Soft-gluon resummation for gluon-induced Higgs-Strahlung Vincent - - PowerPoint PPT Presentation

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Motivation Threshold Resummation Numerical Results Soft-gluon resummation for gluon-induced Higgs-Strahlung Vincent Theeuwes Institut fr Theoretische Physik Westflische Wilhelms-Universitt Mnster In Collaboration with: Robert

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SLIDE 1

Motivation Threshold Resummation Numerical Results

Soft-gluon resummation for gluon-induced Higgs-Strahlung

Vincent Theeuwes

Institut für Theoretische Physik Westfälische Wilhelms-Universität Münster In Collaboration with: Robert Harlander, Anna Kulesza, Tom Zirke

Firenze, 05.09.2014

Threshold resummation for gg → HZ 1

  • V. Theeuwes
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SLIDE 2

Motivation Threshold Resummation Numerical Results

Importance of gg → HZ

  • A Higgs boson found with a mass of 125 GeV
  • Precision study needed to determine if it is SM Higgs
  • One process is Higgs-strahlung (H+Z final state)
  • At LO pp → HZ is described by q¯

q → HZ

  • Drell-Yan corrections up to NNLO [Hamberg, Neerven, Matsuura, ’91]

[Harlander, Kilgore, ’02] [Brein, Djouadi, Harlander, ’04]

  • gg → HZ at NLO [Altenkamp, Dittmaier, Harlander, Rzehak, Zirke, ’12]
  • Large corrections (factor of 2)
  • Still has significant scale dependence

✛ ✚ ✘ ✙

Z∗ Z H q ¯ q Z∗ Z H t Threshold resummation for gg → HZ 2

  • V. Theeuwes
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SLIDE 3

Motivation Threshold Resummation Numerical Results

Results NLO gg → HZ

[Altenkamp, Dittmaier, Harlander, Rzehak, Zirke, ’12]

√s [TeV] mH[GeV] σLO

gg [fb]

σNLO

gg

[fb] 8 115 19.8+61%

−34%

39.3+32%

−24%

8 120 18.7+61%

−34%

37.2+32%

−24%

8 125 17.7+61%

−34%

35.1+32%

−24%

8 130 16.7+61%

−34%

33.1+32%

−24%

14 115 79.1+51%

−31%

152+27%

−21%

14 120 75.1+51%

−31%

144+27%

−21%

14 125 71.1+51%

−31%

136+27%

−21%

14 130 67.2+51%

−31%

129+27%

−21%

Threshold resummation for gg → HZ 3

  • V. Theeuwes
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SLIDE 4

Motivation Threshold Resummation Numerical Results

Importance of Resummation

  • Resummation up to NNLL already improved Higgs production

results [Catani, de Florian, Grazzini, Nason, ’03] [de Florian, Grazzini, ’09]

[de Florian, Grazzini, ’12]

  • gg → HZ similar loop induced process ⇒ threshold resummation

could help further improve results

✵✳✵✵ ✶✵✳✵✵ ✷✵✳✵✵ ✸✵✳✵✵ ✹✵✳✵✵ ✺✵✳✵✵ ✻✵✳✵✵ ✵✳✷✺ ✵✳✺ ✶ ✷ ✹ µ/µ0 σ(gg → H + X)❬♣❜❪ √ S = 14 ❚❡❱ µ0 = mH = 115 ●❡❱

▲❖ ◆▲❖ ◆▲❖✰◆▲▲

Agrees with [Catani, de Florian, Grazzini, Nason, ’03]

Threshold resummation for gg → HZ 4

  • V. Theeuwes
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SLIDE 5

Motivation Threshold Resummation Numerical Results

Definition of Threshold

Q-approach ✛ ✚ ✘ ✙

Z Q2 ⇑

Threshold variable ˆ τQ = Q2

ˆ s Q2: the invariant mass final state particles

1 − ˆ τQ = 1 − Q2 ˆ s ∼ energy of the emitted gluons total available energy M-approach (absolute threshold) ✛ ✚ ✘ ✙ Threshold variable ˆ τM = M 2

ˆ s M = mH + mZ

1 − ˆ τM = 1 − M 2 ˆ s ∼ maximum energy of the emitted gluons total available energy

√ ˆ s: the partonic center of mass energy

Threshold resummation for gg → HZ 5

  • V. Theeuwes
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SLIDE 6

Motivation Threshold Resummation Numerical Results

Logarithms

Q-approach The IR divergences lead to logarithms: ✎ ✍ ☞ ✌ αn

s

logm(1 − ˆ τQ) 1 − ˆ τQ

  • +

≡ αn

s DQ, m (ˆ

τQ) , m ≤ 2n − 1 In general logarithms of 1 − ˆ τQ M-approach For 2 → 2 process: logarithms of 1 − ˆ τM: ✞ ✝ ☎ ✆ αn

s logm(1 − ˆ

τM) ≡ αn

s DM, m−1 (ˆ

τM) , m ≤ 2n Logarithms become large in threshold: ˆ τ → 1

Threshold resummation for gg → HZ 6

  • V. Theeuwes
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SLIDE 7

Motivation Threshold Resummation Numerical Results

Mellin Transform

Mellin transform is used with respect to τ (needed for factorization of phase space): ✤ ✣ ✜ ✢ ˜ Σpp→HZ(N) ≡ 1 dτ τ N−1Σpp→HZ(τ, mZ, mH, µR, µF ) =

  • i,j

˜ fi/p(N + 1, µF ) ˜ fj/p(N + 1, µF )˜ ˆ Σij→HZ(N, µR, µF )

  • ˜

fi/p(N + 1, µF ): Mellin transform with respect to x

  • ˜

ˆ Σij→HZ(N, µR, µF ): Mellin transform with respect to ˆ τ

  • Σij→HZ =

dσij→HZ dQ2

in Q-approach

  • Σij→HZ = σij→HZ in M-approach

Dn (ˆ τ) ⇒ logn+1 N and threshold ˆ τ → 1 ∼ N → ∞

Threshold resummation for gg → HZ 7

  • V. Theeuwes
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SLIDE 8

Motivation Threshold Resummation Numerical Results

Orders of Resummation

Large logarithms log N ≡ L for N → ∞ Perturbation needs to be reordered in αs and L:

[Kodaira, Trentadue, ’82][Sterman, ’87][Catani, d’Emilio, Trentadue, ’88][Catani, Trentadue, ’89]

✞ ✝ ☎ ✆ ˜ σ ∼ ˜ σLO × C(αs) exp [Lg1(αsL) + g2(αsL) + αsg3(αsL) + · · · ] ⇓ ⇓ ⇓ With orders of precision: LL NLL NNLL ⇓ ⇓ ⇓ αn

s logn+1(N)

αn

s logn(N)

αn+1

s

logn(N)

Exponential functions are well known and the same as for gg → H [Catani, de Florian, Grazzini, Nason, ’03]

Threshold resummation for gg → HZ 8

  • V. Theeuwes
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SLIDE 9

Motivation Threshold Resummation Numerical Results

Hard Matching Coefficient (Schematically)

C(αs) = 1 + αs π C(1) + · · · Originates from NLO calculation. Using terms proportional to: ⇒σLO, σLODM, 0, σLODM, 1 OR ⇒σLOδ(Q2 − ˆ s), σLODQ, 0, σLODQ, 1 Mellin transform leads to: αs π [C(1) ˜ ΣLO + O(˜ ΣLO log(N), ˜ ΣLO log2(N)) + · · · ] ⇓ Expansion of exponential

Threshold resummation for gg → HZ 9

  • V. Theeuwes
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SLIDE 10

Motivation Threshold Resummation Numerical Results

Hard Matching Coefficient (Schematically)

C(αs) = 1 + αs π C(1) + · · · Originates from NLO calculation. Using terms proportional to: ⇒σLO, σLODM, 0, σLODM, 1 OR ⇒σLOδ(Q2 − ˆ s), σLODQ, 0, σLODQ, 1 Mellin transform leads to: αs π [C(1) ˜ ΣLO + O(˜ ΣLO log(N), ˜ ΣLO log2(N)) + · · · ] ⇓ Expansion of exponential

Threshold resummation for gg → HZ 9

  • V. Theeuwes
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SLIDE 11

Motivation Threshold Resummation Numerical Results

Hard Matching Coefficient (Schematically)

C(αs) = 1 + αs π C(1) + · · · Originates from NLO calculation. Using terms proportional to: ⇒σLO, σLODM, 0, σLODM, 1 OR ⇒σLOδ(Q2 − ˆ s), σLODQ, 0, σLODQ, 1 Mellin transform leads to: αs π [C(1) ˜ ΣLO + O(˜ ΣLO log(N), ˜ ΣLO log2(N)) + · · · ] ⇓ Expansion of exponential

Threshold resummation for gg → HZ 9

  • V. Theeuwes
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SLIDE 12

Motivation Threshold Resummation Numerical Results

Hard Matching Coefficient (Schematically)

C(αs) = 1 + αs π C(1) + · · · Originates from NLO calculation. Using terms proportional to: ⇒σLO, σLODM, 0, σLODM, 1 OR ⇒σLOδ(Q2 − ˆ s), σLODQ, 0, σLODQ, 1 Mellin transform leads to: αs π [C(1) ˜ ΣLO + O(˜ ΣLO log(N), ˜ ΣLO log2(N)) + · · · ] ⇓ Expansion of exponential

Threshold resummation for gg → HZ 9

  • V. Theeuwes
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SLIDE 13

Motivation Threshold Resummation Numerical Results

Hard Matching Coefficient

ˆ ΣNLO = ˆ ΣR + ˆ ΣV + ˆ ΣC =

  • 3
  • dˆ

ΣR|ǫ=0 − dˆ ΣA|ǫ=0

  • +
  • 2
  • dˆ

ΣV +

  • 1

dˆ ΣA

  • ǫ=0

+ ˆ ΣC

Threshold resummation for gg → HZ 10

  • V. Theeuwes
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SLIDE 14

Motivation Threshold Resummation Numerical Results

Hard Matching Coefficient

ˆ ΣNLO = ˆ ΣR + ˆ ΣV + ˆ ΣC = ✘✘✘✘✘✘✘✘✘✘ ✘

  • 3
  • dˆ

ΣR|ǫ=0 − dˆ ΣA|ǫ=0

  • +
  • 2
  • dˆ

ΣV +

  • 1

dˆ ΣA

  • ǫ=0

+ ˆ ΣC ⇓ Supressed in threshold limit

Threshold resummation for gg → HZ 10

  • V. Theeuwes
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SLIDE 15

Motivation Threshold Resummation Numerical Results

Hard Matching Coefficient

ˆ ΣNLO = ˆ ΣR + ˆ ΣV + ˆ ΣC = ✘✘✘✘✘✘✘✘✘✘ ✘

  • 3
  • dˆ

ΣR|ǫ=0 − dˆ ΣA|ǫ=0

  • +
  • 2
  • dˆ

ΣV +

  • 1

dˆ ΣA

  • ǫ=0

+ ˆ ΣC ⇓ Supressed in threshold limit ⇒ C(1) calculated by: ˆ ΣV + ˆ ΣA + ˆ ΣC In agreement with: [Catani, Cieri, de Florian, Ferrera, Grazzini, ’13]

Threshold resummation for gg → HZ 10

  • V. Theeuwes
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SLIDE 16

Motivation Threshold Resummation Numerical Results

Hard Matching Coefficient (Result)

C(1) = ˆ σvirt ˆ σLO π αs + 2 3TR nl − 11 6 − 2γE

  • CA
  • log

µ2 W 2

  • −

50 9 − 2π2 3 − 2γ2

E

  • CA + 16

9 TR nl

  • Q-approach: Absolute threshold expansion ˆ

σvirt and ˆ σLO, W 2 = Q2

  • W-approach: W 2 = M 2

Threshold resummation for gg → HZ 11

  • V. Theeuwes
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SLIDE 17

Motivation Threshold Resummation Numerical Results

Hard Matching Coefficient (Result)

C(1) = ˆ σvirt ˆ σLO π αs + 2 3TR nl − 11 6 − 2γE

  • CA
  • log

µ2 W 2

  • −

50 9 − 2π2 3 − 2γ2

E

  • CA + 16

9 TR nl

  • Q-approach: Absolute threshold expansion ˆ

σvirt and ˆ σLO, W 2 = Q2

  • W-approach: W 2 = M 2

Threshold resummation for gg → HZ 11

  • V. Theeuwes
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SLIDE 18

Motivation Threshold Resummation Numerical Results

Hard Matching Coefficient (Result)

C(1) = ˆ σvirt ˆ σLO π αs + 2 3TR nl − 11 6 − 2γE

  • CA
  • log

µ2 W 2

  • −

50 9 − 2π2 3 − 2γ2

E

  • CA + 16

9 TR nl

  • Q-approach: Absolute threshold expansion ˆ

σvirt and ˆ σLO, W 2 = Q2

  • W-approach: W 2 = M 2

Threshold resummation for gg → HZ 11

  • V. Theeuwes
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SLIDE 19

Motivation Threshold Resummation Numerical Results

Hard Matching Coefficient (Result)

C(1) = ˆ σvirt ˆ σLO π αs + 2 3TR nl − 11 6 − 2γE

  • CA
  • log

µ2 W 2

  • −

50 9 − 2π2 3 − 2γ2

E

  • CA + 16

9 TR nl

  • Q-approach: Absolute threshold expansion ˆ

σvirt and ˆ σLO, W 2 = Q2

  • W-approach: W 2 = M 2

Threshold resummation for gg → HZ 11

  • V. Theeuwes
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SLIDE 20

Motivation Threshold Resummation Numerical Results

Matching to Fixed Order

Resummed Cross Section

Σ(NLO+NLL)

gg→HZ

(τ) = Σ(NLO)

gg→HZ(τ)

+

  • CT

dN 2πiτ −N ˜ fg/p(N + 1) ˜ fg/p(N + 1) × ˜ ˆ Σ(NLL)

gg→HZ(N) − ˜

ˆ Σ(NLL)

gg→HZ(N)|(NLO)

  • Matching to fixed order required to avoid double counting.

Threshold resummation for gg → HZ 12

  • V. Theeuwes
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SLIDE 21

Motivation Threshold Resummation Numerical Results

Results

M-approach(NLL resummation)

[Harlander, Kulesza, VT, Zirke, in preparation]

PDFs used: MSTW2008NNLO

0.00 20.00 40.00 60.00 80.00 100.00 0.2 0.5 1 2 5 µ/µ0 σ(gg → HZ + X)[fb] √ S = 8 TeV µ0 = (mH + mZ) mH = 125 GeV

LO NLO NLO+NLL (M-approach) NLO+NLL (Q-approach)

0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00 0.2 0.5 1 2 5 µ/µ0 σ(gg → HZ + X)[fb] √ S = 14 TeV µ0 = (mH + mZ) mH = 125 GeV

LO NLO NLO+NLL (M-approach) NLO+NLL (Q-approach)

mt → ∞ limit used and rescaled by

σLO(mt) σthr.

LO (mt→∞)

preliminary

Threshold resummation for gg → HZ 13

  • V. Theeuwes
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SLIDE 22

Motivation Threshold Resummation Numerical Results

Results

Q-approach(NLL resummation)

[Harlander, Kulesza, VT, Zirke, in preparation]

PDFs used: MSTW2008NNLO

0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 0.2 0.5 1 2 5 µ/µ0 σ(gg → HZ + X)[fb] √ S = 8 TeV µ2

0 = (pH + pZ)2

mH = 125 GeV

LO NLO NLO+NLL

0.00 50.00 100.00 150.00 200.00 250.00 0.2 0.5 1 2 5 µ/µ0 σ(gg → HZ + X)[fb] √ S = 14 TeV µ2

0 = (pH + pZ)2

mH = 125 GeV

LO NLO NLO+NLL

preliminary

Threshold resummation for gg → HZ 14

  • V. Theeuwes
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SLIDE 23

Motivation Threshold Resummation Numerical Results

Summary

Conclusions

  • Improvement in scale dependence:

σNLO = 32.7+31%

−24% fb and σNLO+NLL Q

= 38.8+8.3%

−6.9% fb for 8 TeV

σNLO = 124+26%

−21% fb and σNLO+NLL Q

= 143+6.9%

−5.1% fb for 14 TeV

Error determined at Q2/3 and 3Q2

  • Sizable correction:

σNLO+NLL σNLO

= 1.18 (1.15) for 8 (14) TeV

Outlook

  • NNLL resummation
  • Combine into pp → HZ results

Threshold resummation for gg → HZ 15

  • V. Theeuwes
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SLIDE 24

Motivation Threshold Resummation Numerical Results

Summary

Conclusions

  • Improvement in scale dependence:

σNLO = 32.7+31%

−24% fb and σNLO+NLL Q

= 38.8+8.3%

−6.9% fb for 8 TeV

σNLO = 124+26%

−21% fb and σNLO+NLL Q

= 143+6.9%

−5.1% fb for 14 TeV

Error determined at Q2/3 and 3Q2

  • Sizable correction:

σNLO+NLL σNLO

= 1.18 (1.15) for 8 (14) TeV

Outlook

  • NNLL resummation
  • Combine into pp → HZ results

Thank you for your attention

Threshold resummation for gg → HZ 15

  • V. Theeuwes