gauge b-l model with residual z3 symmetry · (dm, dm !light-mediator !sm, sm) is ruled out by the...

Gauge B−L model with residual Z3 symmetry

Mohammadreza Zakeri

University of California, Riverside

[email protected]

May 16, 2017

2017 International Workshop on Baryon and Lepton Number Violation:From the Cosmos to the LHC

Mohammadreza Zakeri (UCR) PLB 750 (2015) 135138 May 16, 2017 1 / 21

Overview

1 Baryon and Lepton Numbers in the Standard Model

2 Gauge B−L Symmetry

3 Collider Signature

4 Dark Matter

5 SIDM


Baryon and Lepton Numbers in the Standard Model

The Standard Model

Baryon(B) and Lepton(L) numbers are accidental globalsymmetries.

Neutrino oscillations −→ Le, Lµ, Lτ are not conserved.

Lepton number as a global symmetry−→ Majorana neutrino masses: breaks down (−1)L (leptonparity).

B−L is conserved.−→ Promote B−L to a gauge symmetry:

SO(10) grand unification: SU(3)C× SU(2)L× SU(2)R× U(1)B−L.String Theory.


Gauge B−L Symmetry

Conventional Gauge B−L

Anomaly Conditions:∑i∈SM

(B − L)i = +3,∑i∈SM

(B − L)3i = +3 (1)

νR1, νR2, νR3 ∼ −1,−1,−1 (2)

∑i

Li · Φ̃ · vRi =∑i

(νiL, liL) ·(φ0

−φ−)· vRi (3)

Dirac Mass for Neutrinos!



Gauge B−L with Exotic Charges

Anomaly Conditions:∑i∈SM

(B − L)i = +3,∑i∈SM

(B − L)3i = +3 (4)

νR1, νR2, νR3 ∼ 5,−4,−4 (5)

5− 4− 4 =− 3, (5)3 − (4)3 − (4)3 =− 3. (6)



Gauge B−L with Exotic Charges

νR1, νR2, νR3 ∼ 5,−4,−4 (7)

Particle B−L

N1,2,3 −1

χ3 3

〈χ3〉 = u3 (8)

νLNRφ0

+NLνR2χ3 +NLνR3χ3 +NLNR ⊂ LYuk (9)



Neutrino Mass Matrix

νLNRφ0

NLνR2χ3 +NLνR3χ3 NLNR

⇓ ⇓ ⇓M0 M3 MN

MνN =

(0 M0

M3 MN

)(10)

ν̄R1 ·NL · χ23 ⊂ L5 , can be added to generate mass for νR1.



Dirac Neutrino Mass from Seesaw

MνN =

(0 M0

M3 MN

)(11)

Mν 'M0M−1N M3 (12)

f1 , f2 : Any pair of two neutral fermions with the same chirality.

B− L(f1) + B− L(f2) mod 3 6= 0 (13)

No operator of any dimension for a Majorana mass term whichviolates B−L.

−→ The neutrinos are exactly Dirac.



New Scalars

NLνR1χ6, χ2NLNL, χ2NRNR, χ32χ6, χ2

3χ6. (14)

〈φ0〉 = v, 〈χ3〉 = u3, 〈χ6〉 = u6 (15)

All neutrinos become massive.

Z3 residual symmetry remains.

All leptons transform as ω = exp(2πi/3) under Z3.

Lepton symmetry which is not Z2 (Majorana ν), nor U(1) or Z4

(Dirac ν).

Z3 is sufficient to guarantee that all the neutrinos remain Dirac.


Collider Signature

Gauge Sector

Br(Z ′ → q+q−) Br(Z ′ → l+l−) Br(Z ′ → νν)

Conventional B−L 1/4 3/8 3/8

This Model 1/18 1/12 5/6

LHC data: 2.5 TeV

Precision e+e− → e+e− measurements at LEP: MZ′/g′ > a few

TeV.


Dark Matter

Stability

χ2 transforms as ω = exp(2πi/3), with no stabilizing symmetry.

Lint =1

2fLχ2NLNL +

1

2fRχ2NRNR +H.c. (16)

χ2

ν̃R

NR

NR

ν̃R

χ2

ν̃L

NL

NL

ν̃L

For mχ = 100 GeV, fL = fR and ζ0 = ζ3 long-lived if:√fζ << 3× 10−11 −→ mN ∼ 1013GeV (17)


Dark Matter

Direct Detection

LUX Constraints:

u,d

χ2χ2

u,d

Z′

u,d

χ∗2χ∗

2

u,d

Z′

0 200 400 600 800 10006

8

10

12

14

16

18

mχ (GeV)

(Mz'

g ')TeV


Dark Matter

Relic Abundance

χ2χ∗2 → Z ′ → SM SM:

χ2

χ∗2

Z ′

SM

SM

P-wave Suppressed!


Dark Matter

Relic Abundance

χ2χ∗2 → h→ SM SM:

χ2

χ∗2

h

SM

SM

In conflict with LUX data!


Dark Matter

Relic Abundance

Assumptions:

mχ2 > mχ3,6 .

hχ2χ∗2 is negligible.

χ2

χ2

χ2

χ2

χ3,6

χ3,6

χ2

χ3,6

χ3,6

χ2

χ2

χ3,6

χ3,6

χ3,6


SIDM

Scalar Sector

Scalar potential: V (Φ, χ2, χ3, χ6).

In general: h mixes with Re(χ3), Re(χ6).

In the decoupling limit:

S =√

2Re(−u3χ3 + 2u6χ6)/√u23 + 4u26, (18)

S′ =√

2Re(2u6χ3 + u3χ6)/√u23 + 4u26, (19)

S is massive ∼ B−L breaking scale.

S′ can be fine tuned to be light ∼ 10 MeV


SIDM

S ′ as a Mediator

S′h mixing is very small ∼ v/u6.S′S′h and S′S′hh can be significant.

Γ(h→ S′S′) =λ206v

2

256πmh=

(λ060.04

)2

0.5 MeV. (20)

Invisible at the LHC because S′ decays slowly to e−e+ (mixingwith h).

mS′ ∼ 10 MeV for SIDM.


SIDM

Constraints on Light Mediators for SIDM

T. Bringmann et al., Phys. Rev. Lett. 118, 141802 (2017)

As the Universe cools down:→ DM velocity decreases→ Enhanced DM annihilation→ Changing reionization history→ Distortion of CMB.

(DM, DM → light-mediator → SM, SM) is ruled out by the CMBand indirect detection experiments.−→ Assumption: The final states interact with plasma.


Conclusion

B−L gauge symmetry −→ Z3.

Neutrinos are Dirac fermions via seesaw mechanism.

Complex neutral scalar χ2, transforming as ω = exp(2πi/3):−→ Not absolutely stable (χ2 → ν ν)

Direct-search experiments constrain mZ′/g′ to be very large:

−→ Impossible to discover Z ′ at the LHC.

Relic abundance of χ2 is determined by χ2 → S′S′.−→ S′ as a light mediator for SIDM is ruled out.−→ S′ may subsequently decay to SM.


Thank You!


References

E. Ma, N. Pollard, R. Srivastava, M. Zakeri, Phys. Lett. B 750 (2015) 135138

J.C. Montero, V. Pleitez, Phys. Lett. B 675 (2009) 64.

E. Ma, R. Srivastava, Phys. Lett. B 741 (2015) 217.

LUX collaboration, D. S. Akerib et al. Phys. Rev. Lett. 116.161301.

L. Feng, S. Profumo, L. Ubaldi, J. High Energy Phys. 1503 (2015) 045.

T. Bringmann, F. Kahlhoefer, K. Schmidt-Hoberg, and P. Walia, Phys. Rev.Lett. 118, 141802 (2017)


gauge b-l model with residual z3 symmetry · (dm, dm !light-mediator !sm, sm) is ruled out by the...

Documents