b6: strong interactions and new physics at the lhc { theory · b6: strong interactions and new...

B6: Strong Interactions and New Physics at the LHC – Theory

Leszek Motyka

Hamburg University & Jagellonian University, Krakow

4 March 2009

In quest for theoretical precision:

Overview

Soft gluon resummation for SUSY partice production at the LHC[A. Kulesza and LM, Phys. Rev. Lett. in print]

Higher twists in Deep Inelastic Scattering[J. Bartels, K. Golec-Biernat and LM]

Soft gluon corrections in SUSY

production at the LHC

SUSY at LHC

Supersymmetric extension of the SM may be The Theory of physics at Terascale (naturalness,

coupling unification, WIMPS, relation to superstrings)

SUSY spectrum contains new heavy particles: e.g. scalar partners of quarks (squarks) and Majorana

fermions: gluinos

R-parity: only pair production of SUSY particles possible

Minimal Supersymmetric Standard Model has free parameters, but typically, gg and q ¯q production

processes are expected to have the largest cross sections at LHC

10-2

10-1

1

10

10 2

10 3

100 150 200 250 300 350 400 450 500

χ2oχ1

+

t1t−1

qq−

gg

νν−

χ2og

χ2oq

NLOLO

√S = 14 TeV

m [GeV]

σtot[pb]: pp → gg, qq− , t1t−1, χ2

oχ1+, νν

−, χ2og, χ2

oq

Prospino2 (T Plehn)

[T. Plehn, Prospino]

L. Motyka SFB B6: Strong Interactions and New Physics at the LHC: Theory page 2/14

Need for precise predictions

Direct determination of masses of SUSY partners may be difficult:

• long decay cascades, leading to multi-particle final states

• some final state particles should escape detection

Ways out:

• end-points of kinematic distributions

• kinematic fits

• precise measurement of total cross-sections

In general: total cross sections may provide precision tests of SUSY parameters.

Quality of the tests and parameter determination depends critically on theoretical precision.

LO, NLO results for q ¯q and gg SUSY-QCD corrections are known, but soft gluon corrections are

expected to be sizable beyond NLO


Squark–antisquark and gluino pair production at LO[Eichten, Dawson, Quigg, 85]

qiqj → q ¯q, gg → q ¯q

qq → gg, gg → gg


Impact of quantum corrections on sparticle mass determination[Beenakker, Hopker, Spira, Zerwas]

Inclusion of one loop corrections at O(αs) from quarks, gluons, squarks and gluinos

−→ Large NLO K-factors predicted for gg and q ¯q production at the LHC:

K ' 1.3 for q ¯q ar mq = 1 TeV K ' 2 for gg at mg = 1 TeV

Higher order corrections may be sizable


Soft gluon corrections at one loop

Velocity of produced particle in the c.m.s. β =

q

1 − 4m2

s , at threshold β → 0

Energy ω of emitted real gluon close to threshold is kinematically limited, ω < mβ2 � m

−→ lack of cancellations between real and virtual corrections

Iteration of soft gluon contributions leads to a tower of corrections

δσ ∼ σ(0)

αns log

2nβ

| {z }Leading Logarithmic

δσ ∼ σ(0)

αns log

2n−1β

| {z }Next to Leading Logarithmic

Resummation of soft gluon effect is based on the Renormalisation Group approach [Sterman, Catani]

Resummed cross sections incorporate quantum corrections at all orders of perturbative expansion

In part of phase space αs log2 β > 1 −→ resummation is necessary


Production of gg at the LHC at NLL accuracy

We obtained one-loop soft anomalous dimension matrices (color space) for qq → gg and gg → gg

Relative NLL correction beyond NLO

KNLL − 1

0

0.05

0.1

0.15

0.2

0.2 0.5 1 1.5 2

K NLL

- 1

mg [ TeV ]

a)

~

r = 0.5 r = 0.8 r = 1.2 r = 1.6 r = 2.0

r = mg/mq

Scale dependence

σ(ξm)/σ(m)

0.7

0.8

0.9

1

1.1

1.2

1.3

0.2 0.5 1 1.5 2

σ(ξµ

0) /

σ(µ 0

)

mg [ TeV ]~

a)

ξ = 1/2

ξ = 2

NLONLL matched

m/2 < µR = µF < 2m

For large gluino mass, sizable effects of soft gluons and

reduction of theory error by factor of ∼ 3


Production of q ¯q at the LHC at NLL accuracy

Relative NLL correction beyond NLO

KNLL − 1

0

0.01

0.02

0.03

0.04

0.2 0.5 1 1.5 2

K NLL

- 1

mq [ TeV ]~

b)

r = 0.5 r = 0.8 r = 1.2 r = 1.6 r = 2.0

r = mg/mq

Scale dependence

σ(ξm)/σ(m)

0.7

0.8

0.9

1

1.1

1.2

1.3

0.2 0.5 1 1.5 2

σ(ξµ

0) /

σ(µ 0

)

mq [ TeV ]

ξ = 1/2

ξ = 2

~

b)

NLONLL matched

m/2 < µR = µF < 2m

Modest correction, modest reduction of scale dependence

SFB B6: Strong Interactions and New Physics at the LHC: Theory page 8/14

Higher twist corrections in DIS at HERA

Probing proton structure in γ∗(Q2)p scattering (DIS)

OPE for hadronic tensor and twists: W µν =X

τ

„Λ

Q

«τ−2 X

i

Cµντ,i ⊗ fτ,i(Q

2/Λ2)

At large scale, Q2 �2, leading twist, τ = 2, dominates −→ universal parton densities

At fixed Q2 importance of higher twist operators in QCD increases quickly with√

s

Reason: rapid evolution of higher twist operators at large Q2 and small x ' Q2/s (∼ 10−3)

Gluons:Twist 4

Twist 2∼

1

Q2R2exp

„q

b log(Q2) log(1/x)

«

Higher twists −→ corrections to main HERA observables: FT and FL, related to cross sections for

virtual photons with T and L polarisations and to F2 = FT + FL

Goal: determination of higher twist corrections to F2 and FL at small x

−→ more precise determination of parton densities from HERA data −→ input for LHC


Evolution and coupling of higher twist gluon operators

At small x the dominant contribution

comes from diagrams that are enhanced by

powers of large gluon density

High energy factorisation leads

to color dipole picture

V(z,p) V (z,p’)

k−k1 1

k2

*

r2−k

Quark box diagram + multiple scattering cross section −→ saturation model

σL,T (x, Q2) =

Z ∞

0

dr2Z

dz˛˛˛ΨL,T (z, r2)

˛˛˛

2

| {z }Photon wave function

σd(x, r2)| {z }color dipole

cross section

Assuming independent scatterings: σd(x, r2) = σ0[1−exp(−r

2αs(C/r

2) xg(x, C/r

2)/σ0)]


Generic features on twists 2 and 4 in F2, FT and FL

Twist decomposition derived using Parsival formula in

Mellin space

σT,L p(x, Q2) =

Z

Cs

ds

2πiσ(x, s) Ψ2

T,L(1 − s, Q2)

f(s) =

Z ∞

0

dr2 f(r2) (r2)s−1

T

Key information about twist 2 and twist 4 contribution is contained in the Mellin poles of the quark

box diagram

FT : twist-2: αs x−λ log(Q2)/Q2 — large, twist-4 : α2s x−2λ/Q4 — suppressed correction

FL: twist-2: αs x−λ/Q2 — small, twist-4: −α2sx

−2λ log(Q2)/Q4 — enhanced correction

F2: twist-2: αs x−λ log(Q2)/Q2

F2: twist-4 : [b(4)T − a

(4)T log(Q2)] α2

s x−2λ/Q4 — correction supressed by the sign structure


Numerical results

Twist ratios: tw-2/exact

Q2

F T(tw-2

) /FT

GBW - solid BGK - dashed x=3 10-4

Q2

F L(tw-2

) /FL

Q2

F 2(tw-2

) /F2

0

0.5

1

1.5

1 2 3 4 5 6 7 8 9

0

1

2

3

1 2 3 4 5 6 7 8 9

0

0.5

1

1.5

1 2 3 4 5 6 7 8 9

Higher twist contribution at

x = 3 · 10−4 and

Q2 = 10 GeV2:

FT : ∼ 1%

FL: ∼ 20%

F2: ∼ 1%

Summary

• We found anomalous dimension matrices and soft gluon corrections to total

cross sections pp → gg and pp → q ¯q production at the LHC at the NLL

accuracy, reducing sizably the theory error for pp → gg cross section

• We evaluated twist 2 and twist 4 contributions to FL and FT measured at

HERA, within saturation model of multiple scattering


b6: strong interactions and new physics at the lhc { theory · b6: strong interactions and new...

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