J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016 Jürgen R. Reuter, DESY New Physics / Resonances in Vector Boson Scattering at the LHC PRD93(16),3. 036004 [1511.00022], PRD91(15),096007 [1408.6207], US Snowmass Summer Study 1310.6708,1309.7890,1307.8180, JHEP 0811.010 [0806.4145], EPJC48(06)353 [hep-ph/0604048] based on work with A. Alboteanu, W. Kilian, T. Ohl, M. Sekulla
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J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016
Jürgen R. Reuter, DESY
New Physics / Resonances in Vector Boson Scattering
at the LHC
PRD93(16),3. 036004 [1511.00022], PRD91(15),096007 [1408.6207], US Snowmass Summer Study 1310.6708,1309.7890,1307.8180,JHEP 0811.010 [0806.4145], EPJC48(06)353 [hep-ph/0604048]
based on work with A. Alboteanu, W. Kilian, T. Ohl, M. Sekulla
J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016
Seen signals, unseen signals, seen un-signals (?)• Discovery of a light Higgs boson leaves still open questions:
1. Nature of Electroweak Symmetry Breaking
2. Higgs boson potential, all the way like the Standard Model!?
3. Does it fulfill the US-fermion/Europe-boson rule?
4. Is the 125 GeV state the only resonance in the system of EW vector bosons?
5. How do EW vector bosons scatter? (true heart of weak interactions)
6. Is there something related to the Little Hierarchy problem (strong or weak)
J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016
Seen signals, unseen signals, seen un-signals (?)• Discovery of a light Higgs boson leaves still open questions:
1. Nature of Electroweak Symmetry Breaking
2. Higgs boson potential, all the way like the Standard Model!?
3. Does it fulfill the US-fermion/Europe-boson rule?
4. Is the 125 GeV state the only resonance in the system of EW vector bosons?
5. How do EW vector bosons scatter? (true heart of weak interactions)
6. Is there something related to the Little Hierarchy problem (strong or weak)
ATLAS-CONF-2015-081 CMS-PAS-EXO-15-004
J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016
Seen signals, unseen signals, seen un-signals (?) Evidence for W+W+jj (electroweak production) Talk by Brigitte Vachon ATLAS PRL 113(2014)14, 141803 [1405.6241]; CMS PRL 114(2015), 051801 [1410.6315]
First limits on New Physics in pure electroweak gauge/Goldstone sector
J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016
Seen signals, unseen signals, seen un-signals (?) Evidence for W+W+jj (electroweak production) Talk by Brigitte Vachon ATLAS PRL 113(2014)14, 141803 [1405.6241]; CMS PRL 114(2015), 051801 [1410.6315]
First limits on New Physics in pure electroweak gauge/Goldstone sector
J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016
Seen signals, unseen signals, seen un-signals (?) Evidence for W+W+jj (electroweak production) Talk by Brigitte Vachon ATLAS PRL 113(2014)14, 141803 [1405.6241]; CMS PRL 114(2015), 051801 [1410.6315]
First limits on New Physics in pure electroweak gauge/Goldstone sector
0.6ATLAS 20.3 fb-1, s = 8 TeV pp → W± W± jj K-matrix unitarization
68% CL95% CLexpected 95% CLStandard Model
confidence intervals
J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016
Seen signals, unseen signals, seen un-signals (?) Evidence for W+W+jj (electroweak production) Talk by Brigitte Vachon ATLAS PRL 113(2014)14, 141803 [1405.6241]; CMS PRL 114(2015), 051801 [1410.6315]
First limits on New Physics in pure electroweak gauge/Goldstone sector
‣ Dim. 8 operators: Eboli et al., 2006; Kilian/JRR/Ohl/Sekulla, 2014+2015
Giudice et al. / Contino at al.
J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016
Operators and Multi(EW)-boson Physics (I)
J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016
Operators and Multi(EW)-boson Physics (I)Dimension-6 operators for Multiboson physics (CP-conserving)
OWWW = Tr[Wµ⌫W⌫⇢Wµ
⇢ ]
OW = (Dµ�)†Wµ⌫(D⌫�)
OB = (Dµ�)†Bµ⌫(D⌫�)
O@� = @µ⇣�†�
⌘@µ
⇣�†�
⌘
O�W =⇣�†�
⌘Tr[Wµ⌫Wµ⌫ ]
O�B =⇣�†�
⌘Bµ⌫Bµ⌫
J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016
Operators and Multi(EW)-boson Physics (I)Dimension-6 operators for Multiboson physics (CP-conserving)
OWWW = Tr[Wµ⌫W⌫⇢Wµ
⇢ ]
OW = (Dµ�)†Wµ⌫(D⌫�)
OB = (Dµ�)†Bµ⌫(D⌫�)
O@� = @µ⇣�†�
⌘@µ
⇣�†�
⌘
O�W =⇣�†�
⌘Tr[Wµ⌫Wµ⌫ ]
O�B =⇣�†�
⌘Bµ⌫Bµ⌫
Dimension-6 operators for Multiboson physics (CP-violating)
OfWW= �†fWµ⌫W
µ⌫�
O eBB = �† eBµ⌫Bµ⌫�
OfWWW= Tr[fWµ⌫W
⌫⇢Wµ⇢ ]
OfW = (Dµ�)†fWµ⌫
(D⌫�)
J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016
Operators and Multi(EW)-boson Physics (I)Dimension-6 operators for Multiboson physics (CP-conserving)
OWWW = Tr[Wµ⌫W⌫⇢Wµ
⇢ ]
OW = (Dµ�)†Wµ⌫(D⌫�)
OB = (Dµ�)†Bµ⌫(D⌫�)
O@� = @µ⇣�†�
⌘@µ
⇣�†�
⌘
O�W =⇣�†�
⌘Tr[Wµ⌫Wµ⌫ ]
O�B =⇣�†�
⌘Bµ⌫Bµ⌫
Dimension-6 operators for Multiboson physics (CP-violating)
OfWW= �†fWµ⌫W
µ⌫�
O eBB = �† eBµ⌫Bµ⌫�
OfWWW= Tr[fWµ⌫W
⌫⇢Wµ⇢ ]
OfW = (Dµ�)†fWµ⌫
(D⌫�)
Affect the following electroweak couplings:
ZWW AWW HWW HZZ HZA HAA WWWW ZZWW ZAWW AAWWOWWW X X X X X XOW X X X X X X X XOB X X X XO�d X XO�W X X X XO�B X X XOW̃WW X X X X X XOW̃ X X X X XOW̃W X X X XOB̃B X X X
J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016
Operators and Multi(EW)-boson Physics (I)Dimension-6 operators for Multiboson physics (CP-conserving)
OWWW = Tr[Wµ⌫W⌫⇢Wµ
⇢ ]
OW = (Dµ�)†Wµ⌫(D⌫�)
OB = (Dµ�)†Bµ⌫(D⌫�)
O@� = @µ⇣�†�
⌘@µ
⇣�†�
⌘
O�W =⇣�†�
⌘Tr[Wµ⌫Wµ⌫ ]
O�B =⇣�†�
⌘Bµ⌫Bµ⌫
Dimension-6 operators for Multiboson physics (CP-violating)
OfWW= �†fWµ⌫W
µ⌫�
O eBB = �† eBµ⌫Bµ⌫�
OfWWW= Tr[fWµ⌫W
⌫⇢Wµ⇢ ]
OfW = (Dµ�)†fWµ⌫
(D⌫�)
Affect the following electroweak couplings:
ZWW AWW HWW HZZ HZA HAA WWWW ZZWW ZAWW AAWWOWWW X X X X X XOW X X X X X X X XOB X X X XO�d X XO�W X X X XO�B X X XOW̃WW X X X X X XOW̃ X X X X XOW̃W X X X XOB̃B X X X
connected to Higgs physics
J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016
Operators and Multi(EW)-boson Physics (II)
OT,0 = Tr⇥Wµ⌫W
µ⌫⇤ · TrhW↵�W
↵�i
OT,1 = TrhW↵⌫W
µ�i· Tr ⇥Wµ�W
↵⌫⇤
OT,2 = TrhW↵µW
µ�i· Tr ⇥W�⌫W
⌫↵⇤
OT,5 = Tr⇥Wµ⌫W
µ⌫⇤ · B↵�B↵�
OT,6 = TrhW↵⌫W
µ�i· Bµ�B
↵⌫
OT,7 = TrhW↵µW
µ�i· B�⌫B
⌫↵
OT,8 = Bµ⌫Bµ⌫B↵�B
↵�
OT,9 = B↵µBµ�B�⌫B
⌫↵
OM,0 = Tr⇥Wµ⌫W
µ⌫⇤ ·h(D��)† D��
i
OM,1 = TrhWµ⌫W
⌫�i·h(D��)† Dµ�
i
OM,2 =⇥Bµ⌫B
µ⌫⇤ ·h(D��)† D��
i
OM,3 =hBµ⌫B
⌫�i·h(D��)† Dµ�
i
OM,4 =h(Dµ�)† W�⌫D
µ�i· B�⌫
OM,5 =h(Dµ�)† W�⌫D
⌫�i· B�µ
OM,6 =h(Dµ�)† W�⌫W
�⌫Dµ�i
OM,7 =h(Dµ�)† W�⌫W
�µD⌫�i
Dimension-8 operators for Multiboson physics OS,0 =h(Dµ�)
† D⌫�i⇥
h(Dµ�)† D⌫�
i
OS,1 =h(Dµ�)
† Dµ�i⇥
h(D⌫�)
† D⌫�i
J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016
Operators and Multi(EW)-boson Physics (II)
WWWW WWZZ ZZZZ WWAZ WWAA ZZZA ZZAA ZAAA AAAAOS,0/1 X X X
OM,0/1/6/7 X X X X X X XOM,2/3/4/5 X X X X X XOT,0/1/2 X X X X X X X X XOT,5/6/7 X X X X X X X XOT,8/9 X X X X X
OT,0 = Tr⇥Wµ⌫W
µ⌫⇤ · TrhW↵�W
↵�i
OT,1 = TrhW↵⌫W
µ�i· Tr ⇥Wµ�W
↵⌫⇤
OT,2 = TrhW↵µW
µ�i· Tr ⇥W�⌫W
⌫↵⇤
OT,5 = Tr⇥Wµ⌫W
µ⌫⇤ · B↵�B↵�
OT,6 = TrhW↵⌫W
µ�i· Bµ�B
↵⌫
OT,7 = TrhW↵µW
µ�i· B�⌫B
⌫↵
OT,8 = Bµ⌫Bµ⌫B↵�B
↵�
OT,9 = B↵µBµ�B�⌫B
⌫↵
OM,0 = Tr⇥Wµ⌫W
µ⌫⇤ ·h(D��)† D��
i
OM,1 = TrhWµ⌫W
⌫�i·h(D��)† Dµ�
i
OM,2 =⇥Bµ⌫B
µ⌫⇤ ·h(D��)† D��
i
OM,3 =hBµ⌫B
⌫�i·h(D��)† Dµ�
i
OM,4 =h(Dµ�)† W�⌫D
µ�i· B�⌫
OM,5 =h(Dµ�)† W�⌫D
⌫�i· B�µ
OM,6 =h(Dµ�)† W�⌫W
�⌫Dµ�i
OM,7 =h(Dµ�)† W�⌫W
�µD⌫�i
Dimension-8 operators for Multiboson physics OS,0 =h(Dµ�)
† D⌫�i⇥
h(Dµ�)† D⌫�
i
OS,1 =h(Dµ�)
† Dµ�i⇥
h(D⌫�)
† D⌫�i
J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016
Operators and Multi(EW)-boson Physics (II)
WWWW WWZZ ZZZZ WWAZ WWAA ZZZA ZZAA ZAAA AAAAOS,0/1 X X X
OM,0/1/6/7 X X X X X X XOM,2/3/4/5 X X X X X XOT,0/1/2 X X X X X X X X XOT,5/6/7 X X X X X X X XOT,8/9 X X X X X
OT,0 = Tr⇥Wµ⌫W
µ⌫⇤ · TrhW↵�W
↵�i
OT,1 = TrhW↵⌫W
µ�i· Tr ⇥Wµ�W
↵⌫⇤
OT,2 = TrhW↵µW
µ�i· Tr ⇥W�⌫W
⌫↵⇤
OT,5 = Tr⇥Wµ⌫W
µ⌫⇤ · B↵�B↵�
OT,6 = TrhW↵⌫W
µ�i· Bµ�B
↵⌫
OT,7 = TrhW↵µW
µ�i· B�⌫B
⌫↵
OT,8 = Bµ⌫Bµ⌫B↵�B
↵�
OT,9 = B↵µBµ�B�⌫B
⌫↵
OM,0 = Tr⇥Wµ⌫W
µ⌫⇤ ·h(D��)† D��
i
OM,1 = TrhWµ⌫W
⌫�i·h(D��)† Dµ�
i
OM,2 =⇥Bµ⌫B
µ⌫⇤ ·h(D��)† D��
i
OM,3 =hBµ⌫B
⌫�i·h(D��)† Dµ�
i
OM,4 =h(Dµ�)† W�⌫D
µ�i· B�⌫
OM,5 =h(Dµ�)† W�⌫D
⌫�i· B�µ
OM,6 =h(Dµ�)† W�⌫W
�⌫Dµ�i
OM,7 =h(Dµ�)† W�⌫W
�µD⌫�i
Dimension-8 operators for Multiboson physics OS,0 =h(Dµ�)
Stereographic projection to Argand circle Formalism does a partial resummation of perturbative series need to construct (orig.) K-matrix as self-adjoint intermediate operator
Problems, if S-matrix non-diagonal, presence of non-perturbative contrib.
i2
i
a
aK
a0
J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016
Different unitarity projections
i2
i
a
aKaK2
T-matrix: Thales circle construction Kilian/Ohl/JRR/Sekulla, 2014
Stereographic projection to Argand circle Formalism does a partial resummation of perturbative series need to construct (orig.) K-matrix as self-adjoint intermediate operator
Problems, if S-matrix non-diagonal, presence of non-perturbative contrib.
i2
i
a
aK
a0
J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016
Different unitarity projections
i2
i
a
aKaK2
T-matrix: Thales circle construction Kilian/Ohl/JRR/Sekulla, 2014
Stereographic projection to Argand circle Formalism does a partial resummation of perturbative series need to construct (orig.) K-matrix as self-adjoint intermediate operator
Problems, if S-matrix non-diagonal, presence of non-perturbative contrib.
i2
i
a
aK
a0
Identical to K matrix for real amplitudesPoints on Argand circle left invariantDoes not rely on perturbation theoryApplicable for amplitudes with imaginary parts (models with resonances)
12
1
aT = aS
a0a02
Im [a]
Re [a]
J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016
Different unitarity projections
i2
i
a
aKaK2
T-matrix: Thales circle construction Kilian/Ohl/JRR/Sekulla, 2014
Stereographic projection to Argand circle Formalism does a partial resummation of perturbative series need to construct (orig.) K-matrix as self-adjoint intermediate operator
Problems, if S-matrix non-diagonal, presence of non-perturbative contrib.
i2
i
a
aK
a0
Identical to K matrix for real amplitudesPoints on Argand circle left invariantDoes not rely on perturbation theoryApplicable for amplitudes with imaginary parts (models with resonances)
12
1
aT = aS
a0a02
Im [a]
Re [a]
i2
i
aS
a0
aT
J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016
J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016
Resonances: Quantum numbers & simplified modelsRise of amplitude / anomalous coupling: Taylor expansion below a resonanceResonances might be in direct reach of LHC EFT framework EW-restored regime: SU(2)L ⨉ SU(2)R , SU(2)L ⨉ U(1)Y gauged
Include EFT operators in addition (more resonances, continuum contribution)Apply T-matrix unitarization beyond resonance (“UV-incomplete” model)
J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016
Resonances: Quantum numbers & simplified modelsRise of amplitude / anomalous coupling: Taylor expansion below a resonanceResonances might be in direct reach of LHC EFT framework EW-restored regime: SU(2)L ⨉ SU(2)R , SU(2)L ⨉ U(1)Y gauged
Include EFT operators in addition (more resonances, continuum contribution)Apply T-matrix unitarization beyond resonance (“UV-incomplete” model)
Spins 0, 2 considered, Spin 1 has different physics (mixing with W/Z)
J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016
Resonances: Quantum numbers & simplified modelsRise of amplitude / anomalous coupling: Taylor expansion below a resonanceResonances might be in direct reach of LHC EFT framework EW-restored regime: SU(2)L ⨉ SU(2)R , SU(2)L ⨉ U(1)Y gauged
Include EFT operators in addition (more resonances, continuum contribution)Apply T-matrix unitarization beyond resonance (“UV-incomplete” model)
Spins 0, 2 considered, Spin 1 has different physics (mixing with W/Z)
J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016
Resonances: Quantum numbers & simplified modelsRise of amplitude / anomalous coupling: Taylor expansion below a resonanceResonances might be in direct reach of LHC EFT framework EW-restored regime: SU(2)L ⨉ SU(2)R , SU(2)L ⨉ U(1)Y gauged
Include EFT operators in addition (more resonances, continuum contribution)Apply T-matrix unitarization beyond resonance (“UV-incomplete” model)
Spins 0, 2 considered, Spin 1 has different physics (mixing with W/Z)
J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016
Resonances: Quantum numbers & simplified modelsRise of amplitude / anomalous coupling: Taylor expansion below a resonanceResonances might be in direct reach of LHC EFT framework EW-restored regime: SU(2)L ⨉ SU(2)R , SU(2)L ⨉ U(1)Y gauged
Include EFT operators in addition (more resonances, continuum contribution)Apply T-matrix unitarization beyond resonance (“UV-incomplete” model)
Spins 0, 2 considered, Spin 1 has different physics (mixing with W/Z)
How to deal with off-shell tensor in realistic processes?
J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016
Tensor resonances: Fierz-Pauli vs. StückelbergStart with Fierz-Pauli Lagrangian for symmetric tensor
LFP =1
2@↵fµ⌫@
↵fµ⌫ � 1
2m2fµ⌫f
µ⌫ � 1
2@↵f
µµ@
↵f⌫⌫ +
1
2m2fµ
µf⌫⌫
� @↵f↵µ@�f�µ � f↵
↵@µ@⌫fµ⌫ + fµ⌫J
µ⌫f
J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016
Tensor resonances: Fierz-Pauli vs. StückelbergStart with Fierz-Pauli Lagrangian for symmetric tensor
LFP =1
2@↵fµ⌫@
↵fµ⌫ � 1
2m2fµ⌫f
µ⌫ � 1
2@↵f
µµ@
↵f⌫⌫ +
1
2m2fµ
µf⌫⌫
� @↵f↵µ@�f�µ � f↵
↵@µ@⌫fµ⌫ + fµ⌫J
µ⌫f
Fierz-Pauli conditions not valid off-shell Fierz-Pauli propagator has bad high-energy behavior Use Stückelberg formalism to make off-shell high-energy behavior explicit Introduce compensator fields ⇒ no propagators with momentum factors
Crucial for MCs
J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016
Tensor resonances: Fierz-Pauli vs. StückelbergStart with Fierz-Pauli Lagrangian for symmetric tensor
LFP =1
2@↵fµ⌫@
↵fµ⌫ � 1
2m2fµ⌫f
µ⌫ � 1
2@↵f
µµ@
↵f⌫⌫ +
1
2m2fµ
µf⌫⌫
� @↵f↵µ@�f�µ � f↵
↵@µ@⌫fµ⌫ + fµ⌫J
µ⌫f
Fierz-Pauli conditions not valid off-shell Fierz-Pauli propagator has bad high-energy behavior Use Stückelberg formalism to make off-shell high-energy behavior explicit Introduce compensator fields ⇒ no propagators with momentum factors
Crucial for MCs L =1
2ffµ⌫
��@2 �m2
f
�fµ⌫f +
1
2fµf µ
✓�1
2
��@2 �m2
f
�◆f⌫f ⌫
+1
2Afµ
�@2 +m2
f
�Aµ
f +1
2�f
��@2 �m2
f
��f
+
✓fµ⌫ � 1p
6�fgµ⌫
◆Jµ⌫f
�
1p2mf
(Afµ@⌫ +Af⌫@µ)�p2p
3m2f
�f@µ@⌫
!Jµ⌫f
• fµ⌫: on-shell fµ⌫
• �: @µ@⌫fµ⌫
• Aµ: @⌫fµ⌫
• �: fµµ
Gauge fixing: � = ��
J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016
J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016
Complete LHC process at 14 TeV
0 500 1000 1500 2000
M (e+, e�, µ+, µ�) [GeV]
0
50
100
150
200
250
N
pp ! e+e�µ+µ�jj at 3 ab�1
Ff = 17.4 TeV�1
SM
Mf = 1.0TeV
J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016
Triple [multiple] Vector Boson Production ?
Relate to ?
Yes, same Feynman rule as in VBS, but …
one external W/Z/γ always far off-shell
Unitarization formalism not available (would need 2 ➝ 3 unitarizations)
Different Wilson coefficients dominate (particularly for resonances)
Important physics (partially) independent from VBS
J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016
Conclusions / Summary
✦ Vector boson scattering one of flagship measurements of Runs II/III
✦ EFT provides a (!) [not the] consistent framework for SM deviations
✦ Very well-defined (and limited) range of applicability
✦ Accounts for access to New Physics in VBS and Di-/Triboson channels
✦ Unitarization for theoretically sane description (allows to calculate ‘best limit’)✦ T-matrix unitarization universal scheme for EFT and resonances✦ Simplified models: generic electroweak resonances ✦ Limits from LHC still incredibly limited: M ∼ 200-300 GeV
✦ Make sure that actual limits are meaningful and comparable
J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016
Conclusions / Summary
✦ Vector boson scattering one of flagship measurements of Runs II/III
✦ EFT provides a (!) [not the] consistent framework for SM deviations
✦ Very well-defined (and limited) range of applicability
✦ Accounts for access to New Physics in VBS and Di-/Triboson channels
✦ Unitarization for theoretically sane description (allows to calculate ‘best limit’)✦ T-matrix unitarization universal scheme for EFT and resonances✦ Simplified models: generic electroweak resonances ✦ Limits from LHC still incredibly limited: M ∼ 200-300 GeV
✦ Make sure that actual limits are meaningful and comparable
J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016
Conclusions / Summary
✦ Vector boson scattering one of flagship measurements of Runs II/III
✦ EFT provides a (!) [not the] consistent framework for SM deviations
✦ Very well-defined (and limited) range of applicability
✦ Accounts for access to New Physics in VBS and Di-/Triboson channels
✦ Unitarization for theoretically sane description (allows to calculate ‘best limit’)✦ T-matrix unitarization universal scheme for EFT and resonances✦ Simplified models: generic electroweak resonances ✦ Limits from LHC still incredibly limited: M ∼ 200-300 GeV
✦ Make sure that actual limits are meaningful and comparable
J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016
whatever approach ....
J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016
whatever approach .... always get the correct ellipses
J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016
BACKUP SLIDES
J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016
Effective Field Theory (EFT) for Weak Interactions✴ SppS: discovery of W, Z (on-shell) ✴ SLC/LEP: proof of non-Abelian weak structure, failure to find (very) light Higgs✴ Measurement of longitudinal Ws: ee ➝ WW (LEP), t ➝ Wb (Tevatron)✴ Using all known d.o.f., parameterizing all possible interactions
SM fermions weak bosons hypercharge boson longitudinal d.o.f.
Building blocks for EFT: , Wµ , Bµ , ⌃ = exp
�i
vw⌧
�
J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016
Effective Field Theory (EFT) for Weak Interactions✴ SppS: discovery of W, Z (on-shell) ✴ SLC/LEP: proof of non-Abelian weak structure, failure to find (very) light Higgs✴ Measurement of longitudinal Ws: ee ➝ WW (LEP), t ➝ Wb (Tevatron)✴ Using all known d.o.f., parameterizing all possible interactions
SM fermions weak bosons hypercharge boson longitudinal d.o.f.
J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016
Effective Field Theory (EFT) for Weak Interactions✴ SppS: discovery of W, Z (on-shell) ✴ SLC/LEP: proof of non-Abelian weak structure, failure to find (very) light Higgs✴ Measurement of longitudinal Ws: ee ➝ WW (LEP), t ➝ Wb (Tevatron)✴ Using all known d.o.f., parameterizing all possible interactions
SM fermions weak bosons hypercharge boson longitudinal d.o.f.
J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016
Effective Field Theory (EFT) for Weak Interactions✴ SppS: discovery of W, Z (on-shell) ✴ SLC/LEP: proof of non-Abelian weak structure, failure to find (very) light Higgs✴ Measurement of longitudinal Ws: ee ➝ WW (LEP), t ➝ Wb (Tevatron)✴ Using all known d.o.f., parameterizing all possible interactions
SM fermions weak bosons hypercharge boson longitudinal d.o.f.
J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016
Parameterizing SM deviations★ Specific models (SUSY, Compositeness, Little Higgses, 2HDM, Modified Higgses, Xdim, ......)
• Could give strong signals in VBS (presumably Little Higgses, Compositeness, Xdim .... )• Could give faint signals in VBS (presumably SUSY, 2HDM [Higgs data!], ....)• Up to parametric uncertainties precise predictions from the models (new independent couplings)• Mostly even beyond tree level predictable • Analysis has to be repeated for each and every model, introduces new parameters
J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016
Parameterizing SM deviations★ Specific models (SUSY, Compositeness, Little Higgses, 2HDM, Modified Higgses, Xdim, ......)
• Could give strong signals in VBS (presumably Little Higgses, Compositeness, Xdim .... )• Could give faint signals in VBS (presumably SUSY, 2HDM [Higgs data!], ....)• Up to parametric uncertainties precise predictions from the models (new independent couplings)• Mostly even beyond tree level predictable • Analysis has to be repeated for each and every model, introduces new parameters
★ Anomalous Couplings
• Usually first “model-independent” proposal• At the moment applied by HXSWG (but under debate)• Only modifications of SM couplings or introduction of new (Lorentz) structures ? • Allows fits of coupling strengths• Possible deviations difficult to interpret in terms of quantum field theory, unitarity!!
J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016
Parameterizing SM deviations★ Specific models (SUSY, Compositeness, Little Higgses, 2HDM, Modified Higgses, Xdim, ......)
• Could give strong signals in VBS (presumably Little Higgses, Compositeness, Xdim .... )• Could give faint signals in VBS (presumably SUSY, 2HDM [Higgs data!], ....)• Up to parametric uncertainties precise predictions from the models (new independent couplings)• Mostly even beyond tree level predictable • Analysis has to be repeated for each and every model, introduces new parameters
★ Anomalous Couplings
• Usually first “model-independent” proposal• At the moment applied by HXSWG (but under debate)• Only modifications of SM couplings or introduction of new (Lorentz) structures ? • Allows fits of coupling strengths• Possible deviations difficult to interpret in terms of quantum field theory, unitarity!!
★ Form factors
• Similar approach to anomalous couplings, partially resums perturbative series• (Almost) completely general and model-independent• Needs parameterizations, violates gauge invariance, unitarity ad-hoc curable (new parameters)
J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016
Parameterizing SM deviations★ Specific models (SUSY, Compositeness, Little Higgses, 2HDM, Modified Higgses, Xdim, ......)
• Could give strong signals in VBS (presumably Little Higgses, Compositeness, Xdim .... )• Could give faint signals in VBS (presumably SUSY, 2HDM [Higgs data!], ....)• Up to parametric uncertainties precise predictions from the models (new independent couplings)• Mostly even beyond tree level predictable • Analysis has to be repeated for each and every model, introduces new parameters
★ Anomalous Couplings
• Usually first “model-independent” proposal• At the moment applied by HXSWG (but under debate)• Only modifications of SM couplings or introduction of new (Lorentz) structures ? • Allows fits of coupling strengths• Possible deviations difficult to interpret in terms of quantum field theory, unitarity!!
★ Form factors
• Similar approach to anomalous couplings, partially resums perturbative series• (Almost) completely general and model-independent• Needs parameterizations, violates gauge invariance, unitarity ad-hoc curable (new parameters)
★ Effective Field Theory
• (Almost) model-independent, consistent calculation of perturbative corrections (power counting !?)• Depends on (possibly) many free parameters• Requires decoupling of New Physics • Range of applicability strongly depends on couplings and scales (unitarity issue)
J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016
General Procedure using EFTs• Use all experimental observables ⟹ global fit to all Wilson coefficients
• Would-be optimal approach
• Too many independent variables ⟹ needs staged fitting
• Need for simplifying assumptions
• Try to find minimal “physically well motivated” operator basis
• Experimental bias: consider only LHC-accessible operators
• Cross check from low-energy physics (flavor / EDMs / EWPO etc. / Higgs!)
• Explore full structure of EW Higgs doublet:
J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016
General Procedure using EFTs• Use all experimental observables ⟹ global fit to all Wilson coefficients
• Would-be optimal approach
• Too many independent variables ⟹ needs staged fitting
• Need for simplifying assumptions
• Try to find minimal “physically well motivated” operator basis
• Experimental bias: consider only LHC-accessible operators
• Cross check from low-energy physics (flavor / EDMs / EWPO etc. / Higgs!)
• Explore full structure of EW Higgs doublet:
O�f = (�†$Dµ�)
�f�µf
� O�W = (�†�)Wµ⌫Wµ⌫
W W W W
Effects in H ➝ Zff related to Z ➝ ff ⟹ constrained by SLC/LEP
visible in Higgs physics: H ➝ WW
redefines only SM parameters⟹ no experimental constraints
J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016
General Procedure using EFTs• Use all experimental observables ⟹ global fit to all Wilson coefficients
• Would-be optimal approach
• Too many independent variables ⟹ needs staged fitting
• Need for simplifying assumptions
• Try to find minimal “physically well motivated” operator basis
• Experimental bias: consider only LHC-accessible operators
• Cross check from low-energy physics (flavor / EDMs / EWPO etc. / Higgs!)
• Explore full structure of EW Higgs doublet:
O�f = (�†$Dµ�)
�f�µf
� O�W = (�†�)Wµ⌫Wµ⌫
W W W W
Effects in H ➝ Zff related to Z ➝ ff ⟹ constrained by SLC/LEP
visible in Higgs physics: H ➝ WW
redefines only SM parameters⟹ no experimental constraints
• Often use vev-subtracted operators: O(�†�) �! O0(�†�� v2)
• EFT allows to systemically calculate higher-order corrections
J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016
How to get EFTs from New Physics✦ Consider effects from heavy states by using (known) low-energy d.o.f.s
H. Georgi, 1993
J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016
How to get EFTs from New Physics✦ Consider effects from heavy states by using (known) low-energy d.o.f.s
H. Georgi, 1993
✦ Integrating out heavy d.o.f.s marginalizes over details of short-distance interactions✦ Toy Example: two interacting scalar fields ',�
Path integralZ[j, J ] =
ZD[�]D['] exp
i
Zdx
⇣12 (@')
2� 12�(2+M
2)���'
2��. . .+J�+j'
⌘�
J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016
How to get EFTs from New Physics✦ Consider effects from heavy states by using (known) low-energy d.o.f.s
H. Georgi, 1993
✦ Integrating out heavy d.o.f.s marginalizes over details of short-distance interactions✦ Toy Example: two interacting scalar fields ',�
Path integralZ[j, J ] =
ZD[�]D['] exp
i
Zdx
⇣12 (@')
2� 12�(2+M
2)���'
2��. . .+J�+j'
⌘�
Completing the square (Gaussian integration)
�0 = �+�
M2
✓1 +
@2
M2
◆�1
'2 =)
J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016
How to get EFTs from New Physics✦ Consider effects from heavy states by using (known) low-energy d.o.f.s
H. Georgi, 1993
✦ Integrating out heavy d.o.f.s marginalizes over details of short-distance interactions✦ Toy Example: two interacting scalar fields ',�
Path integralZ[j, J ] =
ZD[�]D['] exp
i
Zdx
⇣12 (@')
2� 12�(2+M
2)���'
2��. . .+J�+j'
⌘�
Completing the square (Gaussian integration)
�0 = �+�
M2
✓1 +
@2
M2
◆�1
'2 =)
In the Lagrangian remove the high-scale d.o.f.s:
1
2(@�)2� 1
2M2�2��'2� = �1
2�0(M2 + @2)�0
| {z }+
�2
2M2'2
✓1 +
@2
M2
◆�1
'2
| {z }Irrelevant normalization
of the path integralTower of higher and
higher-dim. operators of light fields
J.R.Reuter New Physics in VBS at the LHC BSM Workshop, NTU Singapore, 04.03.2016
Generation of Higher-dimensional Operators
O(I)JJ =
1
⇤2trhJ (I) · J (I)
i
O0�,1 = 1
⇤2
�(D�)†�
� · ��†(D�)�� v2
2 |D�|2
O0�� = 1
⇤2 (�†�� v2/2) (D�)† · (D�)
O0�,3 =
1
⇤2
1
3(�†�� v2/2)3
O0WW = � 1
⇤2
1
2(�†�� v2/2)tr [Wµ⌫W
µ⌫ ]
OB =1
⇤2
i
2(Dµ�)
†(D⌫�)Bµ⌫
O0BB = � 1
F 2
1
4(�†�� v2/2)Bµ⌫B
µ⌫
OV q =1
⇤2q�( /D�)q
Couplings of new states to the longitudinal / transversal diboson system