Phenomenology of a new gauge U boson Directors: Pierre Fayet (LPENS, - - PowerPoint PPT Presentation

Introduction Theoretical background Experiment Phenomenology Analysis Conclusions

Phenomenology of a new gauge U boson

Directors: Pierre Fayet (LPENS, ENS) & Mikhail Shaposhnikov (LPPC, EPFL) María O. Olea Romacho August 22, 2019

María O. Olea Romacho Phenomenology of a new gauge U boson

2HDM subgroup 13 February, 2019

Introduction Theoretical background Experiment Phenomenology Analysis Conclusions

Contents

1

Introduction

2

Theoretical background

3

Experiment

4

Phenomenology

5

Analysis

6

Conclusions

María O. Olea Romacho Phenomenology of a new gauge U boson

Introduction Theoretical background Experiment Phenomenology Analysis Conclusions

Abstract

New fundamental interactions may exist Extra U(1) gauge group resulting in a new neutral gauge boson, the U boson Complete example of the scientific procedure in Beyond the Standard Model (BSM) physics Exclusion region from early beam dump experiments for the mass-coupling parameter space for an axially and feebly coupled light U boson

María O. Olea Romacho Phenomenology of a new gauge U boson

Introduction Theoretical background Experiment Phenomenology Analysis Conclusions

Motivation

Study the simplest case of abelian symmetry groups associated to new neutral spin-1 mediators Natural consequence of a number of BSM theories The U boson, if light, is compatible with a role of mediator of light dark matter particles interactions

María O. Olea Romacho Phenomenology of a new gauge U boson

Introduction Theoretical background Experiment Phenomenology Analysis Conclusions

Framework

General form of the extra U(1) generator before and after Higgs mechanism: restricted by gauge invariance of Yukawa couplings and the Higgs sector content

New current: vectorial or may also have an axial part Axially coupled U boson → much less explored situation

Mass: generated by a Higgs singlet? Mixing effects: either heavy or feebly coupled U bosons Matter fields: DM or just SM particles?

María O. Olea Romacho Phenomenology of a new gauge U boson

Introduction Theoretical background Experiment Phenomenology Analysis Conclusions

Framework

Summary:

2 HIGGS DOUBLETS + 1 SINGLET Light (∼ 1.02− ∼ 100 MeV) neutral gauge boson with feeble non-vanishing axial couplings to SM particles

Probe this theory and point out the special qualitative and quantitative behavior of a light and axially coupled U boson in the ultra-relativistic limit

María O. Olea Romacho Phenomenology of a new gauge U boson

Introduction Theoretical background Experiment Phenomenology Analysis Conclusions

Theoretical background: General expression of the extra U(1) symmetry generator

ϕu,d =

• ϕ+

u,d

ϕ0

u,d

• Yu,d = 1
• ϕ0

u

• = vu

√ 2,

• ϕ0

d

• = vd

√ 2, v2

• v2

u + v2 d

• =

1 GF √ 2 ≃ (246 GeV)2 SU(2) × U(1)Y × U(1)F covariant derivative: iDµ = i∂µ −

• gT · W µ + 1

2g

′YW ′µ + 1

2g

′′FW ′′µ

• María O. Olea Romacho

Phenomenology of a new gauge U boson

Introduction Theoretical background Experiment Phenomenology Analysis Conclusions

Theoretical background: General expression of the extra U(1) symmetry generator

LYukawa = −i √ 2

• mu

vu uR

• ϕu0,

−ϕu+ uL dL

• + md

vd dR

• ϕd -,

ϕd 0∗ uL dL

• +

me vd eR

• ϕd -,

ϕd 0 ∗ νL eL +h.c. Fax =

            

+1/2 for uL, dL, νL, eL −1/2 for uR, dR, eR −1 for ϕu +1 for ϕd,e F = αB + βL + γY + µFax → F = Fax

María O. Olea Romacho Phenomenology of a new gauge U boson

Introduction Theoretical background Experiment Phenomenology Analysis Conclusions

Theoretical background: Z-U mixing effects and U boson mass

Fϕu,d = 0 → No mixing effects Fϕu,d = 0 → Lm = −1

8

• k=u,d

v2

k

• −gW µ

3 + g

′W ′µ + g ′′FϕkW ′′µ2

M2 =

1 4

• v2

u + v2 d

g2 + g′2

−

v2

uFu + v2 dFd

g2 + g′2g′′ −

v2

uFu + v2 dFd

g2 + g′2g′′

v2

u + v2 d

g′′2

• vu = vd

Fu = 1, Fd = −1

María O. Olea Romacho Phenomenology of a new gauge U boson

Introduction Theoretical background Experiment Phenomenology Analysis Conclusions

Theoretical background: Z-U mixing effects and U boson mass

Higgs singlet with a v.e.v. σ =

w √ 2 →

m2

U = 1

4g

′′v2

doublet

+ 1 4g

′′2F 2

ww2

• singlet

= 1 4g

′′2v2/r 2

r 2 = 1 1 +

• Fww

v

2 ≤ 1

María O. Olea Romacho Phenomenology of a new gauge U boson

Introduction Theoretical background Experiment Phenomenology Analysis Conclusions

Theoretical background: Z-U mixing effects and U boson mass

Due to F = Fax → universal current: Jµ

U =

• q,l (SM)

−

g′′

4

• qγµγ5q −

g′′

4

• lγµγ5l

fA = g′′

4 = (GF √ 2)

1/2

2

rmU ≃ 2·10−3rmU (GeV/c2) e = (4πα)1/2 ≃ 0.3 α′′ = f 2

A

4π

María O. Olea Romacho Phenomenology of a new gauge U boson

Introduction Theoretical background Experiment Phenomenology Analysis Conclusions

Theoretical background: anomalies

Think of GSM × U(1)F+SM matter+3 right-handed neutrinos as embedded in the 16 representation of SO(10) × U(1) and this one as if it was embedded in the 27 representation of E6 E6 is an anomaly-free group in all its representations and so it is our extra U(1) gauge theory 11 new fermions for each generation of quarks and leptons

María O. Olea Romacho Phenomenology of a new gauge U boson

Introduction Theoretical background Experiment Phenomenology Analysis Conclusions

Experiment: Set-up

Beam-dump experiment at BNL AGS in 1979 E = 28 GeV L = 45 m

María O. Olea Romacho Phenomenology of a new gauge U boson

Introduction Theoretical background Experiment Phenomenology Analysis Conclusions

Experiment: Limits

Neutral current candidates: σprodσint < 7 × 10−68 cm4 Unassociated e+e− pairs: Rπ = σ

pN → a0X

• σ (pN → π0X) <
• 2 × 10−19 cm−1

βγcτ

María O. Olea Romacho Phenomenology of a new gauge U boson

Introduction Theoretical background Experiment Phenomenology Analysis Conclusions

Equivalence theorem

ǫν ≈ ǫν

L (k1) = kν 1

mU + O

mU

Ek1

• fP = fA

2mf mU =

• GF

√ 2

1/2 mf r,

εA = fA

e ,

αps =

• f 2

P

4π

• María O. Olea Romacho

Phenomenology of a new gauge U boson

Phenomenology

Summary: remarks on the Higgs sector

2 Higgs doublets:

Making possible the existence of an axial invariance that can be gauged, enhancing the gauge boson interactions in the ultrarrelativistic limit due to the Equivalence Theorem.

1 Higgs singlet:

Making possible to render the U boson invisible and explore a wider range in the parameter space.

María O. Olea Romacho Phenomenology of a new gauge U boson

Introduction Theoretical background Experiment Phenomenology Analysis Conclusions

Production

Direct production: Indirect production: π0 → γ U forbidden by charge conjugation if U coupled axially

María O. Olea Romacho Phenomenology of a new gauge U boson

Phenomenology

Production

We would like to estimate the quantity Rπ = σ(pN→UX)

σ(pN→π0X) to

compare to the experimental limit Rπ = σ

pN → a0X

• σ (pN → π0X) <
• 2 × 10−19 cm−1

βγcτ We split the Rπ ratio in two contributions: Rπ (x) = (Rπ (x)) + (Rπ (x))⊥ Benchmark value: Rπ(x) = σ (pp → UX) σ (pp → X) ∼ αU π 1 σT σ(x) =

• (Rπ) + (Rπ)⊥

1

σT σ(x)

María O. Olea Romacho Phenomenology of a new gauge U boson

Introduction Theoretical background Experiment Phenomenology Analysis Conclusions

Production

R = σ (pp → UX) σ (pp → X) ≈

          

αU 3π αU π

αU 3αU Formal treatment of the production cross section may induce potential corrections in R that we will treat as a source of uncertainty

María O. Olea Romacho Phenomenology of a new gauge U boson

Phenomenology

Production: longitudinal contribution

αps π = 1 4π2

• GF

√ 2r 2m2

q

• → We only consider production

involving strange quarks (Rπ) = σ (pN → UX) σ (pN → π0X) ≈ σ (pp → UX) σ (pp → X) =

σ(pp→UX) σ(pp→strange particles X) σ(pp→strange particles X) σ(pp→X)

≈

1 4π2

• GF

√ 2r 2m2

s

• 1

10.

(Rπ) ≈ 3.6 × 10−10r2

María O. Olea Romacho Phenomenology of a new gauge U boson

Introduction Theoretical background Experiment Phenomenology Analysis Conclusions

Production: transversal contribution

(Rπ)⊥ ≈ σ (pN → UX)⊥ σ (pN → π0X) ≈ α′′ π = 1 16π2 GF √ 2r 2m2

U

(Rπ)⊥ ≈ 1.0 × 10−13r 2 mU

• MeV/c22

María O. Olea Romacho Phenomenology of a new gauge U boson

Introduction Theoretical background Experiment Phenomenology Analysis Conclusions

Production: energy dependence

Phenomenological parametrization Assumption: energy distribution of the U boson in its production similar to the one of the pion Light U boson: production and interactions very much as those of the pseudoscalar Goldstone boson corresponding to the broken symmetry as if it was global rather than local Pions: lightest pseudoscalar particles known. Pseudo-Goldstone bosons and their interactions at leading

• rder are described by axial currents

María O. Olea Romacho Phenomenology of a new gauge U boson

Introduction Theoretical background Experiment Phenomenology Analysis Conclusions

Production: energy dependence

Figure: Right (Left): Momentum dependence of π− (π+) production cross-section in p+C collisions at 31 GeV. Circles, squares and triangles are experimental points. Vertical bars and boxes indicate statistical and systematic uncertainties, respectively.

María O. Olea Romacho Phenomenology of a new gauge U boson

Introduction Theoretical background Experiment Phenomenology Analysis Conclusions

Production

Rπ (x) = (Rπ (x)) + (Rπ (x))⊥ can be taken as (Rπ (x)) = 3.6 × 10−10r 2 1 σT dσ

pC → π0X

• dx

(Rπ (x))⊥ = 1.0 × 10−13r 2 mU

• MeV/c22 1

σT dσ

pC → π0X

• dx

, where σT = σ

pC → π0X is the total cross section

María O. Olea Romacho Phenomenology of a new gauge U boson

Introduction Theoretical background Experiment Phenomenology Analysis Conclusions

Detection

They might interact with the active volume of the detector, leaving a neutral current signature They might decay into SM particles inside the detector, leaving a ‘displaced vertex’ signature or an unassociated e+e− pair

María O. Olea Romacho Phenomenology of a new gauge U boson

Introduction Theoretical background Experiment Phenomenology Analysis Conclusions

Detection

τ = 1 Γ = 12π B

• U → ¯

f f

• f 2

AmUβ3 f

l = γ τ β c = x ET mU 12πB

• U → ¯

f f

• f 2

AmUβ3 f

c2 B

U → e+e− = 40%

B (U → νν) = 60%

María O. Olea Romacho Phenomenology of a new gauge U boson

Introduction Theoretical background Experiment Phenomenology Analysis Conclusions

Overview

Detection Procedure Experimental limit Model

• bservable

Neutral Current Signal σprod σint < 7 × 10−68 cm4 σprod σint ≈ 2.1 × 10−70r4 cm4 Unass. Vertex Rπ =

σ pN→a0X σ pN→π0X <

2 × 10−19 cm−1 βγcτ

• Rπ (x) 1

l e− L l dx < 2 × 10−17 m−1

María O. Olea Romacho Phenomenology of a new gauge U boson

Introduction Theoretical background Experiment Phenomenology Analysis Conclusions

Exclusion regions

Lower part blue region→e− L

l ≈ 1,(Rπ) ∼ r2 and l ∼ r2

ε4

A

→ 1

l (Rπ) ∼ ε4 A

Lower part green region→e− L

l ≈ 1,(Rπ)⊥ ∼ ε2

A and l ∼ 1 ε2

Am2 U

→ 1

l (Rπ)⊥ ∼ ε4 Am2 U María O. Olea Romacho Phenomenology of a new gauge U boson

Introduction Theoretical background Experiment Phenomenology Analysis Conclusions

Exclusion regions

αU 3π αU π

αU 3αU → [1.02 − 7.12] MeV [1.02 − 7.31] MeV [1.02 − 7.51] MeV [1.02 − 7.68] MeV María O. Olea Romacho Phenomenology of a new gauge U boson

Introduction Theoretical background Experiment Phenomenology Analysis Conclusions

Exclusion regions

Figure: Excluded regions in the mass-coupling parameter space of the U boson for different proportionality factors for the R ratio with three curves at constant decay lenght, l, for U bosons with energy x = 0.16.

María O. Olea Romacho Phenomenology of a new gauge U boson

Introduction Theoretical background Experiment Phenomenology Analysis Conclusions

Conclusions

mU (MeV) εA r = 1 (no singlet) 1.02 − 7.12 6.86 × 10−6 − 4.78 × 10−5 r = 0.258 (σ ∼ 4v) 1.07 − 12.90 1.85 × 10−6 − 2.23 × 10−5 r = 0.1 (σ ∼ 10v) 1.44 − 19.35 9.65 × 10−7 − 1.30 × 10−5 r = 0.01 (σ ∼ 100v) 11.31 − 48.12 7.60 × 10−7 − 3.23 × 10−6 María O. Olea Romacho Phenomenology of a new gauge U boson

Introduction Theoretical background Experiment Phenomenology Analysis Conclusions

Conclusions

THANK YOU FOR YOUR ATTENTION

María O. Olea Romacho Phenomenology of a new gauge U boson