recent SMEFT analysis at e+e- · recent SMEFT analysis at e+e-Junping Tian (U. of Tokyo) ILC-JP...

recent SMEFT analysis at e+e-

Junping Tian (U. of Tokyo)

ILC-JP Annual Physics &Detector Meeting, March 12-13, 2020

arXiv:1708.09079, 1708.08912; + papers in preparation

2

Global Fit: why do we need it?

suppose we discover a deviation in, e.g. cross section of e+e- -> ZH -> (μμ) (bb)

Z

ZHe+

e<

b

b̄

μ−

μ+

• hbb coupling? • hZZ coupling? • Zμμ coupling? • Zee coupling? • new diagrams?

then we would like to know which coupling is deviated:

3

From observables to couplings — Global Fit

�2 =n�

i=1

(Yi � Y �

i

�Yi)2

n: number of independent observables

Yi: measured values by experimentsYi’: predicted values by underlying theory

ΔYi: measurement uncertainty

kappa formalism

SM Effective Field Theory formalism

(Ai = Z,W, t)

(Bi = b, c, ⌧, µ, g, �, Z,W : decay)Y 0i= Fi ·

g2HAiAi

· g2HBiBi

�0

gHXX = �X ·gSMHXX

4

From observables to couplings — Global Fit

�2 =n�

i=1

(Yi � Y �

i

�Yi)2 + (Yj � Y �

j )T C�1j (Yj � Y �

j )

in case there are correlated observables

Yj: column vector of correlated observables

Cj: covariance matrix for those observables

one example: TGCs in SMEFT fit

5

BSM territory: can deviations be represented by single κZ?

Z

ZHe+

e<

Z

ZH

e +

e <

Z

ZH

e +

e < H Z

Z*∝ κ2

Z ∝?

σ(e+e− → Zh)SM

=Γ(h → ZZ*)

SM= κ2

Z ?

one question in kappa formalism:

6

�L = (1 + �Z)m2

Z

vhZµZµ + �Z

h

2vZµ�Zµ�

the answer is model dependent

Z

ZHe+

e<

�= Z

ZH

e +

e <

Z

ZH

e +

e < H Z

Z*

• BSM can induce new Lorentz structures in hZZ

• need a better, more theoretical sound framework

7

Le� = LSM + �L

= LSM +�

i

ci

�di�4Oi

• (background) kappa formalism not suitable for precision Higgs coupling determination @ future e+e-: model-dependent; radiative corrections

• SMEFT provides a more model independent formalism

• most general effects from BSM represented by higher dimensional ops.

• respect SU(3)xSU(2)xU(1) gauge symmetries

• consistently relate BSM effects in Higgs, W/Z, top, 2-fermion physics: provide a global view of roles of various measurements @ future e+e-

introduction: SM Effective Field Theory @ future e+e-

a global view of physics @ e+e-

8

Higgs

Top EW

BSM

9

global SMEFT fit @ e+e-

• 10 operators modifying couplings for h/Z/W/γ

(Barklow, Fujii, Jung, Peskin, JT, arXiv:1708.09079)

next: highlight a few important implications

Φ: higgs field W, B: SU(2), U(1) gauge L, e: left/right electron

• in total, 23 parameters (see later slides)

(“Warsaw” basis by Grzadkowski et al)

10

Z

ZH

e +

e <

Z

ZHe+

e<

Z

ZH

e +

e <

Z

ZHe+

e<

Z

Z He+

e<

Z

ZHe+

e<

e+e- ->Zhh e+e- ->Zh Z-pole

• Higgs coupling helped by EWPOs at Z-pole: ALR, Γl

• Z coupling helped by Higgs meas. at high √s: δσ ~ s/m2Z

recap 2: Higgs couplings are related to W-/Z- couplings (EWPOs)

+(c′ HL, cHE)

11

Z

Z He+

e<

Z

ZHe+

e<Z

Z

H

e+

e<

ISR

Z

new ideas: improving EWPOs @ ILC250

foreseen a factor of 10 better ALR keep exploring this new idea

a free gift by ISR: Higgs factory is meantime a Z factory

~108 Z events by ILC250, without any change of accelerator

more over, polarized beams

ILC250 = ILC250 + 100xLEP/SLC

radiative return

12

recap 4: role of beam polarizations

P(e-,e+)

(-1,+1)

(+1,-1)

gcos θw

(12

− sin2 θw)

gcos θw

(−sin2 θw)

g sin θw

g sin θw

gcos θw

(cHL + c′ HL)

gcos θw

(cHE)

• large cancellation in (+1,-1) -> weaker dependence on cWW

• ALR in σZH -> improve cWW, cHL+cHL’ and cHE

ζZ ζAZ

• sensitive to different couplings -> lift degeneracy

13

recap 4: role of beam polarizations (e+e- -> Zh)

δσL = − cH + 7.7(8cWW) + . . .

δσR = − cH + 0.6(8cWW) + . . .√s=250 GeV

δσ0 = − cH + 4.6(8cWW) + . . .

(8cWW) ~ 0.16% from other meas.

0.6

e−R

Bμcontribution from

almost cancels out

why?

up to a difference in Z/γ propagator suppressed by m2

Z

s

14

+ 4 SM parameters: g, g’, v, λ10 operators (h,W,Z,γ): cH, cT, c6, cWW, cWB, cBB, c3W, cHL, c’HL, cHE

+ 5 operators modifying h couplings to b, c, τ, μ, g

+ 2 parameters for h->invisible and exotic+ 2 operators for contact interactions with quarks

global SMEFT fit: full formalism (23 pars.)

15

+

Electroweak Precision Observables

Triple Gauge boson Couplings

Higgs observables at LHC & e+e-

+

strategy to determine all the 23 parameters at e+e-

(9)

(3)

(3+12x2)

2 for polarized

• at e+e-, all the 23 parameters can be determined simultaneously

(details in backup)

16

SMEFT: what’s next (an experimenter’s view)

16


0degree of model dependence

SMEFT fit now 23 pars.

precision Higgs couplings; model discriminations;

global views; …

16


reduction




global views; …

16


reductionBSM models




global views; …

16


reductionBSM models

matching; more symmetries;

weak / strong classifications; breaking of SMEFT;

…




global views; …

16


reductionBSM models



…

expansion




global views; …

16


reductionBSM models



…

expansion

including CP-odd ops.




global views; …

16


reductionBSM models



…

expansion


more fermion generations; all couplings




global views; …

16


reductionBSM models



…

expansionSMEFT @ NLO


more fermion generations; all couplings




global views; …

(i) role of each measurement(e.g. Grojean et al, arXiv:1907.04311)

17Is there an easier way?

0 2 4 6 8]-1Integrated Luminosity [ab

0.5

1

1.5

2

2.5

3-1Pr

ecis

ion

Rel

ated

to 2

ab g(hZZ)

g(hbb)g(hcc)2/L

why not following 1/√L? why so different for hZZ/hbb/hcc?

role of each measurement: more transparent understanding(Fujii, Peskin, JT, paper in preparation)

18

role of each measurement: more transparent understanding

19

δghZZ =12

δσZh + 6.4δΓl + 5.3δgZ,eff − 0.015δRγZ − 2.4δκA,eff + 8.9δmh + 0.098δAl + ⋯

New idea: express analytically uncertainty of every EFT coefficient or Higgs coupling directly by a set of input observables

for example: unpolarized e+e- at 250 GeV

σΖh : cross section of e+e- -> Zh Al, Γl : ALR and Γ(Z->ll) at Z-pole gZeff, κΑeff : Triple Gauge Couplings RγZ : BR(h->γZ) / BR(h->ZZ*) mh : Higgs mass

δX =ΔXX

role of each measurement: more transparent understanding(Peskin, JT, paper in preparation)

20

δghZZ =12

δσZh + 6.4δΓl + 5.3δgZ,eff − 0.015δRγZ − 2.4δκA,eff + 8.9δmh + 0.098δAl + ⋯

plug in measurement precisions for current EWPOs + 2 ab-1

for example: unpolarized e+e- at 250 GeV

= 41 ⊕ 66 ⊕ 30 ⊕ 23 ⊕ 14 ⊕ 11 ⊕ 8.7 ⊕ ⋯ × 10−4

EWPOs

TGCsBR(h->γZ)

Higgs mass

σZh

importance hierarchy

21

(ii) what happens at next leading order for SMEFT

• at e+e-, NLO ~ O(α), 1% level• for NLO from W/Z/γ/H, operators constrained to ~<0.01,

overall effect will be < 0.1%

• for NLO from top, operators would be much less constrained, currently ~ O(1) -> overall effect 1% -> potential impact in global fit on Higgs coupling precision

Zhang, et al, arXiv:1804.09766, 1807.02121

Jung, Vos, JT, et al, work in progress

JT@LCWS18

22

our approach to include NLO top effects

• we didn’t try to include full NLO effects for all observables

• instead, include NLO effects that are log-enhanced

• captured by Renormalization Group Evolution (mixing)

·ci ≡ 16π2 dci

d ln μ= γijcj

• ci: Higgs operators; cj: Top operators

• in this way, we can consistently apply power-counting to all observables, e.g. EWPOs (major difference with earlier work)

Jung, Lee, Perello, Vos, JT, paper in preparation

23

typical loop diagrams with logarithmic dependence on top-operators

impact on Higgs couplings

impact on role of EWPOs

impact on synergy with LHC

24

results (I): √s = 250 GeV e+e-

• with the same set of observables, at 250 GeV running only, the global fit will not converge at any of the Higgs factories

• e.g. Higgs couplings could not be determined unambiguously

not surprising, but don’t worry

25

results (II): ILC250 + LHC

• LHC will provide us valuable top data sets, such as

• top operators will be constrained to some extent at (HL-)LHC

(Durieux, et al, arXiv:1907.10619)

pp → tt̄ + Z/W/γ t → Wb

26

results (II): ILC250 + LHC

• with the help of LHC top data, Higgs coupling precisions @ ILC250 are almost restored

• note: top data from LHC Run 2 is not constraining enough

1.75

%

1.99

%

1.81

%

1.75

%

1.28

%

1.62

%

1.89

%

9.79

%

3.64

% 4.16

%

��

0.94

%1.03

%0.55

%0.55

%

1.73

%1.78

%1.1%

1.1%

1.08

%1.15

%0.71

%0.71

%

0.47

%0.64

%0.35

%0.35

%

0.48

%0.54

%0.35

%0.35

% 1.08

%1.11

%1.%

1.%

1.54

%1.59

%0.9%

0.9%

3.95

%3.96

%3.71

%3.71

%

9.05

%9.94

%6.38

%6.38

%

0.3%

0.3%

0.28

%0.28

%

1.51

%1.51

%1.15

%1.16

%

2.2% 2.35

%1.51

%1.51

%

3.27

%3.27

%

0.87

%1.26

%0.66

%0.66

%

w/ top + LHC Run 2w/ top + HL-LHC S2

w/o top w/ top (indirect only)+ HL-LHC S2+ ILC 500 (direct top)

w/o top

0

2

4

6

8

10

Errors[%

]

ILC 250 Stage ILC 500 Stage

12.7%

294%

27

summary

• the capabilities of a e+e- are best represented in SMEFT formalism

• EWPOs/TGCs/Top meas. are related to Higgs couplings

• Higgs/Top measurements from (HL-)LHC are helpful for e+e-

• beam polarizations play an important role

• all proposed Higgs factories can deliver 1% or below precision for many Higgs couplings already at √s = 250 GeV

28

backup

29

recap 1: absolute Higgs couplings (unique role of inclusive σZh)

renormalize kinetic term of SM Higgs field

h (1-cH/2)h

shift all SM Higgs couplings by -cH/2

cH

2�µh�µh

• cH can not be determined by any BR or ratio of couplings

• cH has to rely on inclusive cross section of e+e- -> Zh, enabled by recoil mass technique at e+e-

30

recap 2: Higgs couplings are related to W-/Z- couplings (TGCs)

• higgs coupling helped by meas. of TGCs in e+e- -> WW

• longitudinal modes of W/Z are from Higgs fields

Z

W+

W+W-

W-

A

W+ W-

!Z

W+

W+W-

W-

A

W+ W-

!Z

W+

W+W-

W-

A

W+ W-

!

+(cWW, cBB)

31

recap 3: Higgs couplings are related to themselves

• hZZ/hWW/hγZ/hγγ highly related: SU(2)xU(1) gauge symmetries

(SM structure: kappa like) (Anomalous: new Lorentz structure)

32

recap 3: Higgs couplings are related to themselves (synergy w/ LHC)

• loop induced h->γγ/γΖ depend strongly on cWW/cWB/cBB

two measurements from LHC (model independent)

+ …

+ …

+ …

• h->γγ/γZ at LHC can nicely help higgs couplings at e+e-

Rγγ =BR(h → γγ)

BR(h → ZZ*)RγZ =

BR(h → γZ)BR(h → ZZ*)

528

290

33

SM-like hVV

anomalous hVV

custodial symmetry is broken by cT -> constrained by EWPOs

ci ~ O(10-4-10-3)

• hWW/hZZ ratio can be determined to <0.1%

recap 3: Higgs couplings are related to themselves (hWW/hZZ)

• very important for physics case of any 250 GeV e+e- • hWW can be determined as precisely as hZZ at 250 GeV;

hence precision total width & other couplings

34

coupling ∆g/g kappa-fit EFT-fit

hZZ 0.38% 0.50%

hWW 1.8% 0.50%

hbb 1.8% 0.99%

Γh 3.9% 2.3%

(definition for higgs coupling precision: 1/2 of partial width precision)

ILC250: ∫Ldt = 2 ab-1 @ 250 GeV

SMEFT fit: typical difference with kappa fit

35

recap 4: role of beam polarizations (overall effects)

• 250 GeV e+e-: power of 2 ab-1 polarized ≈ 5 ab-1 unpolarized

ILC250: 2 ab-1 FCCee240: 5 ab-1

(arXiv:1903.01629)

https://arxiv.org/abs/1903.01629

0

0.5

1

1.5

2

2.5

3

3.5

Prec

isio

n of

Hig

gs b

oson

cou

plin

gs [%

]

Z W b τ g c invΓ hΓ γ γZ

1/3×

µ

1/2×

t

1/2×

λ

1/10×

ILC250⊕HL-LHC

ILC500⊕ ILC250 ⊕HL-LHC

dark/light: S1*/S2*

Model Independent EFT Fit LCC Physics WG

36

#qualitative:

precisions at Higgs factories: complementarity with LHC

model independence, hcc coupling

#quantitative (<~1%):hZZ, hWW, hbb, hττ h->invisible/exotic

#synergy:hγγ, hγΖ, hμμ, htt, λ

(arXiv:1903.01629)

https://arxiv.org/abs/1903.01629

37

new operators (to previous SMEFT fit)

38

effect of top operators: example

V V<latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit>

ctWv2

(Q̄�µ⌫t)⌧a�̃W aµ⌫

<latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit>

ctW<latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit>

t<latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit>

higgs operator top operator

log-enhanced

39

results

still preliminary; I will only show a few see more results in talk by S. Jung @ LCWS2019

paper on arXiv soon

40

results (III): polarized vs unpolarized

• polarization now shows its important role

• w/o beam polarizations, even with the help of HL-LHC top data, Higgs coupling precisions @ e+e-250 will suffer a lot

��

HL-LHC S2 + 2 /ab at 250 GeVw/o top

HL-LHC S2 + 5 /ab at 250 GeVw/o top

0.1

0.5

1

5

10

Errors[%

]

Polarized Unpolarized

41

results (IV): √s >= 350 GeV e+e-

• once e+e- -> t t-bar becomes accessible, effects of top operators on the Higgs coupling determination will be well under-control

recent SMEFT analysis at e+e- · recent SMEFT analysis at e+e-Junping Tian (U. of Tokyo) ILC-JP...

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