Magnetic moment (g
2) and new physics
Dominik Stöckinger, TU Dresden
Sussex, November 2011
Magnetic moment (g
2) and new physics
Outline
1
Introduction
Motivation and Prehistory
Legacy of Brookhaven measurement: 3 deviation
2
New g
3
Impact on New Physics in general
4
SUSY could explain the deviation
General behaviour
Two-loop contributions
a , parameter measurements and model discrimination
5
Alternatives to SUSY
6
Conclusions
2 experiments at Fermilab and JParc
Magnetic moment (g
2) and new physics
Outline
1
Introduction
Motivation and Prehistory
Legacy of Brookhaven measurement: 3 deviation
2
New g
3
Impact on New Physics in general
4
SUSY could explain the deviation
General behaviour
Two-loop contributions
a , parameter measurements and model discrimination
5
Alternatives to SUSY
6
Conclusions
2 experiments at Fermilab and JParc
Magnetic moment (g
2) and new physics
Introduction
Muon magnetic moment
Hmagnetic
= 2(1 + a) 2me B~ S~
Measurement:
circular motion:
!c =
spin precession:
!s =
e
m B
(+ )
2 1 a e
2m B
! measure !a = !s !c =
Magnetic moment (g
2) and new physics
a me B
Introduction
Muon magnetic moment
Hmagnetic
= 2(1 + a) 2me B~ S~
Quantum field theory:
i
h
=~ u (p0) F1 + 2mi q a u(p)
! Operator: ma L q R
Magnetic moment (g
2) and new physics
Introduction
Why is a special?
a
m
L R F R
L
Beautifully simple “textbook” quantity, very precise
CP- and Flavour-conserving, chirality-flipping, loop-induced
! s
! ! e
b
compare: EDMs, B
Magnetic moment (g
EWPO
2) and new physics
Introduction
Classification of SM contributions
QED:
had:
:::
had
had
W+
weak:
10
3
10
7
10
9
G
Magnetic moment (g
2) and new physics
Introduction
(Pre)history
’49 Schwinger: QED 1L:
2
’57 Garwin et al:
g
Magnetic moment (g
2) and new physics
2 ) Muon=Dirac particle!
Introduction
(Pre)history
’49 Schwinger: QED 1L:
2
’57 Garwin et al:
g
’68–’78 CERN measurement:
’80-’11 Theory developments:
hadronic cont. needed, confirmed!
QED, hadronic,
Krause, Marciano ’95]
weak cont. [Czarnecki,
[Heinemeyer, DS, Weiglein ’04]
’01–’06 BNL measurement:
weak cont. needed, not confirmed!
Magnetic moment (g
2) and new physics
2 ) Muon=Dirac particle!
Introduction
(Pre)history
’49 Schwinger: QED 1L:
2
’57 Garwin et al:
g
’68–’78 CERN measurement:
’80-’11 Theory developments:
hadronic cont. needed, confirmed!
QED, hadronic,
Krause, Marciano ’95]
weak cont. [Czarnecki,
[Heinemeyer, DS, Weiglein ’04]
’01–’06 BNL measurement:
weak cont. needed, not confirmed!
2 ) Muon=Dirac particle!
Legacy of the CERN experiment
Magnetic moment (g
2) and new physics
Introduction
(Pre)history
’49 Schwinger: QED 1L:
2
’57 Garwin et al:
g
’68–’78 CERN measurement:
’80-’11 Theory developments:
hadronic cont. needed, confirmed!
QED, hadronic,
Krause, Marciano ’95]
weak cont. [Czarnecki,
[Heinemeyer, DS, Weiglein ’04]
’01–’06 BNL measurement:
weak cont. needed, not confirmed!
2 ) Muon=Dirac particle!
Legacy of the BNL experiment
Magnetic moment (g
2) and new physics
Introduction
(Pre)history
’49 Schwinger: QED 1L:
2
’57 Garwin et al:
g
’68–’78 CERN measurement:
’80-’11 Theory developments:
hadronic cont. needed, confirmed!
QED, hadronic,
Krause, Marciano ’95]
weak cont. [Czarnecki,
[Heinemeyer, DS, Weiglein ’04]
’01–’06 BNL measurement:
weak cont. needed, not confirmed!
2 ) Muon=Dirac particle!
Legacy of the BNL experiment
Magnetic moment (g
2) and new physics
Introduction
(Pre)history
’49 Schwinger: QED 1L:
2
’57 Garwin et al:
g
’68–’78 CERN measurement:
’80-’11 Theory developments:
hadronic cont. needed, confirmed!
QED, hadronic,
Krause, Marciano ’95]
weak cont. [Czarnecki,
[Heinemeyer, DS, Weiglein ’04]
’01–’06 BNL measurement:
weak cont. needed, not confirmed!
2 ) Muon=Dirac particle!
Legacy of the BNL experiment
Magnetic moment (g
2) and new physics
Introduction
Era of the muon g
aexp
Magnetic moment (g
2 experiment at Brookhaven
= (11 659 208:9 6:3) 10
2) and new physics
10
Introduction
Current status: SM prediction
Full SM: a 1010
HMNT (06)
JN (09)
Davier et al, τ (09)
dR08:
JN09:
HLMNT09:
Detal09:
JS11:
HLMNT11:
BDDJ11:
+ – w/o BaBar (09)
w/ BaBar (09)
Davier et al, e e
HLMNT (09)
experiment
BNL
BNL (new from shift in λ)
170
180
190
200
210
aµSM × 1010 – 11659000
HMNT (06)
11659000
: : : 178:5(5:1)
: : : 179:0(6:5)
: : : 177:3(4:8)
: : : 183:4(4:9)
: : : 179:7(6:0)
: : : 182:8(4:9)
: : : 175:4(5:3)
JN (09)
Davier et al, τ (10)
Exp:
Davier et al, e+e– (10)
JS (11)
BNL06:
HLMNT (10)
HLMNT (11)
: : : 208:9(6:3)
3 deviation established
experiment
BNL
BNL (new from shift in λ)
170
180
190
200
210
aµ × 1010 – 11659000
Magnetic moment (g
2) and new physics
Introduction
(3:6)
(3:2)
(4:0)
(3:2)
(3:3)
(3:3)
(4:1)
Current status: SM prediction
Hadronic vacuum polarization contributions:
had
$ e+e ! !hadrons
Recent progress:
new exp data (CMD2, SND, KLOE, B-factories)
) significantly more precise!
possible explanations of -based results
! confirmation of e+e -based evaluations
[Benayoun et al ’07][Jegerlehner, Szafron ’11]
assume e+ e
data different
) contradiction to Higgs mass bounds!
Magnetic moment (g
2) and new physics
[Marciano, Passera, Sirlin ’08]
Introduction
Current status: SM prediction
Hadronic light-by-light contributions
new estimates with correct sign,
using different approximations
[Bijnens, Prades ’07]
had
[Melnikov, Vainshtein ’03]
[Jegerlehner ’08]
[Jegerlehner, Nyffeler ’09]
[Prades, Vainshtein, de Rafael ’08]
10:0 4:0
13:6 2:5
11:4 3:8
11:6 4:0
10:5 2:6
Cannot be computed from first principles — Error difficult to assess!
Promising new approaches: lattice, Dyson-Schwinger, perturbative
Magnetic moment (g
2) and new physics
Introduction
Discrepancy
(
SM prediction too low by 25 8
) 10
10
Why?
Confirmation needed!
Note: discrepancy twice as large as aSM;weak
but we expect: aNP
Magnetic moment (g
;weak aSM
2) and new physics
MW
MNP
2
couplings
Introduction
Outline
1
Introduction
Motivation and Prehistory
Legacy of Brookhaven measurement: 3 deviation
2
New g
3
Impact on New Physics in general
4
SUSY could explain the deviation
General behaviour
Two-loop contributions
a , parameter measurements and model discrimination
5
Alternatives to SUSY
6
Conclusions
2 experiments at Fermilab and JParc
Magnetic moment (g
2) and new physics
New g
2 experiments at Fermilab and JParc
The Opportunity
)
Magnetic moment (g
2) and new physics
New g
2 experiments at Fermilab and JParc
The Opportunity
Magnetic moment (g
2) and new physics
New g
2 experiments at Fermilab and JParc
Advantages of Fermilab
decay length 900m vs 88m
6–12 times more stored muons per initial proton
4 times fill frequency
20 times reduced hadronic-induced background at injection
Magnetic moment (g
2) and new physics
New g
2 experiments at Fermilab and JParc
The Collaboration
First collaboration meeting after approval in March
Magnetic moment (g
2) and new physics
New g
2 experiments at Fermilab and JParc
Complementary experiment at JParc (N. Saito)
Magnetic moment (g
2) and new physics
New g
2 experiments at Fermilab and JParc
Complementary experiment at JParc (N. Saito)
Magnetic moment (g
2) and new physics
New g
2 experiments at Fermilab and JParc
Goal of both new (g
aexp
aSM
Data in 4–5 years
2) experiments
= (255?? 16Exp 34Th??) 10
11
Tremendously useful complement of LHC (and flavour physics
experiments), independent of final value [Hertzog, Miller, de Rafael, Roberts, DS ’07]
Benchmark for any new physics scenario
Timely, complementary constraints
This will be demonstrated in the following
Magnetic moment (g
2) and new physics
New g
2 experiments at Fermilab and JParc
Outline
1
Introduction
Motivation and Prehistory
Legacy of Brookhaven measurement: 3 deviation
2
New g
3
Impact on New Physics in general
4
SUSY could explain the deviation
General behaviour
Two-loop contributions
a , parameter measurements and model discrimination
5
Alternatives to SUSY
6
Conclusions
2 experiments at Fermilab and JParc
Magnetic moment (g
2) and new physics
Impact on New Physics in general
Why is a special?
R
CP- and Flavour-conserving, chirality-flipping, loop-induced
! s
! ! e
b
compare: EDMs, B
Magnetic moment (g
EWPO
2) and new physics
Impact on New Physics in general
L
New physics contributions to a
2 = chirality-flipping interaction
R
L
m = chirality-flipping interaction as well
R
L
g
are the two related?
Magnetic moment (g
2) and new physics
Impact on New Physics in general
New physics contributions to a
2 = chirality-flipping interaction
R
L
m = chirality-flipping interaction as well
R
L
g
are the two related?
New physics loop contributions to a , m related by chiral symmetry
[Czarnecki, Marciano ’01]
generally:
Magnetic moment (g
Æa (N:P:) = O(C )
2) and new physics
m 2
M
;
C
= Æmm(N :P:)
Impact on New Physics in general
Very different contributions to a
generally:
Æa (N:P:) = O(C )
m 2
M
;
C
= Æmm(N:P:)
classify new physics: C very model-dependent
Magnetic moment (g
2) and new physics
Impact on New Physics in general
Very different contributions to a
generally:
Æa (N:P:) = O(C )
m 2
M
;
C
= Æmm(N:P:)
classify new physics: C very model-dependent
O(1)
O( 4 : : :)
O( 4 )
Magnetic moment (g
2) and new physics
Z 0 , W 0 , UED, Littlest Higgs (LHT). . .
Impact on New Physics in general
Very different contributions to a
generally:
Æa (N:P:) = O(C )
m 2
M
;
C
= Æmm(N:P:)
classify new physics: C very model-dependent
O(1)
supersymmetry (tan ), unparticles
extra dim. (ADD/RS) (nc ). . .
O( )
Z 0 , W 0 , UED, Littlest Higgs (LHT). . .
4
Magnetic moment (g
[Cheung, Keung, Yuan ’07]
O ( : : :)
4
2) and new physics
[Davioudasl, Hewett, Rizzo ’00]
[Graesser,’00][Park et al ’01][Kim et al ’01]
Impact on New Physics in general
Very different contributions to a
generally:
Æa (N:P:) = O(C )
m 2
M
;
C
= Æmm(N:P:)
classify new physics: C very model-dependent
O(1)
radiative muon mass generation . . .
[Czarnecki,Marciano ’01]
supersymmetry (tan ), unparticles
extra dim. (ADD/RS) (nc ). . .
O( )
Z 0 , W 0 , UED, Littlest Higgs (LHT). . .
4
Magnetic moment (g
[Cheung, Keung, Yuan ’07]
O ( : : :)
4
2) and new physics
[Davioudasl, Hewett, Rizzo ’00]
[Graesser,’00][Park et al ’01][Kim et al ’01]
Impact on New Physics in general
a and new physics
(
Different types of new physics lead to very different Æ a N.P.)
SUSY, RS, ADD, . . . : strong parameter constraints
Z 0 , UED, LHT, . . . : ruled out if deviation confirmed
If new physics found at LHC:
a constitutes a benchmark for new physics models
can sharply distinguish between different types of models
timely, complementary constraints, parameter measurements
Magnetic moment (g
2) and new physics
Impact on New Physics in general
a and new physics
(
Different types of new physics lead to very different Æ a N.P.)
SUSY, RS, ADD, . . . : strong parameter constraints
Z 0 , UED, LHT, . . . : ruled out if deviation confirmed
If new physics found at LHC:
a constitutes a benchmark for new physics models
can sharply distinguish between different types of models
timely, complementary constraints, parameter measurements
Now illustrate general points with examples
Magnetic moment (g
2) and new physics
Impact on New Physics in general
Outline
1
Introduction
Motivation and Prehistory
Legacy of Brookhaven measurement: 3 deviation
2
New g
3
Impact on New Physics in general
4
SUSY could explain the deviation
General behaviour
Two-loop contributions
a , parameter measurements and model discrimination
5
Alternatives to SUSY
6
Conclusions
2 experiments at Fermilab and JParc
Magnetic moment (g
2) and new physics
SUSY could explain the deviation
SUSY and the MSSM
MSSM:
~
free parameters: p masses and mixings, and tan Magnetic moment (g
2) and new physics
SUSY could explain the deviation
2 in the MSSM: chirality flips, , and H2
g
~
H2+
tan = hhHH ii ;
2
1
= H2
~
~
H1+
H1 transition
R
some terms
/ hH1i = m
~
W+
W+
~
/ Mm
! aSUSY
2
2
SUSY
some terms
/ hH2i = m tan potential enhancement / tan Magnetic moment (g
2) and new physics
! aSUSY
/ tan sign() Mm
2
2
SUSY
= 1 : : : 50 (and /sign())
SUSY could explain the deviation
L
g
2 in the MSSM
numerically
SUSY
a
12 10
10
()
tan sign
100GeV
MSUSY
(
SUSY could be the origin of the observed 25 8
2
) 10
10
deviation!
a significantly restricts the SUSY parameters
! generically, positive , large tan /small MSUSY preferred
Precise analysis justified!
Magnetic moment (g
2) and new physics
SUSY could explain the deviation
g
2 in the MSSM
numerically
SUSY
a
12 10
10
()
tan sign
100GeV
MSUSY
2
1-loop and most 2-loop contributions known
remaining theory uncertainty of SUSY prediction:
3 10
ÆaSUSY
Aim in Dresden: reduce error to 1 10
Magnetic moment (g
2) and new physics
[DS ’06]
10
10
) full computation!
SUSY could explain the deviation
Status of SUSY prediction
1-Loop
2-Loop (SUSY 1L)
/ tan / log Mm
e.g.
~t
~f
[Kosower et al ’83],[Yuan et al ’84],. . .
complete
Magnetic moment (g
~; ~
[Marchetti, Mertens, Nierste, DS ’08]
[Schäfer, Stöckinger-Kim,
photonic
tan 2
rest under investigation
2) and new physics
)
; [Chen,Geng’01][Arhib,Baek ’02]
[Heinemeyer,DS,Weiglein ’03]
[Heinemeyer,DS,Weiglein ’04]
v. Weitershausen, DS ’10]
(
H
[Degrassi,Giudice ’98]
[Fayet ’80],. . .
[Lopez et al ’94],[Moroi ’96]
/ tan mt
f
0 ; ~; ~
e.g.
SUSY
0;
2-Loop (SM 1L)
complete
SUSY could explain the deviation
Physics of subleading contributions (examples)
Photonic 2-loop
1-loop bino
B
B
R
~
~
~L
~R
L
/ for ! 1
log (MSUSY=m )
~
2-loop t
~t
2-loop tan2 H2+
W+
~
~
~
~
H1+
R
1
"
+
W+
~
L
H
; mt =MH m~t
Important for drawing precise conclusions from confronting
Exp SM
SUSY-prediction with a
Magnetic moment (g
2) and new physics
SUSY could explain the deviation
Technical details: Photon loops
+
~
All SUSY 1-loop diagrams with additional photon loop
leading log:
7:::
9
%
(
)
[Degrassi, Giudice ’98]
full result: subleading logs, log m =m~ , non-log terms
( %)
additional terms O 1
full result more precise
[v. Weitershausen, Schäfer, Stöckinger-Kim, DS ’09]
technically difficult but useful: contains all infrared divergences
Magnetic moment (g
2) and new physics
SUSY could explain the deviation
Technical details: f =~f -loops
f
0;
~f
~; ~
~
All SUSY 1-loop diagrams with additional f =f -loop (3rd generation)
finite, gauge invariant class of contributions
enhanced by top/bottom Yukawa coupling
partial results
( %)
typically O 1
Magnetic moment (g
[Drechsel, Gnendiger, Passehr, Schäfer, Stöckinger-Kim, DS] [Fargnoli, Stöckinger-Kim]
2) and new physics
SUSY could explain the deviation
Technical details: (tan )2 enhanced corrections
~+ ~ +
H
W
2
~
~
H1+
W+
R "
Æ m
aSUSY
~
L
/ chirality flip / However, one-loop coupling to “wrong” Higgs doublet induces shift
!
1
+ ÆmOS =
or
Corresponding 2-loop shift in aSUSY
aSUSY
Magnetic moment (g
2) and new physics
+ + : : :
m
1
[Marchetti, Mertens, Nierste, DS ’08]
aSUSY
1
! +
SUSY could explain the deviation
Technical details: leading two-loop corrections
60
MSUSY =400 GeV
aΜ SUSY @10
-10
D
500 GeV
40
600 GeV
20
800 GeV
20
40
60
80
100
tanΒ
aSUSY
;1L
= aSUSY
1
4
log
MSUSY
m
%
(tan )2: +1 : : : + 15%, (MSUSY) QED-logs:
Magnetic moment (g
7:::
1
1
+ 9
2) and new physics
0:0018 tan sign
()
SUSY could explain the deviation
SUSY and a
SUSY
a
tan 12 10
10
= vv , = H1-H2 transition
2
1
()
tan sign
—
100GeV
MSUSY
2
central for EWSB
If SUSY signals at LHC:
a complementary for: model selection, parameter measurements
! understand EWSB, link to GUT scale . . .
Magnetic moment (g
2) and new physics
SUSY could explain the deviation
a central complement for SUSY parameter analyses
a sharply distinguishes SUSY models
breaks LHC degeneracies
Magnetic moment (g
2) and new physics
SUSY could explain the deviation
a central complement for SUSY parameter analyses
SPS benchmark points
LHC Inverse Problem (300fb 1 )
can’t be distinguished at LHC
[Sfitter: Adam, Kneur, Lafaye,
a sharply distinguishes SUSY models
Plehn, Rauch, Zerwas ’10]
breaks LHC degeneracies
Magnetic moment (g
2) and new physics
SUSY could explain the deviation
a central complement for SUSY parameter analyses
xp.
e
new
test1
LHC Inverse Problem (300fb 1 )
SPS benchmark points
can’t be distinguished at LHC
[Sfitter: Adam, Kneur, Lafaye,
Plehn, Rauch, Zerwas ’10]
[ATLAS jets+0lepton 02/11]
LHC already rules out small masses in CMSSM
) large tan (SPS1b,4)? Non-CMSSM (heavier squarks)?
aSUSY smaller?
Magnetic moment (g
2) and new physics
SUSY could explain the deviation
Ways to reconcile the LHC bounds with a
LHC mainly constrains squarks/gluinos
Even within the CMSSM: heavy masses + large tan Beyond the CMSSM: sleptons lighter than squarks
Don’t worry, SUSY still viable — but the LHC—b-decays—a tensions
start preferring some parameter regions
If SUSY exists, a will be even important to measure parameters
Magnetic moment (g
2) and new physics
SUSY could explain the deviation
a central complement for SUSY parameter analyses
=
tan vv21
central for understanding EWSB
(
LHC: tan )LHC;masses = 10 4:5 bad
[Sfitter: Lafaye, Plehn, Rauch, Zerwas ’08, assume SPS1a]
a improves tan considerably
[Hertzog, Miller, de Rafael, Roberts, DS ’07]
= MM in the SM:
= ( ) = (t )b ?
vision: test universality of tan , like for cos W
t a
t LHC;masses
t H
( ) =( )
Magnetic moment (g
2) and new physics
W
Z
SUSY could explain the deviation
Outline
1
Introduction
Motivation and Prehistory
Legacy of Brookhaven measurement: 3 deviation
2
New g
3
Impact on New Physics in general
4
SUSY could explain the deviation
General behaviour
Two-loop contributions
a , parameter measurements and model discrimination
5
Alternatives to SUSY
6
Conclusions
2 experiments at Fermilab and JParc
Magnetic moment (g
2) and new physics
Alternatives to SUSY
Littlest Higgs (with T-parity)
[Georgi; Arkani-Hamed,Cohen,Georgi]
Concrete LHT model: [Cheng, Low ’03]
[Hubisz, Meade, Noble, Perelstein ’06]
10 TeV
Bosonic SUSY
partner states, same spin
strong dyn.
cancel quadratic div.s
T-parity)lightest partner stable
1 TeV
states WH ; lH : : :
no enhancement of 4
m 2
M
250 GeV
SM, Higgs
10
aLHT
[Blanke, Buras, et al ’07]
< 1:2 10
Clear-cut prediction, sharp distinction from SUSY possible
Magnetic moment (g
2) and new physics
Alternatives to SUSY
Randall-Sundrum models
:
Big question: Where does the hierarchy MPl MW
Answer: beautifully explained by warp factor e kL
1017 come from?
TeV-scale determined by:
coupling k =MPl
=
scale e kL MPl
theory breaks down at scale
, nc KK-gravitons up to
that scale
R
KK-Graviton
L
Gravity propagates in extra dimension
each KK-Graviton contributes equally,
weakly, no decoupling!
Magnetic moment (g
2) and new physics
2
5nc m
! aRS
16 2 2
Alternatives to SUSY
g
2 and Randall-Sundrum models
Complementarity: LHC
lowest KK-modes
masses
a from KK-loops
feels all KK-modes
e.g. CGrav
guides model building of
full theory
[Kim, Kim, Song’01]
Magnetic moment (g
/ M 2 , CH 1
2) and new physics
Alternatives to SUSY
Other types of new physics
What if the LHC does not find new physics — “Dark force”?
C
/ 10
8,
[Pospelov, Ritz. . . ]
< 1GeV
M
a can be large
could be “seen” by
a -exp.
very light new vector boson
very weak coupling
motivated e.g. by dark matter, not
by EWSB
−3
10
κ
2
−4
10
Excluded by
electron g-2 vs α
Excluded by
muon g-2
−5
10
|muon g-2|<2σ
−6
10
10 MeV
[Pospelov 08]
Magnetic moment (g
2) and new physics
100 MeV
mV
Alternatives to SUSY
500 MeV
Outline
1
Introduction
Motivation and Prehistory
Legacy of Brookhaven measurement: 3 deviation
2
New g
3
Impact on New Physics in general
4
SUSY could explain the deviation
General behaviour
Two-loop contributions
a , parameter measurements and model discrimination
5
Alternatives to SUSY
6
Conclusions
2 experiments at Fermilab and JParc
Magnetic moment (g
2) and new physics
Conclusions
Conclusions
Exp
Currently a
aSM
(25 8) 10
10
— tantalizing
New Fermilab measurement will start soon — very promising!
aN:P: very model-dependent, typically O
I Benchmark, model discriminator
I unique properties
(1 : : : 50) 10
New measurement of a will
10
I sharply distinguish models, even with similar LHC signatures
I break degeneracies
measure central parameters
a will provide essential complementary input in the quest to
understand TeV-scale physics — no matter what the result
BSM physics can look forward to the new a measurement!!
Magnetic moment (g
2) and new physics
Conclusions