Final report of the E821 muon anomalous magne6c moment measurement at BNL G.W. Benne> et al. (Muon(g2)Collabora6on) Phys. Rev. D. 73, 072003 (2006) 1. Muon 2. Anomalous magne6c moment 3. Experiment 4. Analysis 5. Results 6. Summary Shibata Lab. 11B01329 Koji Igarashi Contents 1 st , July, 2014 1
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Final report of the E821 muon anomalous magne6c moment measurement at BNL
G.W. Benne> et al. (Muon(g-‐2)Collabora6on) Phys. Rev. D. 73, 072003 (2006)
g = 2 is expected from the Hamiltonian of the Dirac equa6on
H = −12m
!i∇− qA
"##
$%
&
'(− qφ + qσ
"#⋅B"#*
+,
-
./
However, g-‐factor is not 2 in the Standard Model (SM)
aµ =g− 22: anomalous magnetic moment
3
S!: spin , g : gyromagne6c factor
.
A spin of muon is one-‐half.
4
The anomalous magne6c moment in SM is caused by electronic, weak and hadronic interac6on.
aµSM = aµ
QED + aµweak + aµ
hadronic =11659181(8)×10−10
the difference could be due to new physics.
If there is a difference between the SM value and the experiment value,
QED weak
interac6on ああああ hadronic interac6on
i.e. 0.12%
3. Experiment
5
• The proton beam with E = 24 GeV comes from AGS at BNL.
• Protons strike a target (Ni) and pions are produced.
• Pions decay to muons in flight. • Muons are injected to the storage ring. • Muons travel around the storage ring.
g-2 ring
: muon momentum
: muon spin direc6on rotates in X-‐Y plane
a muon moving in the storage ring
: muon orbit ¤ B!"
Y
X
6
g-2 ring
The muon spin direc6on shiks by + 12 degrees per evolu6on. aμ is determined by accurately measuring the shik of the angle.
B = 1.4513 T
But, directly measuring the shik of the angle is difficult. Therefore, aμ is determined by the frequency of the shik in this experiment.
pµ = 3.09 GeV/c
It takes 4 μsec per evolu6on.
7
ωa
! "!=ωs
!"!−ωc
! "!=g− 22
qB!"
mµ
= aµqB!"
mµ
ωc
! "!ωs
!"!: spin precession frequency : cyclotron frequency
ωs
!"!= g qB
!"
2mµ
+ (1−γ ) qB!"
γmµ
=qB!"
γmµ
ωc
! "!=qB!"
γmµ
If g = 2,
But, g ≠ 2 :
muon moving around the storage ring
rota6on of spin direc6on
in B-‐field
rota6on of muon coordinate
The value of aμ is evaluated by determining ωa and B .
ωa
! "!=ωs
!"!−ωc
! "!= 0
: anomalous precession frequency ωa
! "!
because
(evolu6on frequency)
8
Fiber-lead grid
Inflector
15.24 m diameter
g-2 ring
• Calorimeters are located inside g-‐2 ring. • μ+ decays to e+. ( ) • The e+ is detected by calorimeters. • The fiber-‐lead grid causes an electromagne6c (EM) shower. • EM shower is detected by plas6c scin6llators.
µ+ → e+ +νe +ν µ
calorimeter
To determine muon spin direc6on, this experiment detects e+ from μ+.
e+
μ+ momentum
spin direc6on Y
X
μ+
EMCal
More e+ are detected when muon spin points to EMCal.
W (θ ) =1+
13cosθ
spa6al distribu6on of e+ from the decay of a polarized μ+
θ e+
μ+
Parity is violated in weak interac6on.
The number of detected positrons N(t) is as follows :
N(t) = N0 exp(−t γ τ µ )[1− Acosωat]
The value of ωa is determined by measuring N(t).9
N(t) oscillates with the frequency ωa .
μ+ decays to e+ in flight
4. Analysis
10
• The life6me of muon in flight is γτμ = 64.4 μsec.
• The decays is measured up to 700 μsec. • Asymmetry A≅0.4 • The total number of detected positrons