Relevance and size of EW corrections generic size O ( ) O ( 2 s ) - - PowerPoint PPT Presentation

Electroweak corrections in the determination of αs

Stefan Dittmaier Albert-Ludwigs-Universit¨ at Freiburg

Based on: A.Denner, S.Dittmaier, T.Gehrmann, C.Kurz, Phys.Lett. B679 (2009) 219 [arXiv:0906.0372] A.Denner, S.Dittmaier, T.Gehrmann, C.Kurz, Nucl.Phys. B836 (2010) 37 [arXiv:1003.0986] S.Dittmaier, A.Huss, C.Speckner, JHEP 1211 (2012) 095 [arXiv:1210.0438] S.Dittmaier, A.Huss, K.Rabbertz, to appear in the Les Houches Proceedings soon

Stefan Dittmaier, Electroweak corrections ... High precision fundamental constants at the TeV scale, MITP , March 2014 – 1

Features of and issues in EW precision calculations

Relevance and size of EW corrections generic size O(α) ∼ O(α2

s) suggests

NLO EW ∼ NNLO QCD but systematic enhancements possible, e.g.

• by photon emission

֒ → kinematical effects, mass-singular log’s ∝ α ln(mµ/Q) for bare muons, etc.

• at high energies

֒ → EW Sudakov log’s ∝ (α/s2

W) ln2(MW/Q) and subleading log’s

EW corrections to PDFs at hadron colliders induced by factorization of collinear initial-state singularities, new: photon PDF Instability of W and Z bosons

• realistic observables have to be defined via decay products (leptons, γ’s, jets)
• off-shell effects ∼ O(Γ/M) ∼ O(α) are part of the NLO EW corrections

Combining QCD and EW corrections in predictions

• how to merge results from different calculations
• reweighting procedures in MC’s

Stefan Dittmaier, Electroweak corrections ... High precision fundamental constants at the TeV scale, MITP , March 2014 – 2

Issue of this talk

• EW corrections to two process types important for αs determination:

⋄ jet event-shape observables at e+e− colliders ⋄ jet production at hadron colliders

• review of the situation

⋄ EW corrections under control ? ⋄ future homework ?

Stefan Dittmaier, Electroweak corrections ... High precision fundamental constants at the TeV scale, MITP , March 2014 – 3

Jet event-shape observables at e+e− colliders

Stefan Dittmaier, Electroweak corrections ... High precision fundamental constants at the TeV scale, MITP , March 2014 – 4

Frequently used event-shape observables y

• Thrust:

T = max

• n

P

i |

pi · n| P

i |

pi|

• Normalized heavy jet mass:

ρ = max{M 2

1 , M 2 2 }/s

(Mi = inv. mass flowing into hemispheres Hi defined by plane perpendicular to thrust axis)

• Wide / total jet broadenings:

BW = max{B1, B2}, BT = B1 + B2, Bi = P

j∈Hi |

pj × n| 2 P

k |

pk|

• C parameter:

C = 3(λ1λ2 + λ2λ3 + λ3λ1), {λi} = eigenvalues of Θ = 1 P

i |

pi| X

j

• pj ⊗

pj | pj|

• Jet transition variable:

Y3 = value of ycut at which the event turns from 3-jet to 2-jet type Note: 2-jet configuration appears at an endpoint of dσ(y) dy (e.g. at T → 1) ֒ → shapes of distributions sensitive to 3 and more jets, and thus to αs

Stefan Dittmaier, Electroweak corrections ... High precision fundamental constants at the TeV scale, MITP , March 2014 – 5

Theory prediction for jet event shapes (e+e− → n jets, n≥3) 1 σhad dσ(y) dy = αs CQCD

LO

+ α2

s CQCD NLO

| {z }

R.K.Ellis, Ross, Terrano ’81; Kunszt ’81 Vermaseren, Gaemers, Oldham ’81 Giele, Glover ’92; Catani, Seymour ’96

+ α3

s CQCD NNLO

| {z }

Gehrmann-DeRidder, Gehrmann, Glover, Heinrich ’07–’09; Weinzierl ’08,’09

+ NLL resummation | {z }

Catani, Turnock, Webber, Trentadue ’91,’93

+ NLL/NNLO matching | {z }

Gehrmann, Luisoni, Stenzel ’08

( + NNLL resummation for T | {z }

Becher, Schwartz ’08

) + non-perturbative hadronization effects | {z }

Korchemsky, Sterman ’95; Dokshitzer, Webber ’95,’97 Dokshitzer, Lucenti, Marchesini, Salam ’98

+ α CEW

LO

+ ααs CEW

NLO + α2αs CISR LL

| {z }

Denner, S.D., Gehrmann, Kurz ’09,’10

• Recent NNLO QCD results already included in αs fit to event shapes

Gehrmann, Luisoni, Stenzel ’08; Dissertori et al. ’08; Bethke et al. ’08; Davison, Webber ’08

• NLO EW corrections potentially of same size as NNLO QCD, since O(α) ∼ O(α2

s)

Stefan Dittmaier, Electroweak corrections ... High precision fundamental constants at the TeV scale, MITP , March 2014 – 6

Calculation of NLO corrections

LO diagrams for e+e− → q¯ qg: O(α2αs)

e e q g q γ, Z q e e q g q γ, Zq

q = u, d, s, c, b LO diagrams for e+e− → q¯ qγ: O(α3)

e e q γ q γ, Z q e e q γ q γ, Zq e e e q γ q γ, Z e e e q γ q γ, Z

Comments:

• q¯

qγ final states in LO deliver contributions if γ is merged with q/¯ q, i.e. near 2-jet configurations

• focus of our calculation:

O(α3αs) = NLO EW correction to q¯ qg production = NLO QCD correction to q¯ qγ production

Stefan Dittmaier, Electroweak corrections ... High precision fundamental constants at the TeV scale, MITP , March 2014 – 7

1PI loop insertions in EW one-loop corrections to e+e− → q¯ qg

O(200) diagrams

e e q g q γ,Zγ,Z q e e q g q q q γ,Z e e q g q γ,Z q e e q g q γ,Z q e e q g q γ,Z q e e q g q q e e q q g γ,Z γ, Z e e q q g γ,Z e e q q g

Sample QCD one-loop diagrams for e+e− → q¯ qγ

e e q q γ e γ, Z g q q e e q q γ γ, Z q q g q e e q q γ γ, Z q q g q e e q q γ γ, Z g q q q

Stefan Dittmaier, Electroweak corrections ... High precision fundamental constants at the TeV scale, MITP , March 2014 – 8

Real emission corrections at O(α3αs) and beyond

• e+e− → q¯

qgγ = photon bremsstrahlung to q¯ qg production = gluon bremsstrahlung to q¯ qγ production

• QCD–EW interferences for e+e− → q¯

qq¯ q

e e q q q q e γ/Z γ/Z e e g Z/γ

֒ → non-singular contributions of O(α3αs) = same order as NLO EW Interferences included in our calculation ֒ → effect phenomenologically negligible (< 0.1%)

• higher-order photonic ISR included via leading-log structure functions

up to order LO × O(α3)

Stefan Dittmaier, Electroweak corrections ... High precision fundamental constants at the TeV scale, MITP , March 2014 – 9

Definition of jet observables

Event selection: (closely following the procedure employed by ALEPH)

• 1. Discard particles too close to the beams, i.e. if | cos θi| > cos θcut = 0.965.
• 2. Reject event if Mvisible < 0.9ECM.
• 3. Boost to CM system of observed final-state particles.
• 4. Apply Durham jet algorithm with E recombination and ycut = 0.002 to q, ¯

q, g, γ ֒ → photons appear inside jets

• 5. Reject “photonic events” where photon energy fraction z > zcut = 0.9 in a jet.

Subtleties arising at NLO EW level:

• Step 3 minimizes boost effects from collinear ISR photons

(otherwise two-jet configurations do not always appear at event-shape endpoints)

But: at LEP two-jet events were shifted to endpoints “by hand” ֒ → renders confrontation between theory and LEP results difficult

• Step 5 is not collinear safe

֒ → perturbative result is plagued by quark-mass singularities ∝ α ln mq Solution: include photon fragmentation function with non-perturbative input

Stefan Dittmaier, Electroweak corrections ... High precision fundamental constants at the TeV scale, MITP , March 2014 – 10

Photon–jet separation via photon fragmentation function Dq→γ

Glover, Morgan ’94

Why does a naive γ–jet separation by a jet algorithm not work ?

• collinear quarks and photons have to be recombined → (qγ) = jet
• therwise corrections ∝ ln(m2

q/Q2)

→ perturbative “IR instability”

• quark and gluon jets cannot be distinguished event by event

֒ → common recombination required for quarks/gluons with photons ⇒ (ghard + γsoft) | {z }

EW corr. to 3 jets

and (gsoft + γhard) | {z }

QCD corr. to 2 jets + γ

both appear as 3 jets Solution:

• exclude events with photon energy fraction zγ =

Eγ Ejet + Eγ > z0 for (jet + γ) quasiparticles

• subtract convolution of LO cross section with

DMS

q→γ(zγ, µfact)

˛ ˛ ˛

mass.reg. = Pq→γ(zγ)

" ln m2

q

µ2

fact

+ 2 ln zγ + 1 # ← cancels coll. singularities + DALEPH

q→γ

(zγ, µfact) ← non-perturbative part fitted to ALEPH data on e+e− → jet + γ where Pq→γ(zγ) =

1+(1−zγ )2 zγ

= quark-to-photon splitting function

Stefan Dittmaier, Electroweak corrections ... High precision fundamental constants at the TeV scale, MITP , March 2014 – 11

Numerical results

Total hadronic cross section

Denner, S.D., Gehrmann, Kurz ’09,’10

−0.4 −0.2 0.2 0.4 0.6 0.8 1 1 10 100 1000

σi−σBorn σBorn

√s [ GeV] 0.00001 0.0001 0.001 0.01 0.1 1 10 100 1000 σhad[ nb] e+e− → q¯ q (γ) Born weak O(α) full O(α) O(α)+h.o. LL

• largest EW corrections

due to ISR

(radiative return cut off by cut Mvisible < 0.9√s)

• ISR beyond one loop

relevant (some %) for √s ∼ MZ

• weak corrs. of O(5%),

increasingly negative for large √s

• Note: σhad calculated

to same perturbative order as dσ/dy to obtain a proper normalization

Stefan Dittmaier, Electroweak corrections ... High precision fundamental constants at the TeV scale, MITP , March 2014 – 12

Thrust distribution — normalized to LO hadronic cross section σ0 √s = MZ

Denner, S.D., Gehrmann, Kurz ’09,’10

−0.3 −0.2 −0.1 0.05 0.1 0.15 0.2 0.25 0.3

dσi−dσBorn dσBorn

(1 − T ) 0.05 0.1 0.15 0.2 0.25 0.3 0.35

1 σ0 (1 − T ) dσ dT

Born +Born q¯ qγ weak O(α) full O(α) O(α)+h.o. LL √s = MZ

• large ISR effects

as for σhad

• h.o. ISR ∼ some %
• genuine weak effects
• f few %, but flat
• q¯

qγ final states visible for T → 1

Stefan Dittmaier, Electroweak corrections ... High precision fundamental constants at the TeV scale, MITP , March 2014 – 13

Thrust distribution — normalized to full hadronic cross section σhad √s = MZ

Denner, S.D., Gehrmann, Kurz ’09,’10

0.01 0.02 0.03 0.05 0.1 0.15 0.2 0.25 0.3

dσi−dσBorn dσBorn

(1 − T ) 0.1 0.2 0.3

1 σhad (1 − T ) dσ dT

Born +Born q¯ qγ weak O(α) full O(α) O(α)+h.o. LL √s = MZ

• large ISR effects in dσ

dT

cancel against σhad ֒ → % effects

• h.o. ISR irrelevant

(proper normalization important)

• genuine weak effects

below 0.1%

• q¯

qγ final states ∼ O(2%) for T > ∼ 0.97

Stefan Dittmaier, Electroweak corrections ... High precision fundamental constants at the TeV scale, MITP , March 2014 – 13

Normalized thrust distribution — increasing CM energy √s = 172 GeV

Denner, S.D., Gehrmann, Kurz ’09,’10

0.02 0.04 0.06 0.08 0.1 0.05 0.1 0.15 0.2 0.25 0.3

dσi−dσBorn dσBorn

(1 − T ) 0.1 0.2 0.3

1 σhad (1 − T ) dσ dT

Born +Born q¯ qγ weak O(α) full O(α) O(α)+h.o. LL √s = 172 GeV

• ISR develops structures

that depend on ycut and

• n event selection
• h.o. ISR irrelevant
• genuine weak effects

remain small (∼ 1% at √s = 500 GeV)

• q¯

qγ final states ∼ some % for T > ∼ 0.97

Stefan Dittmaier, Electroweak corrections ... High precision fundamental constants at the TeV scale, MITP , March 2014 – 13

Normalized thrust distribution — increasing CM energy √s = 206 GeV

Denner, S.D., Gehrmann, Kurz ’09,’10

0.02 0.04 0.06 0.08 0.05 0.1 0.15 0.2 0.25 0.3

dσi−dσBorn dσBorn

(1 − T ) 0.1 0.2 0.3

1 σhad (1 − T ) dσ dT

Born +Born q¯ qγ weak O(α) full O(α) O(α)+h.o. LL √s = 206 GeV

• ISR develops structures

that depend on ycut and

• n event selection
• h.o. ISR irrelevant
• genuine weak effects

remain small (∼ 1% at √s = 500 GeV)

• q¯

qγ final states ∼ some % for T > ∼ 0.97

Stefan Dittmaier, Electroweak corrections ... High precision fundamental constants at the TeV scale, MITP , March 2014 – 13

Normalized thrust distribution — increasing CM energy √s = 500 GeV

Denner, S.D., Gehrmann, Kurz ’09,’10

0.02 0.04 0.06 0.08 0.05 0.1 0.15 0.2 0.25 0.3

dσi−dσBorn dσBorn

(1 − T ) 0.1 0.2 0.3

1 σhad (1 − T ) dσ dT

Born +Born q¯ qγ weak O(α) full O(α) O(α)+h.o. LL √s = 500 GeV

• ISR develops structures

that depend on ycut and

• n event selection
• h.o. ISR irrelevant
• genuine weak effects

remain small (∼ 1% at √s = 500 GeV)

• q¯

qγ final states ∼ some % for T > ∼ 0.97

Stefan Dittmaier, Electroweak corrections ... High precision fundamental constants at the TeV scale, MITP , March 2014 – 13

Jet broadenings — yet another example

Denner, S.D., Gehrmann, Kurz ’09,’10

−0.3 −0.2 −0.1 0.05 0.1 0.15 0.2 0.25 0.3

dσi−dσBorn dσBorn

BT 0.1 0.2 0.3 0.4 0.5 0.6 0.7

1 σ0 BT dσ dBT

Born +Born q¯ qγ weak O(α) full O(α) O(α)+h.o. LL √s = MZ −0.3 −0.2 −0.1 0.05 0.1 0.15 0.2 0.25 0.3

dσi−dσBorn dσBorn

BW 0.1 0.2 0.3 0.4 0.5 0.6 0.7

1 σ0 BW dσ dBW

Born +Born q¯ qγ weak O(α) full O(α) O(α)+h.o. LL √s = MZ

Overall size, energy dependence, and qualitative features of EW effects similar for all event shapes.

Stefan Dittmaier, Electroweak corrections ... High precision fundamental constants at the TeV scale, MITP , March 2014 – 14

Jet broadenings — yet another example

Denner, S.D., Gehrmann, Kurz ’09,’10 −0.02 0.02 0.04 0.05 0.1 0.15 0.2 0.25 0.3

dσi−dσBorn dσBorn

BT 0.1 0.2 0.3 0.4 0.5 0.6 0.7

1 σhad BT dσ dBT

Born +Born q¯ qγ weak O(α) full O(α) O(α)+h.o. LL √s = MZ −0.03 −0.02 −0.01 0.01 0.02 0.03 0.05 0.1 0.15 0.2 0.25 0.3

dσi−dσBorn dσBorn

BW 0.1 0.2 0.3 0.4 0.5 0.6 0.7

1 σhad BW dσ dBW

Born +Born q¯ qγ weak O(α) full O(α) O(α)+h.o. LL √s = MZ

Overall size, energy dependence, and qualitative features of EW effects similar for all event shapes.

Stefan Dittmaier, Electroweak corrections ... High precision fundamental constants at the TeV scale, MITP , March 2014 – 14

Jet broadenings — yet another example

Denner, S.D., Gehrmann, Kurz ’09,’10 −0.08 −0.04 0.04 0.08 0.12 0.16 0.2 0.05 0.1 0.15 0.2 0.25 0.3

dσi−dσBorn dσBorn

BT 0.1 0.2 0.3 0.4 0.5 0.6 0.7

1 σhad BT dσ dBT

Born +Born q¯ qγ weak O(α) full O(α) O(α)+h.o. LL √s = 172 GeV −0.06 −0.03 0.03 0.06 0.09 0.05 0.1 0.15 0.2 0.25 0.3

dσi−dσBorn dσBorn

BW 0.1 0.2 0.3 0.4 0.5 0.6 0.7

1 σhad BW dσ dBW

Born +Born q¯ qγ weak O(α) full O(α) O(α)+h.o. LL √s = 172 GeV

Overall size, energy dependence, and qualitative features of EW effects similar for all event shapes.

Stefan Dittmaier, Electroweak corrections ... High precision fundamental constants at the TeV scale, MITP , March 2014 – 14

Jet broadenings — yet another example

Denner, S.D., Gehrmann, Kurz ’09,’10 −0.06 −0.03 0.03 0.06 0.09 0.12 0.05 0.1 0.15 0.2 0.25 0.3

dσi−dσBorn dσBorn

BT 0.1 0.2 0.3 0.4 0.5 0.6

1 σhad BT dσ dBT

Born +Born q¯ qγ weak O(α) full O(α) O(α)+h.o. LL √s = 206 GeV −0.09 −0.06 −0.03 0.03 0.06 0.09 0.05 0.1 0.15 0.2 0.25 0.3

dσi−dσBorn dσBorn

BW 0.1 0.2 0.3 0.4 0.5 0.6

1 σhad BW dσ dBW

Born +Born q¯ qγ weak O(α) full O(α) O(α)+h.o. LL √s = 206 GeV

Overall size, energy dependence, and qualitative features of EW effects similar for all event shapes.

Stefan Dittmaier, Electroweak corrections ... High precision fundamental constants at the TeV scale, MITP , March 2014 – 14

Jet broadenings — yet another example

Denner, S.D., Gehrmann, Kurz ’09,’10 −0.06 −0.03 0.03 0.06 0.09 0.12 0.15 0.05 0.1 0.15 0.2 0.25 0.3

dσi−dσBorn dσBorn

BT 0.1 0.2 0.3 0.4 0.5 0.6

1 σhad BT dσ dBT

Born +Born q¯ qγ weak O(α) full O(α) O(α)+h.o. LL √s = 500 GeV −0.06 −0.03 0.03 0.06 0.05 0.1 0.15 0.2 0.25 0.3

dσi−dσBorn dσBorn

BW 0.1 0.2 0.3 0.4 0.5 0.6

1 σhad BW dσ dBW

Born +Born q¯ qγ weak O(α) full O(α) O(α)+h.o. LL √s = 500 GeV

Overall size, energy dependence, and qualitative features of EW effects similar for all event shapes.

Stefan Dittmaier, Electroweak corrections ... High precision fundamental constants at the TeV scale, MITP , March 2014 – 14

Jet production at hadron colliders

Stefan Dittmaier, Electroweak corrections ... High precision fundamental constants at the TeV scale, MITP , March 2014 – 15

NLO EW corrections to jet and heavy-quark production

• pp → 2 jets

⋄ purely weak NLO corrections known Moretti, Nolten, Ross ’05,’06 (disagree with others); Scharf (prelim.) ’09; S.D., Huss, Speckner ’12 ⋄ photonic NLO corrections unknown (but expected to be <

∼ 1%)

⋄ no EW corrections available for pp → ≥3 jets

• pp → t¯

t

⋄ SM correction Beenakker et al. ’94; Moretti, Nolten, Ross ’06; Kühn, Scharf, Uwer ’06,’13; Bernreuther, Fücker, Si ’08; Hollik, Kollar ’08 ⋄ THDM and MSSM Hollik, Mösle, Wackeroth ’97 ⋄ no EW corrections with top-quark decays yet

• pp → b¯

b

Maina, Moretti, Nolten, Ross ’03; Kühn, Scharf, Uwer ’09

Stefan Dittmaier, Electroweak corrections ... High precision fundamental constants at the TeV scale, MITP , March 2014 – 16

EW corrections to dijet production – typical contributions Tree contributions: O(α2

s), O(αsα), O(α2)

g g g g g g g g g g g g g g g g g g g g g q ¯ q g g g q ¯ q q g g q ¯ q q ui ¯ di ui ¯ di W ui ¯ di ui ¯ di γ, Z ui ¯ di ui ¯ di g

Loop contributions: O(α2

sα)

Note: involves 3-jet final states as well !

8 > > > < > > > : Z, W Z, W Z, W . . . 9 > > > = > > > ; × 8 > > > < > > > : . . . 9 > > > = > > > ; ∗ 8 > > > < > > > : Z, W Z, W Z, W . . . 9 > > > = > > > ; × 8 > > > < > > > : . . . 9 > > > = > > > ; ∗ 8 > > > < > > > : . . . 9 > > > = > > > ; × 8 > > > < > > > : Z, W± . . . 9 > > > = > > > ; ∗

Stefan Dittmaier, Electroweak corrections ... High precision fundamental constants at the TeV scale, MITP , March 2014 – 17

Numerical results

Weak corrections to dijet production – differential cross sections

S.D., Huss, Speckner ’12

10−6 10−4 10−2 100 102 104 1000 2000 3000 4000 5000 6000 M12 [GeV] dσ0/dM12 [nb/GeV] pp − → jj + X √s = 14 TeV −6 −4 −2 2 1000 2000 3000 4000 5000 6000 M12 [GeV] δ [%] δtree

EW+δ1-loop weak

δtree

EW

δ1-loop

weak

10−8 10−6 10−4 10−2 100 102 104 500 1000 1500 2000 2500 3000 kT,1 [GeV] dσ0/dkT,1 [nb/GeV] pp − → jj + X √s = 14 TeV −10 −5 5 10 15 20 500 1000 1500 2000 2500 3000 kT,1 [GeV] δ [%] δtree

EW+δ1-loop weak

δtree

EW

δ1-loop

weak

Weak corrections

• small for integrated XS
• growing in distributions

for larger scales Cancellations between tree and loop corrections (cut-sensitive!)

Stefan Dittmaier, Electroweak corrections ... High precision fundamental constants at the TeV scale, MITP , March 2014 – 18

Weak corrections to dijet production – double-differential cross sections

S.D., Huss, Speckner ’12

−15 −10 −5 5 10 15 20 25 1000 2000 3000 4000 5000 M12 [ GeV] δ [%] y∗ < 0.5 −10 −5 5 10 1000 2000 3000 4000 5000 M12 [ GeV] δ [%] 0.5 < y∗ < 1.0 −10 −8 −6 −4 −2 2 4 6 1000 2000 3000 4000 5000 M12 [ GeV] δ [%] 1.0 < y∗ < 1.5 −6 −4 −2 2 4 1000 2000 3000 4000 5000 M12 [ GeV] δ [%] 1.5 < y∗ < 2.0 −5 −4 −3 −2 −1 1 2 3 1000 2000 3000 4000 5000 M12 [ GeV] δ [%] pp − → jj + X at √s = 14 TeV 2.0 < y∗ < 2.5 δtree

EW +δ1−loop weak

δtree

EW

δ1−loop

weak

Sudakov-like regime (M12 large, y∗ smallp) ֒ → larger corrections Regge-like regime (M12, |y∗| large)

Stefan Dittmaier, Electroweak corrections ... High precision fundamental constants at the TeV scale, MITP , March 2014 – 19

Inclusive jet production @ LHC7 – CMS data and EW corrections

S.D., Huss, Rabbertz ’14

Weak corrections

• ❡

...

• ❡

Stefan Dittmaier, Electroweak corrections ... High precision fundamental constants at the TeV scale, MITP , March 2014 – 20

Inclusive jet production @ LHC7 – CMS data and EW corrections

S.D., Huss, Rabbertz ’14

NLO weak, NLO QCD, and non-perturbative corrections

1 1.2 1.4 10

3

pT (GeV) K

|y| < 0.5 CT10-NLO NLO QCD correction EW correction NP correction

1 1.2 1.4 10

3

pT (GeV) K

0.5 ≤ |y| < 1.0 CT10-NLO NLO QCD correction EW correction NP correction

...

1 1.2 1.4

pT (GeV) K

2.0 ≤ |y| < 2.5 CT10-NLO NLO QCD correction EW correction NP correction

Stefan Dittmaier, Electroweak corrections ... High precision fundamental constants at the TeV scale, MITP , March 2014 – 20

Inclusive jet production @ LHC7 – CMS data and EW corrections

S.D., Huss, Rabbertz ’14

Data w/o EW corrections

...

Stefan Dittmaier, Electroweak corrections ... High precision fundamental constants at the TeV scale, MITP , March 2014 – 20

Inclusive jet production @ LHC7 – CMS data and EW corrections

S.D., Huss, Rabbertz ’14

Data w/ EW corrections

• ✶

• ✶

...

EW effects hardly visible @ 7 TeV, but certainly relevant @ 13−14 TeV with higher luminosity

Stefan Dittmaier, Electroweak corrections ... High precision fundamental constants at the TeV scale, MITP , March 2014 – 20

Conclusions

Stefan Dittmaier, Electroweak corrections ... High precision fundamental constants at the TeV scale, MITP , March 2014 – 21

EW corrections to hadronic event shapes at e+e− colliders

• largest EW corrections due to ISR,

but reduction to % effects by normalization to σhad

• genuine weak effects negligible for LEP energies, at % level for 500 GeV ILC
• q¯

qγ final states separated from 3-jet events via photon fragmentation function ֒ → % effects near 2-jet endpoints of event shapes ⇒ NLO EW corrections completely known and sufficient

(minor relevance for JADE/LEP , but relevant at ILC)

EW corrections to jet production at hadron colliders

• weak corrections to dijet and inclusive-jet production ∼ 5−10% in TeV range

(significant cancellations between EW tree and loop contributions)

• yet unknown:

⋄ photonic corrections ( <

∼ 1% expected)

⋄ EW corrections to (3-jet)/(2-jet) cross-section ratio

֒ → significant cancellations expected (but certainly less dramatic than in e+e−) ⇒ Further work required !

Stefan Dittmaier, Electroweak corrections ... High precision fundamental constants at the TeV scale, MITP , March 2014 – 22

Backup slides

Stefan Dittmaier, Electroweak corrections ... High precision fundamental constants at the TeV scale, MITP , March 2014 – 23

Heavy jet mass and C parameter

Denner, S.D., Gehrmann, Kurz ’09,’10 −0.3 −0.2 −0.1 0.05 0.1 0.15 0.2 0.25 0.3

dσi−dσBorn dσBorn

ρ 0.05 0.1 0.15 0.2 0.25 0.3 0.35

1 σ0 ρ dσ dρ

Born +Born q¯ qγ weak O(α) full O(α) O(α)+h.o. LL √s = MZ −0.3 −0.2 −0.1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

dσi−dσBorn dσBorn

C 0.1 0.2 0.3 0.4 0.5

1 σ0 C dσ dC

Born +Born q¯ qγ weak O(α) full O(α) O(α)+h.o. LL √s = MZ

Overall size, energy dependence, and qualitative features of EW effects similar for all event shapes.

Stefan Dittmaier, Electroweak corrections ... High precision fundamental constants at the TeV scale, MITP , March 2014 – 24

Heavy jet mass and C parameter

Denner, S.D., Gehrmann, Kurz ’09,’10 −0.01 0.01 0.02 0.03 0.05 0.1 0.15 0.2 0.25 0.3

dσi−dσBorn dσBorn

ρ 0.1 0.2 0.3

1 σhad ρ dσ dρ

Born +Born q¯ qγ weak O(α) full O(α) O(α)+h.o. LL √s = MZ −0.04 −0.02 0.02 0.04 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

dσi−dσBorn dσBorn

C 0.1 0.2 0.3 0.4 0.5

1 σhad C dσ dC

Born +Born q¯ qγ weak O(α) full O(α) O(α)+h.o. LL √s = MZ

Overall size, energy dependence, and qualitative features of EW effects similar for all event shapes.

Stefan Dittmaier, Electroweak corrections ... High precision fundamental constants at the TeV scale, MITP , March 2014 – 24

Heavy jet mass and C parameter

Denner, S.D., Gehrmann, Kurz ’09,’10

0.02 0.04 0.06 0.08 0.1 0.05 0.1 0.15 0.2 0.25 0.3

dσi−dσBorn dσBorn

ρ 0.1 0.2 0.3

1 σhad ρ dσ dρ

Born +Born q¯ qγ weak O(α) full O(α) O(α)+h.o. LL √s = 172 GeV

−0.09 −0.06 −0.03 0.03 0.06 0.09 0.12 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

dσi−dσBorn dσBorn

C 0.1 0.2 0.3 0.4 0.5

1 σhad C dσ dC

Born +Born q¯ qγ weak O(α) full O(α) O(α)+h.o. LL √s = 172 GeV

Overall size, energy dependence, and qualitative features of EW effects similar for all event shapes.

Stefan Dittmaier, Electroweak corrections ... High precision fundamental constants at the TeV scale, MITP , March 2014 – 24

Heavy jet mass and C parameter

Denner, S.D., Gehrmann, Kurz ’09,’10

0.02 0.04 0.06 0.08 0.05 0.1 0.15 0.2 0.25 0.3

dσi−dσBorn dσBorn

ρ 0.1 0.2 0.3

1 σhad ρ dσ dρ

Born +Born q¯ qγ weak O(α) full O(α) O(α)+h.o. LL √s = 206 GeV

−0.09 −0.06 −0.03 0.03 0.06 0.09 0.12 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

dσi−dσBorn dσBorn

C 0.1 0.2 0.3 0.4 0.5

1 σhad C dσ dC

Born +Born q¯ qγ weak O(α) full O(α) O(α)+h.o. LL √s = 206 GeV

Overall size, energy dependence, and qualitative features of EW effects similar for all event shapes.

Stefan Dittmaier, Electroweak corrections ... High precision fundamental constants at the TeV scale, MITP , March 2014 – 24

Heavy jet mass and C parameter

Denner, S.D., Gehrmann, Kurz ’09,’10

0.02 0.04 0.06 0.08 0.05 0.1 0.15 0.2 0.25 0.3

dσi−dσBorn dσBorn

ρ 0.1 0.2 0.3

1 σhad ρ dσ dρ

Born +Born q¯ qγ weak O(α) full O(α) O(α)+h.o. LL √s = 500 GeV

−0.06 −0.03 0.03 0.06 0.09 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

dσi−dσBorn dσBorn

C 0.1 0.2 0.3 0.4

1 σhad C dσ dC

Born +Born q¯ qγ weak O(α) full O(α) O(α)+h.o. LL √s = 500 GeV

Overall size, energy dependence, and qualitative features of EW effects similar for all event shapes.

Stefan Dittmaier, Electroweak corrections ... High precision fundamental constants at the TeV scale, MITP , March 2014 – 24