[PPT] - SUPERWEAK FORCE Zoltn Trcsnyi Etvs University and MTA-DE Particle PowerPoint Presentation

SLIDE 1

SUPERWEAK FORCE

Zoltán Trócsányi Eötvös University and MTA-DE Particle Physics Research Group Matter to the Deepest, Chorzów, 4 September 2019

SLIDE 2

OUTLINE

1. Status of particle physics
2. U(1)Z extension of SM
3. Constraints on the parameter space

2

SLIDE 3

Status of particle physics: energy frontier

3

LEP, LHC: SM describes final states of particle collisions precisely SM is unstable No proven sign of new physics beyond SM at colliders*

*There are some indications below discovery significance (such as lepton flavor non-universality in meson decays)

SLIDE 4

Status of particle physics: cosmic and intensity frontiers

4

Universe at large scale described precisely by cosmological SM: ΛCDM (Ωm =0.3), without astrophysical explanation Neutrino flavours oscillate requiring neutrino masses Existing baryon asymmetry cannot be explained by CP asymmetry in SM Inflation of the early, accelerated expansion of the present Universe

SLIDE 5

Extension of SM

5

There are many extensions proposed, mostly with the aim of predicting some observable effect at the LHC — but those have not been

bserved so far, so why not try something else

SLIDE 6

Extension of SM

5

There are many extensions proposed, mostly with the aim of predicting some observable effect at the LHC — but those have not been

bserved so far, so why not try something else

SM is highly efficient — let us stick to efficiency

the only exception of economical description is the relatively large number of Yukawa couplings

SLIDE 7

Extension of SM

6

Neutrinos must play a key role

with non-zero masses they must feel another force apart from the weak

ne, such as Yukawa coupling to a scalar, which requires the existence of

right-handed neutrinos

SLIDE 8

Extension of SM

6

Neutrinos must play a key role

with non-zero masses they must feel another force apart from the weak

ne, such as Yukawa coupling to a scalar, which requires the existence of

right-handed neutrinos

Simplest extension of GSM=SU(3)c×SU(2)L×U(1)Y is to G=GSM×U(1)Z

SLIDE 9

Extension of SM

6

Neutrinos must play a key role

with non-zero masses they must feel another force apart from the weak

ne, such as Yukawa coupling to a scalar, which requires the existence of

right-handed neutrinos

Simplest extension of GSM=SU(3)c×SU(2)L×U(1)Y is to G=GSM×U(1)Z

renormalizable gauge theory without any other symmetry

Fix Z-charges by requirement of

SLIDE 10

Extension of SM

6

Neutrinos must play a key role

with non-zero masses they must feel another force apart from the weak

ne, such as Yukawa coupling to a scalar, which requires the existence of

right-handed neutrinos

Simplest extension of GSM=SU(3)c×SU(2)L×U(1)Y is to G=GSM×U(1)Z

renormalizable gauge theory without any other symmetry

Fix Z-charges by requirement of

gauge and gravity anomaly cancellation and gauge invariant Yukawa terms for neutrino mass generation

SLIDE 11

Focus only on addition to the SM, find SM in this new book:

7

SLIDE 12

fermion fields: where (νL can νR can also be Majorana neutrinos, embedded into different Dirac spinors) covariant derivative (includes kinetic mixing):

Fermions (with new highlighted)

8

f

q,1 =

✓U f Df ◆

L

f

q,2 = U f R ,

f

q,3 = Df R

f

l,1 =

✓⌫f `f ◆

L

f

l,2 = ⌫f R ,

f

l,3 = `f R

L/R ⌘ ⌥ = 1 2 (1 ⌥ 5) ⌘ PL/R ,

Dµ

j = @µ + igL T · W µ + igY yjB0µ + i(g0 Z zj − g0 Y yj)Z0µ ≡g0

Zrj+(g0 Z−g0 Y )yj

z }| {

SLIDE 13

Scalars

9

Standard Φ complex SU(2)L doublet and new complex singlet: with scalar potential

Lφ,χ = [D(φ)

µ φ]⇤D(φ) µφ + [D(χ) µ χ]⇤D(χ) µχ − V (φ, χ)

(

V (φ, χ) = V0 − µ2

φ|φ|2 − µ2 χ|χ|2 +

|φ|2, |χ|2 ✓λφ

λ 2 λ 2

λχ ◆ ✓|φ|2 |χ|2 ◆

SLIDE 14

Scalars

9

Standard Φ complex SU(2)L doublet and new complex singlet: with scalar potential After SSB, G → SU(3)c×U(1)QED: &

Lφ,χ = [D(φ)

µ φ]⇤D(φ) µφ + [D(χ) µ χ]⇤D(χ) µχ − V (φ, χ)

(

= 1 p 2 eiT ·ξ(x)/v ✓ v + h0(x) ◆

(x) = 1 p 2 ei⌘(x)/w w + s0(x)

V (φ, χ) = V0 − µ2

φ|φ|2 − µ2 χ|χ|2 +

|φ|2, |χ|2 ✓λφ

λ 2 λ 2

λχ ◆ ✓|φ|2 |χ|2 ◆

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Anomaly free charge assignment

10

(a) anomaly free charges (b) from neutrino-scalar interactions (c) from re-parametrization of couplings

(a) (b) (c)

is added for later convenience. . field SU(3)c SU(2)L yj zj zj rj = zj/zφ − yj UL, DL 3 2

1 6

Z1

1 6

UR 3 1

2 3

Z2

7 6 1 2

DR 3 1 − 1

3

2Z1 − Z2 − 5

6

− 1

2

⌫L, `L 1 2 − 1

2

−3Z1 − 1

2

⌫R 1 1 Z2 − 4Z1

1 2 1 2

`R 1 1 −1 −2Z1 − Z2 − 3

2

− 1

2

1

2

1 2

zφ 1

1 2

1

1 zχ −1 −1

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Fermion-scalar interactions

11

Standard Yukawa terms: lead to fermion masses after SSB:

LY =  cD ¯ U, ¯ D

L

✓(+) (0) ◆ DR + cU ¯ U, ¯ D

L

✓ (0) ⇤ (+) ⇤ ◆ UR + c`

¯

⌫`, ¯ `

L

✓(+) (0) ◆ `R

+ h.c.

LY = − ✓ 1 + h(x) v ◆ ⇥ ¯ DL MD DR + ¯ UL MU UR + ¯ `L M` `R ⇤ + h.c.

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Fermion-scalar interactions

11

Standard Yukawa terms: lead to fermion masses after SSB: Neutrino Yukawa terms ( ):

LY =  cD ¯ U, ¯ D

L

✓(+) (0) ◆ DR + cU ¯ U, ¯ D

L

✓ (0) ⇤ (+) ⇤ ◆ UR + c`

¯

⌫`, ¯ `

L

✓(+) (0) ◆ `R

+ h.c.

LY = − ✓ 1 + h(x) v ◆ ⇥ ¯ DL MD DR + ¯ UL MU UR + ¯ `L M` `R ⇤ + h.c.

Lν

Y = −

X

i,j

✓ (cν)ij ¯ Li,L · ˜ φ νj,R + 1 2(cR)ij νc

i,Rνj,R χ

◆ + h.c.

lation zχ = −2zνR

(Dirac mass terms)

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Fermion-scalar interactions

11

Standard Yukawa terms: lead to fermion masses after SSB: Neutrino Yukawa terms ( ):

LY =  cD ¯ U, ¯ D

L

✓(+) (0) ◆ DR + cU ¯ U, ¯ D

L

✓ (0) ⇤ (+) ⇤ ◆ UR + c`

¯

⌫`, ¯ `

L

✓(+) (0) ◆ `R

+ h.c.

LY = − ✓ 1 + h(x) v ◆ ⇥ ¯ DL MD DR + ¯ UL MU UR + ¯ `L M` `R ⇤ + h.c.

Lν

Y = −

X

i,j

✓ (cν)ij ¯ Li,L · ˜ φ νj,R + 1 2(cR)ij νc

i,Rνj,R χ

◆ + h.c.

lation zχ = −2zνR

(Majorana mass terms)

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Charge assignment from gauge invariant neutrino interactions

12

(a) anomaly free charges (b) from neutrino-scalar interactions (c) from re-parametrization of couplings

(a) (b) (c)

is added for later convenience. . field SU(3)c SU(2)L yj zj zj rj = zj/zφ − yj UL, DL 3 2

1 6

Z1

1 6

UR 3 1

2 3

Z2

7 6 1 2

DR 3 1 − 1

3

2Z1 − Z2 − 5

6

− 1

2

⌫L, `L 1 2 − 1

2

−3Z1 − 1

2

⌫R 1 1 Z2 − 4Z1

1 2 1 2

`R 1 1 −1 −2Z1 − Z2 − 3

2

− 1

2

1

2

1 2

zφ 1

1 2

1

1 zχ −1 −1

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Charge assignment from re-parametrization of couplings

13

(a) anomaly free charges (b) from neutrino-scalar interactions (c) from re-parametrization of couplings

(a) (b) (c)

is added for later convenience. . field SU(3)c SU(2)L yj zj zj rj = zj/zφ − yj UL, DL 3 2

1 6

Z1

1 6

UR 3 1

2 3

Z2

7 6 1 2

DR 3 1 − 1

3

2Z1 − Z2 − 5

6

− 1

2

⌫L, `L 1 2 − 1

2

−3Z1 − 1

2

⌫R 1 1 Z2 − 4Z1

1 2 1 2

`R 1 1 −1 −2Z1 − Z2 − 3

2

− 1

2

1

2

1 2

zφ 1

1 2

1

1 zχ −1 −1

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After SSB neutrino mass terms appear

14

where 6x6 symmetric matrix (mD complex, MM real)

Lν

Y = −1

2 X

i,j

"

νL, νc

R

i M(h, s)ij

✓ νc

L

νR ◆

j

+ h.c. #

M(h, s)ij = mD

1 + h

v

mD
1 + h

v

MM
1 + s

w

!

ij

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After SSB neutrino mass terms appear

14

where 6x6 symmetric matrix (mD complex, MM real) in diagonal: Majorana mass terms (so νL massless!)

Lν

Y = −1

2 X

i,j

"

νL, νc

R

i M(h, s)ij

✓ νc

L

νR ◆

j

+ h.c. #

M(h, s)ij = mD

1 + h

v

mD
1 + h

v

MM
1 + s

w

!

ij

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After SSB neutrino mass terms appear

14

where 6x6 symmetric matrix (mD complex, MM real) in diagonal: Majorana mass terms (so νL massless!) but νL and νR have the same q-numbers, can mix, leading to type-I see-saw

Lν

Y = −1

2 X

i,j

"

νL, νc

R

i M(h, s)ij

✓ νc

L

νR ◆

j

+ h.c. #

M(h, s)ij = mD

1 + h

v

mD
1 + h

v

MM
1 + s

w

!

ij

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Effective light neutrino masses

15

If mi << Mj , can integrate out the heavy neutrinos where are Majorana masses

Lν

dim5 = 1

2 X

i

mM,i ✓ 1 + h v ◆2 ⇣ ν

0c

i,Lν0 i,L + h.c.

⌘

mM,i = m2

i

Mi

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Effective light neutrino masses

15

If mi << Mj , can integrate out the heavy neutrinos where are Majorana masses if mi ~ O(100keV) and Mj ~ O(100GeV), then mM,i ~ O(0.1eV)

Lν

dim5 = 1

2 X

i

mM,i ✓ 1 + h v ◆2 ⇣ ν

0c

i,Lν0 i,L + h.c.

⌘

mM,i = m2

i

Mi

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Mixing in the neutral gauge sector

16

  W 3

µ

B0

µ

Z0

µ

  = M(sin θW, sin θT)   Z0

µ

Tµ Aµ  

QED current remains unchanged:

, Jµ

em = 3

X

f=1 3

X

j=1

ej ⇣ ψ

f q,j(x)γµψf q,j(x) + ψ f l,j(x)γµψf l,j(x)

⌘

LQED = −eAµJµ

em

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Neutral current interactions

17

current with Z0 remains unchanged, but mixes with new current JT of new couplings:

LZ = −eZµ ⇣ cos θTJµ

Z − sin θTJµ T

⌘ = −eZµJµ

Z + O(θT)

(

LT = −eTµ ⇣ sin θTJµ

Z + cos θTJµ T

⌘ = −eTµJµ

T + O(θT) .

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Neutral current interactions

17

current with Z0 remains unchanged, but mixes with new current JT of new couplings:

both can be written as v-a interactions for non-chiral fields: with X = Z or T and summation over q and l flavors

LZ = −eZµ ⇣ cos θTJµ

Z − sin θTJµ T

⌘ = −eZµJµ

Z + O(θT)

(

LT = −eTµ ⇣ sin θTJµ

Z + cos θTJµ T

⌘ = −eTµJµ

T + O(θT) .

Jµ

X =

X

f

ψf(x)γµ v(X)

f

a(X)

f

γ5

ψf(x)

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Possible consequences with 5 new parameters

18

The lightest massive new particle is a natural candidate for WIMP dark matter if it is sufficiently stable. Majorana neutrino mass terms are generated by the SSB of the scalar fields, providing the origin of neutrino masses and

scillations.

Diagonalization of neutrino mass terms leads to the PMNS matrix, which in turn can be the source of lepto-baryogenesis. The vacuum of the χ scalar is charged (zj = −1) that may be a source

f accelerated expansion of the universe as seen now.

The second scalar together with the established BEH field may be the source of hybrid inflation.

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Credibility requirement

19

Is there any region of the parameter space of the model that is not excluded by experimental results, both established in standard model phenomenology and elsewhere?

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Credibility requirement

19

Is there any region of the parameter space of the model that is not excluded by experimental results, both established in standard model phenomenology and elsewhere? Answer is not immediate, extensive studies are needed

SLIDE 32

A’ explanation of the muon magnetic moment anomaly ruled out?

20

CERN Courier April 2017

dark-sector models (see fjgure).

“This paper is the fjnal word from aar

Roney. “ut we are continuing to search for

that have visible decay modes.”

→
. Again, no

a mass less than around 0.1 e.

models. “In contrast to massless dark

then can decay. They are more like dark bosons than dark photons.”

→

the analysis places 0 confjdence-level

eccentricity (see fjgure on previous page).

The fjnal eccentricities are signifjcantly refmecting the longer lifetime of the system but predict smaller fjnal-source eccentricity The fjnal-state source eccentricity radii relative to the higher-harmonic (n 3) fmow planes, which is directly sensitive velocity fjelds.

a fmagship measurement

in fmavour physics. It is

the decay was fjrst announced in a joint paper

allowed signifjcant improvements to be made in background rejection, which increased the experiments sensitivity. The → meson to its left (see fjgure, top). The signifjcance of the former is . corresponding to the fjrst observation of this decay by a single experiment. At just 1. peak is not signifjcant. →

→

effjciencies, the →

For the fjrst time, LHCb also measured

→ disentangled by fjtting a single exponential to the lifetime distribution (fjgure, below). The fjtted effective lifetime is consistent

ass fit of dimuon candidates in the

high-purity region of the machine-learning algorithm output top, and decay-time distribution of background-subtracted → signal with lifetime fit superimposed below.

dark-sector models (see fjgure).

“This paper is the fjnal word from aar

Roney. “ut we are continuing to search for

that have visible decay modes.”

→
. Again, no

a mass less than around 0.1 e.

models. “In contrast to massless dark

g then can decay. They are more like dark bosons than dark photons.”

Further reading

BaBar Collaboration 2017 arXiv:1702.03327. NA64 Collaboration 2017 Phys. Rev. Lett. 118 011802.

→

the analysis places 0 confjdence-level

eccentricity (see fjgure on previous page).

The fjnal eccentricities are signifjcantly refmecting the longer lifetime of the system but predict smaller fjnal-source eccentricity The fjnal-state source eccentricity radii relative to the higher-harmonic (n 3) fmow planes, which is directly sensitive velocity fjelds.

a fmagship measurement

in fmavour physics. It is

the decay was fjrst announced in a joint paper

allowed signifjcant improvements to be made in background rejection, which increased the experiments sensitivity. The → meson to its left (see fjgure, top). The signifjcance of the former is . corresponding to the fjrst observation of this decay by a single experiment. At just 1. peak is not signifjcant. →

→

effjciencies, the →

For the fjrst time, LHCb also measured

→ disentangled by fjtting a single exponential to the lifetime distribution (fjgure, below). The fjtted effective lifetime is consistent

ass fit of dimuon candidates in the

high-purity region of the machine-learning algorithm output top, and decay-time distribution of background-subtracted → signal with lifetime fit superimposed below.

10–3 10–4 10–3 10–2 10–1 1 mA′ (GeV) 10 10–2 BaBar 2017 NA64

f a v

u

r e d

(g-2)e

(g-2)μ ± 5

K → πνν ε

f

n

dark-sector models (see fjgure). “This paper is the fjnal word from aar

Roney. “ut we are continuing to search for

that have visible decay modes.” t

→
. Again, no

a mass less than around 0.1 e.

f Caltech, who has worked on dark-photon
models. “In contrast to massless dark

then can decay. They are more like dark bosons than dark photons.”

→

the analysis places 0 confjdence-level

eccentricity (see fjgure on previous page).

The fjnal eccentricities are signifjcantly refmecting the longer lifetime of the system but predict smaller fjnal-source eccentricity The fjnal-state source eccentricity radii relative to the higher-harmonic (n 3) fmow planes, which is directly sensitive velocity fjelds.

a fmagship measurement

in fmavour physics. It is

the decay was fjrst announced in a joint paper

allowed signifjcant improvements to be made in background rejection, which increased the experiments sensitivity. The → meson to its left (see fjgure, top). The signifjcance of the former is . corresponding to the fjrst observation of this decay by a single experiment. At just 1. peak is not signifjcant. →

→

effjciencies, the →

For the fjrst time, LHCb also measured

→ disentangled by fjtting a single exponential to the lifetime distribution (fjgure, below). The fjtted effective lifetime is consistent

ass fit of dimuon candidates in the

high-purity region of the machine-learning algorithm output top, and decay-time distribution of background-subtracted → signal with lifetime fit superimposed below.

SLIDE 33

Contribution of the new gauge boson to a

21

experimentally: a(exp)

µ

− a(SM)

µ

= 268(76) · 1011

= a(T+SM)

µ

a(SM)

µ

=

= GFm2

µ

6 p 2π2 ✓(1 + ρ0

Z) cos2 θW 1 2

tan β + O(θT, γ0

Z)

◆2

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

tan β

2.0
1.5
1.0
0.5

0.0 0.5 1.0 1.5 2.0

ρ0

Z

ρ0

Z = 1 − g0

Y

g0

Z

tan β = w

v

SLIDE 34

Favoured region by Δa differs from that in kinetic mixing model

22

γ
γ
→

✏eff = s (e+e → T0) (e+e → A0)/✏2

Favoured region of Δa = a(exp) -a(SM) = (268 ±76) 10-11 in the kinetic mixing—vector boson mass plane with the existence of a T0 boson

10−5

2 5

10−4

2 5

10−3

2 5

✏eff

10−1 2

5

1

2 5

10

2 5 102 2 5 103

MT [MeV]

favoured by ∆aµ: Z = 10−4 Z = 10−4.5 Z = 10−5

SLIDE 35

Favoured region by Δa differs from that in kinetic mixing model

23

γ
γ
→

✏eff = s (e+e → T0) (e+e → A0)/✏2

BaBar and NA64 together allow for the interpretation of Δa = a(exp) -a(SM) = (268 ±76) 10-11 with the existence of a T0 boson

nly if MT < 1.1 MeV

10−5

2 5

10−4

2 5

10−3

2 5

✏eff

10−1 2

5

1

2 5

10

2 5 102 2 5 103

MT [MeV]

excluded by BaBar [1702.03327] NA64 [1906.00176] favoured by ∆aµ: Z = 10−4 Z = 10−4.5 Z = 10−5

SLIDE 36

Conclusions

24

Established observations require physics beyond SM, but do not suggest a rich BSM physics U(1)Z extension has the potential of explaining all known results Anomaly cancellation and neutrino mass generation mechanism are used to fix the Z-charges up to reasonable assumptions Parameter space can and need be constrained from existing experimental results (like searches in missing energy events)

SLIDE 37

SM@LHC: theory vs. 36 measurements at CMS

25

SLIDE 38

SM is unstable

26

102 104 106 108 1010 1012 1014 1016 1018 1020

0.04
0.02

0.00 0.02 0.04 0.06 0.08 0.10 RGE scale m in GeV Higgs quartic coupling l 3s bands in Mt = 173.1 ± 0.6 GeV HgrayL a3HMZL = 0.1184 ± 0.0007HredL Mh = 125.7 ± 0.3 GeV HblueL Mt = 171.3 GeV asHMZL = 0.1163 asHMZL = 0.1205 Mt = 174.9 GeV

50 100 150 200 50 100 150 200 Higgs mass Mh in GeV Top mass Mt in GeV Instability Non-perturbativity Stability M e t a

s

t a b i l i t y

Degrassi et al., arXiv:1205.6497

SLIDE 39

Neutrino masses

27

First diagonalize mD and MM by defining so where with m and M diagonal, unitary matrix

ν0

L,i =

X

j

(UL)ijνL,j and ν0

R,i =

X

j

(OR)ijνR,j

Lν

Y = 1

2 X

i,j

" ⇣ ν0

L, ν

0c

R

⌘

i M 0(h, s)ij

✓ ν

0c

L

ν0

R

◆

j

+ h.c. #

M 0(h, s) = mV

1 + h

v

V †m
1 + h

v

M
1 + s

w

!
while V = U T

L OR