Top-Quark Pair Production Close to Threshold QCD and Electroweak - - PowerPoint PPT Presentation

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Top-Quark Pair Production Close to Threshold QCD and Electroweak - - PowerPoint PPT Presentation

Jan 07, 2023 203 likes •472 views

Top-Quark Pair Production Close to Threshold QCD and Electroweak Effects Johann H. K uhn I. QCD (based on EPJ (2009); Kiyo, JK, Moch, Steinhauser, Uwer) II. Electroweak Corrections (with Scharf, Uwer) I) QCD and Threshold Effects Remember

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SLIDE 1

Top-Quark Pair Production Close to Threshold QCD and Electroweak Effects

Johann H. K¨ uhn

  • I. QCD

(based on EPJ (2009); Kiyo, JK, Moch, Steinhauser, Uwer)

  • II. Electroweak Corrections

(with Scharf, Uwer)

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SLIDE 2

I) QCD and Threshold Effects

Remember the ILC Original idea from e+e− annihilation

σ(e+e− → t¯ t) ∼ ∑

n

|Ψn(0)|2πδ(√s−Mn)

for narrow t¯

t-resonances with masses Mn and “stable” top quarks.

Finite width: πδ(√s−Mn) ⇒ Im

1 Mn−iΓt−√s

∑

n

Ψn(0)Ψ∗

n(0)

Mn −iΓt −√s = ImG(

  • r = 0,

r′ = 0,√s+iΓt)

numerical or perturbative analytical solution of Lippmann-Schwinger equation

  • (E +iΓt)−
  • −∇2

m2

t

+V(

  • r)
  • G(
  • r,

r′ = 0,E +iΓt) = δ(

  • r)

2

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SLIDE 3

Greens function G involves “long distances” (P ∼ 20 GeV) still in perturbative region In addition: short distance corrections (1− 16

3 αs π +...)

344 345 346 347 348 349 350 351 352

  • q2 GeV

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 R

HoangTeubner

344 345 346 347 348 349 350 351 352

  • q2 GeV

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 R

MYYNOS

344 345 346 347 348 349 350 351 352

  • q2 GeV

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 R

PeninPivovarov

344 345 346 347 348 349 350 351 352

  • q2 GeV

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 R

BenekeSignerSmirnov

determination of mt with δmt ∼ 50 MeV (Linear Collider)

⇒ important impact on stability of vacuum in the SM.

3

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SLIDE 4

Hadron Colliders Tevatron, LHC: δmt ∼ 1 GeV systematics limited: Kinematical reconstruction from decay products of top quarks (color triplet) “Monte Carlo” defintion (∼ close to pole mass)

4

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SLIDE 5

fundamental processes:

q ¯ q → g∗ → t + ¯ t

(Tevatron)

տ ր

color octet (8s)

gg → t + ¯ t 8⊗8 = 1s ⊕8s ⊕8a ⊕10a ⊕10a ⊕27s 3⊗ ¯ 3 = 1s ⊕8s

QCD potential

  • V [1,8]

C

( q) = −4παs(µr)C[1,8]

  • q2
  • 1+ αs(µr)

4π

  • β0 ln µ2

r

  • q2 +a1
  • +...
  • ,

with C[1] = CF = 4/3 and C[8] = CF −CA/2 = −1/6, and a1 = (31/9)CA −(20/9)TF n f

singlet: attractive

  • ctet: repulsive

5

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SLIDE 6

t¯ t bound states? Γt ≈ 1.36 GeV;

Rydberg constant (C[1]αs)2 mt

4 ≈ 1.5 GeV

singlet ⇒ enhancement around 1S peak

  • ctet ⇒ suppression

0.01 0.02 0.03 0.04 0.05 335 340 345 350 355 360

M [GeV] Im Gc / mt

2

Imaginary part of the Green’s functions for the color singlet (upper solid line) and color octet (lower solid line) cases as functions of top quark invariant mass. For comparison, also the expansions of G in fixed order up to O(αs) with (dashed) and without (dotted line) Γt are plotted. The imaginary part of the NNLO Green’s function for the color-singlet case is shown as dash-dotted line.

6

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SLIDE 7

Production cross section close to threshold partonic cross section

Born: i+ j → t + ¯

t

QCD-corrections:

i+ j → t + ¯ t(+X)

(e.g. q+ ¯

q → t + ¯ t +g etc) Mdˆ σi j→t¯

t

dM (ˆ s,M2,µ2

f)

= Fi j→t¯

t(ˆ

s,M2,µ2

f) 1

m2

t

ImG[1,8](M +iΓt),

Perturbative NLO evaluation:

Fi j→t¯

t(ˆ

s,M2,µ2

f)

= Ni j→t¯

t

π2α2

s(µr)

3ˆ s

  • 1+ αs(µr)

π

Ch

  • ×
  • δi j→t¯

t δ(1−z)+ αs(µr)

π

  • Ac(z)+Anc(z)
  • .

restrict to S-waves:

1S[1] 0 , 1S[8] 0 , 3S[1] 1 , 3S[8] 1

spin singlet and triplet, color singlet and octet (result for spin and color singlet: JK+Mirkes 1993)

7

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SLIDE 8
  • Ni j: normalization
  • Ch: hard virtual corrections
  • Ac: collinear parton splitting (involves splitting functions)
  • Anc: non-collinear real emission

example (t¯

t in spin singlet & color singlet configuration)

Ch[gg → 1S[1]

0 ]

= β0 2 ln µ2

r

M2

  • +CF

π2 4 −5

  • +CA
  • 1+ π2

12

  • ,

Ac[gg → 1S[1,8]

] = (1−z)Pgg(z)

  • 2

ln(1−z) 1−z

  • +

+ 1 1−z

  • +

ln

  • M2

zµ2

f

  • − β0

2 δ(1−z)ln

  • µ2

f

M2

  • ,

Ac[gq → 1S[1,8]

] = 1 2 Pgq(z) ln

  • M2(1−z)2

zµ2

f

  • + CF

2 z,

Anc[gg → 1S[1]

0 ]

= −CA 6z(1−z)2(1+z)3

  • 12+11z2 +24z3 −21z4 −24z5 +9z6

−11z8 +12

  • −1+5z2 +2z3 +z4 +3z6 +2z7

lnz

  • ,

Anc[q ¯

q → 1S [1]

0 ]

= 32CF 3N2

c

z (1−z)

similarly for 1S[8]

0 , also contributions from gq, q ¯

q

8

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SLIDE 9

Results

leading subprocesses: gg → 1S [1,8] and q ¯

q → 3S [8]

0.2 0.4 0.6 0.8 1 1.2 1.4 335 340 345 350 355 360 365 370 375 380

M [GeV] dσ / dM [pb/GeV] LHC √ s = 14 TeV gg → 1S0

[8]

gg → 1S0

[1]

qq

– → 3S1 [8]

  • ctet:

suppressed (repulsive potential ⇒ Greens function) enhanced (color degrees of freedom)

9

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SLIDE 10

0.5 1 1.5 2 2.5 3 3.5 335 340 345 350 355 360 365 370 375 380

M [GeV] dσ / dM [pb/GeV] LHC √ s = 14 TeV total color-octet color-singlet

all production channels

0.5 1 1.5 2 2.5 3 3.5 4 335 340 345 350 355 360 365 370 375 380

M [GeV] dσ / dM [pb/GeV] LHC √ s = 14 TeV

boundstate result vs NLO (continuum pQCD)

10

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SLIDE 11

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 335 340 345 350 355 360 365 370 375 380

M [GeV] dσ / dM [pb/GeV] LHC √ s = 10 TeV total color-octet color-singlet

LHC (10 TeV)

0.01 0.02 0.03 0.04 0.05 0.06 335 340 345 350 355 360 365 370 375 380

M [GeV] dσ / dM [pb/GeV] Tevatron √ s = 1.96 TeV total color-octet color-singlet

Tevatron (1.96 TeV) small gg-luminosity

12

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SLIDE 12

SUMMARY on QCD

differential distribution dσ

dM

carries important information on t − ¯

t−dynamics

threshold enhancement ∼ 10 pb [small compared to σtot

∼ 200 pb (8 TeV) ∼ 800 pb (14 TeV)]

studies of dσ

dM close to threshold might exhibit structure similar to those at e+e− colliders

⇒ mass of t¯ t bound state

Impact of weak corrections?

13

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SLIDE 13

II) Electroweak Corrections

  • I. Results at Partonic Level

q ¯ q → t ¯ t :

g q t

∼ O(αs)

no interference with

q t Z

∼ O(αweak)

gg → t ¯ t :

t g

t g

∼ O(αs)

14

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SLIDE 14

O(α2

sαweak) weak corrections (q ¯

q → t ¯ t )

Z, W Z, W

+

Z, W, H, φ, χ

q q t

+

q q t

cuts of second group individually IR-divergent

15

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SLIDE 15

O(α2

sαweak) weak corrections (gg → t ¯

t )

Γ Γ

Γ

Γ Z, χ, H

t, b

16

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SLIDE 16
  • analytical & numerical results available

(earlier partial results by Beenakker et al., some disagreements) independent evaluation by Bernreuther & F¨ ucker

  • (box contribution)up−quark = −(box contribution)down−quark

⇒ suppression

  • box contribution moderately ˆ

s-dependent

  • strong increase of negative corrections with ˆ

s

  • sizable Mh-dependence, large effect close to threshold

17

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SLIDE 17
  • 30
  • 20
  • 10

10 10

3

10

4

Mh = 120 GeV Mh = 240 GeV Mh = 1000 GeV

√s

∧ [GeV]

qq

– → tt –

  • 15
  • 10
  • 5

10

3

10

4 Mh = 120 GeV Mh = 240 GeV Mh = 1000 GeV

gg → tt

–

√s

∧ [GeV]

sizable negative corrections for large Ecm = M(t¯ t) ⇒ Sudakov logarithms weak charges in initial and final state ⇒ factor two enhanced corrections significant dependence on mH close to threshold

18

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SLIDE 18
  • II. Tevatron and LHC

Small effects for total cross section (dominated by

√ ˆ s ∼ 360-380 GeV)

  • 2
  • 1

1 165 170 175 180

mH = 120 GeV mH = 200 GeV mH = 1000 GeV

Tevatron

mt [GeV] relative weak corrections [%]

  • 3
  • 2.5
  • 2
  • 1.5
  • 1

165 170 175 180

mH = 120 GeV mH = 200 GeV mH = 1000 GeV

mt [GeV] relative weak corrections [%]

LHC

19

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SLIDE 19

differential distributions composition: q ¯

q vs gg

10−7 10−6 10−5 10−4 10−3 10−2 10−1 100 101 1000 2000 3000 4000 5000 Mt¯

t[GeV]

LHC (14 TeV)

dσLO dMt¯

t

[pb/GeV]

gg → t¯ t q ¯ q → t¯ t sum 10−7 10−6 10−5 10−4 10−3 10−2 10−1 100 101 250 500 750 1000 1250 1500 1750 2000 pT,t[GeV] LHC (14 TeV)

dσLO dpT,t [pb/GeV]

gg → t¯ t q ¯ q → t¯ t sum

large pt: dominated by q ¯

q annihilation

20

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SLIDE 20

−10 −5 500 1000 1500 2000 2500 3000 Mt¯

t[GeV]

LHC (8 TeV) dδσNLO dMt¯

t /dσLO

dMt¯

t [%]

MH = 126 GeV MH = 1 TeV −20 −15 −10 −5 250 500 750 1000 1250 1500 pT,t[GeV] LHC (8 TeV) dδσNLO dpT,t /dσLO dpT,t [%] MH = 126 GeV MH = 1 TeV −15 −10 −5 1000 2000 3000 4000 5000 Mt¯

t[GeV]

LHC (14 TeV) dδσNLO dMt¯

t /dσLO

dMt¯

t [%]

MH = 126 TeV MH = 1 TeV −20 −15 −10 −5 250 500 750 1000 1250 1500 1750 2000 pT,t[GeV] LHC (14 TeV) dδσNLO dpT,t /dσLO dpT,t [%] MH = 126 GeV MH = 1 TeV

Relative weak corrections for the invariant t¯

t mass (left) and transverse momentum (right) distribution

for LHC8 (upper) and LHC14 (lower plots) and for Higgs masses of 126 GeV and 1 TeV.

21

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SLIDE 21

0.1 0.2 0.3 0.4 0.5 −5 −4 −3 −2 −1 1 2 3 4 5 ∆yt¯

t

LHC (8 TeV) Mt¯

t > 1 TeV

dσ d∆yt¯

t

[pb] LO 0.02 0.03 0.04 0.05 0.06 0.07 0.08 −5 −4 −3 −2 −1 1 2 3 4 5 ∆yt¯

t

LHC (14 TeV) Mt¯

t > 2 TeV

dσ d∆yt¯

t

[pb] LO −8 −6 −4 −2 2 −5 −4 −3 −2 −1 1 2 3 4 5 ∆yt¯

t

LHC (8 TeV) dδσNLO d∆yt¯

t /dσLO

d∆yt¯

t [%]

Mt¯

t > 1 TeV

MH = 126 GeV MH = 1 TeV −15 −10 −5 −5 −4 −3 −2 −1 1 2 3 4 5 ∆yt¯

t

LHC (14 TeV) dδσNLO d∆yt¯

t /dσLO

d∆yt¯

t [%]

Mt¯

t > 2 TeV

MH = 126 GeV MH = 1 TeV

Rapidity distributions with invariant mass cuts at leading order (upper plots) and relative weak corrections to these distributions (lower plots) for LHC8 (left) and LHC14 (right). rapidity difference ˆ

= scattering angle

distortions of order 10% (large corrections for ∆yt¯

t = 0 !

ˆ =

scattering at 90◦)

22

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SLIDE 22
  • III. Higgs exchange and Yukawa potential

VY(r) = −κ 1 r e−r/rY with κ = g2

Y

4π = √ 2GFM2

t

4π ≈ 0.0337 and rY = 1/MH

short range potential relative to bound state range of potential = rY = 1/MH size of bound state = rBohr = 4

3αsMt 2 rY rBohr ≈ 1 6

correction factor

  • 1+κ Mt

MH

  • ≈ (1+0.05)

rapid variation below Mt¯

t = 400 GeV

23

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SLIDE 23

−5 5 10 15 20 350 400 450 500 550 600 Mt¯

t[GeV]

LHC (8 TeV) dδσNLO dMt¯

t /dσLO

dMt¯

t [%]

MH = 126 GeV MH = 126 GeV, gY = 2×gSM

Y

MH = 1 TeV −5 5 10 15 20 350 400 450 500 550 600 Mt¯

t[GeV]

LHC (14 TeV) dδσNLO dMt¯

t /dσLO

dMt¯

t [%]

MH = 126 GeV MH = 126 GeV, gY = 2×gSM

Y

MH = 1 TeV

Relative weak corrections for the mass distribution in the framework of the SM assuming MH =

126 GeV (solid blue curve) and 1000 GeV (dashed red curve), and for the case of an enhanced

Yukawa coupling gY = 2gSM

Y

with MH = 126 GeV (dotted black curve). The two plots represent LHC8 and LHC14.

24

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SLIDE 24

more pronounced for Tevatron!

−5 5 10 15 20 350 400 450 500 550 600 Mt¯

t[GeV]

Tevatron dδσNLO dMt¯

t /dσLO

dMt¯

t [%]

dδσNLO dMt¯

t /dσLO

dMt¯

t [%]

MH = 126 GeV MH = 126 GeV, gY = 2×gSM

Y

MH = 1 TeV

⇒ non-trivial limit on Yukawa coupling within reach! (gY < 2gSM ?) ⇒ detailed theoretical understanding of threshold region required!

25

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SLIDE 25

SUMMARY

LHC = Top Quark Factory (Millions of top quarks) extreme regions will be explored:

large pT of O(1TeV) ⇒ large weak corrections close to threshold ⇒ complicated dynamics, remnant of t¯ t resonances; ⇒ QCD and Yukawa potential NLO results available for strong and electroweak interactions

26