-m2c4) where m is the appropriate mass for the particle type represented by the line. Note that this says that the more "virtual" the particle represented by a line is, the smaller the contribution of the diagram.

• Add the amplitude factors from all possible diagrams to get the total amplitude for the process.


34

Feynman Diagram ComponentsImage Description Particle Represented

straight line, arrow to the right

electron

straight line, arrow to the left

positron

wavy line photon


35

Feynman Diagram Rules


36

A Few Example Feynman Diagrams


37

A Few Feynman Diagram Exercises

• Leptonic decays of W+, W- and Z0• Leptonic decay of p-, p+ and p0• Top quark decay (tbW) possibilities• P and P collisions• WH production and final states from P and P

collisions

Wednesday, Nov. 29, 2006PHYS 3446, Fall 2006 Jae Yu 1 PHYS 3446 – Lecture #22 Wednesday, Nov. 29, 2006 Dr. Jae Yu 1. The Standard Model Symmetry Breaking.

Documents