SMEFT studies of LHC data: status and perspective

(1)

SMEFT studies of LHC data:

status and perspective

Ilaria Brivio

Institut f¨ ur Theoretische Physik,

Universit¨ at Heidelberg

(2)

What is SMEFT?

SMEFT = S tandard M odel E ffective F ield T heory

(3)

What is SMEFT?

SMEFT = S tandard M odel E ffective F ield T heory

What is an EFT?

a field theory that approximates

another one in a specific

kinematic/parameters limit

(4)

Example: Fermi interactions

E mW

! 1

9G F „ 1

m

²

W ` O ´

E

⁴

m

⁴_W

¯

EFT = QFT valid in a regime E{m

W

! 1 Ø Taylor expansion in E{m

W

(5)

the EFT can also be formulated from the bottom up . One specifies:

fields & symmetries at the E of the measurement + power counting

(6)

Example: Fermi interactions

fields & symmetries at the E of the measurement + power counting ñ L EFT “ ř

i C i O i

C i = Wilson coefficients: O i = operators

(7)

fields & symmetries at the E of the measurement + power counting ñ L EFT “ ř

i C i O i

knowledge of the SM is not required.

the EFT can match any model leading to β decays.

(8)

Example: Fermi interactions, from the bottom up

1933 4-fermion interaction made of known fields (`ν) and QED-invariant

G F p pγ ¯

µ

nqp¯ eγ

µ

νq

(9)

Example: Fermi interactions, from the bottom up

1933 4-fermion interaction made of known fields (`ν) and QED-invariant

G F p pγ ¯

µ

nqp¯ eγ

µ

νq

§ energy spectra ñ G F » p290 GeV q

^´2

» v

^´2

Ñ scale of underlying physics!

§ all β-decays have the same G F

§ angular distributions ñ the currents have left-handed chirality

Ñ very strong hints at the nature of EW interactions

(10)

SMEFT is the new Fermi theory

Standard Model Effective Field Theory:

The EFT constructed with Standard Model field & symmetries Ñ expansion in canonical dimensions d :

L

_SMEFT

“ L

_SM

` 1

Λ L

₅

` 1

Λ

²

L

₆

` 1

Λ

³

L

₇

` 1

Λ

⁴

L

₈

` . . . L d “ ÿ

i

C i O

^pdq

i

Introducing explicitly a new-physics scale parameter Λ, all C i are dimensionless.

Ñ Taylor series in v{Λ or E {Λ (multi-scale!)

(11)

d=6: the Warsaw basis

Grzadkowski,Iskrzynski,Misiak,Rosiek 1008.4884

(12)

(13)

SMEFT is the new Fermi theory

Standard Model Effective Field Theory:

The EFT constructed with Standard Model field & symmetries Ñ expansion in canonical dimensions d :

L

_SMEFT

“ L

_SM

` 1

Λ L

₅

` 1

Λ

²

L

₆

` 1

Λ

³

L

₇

` 1

Λ

⁴

L

₈

` . . . L d “ ÿ

i

C i O

^pdq

i

SMEFT describes „ any beyond-SM physics living at Λ " v (nearly decoupled)

measure C i to extract information about BSM!

(14)

A worthy challenge!

new physics seems indeed

nearly decoupled

(15)

A worthy challenge!

new physics seems indeed nearly decoupled

collider physics is entering a precision era

we are

HERE

(16)

A worthy challenge!

indirect searches more and more competitive

with direct ones

02

direct

ATL-PHYS-PU

indirect

(17)

A worthy challenge!

indirect searches more and more competitive

with direct ones SMEFT-based searches at the LHC are crucial

+ a proper QFT :

renormalizable order by order, well-defined radiative corrections and RGE + minimal commitment to a specific UV

+ systematically includes all BSM effects, compatible with assumptions

+ universal language for data interpretation: can connect to other experiments

(18)

A booming field

2010 2012 2014 2016 2018 2020 0

20 40 60 80 100 120

InspireHEP entries

SMEFT or “standard model effective field theory”

(“effective field theory” or “eft”)

and (cn atlas or cn cms)

(19)

A booming field

SMEFT or “standard model effective field theory”

(“effective field theory” or “eft”) and (cn atlas or cn cms)

2010 2012 2014 2016 2018 2020 0

50 100 150 200

InspireHEP entries refersto:recid:866649

+ dedicated seminar series, conferences, working groups. . .

(20)

SMEFT @ LHC: status

calculation measurement global analysis interpretation

(21)

SMEFT @ LHC: status

# parameters known for all orders

Lehman(Martin) 1410.4193,1510.00372 Henning,Lu,Melia,Murayama 1512.03433

(22)

SMEFT @ LHC: status

complete bases up to d “ 9

5: Weinberg PRL43(1979)1566

6: Buchmller,Wyler Nucl.Phys.B268(1986)621, Grzadkowski et al 1008.4884 7: Lehman 1410.4193, Henning,Lu,Melia,Murayama 1512.0343

8: Li,Ren,Shu,Xiao,Yu,Zheng 2005.00008, Murphy 2005.00059 9: Li,Ren,Xiao,Yu,Zheng 2007.07899, Liao,Ma 2007.08125

(23)

SMEFT @ LHC: status

complete bases up to d “ 9

interplay with helicity amplitudes

Shadmi,Weiss 1809.09644

Henning,Melia 1901.06747,1902.06754,1902.06747 Ma,Shu,Xiao 1902.06752

Aoude,Machado 1905.11433

Durieux,Kitahara,(Machado),Shadmi,Weiss 1909.10551,2008.09652

Durieux,Machado 1912.08827 Craig,Jiang,Li,Sutherland 2001.00017

(24)

SMEFT @ LHC: status

complete bases up to d “ 9 interplay with helicity amplitudes

geometric formulation

Alonso,Jenkins,Manohar 1511.00724,1605.03602 Dedes,Materkowska,Paraskevas,Rosiek,Suxho 1704.03888 Helset,Paraskevas,Trott 1803.08001

Corbett,Helset,Trott 1909.08470

(Hays),Helset,Martin,Trott 2001.01453,2007.00565

(25)

SMEFT @ LHC: status

geometric formulation

RGE up to d “ 6

Alonso,Jenkins,Manohar,Trott 1308.2627,1310.4838,1312.2014 Grojean,Jenkins,Manohar,Trott 1301.2588

Alonso,Chang,Jenkins,Manohar,Shotwell 1405.0486 Ghezzi,Gomez-Ambrosio,Passarino,Uccirati 1505.03706 Miro,Ingoldby,Riembau 2005.06983

Baratella,Fernandez,Pomarol 2005.07129

(26)

SMEFT @ LHC: status

RGE up to d “ 6

flavor structure

Brivio,Jiang,Trott 1709.06492 Bordone,Cat`a,Feldmann 1910.02641 Faroughy,Isidori,Wilsch,Yamamoto 2005.05366

(27)

SMEFT @ LHC: status

complete bases up to d “ 9 interplay with helicity amplitudes

RGE up to d “ 6 flavor structure

NLO SMEFT

Pruna,Signer 1408.3565

Hartmann,(Shepherd),Trott 1505.02646,1507.03568,1611.09879 Ghezzi,Gomez-Ambrosio,Passarino,Uccirati 1505.03706 (Cullen,Gauld),Pecjak,Scott 1512.02508,1904.06358,2007.15238 Dawson,Giardino 1801.01136,1807.11504,1808.05948,1909.02000 Deutschmann,Duhr,Maltoni,Vryonidou 1708.00460

Grazzini,Ilnicka,Spira 1806.08832

Boughezal,Chen,Petriello,Wiegand 1907.00997 Dedes,Paraskevas,Rosiek,Suxho,Trifyllis 1805.00302 + several NLO QCD

(28)

SMEFT @ LHC: status

RGE up to d “ 6

flavor structure

(29)

SMEFT @ LHC: status

automation § basis handling

Falkowski et al 1508.05895 Aebischer et al 1712.05298 Criado 1901.03501

§ matching & running

(Celis),Fuentes-Martin,(Ruiz-Femenia),Vicente,Virto 1704.04504,2010.16341

Aebischer,Kumar,Straub 1804.05033

§ Feynman rules

Dedes,(Materkowska),Paraskevas,Rosiek,Suxho,(Trifyllis) 1704.03888,1904.03204, Brivio,Jiang,Trott 1907.04692 Corbett 2010.15852

§ LO predictions

Alloul,Fuks,Sanz 1310.5150 Durieux,Mattelaer 1802.07237 Brivio,(Jiang,Trott) 1907.04692,2012.11343

§ NLO QCD predictions

Degrande,Durieux,Maltoni,Mimasu,Vryonidou 2008.11743

(30)

SMEFT predictions in practice: SMEFTsim

a set of models that enable LO Monte Carlo simulations with the complete Warsaw basis

Brivio,Jiang,Trott 1709.06492 Brivio 2012.11343

SMEFTsim.github.io

Automates all the steps required:

1. bosonic: make kinetic terms canonical, define vev. properly fermionic: fix flavor structure

2. choose input parameters

3. Feynman diagram calculation (MC). subtlety: propagator corrections

Example: h Ñ e

^`

e

^´

µ

^`

µ

^´

at tree-level, O pΛ

^´2

q = SM- L

₆

interference

(31)

SMEFT flavor structure

also: Faroughy,Isidori,Wilsch,Yamamoto 2005.05366

w/o flavor assumptions L

₆

has 2499 free parameters

›

O He,pr “ pH Ð Ñ

iD

µ

Hqp¯ e p γ

^µ

e r q has 9 independent par.

O ledq,prst “ p l ¯ p i e r qp d ¯ s q t i q has 162

freedom can be reduced imposing a symmetry. Maximal:

Up3q

⁵

” U p3q q ˆ Up3q u ˆ Up3q d ˆ U p3q l ˆ U p3q e

Ñ only invariant contractions allowed

Ñ Yukawa couplings typically promoted to spurions:

Y u ÞÑ Ω u Y u Ω

^:

q , Y d ÞÑ Ω d Y d Ω

^:

q , Y e ÞÑ Ω e Y e Ω

^:

l

›

O He,pr δ pr has 1 independent par.

O ledq,prst pY e

^:

q pr pY d q st has 2

L

₆

+ U p3q

⁵

has 85

free parameters

(32)

SMEFT flavor structure

also: Faroughy,Isidori,Wilsch,Yamamoto 2005.05366

several options implemented:

general free indices 2499

U35 Up3q q ˆ U p3q u ˆ U p3q d ˆ Up3q l ˆ Up3q e 85 MFV Up3q q ˆ U p3q u ˆ U p3q d ˆ Up3q l ˆ Up3q e

`leading spurion insertions 9Y u Y u

^:

, Y d Y d

^:

, . . . 120

topU3l Up2q q ˆ U p2q u ˆ U p2q d ˆ Up3q l ˆ Up3q e 182

top Up2q q ˆ U p2q u ˆ U p2q d ˆ Up1q

³

l`e 275

(33)

Input parameters

O n g i P

SM

input obs. L param. predicted obs.

α

s

, d

_N

, m

_Z

, α

em

, G

F

,m

h

, m

f

,

meson decay/osc

g

s

, θ

_QCD

, g

₁

, g

w

, v, λ, y

f

,

θ

_1,2,3

, δ CKM

m

_W

, Γ

h

, Γ

Z

,

σ p pp Ñ X q

. . .

(34)

Input parameters

O n g i P

SM

O

_n

“ F

_n^SM

p g q

G

F

“

^?_2v¹2

(35)

Input parameters

O n g i P

SM

O

_n

“ F

_n^SM

p g q G

F

“

^?_2v¹2

g

i

“ K

_i^SM

p O q

v “

₂1{4¹

?

_G

F

P “ P

^SM

p g q “ P

^SM

p K

^SM

p O qq

(36)

Input parameters

O n g i P

SMEFT

O

_n

“ F

_n^SM

p g q G

F

“

^?_2v¹2

g

i

“ K

_i^SM

p O q

` 1

Λ

²

F

n^p2q

p g ,C q ` . . .

` 1

Λ

²

K

_i^p2q

p O , C q ` . . .

`

^?_2Λ¹2

´

2C

_Hl^p3q

´ C

_ll¹

¯

` . . .

, K

_i^p2q

“ ´

„ B F

^SM

B g



´1 in

F

n^p2q

(37)

Input parameters

O n g i P

SMEFT

P “ P

^SM

p g q ` 1 Λ

²

«

P

^p2q

p g q ´ B P

^SM

B g

i

„ B F

_n^SM

B g

i



´1

F

n^p2q

ﬀ

` . . .

direct corr. input shift

contribution

(38)

EW input schemes

Two most used options for the EW sector:

tα

em

, m Z , G F u Ñ ∆α

em

” 0

Ñ ∆m

²

W ‰ 0 p„ C HD , C HWB , C Hl

^p3q

, C ll

¹

q

tm W , m Z , G F u Ñ ∆α

em

‰ 0 p„ C HD , C HWB , C Hl

^p3q

, C ll

¹

q

Ñ ∆m

²

W ” 0

(39)

EW input schemes

Two most used options for the EW sector:

tα

em

, m Z , G F u Ñ ∆α

em

” 0

Ñ ∆m

²

W ‰ 0 p„ C HD , C HWB , C Hl

^p3q

, C ll

¹

q

tm W , m Z , G F u Ñ ∆α

em

‰ 0 p„ C HD , C HWB , C Hl

^p3q

, C ll

¹

q

Ñ ∆m

²

W ” 0

(40)

Propagator corrections

i p´η

^µν

` q

^µ

q

^ν

{m

²_W

q p

²

´ m

²_W

` i Γ

W

m

W

»

–1 ` im

W

∆Γ

W

p

²

´ m

_W²

` i Γ

W

m

W

´ p2m

W

´ iΓ

W

q ∆m

W

p

²

´ m

_W²

` i Γ

W

m

W

ﬁ

ﬂ ` O pΛ

^´4

q

(41)

Example: H Ñ 4f in the SMEFT

① corrections to SM diagrams

9 g

µν

(SM-like)

9 g

µν

p¨q´p

ν

q

µ

(Z

µν

Z

^µν

h)

δg L , δg R

´im Z δΓ Z ` p2m Z ´ iΓ Z qδm Z

p

²

´ m

²

Z ` iΓ Z m Z

② genuine SMEFT diagrams

h γ γ

h γ(Z) Z(γ)

h Z

h W⁻

(42)

Example: h Ñ 4 f in the SMEFT

Results with U p3q

⁵

symmetry, tm W , m Z , G F u inputs.

Γ “ Γ SM

” 1 ` ř

α

C ¯

α

N

α

ı , C ¯

α

“ C

α

v

²

Λ

²

Ó

(43)

SMEFT @ LHC: status

calculation measurement global analysis interpretation Higgs + EW

Alves et al 1211.4580,1805.11108, Butter et al 1604.03105

Corbett et al 1509.01585, de Blas et al 1608.01509,1710.05402,1910.14012 Ellis,Murphy,Sanz,You 1803.03252 da Silva Almeida et al 1812.01009 Biek¨otter,Corbett,Plehn 1812.07587, Dawson,Homiller,Lane 2007.01296

top

Englert et al 1506.08845,1512.05560,1901.03164

Cirigliano,Dekens,deVries,Mereghetti 1605.04311 Hartland et al 1901.05965 Brivio et al 1910.0306, Durieux,Irles,Miralles,Pe˜nuelas,P¨oschl 1907.10619

Higgs + EW + top

Ellis,Madigan,Mimasu,Sanz,You 2012.02779

top + B physics

Bißmann,(Erdmann),Grunwald,Hiller,Kro¨oninger 1909.13632, 2012.10456 Bruggisser,Sch¨afer,Westhoff,VanDyk 2101.07273

diboson (+ VBS)

Baglio,Dawson,Homiller,(Lane,Lewis) 1812.00214, 1909.11576, 2003.07862 Ethier,Gomez-Ambrosio,Magni,Rojo 2101.03180

Higgs combination within ATLAS

2004.03447, ATLAS-CONF-2020-053

impact analysis of NLO corrections and quadratic SMEFT terms several statistical methods: information geometry, bayesian reweighting,

replica model, Partial Component Analysis. . .

(44)

Global analysis of top quark observables

§ U p2q q ˆ U p2q u ˆ Up2q d

§ top interactions only Ñ 24 param.

§ up to NLO QCD, quadratic SMEFT (predictions with SMEFT@NLO)

§ fitted with SFitter

Brivio,Bruggisser,Maltoni,Moutafis,Plehn, Vryonidou,Westhoff,Zhang 1910.03606

also:SMEFiT. Hartland,Maltoni,Nocera, Rojo,Slade,Vryonidou,Zhang 1901.05965 TopFitter1506.08845,1512.03360

t^t

¯

single

^t

t

¯

^tZ

,

^t^tW

¯

tZ

(45)

A typical issue: flat directions

e.g. q q ¯ Ñ t ¯ t at tree-level, linear order in C i :

¯q q

¯t t

+

q¯ q

¯t t

(46)

e.g. q q ¯ Ñ t ¯ t at tree-level, linear order in C i :

¯q q

¯t t

+

q¯ q

¯t t

q

L

u

R

d

R

ˆ Q

^L

t

R

(47)

¯q q

¯t t

+

q¯ q

¯t t

q

L

u

R

d

R

ˆ Q

^L

t

R

ˆ σ

¹i

¨

¹

¨ σ

ⁱ

(48)

¯q q

¯t t

+

q¯ q

¯t t

q

L

u

R

d

R

ˆ Q

^L

t

R

ˆ σ

¹i

¨

¹

¨ σ

ⁱ

ˆ T

¹A

¨

¹

¨ T

^A

= 14 operators

interfering with SM:

7 4-fermion operators

C LL

⁸

„ C Qq

^p1,8q

, C Qq

^p3,8q

C LR

⁸

„ C tq

⁸

C RL

⁸

„ C Qu

⁸

, C Qd

⁸

C

⁸

„ C

⁸

, C

⁸

(49)

¯q q

¯t t

∆σ

_t^int_t_¯

9 ”

C

_LL⁸

` C

_RR⁸

` C

_LR⁸

` C

_RL⁸

ı ˆ

1 ` β

_t²

c

_t²

` 2m

t²

s

˙

` ”

C

_LL⁸

` C

_RR⁸

´ C

_LR⁸

´ C

_RL⁸

ı 2β

t

c

t

β

t²

“ 1 ´ 4m

²t

{s

c

t

“ cos θp~ p

t

, ~ p

q

q in c.m. frame

breaking down each pairs requires ÑNLO QCD

Ñ pC

i

C

j

q terms

Ñ other processes (eg. single top)

the two pairs can be distinguished already at this order, with

kinematics

(50)

Same vs. different chiralities in t t ¯

∆σ

^intt¯t

9

„

C

LL⁸

`C

RR⁸

` C

LR⁸

`C

RL⁸

 ˆ

1 ` β

t²

c

t²

` 2m

²t

s

˙

`

„

C

LL⁸

`C

RR⁸

´ C

LR⁸

´C

RL⁸

 2β

t

c

t

likelihood contours:

ln L ´ ln L = 1/2

(51)

∆σ

^intt¯t

9

„

C

LL⁸

`C

RR⁸

` C

LR⁸

`C

RL⁸

 ˆ

1 ` β

t²

c

t²

` 2m

²t

s

˙

`

„

C

LL⁸

`C

RR⁸

´ C

LR⁸

´C

RL⁸

 2β

t

c

t

ln L

_max

´ ln L = 1/2 2 ( „ ∆χ

²

“ 1, 4 in Gaussian limit )

σ t

¯

t ` m t t

¯

dist

(52)

∆σ

^intt¯t

9

„

C

LL⁸

`C

RR⁸

` C

LR⁸

`C

RL⁸

 ˆ

1 ` β

t²

c

t²

` 2m

²t

s

˙

`

„

C

LL⁸

`C

RR⁸

´ C

LR⁸

´C

RL⁸

 2β

t

c

t

ln L ´ ln L = 1/2 σ t

¯

t ` m t t

¯

dist charge asymmetry

A C

(53)

Impact of quadratic SMEFT contributions

∆σ

^quad_t¯_t

9

„

pC

_LL⁸

q

²

`pC

_RR⁸

q

²

` pC

_LR⁸

q

²

`pC

_RL⁸

q

²

` 9 2 ˆ

pC

_LL¹

q

²

` pC

_RR¹

q

²

` pC

_LR¹

q

²

` pC

_RL¹

q

²

˙

` 1 ` β

_t²

c

_t²

˘

`

„

pC

_LL⁸

q

²

`pC

_RR⁸

q

²

´ pC

_LR⁸

q

²

´pC

_RL⁸

q

²

` 9 2 ˆ

pC

_LL¹

q

²

` pC

_RR¹

q

²

´ pC

_LR¹

q

²

´ pC

_RL¹

q

²

˙

2β

t

c

_t

`

„

C

_LL⁸

C

_LR⁸

` C

_RR⁸

C

_RL⁸

` 9 2 ˆ

C

_LL¹

C

_LR¹

` C

_RR¹

C

_RL¹

˙

4m

²_t

{s

ln L

max

´ ln L = 1/2 2

( „ ∆χ

²

“ 1, 4 in Gaussian limit ) interf. + quad.

Quadratic terms modify

the geometry of the fit

(54)

(55)

(56)

Next step: top + EW + Higgs

Higgs EW

Top

À 50 parameters

@ LO interference

(57)

Next step: top + EW + Higgs

Ellis,Madigan,Mimasu,Sanz,You 2012.02779

(58)

SMEFT @ LHC: status

(59)

SMEFT @ LHC: status

§ CDE / UOLEA: up to 1-loop

Henning,Lu,Murayama 1412.1837,1604.01019 del Aguila,Kunszt,Santiago 1602.00126 Drozd,Ellis,Quevillon,You 1512.03003 Boggia,Gomez-Ambrosio,Passarino 1603.03660 Ellis,Quevillon,(Vuong),You,Zhang 1604.02445,1706.07765,2006.16260

Fuentes-Martin,Portoles,Ruiz-Femenia 1607.02142 Zhang 1610.00710, Cohen,Lu,Zhang 2011.02484 (Kr¨amer),Summ,Voigt 1806.05171,1908.04798

§ matching via amplitudes up to 1-loop

Craig,Jiang,Li,Sutherland 2001.00017

§ complete tree-level dictionary

de Blas,Criado,P´erez-Victoria,Santiago 1711.10391

§ “v-improved” matching

(Brehmer),Freitas,L´opez-Val,Plehn 1510.03443, 1607.08251

§ automated matching

Criado 1710.06445, Bashki,Chakrabortty,Kumar Patra 1808.04403 Cohen,Lu,Zhang 2012.07851

Fuentes-Martin,K¨onig,Pag`es,Thomsen,Wilsch 2012.08506

§ reduced fits

Gorbahn,No,Sanz 1502.07352, Drozd,Ellis,Quevillon,You 1504.02409 Ellis,(Madigan,Mimasu,Murphy),Sanz,You 1803.03252,2012.02779 Dawson,Homiller,Lane 2007.01296,2102.02823

Bakshi,Chakrabortty,Englert,Spannowsky,Stylianou 2009.13394 Anisha,Bakshi,Chakrabortty,Kumar Patra 2010.04088

(60)

Example: SM + vector triplet

Brivio,Bruggisser,Geoffray,Kr¨amer,Plehn,Summ in preparation

L V “ ´ 1

4 V

_µν

i V iµν ´ g M

2 V

_µν

i W iµν ` m

²

V

2 V

_µ

i V iµ ` g H

2 V

_µ

i pH

^:

i Ð Ñ D iµ Hq

` g l

2 V

_µ^´

ℓγ ¯

^µ

σ i ℓ ` g q

2 V

_µ^´

qγ ¯

^µ

σ i q ` g VH

2 pH

^:

HqV

_µ

i V iµ

(61)

Example: SM + vector triplet

L V “ ´ 1

4 V

_µν

i V iµν ´ g M

2 V

_µν

i W iµν ` m

²

V

2 V

_µ

i V iµ ` g H

2 V

_µ

i pH

^:

i Ð Ñ D iµ Hq

` g l

2 V

_µ^´

ℓγ ¯

^µ

σ i ℓ ` g q

2 V

_µ^´

qγ ¯

^µ

σ i q ` g VH

2 pH

^:

HqV

_µ

i V iµ

field redefinition to remove kinetic mixing

$

’ ’

&

’ ’

%

V

_µⁱ

Ñ 1 b

1 ´ g

_M²

V

_µⁱ

W

_µⁱ

Ñ W

_µⁱ

´ g

M

b 1 ´ g

_M²

V

_µⁱ

matching onto Warsaw basis, up to 1-loop

SMEFT fit Ñ constraints on g i couplings

(62)

L V “ ´ 1

4 V

_µν

i V iµν ´ g M

2 V

_µν

i W iµν ` m

²

V

2 V

_µ

i V iµ ` g H

2 V

_µ

i pH

^:

i Ð Ñ D iµ Hq

` g l

2 V

_µ^´

ℓγ ¯

^µ

σ i ℓ ` g q

2 V

_µ^´

qγ ¯

^µ

σ i q ` g VH

2 pH

^:

HqV

_µ

i V iµ e.g. Q Hl

^p3q

“ pH

^:

i Ð Ñ

D iµ Hqp ℓγ ¯

^µ

σ i ℓq

p C

_Hl^p3q

q

^ij

“ ´ g

l

g

H

4m

²_V

δ

ij

` 1 36864π

²

m

²_V

δ

_ij

1 ´ g

_M²

«

g

_w⁴

p 288 ` 1531g

_M²

` 2989g

_M⁴

q

` g

_w³

p 2642g

H

g

M

` 2340

g

lg

M

` 7942g

H

g

_M³

` 6732g

l

g

_M³

q

` g

_w²

p g

_l²

p´ 102 ` 3054g

M²

q ` g

_H²

p 49 ` 5711g

M²

qq

` g

w

g

M

p 1080g

_H³

` 5400g

_H²

g

l

` 2304g

H

g

_l²

` 432g

_l³

` 1440h

H

g

VH

` 1440g

l

g

VH

q

(63)

L V “ ´ 1

4 V

_µν

i V iµν ´ g M

2 V

_µν

i W iµν ` m

²

V 2 V

_µ

i V iµ

` g H

2 V

_µ

i pH

^:

i Ð Ñ

D iµ Hq ` g l

2 V

_µ^´

ℓγ ¯

^µ

σ i ℓ

fit to EWPO+EW+Higgs preliminary! scaled

likelihood

m V “ 2 TeV , tree-level matching

−3 −2 −1 0 1 2 3

−3

−2

−1 0 1 2 3

−6 −4 −2 0 2 4 6 −6 −4 −2 0 2 4 6

−3

−2

−1 0 1 2 3

0.0 0.2 0.4 0.6 0.8 1.0 1.2

all g i unconstrained

g M

g l

g H

(64)

L V “ ´ 1

4 V

_µν

i V iµν ´ g M

2 V

_µν

i W iµν ` m

²

V 2 V

_µ

i V iµ

` g H

2 V

_µ

i pH

^:

i Ð Ñ

D iµ Hq ` g l

2 V

_µ^´

ℓγ ¯

^µ

σ i ℓ

fit to EWPO+EW+Higgs preliminary! scaled

likelihood

m V “ 2 TeV , 1-loop matching

−3

−2

−1 0 1 2 3

−1.5

−1.0 0.5 0.0 0.5 1.0 1.5

0.2 0.4 0.6 0.8 1.0 1.2

g l

g H

(65)

SMEFT @ LHC: open questions

calculation measurement global analysis interpretation

§ treatment of SMEFT uncertainties, L

₈

terms

§ anomaly constraints?

§ automation of NLO SMEFT EW

§ more NLO SMEFT results

§ machine learning predictions?

§ SMEFT effects in PDFs,

hadronization, extraction of α

s

. . . § fits with 50-60 parameters

§ combination EW+Higgs+top+flavor

§ combinations within the experiments

§ improved treatment of correlations, uncertainties etc

§ SMEFT or HEFT?

§ how to combine with direct searches?

§ 1-loop matching dictionary

§ 2-loop RG running

(66)

Summary

§ SMEFT is the best framework for indirect searches of new physics at LHC Ñ current direct bounds consistent with pv {Λ BSM q ! 1

Ñ collider physics entering precision era

§ A challenging task! Developments are needed in

◎ precision calculations

P numerical predictions & analysis strategies

` statistical analyses

theory understanding . . .

N

W E

§ A community effort: combining is key

S

Ñ both theory and experiment increasingly involved

(67)

Backup slides

(68)

Prospects for HL-LHC

(69)

Prospects for HL-LHC

0 2 4 6 8 10 12 14

Mass scale [TeV]

L = 15 ab-1

, = 27 TeV s

HE-LHC

L = 3 ab-1

, = 14 TeV s

HL-LHC

L = 15 ab-1

, = 27 TeV s

HE-LHC

L = 3 ab-1

, = 14 TeV s

HL-LHC Discovery (dash) 95% CL Limit (solid), 5

Model spin

✁

❍

✰✰

❍

❾❾

✂✄❤☎

➧

☎

✆

☎

✆

■❍ 0

❍

✰✰

❍

❾❾

✂✄❤☎

➧

☎

✆

☎

✆

◆❍ 0

▲✝✂t✄ 0

▲✝✂t✞ 0

▲✝♣✟✐r♣r♦✠ ✂❜✄ 0

☎

✡

✂☎☛

2 1

☞

✌✍❛✈②

♠

✎

♠

❊ 2

1

☞

▼❛❥✏✑❛♥❛

✂☎q

✒

q

✓

2 1

✝

✡

✂

✔✔ 2

1

❲

✓

❘

✂t

✒

❜✂❜

✒

❜☎☞ 1

❲

✓

❙❙ ▼

✂☎☞ 1

❲

✓

❙❙ ▼

✂✄☞ 1

❩

✓

❙ ❙▼

✂✄

✰

✄

❾ 1

❩

✓

❙ ❙▼

✂☎

✰

☎

❾ 1

❩

✓

✕

✂☎

✰

☎

❾ 1

❩

✓

❙ ❙▼

✂t

✒

t 1

❩

✓

❚✖✷

✂t

✒

t 1

●

❘❙

✂t

✒

t 1

●

❘❙

✂❲

✰

❲

❾ 1

❍✗✘✂✗✗ 1

❑❑ ✂ ❜ 2

Section

HL/HE-LHC

5.1.1 5.1.1 5.1.1 5.1.1 5.2.1 5.2.1 5.2.3 5.2.4 6.3.1 5.1.1 5.1.1 5.1.3 5.1.3 6.4.6 6.2.6 6.2.6 6.2.7 6.2.4 6.2.5 6.2.4 6.2.5 6.2.5 6.4.6 6.2.3 6.4.6 6.2.2 6.2.2 6.4.6 6.4.4 6.4.4 6.1.1

arXiv:1812.07831

Yellow report on LH-LHC and HE-LHC physics 1812.07831

(70)

d=6: the Warsaw basis

(71)