Precise Predictions for Hadronic Collisions from On-Shell Methods - - PowerPoint PPT Presentation

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Precise Predictions for Hadronic Collisions from On-Shell Methods - - PowerPoint PPT Presentation

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Precise Predictions for Hadronic Collisions from On-Shell Methods Carola F. Berger CTP, MIT PHENO 2009, May 12th 2009 BlackHat and Sherpa BlackHat: Outline BlackHat and CFB, Zvi Bern, Lance Dixon, Fernando Febres Sherpa Outline

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SLIDE 1

Precise Predictions for Hadronic Collisions from On-Shell Methods

Carola F. Berger

CTP, MIT

PHENO 2009, May 12th 2009

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SLIDE 2

Outline

  • BlackHat and

Sherpa

  • Outline

Introduction BlackHat Summary Carola F. Berger PHENO 2009, May 12th 2009 Precise Predictions for Hadronic Collisions, BlackHat - 2/15

BlackHat and Sherpa

BlackHat: CFB, Zvi Bern, Lance Dixon, Fernando Febres Cordero, Darren Forde, Harald Ita, David Kosower, Daniel Maitre

BlackHat: arXiv:0902.2760, PRD78 (2008) 036003. Badger: JHEP 0901 (2009) 049. Forde: PRD75 (2007) 125019. CFB, Bern, Dixon, Forde, Kosower: PRD74 (2006) 036009.

Sherpa liaison (real emissions): Tanju Gleisberg

Gleisberg et al, JHEP 0902 (2009) 007. Gleisberg, Krauss, Eur. Phys. J C53 (2008) 501.

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SLIDE 3

Outline

  • BlackHat and

Sherpa

  • Outline

Introduction BlackHat Summary Carola F. Berger PHENO 2009, May 12th 2009 Precise Predictions for Hadronic Collisions, BlackHat - 3/15

Outline

■ Introduction

Do we really need NLO?

■ What is BlackHat? ◆ Terms with logarithms (dilogs, ...) from

generalized unitarity

◆ Rational terms ■ Physics Results – W + 3 jets

⇒ Fernando’s Talk!

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SLIDE 4

Outline Introduction

  • Precision

Calculations

  • The LHC Wishlists
  • NLO Corrections

to LHC Processes BlackHat Summary Carola F. Berger PHENO 2009, May 12th 2009 Precise Predictions for Hadronic Collisions, BlackHat - 4/15

Precision Calculations

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SLIDE 5

Outline Introduction

  • Precision

Calculations

  • The LHC Wishlists
  • NLO Corrections

to LHC Processes BlackHat Summary Carola F. Berger PHENO 2009, May 12th 2009 Precise Predictions for Hadronic Collisions, BlackHat - 4/15

Precision Calculations

Dissertori (CMS)

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SLIDE 6

Outline Introduction

  • Precision

Calculations

  • The LHC Wishlists
  • NLO Corrections

to LHC Processes BlackHat Summary Carola F. Berger PHENO 2009, May 12th 2009 Precise Predictions for Hadronic Collisions, BlackHat - 5/15

The (In)Famous Experimenters’ Wishlists

Les Houches 2005

process wanted at NLO background to (V ∈ {Z, W, γ})

  • 1. pp → V V + jet

t¯ tH, new physics

  • 2. pp → H + 2 jets

H production by vector boson fusion (VBF)

  • 3. pp → t¯

tb¯ b t¯ tH

  • 4. pp → t¯

t + 2 jets t¯ tH

  • 5. pp → V V b¯

b VBF → H → V V , t¯ tH, new physics

  • 6. pp → V V + 2 jets

VBF → H → V V

  • 7. pp → V + 3 jets

new physics

  • 8. pp → V V V

SUSY trilepton

2 → 3, computed via standard methods, + one process 2 → 4

Bredenstein, Dittmaier, Denner, Pozzorini

2 → 4, computed via on-shell methods (BlackHat and (partially) Rocket)

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SLIDE 7

Outline Introduction

  • Precision

Calculations

  • The LHC Wishlists
  • NLO Corrections

to LHC Processes BlackHat Summary Carola F. Berger PHENO 2009, May 12th 2009 Precise Predictions for Hadronic Collisions, BlackHat - 5/15

The (In)Famous Experimenters’ Wishlists

Run II Monte Carlo Workshop 2001

Single boson Diboson Triboson Heavy flavor W + ≤ 5j W W + ≤ 5j W W W + ≤ 3j t¯ t+ ≤ 3j W + b¯ b+ ≤ 3j W W + b¯ b+ ≤ 3j W W W + b¯ b+ ≤ 3j t¯ t + γ+ ≤ 2j W + c¯ c+ ≤ 3j W W + c¯ c+ ≤ 3j W W W + γγ+ ≤ 3j t¯ t + W + ≤ 2j Z+ ≤ 5j ZZ+ ≤ 5j Zγγ+ ≤ 3j t¯ t + Z+ ≤ 2j Z + b¯ b+ ≤ 3j ZZ + b¯ b+ ≤ 3j W ZZ+ ≤ 3j t¯ t + H+ ≤ 2j Z + c¯ c+ ≤ 3j ZZ + c¯ c+ ≤ 3j ZZZ+ ≤ 3j t¯ b+ ≤ 2j γ+ ≤ 5j γγ+ ≤ 5j tb¯ b+ ≤ 3j γ + b¯ b+ ≤ 3j γγ + b¯ b+ ≤ 3j γ + c¯ c+ ≤ 3j γγ + c¯ c+ ≤ 3j W Z+ ≤ 5j W Z + b¯ b+ ≤ 3j W Z + c¯ c+ ≤ 3j W γ+ ≤ 3j Zγ+ ≤ 3j

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SLIDE 8

Outline Introduction

  • Precision

Calculations

  • The LHC Wishlists
  • NLO Corrections

to LHC Processes BlackHat Summary Carola F. Berger PHENO 2009, May 12th 2009 Precise Predictions for Hadronic Collisions, BlackHat - 6/15

NLO Corrections to LHC Processes

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SLIDE 9

Outline Introduction

  • Precision

Calculations

  • The LHC Wishlists
  • NLO Corrections

to LHC Processes BlackHat Summary Carola F. Berger PHENO 2009, May 12th 2009 Precise Predictions for Hadronic Collisions, BlackHat - 7/15

NLO Corrections to LHC Processes

■ Relevant processes all 2 → n ≥ 3

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SLIDE 10

Outline Introduction

  • Precision

Calculations

  • The LHC Wishlists
  • NLO Corrections

to LHC Processes BlackHat Summary Carola F. Berger PHENO 2009, May 12th 2009 Precise Predictions for Hadronic Collisions, BlackHat - 7/15

NLO Corrections to LHC Processes

■ Relevant processes all 2 → n ≥ 3 ■ Real-virtual cancellations a solved problem,

automated

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SLIDE 11

Outline Introduction

  • Precision

Calculations

  • The LHC Wishlists
  • NLO Corrections

to LHC Processes BlackHat Summary Carola F. Berger PHENO 2009, May 12th 2009 Precise Predictions for Hadronic Collisions, BlackHat - 7/15

NLO Corrections to LHC Processes

■ Relevant processes all 2 → n ≥ 3 ■ Real-virtual cancellations a solved problem,

automated

■ Bottleneck: 1-loop virtual amplitudes

It took 11 years to go from 5-gluon 1-loop amplitudes to 6 gluons!

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SLIDE 12

Outline Introduction

  • Precision

Calculations

  • The LHC Wishlists
  • NLO Corrections

to LHC Processes BlackHat Summary Carola F. Berger PHENO 2009, May 12th 2009 Precise Predictions for Hadronic Collisions, BlackHat - 7/15

NLO Corrections to LHC Processes

■ Relevant processes all 2 → n ≥ 3 ■ Real-virtual cancellations a solved problem,

automated

■ Bottleneck: 1-loop virtual amplitudes

It took 11 years to go from 5-gluon 1-loop amplitudes to 6 gluons!

■ New methods based on (generalized) unitarity and

recursion ⇒ new codes: BlackHat, Rocket (D-dim unitarity), CutTools/OneLOop (D-dim unitarity at integrand level)

Rocket: Ellis, Giele, Kunszt, Melnikov, Zanderighi. CutTools/OneLOop: van Hameren, Ossola, Papadopoulos, Pittau

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SLIDE 13

Outline Introduction BlackHat

  • One-Loop

Decomposition

  • Generalized

Unitarity

  • Tree Level
  • Proof at Tree-Level
  • Rational Terms

from Recursion

  • Rational Terms -

D-dim Unitarity Summary Carola F. Berger PHENO 2009, May 12th 2009 Precise Predictions for Hadronic Collisions, BlackHat - 8/15

One-Loop Decomposition

I I I

4 3 2

Any n-leg (massless) one-loop amplitude expressible in terms of scalar box, triangle and bubble integrals: A = c4I4 + c3I3 + c2I2 + rational With massive partons there are additionally I1 (tadpoles) We know the integrals, the task is to determine the coefficients

Bern, Dixon, Dunbar, Kosower

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SLIDE 14

Outline Introduction BlackHat

  • One-Loop

Decomposition

  • Generalized

Unitarity

  • Tree Level
  • Proof at Tree-Level
  • Rational Terms

from Recursion

  • Rational Terms -

D-dim Unitarity Summary Carola F. Berger PHENO 2009, May 12th 2009 Precise Predictions for Hadronic Collisions, BlackHat - 9/15

Generalized Unitarity

c4I4 = c4

  • d4l

1 l2(l − K1)2(l − K2)2(l − K3)2 1 P 2 + iε = 1 P 2 + iδ+(P 2) Box integrals have unique leading singularity ⇒ generalized unitarity

c4∆LSI4 =

  • d4lδ+(l2)δ+((l − K1)2)

×δ+((l − K2)2)δ+((l − K3)2) ×Atree

1

(l) × Atree

2

(l) × Atree

3

(l) × Atree

4

(l) c4 = Atree

1

(lsol)×Atree

2

(lsol)×Atree

3

(lsol)×Atree

4

(lsol)

Tree graphs on shell Trees “recycled” into loops

Britto, Cachazo, Feng

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SLIDE 15

Outline Introduction BlackHat

  • One-Loop

Decomposition

  • Generalized

Unitarity

  • Tree Level
  • Proof at Tree-Level
  • Rational Terms

from Recursion

  • Rational Terms -

D-dim Unitarity Summary Carola F. Berger PHENO 2009, May 12th 2009 Precise Predictions for Hadronic Collisions, BlackHat - 10/15

On-Shell Recursion Relations at Tree Level

p = 0

An

2

Complex continue (shift) spinors and momenta: pi → pi(z) pj → pj(z) pi + pj → pi + pj Momentum conservation is maintained, momenta

  • n-shell (pi(z)2 = pj(z)2 = 0).

A n−1 n 1 2 An

=

A p = 0

2 L R

i

j

^ ^

Britto, Cachazo, Feng

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SLIDE 16

Outline Introduction BlackHat

  • One-Loop

Decomposition

  • Generalized

Unitarity

  • Tree Level
  • Proof at Tree-Level
  • Rational Terms

from Recursion

  • Rational Terms -

D-dim Unitarity Summary Carola F. Berger PHENO 2009, May 12th 2009 Precise Predictions for Hadronic Collisions, BlackHat - 11/15

Proof at Tree-Level

Propagators and thus amplitudes are now functions

  • f the complex parameter:

1/P 2

l...j...m

→ 1/P 2

l...j...m(z)

A(z) =

  • l,m
  • h

Ah

L(z)

1 P 2

l...j...m(z)A−h R (z)

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SLIDE 17

Outline Introduction BlackHat

  • One-Loop

Decomposition

  • Generalized

Unitarity

  • Tree Level
  • Proof at Tree-Level
  • Rational Terms

from Recursion

  • Rational Terms -

D-dim Unitarity Summary Carola F. Berger PHENO 2009, May 12th 2009 Precise Predictions for Hadronic Collisions, BlackHat - 11/15

Proof at Tree-Level

Propagators and thus amplitudes are now functions

  • f the complex parameter:

1/P 2

l...j...m

→ 1/P 2

l...j...m(z)

A(z) =

  • l,m
  • h

Ah

L(z)

1 P 2

l...j...m(z)A−h R (z)

If A(z → ∞) → 0 - Cauchy’s theorem 1 2πi

  • C

dz z A(z) = 0

z C

A(0) = −

  • poles α

Res

z=zα

A(z) z =

  • poles α
  • h

Ah

L(zα)

1 P 2

l...j...m

A−h

R (zα)

Britto, Cachazo, Feng, Witten

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SLIDE 18

Outline Introduction BlackHat

  • One-Loop

Decomposition

  • Generalized

Unitarity

  • Tree Level
  • Proof at Tree-Level
  • Rational Terms

from Recursion

  • Rational Terms -

D-dim Unitarity Summary Carola F. Berger PHENO 2009, May 12th 2009 Precise Predictions for Hadronic Collisions, BlackHat - 12/15

Rational Terms from Recursion

A =

  • i

ciIi + rational =

+ +

configs

R R R

R =

  • configs

AL 1 P 2

l...m

AR

CFB, Bern, Dixon, Forde, Kosower

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SLIDE 19

Outline Introduction BlackHat

  • One-Loop

Decomposition

  • Generalized

Unitarity

  • Tree Level
  • Proof at Tree-Level
  • Rational Terms

from Recursion

  • Rational Terms -

D-dim Unitarity Summary Carola F. Berger PHENO 2009, May 12th 2009 Precise Predictions for Hadronic Collisions, BlackHat - 13/15

Rational Terms - D-dim Unitarity

Unitarity in D = 4 − 2ε: Split up into 4-D piece and (−2ε)-dim. piece (∼ small “mass”) l2

D = l2 4 + l2 [−2ε] = l2 4 + µ2

  • dDl

(2π)D =

  • d4l4

(2π)4 d−ε(µ2) (2π)−2ε Extract rational part R by keeping track of µ-dependence in generalized unitarity cuts ⇒ loosely speaking, 4-D unitarity, but trees are now “massive” (µ2)

Badger, Forde. See also Ossola, Papadopoulos, Pittau (CutTools); Ellis, Giele, Kunszt, Melnikov, Zanderighi (Rocket).

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SLIDE 20

Outline Introduction BlackHat Summary

  • BlackHat
  • Summary

Carola F. Berger PHENO 2009, May 12th 2009 Precise Predictions for Hadronic Collisions, BlackHat - 14/15

BlackHat

A =

  • i

ciIi + rational

■ Cut parts from 4-D unitarity

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SLIDE 21

Outline Introduction BlackHat Summary

  • BlackHat
  • Summary

Carola F. Berger PHENO 2009, May 12th 2009 Precise Predictions for Hadronic Collisions, BlackHat - 14/15

BlackHat

A =

  • i

ciIi + rational

■ Cut parts from 4-D unitarity ■ Rational parts from loop recursion

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SLIDE 22

Outline Introduction BlackHat Summary

  • BlackHat
  • Summary

Carola F. Berger PHENO 2009, May 12th 2009 Precise Predictions for Hadronic Collisions, BlackHat - 14/15

BlackHat

A =

  • i

ciIi + rational

■ Cut parts from 4-D unitarity ■ Rational parts from loop recursion ■ OR rational parts from D-dim unitarity

⇒ 4-D unitarity with small “mass”

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SLIDE 23

Outline Introduction BlackHat Summary

  • BlackHat
  • Summary

Carola F. Berger PHENO 2009, May 12th 2009 Precise Predictions for Hadronic Collisions, BlackHat - 14/15

BlackHat

A =

  • i

ciIi + rational

■ Cut parts from 4-D unitarity ■ Rational parts from loop recursion ■ OR rational parts from D-dim unitarity

⇒ 4-D unitarity with small “mass”

■ Basic ingredients: tree amplitudes, low-point

1-loop amplitudes

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SLIDE 24

Outline Introduction BlackHat Summary

  • BlackHat
  • Summary

Carola F. Berger PHENO 2009, May 12th 2009 Precise Predictions for Hadronic Collisions, BlackHat - 14/15

BlackHat

A =

  • i

ciIi + rational

■ Cut parts from 4-D unitarity ■ Rational parts from loop recursion ■ OR rational parts from D-dim unitarity

⇒ 4-D unitarity with small “mass”

■ Basic ingredients: tree amplitudes, low-point

1-loop amplitudes

■ NO integrals or PV reductions are performed

⇒ Numerically very stable, excellent scaling with number of external legs (number of Feynman graphs grows factorially)

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SLIDE 25

Outline Introduction BlackHat Summary

  • BlackHat
  • Summary

Carola F. Berger PHENO 2009, May 12th 2009 Precise Predictions for Hadronic Collisions, BlackHat - 14/15

BlackHat

A =

  • i

ciIi + rational

■ Cut parts from 4-D unitarity ■ Rational parts from loop recursion ■ OR rational parts from D-dim unitarity

⇒ 4-D unitarity with small “mass”

■ Basic ingredients: tree amplitudes, low-point

1-loop amplitudes

■ NO integrals or PV reductions are performed

⇒ Numerically very stable, excellent scaling with number of external legs (number of Feynman graphs grows factorially)

■ Fully automatizable for any process (incl. BSM –

just need relevant trees/low-order loops and color/coupling info)

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SLIDE 26

Outline Introduction BlackHat Summary

  • BlackHat
  • Summary

Carola F. Berger PHENO 2009, May 12th 2009 Precise Predictions for Hadronic Collisions, BlackHat - 15/15

Summary

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SLIDE 27

Outline Introduction BlackHat Summary

  • BlackHat
  • Summary

Carola F. Berger PHENO 2009, May 12th 2009 Precise Predictions for Hadronic Collisions, BlackHat - 15/15

Summary

Physics results ⇒ Fernando’s talk next!