NLO SUSY pair production in MadGOLEM fileOutline Perturbative (SUSY-)QCD Motivations Structure of the NLO corrections One major LHC search channel: SUSY Monojet signatures Summary

2nd IMPRS seminar November 18 2011 Heidelberg

Dorival Gonçalves-Nettocollaborators D. Lopez-Val, T. Plehn, K. Mawatari, I. Wigmore

ITP - Universität Heidelberg

NLO SUSY pair production in MadGOLEM

Friday, November 18, 2011

Outline

Perturbative (SUSY-)QCD

Motivations

Structure of the NLO corrections

One major LHC search channel: SUSY Monojet signatures

Summary

Catani-Seymour Subtraction Method

NLO corrections

Pheno analysis

MadGOLEM


Motivations

Why Next-to-Leading order (NLO)?

Less sensibility from unphysical factorization/renormalization scales

Not yet fully automated

Improve shape of distributions

New channels & kinematics arising from NLO can have a high impact (particularly in the presence of cuts)


PROSPINO (PROduction of Supersymmetric Particles in Next-to-leading Order) [Beenakker, Höpker, Krämer, Plehn, Spira, Zerwas]

The only public available code to do SUSY NLO cross sections

It’s hard coded, process dependent

Just gives total cross sections (no distributions).

MadGOLEM: Fully automated tool to perform NLO QCD for BSM (main focus on SUSY models)

Process independent

Gives total cross sections and distributions

Allow the user to apply cuts...

Motivations


“SUSY signal samples are generated with HERWIG++, normalized using the NLO cross section determined by PROSPINO.” [1109.6572[hep-ex]]

NLO correction quantitatively relevant!

SUSY pair production at the LHC:

Motivations


Perturbative QCD

Master Formula: Factorizes the hard and soft processes.

Perturbative expansion from the partonic cross section:

Leading Order

Next-to-Leading Order

Next-to-Next-to-Leading Order

Ilustration by M. Mangano



UV divergent

Renormalization

UV finiteIR divergent IR divergent IR divergent

Real emissionBorn matrix with n+1

partons

Collinear subtractionFrom factorization of initial state collinear singularities

Virtual correctionsInterference term of

1-loop & Born matrix



UV divergent

Renormalization

UV finiteIR divergent IR divergent IR divergent+ +

Finite and IR safe(KLN & Factorization Theorem)

Real emissionBorn matrix with n+1

partons

Collinear subtractionFrom factorization of initial state collinear singularities

Virtual correctionsInterference term of

1-loop & Born matrix

Problems:

Analytic integration in d dimensions only feasible for very simple fully inclusive processes

How to get individual contributions finite via MC methods?


Vij,k is a singular factor, and depends only on the quantum numbers of i, j and k, and on their momenta. It is completely process independent.


Subtraction Method (Warm up):

Catani-Seymour Subtraction Method: construction of local counter terms using the universality of soft and collinear limits



Catani-Seymour Subtraction Method: construction of local counter terms using the universality of soft and collinear limits

Subtraction Method (Warm up):

The Virtual part can be integrable in 4D just after cancelation of the poles, where their pole counter part come from the integrated dipoles


1e-08

1e-06

0.0001

0.01

1

1e+02

1e+04

|M|2

Dipole

Soft limit for gluone+e- > ulul~g, E

cm = 500 GeV, m

ul = 150 GeV

-1

0

1

Dipole/|M|2

1e-12 1e-11 1e-10 1e-09 1e-08 1e-07 1e-06 1e-05 0.0001 0.001 0.01 0.1 1

Eg

2 / E

cm

2

-0.04-0.020.000.020.04

|M|2

- Dipole



process card.dat param card.dat run card.dat

MadGraphLO amplitude

user interfacereal corrections

Extended

MadDipole IR Subtraction

MadOS OS Subtraction

Qgraf

Golem

Counterterm

generator

virtual corrections

Event Generator

NLO

cross-section

NLO

distributions

NLO

amplitude

DGN, D. Lopez-Val, T. Plehn, K. Mawatari, I. Wigmore

MadGOLEM


MadGOLEM




Extended



Qgraf

Golem

Counterterm

generator

virtual corrections

Event Generator

NLO

cross-section

NLO

distributions

NLO

amplitude

DGN, D. Lopez-Val, T. Plehn, K. Mawatari, I. Wigmore Friday, November 18, 2011

MadGOLEM




Extended



Qgraf

Golem

Counterterm

generator

virtual corrections

Event Generator

NLO

cross-section

NLO

distributions

NLO

amplitude


MadGOLEM




Extended



Qgraf

Golem

Counterterm

generator

virtual corrections

Event Generator

NLO

cross-section

NLO

distributions

NLO

amplitude


MadGOLEM




Extended



Qgraf

Golem

Counterterm

generator

virtual corrections

Event Generator

NLO

cross-section

NLO

distributions

NLO

amplitude


though hard to extract any model parameters beyond masses of new particles

For SUSY there are 3 main production modes at the LHC: (mediated by strong interactions)

Important to study production process involving the weakly interacting sector

Associated production: semi-weak process, but favored by

=

interactions determined by gauge symmetry and SUSY, e.g.

One hard jet in association + is one major LHC search channel for BSM

Squark-neutralino at NLO


Flavor-locked & semi-weak process sensitive to coupling: qq!1



Couplings size correlated with SUSY breaking:

Flavor-locked & semi-weak process sensitive to coupling: qq!1



First application of MadGOLEM

Provides information on coupling

Reveals the nature of the LSP (bino or wino-like)

Bino (wino) coupling proportional to g’ (g)

Extra info on this coupling would help DM direct detection bounds

Recent analysis @LO [Allanach, Grab, Haber arXiv:1010.4261]Process not yet studied @NLO!

qq!1

QCD corrections are quantitatively relevant and important to reduce scale dependence and normalize distributions



Real emission diagrams : quark or gluon emission pp! q!1j









g

g

uR

!01

u

uR

uR

To avoid double counting subtract on-shell amplitudes:

g

g

uR

!01

u

uR

uR

g

g

uR

!01

u

uR

uR

x_

! (gg ! q ¯q) "BR (¯q ! "1q)! (gg ! q"1q)

On-shell subtraction method: differentiation between off & on-shell productionto avoid double counting [Beenakker, Hopker, Spira, Zerwas ’97] (Prospino scheme)

squark neutralino production

squark pair production


ΓOS is regarded as a regulator


Virtual QCD and SUSY-QCD corrections:

a) self energy corrections; b) vertex corrections; c) box diagrams; d) UV counter terms






















After all this have been automatically calculated, let’s look at the physics results!


Scale Dependence

0.1 1 10µR,F / µ0

010203040506070

σ (

pp →

uR~χ 10~

) [fb

]

110µF / µ0

1µR / µ0

1µF / µ0

1µR / µ0

SPS1a1000

1 2

3

4

5

√S = 7 TeV(1) (2) µR=10 µ0 (3) µF=0.1 µ0 (4) µR=0.1 µ0 (5) µF=10 µ0

NLO

LO

µR

µF

T. Binoth, DGN, D. Lopez-Val, T. Plehn, K. Mawatari, I. Wigmore [Phys. Rev. D84 (2011) 075005]Friday, November 18, 2011

300 400 500 600 700 800 900 1000mu~R

[GeV]

100

101

102

103

σ (

pp →

uR~χ 10~

) [fb

]SPS1a1000

√S = 7 TeV

µ0/2 < µR,F < 2µ0

NLO

√S = 14 TeV

LO

[Phys. Rev. D84 (2011) 075005]

Scale Dependence


10-2

10-1

100

101

102

103

σ [f

b]

400 600 800mu~R

[GeV]

1

1.2

1.4

1.6

K fa

ctor

400 600 800mu~L

[GeV]

SPS1a1000

pp → uR~ χ1

0~ pp → uL~ χ1

0~

mu~L− m u~R

= 20 GeV

√S = 7 TeV

σreal < 0

σreal > 0

σNLO

σNLO

σvirtual

σvirtual

σreal

σLO

σLO

Kreal Kreal

Kvirtual

KNLOKvirtual

KNLO


[Phys. Rev. D84 (2011) 075005]


Structure of the NLO corrections[Phys. Rev. D84 (2011) 075005]


100 150 200 250 300mχ~ [GeV]

0

50

100

150

200

σ [f

b]SPS1a1000

NLO

q~χ1

~±

NLO

q~χ1

~0

LOq~χ

2~0

LO

√S = 7 TeV

NLOLO

squark-gaugino channels[Phys. Rev. D84 (2011) 075005]


Comparison with Multi-jet Merging

0 100 200 300 400 500p

T(u~R) [GeV]

0

1!10-3

2!10-3

3!10-3

4!10-3

1/"

d"

/dp

T [

GeV

-1]

0 100 200 300 400 500

pT

(#1

~0) [GeV]

NLO

LO

$Virtual

Real Real

$Virtual

LO

NLO

0+1+2 hard-jet merging 0+1+2 hard-jet merging

SPS1a1000

%S = 14 TeV

pp & uR

~ #10 ~

NLO distributions for the heavy final states in good agreement withmulti-jet merged calculation via MLM matching with MadGraph5.

Jet merging: combine ME + Parton Shower without double counting

Partons are hard and well separated

Partons are soft/collinear (resums large logs)

Complementary

[Phys. Rev. D84 (2011) 075005]


Summary

Scale uncertainty largely reduced from 70% @LO to 20% @NLO

High K for all SPS points K~1.4

NLO distributions in agreement with MLM matching

K factors largely insensitive to each SPS pointDominance from genuine QCD effects

(First fully automized BSM NLO computation)

Source of mono-jets +

Structures of the NLO correction

Outlook: All SUSY pair production will be publicly available soon in MadGOLEM


MSSM parameter space

Total cross section strongly depend on the SPS points:

a) Kinematics: dependence on the final state masses in phase space

b) Dynamics: coupling changes substantially for each scenario


Backup slides


1e-05 0.0001 0.001 0.01 0.1!

os=wos/mos

0

0.0005

0.001

0.0015

0.002

" [

fb]

TotalNon_divos_ur

On-Shell Subtraction SPS1a gg>urn1ux

g

g

uR

!01

u

uR

uR

1 possible OS particle: ur

gg>urn1ux

ΓOS is a regulator!

Backup slides


Documents

NLO SUSY pair production in MadGOLEM fileOutline Perturbative (SUSY-)QCD Motivations Structure of the NLO corrections One major LHC search channel: SUSY Monojet signatures Summary