Introduction Theoretical background Experiment Phenomenology Analysis Conclusions 2HDM subgroup Phenomenology of a new gauge U boson Directors: Pierre Fayet (LPENS, ENS) & Mikhail Shaposhnikov (LPPC, EPFL) 13 February, 2019 María O. Olea Romacho María O. Olea Romacho Phenomenology of a new gauge U boson August 22, 2019
Introduction Theoretical background Experiment Phenomenology Analysis Conclusions Contents Introduction 1 Theoretical background 2 Experiment 3 Phenomenology 4 Analysis 5 Conclusions 6 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 � � ϕ + u , d ϕ u , d = Y u , d = 1 ϕ 0 u , d = v u = v d 1 � � � � � � 2 ≃ (246 GeV ) 2 ϕ 0 ϕ 0 v 2 v 2 u + v 2 √ 2 , √ 2 , = √ u d d G F SU(2) × U(1) Y × U(1) F covariant derivative: � � gT · W µ + 1 ′ µ + 1 iD µ = i ∂ µ − ′ YW ′′ FW ′′ µ 2 g 2 g 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 L Yukawa = � − ϕ u + � � � ϕ d 0 ∗ � � � √ � u L � u L m u ϕ u 0 , + m d ϕ d - , − i 2 v u u R v d d R + d L d L ϕ d 0 ∗ � � � � � ν L m e ϕ d - , v d e R +h.c. e L +1 / 2 for u L , d L , ν L , e L − 1 / 2 for u R , d R , e R F ax = − 1 for ϕ u +1 for ϕ d , e F = α B + β L + γ Y + µ F ax → F = F ax 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 F ϕ u , d = 0 → No mixing effects � ′′ µ � 2 ′ µ + g � − gW µ F ϕ u , d � = 0 → L m = − 1 v 2 ′ W ′′ F ϕ k W 3 + g 8 k k = u , d M 2 = � � � � g 2 + g ′ 2 � � � � v 2 � v 2 g 2 + g ′ 2 g ′′ u + v 2 u F u + v 2 − d F d 1 d � g ′′ 2 � � � v 2 g 2 + g ′ 2 g ′′ � v 2 u F u + v 2 u + v 2 4 − d F d d v u = v d F u = 1 , F d = − 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 w Higgs singlet with a v.e.v. � σ � = 2 → √ U = 1 + 1 = 1 m 2 ′′ v 2 ′′ 2 F 2 w w 2 ′′ 2 v 2 / r 2 4 g 4 g 4 g � �� � � �� � doublet singlet 1 r 2 = � 2 ≤ 1 � F w w 1 + v 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 = F ax → universal current: � g ′′ � � g ′′ � � J µ q γ µ γ 5 q − l γ µ γ 5 l U = − 4 4 q , l ( SM ) √ 1 / 2 4 = ( G F 2 ) f A = g ′′ rm U ≃ 2·10 − 3 rm U (GeV / c 2) e = 2 (4 πα ) 1 / 2 ≃ 0 . 3 α ′′ = f 2 A 4 π María O. Olea Romacho Phenomenology of a new gauge U boson
Introduction Theoretical background Experiment Phenomenology Analysis Conclusions Theoretical background: anomalies Think of G SM × 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 E 6 E 6 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: σ prod σ int < 7 × 10 − 68 cm 4 Unassociated e + e − pairs: � pN → a 0 X � R π = σ � 2 × 10 − 19 cm − 1 � σ ( pN → π 0 X ) < βγ c τ María O. Olea Romacho Phenomenology of a new gauge U boson
Introduction Theoretical background Experiment Phenomenology Analysis Conclusions Equivalence theorem � m U � L ( k 1 ) = k ν ǫ ν ≈ ǫ ν 1 + O m U E k 1 √ � � � 1 / 2 m f r , � f 2 2 m f ε A = f A f P = f A m U = G F 2 e , α ps = P 4 π 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 single t: 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 : π 0 → 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 R π = σ ( pN → UX ) σ ( pN → π 0 X ) to compare to the experimental limit � pN → a 0 X � R π = σ � 2 × 10 − 19 cm − 1 � σ ( pN → π 0 X ) < βγ c τ We split the R π ratio in two contributions: R π ( x ) = ( R π ( x )) � + ( R π ( x )) ⊥ Benchmark value: � 1 R π ( x ) = σ ( pp → UX ) σ ( pp → X ) ∼ α U 1 � σ ( x ) = ( R π ) � + ( R π ) ⊥ σ ( x ) π σ T σ T María O. Olea Romacho Phenomenology of a new gauge U boson
Introduction Theoretical background Experiment Phenomenology Analysis Conclusions Production α U 3 π R = σ ( pp → UX ) α U σ ( pp → X ) ≈ π α U 3 α U 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 √ � � 1 α ps 2 r 2 m 2 π = → We only consider production G F q 4 π 2 involving strange quarks σ ( pN → UX ) � σ ( pp → UX ) � ( R π ) � = σ ( pN → π 0 X ) ≈ σ ( pp → X ) σ ( pp → UX ) � σ ( pp → strange particles X ) = ≈ σ ( pp → strange particles X ) σ ( pp → X ) √ � � 1 1 2 r 2 m 2 G F 10 . s 4 π 2 ( R π ) � ≈ 3 . 6 × 10 − 10 r 2 María O. Olea Romacho Phenomenology of a new gauge U boson
Introduction Theoretical background Experiment Phenomenology Analysis Conclusions Production: transversal contribution σ ( pN → π 0 X ) ≈ α ′′ ( R π ) ⊥ ≈ σ ( pN → UX ) ⊥ 1 √ 2 r 2 m 2 π = 16 π 2 G F U MeV/ c 2 �� 2 ( R π ) ⊥ ≈ 1 . 0 × 10 − 13 r 2 � � m U María O. Olea Romacho Phenomenology of a new gauge U boson
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