PHYS 5326 – Lecture #9 & 10

Friday, Feb. 21, 2003 PHYS 5326, Spring 2003Jae Yu

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PHYS 5326 – Lecture #9 & 10

Friday, Feb. 21, 2003Dr. Jae Yu

1. Interpretation of Sin2W results

2. The link to Higgs3. Neutrino Oscillation

•Next makeup class is Friday, Mar. 14, 1-2:30pm, rm 200.


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SM Global Fits with New ResultsWithout NuTeVdof=20.5/14: P=11.4%With NuTeVdof=29.7/15: P=1.3%Confidence level in upper Mhiggs limit weakens slightly.

LEP EWWG: http://www.cern.ch/LEPEWWG

http://www.cern.ch/LEPEWWG


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Tree-level Parameters: and sin2W(on-shell)

• Either sin2W(on-shell) or 0 could agree with SM but both agreeing

simultaneously is unlikely

150GeV

Mln0.00032

50GeV

175GeVM0.00022θδsin

H

2

22tshell)(On

W2

0.0400.9983ρ

0.00310.2265θsin

0

W2


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• R can be expressed in terms of quark couplings:

Model Independent Analysis

2R

2L-

--

grgR 1

XN

XN

Where

2

1

XνNσ

XNνσr

Paschos-Wolfenstein formula can be expressed as

2R

2L

νν

W22

νCC

νCC

νNC

νNC gg

r1

rRRθsin

2

1ρ

σσ

σσR


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• Performed a fit to quark couplings (and gL and gR)– For isoscalar target, the N couplings are


W

4W

220

2L

2L

2L θsin

9

5θsin

2

1ρdug

0.00110.0310g2R

(SM: 0.3042 -2.6deviation)

(SM: 0.0301 Agreement)

expRexpR– From two parameter fit to and

0.00140.3005g2L

W42

02R

2R

2R θsin

9

5ρdug


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Difficult to explain the disagreement with SM by:Parton Distribution Function or LO vs NLO or Electroweak Radiative Correction: large MHiggs


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• R- technique is sensitive to q vsq differences and NLO effect– Difference in valence quark and anti-quark

momentum fraction • Isospin symmetry assumption might not be

entirely correct– Expect violation about 1% NuTeV reduces this

effect by using the ratio of and cross sections Reducing dependence by a factor of 3

What is the discrepancy due to (Old Physics)?


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• s vss quark asymmetry– s and s needs to be the same but the momentum

could differ• A value of s=xs -xs ~+0.002 could shift sin2W by -

0.0026, explaining ½ the discrepancy (S. Davison, et. al., hep-ph/0112302)

• NuTeV di- measurement shows that s~-0.0027+/-0.0013


Use opposite sign di- events to measure s and s.


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• NLO and PDF effects– PDF, mc, Higher Twist effect, etc, are small changes

• Heavy vs light target PDF effect (Kovalenko et al.,

hep-ph/0207158)– Using PDF from light target on Iron target could make up the

difference NuTeV result uses PDF extracted from CCFR (the same target)



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es Oscillations with Large M• LSND result implicate a largem2 (~10 —

100eV2) solution for e oscillation MiniBooNe at FNAL is running to put the nail on the coffin

• How would this affect NuTeV sin2W?

r1

rRR

2

1θsin

νν

W2

Long

Short

N

NNR e

MCand

If es with seP

seeeeeeP1-NPNN MCMCthen

Thus, MC will subtract more than it is in nature, causing measured R to be smaller and thereby increasing sin2W


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• Extra U(1) gauge group giving rise to interactions mediated by heavy Z’ boson (MZ’>>MZ)

• While couplings in these groups are arbitrary, E(6) gauge groups can provide mechanism for extra U(1) interaction via heavy Z’.

• Can give rise to gR but not gL which is strongly constrained by precision Z measurement

New Physics: Interactions from Extra U(1) – Z’


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• Heavy non-SM vector boson exchange: Z’, LQ, etc– Suppressed Z (invisible)

coupling– LL coupling enhanced than LR

needed for NuTeV

What other explanations (New Physics)?

Both precision data are lower than SM


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• Propagator and coupling corrections– Small compared to the effect

• MSSM : Loop corrections wrong sign and small for the effect

• Many other attempts in progress but so far nothing seems to explain the NuTeV results – Lepto-quarks– Contact interactions with LL coupling (NuTeV wants mZ’~1.2TeV, CDF/DØ:

mZ’>700GeV)– Almost sequential Z’ with opposite coupling to

What other explanations (New Physics)?

Langacker et al, Rev. Mod. Phys. 64 87; Cho et al., Nucl. Phys. B531, 65; Zppenfeld and Cheung, hep-ph/9810277; Davidson et al., hep-ph/0112302


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Linking sin2W with Higgs through Mtop vs MW

150GeVM

ln0.0003250GeV

175GeVM0.00022θδsin H

2

22tshell)(On

W2

One-loop correction to sin2W


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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• Oscillation probability depends on

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


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Neutrino Oscillation Formalism• Two neutrino mixing case:

21

21e

cossin

sincos

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

2

1

cos sin

sin cos

eOR


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Oscillation Probability• Let at time t=0 be the linear combination of 1 and 2

with masses m1 and m1, the wave function becomes:

21 cossin0 t

21

tEitEit

21 expcosexpsin

• Then later time t the wave function becomes:

• For relativistic neutrinos (E>>mi), the energies of the mass eigenstates are:

p

mpmpE k

kk 2

222


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Oscillation Probability• Substituting the energies into the wave function:

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


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Homework Assignments• Produce an electron ET spectrum of the highest ET electrons

in your samples– Due Wednesday, Feb. 26

• Complete the derivation of the probability for nm of energy E to oscillate to e at the distance L away from the source of .

• Draw the oscillation probability distributions as a function of– Distance L for a fixed neutrino beam energy E (=5, 50, 150 GeV)– E for a detector at a distance L (=1.5, 735, 2200km) away from

the source• Due Wednesday, Mar. 5

Documents

PHYS 5326 – Lecture #9 & 10