PDF Automated Dipole Subtraction and the Application to LHC

Kick-off meeting of the LHCPhenoNet Initial Training Network, 3th February 2011, Valencia

Automated Dipole Subtraction and

the Application to LHC

K. Hasegawa

Collaboration with S. Moch and P. Uwer

Humboldt-Universität zu Berlin

Reference:

Comput.Phys.Commun.181(2010)1802 ; arXiv:0911.4371 [hep-ph]

K. Hasegawa, Eur.Phys.J.C.70(2010)285 ; arXiv:1007.1585 [hep-ph]

K. Hasegawa, S. Moch, P. Uwer, Nucl.Phys.Proc.Suppl.183(2008)268 : arXiv:0807.3701 [hep-ph]

1. AutoDipole

2

- LHC - Discovery of Higgs and SUSY - Confirmation of top

-

- QCD NLO correction for reliable phenomenology - QCD correction is large

-dependence

µ

^R

- Reduce

(Observed events) = (Signal) + (Background)

- One general and practical procedure for QCD NLO prediction Dipole Subtraction

Introduction

Catani, Dittmaier, Seymour, Trocsanyi, 2002 Catani and Seymour, ‘97

Dipole Subtraction

σ

_NLO

= σ

_LO

+ δσ

_NLO

=

!

dΦⁿ⁺¹|M|²real +

!

dΦⁿ|M|²virtual +

! ¹

0

dx

!

dΦⁿ 1

! P(x)|M|²LO

Catani, Dittmaier, Seymour, Trocsanyi, 2002 Catani and Seymour, ‘97

=

!

dΦⁿ⁺¹

"

|M|²real−#

i

Dⁱ

$ +

!

dΦⁿ%

|M|²virtual+#

i

Iⁱ&

+

! ¹

0

dx

!

dΦⁿ #

i

(Pⁱ+Kⁱ)

All integrals are separately finite in 4-dimensioin

Monte Carlo integration can be applied

NLO correction to multi-parton processes is possible

2 → 2 , 3

, 4 , 5

-All integrals have IR(Soft/Collinear) singularities and separately diverge -They are cancelled in observables (KLN theorem)

δσ

_NLO

σ

_real

σ

_virtual

σ

_collinear

=

+

⁺

gg → t¯tg

Input process Mathematica code D, I, P, K ^Transform D, I, P, K

Mathematica expression

|M|²real, < M⁰|Tˆⁱ · Tˆ^k|M⁰ >

Shell script MadGraph

Fortran code

- Packages with similar functionality :

- MadDipole : Frederix, Gehrmann, Greiner, JHEP0809:122, JHEP 1006:086 - TevJet : Seymour, Tevlin, arXiv0803.2231

- : Gleisberg, Krauss, Eur.Phys.J.C53(2008)501

- Helac-Dipole : Czakon, Papadopoulos, Worek, JHEP0908:085

Stelzer, Long, ‘94

Alwall, Demin, Visscher, Frederix, Herquet, Maltoni, Plehn, Rainwater, Stelzer, 2007

Automation

AutoDipole package (V1.2.3) Comput.Phys.Commun.181(2010)1802 Hasegawa, Moch, Uwer, Nucl.Phys.Proc.Suppl.183(2008)268

MSSM extension

SuperAutoDipole package

Hasegawa, Eur.Phys.J.C.70(2010)285

g~

q~

SUSY QCD

D, I, P, K ! V · < M₀|Tˆ · Tˆ|M₀ >

MSSM processes

Cho, Hagiwara, Kanzaki, Plehn, Rainwater, Stelzer, 2006

SMadGraph

All fields in SM and MSSM

Advantages 1 :

LO NLO-real

D I PK

12 12

8 8

1. gg → t¯t 2. uu¯ → t¯t

1. gg → ttg¯ 2. uu¯ → t¯tg 3. ug → ttu¯

4. ug¯ → t¯tu¯

(Input )

15 15 9 9 D(1) = D(2) =

D(4) = D(3) =

I(1) = I(2) =

PK(1) = PK(2) =

Advantages 2:

Minimally constructed outputs - Easy to identify outputs and comfortable to use

pp → t¯t Example:

- Correspondence is clear

!

dΦ⁽ⁿ⁺¹⁾

"

|M(real-i)|²real − D(i)

#

!

dΦ⁽ⁿ⁾

"

|M(^LO-i)|²_1-loop − ^I(i)

#

! dx

!

dΦ⁽ⁿ⁾ PK(i)

- - -

: i = 1 → # of real processes

: i = 1 → # of LO processes

)

User friendly

(Continue) - Creation algorithm

Input: LO-i + g uu¯ → t¯tg

CLBS Dipoles

D^αβ,γ

tg, ¯t

¯ u u

¯tg, t

¯ u u

ug,

¯ ug,

t

¯ u

¯ t

t

¯ t u

!B1|T^aT^b|B1"

!B2|T^aT^b|B2"

dipole 1

!Born|T_aT_b|Born"

dipole 2

t,

u,

¯ u,

¯t,

¯ t

¯ u u

t

¯ u u

t

¯ u

¯ t

t

¯ t u

t¯t,

u

¯ u

g g,

u

¯ u

g

LO-i + g

dipole 1 of ( ) always contains Complete set of CLBS of

{!LO-i|T_aT_b|LO-i"}comp

LO-i

Reduced Born

B2 = uu¯ → gg B1 = uu¯ → t¯t

= LO-i

t

dipole 1

dipole 2 dipole 3

dipole 4 Emitter

- dipole creation

u t

¯

u ¯t

Advantages 2:

Minimally constructed outputs

- Creation algorithm (Continue)

- I and PK terms creation - dipole creation is finished Input: LO-i + g

uu¯ → t¯tg

Input: LO-i uu¯ → tt¯

I term: I(i) = !

a,b

C_ab!LO-i|TaTb|LO-i" = {!LO-i|T_aT_b|LO-i"}comp

PK term: PK(i) = !

a,b

C^!

ab!LO-i|TaTb|LO-i"

⊂

{!LO-i|T_aT_b|LO-i"}comp

Initial state: a=1,2

{!LO-i|T_aT_b|LO-i"}comp

I(i) and PK(i) are created from the complete set

LO-i + g

which exists in dipole 1 in the real process

Advantages 2:

Minimally constructed outputs (Continue)

LO-1 LO-2 LO-3 LO-4 LO-5 LO-6 LO-7

LO

(Input )

NLO-real

LO-i + g

I

^PK

Real-8 Real-9

Real-18

· · ·

D

D(1) D(2) D(3) D(4) D(5) D(6) D(7)

I(1) I(2) I(3) I(4) I(5) I(6) I(7)

PK(1) PK(2) PK(3) PK(4) PK(5) PK(6) PK(7)

D(8) D(9)

D(18)

· · ·

Input for AutoDipole

1 2 3 4

5 6 7

Kardosa, Papadopoulos, Trocsanyi, arXiv:1101.2672 [hep-ph]

pp → t¯t + 1 jet + X Eaxmple:

(Continue)

Advantages 2:

Minimally constructed outputs

2. Application

10

σ_pp→X = !

i,j

"

dx₁dx₂ f_i(x₁)f_j(x₂) ˆσ_ij→{k} ⊗ J_{k}→X

Total cross section :

dσ_pp

→X

Distribution : dO with observables

O = p

T

, y, η, E

^miss_T

, M

_µ⁺_µ−

, Jets #, · · ·

- Monte Carlo Integration

Jet algorithm

⊗

⊗ Parton shower Hadronization

Traditional working horse: VEGAS MC, Lepage ’76 - Important sampling

- Stratified sampling

]

Adaptive

I =

!

¹

0

dx

!

¹

0

dy f ( x, y ) ! S

^N

= 1 N

"

N

i=1

f ( x

ⁱ

, y

ⁱ

)

1 O x

y

f(x, y)

1

Collider observables

e

⁻

e → t ˜

₁

t ˜

^∗

Stop pair production:

1

¯

σ^real =

!

dΦ⁽³⁾

"

|M(e⁻e⁺ → ˜t₁˜t^∗₁g)|²real −

2

#

i=1

Dⁱ

$

= πα²eQ²tNc

3s12 · αs

π CF ·

! "

1−4ρ²

1−2ρ² (1 + 4ρ−4ρ² −16ρ³ + 12ρ⁴) + · · ·

#

ρ = m/√ s₁₂

with

9.2545e-05 9.255e-05 9.2555e-05 9.256e-05 9.2565e-05 9.257e-05 9.2575e-05 9.258e-05

1e-06 1e-05 0.0001 0.001

MC result Analytical result

+ · · ·

δ

_tec

[ab]

5 × 10⁸

- Vegas MC : 10 iteration

Phase space s₃₅

s₁₂

s₄₅ s₁₂

and ≥ δ_{tec is allowed}

(Cut for soft limit of gluon) - 14 cuts dependence :

points ×

√s

12 = 4[TeV]

-

- ^{m = 399.7[GeV]} , ^{αs = 0.1180} , ^{αe = 0.007816}

(MC results) = 92.5719693 ± 0.0001715 [ab]

(Analytical results) = 92.5719027 [ab]

Perfect agreement Hasegawa 2010

Top pair production with 1 jet at LHC:

^pp _→ ^t¯t + 1 jet + X

Eur. Phys. J. C59 (2009) 625 and Phys.Rev.Lett.98(2007)262002 [1] Dittmaier, Uwer, Weinzierl

Perfect agreement

(Result in [1]) = −(50.6894 ± 0.15202) [pb]

(MC result) = −(50.68789 ± 0.16320) [pb]

- Vegas MC : 10 iteration

9.5 ms/ps, total=160 hours - Timing :

- 16 cuts dependence : -

6 × 10⁶

√s = 14 [TeV]

- PDF=CTEQ6M with ^{µF = mtop} = 174 [GeV]

-

^{PT,cut = 50 [GeV]}

- Jet algorithm = Ellis-Soper with R = 1

points ×

s_ij/s ≥ δ^tec

gg mode :

δ

_tec

-54 -53 -52 -51 -50 -49 -48

1e-07 1e-06 1e-05 0.0001 0.001 0.01

MC result Result in [1]

[pb]

+ · · ·

¯

σ^real =

!

dx₁dx₂ f_g(x₁)f_g(x₂)

!

dΦ⁽⁴⁾

"

|M(gg → t¯tgg)|²real⊗J_t⁽⁴⁾_t+1jet¯ −#

i

Di⊗J_t⁽³⁾_t+1jet¯

$

Single top production with 2 jets at LHC: pp → t + 2 jets + X

Work in progress

All collinear safeties are confirmed (Input )

LO NLO-real

D I PK

36 28

36 28

20 20

20

1. ud¯→ t¯bg 20

2. ug → t¯bd 3. dg¯ → t¯bu¯ 4. ub → tdg 5. db¯ → tug¯ 6. gb → tud¯

20 20

20 20 1.

2.

3.

4.

5.

6.

7.

8.

17. 16.

LO + g

· · · · · ·

· · ·

· · ·

gg → t¯bud¯ ud¯→ t¯buu¯

bu → tudu¯ bu¯ → tud¯ u¯

· · ·

24 8

8 8

u

¯

d _¯b

W t

3. Outlook

14

Summary

- AutoDipole : - General and practical : ² _→ ^{2, 3, 4, 5} in SM and MSSM

- Application : e⁻e⁺ → ˜tt˜^∗

pp → tt¯+ 1 jets pp → t + 2 jets Plan

- Application of tool to challenging LHC processes

pp

SUSY(˜t˜t^∗,· · ·) + n jets

t + 2 jets

Quarkonium(J/Ψ,· · ·) + n jets Other new physics processes

- NLO QCD corrections are important for LHC precise phenomenology

- Technical challenge can be overcome by general procedure and automation

- Publicly available :

- User friendly : Minimally constructed outputs

http://www-zeuthen.desy.de/~moch/autodipole/index.html

- User support : please contact us