G. Moreau Laboratoire de Physique Thorique, Orsay, France Based on - - PowerPoint PPT Presentation

• G. Moreau

Laboratoire de Physique Théorique, Orsay, France

Based on arXiv:1210.3977 (will be updated tuesday) & Work in progress with A. Djouadi

Aspects of Aspects of Higgs Higgs rate rate fi fits ts

Warsaw

• 17/03/2013 -

« Electroweak Breaking After First Three Years at the LHC »

Outline

II) Constraining single Extra-Fermions I) The Higgs fits with Extra-Fermions II) Fitting ratios of signal strengths

1/24 ¡

B – The interests of rate ratios A - Focusing on new fermions I) Get rid of the theoretical uncertainty

Today : The LHC has discovered a resonance of ~ 125.5 GeV it is probably the B.E.Higgs boson => EWSB mechanism + Tevatron and LHC provide 58 measurements of the Higgs rates = new precious source of indirect information on BSM physics nature of the EWSB : within the SM or a BSM context !?

2/24 ¡

I) The Higgs fits with Extra-Fermions A - Focusing on new fermions

On the theoretical side: New fermions arise in most (all?) of the SM extensions, – little Higgs [fermionic partners] – supersymmetry [gauginos / higgsinos] – composite Higgs [excited bounded states] – extra-dimensions [Kaluza-Klein towers] – 4th generations [new families] – GUT [multiplet components] – etc… What are the present constraints on extra-fermions from all the experimental Higgs boson results ?

3/24 ¡

f ’ ¡ f ’’ ¡ h ¡ fR

SM ¡

fL

SM ¡

4/24 ¡

Effective approach : Corrections on the Higgs couplings from any extra-fermions (via mixing, new loops) Modifications of Yf Yukawa couplings via (f ’) EF mixings : Lh = − ctYt h ¯ tL tR − cbYb h ¯ bL bR − cτYτ h ¯ τL τR + Chγγ α πv h F µνFµν + Chgg αs 12πv h GaµνGa

µν + h.c.

5/24 ¡

Chgg = 2C(t) A[τ(mt)] (ct + cgg) + 2C(b) A[τ(mb)] cb + 2C(c) A[τ(mc)],

Chγγ = Nt

c

6 Q2

tA[τ(mt)] (ct + cγγ) + Nb c

6 Q2

bA[τ(mb)] cb + Nc c

6 Q2

cA[τ(mc)] + Nτ c

6 Q2

τA[τ(mτ)] cτ + 1

8A1[τ(mW)],

b’ , q5/3 , … b’ , q5/3 , …

σgg!h σSM

gg!h

'

• (ct + cgg)A[τ(mt)] + cbA[τ(mb)] + A[τ(mc)]
• 2
• A[τ(mt)] + A[τ(mb)] + A[τ(mc)]
• 2

Γh! ΓSM

h!

'

• 1

4A1[τ(mW )] + ( 2 3)2(ct + c)A[τ(mt)] + ( 1 3)2cbA[τ(mb)] + ( 2 3)2A[τ(mc)] + 1 3c⌧A[τ(m⌧)]

• 2
• 1

4A1[τ(mW )] + ( 2 3)2A[τ(mt)] + ( 1 3)2A[τ(mb)] + ( 2 3)2A[τ(mc)] + 1 3A[τ(m⌧)]

• 2

, σh¯

tt

σSM

h¯ tt

' |ct|2

Γh!¯

bb

ΓSM

h!¯ bb

' |cb|2

, Γh!¯

⌧⌧

ΓSM

h!¯ ⌧⌧

' |c⌧|2 6/24 ¡

Higgs production cross sections over their SM expectations : Higgs partial decay widths over the SM predictions (no new channels) :

7/24 ¡

Measured signal strengths all of the form (exp. selection efficiencies) : For the fit analysis, we define a function :

µp

s,c,i '

gg!h|s +

✏hqq ✏gg!h|p s,c,i SM hqq|s + ✏hV ✏gg!h|p s,c,i SM hV |s + ✏h¯

tt

✏gg!h|p s,c,i h¯ tt|s

SM

gg!h|s + ✏hqq ✏gg!h|p s,c,i SM hqq|s + ✏hV ✏gg!h|p s,c,i SM hV |s + ✏h¯

tt

✏gg!h|p s,c,i SM h¯ tt |s

Bh!XX BSM

h!XX

2 = X

p,s,c,i

(µp

s,c,i µp s,c,i|exp)2

(µp

s,c,i)2

2(ct, cb, cτ, cgg, cγγ) d

8/24 ¡

Taking ¡the ¡latest ¡experimental ¡results… ¡

9/24 ¡

Higgs fit results : ( 3 free param.)

gg γγ

e χ2

min = 52.36.

+ + + +

cb @cD ct = 1

= 2.08

ct = 1.5

1 0.5

99% 95% 68%

b'

• 4
• 3
• 2
• 1

1 2

• 10
• 5

5 10 15

cgg cgg cb ct @dD

= 1 = 10

ct = 1.8

1

• 1.9

99% 95% 68% 99% 95%

b'

• 10
• 5

5 10

• 40
• 20

20 40

cgg cgg cb ct = 1

= 1

ct = 2.5

1 0.5

99% 95% 68%

@bD

t'

SM

• 4
• 3
• 2
• 1

1 2

• 5

5 10

cgg cgg

cb ct = 1

= 0.75

ct = 1.5

1 0.5

99% 95%

@aD

• 3
• 2
• 1

1

• 5

5 10

cgg cgg

f, ∆χ2 = χ2 −χ2

min,

10/24 ¡

* Determination of and relies on the knowledge of Yt

EF ( ct )

* Yb

EF ( cb ) B(h VV) compensated by σgg->h i.e.

Yb cannot be determined by the (previous) Higgs fit suggestion : avoid compensations by measuring

= 0; cγγ

= 1; cgg = 1; cgg

b (or equivalently the bottom

cesses, ¯ qq ! h¯ bb and gg ! h¯ bb

estigate the y, h ! ¯ bb.

« 3 conclusions for this first fit… » * The SM point ( ) does not belong to the 1σ region } e, χ2

SM = 57.10

Higgs fit results : ( 3 free param.)

gg γγ

e χ2

min = 52.36.

f, ∆χ2 = χ2 −χ2

min,

cb ct = 1

= 0.75

ct = 1.5

1 0.5

99% 95% 68%

• 3
• 2
• 1

1

• 4
• 2

2 4 6 8 10

cgg cgg

cb ct = 1

= 1

ct = 1.5

1 0.5

99% 95% 68%

t'

SM

• 3
• 2
• 1

1

• 4
• 2

2 4 6 8 10

cgg cgg

+ + + +

cb ct = 1

= 1.09

ct = 1.5

1 0.5

99% 95% 68%

b'

• 3
• 2
• 1

1

• 4
• 2

2 4 6 8 10

cgg cgg

cb ct = 1

= 2

ct = 1.5

1 0.5

99% 95%

b'

• 3
• 2
• 1

1 2

• 5

5 10

cgg cgg

AFTER MORIOND...

Varying the last parameter :

|cτ|

cb ct = 0.05

= 1.09

ct = 1.5

1 0.5

99% 95% 68%

• 3
• 2
• 1

1

• 2

2 4 6 8 10

cgg cgg

+ + + +

cb ct = 1

= 1.09

ct = 1.5

1 0.5

99% 95% 68%

b'

• 3
• 2
• 1

1

• 4
• 2

2 4 6 8 10

cgg cgg

cb ct = 1.6

= 1.09

ct = 1.5

1 0.5

99% 95% 68%

• 3
• 2
• 1

1

• 2

2 4 6 8 10

cgg cgg

11/24 ¡

12/24 ¡

Single extra-fermion (starting approximation) => new loop-contributions : (same color repres. as the top)

cgg = 1 C(t)A[τ(mt)]/v  C(t0) Yt0 mt0 A[τ(mt0)] C(q5/3) Yq5/3 mq5/3 A[τ(mq5/3)] + . . .

• 

✓ ◆ ✓ ◆



• c =

1 N t

cQ2 tA[τ(mt)]/v

 3 ✓2 3 ◆2 Yt0 mt0 A[τ(mt0)] N

q5/3 c

✓5 3 ◆2 Yq5/3 mq5/3 A[τ(mq5/3)] Q2

`0 Y`0

m`0 A[τ(m`0)] + . . .

• c

cgg

• q0

= Q2

q0

(2/3)2

II) Constraining single Extra-Fermions

13/24 ¡

independently of Yq’ , masses, SU(2)L repres. (2 free parameters)

cb cΤ 1

1

ct

1

99 95 68

13 83 23 73 53 43

Qpert. Qq 0

2.0 1.5 1.0 0.5 0.0 5 5 10

cgg cΓΓ

cb cgg = 0

= 1

ct

= 1 = -1

99% 95% 68%

Ql¢

• 2
• 1

1 2

• 2

2 4 6 8 10

ct cgg

l’ ¡

independently of Yq’ , masses, SU(2)L repres. (2 free parameters)

AFTER MORIOND...

cb cgg = 0

= 1

ct

= 1 = -1

99% 95% 68%

Ql¢

• 2
• 1

1 2

• 2

2 4 6 8 10

ct cgg

cb ct = 1

= 1

ct

= 1

99% 95% 68%

• 1ê3

8ê3 2ê3

• 7ê3

5ê3

• 4ê3

»Q»pert. Qq¢ = 0

• 2.0
• 1.5
• 1.0
• 0.5

0.0

• 5

5 10

cgg cgg

14/24 ¡ For low-charge q’ , Ex Exts tsa-dys ysfe fermiophilia : …increasing the diphoton rates.

sign ✓−Yq0 mq0 ◆ < 0

(1 free param.)

s, q8/3 ! tW+W+, e, q5/3 ! tW+,

Con

• nclus

usion ions (A)

Potentially stringent constraints on extra-quark electric charges independently of the Yukawa’s, masses, SU(2)L representations The obtained plots can be used for any scenario with new fermions Extra-dysfermiophilia for low-charge single q’ (colored as the top) Already non-trivial & generic constraints on extra-fermions from the Higgs rate fit :

15/24 ¡

+ Difficult and correlated determinations of some Yukawa couplings and parameters for the new loop-contributions to hgg , hγγ.

B – The interests of rate ratios I) Get rid of the theoretical uncertainty

16/24 ¡

The ¡QCD ¡uncertainty ¡ ¡(PDF, ¡αs

2 ¡@ ¡LO, ¡scale ¡dependence) ¡ ¡on ¡the ¡

inclusive ¡Higgs ¡production ¡cross ¡section ¡reaches ¡ ¡~ ¡15-­‑20% ¡ ¡[LHCHWG] ¡

µXX|exp = Nevts.(pp → H → XX)

• i X

i σi(H) BR(H → XX)|SM × L

• µXX|th =
• i X

i σi(H) BR(H → XX)

• i X

i σi(H) BR(H → XX)|SM

δth δexp

..it ¡affects ¡ the ¡ ¡ ¡ ¡’s ¡fit ¡

µXX

17/24 ¡

δexp

µXX µY Y

• exp = Nevts.(pp → H → XX)

Nevts.(pp → H → Y Y )

• i Y

i σi(H)|SM

• i X

i σi(H)|SM

BR(H → Y Y )|SM BR(H → XX)|SM

• µXX

µY Y

• th = X

ggσ(gg →H)+X VBFσ(qq→Hqq)+X HV σ(q¯

q→V H) + X

t¯ tHσ(gg →t¯

tH) Y

ggσ(gg →H) + Y VBFσ(qq→Hqq) + Y HV σ(q¯

q→V H) + Y

t¯ tHσ(gg →t¯

tH)

×

• i Y

i σi(H)|SM

• i X

i σi(H)|SM Γ(H→XX) Γ(H→XX)|SM Γ(H→Y Y ) Γ(H→Y Y )|SM

can ¡cancel ¡out ¡! ¡ Taking ¡ ¡ ¡ ¡ ¡ratios ¡can ¡allow ¡to ¡suppress ¡the ¡QCD ¡error ¡: ¡

µXX

DXY (cf, cV ) (

II) Fitting ratios of signal strengths

18/24 ¡

Lh = cW gHW W H W +

µ W −µ + cZ gHZZ H Z0 µZ0µ

¯

− ctYt H ¯ tL tR − ccYc H ¯ cL cR − cbYb H ¯ bL bR − cτYτ H ¯ τL τR + h.c.

χ2 =

• i

[µi(cf, cV ) − µi|exp]2 (δµi)2

e Yt,c,b,τ = mt,c,b,τ/v ), gHW W = 2m2

W/v, gHZZ = m2 Z/v

and thus contain the e δµi =

• δµi|2

exp + δµi|2 th. 2

Usual ¡fits ¡of ¡the ¡Higgs ¡rates ¡: ¡ ( ¡ ) ¡

19/24 ¡

(2 free parameters)

• Moriond 2013

Signal Strength Fit

99 95 68

1.0 0.5 0.0 0.5 1.0 1.5 1.0 0.5 0.0 0.5 1.0 1.5

cV cf

Symmetry: ¡

cf → −cf, cV → −cV , a

(without ¡the ¡CMS ¡ ¡ diphoton ¡data ¡from ¡ Moriond ¡QCD) ¡

20/24 ¡

Now ¡fitting ¡ratios ¡of ¡the ¡Higgs ¡rates ¡: ¡

χ2

r =

[Dgg

Zγ(cf, cV ) − µZZ µγγ |gg exp]2

[δ(µZZ

µγγ )gg]2

+ [Dgg

τW (cf, cV ) − µττ µWW |gg exp]2

[δ( µττ

µWW )gg]2

+ [DVBF

τW (cf, cV ) − µττ µWW |VBF exp ]2

[δ( µττ

µWW )VBF]2

Dgg

Zγ ≃ Γ(H→ZZ) Γ(H→ZZ)|SM Γ(H→γγ) Γ(H→γγ)|SM

, Dgg

τW ≃ DVBF τW ≃ Γ(H→ττ) Γ(H→ττ)|SM Γ(H→W W ) Γ(H→W W )|SM

DZγ ≃ |cZ|2 |1

4cWA1[mW ] + (2 3)2ctA[mt] + (− 1 3)2cbA[mb] + (2 3)2ccA[mc] + 1 3cτA[mτ]|2

|1

4A1[mW] + (2 3)2A[mt] + (− 1 3)2A[mb] + (2 3)2A[mc] + 1 3A[mτ]|2

−1 DτW ≃ |cτ|2 |cW |2 t A[τ(m) 1] → 1 a

h τ(m) = m2

H/4m2

more Higgs decay c

• →

(for mH ≃ 125 GeV, A1[τ(mW )] ≃ −8.3)

( ¡ ) ¡

21/24 ¡

(2 free parameters) Less informations than on individual signal strengths + Combined Num. & Denominator experimental errors Best-fit regions larger for ratios and containing the domains at 1 (theoretical error in quadrature for => negligible)

• Moriond 2013

Fit of Μ ratios

99 95 68 99 95 68

1.0 0.5 0.0 0.5 1.0 1.5 1.0 0.5 0.0 0.5 1.0 1.5

cV cf

µXX 1σ χ2

22/24 ¡

(2 free parameters) Theoretical error added linearly (no statistical distribution) Best-fit regions larger domains rule out regions at 1 including the SM point ! (more constraining with as no theoretical error)

χ2

2013

ratios

99 95 68 99 95 68

1.0 0.5 0.0 0.5 1.0 1.5 1.0 0.5 0.0 0.5 1.0

• Th. uncertainty

linearly

Moriond 2013

Fit of Μ ratios

99 95 68 99 95 68

SM

1.0 0.5 0.0 0.5 1.0 1.5 1.0 0.5 0.0 0.5 1.0 1.5

cV cf

χ2

r

1σ

χ2

χ2

r

23/24 ¡

• LHC , 14TeV

300 fb1

Fit of Μ ratios

99 95 68

0.0 0.2 0.4 0.6 0.8 0.8 0.6 0.4 0.2 0.0

cV cf

• LHC , 14TeV

3000 fb

1

Fit of Μ ratios

99 95 68

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.5 0.4 0.3 0.2 0.1 0.0

cV cf

Assuming ¡the ¡statistical ¡error ¡to ¡decrease ¡like ¡1/ ¡ ¡ ¡ we ¡add ¡up ¡14TeV ¡LHC ¡results ¡in ¡the ¡fits… ¡ ¡ ¡ ¡ ¡ ¡ ¡dominated ¡by ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡=> ¡constant ¡region ¡sizes ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡uncertainties ¡decrease ¡=> ¡more ¡precise ¡c’s ¡ ¡

|ex s, √σiL

χ2

δth

χ2

r

Crucial ¡ ¡ ¡ ¡ ¡ ¡rôle ¡

χ2

r

Con

• nclus

usion ions (B)

Combining the fits of the signal strengths and of their ratios can turn out to be crucial for the precise determination of the Higgs couplings @ LHC. Fitting the ratios of Higgs rates already improves the constraints on the cf , cV parameters (for linear combination of exp./th. uncertainties)

24/24 ¡

Back up