Model Independent Constraints on Physics Beyond the Standard Model - - PowerPoint PPT Presentation
Adam Falkowski (LPT Orsay) Model Independent Constraints on Physics Beyond the Standard Model Florence, 17 September 2015 Based on my 1505.00046, 1503.07872 with Aielet Efrati and Yotam Soreq, 1411.0669 with Francesco Riva, and 1508.00581
Based on my 1505.00046, 1503.07872 with Aielet Efrati and Yotam Soreq, 1411.0669 with Francesco Riva, and 1508.00581 with Martín Gonzalez-Alonso, Admir Greljo, and David Marzocca
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New physics scale Λ separated from EW scale v, Λ >> v Linearly realized SU(3)xSU(2)xU(1) local symmetry spontaneously broken by VEV
Basic assumptions EFT Lagrangian beyond the SM expanded in operator dimension D Alternatively, non-linear Lagrangians with derivative expansion
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New physics scale Λ separated from EW scale v, Λ >> v Linearly realized SU(3)xSU(2)xU(1) local symmetry spontaneously broken by VEV
Basic assumptions EFT Lagrangian beyond the SM expanded in operator dimension D
Lepton number violating, hence too small to probe at LHC By assumption, subleading to D=6
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Grządkowski et al. 1008.4884 see e.g. Grządkowski et al. 1008.4884 Giudice et al hep-ph/0703164 Contino et al 1303.3876 Buchmuller,Wyler pre-arxiv (1986)
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For D=6 Lagrangian several complete non-redundant set
(so-called basis) proposed in the literature
Grządkowski et al. 1008.4884
Warsaw Basis SILH basis
Giudice et al hep-ph/0703164 Contino et al 1303.3876
h basis
Gupta et al 1405.0181
HISZ basis Primary basis
LHCHXSWG-INT-2015-001
Hagiwara et al (1993)
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H4D2 and H6 OH ⇥ @µ(H†H) ⇤2 OT ⇣ H†← → DµH ⌘2 O6H (H†H)3 f2H3 Oe −(H†H − v2
2 )¯
eH†` Ou −(H†H − v2
2 )¯
u e H†q Od −(H†H − v2
2 ) ¯
dH†q V 3D3 O3G g3
sfabcGa µ⌫Gb ⌫⇢Gc ⇢µ
Of
3G
g3
sfabc e
Ga
µ⌫Gb ⌫⇢Gc ⇢µ
O3W g3✏ijkW i
µ⌫W j ⌫⇢W k ⇢µ
Og
3W
g3✏ijkf W i
µ⌫W j ⌫⇢W k ⇢µ
V 2H2 OGG
g2
s
4 H†H Ga µ⌫Ga µ⌫
Og
GG g2
s
4 H†H e
Ga
µ⌫Ga µ⌫
OWW
g2 4 H†H W i µ⌫W i µ⌫
O ]
WW g2 4 H†H f
W i
µ⌫W i µ⌫
OBB
g02 4 H†H Bµ⌫Bµ⌫
Og
BB g02 4 H†H e
Bµ⌫Bµ⌫ OWB gg0H†iH W i
µ⌫Bµ⌫
O g
WB
gg0H†iH f W i
µ⌫Bµ⌫
f2H2D OH` i¯ `µ`H†← → DµH O0
H`
i¯ `iµ`H†i← → DµH OHe i¯ eµ¯ eH†← → DµH OHq i¯ qµqH†← → DµH O0
Hq
i¯ qiµqH†i← → DµH OHu i¯ uµuH†← → DµH OHd i ¯ dµdH†← → DµH OHud i¯ uµd ˜ H†DµH f2V HD OeW g¯ `µ⌫eiHW i
µ⌫
OeB g0¯ `µ⌫eHBµ⌫ OuG gs¯ qµ⌫T au e H Ga
µ⌫
OuW g¯ qµ⌫ui e H W i
µ⌫
OuB g0¯ qµ⌫u e H Bµ⌫ OdG gs¯ qµ⌫T adH Ga
µ⌫
OdW g¯ qµ⌫diH W i
µ⌫
OdB g0¯ qµ⌫dH Bµ⌫ (¯ LL)(¯ LL) and (¯ LR)(¯ LR) O`` (¯ `µ`)(¯ `µ`) Oqq (¯ qµq)(¯ qµq) O0
(¯ qµiq)(¯ qµiq) O`q (¯ `µ`)(¯ qµq) O0
`q
(¯ `µi`)(¯ qµiq) Oquqd (¯ qju)✏jk(¯ qkd) O0
quqd
(¯ qjT au)✏jk(¯ qkT ad) O`equ (¯ `je)✏jk(¯ qku) O0
`equ
(¯ `jµ⌫e)✏jk(¯ qkµ⌫u) O`edq (¯ `je)( ¯ dqj) ( ¯ RR)( ¯ RR) Oee (¯ eµe)(¯ eµe) Ouu (¯ uµu)(¯ uµu) Odd ( ¯ dµd)( ¯ dµd) Oeu (¯ eµe)(¯ uµu) Oed (¯ eµe)( ¯ dµd) Oud (¯ uµu)( ¯ dµd) O0
ud
(¯ uµT au)( ¯ dµT ad) (¯ LL)( ¯ RR) O`e (¯ `µ`)(¯ eµe) O`u (¯ `µ`)(¯ uµu) O`d (¯ `µ`)( ¯ dµd) Oqe (¯ qµq)(¯ eµe) Oqu (¯ qµq)(¯ uµu) O0
qu
(¯ qµT aq)(¯ uµT au) Oqd (¯ qµq)( ¯ dµd) O0
qd
(¯ qµT aq)( ¯ dµT ad)
59 different kinds of operators,
Grządkowski et al. 1008.4884
2499 distinct operators, including flavor structure and CP conjugates
Alonso et al 1312.2014
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Connection between operators and observables a bit obscured in Warsaw or SILH
h-basis proposed by LHCHXSWG2 to separate combinations of Wilson coefficients strongly constrained by EWPT from those relevant for LHC Higgs studies Rotation of any other D=6 basis such that one isolates linear combinations affecting Higgs observables and not constrained severely by precision tests LHCHXSWG-INT-2015-001
Similar “EFT Primaries” of Gupta et al 1405.0181
2499x2499 dimensional transformation matrix Linear transformation 2499 dimensional vector of Wilson coefficients 2499 parameters defining Higgs Basis
Relevant for LHC Higgs Very constrained parameters Irrelevant for LHC Higgs
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h-basis is defined via effective Lagrangian of mass eigenstates after electroweak symmetry breaking (photon,W,Z,Higgs boson, top). SU(3)xSU(2)xU(1) is not manifest but hidden in relations between different couplings Feature #1: In the tree-level Lagrangian, all kinetic terms are canonically normalized, and there’ s no kinetic mixing between mass
are zero, except for a correction to the W boson mass Feature #2: Tree-level relation between the couplings in the Lagrangian and SM input observables is the same as in the SM. In particular, photon and gluon couple as in SM, and there’ s no correction to Z mass term Features #1 and #2 can always be obtained without any loss of generality, via integration by parts, fields and couplings redefinition
LHCHXSWG-INT-2015-001
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By construction, photon and gluon couplings as in the SM. Only W and Z couplings are affected Effects of dimension-6 operators are parametrized by a set of vertex corrections
Relations enforced by linearly realized SU(3)xSU(2)xU(1) symmetry at the level of dimension-6 operators
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In HB, Higgs couplings to gauge bosons described by 6 CP even and 4 CP odd parameters that are unconstrained by LEP-1 D=6 EFT with linearly realized SU(3)xSU(2)xU(1) enforces relations between Higgs couplings to gauge bosons (otherwise, more parameters) Corrections to Higgs Yukawa couplings to fermions are also unconstrained by EWPT Apart from δm and δg, additional 6+3x3x3 CP-even and 4+3x3x3 CP-odd parameters to parametrize LHC Higgs physics
relative correction to W mass
LHCHXSWG-INT-2015-001
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SM predicts TGCs in terms of gauge couplings as consequence of SM gauge symmetry and renormalizability: In EFT with D=6 operators, new “anomalous”contributions to TGCs arise These depend on previously introduced h-basis parameters describing Higgs couplings to electroweak gauge bosons, and on 2 new parameters
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Working at order 1/Λ^2 in EFT expansion. Taking into account corrections from D=6 operators, and neglecting D=8 and higher
are linear in h-basis parameters, that is to say, only interference terms between SM and new physics. Quadratic corrections are formally of order 1/Λ^4, much as D=8 operators that are neglected.) Working at tree-level in EFT parameters (SM predictions taken at NLO
tree-level SM amplitude taken into account) Except on las slide, restrict to observables that do not depend on 4- fermion operators (they are *not* neglected - just do not contribute at tree-level; constraints on 4-fermion operators left for future work) Allowing all dimension-6 operators to be present simultaneously with arbitrary coefficients (within EFT validity range). Constraints are
and correlations matrix is computed. Unless otherwise noted, dimension-6 operators are allowed with arbitrary flavor structure
Han,Skiba hep-ph/0412166 Efrati,AA,Soreq 1503.07782
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For observables with Z or W bosons on-shell, interference between SM amplitudes and 4-fermion operators is suppressed by Γ/m and can be neglected Corrections from dimension-6 Lagrangian to pole observables can be expressed just by vertex corrections δg and W mass correction δm I will not assume anything about δg: they are allowed to be arbitrary, flavor dependent, and all can be simultaneously present
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Including leading order new physics corrections amount to replacing Z coupling to fermions with effective couplings These effective couplings encode the effect of vertex and oblique corrections Shift of the effective couplings in the presence of dimension-6 operators allows one to read off the dependence of observables on dimension-6 operators In general, pole observables constrain complicated combinations of coefficients of dimension-6 operators However, in h-basis, oblique corrections are absent (except for δm) thus δg directly constrained
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Observable Experimental value Ref. SM prediction Definition ΓZ [GeV] 2.4952 ± 0.0023 [21] 2.4950 P
f Γ(Z → f ¯
f) σhad [nb] 41.541 ± 0.037 [21] 41.484
12π m2
Z
Γ(Z→e+e−)Γ(Z→q¯ q) Γ2
Z
Re 20.804 ± 0.050 [21] 20.743
P
q Γ(Z→q¯
q) Γ(Z→e+e−)
Rµ 20.785 ± 0.033 [21] 20.743
P
q Γ(Z→q¯
q) Γ(Z→µ+µ−)
Rτ 20.764 ± 0.045 [21] 20.743
P
q Γ(Z→q¯
q) Γ(Z→τ +τ −)
A0,e
FB
0.0145 ± 0.0025 [21] 0.0163
3 4A2 e
A0,µ
FB
0.0169 ± 0.0013 [21] 0.0163
3 4AeAµ
A0,τ
FB
0.0188 ± 0.0017 [21] 0.0163
3 4AeAτ
Rb 0.21629 ± 0.00066 [21] 0.21578
Γ(Z→b¯ b) P
q Γ(Z→q¯
q)
Rc 0.1721 ± 0.0030 [21] 0.17226
Γ(Z→c¯ c) P
q Γ(Z→q¯
q)
AFB
b
0.0992 ± 0.0016 [21] 0.1032
3 4AeAb
AFB
c
0.0707 ± 0.0035 [21] 0.0738
3 4AeAc
Ae 0.1516 ± 0.0021 [21] 0.1472
Γ(Z→e+
Le− L )−Γ(Z→e+ Re− R)
Γ(Z→e+e−)
Aµ 0.142 ± 0.015 [21] 0.1472
Γ(Z→µ+
Lµ− L )−Γ(Z→e+ µ µ− R)
Γ(Z→µ+µ−)
Aτ 0.136 ± 0.015 [21] 0.1472
Γ(Z→τ +
L τ − L )−Γ(Z→τ + R τ − R )
Γ(Z→τ +τ −)
Ab 0.923 ± 0.020 [21] 0.935
Γ(Z→bL¯ bL)−Γ(Z→bR¯ bR) Γ(Z→b¯ b)
Ac 0.670 ± 0.027 [21] 0.668
Γ(Z→cL¯ cL)−Γ(Z→cR¯ cR) Γ(Z→c¯ c)
As 0.895 ± 0.091 [22] 0.935
Γ(Z→sL¯ sL)−Γ(Z→sR¯ sR) Γ(Z→s¯ s)
Ruc 0.166 ± 0.009 [23] 0.1724
Γ(Z→u¯ u)+Γ(Z→c¯ c) 2 P
q Γ(Z→q¯
q)
µttZ 0.81 ± 0.24 [24,25] 1.00
(gZt
L )2+(gZt R )2
(gZu
L,SM)2+(gZu R,SM)2
Table 1: Z boson pole observables. The experimental errors of the observables between the double lines are correlated, which is taken into account in the fit. The results for Ae,µ,τ listed above come from the combination of leptonic polarization and left-right asymmetry measurements at the SLD; we also include the results Aτ = 0.1439± 0.0043, Ae = 0.1498± 0.0049 from tau polarization measurements at LEP-1 [21]. For the theoretical predictions we use the best fit SM values from GFitter [20]. We also include the model-independent measurement of on-shell Z boson couplings to light quarks in D0 [26].
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Observable Experimental value Ref. SM prediction Definition mW [GeV] 80.385 ± 0.015 [27] 80.364
gLv 2 (1 + δm)
ΓW [GeV] 2.085 ± 0.042 [23] 2.091 P
f Γ(W → ff 0)
Br(W → eν) 0.1071 ± 0.0016 [28] 0.1083
Γ(W!eν) P
f Γ(W!ff0)
Br(W → µν) 0.1063 ± 0.0015 [28] 0.1083
Γ(W!µν) P
f Γ(W!ff0)
Br(W → τν) 0.1138 ± 0.0021 [28] 0.1083
Γ(W!τν) P
f Γ(W!ff0)
RWc 0.49 ± 0.04 [23] 0.50
Γ(W!cs) Γ(W!ud)+Γ(W!cs)
Rσ 0.998 ± 0.041 [29] 1.000 gWq3
L
/gWq3
L,SM
Table 2: W-boson pole observables. Measurements of the 3 leptonic branching fractions are
GFitter [20], while for the leptonic branching fractions we take the value quoted in [28].
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Z coupling to charged leptons constrained at 0.1% level W couplings to leptons constrained at 1% level Some couplings to quarks (bottom, charm) also constrained at 1% level Some couplings very weakly constrained in a model-independent way, in particular Z couplings to light quarks (though their combination affecting *total* hadronic Z- width is strongly constrained) Some off-diagonal vertex corrections can also be constrained
All diagonal vertex corrections except for δgWqR and δgZtR simultaneously constrained in a completely model-independent way Efrati,AA,Soreq 1503.07872
m = (2.6 ± 1.9) · 10−4.
[δgW e
L ]ii =
−1.00 ± 0.64 −1.36 ± 0.59 1.95 ± 0.79 × 10−2, [δgZe
L ]ii =
−0.26 ± 0.28 0.1 ± 1.1 0.16 ± 0.58 × 10−3, [δgZe
R ]ii =
−0.37 ± 0.27 0.0 ± 1.3 0.39 ± 0.62 × 10−3, [δgZu
L ]ii =
−0.8 ± 3.1 −0.16 ± 0.36 −0.28 ± 3.8 × 10−2, [δgZu
R ]ii =
1.3 ± 5.1 −0.38 ± 0.51 × × 10−2, [δgZd
L ]ii =
−1.0 ± 4.4 0.9 ± 2.8 0.33 ± 0.16 × 10−2, [δgZd
R ]ii =
2.9 ± 16 3.5 ± 5.0 2.30 ± 0.82 × 10−2.
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Full correlation matrix is also derived From that, one can reproduce full likelihood function as function of 21 parameters δg and δm If dictionary from h-basis to other bases exists, results can be easily recast to another form Similarly, when mapping to d=6 basis from (fewer) parameters of particular BSM models is given, results can be easily recast as constraints
1σ Errors Correlation Matrix Central Values
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δgW ℓ
L
= c′
Hℓ + f(1/2, 0) − f(−1/2, −1),
δgZν
L
= 1 2 (c′
Hℓ − cHℓ) + f(1/2, 0),
δgZe
L
= −1 2 (c′
Hℓ + cHℓ) + f(−1/2, −1),
δgZe
R
= −1 2cHe + f(0, −1), f(T 3, Q) = I
g2
Lg2 Y
g2
L − g2 Y
+ (cT − δv)
g2
Y
g2
L − g2 Y
δgW q
L
= c′
HqV + f(1/2, 2/3)V − f(−1/2, −1/3)V,
δgW q
R
= cHud, δgZu
L
= 1 2
Hq − cHq
δgZd
L
= −1 2V † c′
Hq + cHq
δgZu
R
= −1 2cHu + f(0, 2/3), δgZd
R
= −1 2cHd + f(0, −1/3).
[ˆ c′
Hℓ]ii =
−1.09 ± 0.64 −1.45 ± 0.59 1.87 ± 0.79 × 10−2, [ˆ cHℓ]ii = 1.03 ± 0.63 1.32 ± 0.62 −2.01 ± 0.80 × 10−2, [ˆ cHe]ii = 0.22 ± 0.66 −0.6 ± 2.6 −1.4 ± 1.3 × 10−3, c′
ℓℓ = (−1.21 ± 0.41) × 10−2,
c′
Hq
0.1 ± 2.7 −1.2 ± 2.8 −0.7 ± 3.8 × 10−2, [ˆ cHq]ii = 1.8 ± 7.0 −0.8 ± 2.9 0.0 ± 3.8 × 10−2, [ˆ cHu]ii = −3 ± 10 0.8 ± 1.0 × × 10−2, [ˆ cHd]ii = −6 ± 32 −7 ± 10 −4.6 ± 1.6 × 10−2.
[ˆ c′
Hℓ]ij
= [c′
HL]ij +
LcW B − g2 L
g2
Y
cT
[ˆ cHℓ]ij = [cHL]ij − cT δij, [ˆ cHe]ij = [cHE]ij − 2cTδij,
c′
Hq
=
HQ
LcW B − g2 L
g2
Y
cT
[ˆ cHq]ij = [cHQ]ij + 1 3cTδij, [ˆ cHu]ij = [cHU]ij + 4 3cTδij, [ˆ cHd]ij = [cHD]ij − 2 3cTδij.
Note in Warsaw basis only combinations of Wilson coefficients are constrained by pole observables
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In SILH basis pole constraints look simpler, though important correlations remain, notably between cW+cB and leptonic couplings
[s``]1221 = (4.8 ± 1.6) × 102, sW + sB 2 = −0.43 ± 0.26, sT = (−1.03 ± 0.63) × 102, [s0
H`]ii =
@ −0.36 ± 0.92 3.0 ± 1.3 1 A × 102, [sH`]ii = @ 0.29 ± 0.95 −3.0 ± 1.3 1 A × 102, [sHe]ii = @ −2.0 ± 1.3 −2.1 ± 1.3 −2.2 ± 1.3 1 A × 102, ⇥ s0
Hq
⇤
ii =
@ 1.2 ± 2.8 −0.1 ± 2.9 0.4 ± 3.8 1 A × 102, [sHq]ii = @ 2.1 ± 7.1 −0.4 ± 2.9 0.3 ± 3.8 1 A × 102, [sHu]ii = @ −1 ± 10 2.2 ± 1.3 × 1 A × 102, [sHd]ii = @ −6 ± 32 −7 ± 10 −5.3 ± 1.7 1 A × 102, (
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Peskin Takeuchi pre-arxiv Barbieri et al hep-ph/0405040
Equivalent to restricted form of flavor-diagonal vertex corrections, W-mass corrections, and 4-fermion operators:
≈
0.0 0.1 0.2 0.3
0.0 0.1 0.2 0.3
S T Pole observables
Same likelihood for pole observables can be used to constrain up to 3 oblique params
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Channel µ Production Ref.
−0.18
2D [31] 1.0+1.6
−1.6
Wh [34] 0.1+3.7
−0.1
Zh [34] 0.58+0.93
−0.81
Vh [33] 1.30+2.62
−1.75 & 2.7+2.4 −1.7
tth [33, 34] Z 2.7+4.5
−4.3 & −0.2+4.9 −4.9
total [34, 35] ZZ∗ 1.31+0.27
−0.14
2D [31] WW ∗ 1.11+0.18
−0.17
2D [31] 2.1+1.9
−1.6
Wh [36] 5.1+4.3
−3.1
Zh [36] 0.80+1.09
−0.93
Vh [33] ⌧⌧ 1.12+0.25
−0.23
2D [31] 0.87+1.00
−0.88
Vh [33] bb 1.11+0.65
−0.61
Wh [32] 0.05+0.52
−0.49
Zh [32] 0.89+0.47
−0.44
Vh [33] 2.8+1.6
−1.4
VBF [37] 1.5+1.1
−1.1 & 1.2+1.6 −1.5
tth [38, 39] µµ −0.7+3.7
−3.7 & 0.8+3.5 −3.4
total [34, 40] multi-` 2.1+1.4
−1.2 & 3.8+1.4 −1.4
tth [41, 42]
Including 2D likelihoods from recent ATLAS+CMS combination
ATLAS-CONF-2015-044 CMS-PAS-HIG-15-002
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In Higgs basis, Higgs couplings to gauge bosons are described by 10 parameters These parameters are
multiple Higgs production (ggF , VBF , VH) and Higgs decay (γγ, Zγ, VV^*→4f) processes Linearly realized SU(3)xSU(2)xU(1) with D=6
between Higgs couplings to gauge bosons (otherwise, 5 more parameters)
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In Higgs basis, Higgs couplings to fermions are described by 3 general complex 3x3 matrices Here I will assume MFV couplings, thus reducing number
Without that assumption, couplings to light fermions are unconstrained, leading to flat directions; their effect on other parameters is similar to adding additional invisible width
∆LD=6
hff
= −h v
δyf eiφf mff cf + h.c..
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→ σW h σSM
W h
≃ 1 + 2δcw + 6.39 6.51 6.96 cw + 1.49 1.49 1.50 cww → 1 + 2δcz + 9.26 9.43 10.08 cz + 4.35 4.41 4.63 czz − 0.81 0.84 0.93 czγ − 0.43 0.44 0.48 cγγ σZh σSM
Zh
≃ 1 + 2δcz + 5.30 5.40 5.72 cz + 1.79 1.80 1.82 czz + 0.80 0.82 0.87 cγ + 0.22 0.22 0.22 czγ, → 1 + 2δcz + 7.61 7.77 8.24 cz + 3.31 3.35 3.47 czz − 0.58 0.60 0.65 czγ + 0.27 0.28 0.30 cγγ. (4.7
→ σV BF σSM
V BF
≃ 1 + 1.49δcw + 0.51δcz − 1.08 1.11 1.23 cw − 0.10cww − 0.35 0.35 0.40 cz −0.04czz − 0.10cγ − 0.02czγ → 1 + 2δcz − 2.25cz − 0.83czz + 0.30czγ + 0.12cγγ.
− − × ≃ σggh σSM
ggh
≃ 1 + 237cgg + 2.06δyu − 0.06δyd.
→ σtth σSM
tth
≃ 1 + 2δyu.
7 8 13
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Γcc ΓSM
cc
≃ 1 + 2δyu, Γbb ΓSM
bb
≃ 1 + 2δyd, Γττ ΓSM
ττ
≃ 1 + 2δye,
Γ2ℓ2ν ΓSM
2ℓ2ν
≃ 1 + 2δcw + 0.46cw − 0.15cww → 1 + 2δcz + 0.67cz + 0.05czz − 0.17czγ − 0.05cγγ.
¯ Γ4ℓ ¯ ΓSM
4ℓ
≃ 1 + 2δcz +
0.39
0.14
0.05
0.02
0.03
→ 1 + 2δcz + 0.35 0.32
0.19 0.19
0.09 0.08
0.01 0.02
(4.13)
h h
ΓV V ΓSM
V V
≃
cvv cSM
vv
, vv ∈ {gg, γγ, zγ}, ˆ cγγ = cγγ, cSM
γγ ≃ −8.3 × 10−2,
ˆ czγ = czγ, cSM
zγ ≃ −5.9 × 10−2,
2e2μ 4e
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µX;Y = σ(pp → X) σ(pp → X)SM Γ(h → Y ) Γ(h → Y )SM Γ(h → all)SM Γ(h → all) .
In EFT, assuming no other degrees of freedom, so total width is just sum of partial width into SM particle no invisible width in this analysis
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Below is a comparison of the L (x0 ± 1 σ) δcz −0.12 ± 0.20 czz 0.6 ± 1.9 cz2 −0.25 ± 0.83 cγγ 0.015 ± 0.029 czγ 0.01 ± 0.10 cgg −0.0056 ± 0.0028 δyu 0.55 ± 0.30 δyd −0.42 ± 0.45 δye −0.18 ± 0.36 (I haven’t computed all t
Not all parameters yet constrained enough that EFT approach is valid Results sensitive to including corrections to Higgs observables quadratic in EFT parameters which are formally O(1/Λ^4). Thus, in general, results may be sensitive to including dimension-8 operators Flat direction Needs more data
in h->4f decays
AA 1505.00046
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Corbett et al 1304.1151 Dumont et al 1304.3369 Pomarol Riva 1308.2803 Masso 1406.6377 Ellis et al 1410.7703
AA,Gonzalez-Alonso,Greljo,Marzocca 1508.00581
Consistent EFT analysis at O(1/Λ^2)
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In Higgs basis formalism, all but 2 TGCs are dependent couplings and can be expressed by Higgs couplings to gauge bosons Therefore constraints on δg1z and δκγ imply constraints on Higgs couplings But for that, all TGCs have to be simultaneously constrained in multi-dimensional fit, and correlation matrix should be given Note that c_zγ c_zz and c_zBox are difficult to access experimentally in Higgs physics Important to combine Higgs and TGC data!
Linearly realized SU(3)xSU(2)xU(1) at D=6 level enforces relations between TGC and Higgs couplings in the Higgs basis Higgs TGC
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Flat direction between c_zz and c_zBox lifted to large extent by WW data! Much better constraints on some parameters. Most parameters (marginally) within the EFT regime Lower sensitivity to the quadratic terms (though still not completely negligible, especially for δcz and δyd)
cz czz cz⇤ c cz cgg yu yd ye z = −0.07 ± 0.14 0.65 ± 0.42 −0.29 ± 0.21 −0.005 ± 0.014 −0.005 ± 0.095 −0.0053 ± 0.0027 0.55 ± 0.30 −0.44 ± 0.24 −0.22 ± 0.18 −0.152 ± 0.080 ,
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TGC Higgs TGC+Higgs 1.5 1.0 0.5 0.0 1.0 0.5 0.0 0.5 1.0 ∆g1,z ∆ΚΓ
LHC Higgs and LEP-2 WW data by itself do not constrain TGCs robustly due to each suffering from 1 flat direction in space of 3 TGCs However, the flat directions are orthogonal and combined constraints lead to robust O(0.1) limits on aTGCs
δg1,z δκγ λz = 0.037 ± 0.041 0.133 ± 0.087 −0.152 ± 0.080 , ρ = 1 0.62 −0.84 0.62 1 −0.85 −0.84 −0.85 1
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Non-trivial constraints at linear (1/Λ^2) level Quadratic (1/Λ^4) terms not completely negligible yet, but they do not change fit qualitatively
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zz
mZh 200 300 400 500 600 700 800 900 0.00 0.05 0.10 0.15 mZh (pb/bin)
For VH production, quadratic (1/Λ^4) contributions are comparable to linear (1/Λ^2)
They are numerically important but don’ t change fit significantly because they constrain similar direction in parameter space as linear ones Sensitivity to 1/Λ^4 terms greatly reduced if VH signal strength with cut mVH<400 GeV was quoted
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[O``]1111 = (¯ `1¯ µ`1)(¯ `1¯ µ`1), [O`e]1111 = (¯ `1¯ µ`1)(ec
1µ¯
ec
1),
[Oee]1111 = (ec
1µ¯
ec
1)(ec 1µ¯
ec
1).
1 10 10 2 10 3
0.5 1 10 10 2 10 3
0.5
3 3
LEP Averaged d σ / d cosθ (e+e-)
189 GeV
cosθe dσ/dcosθ (pb)
192 GeV
cosθe dσ/dcosθ (pb) (pb) (pb)
AA, Mimouni, to appear
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There are strong constraints on certain combinations of dimension-6 operators from the pole observables measured at LEP-1 and other colliders. These can be conveniently presented as correlated constraints on vertex corrections and W mass corrections. Assuming MFV , these constraints allow one to describe LO EFT deformations of single Higgs signal strength LHC observables by just 9 parameters There are non-trivial constraints on all of these 9 parameters from Higgs and WW data Synergy of TGC and Higgs coupling measurements is crucial for deriving meaningful bounds
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