A Gauge Theory for
Baryon and Lepton Numbers
Michael Duerr
Max-Planck-Institut für Kernphysik, Heidelberg, Germany
BLV2013, 9 April 2013
Based on arXiv:1304.0576 [hep-ph]
with: Pavel Fileviez Pérez (MPIK),
Mark B. Wise (Caltech).
Michael Duerr (MPIK)
A Gauge Theory for B and L
BLV2013, 9 April 2013
1
Introduction
Motivation: Are B and L broken?
B and L accidental global symmetries in the SM.
B. Viren, arXiv:hep-ex/9903029
Violation of B:
Baryon asymmetry of the Universe.
Proton decay (ΔB = 1, ΔL = odd):
τp ≥ 10
32−34
γ
π0
yrs.
Violation of L:
Individual lepton flavor numbers Le ,
Lμ , and Lτ are not conserved (neutrino
oscillation experiments).
Total lepton number could be
conserved (test with 0νββ).
Michael Duerr (MPIK)
P
e+
γ
A Gauge Theory for B and L
dL
dL
L
e−
L
e−
L
L
BLV2013, 9 April 2013
2
Introduction
Motivation: The Big Desert
S. Weinberg, Phys. Rev. Lett. 49 (1979) 1566
c5
LLHH
ΛL
c6
Λ2B
QQQL
commons.wikimedia.org
Electroweak scale
(∼ 102 GeV)
http://commons.wikimedia.org
Michael Duerr (MPIK)
A Gauge Theory for B and L
GUT scale
(∼ 1015 GeV)
BLV2013, 9 April 2013
3
Introduction
Motivation: The Big Desert
S. Weinberg, Phys. Rev. Lett. 49 (1979) 1566
c5
c5
LLHH
ΛL
LLHH
ΛL
c6
Λ2B
QQQL
commons.wikimedia.org
Electroweak scale
(∼ 102 GeV)
http://commons.wikimedia.org
Michael Duerr (MPIK)
A Gauge Theory for B and L
GUT scale
(∼ 1015 GeV)
BLV2013, 9 April 2013
3
Introduction
Aim of this Talk
Define an anomaly-free theory where
B and L are local gauge theories
that may be broken at a low scale
without the need for a desert.
Michael Duerr (MPIK)
A Gauge Theory for B and L
BLV2013, 9 April 2013
4
Gauging Baryon and Lepton Numbers
B and L in the SM
SU(3)
SU(2)
U(1)Y
U(1)B
U(1)L
3
2
1
6
1
3
0
3
1
2
3
1
3
0
3
1
− 31
1
3
0
1
2
− 21
0
1
νR
1
1
0
0
1
()
eR
1
1
−1
0
1
H
1
2
1
2
0
0
Field
SM: B and L are accidental
symmetries, not free of
anomalies.
⇒ we need additional
fermions for anomaly
cancellation.
()
QL
()
R
()
dR
()
L
()
B and L may be gauged to obtain the gauge group:
SU(3) ⊗ SU(2) ⊗ U(1)Y ⊗ U(1)B ⊗ U(1)L
Michael Duerr (MPIK)
A Gauge Theory for B and L
BLV2013, 9 April 2013
5
Gauging Baryon and Lepton Numbers
Anomalies
Purely baryonic anomalies:
€
Š
€
Š
A1 SU(3)2 ⊗ U(1)B , A2 SU(2)2 ⊗ U(1)B ,
Š
€
Š
€
A3 U(1)2Y ⊗ U(1)B , A4 U(1)Y ⊗ U(1)2B ,
€
Š
A5 (U(1)B ) , A6 U(1)3B .
Only non-zero values in the SM:
A2 = −A3 =
Michael Duerr (MPIK)
3
2
A Gauge Theory for B and L
BLV2013, 9 April 2013
6
Gauging Baryon and Lepton Numbers
Anomalies
Purely leptonic anomalies:
€
Š
€
Š
A7 SU(3)2 ⊗ U(1)L , A8 SU(2)2 ⊗ U(1)L ,
€
Š
€
Š
A9 U(1)2Y ⊗ U(1)L , A10 U(1)Y ⊗ U(1)2L ,
€
Š
A11 (U(1)L ) , A12 U(1)3L .
Only non-zero values in the SM
with right-handed neutrinos:
A8 = −A9 =
Michael Duerr (MPIK)
3
2
A Gauge Theory for B and L
BLV2013, 9 April 2013
6
Gauging Baryon and Lepton Numbers
Anomalies
Mixed anomalies:
€
Š
€
Š
A13 U(1)2B ⊗ U(1)L , A14 U(1)2L ⊗ U(1)B ,
A15 (U(1)Y ⊗ U(1)L ⊗ U(1)B ) .
All vanish in the SM.
Attention: Not introduce SM anomalies!
Michael Duerr (MPIK)
A Gauge Theory for B and L
BLV2013, 9 April 2013
6
Gauging Baryon and Lepton Numbers
Possible Solutions
Sequential/Mirror family:
P. Fileviez Perez, M. B. Wise, arXiv:1002.1754 [hep-ph]
Ruled out: new quarks change gluon fusion production;
Landau poles of the new Yukawas near the weak scale.
Vector-Like fermions:
P. Fileviez Perez, M. B. Wise, arXiv:1106.0343 [hep-ph]
Ruled out: new charged leptons reduce BR of H → γγ by a
factor of 3.
One family of leptoquarks:
FL ∼ (3, 2, 0, −1, −1), jR ∼ (3, 1,
P. V. Dong, H. N. Long, arXiv:1010.3818 [hep-ph]
1
1
, −1, −1), kR ∼ (3, 1, − , −1, −1).
2
2
Ruled out: stable charged fields.
Michael Duerr (MPIK)
A Gauge Theory for B and L
BLV2013, 9 April 2013
7
Fermionic Leptoquarks
New Solution
Field
SU(3)
SU(2)
U(1)Y
U(1)B
U(1)L
ΨL
N
2
Y1
B1
L1
ΨR
N
2
Y1
B2
L2
ηR
N
1
Y2
B3
L3
ηL
N
1
Y2
B4
L4
χR
N
1
Y3
B5
L5
χL
N
1
Y3
B6
L6
M. Duerr, P. Fileviez Perez, M. B. Wise, arXiv:1304.0576 [hep-ph]
Michael Duerr (MPIK)
A Gauge Theory for B and L
BLV2013, 9 April 2013
8
Fermionic Leptoquarks
Anomaly Cancellation
SU(2)2 ⊗ U(1)B : B1 − B2 = −
3
N
SU(2)2 ⊗ U(1)L : L1 = −L2 = −
, choose B1 = −B2 = −
3
2N
3
2N
SU(3)2 ⊗ U(1)B : B1 = B3 = B5
U(1)2Y ⊗ U(1)B : Y22 + Y32 − 2Y12 =
Useful solutions:
¨
1
1
1
.
2
2
1
1
1
«
(Y1 , Y2 , Y3 ) ∈ (± , ±1, 0), (± , ± , ± ), (0, ± , ± )
2
6
3
3
2
2
M. Duerr, P. Fileviez Perez, M. B. Wise, arXiv:1304.0576 [hep-ph]
Michael Duerr (MPIK)
A Gauge Theory for B and L
BLV2013, 9 April 2013
9
Fermionic Leptoquarks
General Solution
All anomalies are cancelled with the following setup:
Field
SU(3)
SU(2)
U(1)Y
U(1)B
U(1)L
ΨL
N
2
Y1
3
− 2N
3
− 2N
ΨR
N
2
Y1
3
+ 2N
3
+ 2N
ηR
N
1
Y2
3
− 2N
3
− 2N
ηL
N
1
Y2
3
+ 2N
3
+ 2N
χR
N
1
Y3
3
− 2N
3
− 2N
χL
N
1
Y3
3
+ 2N
3
+ 2N
«
¨
1
1
2
1
1
1
(Y1 , Y2 , Y3 ) ∈ (± , ±1, 0), (± , ± , ± ), (0, ± , ± )
2
6
3
3
2
2
M. Duerr, P. Fileviez Perez, M. B. Wise, arXiv:1304.0576 [hep-ph]
Michael Duerr (MPIK)
A Gauge Theory for B and L
BLV2013, 9 April 2013
10
Fermionic Leptoquarks
Possible Scenarios
M. Duerr, P. Fileviez Perez, M. B. Wise, arXiv:1304.0576 [hep-ph]
Guideline:
1
new fields should have direct coupling to SM fields, or
2
the lightest new particle is neutral and stable.
Michael Duerr (MPIK)
A Gauge Theory for B and L
BLV2013, 9 April 2013
11
Fermionic Leptoquarks
Possible Scenarios
M. Duerr, P. Fileviez Perez, M. B. Wise, arXiv:1304.0576 [hep-ph]
Guideline:
1
new fields should have direct coupling to SM fields, or
2
the lightest new particle is neutral and stable.
N = 1: Use Y1 = ±1/ 2, Y2 = ±1, Y3 = 0.
If the lightest field is neutral → DM. This is our model!
Michael Duerr (MPIK)
A Gauge Theory for B and L
BLV2013, 9 April 2013
11
Fermionic Leptoquarks
Possible Scenarios
M. Duerr, P. Fileviez Perez, M. B. Wise, arXiv:1304.0576 [hep-ph]
Guideline:
1
new fields should have direct coupling to SM fields, or
2
the lightest new particle is neutral and stable.
N = 1: Use Y1 = ±1/ 2, Y2 = ±1, Y3 = 0.
If the lightest field is neutral → DM. This is our model!
N = 3: Use Y1 = ±1/ 6, Y2 = ±2/ 3, Y3 = ±1/ 3.
Scalar SBL ∼ (1, 1, 0, −1, −1) leads to dimension-7 proton
decay operator.
Michael Duerr (MPIK)
A Gauge Theory for B and L
BLV2013, 9 April 2013
11
Fermionic Leptoquarks
Possible Scenarios
M. Duerr, P. Fileviez Perez, M. B. Wise, arXiv:1304.0576 [hep-ph]
Guideline:
1
new fields should have direct coupling to SM fields, or
2
the lightest new particle is neutral and stable.
N = 1: Use Y1 = ±1/ 2, Y2 = ±1, Y3 = 0.
If the lightest field is neutral → DM. This is our model!
N = 3: Use Y1 = ±1/ 6, Y2 = ±2/ 3, Y3 = ±1/ 3.
Scalar SBL ∼ (1, 1, 0, −1, −1) leads to dimension-7 proton
decay operator.
N = 8: Extra colored fields, e.g., color octet scalars, to
couple the new fermions to leptons.
Michael Duerr (MPIK)
A Gauge Theory for B and L
BLV2013, 9 April 2013
11
The Model
The N = 1 Model: Particle Content
Field
SU(3)
SU(2)
U(1)Y
U(1)B
U(1)L
ΨL
1
2
− 12
− 32
− 32
ΨR
1
2
− 12
+ 32
+ 32
ηR
1
1
−1
− 23
− 32
ηL
1
1
−1
+ 32
+ 32
χR
1
1
0
− 23
− 32
χL
1
1
0
+ 23
+ 32
M. Duerr, P. Fileviez Perez, M. B. Wise, arXiv:1304.0576 [hep-ph]
Michael Duerr (MPIK)
A Gauge Theory for B and L
BLV2013, 9 April 2013
12
The Model
Interactions
Responsible for the new fermion masses:
−L ⊃ h1 ΨL HηR + h2 ΨL H̃χR + h3 ΨR HηL + h4 ΨR H̃χL
+ λ1 ΨL ΨR SBL + λ2 ηR ηL SBL + λ3 χR χL SBL
+ 1 χL χL SBL + 2 χR χR S†BL + h.c.
with SBL ∼ (1, 1, 0, −3, −3)
Neutrino masses:
−Lν = Yν ℓL H̃νR +
λR
2
νR νR SL + h.c.
with SL ∼ (1, 1, 0, 0, −2)
M. Duerr, P. Fileviez Perez, M. B. Wise, arXiv:1304.0576 [hep-ph]
Michael Duerr (MPIK)
A Gauge Theory for B and L
BLV2013, 9 April 2013
13
The Model
Further Aspects
Symmetry breaking:
SBL breaks U(1)B and U(1)L (ΔB = ±3, ΔL = ±3),
SL contributes to breaking of U(1)L (ΔL = ±2).
Fermionic sector:
4 neutral and 4 charged new chiral fermions after
symmetry breaking.
No coupling to the SM fermions → no new source of flavor
violation.
Lightest new fermion automatically stable → DM candidate.
M. Duerr, P. Fileviez Perez, M. B. Wise, arXiv:1304.0576 [hep-ph]
Michael Duerr (MPIK)
A Gauge Theory for B and L
BLV2013, 9 April 2013
14
The Model
B and L Violating Processes
Baryon number broken in three units → no proton decay
ΔL = 2 Majorana mass terms → 0νββ
Lowest-dimensional B and L violating operator containing
just SM fermions:
O19 =
c15
Λ15
(R R dR eR )3 SBL .
M. Duerr, P. Fileviez Perez, M. B. Wise, arXiv:1304.0576 [hep-ph]
Michael Duerr (MPIK)
A Gauge Theory for B and L
BLV2013, 9 April 2013
15
Summary
Summary
Simple extension of the SM:
B and L are gauge symmetries broken at
a low scale.
no proton decay ⇒ no need for a desert.
No new sources of flavor violation.
Fermionic DM candidate.
M. Duerr, P. Fileviez Perez, M. B. Wise, arXiv:1304.0576 [hep-ph]
Michael Duerr (MPIK)
A Gauge Theory for B and L
BLV2013, 9 April 2013
16
Summary
Summary
Simple extension of the SM:
B and L are gauge symmetries broken at
a low scale.
no proton decay ⇒ no need for a desert.
No new sources of flavor violation.
Fermionic DM candidate.
Thank you!
M. Duerr, P. Fileviez Perez, M. B. Wise, arXiv:1304.0576 [hep-ph]
Michael Duerr (MPIK)
A Gauge Theory for B and L
BLV2013, 9 April 2013
16
Backup slides
Michael Duerr (MPIK)
A Gauge Theory for B and L
BLV2013, 9 April 2013
1
Model with vector-like fermions
Possible modification:
Add Higgs with lepton number
and vector-like mass terms for
the charged leptons
dimensions-9 proton decay
operators
→ cutoff Λ ≥ 107−8 GeV
This is half of the desert.
Michael Duerr (MPIK)
A Gauge Theory for B and L
BLV2013, 9 April 2013
2