U(1)’ instead of R-parity
2
sin
θW theory and new physics
(a new physics scenario sensitive to Low-Q2 parity test)
Hye-Sung Lee
Institute for Basic Science
International Workshop on e+e- collisions from Phi to Psi 2015
USTC, Hefei (September 23-26, 2015)
1
Outline
1. Brief history of sin2 θW physics
2. Dark Photon and Dark Z
3. Importance of Low-Q2 parity test (precise measurement of sin2 θW)
History of sin2 θW physics
1961. Glashow introduced SU(2)L×U(1)Y symmetry (W±, W0, B).
Aµ = cos ✓W Bµ + sin ✓W Wµ0 ,
Zµ =
sin ✓W Bµ + cos ✓W Wµ0
1967. Weinberg added the Higgs mechanism (with a Higgs doublet and a vev).
mW = mZ cos ✓W (mass relation with θW is given)
and also predicted the weak neutral currents.
1973. Neutral currents (predicted in the SM) were discovered in 𝜈 scatterings.
But is the SM a correct theory for the neutral currents?
g
Zµ f¯ µ T3f 2Qf sin2 ✓W T3f 5 f
cos ✓W
Parity Test (weak mixing angle) can tell.
CERN Gargamelle
1978. SLAC E122 (polarized eD scattering) measured Parity Violation asymmetry
(σR-σL / σR+σL), which gave sin2 θW ≈ 0.22(2). (Agree with the SM)
Parity Test established SU(2)L×U(1)Y as the EW interaction structure.
See a review by Kumar, Mantry, Marciano, Souder 2013
Lessons from the history
Establishment of the SU(2)L×U(1)Y by the parity test (1978) at SLAC occurred much
earlier than the direct discovery of the W±/Z boson resonances (1983) at CERN
SPS.
In the Press release from Nobel foundation:
Neutral Current
Parity Test
LESSONS from the history:
(i) Parity Test (by precise measurement of sin2 θW) can be a critical way to search
for a new gauge interaction.
(ii) Its finding may precede the direct discovery of a gauge boson (by bump search).
Weak mixing angle running and current constraints
0.242
sin2 ΘW #Q2 $
0.240
SM prediction
0.238
0.236
0.234
0.232
0.230
!3
!2
!1
0
1
Log10 Q !GeV"
2
3
Weak mixing angle running and current constraints
0.242
Qweak !first"
sin2 ΘW !Q2 "
0.240
Ν"DIS
E158
0.238
0.236
APV!Cs"
PVDIS
0.234
LEP
0.232
SLAC
0.230
"3
"2
"1
0
1
Log10 Q #GeV$
2
3
Weak mixing angle running and current constraints
0.242
Qweak !first"
sin2 ΘW !Q2 "
0.240
Ν"DIS
E158
0.238
0.236
APV!Cs"
PVDIS
0.234
0.232
APV!Ra "
#
Moller
0.230
"3
LEP
P2
Qweak
SOLID
''Anticipated sensitivities''
"2
"1
0
1
Log10 Q #GeV$
SLAC
2
3
Dark force (Light Z’) models
and bump searches
New physics illustration with Z’
Heavy Z’ (~ TeV scale)
: Traditional target of discovery.
⎮ ⎮ ⎮ ⎮ ⎮ ⎮ ⎮ ⎮ ⎮ ⎮ ⎮ ⎮ MeV
GeV
TeV
PeV
(Z’ mass)
Light Z’ (~ MeV - GeV scale)
: Recently highlighted subject with growing interest.
(Light Z’ with sufficiently small couplings is allowed.)
massive & neutral gauge boson from an extra gauge symmetry
f
f
γ
f¯
ε
×
Light Z’ models
Z′
f¯
a gauge boson of dark sector U(1).
Lkin =
1
1 "
Bµ⌫ B µ⌫ +
Bµ⌫ Z 0µ⌫
4
2 cos ✓W
Z
εZ
×
Z′
1 0 0µ⌫
Z Z
4 µ⌫
Z’ : couples to the SM particles only through small mixing with SM gauge bosons.
(i) Popular Model: “Dark Photon” [Arkani-Hamed et al (2008); and others]
• Z’ mass = MeV - GeV
• Z’ coupling = ε×(Photon coupling)
(ii) New Model: “Dark Z”
[Davoudiasl, LEE, Marciano (2012)]
• Z’ mass = MeV - GeV
(cf. Z mass = 91 GeV)
• Z’ coupling = ε×(Photon coupling) + εZ×(Z coupling)
inherits properties of Z boson like parity violation.
(different couplings for left/right-handed particles)
Effects of New Model (Dark Z)
mZ’ << mZ
Parameter space (Z’ mass and coupling to the SM) is extended from 2D to 3D.
(Dark Photon)
ε
ε
(Dark Z)
Z’ mass
Z’ mass
εZ (Z-Z’ mixing) : parity violating
Lint =
µ
" eJem
Zµ0
Lint =
µ
µ
0
[" eJem
+ "Z (g/2 cos ✓W )JN
]
Z
µ
C
‧． Dark Z
= Dark Photon with more general coupling.
‧．Dark Photon = a special case of Dark Z (εZ = 0 limit).
Some experiments irrelevant to Dark Photon searches become relevant to
Dark Z searches. They include “Low-Q2 Parity Tests”.
(will be back to this later)
Bump searches of Light Z’
[ 2015 constraints]
(𝜺2 = 𝛼’/𝛼)
Bremsstrahlung
Z’
e
fixed target
Meson decays
γ
d
π
d¯
γ
arXiv:1507.02330
ε
×
e+
Z′
e−
and more …
EventsêH1 MeVL
108
107
106
105
5s
2s
104
1000
100
dilepton search
180
200 220 240
e+ e- mass HMeVL
260
See many talks discussing Dark Photon in this workshop
including tomorrow’s talks from KLOE, NA48, BABAR.
Bump searches of Light Z’
[ 2011 constraints and plans]
10
10-4
ae
cluded
aµ A' is ex
-5
10
10-5
elcome'
aµ A' is 'w
KLOE
-6
𝜺2 = 𝛼’/𝛼
α'/α
10
DarkLight
10-7
Test
APEX
Full
BaBar
MAMI
VEPP3
E774
10
10-8
HPS
E141
10-9
E137
10
10-10
-2
10-2
-1
10-1
m U (GeV)
1
“Dark gauge boson” physics is a rapidly-developing field.
Dark Force searches in the Labs
Mainz (Germany)
FNAL (USA)
SLAC (USA)
Orsay (France) GSI (Germany)
BNL (USA)
JLab (USA)
CERN (Europe)
INFN (Italy)
VEPP (Russia)
KEK (Japan)
BES (China)
Many searches for Dark Force in the Labs around the world (ongoing/proposed).
Exciting time!
(With some exaggeration) Whole world is searching for a new fundamental force.
Another possible Dark force searches
: Low-Energy Parity Test
(applying to Dark Z)
“Dark Z” effects on Weak Neutral Current phenomenology
[Davoudiasl, LEE, Marciano (2012)]
Dark Z : Lint =
µ
µ
0
[" eJem
+ "Z (g/2 cos ✓W )JN
]
Z
µ
C
Dark Z modifies the effective Lagrangian of Weak Neutral Current scattering.
4GF µ
Le↵ = p JN C (sin2 ✓W )JµN C (sin2 ✓W )
2
✓
◆
✓
◆
1
mZ 0
2
"Z =
GF ! 1 +
GF
2
2
mZ
1 + Q /mZ 0
✓
◆
mZ cos ✓W
1
2
2
sin ✓W ! 1 "
sin
✓W
2
2
mZ 0 sin ✓W 1 + Q /mZ 0
2
g
X
- Sensitive only to Low-Q2 (momentum transfer).
m2X + Q2
!0
(for Q2
m2X )
- Low-Q2 Parity-Violating experiments (measuring sin2 ✓W ) are good places to look.
Dark Z effectively changes the weak neutral current scattering
(including parity), but only for the “Low” momentum transfer (Q).
Weak mixing angle running and current constraints
0.242
Qweak !first"
sin2 ΘW !Q2 "
0.240
Ν"DIS
E158
0.238
0.236
APV!Cs"
PVDIS
0.234
0.232
APV!Ra "
#
Moller
0.230
LEP
P2
Qweak
SOLID
''Anticipated sensitivities''
SLAC
0
1
2
3
Log10 Q #GeV$
Low-Q2 Parity Test (measuring Weinberg angle) can search for the Dark force.
Atomic Parity Violation, Low-Q2 Polarized Electron Scatterings, DIS
"3
"2
"1
Weinberg angle shift due to Dark Z (very light Z’)
[Davoudiasl, LEE, Marciano (2014)]
Deviations from the SM prediction (due to Dark Z)
can appear “only” in the Low-E experiments.
0.242
Qweak !first"
sin2 ΘW !Q2 "
0.240
2
2
sin ✓W (Q ) '
Ν#DIS
mZ
1
0.42 "
mZ 0 1 + Q2 /m2Z 0
mdark Z ! 100 MeV
mdark Z ! 200 MeV
E158
0.238
0.236
APV!Cs"
PVDIS
0.234
0.232
APV!Ra "
$
Moller
MESA
Qweak
0.230
LEP
SOLID
''Anticipated sensitivities''
SLAC
0
1
2
3
Log10 Q #GeV$
Low-Q2 Parity Test (measuring Weinberg angle) can search for the Dark force.
Atomic Parity Violation, Low-Q2 Polarized Electron Scatterings, DIS
#3
#2
#1
Weinberg angle shift due to Dark Z (intermediate mass case)
[Davoudiasl, LEE, Marciano (2015)]
0.242
Qweak "first#
sin2 ΘW "Q2 #
0.240
Ν"DIS
E158
"0.0010 # !∆' # "0.0003
!!∆'! % 0.0008 "light color#
0.238
0.236
mdark Z ! 15 GeV
APV"Cs#
PVDIS
0.234
0.232
APV"Ra #
'
Moller
0.230
LEP
P2
Qweak
SOLID
''Anticipated sensitivities''
SLAC
0
1
2
3
Low-Q2 measurements (Cs APV, E158,Log
NuTeV)
show 1.8σ deviation from the SM.
10 Q $GeV%
Introduction of Dark Z (~ 10 GeV) can help fitting. (Blue band: less than 1σ deviation)
"3
"2
"1
Summary
0.242
Qweak !first"
sin2 ΘW !Q2 "
0.240
Ν#DIS
mdark Z ! 100 MeV
mdark Z ! 200 MeV
E158
0.238
0.236
APV!Cs"
PVDIS
0.234
0.232
APV!Ra$ "
Moller
MESA
Qweak
0.230
#3
LEP
SOLID
SLAC
''Anticipated sensitivities''
#2
#1
0
1
Log10 Q #GeV$
2
3
The Parity Test (precise measurement of sin2 θW) has been important in studying new
gauge interactions. (Critically helped establishing the SU(2)L×U(1)Y model.)
There is a growing interest in the dark gauge interaction (mediated by a light Z’) around
the world. (Partly because many existing low-energy facilities can join the searches.)
While most searches of the light Z’ are based on the direct bump searches, the parity
tests in Low-Q2 (APV, Polarized e scatterings, DIS) are important and complementary
searches.
History may repeat! (Dark Force evidence from Low-Q2 parity test before resonance?)
- Thank you. -
Backup Slides
Higgs structure matters
Model-dependence in coupling comes from how Z’ gets a mass (or Higgs sector).
- Dark Photon: (Example) additional Higgs singlet gives mass to Z’
coupling = ε×(Photon coupling)
µ
Lint = " eJem
Zµ0
(Coupling[ to JN C is largely cancelled, for mZ] 0 ⌧ mZ .)
(
- Dark Z: (Example) additional Higgs doublet (+ singlet) gives mass to Z’
coupling = ε×(Photon coupling) + εZ×(Z coupling)✓
◆
◆
✓
µ
µ
0
1
1
Lint = [" eJem + "Z (g/2 cos ✓W )JN C ] Zµ
[J = 2 T Q sin ✓ f¯ f 2 T f¯
NC
µ
3f
f
2
W
µ
3f
)
(Example) Dark Photon case
: Z-Z’ kinetic mixing is cancelled by Z-Z’ mass mixing (which is “induced by
kinetic mixing”) at Leading Order.
µ
µ
Lint ⇠ eJem
Aµ (g/2 cos ✓W )JN
C Zµ
µ
µ
0
(Kinetic mixing diagonalization) ! eJem
[Aµ + "Zµ ] (g/2 cos ✓W )JN C [Zµ + O(")Zµ0 ]
(Z-Z’ mass matrix diagonalization) !
(depends on Higgs sector)
µ
eJem
[Aµ + "Zµ0 ]
µ
(g/2 cos ✓W )JN
C Zµ
(for Higgs singlet)
Dark Force couplings depend on “Higgs sector”.
]
µ 5f
Anomalous Magnetic Moment
1 $ 10%4
γ
5 $ 10%5
a Μ !3Σ"
5 $ 10
%6
1 $ 10%6
1 $ 10%7
5
Z′
µ
(magnetic moment) =
gµB S
~
Green band: explains the 3.6σ deviation in 𝑎µ
(possibly early hint of Dark Force)
ae
5 $ 10%7
!9
!3Σ
"
!
2
ae
!95 Σ"
#"
aΜ
ed
n
i
a
l
exp
L"
C
0#
µ
ae
𝜺2 = 𝛼’/𝛼
!2
1 $ 10%5
[Gninenko, Krasnikov (2001); Pospelov (2008)]
10
50
m
100
#MeV$
photon
Mdarkdarkphoton
[MeV]
500
1000
Deviation confirmed by
both KLOE and BESIII
𝑎µ = (gµ - 2) / 2 : Always an important motivation/constraint for New Physics.
-
One of the major motivations for the light Dark gauge boson (Z’).
Unlike other motivations, it is independent of the unknown DM properties.
It is independent of the Z’ decay BR.
Visible/Invisible decay of Dark gauge boson
2 main categories of Dark force search (in terms of the dominant decay modes) :
gd Branching Ratio
(i) “Dilepton Resonance” search (typical search)
Visible Dark Gauge Boson
0.70
e+em+ m -
0.50
BR
Z’ → ℓ𝓁+ℓ𝓁− is the major decay
mode in an ordinary scenario.
𝝆𝝓
1.00
0.30
Hadrons
0.20
0.15
0.10
Whole green band (gµ-2 favored) is excluded.
0.10
0.15 0.20
gd Mass @GeVD
0.30
0.50 0.70 1.00
1.50 2.00
3.00
[Batell, Pospelov, Ritz (2009)]
[Falkowski et al (2010)]
(ii) “Missing Energy” (or invisible) search
Invisible Dark Gauge Boson
Z’ → 𝝌𝝌 is the major decay mode,
if 𝝌 (very light dark sector particle) exists.
BR(Z’ → MET) ≈ 1 is taken.
Invisibly decaying Dark gauge boson
(ii) Missing Energy (Z’ → 𝝌𝝌) searches
(i) K+ → π+ + nothing (BNL E787+E949)
[Pospelov (2009); and others]
1 & 10'4
5 & 10'5
[Dark Photon]
Izaguirre et al.
1 & 10
Essig et al.
aΜ
'5
5 & 10'6
d
!2
aine
l
p
x
e
aΜ
!2Σ
"
1 & 10'6
E787#E949
ae
5 & 10'7
(ii) e+e− → 𝛾 + nothing (BABAR)
[Izaguirre et al (2013); Essig et al (2013)]
BR!Zd $missing" % 1
1 & 10'7
5
10
50
100
Zd mass #MeV$
500
1000
More constraints through 𝝌 interaction at detectors in some beam-dump experiments
are possible, but they depend on the 𝝌 coupling (αD). (will come back to this later)
In Dark Photon model, small portion of the green band survives the constraints.
Invisibly decaying Dark gauge boson
(ii) Missing Energy (Z’ → 𝝌𝝌) searches
[Davoudiasl, LEE, Marciano (2014)]
1 & 10'4
5 & 10'5
1 & 10'4
[Dark Photon]
5 & 10'5
[Dark Z boson]
Izaguirre et al.
d
aine
l
p
x
e
aΜ
!2
'6
1 & 10
"
E787#E949
'6
5 & 10'7
ae
5 & 10'7
ained
l
p
x
e
aΜ
5
10
More green band survives
in the Dark Z case
Max suppression
BR!Zd $missing" % 1
BR!Zd $missing" % 1
1 & 10'7
E787#E949
ae
!2Σ
"
1 & 10
5 & 10'6
!2Σ
5 & 10'6
1 & 10
Essig et al.
aΜ
'5
!2
1 & 10
Essig et al.
aΜ
'5
Izaguirre et al.
50
100
Zd mass #MeV$
500
1000
1 & 10'7
5
10
50
100
Zd mass #MeV$
500
In Dark Z model, because of the additional term (εZ term), there can be a sizable
interference in the flavor-changing meson decays.
The “K ➞ π + Z’ (nothing)” constraints (orange) can be much weaker (1/7 times).
1000
Example: JLab BDX (Beam-Dump eXperiment)
[BDX Collaboration]
JLab experiment
to test invisibly decaying Z’
(plastic scintillator)
12 GeV
unknown DM coupling
Nucleon Scattering Erec > 1 MeV , aD = 0.1 , m c = 10 MeV
10-4
αD
BaBar
10-5
K+
e2
10-6
-7
scattering to produce Z’
(promptly decaying to 𝝌)
✏
2
/m2A0
10
LSND
E137
scattering to detect 𝝌
10-8
(via Z’)
↵D ✏
2
/m2A0
BDX 1000
BDX 100
10-9
BDX 10
50
100
200
m A' HMeVL
500
(i) Test experiment at JLab Hall D with low current (0.2 µA).
(ii) Full experiment at JLab Hall A or C with high current (100 µA). EOT ~ 1012.
(iii) Signals: nucleon/electron recoils.
↵D ✏ 4
(iv) 2 scatterings are required to produce and detect. N ⇠ 4
mA
(v) BKG from comic rays (neutrons, muons).
0
1000
Example: P348 (beam-dump for dark gauge boson) at CERN SPS
[P348 Collaboration]
10(2
DarkLight
BaBar
K!ΜΝA'
K!ΠA'
aΜ
10
(3
E787, E949
aΜ favored
BaBar
improved
Belle II
low-EΓ
Ε
ae
Belle II
K!ΠA'
converted
!a,b"
ORKA
component for
invisible decay
10
Belle II
VEPP-3
(4
109
standard
1012
30 GeV
100 GeV
LSND
ΑD %0.1
10(5
1012.
10(2
m A' #GeV$
10(1
1
10
(i) Primarily e-beam (10-300 GeV). EOT ~
(ii) Detector is hermetic (catching all SM particles except for neutrinos) and
measures total energy deposit.
(iii) Test “energy loss” (Missing E) by invisibly decaying Z’. (Essentially BKG free.)
(iv) Does not depend on unknown αD (DM coupling).
(v) Can search for the visibly-decaying Z’ as well.
Neutral currents observed at CERN Gargamelle
We live in a Dark World
Positron excess
(observed in satellite experiments)
Dark Energy
68%
Dark Matter
27%
Atoms
5%
“Dark Force”
(Force among Dark Matters)
No corresponding antiproton excess
: Typical
… DM annihilation would
produce both e+e- and p+p-
Dark Force (Force among Dark Matters)
Z’
(Dark Force carrier)
- New gauge boson of MeV-GeV scale (cf. Proton: 1 GeV)
- Extremely weak couplings to the SM particles
dark matter halo
e+
galaxy
DM
DM
Z′
Z′
e−
e+
e−
Dark Matter annihilations with Dark Force can
explain anomalies including the positron excess.
[Arkani-Hamed, Finkbeiner, Slatyer, Weiner (2008)]
Dark Z lifetime
Z0
Lint
=
µ
[" eJem
+
µ
0
"Z (g/ cos ✓W )JN
]
Z
µ
C
BR(Z ! e e )
1 1
' +
0
BR(Z ! 3⌫ ⌫¯)
6 2
0
+
✓
"
"Z
◆2
Bounds on δ (in Dark Z)
✓
mZ 0
"Z =
mZ
◆
Electroweak precision constraints
0.200
0.100
0.050
0.020
0.01
0.01
0.010
0.005
0.005
0.005
0.001
0.001
0.002
0.001
0.1
1
91.1
91.1
Z⇥
10
100
Dark Photon
Mass GeV⇥
mZ ⇥ (GeV)
91.15
91.2 91.25
91.2
1000
1.00
0.50
0.20
0.10
0.05
0.02
0.01
[Hook, Izaguirre, Wacker (2010)]
0
20
The constraints from the EWPT are not strong (Z pole shift [cyan] is strongest).
40
Dark
Beam-dump Experiments
e−
E0
shield
γ′
e−
Eγ ′
e+
detector
Sensitive to beam-dumps
(Long-lived Z’)
target
In most beam facilities,
beams are dumped to thick shield
at the end of the experiments.
Ltot
Lsh
Ldec
[Andreas, Niebuhr, Ringwald (2012)]
Z’ is produced via Dark Photon bremsstrahlung (like Fixed target experiments).
Z’ decays after shield (long-lived Z’: very small mass, very small coupling).
(Ex) SLAC E141 (1986): 9 GeV e- beam, 10-12cm tungsten shield, 35m decay
chamber, to search for high-E e+ (from Z’ or Axion) at 0º angle with spectrometer.
(Photon converter (using Primakoff effect) can be used for axion->photon.)
Dark Force searches at Jefferson Lab
Nuclear/Hadronic Physics Lab
BDX
Free Electron Laser
Continuous
Electron Beam
(up to 12 GeV)
FEL: DarkLight
3 Bump searches (visible)
+ 1 Beam-dump (invisible)
+ 2 Parity violation tests
Text
Low-Q2 polarized electron scatterings
AP V ⌘
R
R
L
+
L
/ (1
←L Theory Center L
& etc.
/Z/Z’
4 sin2 ✓W ) [Moller]
Hall A: APEX
A
B
C
Hall B: HPS
Hall A: Moller
Hall C: Qweak
“Dark Z” searches
(2 more experiments relevant to Dark Force searches)