Gauge Theories for Baryon Number.
Michael Duerr International Workshop on Baryon and Lepton Number Violation 2017 (BLV 2017) Case Western Reserve University, 18 May 2017 Thanks to my collaborators.
This talk is based on
arXiv:1304.0576 [hep-ph], arXiv:1306.0568 [hep-ph], arXiv:1309.3970 [hep-ph], arXiv:1409.8165 [hep-ph], arXiv:1508.01425 [hep-ph], arXiv:1604.05319 [hep-ph], arXiv:1704.03811 [hep-ph]
together with
Pavel Fileviez Pérez (CWRU), Manfred Lindner (MPIK), Juri Smirnov (INFN and University Firenze), Mark B. Wise (Caltech)
Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 2 The Standard Model of particle physics.
> Standard Model gauge group:
GSM = SU(3)C SU(2)L U(1)Y ⊗ ⊗
Field SU(3)C SU(2)L U(1)Y U(1)B U(1)L
QL 3 2 1/6 1/3 0
R 3 1 2/3 1/3 0
dR 3 1 1/3 1/3 0 − ℓL 1 2 1/2 0 1 − eR 1 1 1 0 1 − H 1 2 1/2 0 0
Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 3 Baryon number.
> Standard Model: > accidental global symmetry of the renormalizable couplings (broken by non-perturbative quantum effects) > stable p and no n–n¯ oscillations in the renormalizable SM > Generic GUT: > proton decay due to new gauge interactions > if quarks and leptons in the same multiplet one cannot define baryon number →
> What do we know about violation of B? [Figure: Viren, arXiv:hep-ex/9903029]
> Baryon asymmetry of the Universe: γ π 0 P 10 e+ (nB nB¯)/nγ 10− − ∼ γ > Proton decay( ΔB = 1, ΔL = odd):
32 34 τp 10 − years ≥ Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 4 Side remark: lepton number.
> Lepton number L conserved at the renormalizable level in the Standard Model as well > What do we know about violation of L? >ν oscillation experiments:
ΔLe = 0, ΔLμ = 0, ΔLτ = 0 6 6 6 > ΔL = 2: Majorana neutrino masses (test with 0νββ)
[Figure: Mohapatra et al., arXiv:hep-ph/0412099]
Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 5 The desert of particle physics.
c6 QQQL 2 ΛB
[Weinberg, PRL 43 (1979) 1566]
Low scale High scale Electroweak scale e.g. GUT scale 2 (Λ 1015 GeV) (ΛEW 10 GeV) ¦ ∼ [Figure: Wikipedia] Energy
Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 6 The desert of particle physics.
c6 QQQL 2 ΛB
[Weinberg, PRL 43 (1979) 1566]
Low scale High scale Electroweak scale e.g. GUT scale 2 (Λ 1015 GeV) (ΛEW 10 GeV) ¦ ∼ [Figure: Wikipedia] Energy
Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 6 The desert of particle physics.
c5 LLHH ΛL
c6 QQQL 2 ΛB
[Weinberg, PRL 43 (1979) 1566]
Low scale High scale Electroweak scale e.g. GUT scale 2 (Λ 1015 GeV) (ΛEW 10 GeV) ¦ ∼ [Figure: Wikipedia] Energy
Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 6 The desert of particle physics.
c5 LLHH ΛL
c6 QQQL 2 ΛB
[Weinberg, PRL 43 (1979) 1566]
Low scale High scale Electroweak scale e.g. GUT scale 2 (Λ 1015 GeV) (ΛEW 10 GeV) ¦ ∼ [Figure: Wikipedia] Energy
Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 6 The desert of particle physics.
c5 LLHH ΛL
c6 QQQL 2 ΛB
[Weinberg, PRL 43 (1979) 1566]
Low scale High scale Electroweak scale e.g. GUT scale 2 (Λ 1015 GeV) (ΛEW 10 GeV) ¦ ∼ [Figure: Wikipedia] Energy
Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 6 The Standard Model of particle physics.
> Standard Model gauge group:
GSM = SU(3)C SU(2)L U(1)Y ⊗ ⊗
Field SU(3)C SU(2)L U(1)Y U(1)B U(1)L
QL 3 2 1/6 1/3 0
R 3 1 2/3 1/3 0
dR 3 1 1/3 1/3 0 − ℓL 1 2 1/2 0 1 − eR 1 1 1 0 1 − H 1 2 1/2 0 0
Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 7 The Standard Model of particle physics.
> Extension of the SM gauge group:
SU(3)C SU(2)L U(1)Y U(1)B U(1)L ⊗ ⊗ ⊗ ⊗
Field SU(3)C SU(2)L U(1)Y U(1)B U(1)L
QL 3 2 1/6 1/3 0
R 3 1 2/3 1/3 0
dR 3 1 1/3 1/3 0 − ℓL 1 2 1/2 0 1 − eR 1 1 1 0 1 − H 1 2 1/2 0 0
Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 7 The Standard Model of particle physics.
> Extension of the SM gauge group:
SU(3)C SU(2)L U(1)Y U(1)B U(1)L ⊗ ⊗ ⊗ ⊗
Field SU(3)C SU(2)L U(1)Y U(1)B U(1)L Gauge theories for B (and L) QL 3 2 1/6 1/3 0 How to define a realistic theory R 3 1 2/3 1/3 0 where B (and L) are local gauge dR 3 1 1/3 1/3 0 symmetries that can− be broken at ℓL 1the low 2 (TeV) scale?1/2 0 1 − eR 1 1 1 0 1 − H 1 2 1/2 0 0
Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 7 Some history.
Phys. Rev. 98, 1501 (1955)
> heavy particle (= neutrons and protons) gauge transformation: α α ψN e ψN, ψP e ψP → → 45 > massless vector boson: gauge coupling must be tiny (αB ® 10− )
Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 8 Some history.
Phys. Rev. D 8, 1844 (1973)
> Use the Higgs mechanism to break B!
Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 9 Some history.
> Early discussions of gauging B (and L): anomaly cancellation, introduction of new fermions, properties of the gauge boson . . . > S. Rajpoot, Int. J. Theor. Phys. 27, 689 (1988) > R. Foot, G. C. Joshi, H. Lew, PRD 40, 2487 (1989) > C. D. Carone, H. Murayama, PRD 52, 484 (1995) > H. Georgi, S. L. Glashow, PLB 387, 341 (1996) > First realistic model (sequential/mirror family with B = 1) ± > P. Fileviez Pérez, M. B. Wise, PRD 82, 011901 (2010) Ruled out: new chiral quarks get mass from SM Higgs change gluon fusion Higgs production + Landau poles ⇒ > This talk will focus on the following models: > P. Fileviez Pérez, M. B. Wise, JHEP 08 (2011) 068 > MD, P. Fileviez Pérez, M. B. Wise, PRL 110 (2013) 231801 > P. Fileviez Pérez, S. Ohmer, H. H. Patel, Phys. Rev. D 90 (2014) 037701
Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 10 Features of these models.
> Framework for the spontaneous breaking of local baryon number at the low scale in agreement with experiments. > Proton is stable (or long-lived) think about the possibility of low-scale unification.→ > Vector-like fermions F with baryon number to cancel anomalies (with or without color). > Cold dark matter candidate χ: lightest neutral field in the new sector. > Leptophobic gauge boson coupling to SM quarks and new fermions: ZB qq,¯ χχ, FF¯ → > New Higgs Boson hB qq,¯ ZBZB, FF¯ → > Connection between the DM and baryon asymmetries.
Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 11 Outline.
> Local baryon number
> Baryonic dark matter
> Baryon asymmetry
> Collider signatures
> Towards low-scale unification
> Summary
Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 12 Anomaly cancellation.
> New gauge group: Field SU(3) SU(2) U(1)Y U(1)B U(1)L
1 1 QL 3 2 6 3 0 SU(3) SU(2) U(1)Y U(1)B 2 1 R 3 1 3 3 0 ⊗ ⊗ ⊗ 1 1 dR 3 1 3 3 0 − > Baryonic anomalies: νR 1 1 0 0 1
eR 1 1 1 0 1 − 1 2 2 2 H 1 2 2 0 0 1 SU(3) U(1)B , 2 SU(2) U(1)B , 3 U(1)Y U(1)B , A ⊗ A ⊗ A ⊗ 2 3 4 U(1)Y U(1)B , 5 (U(1)B) , 6 U(1)B . A ⊗ A A
U(1)B Standard Model 3 SU(2)L SU(2)L 2 = 3 = ¡ A −A 2 > New fermions needed to cancel non-trivial anomalies > 0 simplest solution: colorless fields A1 = ⇒ Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 13 How many new fermion multiplets?.
> Two fermion multiplets
ΨL (1,N,Y1,B1) and ΨR (1,M,Y2,B2) ∼ ∼ > U 1 0 requires B MB /N A5 ( ( )B) = 1 = 2 > Then U 1 3 0 requires M N and B B A6 ( )B = = 1 = 2 2 > 2 SU(2) U(1)B cannot be canceled A ⊗ > No solution with two new fermion multiplets
[Fileviez Pérez, Ohmer, Patel, arXiv:1403.8029]
Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 14 How many new fermion multiplets?.
> Three fermion multiplets
L (1, N, Y, B1), R (1, N, Y, B2), and χL (1,M, 0,B3) ∼ ∼ ∼ > Anomaly cancellation requires
2 2 3 M = 2N,Y = N /4,B1 = B2 = B3 = 3/N − − >χ L: fermions with fractional electric charge that cannot decay to SM particles > more general assignments lead to same conclusion > consistent with anomaly cancellation but in conflict with cosmology [Fileviez Pérez, Ohmer, Patel, arXiv:1403.8029]
Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 14 How many new fermion multiplets?.
> Three fermion multiplets
L (1, N, Y, B1), R (1, N, Y, B2), and χL (1,M, 0,B3) ∼ ∼ ∼ > Anomaly cancellation requires
2 2 3 M = 2N,Y = N /4,B1 = B2 = B3 = 3/N − − >χ L: fermions with fractional electric charge that cannot decay to SM particles > more general assignments lead to same conclusion > consistent with anomaly cancellation but in conflict with cosmology [Fileviez Pérez, Ohmer, Patel, arXiv:1403.8029]
Anomaly cancellation = phenomenologically viable model 6
Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 14 Solution with four fermion multiplets.
1 3 1 3 ΨL 1, 2, , , ΨR 1, 2, , ∼ 2 2 ∼ 2 − 2 3 3 L 1, 3, 0, , χL 1, 1, 0, ∼ − 2 ∼ − 2
[Fileviez Pérez, Ohmer, Patel, arXiv:1403.8029]
[Ohmer, Patel, arXiv:1506.00954]
> No fractional charges in the particle spectrum > particle content allows for vector-like masses > Majorana dark matter candidate
Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 15 A very general solution.
All anomalies can be cancelled with the following setup:
Field SU(3) SU(2) U(1)Y U(1)B
ΨL N 2 Y1 B1
ΨR N 2 Y1 B2
ηR N 1 Y2 B1
ηL N 1 Y2 B2
χR N 1 Y3 B1
χL N 1 Y3 B2
Anomaly cancellation demands: B1 B2 = 3/(NnF), − − Y2 = Y1 1/2 and Y3 = Y1 1/2 [Fileviez Pérez, Wise, arXiv:1106.0343 [hep-ph]]∓ ± Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 16 [MD, Fileviez Pérez, Wise, arXiv:1304.0576 [hep-ph]] >N = 1: Use Y1 = 1/2, Y2 = 1, Y3 = 0 lightest new fermion± can be± neutral and a DM candidate
>N = 3: use at least one hypercharge as for the SM quarks > Scenario I: Y1 = 1/6, Y2 = 2/3, Y3 = 1/3 > Scenario II: Y1 = 5/6, Y2 = 4/3, Y−3 = 1/3 > Scenario III: Y1 =−7/6, Y2 = 5−/3, Y3 = 2/3− nF = 3: dimension-9 operator for proton decay suppressed, even if cutoff of the theory not very large⇒
>N = 8: interesting but non-minimal
Possible scenarios.
Guidelines: > new fields should have direct coupling to SM fields, or > the lightest new particle is neutral and stable.
Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 17 >N = 3: use at least one hypercharge as for the SM quarks > Scenario I: Y1 = 1/6, Y2 = 2/3, Y3 = 1/3 > Scenario II: Y1 = 5/6, Y2 = 4/3, Y−3 = 1/3 > Scenario III: Y1 =−7/6, Y2 = 5−/3, Y3 = 2/3− nF = 3: dimension-9 operator for proton decay suppressed, even if cutoff of the theory not very large⇒
>N = 8: interesting but non-minimal
Possible scenarios.
Guidelines: > new fields should have direct coupling to SM fields, or > the lightest new particle is neutral and stable.
>N = 1: Use Y1 = 1/2, Y2 = 1, Y3 = 0 lightest new fermion± can be± neutral and a DM candidate
Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 17 >N = 8: interesting but non-minimal
Possible scenarios.
Guidelines: > new fields should have direct coupling to SM fields, or > the lightest new particle is neutral and stable.
>N = 1: Use Y1 = 1/2, Y2 = 1, Y3 = 0 lightest new fermion± can be± neutral and a DM candidate
>N = 3: use at least one hypercharge as for the SM quarks > Scenario I: Y1 = 1/6, Y2 = 2/3, Y3 = 1/3 > Scenario II: Y1 = 5/6, Y2 = 4/3, Y−3 = 1/3 > Scenario III: Y1 =−7/6, Y2 = 5−/3, Y3 = 2/3− nF = 3: dimension-9 operator for proton decay suppressed, even if cutoff of the theory not very large⇒
Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 17 Possible scenarios.
Guidelines: > new fields should have direct coupling to SM fields, or > the lightest new particle is neutral and stable.
>N = 1: Use Y1 = 1/2, Y2 = 1, Y3 = 0 lightest new fermion± can be± neutral and a DM candidate
>N = 3: use at least one hypercharge as for the SM quarks > Scenario I: Y1 = 1/6, Y2 = 2/3, Y3 = 1/3 > Scenario II: Y1 = 5/6, Y2 = 4/3, Y−3 = 1/3 > Scenario III: Y1 =−7/6, Y2 = 5−/3, Y3 = 2/3− nF = 3: dimension-9 operator for proton decay suppressed, even if cutoff of the theory not very large⇒
>N = 8: interesting but non-minimal
Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 17 Simplest scenario.
Consider only uncolored fields:
Field SU(3) SU(2) U(1)Y U(1)B 1 ΨL 1 2 2 B1 ± 1 ΨR 1 2 2 B2 ± ηR 1 1 1 B1 ± ηL 1 1 1 B2 ± χR 1 1 0 B1
χL 1 1 0 B2
Anomaly cancellation demands: B1 B2 = 3 [MD, Fileviez Pérez, Wise, arXiv:1304.0576] − −
arXiv:1309.3970 [MD, Fileviez Pérez, ] Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 18 What about lepton number.
> New gauge group: Field SU(3) SU(2) U(1)Y U(1)B U(1)L
1 1 QL 3 2 6 3 0
3 1 2 1 0 SU(3) SU(2) U(1)Y U(1)B U(1)L R 3 3 1 1 dR 3 1 3 3 0 ⊗ ⊗ ⊗ ⊗ − 1 ℓL 1 2 2 0 1 > Purely baryonic anomalies: − νR 1 1 0 0 1
eR 1 1 1 0 1 2 2 2 − SU 3 U 1 , SU 2 U 1 , U 1 U 1 , 1 1 ( ) ( )B 2 ( ) ( )B 3 ( )Y ( )B H 1 2 0 0 A ⊗ A ⊗ A ⊗ 2 2 3 4 U(1)Y U(1)B , 5 (U(1)B) , 6 U(1)B . A ⊗ A A > Purely leptonic anomalies: SM + right-
2 2 2 handed ν’s 7 SU(3) U(1)L , 8 SU(2) U(1)L , 9 U(1)Y U(1)L , A ⊗ A ⊗ A ⊗ U 1 U 1 2 , U 1 , U 1 3 . 3 A10 ( )Y ( )L A11 ( ( )L) A12 ( )L ⊗ 2 = 3 = , A A 2 > Mixed anomalies: − 3 U 1 2 U 1 , U 1 2 U 1 , 13 ( )B ( )L 14 ( )L ( )B 8 = 9 = A ⊗ A ⊗ A A 2 15 (U(1)Y U(1)L U(1)B) . − A ⊗ ⊗
Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 19 [MD, Fileviez Pérez, arXiv:1309.3970]
Simplest scenario: lepto-baryons.
Assign lepton number to the same fields that cancel the baryonic anomalies
Field SU(3) SU(2) U(1)Y U(1)B U(1)L 1 ΨL 1 2 2 B1 L1 ± 1 ΨR 1 2 2 B2 L2 ± ηR 1 1 1 B1 L1 ± ηL 1 1 1 B2 L2 ± χR 1 1 0 B1 L1
χL 1 1 0 B2 L2
Anomaly cancellation demands: B1 B2 = 3, L1 L2 = 3 − − − − [MD, Fileviez Pérez, Wise, arXiv:1304.0576] Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 20 Simplest scenario: lepto-baryons.
Assign lepton number to the same fields that cancel the baryonic anomalies
Field SU(3) SU(2) U(1)Y U(1)B U(1)L 1 ΨL 1 2 2 B1 L1 ± 1 ΨR 1 2 2 B2 L2 ± ηR 1 1 1 B1 L1 ± ηL 1 1 1 B2 L2 ± χR 1 1 0 B1 L1
χL 1 1 0 B2 L2
Anomaly cancellation demands: B1 B2 = 3, L1 L2 = 3 − − − − [MD, Fileviez Pérez, Wise, arXiv:1304.0576] Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 20 [MD, Fileviez Pérez, arXiv:1309.3970] Spontaneous symmetry breaking.
> Relevant interactions of the new fields (for B1 = B2): 6 − h1ΨLHηR + h2ΨLHχ˜ R + h3ΨRHηL + h4ΨRHχ˜ L −L ⊃ + λ1ΨLΨRSB + λ2ηRηLSB + λ3χRχLSB + h.c.
New Higgs: SB (1, 1, 0,B1 B2) ∼ − > SB = 0 generates vector-like masses: 〈 〉 6
MΨΨLΨR + MηηRηL + MχχRχL + h.c. −L ⊃ SB (1, 1, 0, 3) ΔB = 3 no proton decay no desert ∼ − ⇒ ⇒ ⇒ > Remnant stabilizes lightest new fermion. Z2
Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 21 Baryonic dark matter.
thermal freeze-out (early Univ.) > Dirac DM, SM singlet-like: χ = χR + χL indirect detection (now) > Coupling to the new gauge boson: DM SM
μ gBχγμZB(B2PL + B1PR)χ L ⊃ DM annihilation and direct detection direct detection > Model has only six free parameters: DM SM
production at colliders Mχ,MZB , gB,B B1 + B2 and Mh2 , θB χ ≡ q χ χ
ZB
ZB
χ q N N
[MD, Fileviez Pérez, arXiv:1309.3970, arXiv:1409.8165Michael Duerr] | Gauge Theories for Baryon Number | 18 May 2017 | page 22 Dark matter relic density.
1 B = 2 101
0 10 χ q
ZB 1 10− 2 h DM
Ω 2 10− χ q
3 2 10− > Planck: Ω h Planck DM =
MZB = 1.5 TeV, gB = 0.5 0.1199 0.0027 M 1.0 TeV, g 0.3 4 ZB = B = ± 10− 200 400 600 800 1000 1200 1400 Mχ [GeV]
Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 23 Dark matter relic density.
B = 2 100
1 10− χ q
ZB 10 2
2 − h DM
Ω 3 10− χ q
4 2 10− > Planck: Ω h Planck DM =
MZB = 1.5 TeV, gB = 0.5 0.1199 0.0027 M 1.0 TeV, g 0.3 5 ZB = B = ± 10− 200 400 600 800 1000 1200 1400 Mχ [GeV]
Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 23 Dark matter direct detection.
2 ΩDMh = 0.1199 0.0027 ± χ χ 43 10− ZB
44 N N 10− ] 2
LUX
cm 2
[ 45 > Planck: ΩDMh 10− = SI χN
σ 0.1199 0.0027 ± XENON1T 46 10− B = 1/2 B 2 = MZ 0.5, 5.0 TeV 47 B [ ] 10− ∈ 500 1000 1500 2000 gB [0.1, 0.5] Mχ [GeV] ∈
Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 24 Scalar dark matter.
> Scalar DM can arise in these models as well.
> If vector-like colored fermions (Q0, 0, d0) cancel the anomalies, they should decay. > Introduce new scalar field X with baryon number BX = 1/3 BQ : − R0
λ1XQLQR0 + λ2XRL0 + λ3XdRdL0 + h.c. −L ⊃ > Possible annihilation channels:
† ∗ ¯ † ∗ XX ZB qq or XX H SM SM → → → → > viable DM candidate in part of the parameter space
Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 25 Baryon asymmetry and dark matter.
> Symmetries of the model:
> (B L)SM − > Accidental η symmetry in the new sector:
η ΨL,R e ΨL,R, → η ηL,R e ηL,R, → η χL,R e χL,R. → DM stability ⇒ > Relevant interactions:
h1ΨLHηR + h2ΨLHχ˜ R + h3ΨRHηL + h4ΨRHχ˜ L −L ⊃ + λ1ΨLΨRSB + λ2ηRηLSB + λ3χRχLSB + h.c.
Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 26 Baryon and dark matter asymmetries.
g: internal degrees of freedom, > For μ T: s: entropy density, g∗: total number of relativistic degrees of freedom, Δn n+ n 15g μ 2 for fermions, − , ξ = = − = 2 1 for bosons. s s 2π g∗ξ T >B L asymmetry in the SM sector − 45 Δ B L μ μ μ μ μ μ μ , ( )SM = 2 ( L + R + dL + dR νL eL eR ) − 4π g∗T − − − >η charge density 15 Δη 2μ 2μ μ μ μ μ . = 2 ΨL + ΨR + χL + χR + ηL + ηR 4π g∗T > Baryon asymmetry nq nq¯ 15 BSM 3 μ μ μ μ . ƒ = − = 2 L + R + dL + dR s 4π g∗T
P. Fileviez Pérez, H. H. Patel, arXiv:1311.6472 [hep-ph]Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 27 Baryon and dark matter asymmetries.
32 15 14B SM ( 2) Bƒ = Δ(B L)SM + − Δη, 99 − 198 Initial Asymmetry
Sphalerons 3 (QQQL) ψ¯RψL Consistent picture for baryogenesis! Baryon Asymmetric Asymmetry Dark Matter
3(3μL + μeL ) + μΨL μΨR = 0. − P. Fileviez Pérez, H. H. Patel, arXiv:1311.6472 [hep-ph]
Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 28 Dijet searches.
> Since the leptophobic gauge boson ZB is produced from quarks, it can decay back to quarks dijet searches → q¯ q
ZB
q q
mQ = 1 TeV, B1 = 1, B2 =4/3 100 ) B
Z 1 10− BR(
jj tt¯ ATLAS highest-mass dijet event (Event 4144227629, Run 305777) QQ¯ 2 10− 500 1000P 1500 2000 2500 3000
MZ [GeV] B Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 29 Limits on mass vs. gauge coupling.
LHC dijet searches 2
1
0.5 B g
0.3
0.2 Combination from 1605.07940 1 1 CMS 27 fb− & 36 fb− (13 TeV) 1 ATLAS 37.0 fb− (13 TeV) 1 ATLAS 3.4 fb− (13 TeV); Trigger-object Level Analysis 0.1 500 1000 1500 2000 2500 3000 3500 4000
MZB [GeV] [MD, Fileviez Pérez, Smirnov, arXiv:1704.03811]
Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 30 Low-mass region.
> New CMS search with ISR jet (CMS-PAS-EXO-17-001) [See talk by A. de Roeck]
CMS Preliminary 35.9 fb-1 (13 TeV)
q 1 Observed UA2
Expected CDF Run 1 0.4 ± 1 std. deviation CDF Run 2 0.3 ± 2 std. deviation coupling, g 0.2
0.1
ATLAS13, 15.5 fb-1, ISR γ 0.04 ATLAS13, 15.5 fb-1, ISR jet 0.03 CMS8, 18.8 fb-1, Scouting Z Width (indirect) 0.02 50 60 100 200 300 400 1000 Z' mass (GeV) g Z qγ¯ q g 3g L q μ0 μ B = q ⊃ Michael Duerr | Gauge⇒ Theories for Baryon Number | 18 May 2017 | page 31 Baryonic Higgs at the LHC.
P. Fileviez Pérez, M. B. Wise, arXiv:1106.0343 [hep-ph]
MD, P. Fileviez Pérez, J. Smirnov, arXiv:1704.03811 [hep-ph]
Cancel the anomalies with vector-like quarks.
> Use three copies (analogy to the SM families) B1 B2 = 1/3 ⇒ − −Scenario III 1
1 > Scenario I: Y1 = 1/6, Y2 = 2/3, 10− Y3 1/3 = 1 TeV = B − h M 2 > Scenario II: Y1 = 5/6, Y2 = 4/3, 10− hB gg
− − ) for Y3 = 1/3 h → W W B B → h hB ZZ − 3 → > Scenario III: Y1 = 7/6, Y2 = 5/3, 10− hB γγ
BR( → hB Zγ → ¯ Y3 = 2/3 hB tt h → h h B → 1 1 4 10− 0.001 0.01 0.1 0.3
θB BR into photons large compared to SM Higgs, colored new fermions in the loop.
[See parallel talk by J. Smirnov] Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 32 Baryonic Higgs at the LHC.
P. Fileviez Pérez, M. B. Wise, arXiv:1106.0343 [hep-ph]
MD, P. Fileviez Pérez, J. Smirnov, arXiv:1704.03811 [hep-ph]
Cancel the anomalies with vector-like quarks.
> Use three copies (analogy to the SM families) B1 B2 = 1/3 ⇒ − Scenario− III
1
> Scenario I: Y1 1/6, Y2 2/3, 1 = = 10−
Y3 = 1/3 ) B
− h > Scenario II: Y1 = 5/6, Y2 = 4/3, BR( 2 − − 10 hB gg Y3 = 1/3 − → hB W W − h → ZZ B → > Scenario III: Y1 = 7/6, Y2 = 5/3, hB γγ → hB Zγ Y 2/3 → ¯ 3 = 3 hB QQ 10− → hB ZBZB → P 500 1000 1500 2000 2500 3000 3500
MhB [GeV] BR into photons large compared to SM Higgs, colored new fermions in the loop.
[See parallel talk by J. Smirnov] Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 32 Baryonic Higgs at the LHC.
MD, P. Fileviez Pérez, J. Smirnov, arXiv:1704.03811 [hep-ph]
Di-photon channel can severely constrain the baryonic scale.
LHC γγ searches Lower bound on vB from LHC γγ searches 103 105 1 1 CMS 16.2 fb− (13 TeV) + 19.7 fb− (8 TeV) Scenario I: θB = 0, ATLAS 1 ATLAS 15.4 fb− (13 TeV) Scenario I: θB = 0, CMS Scenario I: θB = 0 Scenario II: θB = 0, ATLAS Scenario I: θB = 0.3 Scenario II: θB = 0, CMS
) [fb] 102 Scenario II: θB = 0 Scenario III: θB = 0, ATLAS Scenario II: θB = 0.3 Scenario III: θB = 0, CMS γγ Scenario III: θB = 0 104 → Scenario III: θB = 0.3 B h 101 [GeV] BR( B × v )
B 3 h 10
→ 1 pp ( σ
MhB > vB
1 2 10− 10 200 500 1000 2000 200 500 1000 2000
MhB [GeV] MhB [GeV] Dominant production via gluon fusion with colored new fermions in the loop.
[See parallel talk by J. Smirnov]
Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 33 Left–right symmetric model.
GLR = SU(2)L SU(2)R U(1)B L SM fields ⊗ ⊗ − > Connects neutrino masses and QL (2, 1, 1/3) ∼ spontaneous parity violation. QR (1, 2, 1/3) ∼ > Standard version uses hybrid version of ℓL (2, 1, 1) type I and type II seesaw mechanism ∼ − ℓR (1, 2, 1) for neutrino masses. ∼ − Pati, Salam, PRD 10 (1974) 275, Mohapatra, Pati, PRD 11 (1975) 2558, Senjanovic, Mohapatra, PRD 12 (1975) 1502 > Promote gauge group to
SU(2)L SU(2)R U(1)B U(1)L ⊗ ⊗ ⊗
He, Rajpoot, PRD 41 (1990) 1636
Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 34 Anomaly cancellation: type III seesaw.
> Anomalies that need to be > Simplest solution: type III cancelled: seesaw fields A 2 1 SU(2)L U(1)B = 3/2 ⊗ ρL 3, 1, 3/4, 3/4 , 2 ( ) A2 SU 2 U 1 L 3/2 ∼ − − ( )L ( ) = ρ 1, 3, 3/4, 3/4 ⊗ R ( ) A 2 ∼ − − 3 SU(2)R U(1)B = 3/2 ⊗ − A 2 > Neutrino mass matrix: 4 SU(2)R U(1)L = 3/2 ⊗ − 1 2 0 0 0 mD mD 0 m 0 m3 m4 1 D D 3+2 5 6 ν = 0 0 m2 mD mD . M 1 3 5 mD mD mD 0 0 2 4 6 HL SBL HL mD mD mD 0 0 ¡〈 〉〈 〉〈 〉 > Two light sterile neutrinos. νL 0 0 νL ρL ρL MD, P. Fileviez Pérez, M. Lindner, arXiv:1306.0568 [hep-ph]
Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 35 Towards low-scale unification.
> Step 1: Unification of gauge interactions at the low scale
P. Fileviez Pérez, S. Ohmer, arXiv:1405.1199 > Fields in minimal theory for B and L allow for unification at the low scale (proton is stable!) > Step 2: Find UV completion and embed baryon number into a non-abelian gauge symmetry
P. Fileviez Pérez, S. Ohmer, arXiv:1612.07165 > If quarks and leptons live in the same multiplets, B and L cannot be defined > With extra matter one can have multiplets with definite baryon number, one of the generators can be identified with baryon number > Color and baryon number can be unified in SU(4)C similar to Pati, Salam, Phys. Rev. D 10 (1974) 275 Fileviez Pérez, Wise, arXiv:1307.6213 Fornal, Rajaraman, Tait, arXiv:1506.06131
[See parallel talk by S. Ohmer for details.] Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 36 Gauge coupling unification.
> Running of gauge couplings (@ 1-loop): >k : normalization >M F: mass scale of the new fermions B (here: 500 GeV) 1 1 kα− (M) = α− (MZ ) log(M/MZ ) >n F: number of new fermion copies − 2π log M/M SM new ( F) P. Fileviez Pérez, S. Ohmer, B = b + Θ(M MF)nFb arXiv:1405.1199 [hep-ph] − log(M/MZ )
60 SM -1 Α1 50 > Model with SU(2) triplet: - Α SM 1 40 2 1 I M
- nF unification scale [TeV] k1 i SM -1 Α Α 30 -1 3 9 Α2 1 1.24 10 2.05 I M -1 × 6 20 Α1 2 4.96 10 2.67 -1 I M × 4 HΑ3 L 4 2.14 10 3.62 10 × 3 H L 5 4.58 10 3.99 4 6 8 10 12 14 16 × H L Log10 M GeV
H L
Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 37 Gauge coupling unification.
> Running of gauge couplings (@ 1-loop): >k : normalization >M F: mass scale of the new fermions B (here: 500 GeV) 1 1 kα− (M) = α− (MZ ) log(M/MZ ) >n F: number of new fermion copies − 2π log M/M SM new ( F) P. Fileviez Pérez, S. Ohmer, B = b + Θ(M MF)nFb arXiv:1405.1199 [hep-ph] − log(M/MZ )
35 60 Α -1 SM -1 L Α1 30 Α -1 50 2 -1 25 Α SM -1 2 HΑ1 L -1 40 ΑB 1 I M 1 - - i SM -1 i 20 H L Α Α Α -1 3 30 Α2 I M 15 H L -1 H L Α1 20 -1 Α3 -1 I M 10 HΑ3 L 10 5 H 4L 6 8 10 12 14 16 3 4 5 6 7 H L H L Log10 M GeV Log10 M GeV
Unification of gauge interactions possible with small αB (and H L H L αL) at the low scale.
Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 37 Baryon number as the fourth color.
> Embed SM U(1)B into SU(4)C SU(3)L SU(3)R P. Fileviez Pérez, S. Ohmer,⊗ arXiv:1612.07165 ⊗ ⊗
> SM fermions
dr r Dr db b Db ¯ Q = (4, 3, 1) dg g Dg ∼ Ψd Ψ ΨD dc dc dc ηc r¯ b¯ g¯ d c c c c ηc ¯ Q = r¯ b¯ g¯ (4, 1, 3) Dc Dc Dc ηc ∼ r¯ b¯ g¯ D N1 E+ ν L = E N2 e (1, 3, 3¯) −c − ν e+ N3 ∼
> extra fermions (anomalies) c Ψ (1, 3, 1) and η (1, 1, 3¯) ∼ ∼ > Possible embedding into SU(4)C SU(4)L SU(4)R (plus Z3 symmetry) ⊗ ⊗ Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 38 [See parallel talk by S. Ohmer for details.] Summary.
> I presented simple theories for the spontaneous breaking of baryon number (and lepton number). > Features include: > No proton decay even though B can be broken at the low scale. > DM stability as an automatic consequence of the gauge symmetry. > Leptophobic ZB that can be searched for at colliders. > Unification could be realized at the low scale since the desert is not needed.
Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 39 Backup slides.
Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 1 Baryonic dark matter.
Condition from anomaly cancellation: B1 B2 = 3 two options: − − ⇒ B1 = B2 B1 = B2 = 3/2: 6 − − − > Dirac DM, SM singlet-like: > Majorana DM with axial coupling to the ZB: χ = χR + χL 3 5 μ gBχγ¯ μγ χZB > Coupling to the ZB: −L ⊃ 2 μ > five free parameters (plus gBχγμZB(B2PL + B1PR)χ extra fermion masses): −L ⊃ > six free parameters (plus Mχ,MZB , gB, and Mh2 , θB extra fermion masses): [MD, Fileviez Pérez, Smirnov, arXiv:1508.01425]
Mχ,MZB , gB,B B1 + B2,Mh2 , θB [MD, Fileviez Pérez, arXiv:1309.3970≡ , arXiv:1409.8165]
Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 2 What about the additional fermions?.
> Decays of SB: > Majorana DM (B1 = B2): > For θ 0, the branching fractions of the − fermion-loop-mediated→ decays of SB may loop-mediated DM annihilation provide clues about the fermion content to photons of the model at the LHC > Model with SU 2 triplet: 2 ( ) ΩDMh =0.1199 0.0027, MZB =1.2Mχ 26 ± 10− WW : ZZ : Zγ : γγ = 20 : 7 : 3 : 1
27 10− H.E.S.S. ] 1
− 28
s 10−
3 FermiLAT
[cm 10 29 γγ − → ¯ χχ i 30 10− σv h
Mη = Mχ, MΨ =2Mχ 31 10− Mη =2Mχ, MΨ =3Mχ
32 10− 200 1000 10000 [Ohmer, Patel, arXiv:1506.00954] Mχ [GeV] > Vector-like model: 3 [MD, Fileviez Pérez, Smirnov, arXiv:1508.01425] WW : ZZ : Zγ : γγ = 2 : 1 : 10− : 1
Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 3 Even lower-mass region.
3 2 Ψ Z width 1 U 0.5
z 0.3 g 3 0.2 = 450 GeV f = f m 0.1 90 GeV, N 90 GeV = = 0.05 f f m m ' model 0.03 ZB 0.3 0.5 1 2 3 5 10 20 30 50
MZ' HGeVL
[Dobrescu, Frugiuele, arXiv:1404.3947]
Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 4 Gauging B and L in SUSY setups.
> Lepto-baryon fields:
J. M. Arnold, P. Fileviez Pérez, B. Fornal, S. Spinner, arXiv:1310.7052 [hep-ph]
>U (1)B and U(1)L breaking scale linked to SUSY breaking scale > R-parity must be spontaneously broken > Stable DM candidate
> Vector-like family: P. Fileviez Pérez, M. B. Wise, arXiv:1106.0343 [hep-ph]
>U (1)B and U(1)L breaking scale linked to SUSY breaking scale > Low B breaking renders the lightest neutralino unstable no DM candidate ⇒
Michael Duerr | Gauge Theories for Baryon Number | 18 May 2017 | page 5