Introduction
The U(1)0BGL Model
Phenomenology
Family non-universal Z 0 models with protected
flavour-changing interactions
Martin Jung
in collaboration with A. Celis, J. Fuentes-Martı́n and H. Serôdio
PRD92 (2015) 1, 015007 [arXiv:1505.03079]
51st Rencontres de Moriond 2016
La Thuile, Italy
16th of March 2016
Conclusions
The U(1)0BGL Model
Introduction
Phenomenology
Conclusions
Have we seen NP in b → s``?
The
anomalies
[see also talks by J.Albrecht, L.Hofer, G.Hiller, N.Kosnik]
• Global fits necessary
[Descotes-Genon+,Beaujean+,Ghosh+,
Altmannshofer+,Hurth+,Sinha+,Ciuchini+]
• QCD under control? [Camalich/
•
Jäger’15,Lyon/Zwicky’14,Ciuchini+’15]
Agreed: C9µ ∼ −1 improves fits
RK =
BR(B → K µ+ µ− )
BR(B → K e + e − )
!
= 0.745+0.090
−0.074 ± 0.036 ≈ 1
[Hiller/Krüger,Bobeth+]
Here: data at face value
The U(1)0BGL Model
Introduction
Phenomenology
Some model building
We require:
1. Sizable contributions to b → s`+ `−
specifically to C9 , i.e. vector coupling
2. Lepton non-universal couplings
3. Limited contributions to established constraints:
• EW precision constaints
• Unitarity triangle constraints
• ...
Z 0 models good candidates
[e.g. Altmannshofer+,Buras+,Crivellin+,Gauld+,Descotes-Genon+,Sierra+]
Alternatives:
[e.g. Becirevic+,Bhattacharya+,Gripaios+,Hiller+,Niehoff+]
Wish list:
• Minimal particle content (no new fermions)
• Predictivity for up-, down-, lepton-FCNCs
Conclusions
Introduction
The U(1)0BGL Model
Phenomenology
Conclusions
Incarnations of U(1)0
Z’ models have been popular for a long time
[review e.g. Langacker’08]
Starting a new construction:
1. SM particle content: Lα − Lβ only option
No coupling to quarks, mostly used
in ν sector → Lµ − Lτ
[2×He+’91]
2. Adding vector-like quarks (+scalars) →
effective Z 0 q̄q 0 -coupling [Altmannshofer+’14]
µ(0)
LHCb anomalies , independent C9
no Z 0 ee-coupling → avoid LEP bounds
∆ms → u, d couplings small
ΜΜ
preferred by C9
1Σ
2Σ
1.2
a=1
1.0
a
0.8
0.6
0.4
excluded by NTP
3. Gauging Lµ − Lτ − a(B1 + B2 − 2B3 )
→ new scalars suffice [Crivellin+’15]
LHCb anomalies , |C9µ | |C9µ0 |
L and B separately anomaly-free
down-FCNCs approximately ∼ Vti Vtj∗
arbitrary up-FCNCs
g
a = 12
d
we
llo
a = 13
by
Bs
xin
mi
a
0.2
0.0
0
2
4
mZ' g' @TeVD
6
8
Introduction
The U(1)0BGL Model
Phenomenology
Conclusions
Flavour violation in 2HDMs
Generic 2HDMs: huge flavour violation
solution to this a main characteristic
Option 1: Avoid tree-level FCNCs → NFC, MFV, Alignment, . . .
Option 2: Allow for controlled FCNCs
• Cheng-Sher ansatz/Type III → little predictivity
• Branco-Grimus-Lavoura (BGL) models [BGL’96]
• Use flavour symmetry to relate all flavour-change to CKM
Unique pattern in 2HDMs! [Ferreira/Silva’11,Serôdio’13]
• Choice: top quark only couples to φ2 → FCNCs in down-sector
1
Up Yukawas:
∆BGL
=
1
2
2
2
3
3
1
Down Yukawas:
Γ1
=
1
1
1
BGL
3
1
2
2
2
2
3
3
2
1
2
3
3
1
3
3
2
3
1
1
∆BGL
=
2
2
1
BGL
Γ2
=
3
1
2
3
1
2
3
1
1
2
2
3
3
1
2
3
Introduction
The U(1)0BGL Model
Phenomenology
Gauging BGL models
• BGL via discrete symmetries yields accidental U(1)
• Scalars disfavoured as solution for b → s anomalies
Idea: Gauge BGL models!
[Celis/Fuentes-Martı́n/MJ/Serôdio]
Conclusions
Introduction
The U(1)0BGL Model
Phenomenology
Gauging BGL models
• BGL via discrete symmetries yields accidental U(1)
• Scalars disfavoured as solution for b → s anomalies
Idea: Gauge BGL models!
[Celis/Fuentes-Martı́n/MJ/Serôdio]
Require U(1)BGL to be anomaly-free: 5 non-linear conditions
• Automatic in the SU(3)C sector [Celis+’14]
• Not possible using only the SM quark sector
Include lepton sector
Conclusions
Introduction
The U(1)0BGL Model
Phenomenology
Conclusions
Gauging BGL models
• BGL via discrete symmetries yields accidental U(1)
• Scalars disfavoured as solution for b → s anomalies
Idea: Gauge BGL models!
[Celis/Fuentes-Martı́n/MJ/Serôdio]
Require U(1)BGL to be anomaly-free: 5 non-linear conditions
• Automatic in the SU(3)C sector [Celis+’14]
• Not possible using only the SM quark sector
Include lepton sector
Most general charges: arbitrary X`L,R with ` = e, µ, τ
Highly non-trivial system to solve, only one class of solutions!
1 physical free charge → Xφ2 ≡ 0, 6 permutations
Patterns in quark sector imply (independent of charge choice):
1. Lepton-flavour non-universality
2. Lepton-flavour conservation
Introduction
The U(1)0BGL Model
Phenomenology
U(1)0BGL – Overview
Features of the U(1)0BGL model:
• Controlled tree-level down-FCNCs, determined by CKM
e,µ
` | < ()|C ` |
left-handed, C9,10
, |C10
9
• No FCNCs in the up-quark sector
• Symmetry yields lepton-flavour non-universality without
lepton-flavour violation
• Higgs sector phenomenologically viable, no large effects
• Z 0 extremely predictive: 2 parameters (plus one charge)
Let’s check the available constraints. . .
Conclusions
Introduction
The U(1)0BGL Model
Phenomenology
Conclusions
Phenomenological consequences - Generalities
What can we say without a detailed analysis?
• Strong direct limits ⇒ potential Z 0 is very heavy
2 /M 2 . 0.1%!
MW
Z0
Most observables are unaffected!
Effects only for SM suppression in addition to GF +CKM
EW penguin decays, mixing, CP violation, leptonic decays, . . .
• Z 0 gives the dominant NP effect almost everywhere
A bit more detail:
• UT analysis basically unaffected (exceptions K and ∆md,s ,
but ∆md /∆ms = ∆md /∆ms |SM )
• ∆md , ∆ms , K give similar bounds.
From ∆ms : MZ 0 /g 0 ≥ 16 TeV (95% CL)
Improvement here just depends on LQCD!
Introduction
The U(1)0BGL Model
Phenomenology
Conclusions
Phenomenological consequences - Generalities
What can we say without a detailed analysis?
• Strong direct limits ⇒ potential Z 0 is very heavy
2 /M 2 . 0.1%!
MW
Z0
Most observables are unaffected!
Effects only for SM suppression in addition to GF +CKM
EW penguin decays, mixing, CP violation, leptonic decays, . . .
• Z 0 gives the dominant NP effect almost everywhere
A bit more detail:
• UT analysis basically unaffected (exceptions K and ∆md , but
∆md /∆ms = ∆md /∆ms |SM )
• ∆md , ∆ms , K give similar bounds.
From ∆ms : MZ 0 /g 0 ≥ 25 TeV (95% CL)
Improvement here thanks to LQCD!
[Bazazov+’16]
Introduction
The U(1)0BGL Model
Phenomenology
Conclusions
RK and its sisters
q
RM
≡
Br(Bq → M̄µ+ µ− )
Br(Bq → M̄e + e − )
M ∈ {K , K ∗ , Xs , φ, . . .}, q = u, d, s
Note: R(Xs ) = 0.42 ± 0.25 (Belle) 0.58 ± 0.19 (BaBar)
(but not a consistent picture [cf. Hiller/Schmaltz’15] )
Model
(1,2,3)
C9NPµ (1σ)
–
C9NPµ (2σ)
[−2.92, −0.61]
(3,1,2)
[−0.93, −0.43]
[−1.16, −0.17]
(3,2,1)
[−1.20, −0.53]
[−1.54, −0.20]
Fits B → K ∗ µ+ µ−
Furthermore:
3
bM ≡ RM = 1
R
RK
“Easily” verifiable for any
charge assignment
Introduction
The U(1)0BGL Model
Phenomenology
Conclusions
RK and its sisters
q
RM
≡
Br(Bq → M̄µ+ µ− )
Br(Bq → M̄e + e − )
M ∈ {K , K ∗ , Xs , φ, . . .}, q = u, d, s
Note: R(Xs ) = 0.42 ± 0.25 (Belle) 0.58 ± 0.19 (BaBar)
(but not a consistent picture [cf. Hiller/Schmaltz’15] )
Model
(1,2,3)
C9NPµ (1σ)
–
C9NPµ (2σ)
[−1.20, −0.61]
(3,1,2)
[−0.63, −0.43]
[−0.63, −0.17]
(3,2,1)
[−1.20, −0.53]
[−1.20, −0.20]
Fits B → K ∗ µ+ µ−
Furthermore:
3
bM ≡ RM = 1
R
RK
“Easily” verifiable for any
charge assignment
Introduction
The U(1)0BGL Model
Phenomenology
Conclusions
Combination with direct searches and perturbativity
Obvious way to search for Z 0 : σ(pp → Z 0 (→ f f¯)X )
Strong semi-model-independent limits from ATLAS and CMS:
[Carena+’04,Accomando+’11,ATLAS’12,’14,CMS’12,’15]
• 2.5 models survive all constraints, MZ 0 ≥ 3 − 4 TeV
• Strong upper bound on one model from perturbativity
• Differentiable from each other and different models:
(i) Flavour (LNU vs. FCNC) (ii) µff 0 = σ(Z 0 → f f¯)/σ(Z 0 → f 0 f¯0 )
Introduction
The U(1)0BGL Model
Phenomenology
Conclusions
Combination with direct searches and perturbativity
Obvious way to search for Z 0 : σ(pp → Z 0 (→ f f¯)X )
Strong semi-model-independent limits from ATLAS and CMS:
[Carena+’04,Accomando+’11,ATLAS’12,’14,CMS’12,’15]
• 2.5 models survive all constraints, MZ 0 ≥ 3 − 4 TeV
• Strong upper bound on one model from perturbativity
• Differentiable from each other and different models:
(i) Flavour (LNU vs. FCNC) (ii) µff 0 = σ(Z 0 → f f¯)/σ(Z 0 → f 0 f¯0 )
Introduction
The U(1)0BGL Model
Phenomenology
Conclusions
Further constraints
We also considered the following observables:
• Neutrino trident production
• Atomic parity violation
• EDMs (cancellations in the Higgs sector [MJ/Pich’14] )
• g −2
All of these are weaker than the ones discussed earlier
Model predicts change in Bd,s → µµ central values:
[see talks by S.Palestini + S.Swain]
BR(Bs → µ+ µ− )
BR(Bd → µ+ µ− )
=
+
−
BR(Bs → µ µ )|SM
BR(Bd → µ+ µ− )|SM
wait for additional data, value uncorrelated with Z 0 observables
Introduction
The U(1)0BGL Model
Phenomenology
Conclusions
LHCb anomalies persist:
• Require large C9NP , non-universal couplings
• Z’ models possible explanations
Interplay of flavour-observables and direct searches
U(1)0BGL viable, predictive model:
• Starting point: 2HDM solving FCNC problem
No FCNCs for up-quarks
Controlled FCNCs on tree-level for down-quarks
All flavour-changing interactions determined by CKM
• Gauging symmetry yields LNU, but no LFV
• Z 0 sector depends only on g 0 /MZ 0 and MZ 0
Will be further tested soon
Conclusions
Introduction
The U(1)0BGL Model
Phenomenology
Conclusions
Scalar sector of the U(1)0BGL model
Higgs sector has 2 doublets Φi and 1 complex singlet S:
• vev for S (vS ) yields U(1)0 breaking
vS /v 1 ⇒ characterizes scalar sector
• Parameters: 10 dof ⇒ 6 scalars, 4 massive Goldstone bosons
• Spectrum: H1,2,3 , H ± , A, MH1 ∼ v , MH ± ,H2,3 ,A ∼ vS
• Potential CP-invariant because of U(1)0
• Spontaneous CP violation is also absent
• H3 couplings additionally suppressed by v /vS
Phenomenology:
• BGL structure in 2HDMs viable for M ∼ few × 100 GeV
[Botella+’14,Batthacharya+’14]
• Here scalars mostly decoupling ⇒ Higgs measurements fine
• Basically one constraint from flavour: Bd,s → µ+ µ−
Uncorrelated to Z 0 constraints
Gauging BGL models - including leptons
Most general charges: arbitrary X`L,R with ` = e, µ, τ
Anomaly conditions from 5 combinations:
• Linear: U(1)0 [SU(2)L ]2 , U(1)0 [U(1)Y ]2 , U(1)0 [(gravity)]2
• Quadratic: [U(1)0 ]2 U(1)Y
• Cubic: [U(1)0 ]3
Highly non-trivial system to solve, only one class of solutions!
Involves one free charge (physical choice) with 6 permutations
Here: Xφ2 ≡ 0 ⇒ Z − Z 0 mixing suppressed (tan β 1)
Patterns in quark sector imply (independent of charge choice):
1. Lepton-flavour non-universality
2. Lepton-flavour conservation
Anomaly-free top-BGL implementation
[Slide from J. Fuentes-Martı́n]
ψ
ψ 0 → e iX ψ 0
Only one class of models (with XΦ2 and XdR free parameters)
7 7
5 5
q
u
XR = diag − , − , 1
XL = diag − , − , 1
4 4
2 2
XRd = 1
XL`
XΦ
9 21
= diag
, , −3
4 4
9
= diag − , 0
4
XRe
= diag
9 15
, , −3
2 2
• XdR = 1, unphysical normalization. But it also normalizes g 0 !
• XΦ2 = 0 to avoid large Z − Z 0 mass mixing (for large tβ )
• Six possible model variations (e, µ, τ ) = (i, j, k)
Z 0 couplings of the U(1)0BGL model
Mass eigenbasis:
• Couplings to uL , uR , dR : diagonal and 2-family universal (1,2)
• Couplings to `L , eR : diagonal and family-non-universal
• Couplings to dL :

∗
|Vtd |2 Vts Vtd
9
5
d
∗
2
XeL = − 1 +  Vtd Vts |Vts |
4
4
∗
∗
Vtd Vtb
Vts Vtb

∗
Vtb Vtd
Vtb Vts∗ 
|Vtb |2
Controlled Z 0 -mediated FCNCs:
f
Z′
= g 0 γ µ XeLf PL + XeRf PR
f¯
Details on direct searches
Approximation for NWA, negligible SM interference and
flavour-universal quark couplings:
i
π h f
cu wu s, MZ2 0 + cdf wd s, MZ2 0
σ=
48s f
2
2
cu,d ' g 0 2 XqL
+ X(u,d)R
Br Z 0 → f f¯
Applicable for g 0 ≤ 0.2!
First two generations dominate and couple universally
CMS model-independent bounds: [CMS-EXO-12-061]
⇒
`
Correlations among the effective operators O9,10
NPµ
NPe /C NPµ
Model C10
/C9NPµ C9NPe /C9NPµ C10
9
(1,2,3)
3/17
9/17
3/17
(1,3,2)
0
(2,1,3)
1/3
−9/8
−3/8
(2,3,1)
0
(3,1,2)
1/3
−17/8
−3/8
(3,2,1)
3/17
−8/17
0
17/9
−8/9
1/3
0