unification without supersymmetry - agenda (indico) · 2016. 5. 25. · frezzotti, rossiphys. rev....
TRANSCRIPT
Unification without supersymmetry
R. Frezzottia)b), M. Garofaloc), G.C. Rossia)b)d)
a)Dipartimento di Fisica - Università di Roma Tor Vergatab)INFN - Sezione di Roma Tor Vergata
c)University of Edinburghd)Centro Fermi
Frezzotti, Rossi Phys. Rev. D 92 (2015) 5, 054505Frezzotti, Garofalo, Rossi [arXiv:1602.03684] to be published in PRD
May 24, 2016
Frezzotti Garofalo Rossi (ToV- Edinburgh) Gauge coupling nification May 24, 2016 1 / 18
Outline of the talk1 Motivation & Introduction
expose a non-Susy model with a level of unification as in MSSM2 The model
SM matter + superstrongly interacting extra matter→a kind of BSMM with
NP generation of all elementary particle massesnatural mass hierarchy
3 Unificationstrong & electro-weak coupling unification owing to
new matter (superstrongly interacting quarks and leptons)with unusual hypercharge assignment (half-integer charges)
superstrong, strong & electro-weak coupling unification owing tofurther extra fermions endowed with only superstrong interactionsand masses around the unification scale ΛGUT
4 Conclusions & Outlooklattice checks of the NP mass generation mechanismlook for a GUT group
Frezzotti Garofalo Rossi (ToV- Edinburgh) Gauge coupling nification May 24, 2016 2 / 18
Motivation
Figure : Running of electro-weak and strong couplings in SM (black dottedlines) and MSSM. Displacement of blue and red curves at small scales isassociated to the opening of the SUSY threshold, either 0.5 TeV (bluecurve) or 1.5 TeV (red curve) with initial conditions αs(mZ ) = 0.117 andαs(mZ ) = 0.121, respectively.
Frezzotti Garofalo Rossi (ToV- Edinburgh) Gauge coupling nification May 24, 2016 3 / 18
A non-supersymmetric model
LBSMM =14(F BF B + F W F W + F AF A)+
+
ng∑f=1
[q̄f
L /DBWAqf
L + q̄f uR /DBAqf u
R + q̄f dR /DBAqf d
R +
+¯̀fL /D
BW `fL + ¯̀f u
R /DB`f uR + ¯̀f d
R /DB`f dR
]+ SM masses +
+14
F GF G+
νQ∑s=1
[Q̄s
L /DBWAGQs
L + Q̄s uR /DBAGQs u
R + Q̄s dR /DBAGQs d
R
]+
+
νL∑t=1
[L̄t
L /DBWGLt
L + L̄t uR /DBGLt u
R + L̄t dR /DBGLt d
R
]+ O(TeV) masses
DBWAGµ = ∂µ − iYgY Bµ − igwτ
r W rµ − igs
λa
2Aaµ − igT
λαT2
Gαµ
Frezzotti Garofalo Rossi (ToV- Edinburgh) Gauge coupling nification May 24, 2016 4 / 18
A non-supersymmetric BSM model
LBSMM =14(F BF B + F W F W + F AF A)+
+
ng∑f=1
[q̄f
L /DBWAqf
L + q̄f uR /DBAqf u
R + q̄f dR /DBAqf d
R +
+¯̀fL /D
BW `fL + ¯̀f u
R /DB`f uR + ¯̀f d
R /DB`f dR
]+
+14
F GF G+
νQ∑s=1
[Q̄s
L /DBWAGQs
L + Q̄s uR /DBAGQs u
R + Q̄s dR /DBAGQs d
R
]+
+
νL∑t=1
[L̄t
L /DBWGLt
L + L̄t uR /DBGLt u
R + L̄t dR /DBGLt d
R
]+
+ . . .
—————————————————————————————-
mQ = O(αTαT )ΛT mtop = O(αsαT )ΛT mτ = O(αYαT )ΛT
MW = O(√αW )ΛT
ΛT ∼ O(TeV )
Frezzotti Garofalo Rossi (ToV- Edinburgh) Gauge coupling nification May 24, 2016 5 / 18
SM hypercharge assignments
q `
yuL = 23 − 1
2 = 16 yνL = 0− 1
2 = −12
yuR = 23 − 0 = 2
3 yνR = 0
ydL = −13 + 1
2 = 16 yelL = −1 + 1
2 = −12
ydR = −13 − 0 = −1
3 yelR = −1− 0 = −1∑y2
q = 2236
∑y2` = 3
2
Table : Hypercharges of SM fermions
Q = T 3 + YAnomaly cancellation occurs between quarks and leptons
Frezzotti Garofalo Rossi (ToV- Edinburgh) Gauge coupling nification May 24, 2016 6 / 18
Non-standard hypercharge assignments→ unique
Q L
yUL = 12 − 1
2 = 0 yNL = 12 − 1
2 = 0
yUR = 12 − 0 = 1
2 yNR = 12 − 0 = 1
2
yDL = −12 + 1
2 = 0 yLL = −12 + 1
2 = 0
yDR = −12 − 0 = −1
2 yLR = −12 − 0 = −1
2∑y2
Q = 12
∑y2
L = 12
Table : Non-standard hypercharge assignments
Anomalies separately zero for quarks and leptons→ YL = 0L-handed doublets→ QL = T 3
L = ±1/2R-handed singlets→ QR = YR
QR = QL = ±1/2The above is the only possible choice
Frezzotti Garofalo Rossi (ToV- Edinburgh) Gauge coupling nification May 24, 2016 7 / 18
BSMM β-functionsTable 2 assignment for SIP hypercharges→ above TeV scale we get
βBSMMT = −
[113
NT −43
(NcνQ + νL)
]g3
T(4π)2
βBSMMs = −
[113
Nc −43
(NTνQ + ng)
]g3
s
(4π)2
βBSMMw = −
[2
113− 1
3ng(Nc + 1)− 1
3NT (NcνQ + νL)
]g3
w
(4π)2
βBSMMY =
{23
[(2236
Nc +32
)ng +
12
NT (NcνQ + νL)
]}g3
Y(4π)2
Alternatively with the standard assignment one would have
βBSMMY st =
{23
[(2236
Nc +32
)ng +
12
NT
(2218
NcνQ + 3νL
)]}g3
Y(4π)2
with ng , νQ , νL = # of generations of (q, `), Q and L
Frezzotti Garofalo Rossi (ToV- Edinburgh) Gauge coupling nification May 24, 2016 8 / 18
SM β-functions
βSMs = −
(113
Nc −43
ng
)g3
s(4π)2 ,
βSMw = −
[2
113− 1
3ng(Nc + 1)− 1
6
]g3
w(4π)2 ,
βSMY =
[23
(2236
Nc +32
)ng +
16
]g3
Y(4π)2 .
Frezzotti Garofalo Rossi (ToV- Edinburgh) Gauge coupling nification May 24, 2016 9 / 18
GUT normalization conditions - BSSM
If all the fermions must belong to an irreducible GGUT representation,one must have
Tr[(gY Y )2
]= Tr
[(12
gwτ3)2]
= Tr[
(12
gsλ3)2]
= Tr[
(12
gTλ3T )2]
An explicit computation reveals that the unifying couplings arenon-standard hypercharge assignments
g21 :=
43
g2Y , g2
2 := g2w , g2
3 := g2s , g2
4 :=23
g2T
standard hypercharge assignments
g21 :=
53
g2Y , g2
2 := g2w , g2
3 := g2s , g2
4 :=23
g2T
We took for concreteness NT = Nc = ng = 3 & νQ = νL = 1
Frezzotti Garofalo Rossi (ToV- Edinburgh) Gauge coupling nification May 24, 2016 10 / 18
GUT normalization conditions - SM
Tr[(gY Y )2
]= Tr
[(12
gwτ3)2]
= Tr[
(12
gsλ3)2]
g21 :=
53
g2Y , g2
2 := g2w , g2
3 := g2s
Frezzotti Garofalo Rossi (ToV- Edinburgh) Gauge coupling nification May 24, 2016 11 / 18
Evolution equations
dgi
d logµ= βgi , i = 1,2,3,4
BSMM 1-loop β-functions with GUT normalization
βg1 = 8g3
1(4π)2 , βg2 =
46
g32
(4π)2 ,
βg3 = −3g3
3
(4π)2 , βg4 = −172
g34
(4π)2
Standard and non-standard Y assignments yield the same βg1
SM 1-loop β-functions with GUT normalization
βg1 =4110
g31
(4π)2 , βg2 = −196
g32
(4π)2 , βg3 = −7g3
3(4π)2
Note - βg2 is positive in the BSMM and negative in the SM.
Frezzotti Garofalo Rossi (ToV- Edinburgh) Gauge coupling nification May 24, 2016 12 / 18
BSMM vs. SM
0
10
20
30
40
50
60
70
80
1e+02 1e+04 1e+06 1e+08 1e+10 1e+12 1e+14 1e+16 1e+18 1e+20
α-1
µ(GeV)
Figure : The 1-loop running of electro-weak and strong couplings in theBSMM (red curves) and in the SM (black curves). The visible change ofslope of red curves at “low” scales is associated with the opening of thesuperstrong threshold that we take at ΛT = 5 TeV
SM
α−11 (mZ ) = 59.01 ± 0.02
α−12 (mZ ) = 29.57 ± 0.02
α−13 (mZ ) = 8.45 ± 0.05
BSSM
α−11 (mZ ) = 73.76 ± 0.02
α−12 (mZ ) = 29.57 ± 0.02
α−13 (mZ ) = 8.45 ± 0.05
Frezzotti Garofalo Rossi (ToV- Edinburgh) Gauge coupling nification May 24, 2016 13 / 18
BSMM vs. MSSM
0
10
20
30
40
50
60
70
80
1e+02 1e+04 1e+06 1e+08 1e+10 1e+12 1e+14 1e+16 1e+18 1e+20
α-1
µ(GeV)
Figure : The 1-loop running of electro-weak and strong couplings in theBSMM (red curves) and in the MSSM (blue curves). The superstrong andsupersymmetry thresholds have been set at ΛT = 5 and ΛMSSM = 1 TeV,respectively
MSSM
α−11 (mZ ) = 59.01 ± 0.02
α−12 (mZ ) = 29.57 ± 0.02
α−13 (mZ ) = 8.45 ± 0.05
BSSM
α−11 (mZ ) = 73.76 ± 0.02
α−12 (mZ ) = 29.57 ± 0.02
α−13 (mZ ) = 8.45 ± 0.05
Frezzotti Garofalo Rossi (ToV- Edinburgh) Gauge coupling nification May 24, 2016 14 / 18
Changing hypercharge assignment to SIPs
0
10
20
30
40
50
60
70
80
1e+02 1e+04 1e+06 1e+08 1e+10 1e+12 1e+14 1e+16 1e+18 1e+20
α-1
µ(GeV)
Figure : The 1-loop running of electro-weak and strong couplings in theBSMM with the hyperchage assignment of Table 2 (red curves) and the“standard” hyperchage assignment of Table 1 (green curve)
Frezzotti Garofalo Rossi (ToV- Edinburgh) Gauge coupling nification May 24, 2016 15 / 18
A full unification in BSMM?
0
10
20
30
40
50
60
70
80
1e+02 1e+04 1e+06 1e+08 1e+10 1e+12 1e+14 1e+16 1e+18 1e+20
α-1
µ(GeV)
Figure : The 1-loop running of electro-weak strong and superstrongcouplings in the BSMM with NS extra particles having purely superstrongvector interactions and masses O(ΛGUT ). NS = 4 (blue line) NS = 5 (blackline), NS = 6 (green line)
Frezzotti Garofalo Rossi (ToV- Edinburgh) Gauge coupling nification May 24, 2016 16 / 18
Conclusions
A non-SUSY BSMM model with unification at the level of MSSMThe salient features of the BSMM outlined in slide 5 are
elementary particle masses generated by a NP mechanismtriggered by irrelevant d = 6 chiral breaking op’s in L → no Higgsa neat solution of “naturalness” & “hierarchy” problems
at the price of giving up a bit of universalitycorrect order of magnitude of the NP-ly generated top mass =⇒
SIPs with an RGI scale ΛT � ΛQCD , ΛT ∼ O(TeV)SIPs (must) have unusual hypercharge assignments
electric charge quantized in units of e/2.neutral SIP bound states with non-zero fermion number→ CDM?
125 resonance is a WW/ZZ state bound by superstrong forces
TM
QT
+ . . . =⇒ + . . . =⇒ h
(a) (b) (c)
Existence of NP effects needs a numerical confirmation
Frezzotti Garofalo Rossi (ToV- Edinburgh) Gauge coupling nification May 24, 2016 17 / 18
Thank you for your attention
Frezzotti Garofalo Rossi (ToV- Edinburgh) Gauge coupling nification May 24, 2016 18 / 18