Implications of the Higgs discovery· · ·
Abdelhak DJOUADI (LPT Paris-Sud)
• First, is it a Higgs?
• Implications for the SM
• Implications for the MSSM: mass
• Other implications for the MSSM
• What next?
ICTP School, 13/06/2013 Implications of the Higgs discovery – A. Djouadi – p.1/26
1. Is it a Higgs?After 48 years of postulat, 30 years of search (and a few heart attacks),“a boson” is discovered at LHC on the 4th of July: Hi(gg)stori cal day!
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ICTP School, 13/06/2013 Implications of the Higgs discovery – A. Djouadi – p.2/26
1. First, is it a Higgs?A longstanding and most crucial problem in particle physics :
how to generate particle masses in an SU(2) ×U(1) gauge invariant way?in the Standard Model ⇒ the Higgs–Englert–Brout mechanism
Introduce a doublet of scalar fields Φ=(Φ+
Φ0 ) with 〈0|Φ0|0〉 6= 0:fields/interactions symmetric under SU(2) ×U(1) but vaccum not.
LS=DµΦ†DµΦ−µ2Φ†Φ−λ(Φ†Φ)2
v = (−µ2/λ)1/2 = 246 GeV⇒ three d.o.f. for MW± and MZ.For fermion masses, use same Φ:
LYuk=−fe(e, ν)LΦeR + ...
Residual d.o.f corresponds to spin–0 H particle.
• The scalar Higgs boson: JPC = 0++ quantum numbers (CP–even).• Masses and self–couplings from V : M2
H=2λv2,gH3 = 3M2
H
v, ...
• Higgs couplings ∝ particle masses: gHff = mf
v,gHVV = 2
M2V
v
(since v is known, the only free parameter in the SM is MH or λ).
ICTP School, 13/06/2013 Implications of the Higgs discovery – A. Djouadi – p.3/26
1. First, is it a Higgs?
Spin: the state decays into γγ• not spin–1: Landau–Yang• could be spin–2 like graviton? Ellis et al.– miracle that couplings fit that of H,– “prima facie” evidence against it:
e.g.: cg 6= cγ, cV ≫ 35cγmany th. analyses (no suspense).
CP: is it CP–even or CP–odd?
HVµVµ vs HǫµνρσZµνZρσ
⇒ dΓ(H→ZZ∗)dM∗
and dΓ(H→ZZ)dφ
ATLAS/CMS: ≈ 3σ for CP-even..
Problem : if H is CP mixture, only0+ component is projected out!(or very large 0 −VV loop cplg).⇒ better probe: µZZ=1.1±0.4!
M* (GeV)
No.
of
Eve
nts
SM
H → Z*Z → (f1f–
1)(f2f–
2)MH = 150 GeV
Spin 1Spin 2
0
5
10
15
20
25
30
30 35 40 45 50 55ϕ
1/Γ
dΓ/d
ϕ
H → ZZ → (f1f–
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2)MH = 280 GeV
SMpseudoscalar
0.1
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0.14
0.16
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ln(L× -2 -30 -20 -10 0 10 20 30
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xper
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500
1000
1500
2000
2500
3000
SM, 0+
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CMS data
CMS Preliminary -1 = 8 TeV, L = 12.2 fbs -1 = 7 TeV, L = 5.1 fbs
ICTP School, 13/06/2013 Implications of the Higgs discovery – A. Djouadi – p.4/26
1. First, is it a Higgs?
)µSignal strength ( -1 0 +1
Combined
4l→ (*) ZZ→H
γγ →H
νlν l→ (*) WW→H
ττ →H
bb→W,Z H
-1Ldt = 4.6 - 4.8 fb∫ = 7 TeV: s-1Ldt = 5.8 - 13 fb∫ = 8 TeV: s
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-1Ldt = 13 fb∫ = 8 TeV: s
-1Ldt = 4.6 fb∫ = 7 TeV: s-1Ldt = 13 fb∫ = 8 TeV: s
-1Ldt = 4.7 fb∫ = 7 TeV: s-1Ldt = 13 fb∫ = 8 TeV: s
= 126 GeVHm
0.3± = 1.3 µ
ATLAS Preliminary
SMσ/σBest fit -2 0 2 4
ZZ→H
WW (VH tag)→H
WW (VBF tag)→H
WW (0/1 jet)→H
(VBF tag)γγ →H
(untagged)γγ →H
(VH tag)ττ →H
(VBF tag)ττ →H
(0/1 jet)ττ →H
bb (ttH tag)→H
bb (VH tag)→H
-1 12.2 fb≤ = 8 TeV, L s -1 5.1 fb≤ = 7 TeV, L s
CMS Preliminary = 125.8 GeVH m
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From ATLAS/CMS results:
Higgs couplings to elementary particles as predicted by Hig gs mechanism:• couplings to WW,ZZ, γγ roughly as expected for a CP-even Higgs• couplings proportionial to masses as expected for the Higgs bosonSo, it is not only a “new particle”, the “126 GeV boson”, a “new state”...
IT IS A HIGGS BOSON!
But is it THE SM Higgs boson or A Higgs boson from some extension?ICTP School, 13/06/2013 Implications of the Higgs discovery – A. Djouadi – p.5/26
1. First, is it a Higgs?a SM or a BSM Higgs?
To check this you need very precise measurements to see small deviations...
ICTP School, 13/06/2013 Implications of the Higgs discovery – A. Djouadi – p.6/26
2. Implications in the SMSo its looks like expected in SM ⇒a triumph for high-energy physics!Indirect constraints from EW data a
H contributes to RC to W/Z masses:
HW/Z W/Z
∝ απlog MH
MW+· · ·
Fit the EW precision measurements,one obtains MH = 92+34
−26 GeV, or
MH<∼ 160 GeV at 95% CL
compared with the measured mass
MH≈126 GeV.A very non–trivial consistency check!(remember the stop of the top quark!).The SM is a very successfull theory!
a Still some problems with AbFB (LEP), At
FB (TeV) and g−2 but not severe...
0
1
2
3
4
5
6
10030 300
mH [GeV]
∆c
2
Excluded
∆ahad =∆a
(5)
0.02750±0.000330.02749±0.00010incl. low Q2 data
Theory uncertaintyJuly 2011 mLimit = 161 GeV
(GeV)Xm120 122 124 126 128 130
SMs/
s
0.0
0.5
1.0
1.5
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2.5
3.0
3.5
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024
68101214161820
CMS Preliminary -1 12.2 fb£ = 8 TeV, L s -1 5.1 fb£ = 7 TeV, L s
ZZ® + H gg ®H
ICTP School, 13/06/2013 Implications of the Higgs discovery – A. Djouadi – p.7/26
2. Implications in the SM• The theory preserves unitarity:
without H: |A0(VV→VV)|∝E2
including H: |A0|∝M2H/v
2
theory unitary if MH<∼700 GeV...
V
V
V
V H
• Particle spectrum complete:Fourth generation excluded byH → ZZ,WW, γγ,bb rates...
• Extrapolable up to highest scales.λ(Q2)λ(v2)
≈1+ 32M4
W+M4
Z−4m4
t
16π2v4 logQ2
v2
tops make λ<0: unstable vacuum
ΛC∼MPl ⇒ MH>∼129GeV!
at 2loops for mpolet =173 GeV.....
Degrassi et al., Bezrukov et al.but what is measured mt value?• SM = TOE? Maybe not (?):
mν , DM, GUT, hierarchy...
mb′ =mt′+50 GeV=600 GeV
γγ@LHC
MH=125 GeV
Vbb@Tevatron
σ(H)×BR|SM4/SM
mν′ = mℓ′ [GeV]100 200 300 400 500 600
1
0.1
H+ +
f/V
Tev⊕lHCLHCILCstable
stablemeta-
unstable
EW vacuum:
95%CL
MH [GeV]
mpole
t[G
eV
]
132130128126124122120
182
180
178
176
174
172
170
168
166
164
ICTP School, 13/06/2013 Implications of the Higgs discovery – A. Djouadi – p.8/26
2. Implications in the SM
Rates compatible withthose expected in the SM
Fit of all LHC Higgs data ⇒,
agreement at 20–30% levelwith SM predictions!
Moreau+ADand >20 TH+EXP analyses
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Some beyond the SM scenarios are in ‘mortuary”:• Higgsless models, extreme Technicolor and composite scena rios, ..• fermiophobic Higgs, gauge-phobic Higgs, 4th generation, . ..Some beyond the SM scenarios are in “hospital”:Other BSM scenarios are strongly constrained...
Here, I discuss the example of Supersymmetry and the MSSM:ICTP School, 13/06/2013 Implications of the Higgs discovery – A. Djouadi – p.9/26
3. Implications for the MSSM: mass
In the MSSM: two Higgs doublets: H1 =(
H01
H−
1
)
and H2 =(
H+
2
H02
)
,
After EWSB (which can be made radiative: more elegant than in SM):
Three dof to make W±L ,ZL ⇒ 5 physical states left out: h,H,A,H±
Only two free parameters at tree–level: tanβ,MA but rad. cor. important:
Mh<∼MZ|cos2β|+RC<∼130 GeV , MH≈MA≈MH±<∼MEWSB
– Couplings of h,H to VV are suppressed; no AVV couplings (CP).– For tanβ ≫ 1: couplings to b (t) quarks enhanced (suppressed).
Φ gΦuu gΦdd gΦV V
h cosαsinβ→ 1 sinα
cos β→ 1 sin(β − α)→ 1H sinα
sinβ→ 1/ tan β cosαcos β → tan β cos(β − α)→ 0
A 1/ tan β tanβ 0In the decoupling limit: MSSM reduces to SM but with a light SM Higgs .
this decoupling limit occurs in many extensions....At tan β≫1, one SM–like and two CP–odd like Higgses with cplg to b, τMA≤Mmax
h ⇒h≡A,H≡HSM , MA≥Mmaxh ⇒H≡A,h ≡HSM
ICTP School, 13/06/2013 Implications of the Higgs discovery – A. Djouadi – p.10/26
3. Implications for the MSSM: massThe mass value 126 GeV is rather large for the MSSM h boson,
⇒ one needs from the very beginning to almost maximize it...Maximizing Mh is maximizing the radiative corrections; at 1-loop:
MhMA≫MZ→ MZ|cos2β|+ 3m4
t
2π2v2sin2 β
[
logM2
S
m2t
+X2
t
M2S
(
1− X2t
12M2S
)]
• decoupling regime with MA∼O(TeV);• large values of tan β >∼ 10 to maximize tree-level value;• maximal mixing scenario: Xt =
√6MS;
• heavy stops, i.e. large MS=√mt1
mt2;
we choose at maximum MS<∼3 TeV, not to have too much fine-tuning....
• Do the complete job: two-loop corrections and full SUSY spec trum• Use RGE codes (Suspect) with RC in DR/compare with FeynHiggs (OS).Perform a full scan of the phenomenological MSSM with 22 free parameters• determine the regions of parameter space where 123≤Mh ≤129GeV(3 GeV uncertainty includes both “experimental” and “theor etical” error)• require h to be SM–like: σ(h)×BR(h)≈ HSM (H = HSM) later)Many anlayses! Here, the one from Arbey et al. 1112.3028+120 7.1348
ICTP School, 13/06/2013 Implications of the Higgs discovery – A. Djouadi – p.11/26
3. Implications for the MSSM: mass
Main results:• Large MS values needed:– MS ≈ 1 TeV: only maximal mixing– MS ≈ 3 TeV: only typical mixing.• Large tan β values favoredbut tan β≈3 possible if MS≈3TeV
How light sparticles can be withthe constraint Mh = 126 GeV?• 1s/2s gen. q should be heavy...But not main player here: the stops:⇒ mt1
<∼ 500 GeV still possible!•M1,M2 and µ unconstrained,• non-univ. mf : decouple ℓ from qEW sparticles can be still very lightbut watch out the new limits..
ICTP School, 13/06/2013 Implications of the Higgs discovery – A. Djouadi – p.12/26
3. Implications for the MSSM: mass
Constrained MSSMs are interesting from model building poin t of view:
– concrete schemes: SSB occurs in hidden sectorgravity,..→ MSSM fields
– provide solutions to some MSSM problems: CP, flavor, etc..– parameters obey boundary conditions ⇒ small number of inputs...• mSUGRA: tan β , m1/2 , m0 , A0 , sign(µ)• GMSB: tanβ , sign(µ) , Mmes , ΛSSB , Nmess fields
• AMSB: , m0 , m3/2 , tan β , sign(µ)full scans of the model parameters with 123 GeV≤Mh≤129 GeV
very strong constraints and some (minimal) models ruled out ...ICTP School, 13/06/2013 Implications of the Higgs discovery – A. Djouadi – p.13/26
3. Implications for the MSSM: mass
As the scale MS seems to be large, consider two extreme possibilities
• Split SUSY: allow fine–tuningscalars (including H2) at high scalegauginos–higgsinos at weak scale(unification+DM solutions still OK)Mh ∝ log(MS/mt) → large• SUSY broken at the GUT scale...give up fine-tuning and everything elsestill, λ∝M2
H related to gauge cplgs
λ(m)=g21(m)+g2
2(m)
8(1+ δm)
... leading to MH=120–140 GeV ...In both cases small tanβ needed...note 1: tanβ ≈ 1 possiblenote 2: MS large and not MA possible!?Consider general MSSM with tanβ ≈ 1!
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ICTP School, 13/06/2013 Implications of the Higgs discovery – A. Djouadi – p.14/26
4. Other implications for the MSSM
There are other (stringent) constraints on pMSSM to be inclu ded:• production/decay rates of the observed Higgs particle;• CMS and ATLAS pp → A/H/(h)→ττ and t → bH+ searches;• non observation of heavier Higgses in the ZZ,WW,tt channels ;• constraints from sparticle searches and eventually Dark Ma tter,• constraints from flavor: at least (direct!) limits from Bs→µµ...
)mSignal strength ( -1 0 +1
Combined
4l® (*) ZZ®H
gg ®H
nln l® (*) WW®H
tt ®H
bb®W,Z H
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= 126 GeVHm
0.3± = 1.3 m
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SM
σ/σ
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ICTP School, 13/06/2013 Implications of the Higgs discovery – A. Djouadi – p.15/26
4. Other implications for the MSSM
Higgs searches are more complicated/challenging in the MSS M case
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• More Higgs particles: Φ=h,H,A,H±:– some couple almost like the SM Higgs,– but some are more weakly coupled.• In general same production as in SMbut also new/more complicated processses(rates can be smaller or larger than in SM).• Possibility of different decay modes(and clean decays eg into γγ suppressed)• Impact of light SUSY particles?⇒ In general very complicated situation!But simpler in the decoupling regime:– h as in SM with Mh=115−130GeV– dominant mode: gg,bb→H/A→ττIt is even more tricky in beyond MSSM!and also in some non–SUSY extensions...
ICTP School, 13/06/2013 Implications of the Higgs discovery – A. Djouadi – p.16/26
4. Other implications for the MSSM
There are other (stringent) constraints on pMSSM to be inclu ded:• production/decay rates of the observed Higgs particle;• CMS and ATLAS pp → A/H/(h)→ττ and t → bH+ searches;• non observation of heavier Higgses in the ZZ,WW,tt channels ;• constraints from sparticle searches and eventually Dark Ma tter,• constraints from flavor: at least (direct!) limits from Bs→µµ...
ICTP School, 13/06/2013 Implications of the Higgs discovery – A. Djouadi – p.17/26
4. Other implications for the MSSMWhat about the low tan β regime?
• tanβ<∼3 usually “excluded” by LEP2:Mh
>∼114 GeV for BMS with MS≈1 TeV.
Be we can be more relaxed: MS ≫ MZ
⇒ tanβ as low as 1 could be allowed!
• We turn Mh≈MZ| cos 2β|+RC toRC= 126 GeV - f(MA, tan β)
ie. we ”trade” RC with the measured Mh
MSSM with only 2 inputs at HO: MA, tan β⇒ model indep. effective approach!
• Constraints on the low tan β region:– H→WW,ZZ in SM– H→tt in BSM scenarios– H→hh and A →hZ..Use current data for constraints...
Quevillon+AD
ICTP School, 13/06/2013 Implications of the Higgs discovery – A. Djouadi – p.18/26
4. Other implications from the MSSM
Sets stingent constraints on pMSSM regimes/benchmark scen arios?• Heavier CP–even H being the observed Higgs is now excluded..• Close h,H,A,H± (intense coupling regime) excluded..• Small αeff scenario with ghbb ≈ 0 and thus small Γh:ruled out by LHC/Tevatron data: ex: loose Wh →ℓνbb signal..• gluophobic h with ghgg ≪ gHSMgg due to squark loops?ruled out by ZZ,WW, γγ signals at LHC (and also the h mass)
But some difference with the SM!a >∼ 2σ excess in H → γγ.• Statistical fluctuation?• Systematics problem?• Maybe QCD uncertainties?
or a combination of the three..Hope it is due to SUSY!– total Higgs width suppressed?– SUSY effects in h γγ loop?
∆thLHCHWG
∆thµ+PDF+EFT
ATLAS ⊕ CMS
ATLAS
CMS
MH = 126 GeV √s = 7⊕ 8 TeV
RH→γγ
σobs/σSM
2.521.510.50
ICTP School, 13/06/2013 Implications of the Higgs discovery – A. Djouadi – p.19/26
4. Other implications for the MSSM
A 126 GeV Higgs provides information on BSM and SUSY in partic ular:•MH=119 GeV would have been a boring value: everybody OK..•MH=145 GeV would be a devastating value: mass extinction..•MH≈126 GeV is Darwinian: (natural) selection among models..SUSY spectrum heavy; except maybe for weakly interactingsparticles and also stops ⇒ more focus on them in SUSY searches!
One has to include other Higgs/SUSY searches in particular:•H/A/H± searches at the LHC are becoming very constraining..• SUSY searches and flavor constraints are to be taken into acco unt.• No more room for some search channels such as H/A → µµ,bb,..(need to start thinking bout changing the benchmark scenari os....)• Some search channels at low tan β still relevant: H →WW,ZZ,tt,hh,..(need to continue/adapt the SM Higgs searches at high masses !)
7–8 TeV LHC for the lightest h and 13–14 TeV LHC for H/A/H +?and maybe some supersymmetric particles will show up?
ICTP School, 13/06/2013 Implications of the Higgs discovery – A. Djouadi – p.20/26
5. What next?Even if no sign of BSM physics is seen: is Particle Physics “cl osed”?
No! Need to check that H is indeed responsible of sEWSB (and SM -like?)Measure its fundamental properties in the most precise way:
• its mass and total decay width (invisible width due to dark ma tter?),• its spin–parity quantum numbers and check SM prediction for them,• its couplings to fermions and gauge bosons and check that the y areindeed proportional to the particle masses (fundamental pr ediction!),• its self–couplings to reconstruct the potential VH that makes EWSB.Possible for MH≈ 126 GeV as all production/decay channels useful!
ttH
ZH
WH
Hqq
gg→H√
s = 14 TeV
σ(pp → H + X) [pb]
MH [GeV]500400300230180145120100
100
10
1
0.1Zγ
γγ
tt
ZZ
WW
gg
µµ
ss
cc
ττ
bb
BR(H)
MH [GeV]500400300250200145120100
1
0.1
0.01
0.001
0.0001
ICTP School, 13/06/2013 Implications of the Higgs discovery – A. Djouadi – p.21/26
5. What next?
• Look at various H production/decaychannels and measure Nev = σ ×BR• But large errors mainly due to:– experimental: stats, system., lumi...– theory: PDFs, HO/scale, jetology...total error about 20–30% in gg → HHjj contaminates VBF (now 30%)..⇒ ratios of σxBR: many errors out!Deal with width ratios ΓX/ΓY
– TH on σ and some EX errors– parametric errors in BRs– TH ambiguities from Γtot
H
• Achievable accuracy:– now: 20–30% on γγ/VV, ττ/VV– future: few % at HL–LHC!
Moreau+ADSufficient to probe BSM physics?
Baglio+AD
500250115
1.301.151.000.850.70
∆total (NNLO+EW)
MSTW
√s = 7 TeV
σ(gg → H) [pb]
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ICTP School, 13/06/2013 Implications of the Higgs discovery – A. Djouadi – p.22/26
5. What next?Challenge: measurement of Higgs self-couplings and access to VH.
• gH3 from pp → HH+X ⇒• gH4 from pp →3H+X, hopeless.Various processes for HH prod:only gg → HHX relevant...
qq → ZHH
qq′ → WHH
qq′ → HHqq′
gg → HH
√s = 14 TeV, MH = 125 GeV
σ(pp → HH +X)/σSM
λHHH/λSMHHH
5310-1-3-5
40
35
30
25
20
15
10
5
0
Baglio et al., arXiv:1212.5581
� �
HH
H
gg
Q
�
�
V
�
V
HH
� �
V
�
V
�
HH
1
LO QCD
NNLO QCD
NLO QCD
NLO QCD
qq/gg → ttHH
qq → ZHHqq′ → WHH
qq′ → HHqq′
gg → HHMH = 125 GeV
σ(pp → HH+X) [fb]
√s [TeV]
1007550258
1000
100
10
1
0.1
•H → bb decay alone not clean•H → γγ decay very rare,•H → ττ would be possible?•H → WW not useful?– bbττ,bbγγ viable?– but needs very large luminosity.
Maybe even needs an ILC.....ICTP School, 13/06/2013 Implications of the Higgs discovery – A. Djouadi – p.23/26
5. What next?
e−
e+
Z∗•
H
Z
•
e−
e+V∗
V∗
H
νe/e−
νe/e+
•
e+
e−
H
t
t
•
e+
e−
H
H
Z
HHνν
HHZ
Htt
HZ
He+e−
Hνν
MH=125 GeVσ(e+e− → HX) [fb]
√s [GeV]
200 350 500 700 1000 2000 3000
1000
100
10
1
0.1
0.01
Very precise measurementsmostly at
√s<∼ 500 GeV
and mainly in e+e− → ZH(with σ ∝ 1/s) and ZHH, ttH
gHWW ±0.012gHZZ ±0.012gHbb ±0.022gHcc ±0.037gHττ ±0.033gHtt ±0.030λHHH ±0.22MH ±0.0004ΓH ±0.061CP ±0.038
⇒ difficult to be beaten by anything else for ≈ 125 GeV Higgs⇒ welcome to the ILC!
ICTP School, 13/06/2013 Implications of the Higgs discovery – A. Djouadi – p.24/26
5. What next?
Now, this is not the end.
It is not even the beginning to the end.
But it is, perhaps, the end of the beginning.
Sir Winston Churchill, November 1942
We hope that at the end we finallyunderstand the EWSB mechanism,but there is a long way untill then....and there might be many surprises!
ICTP School, 13/06/2013 Implications of the Higgs discovery – A. Djouadi – p.25/26