Electro not-so-weak interactions

Paolo CiafaloniINFN – Sezione di Lecce

In this talk

What is the asymptotic behaviour of cross sections

What is the relevance for LHC, LC?

Standard Model of EW int. E>>Mw,Mz,mt~M~100 GeV

Only relevant scale for the process

How the story beginsHow the story begins

on a day of last century......

RGE

1 loop

• Why not RGE-driven?• ∆σ≈10 %@ TeV higher orders• LEP: leading terms in mtⁿ, (log E)ⁿ

At high energies Z,W similar to g, At high energies Z,W similar to g, P. Ciafaloni, D. Comelli ‘98

• Singularity for k → 0, k ~ p log2μ (EW: μ → M)• Asymptotic behaviour dictated by IR (not UV)• Emission probability ~ log2(E/M) (non )

p p+k

k

Asymptotic expansion

IR UV

LHC, LC LEP

n loops:

• Unusual situation! QED, QCD (α log)ⁿ• Dependence on IR cutoff M for any E

LL NLL NNLL

2 fermions→2 fermions B. JantzenV.A. Smirnovhep-ph/0603133

2 loops SU(2)

productionttS. Moretti, M. Nolten, D. Ross, hep-ph/0603083

%20th

Inclusive observables

P P 2 j + X W,Z X

“hard”: E > 1 TeV

“soft”: 100 GeV < E << 1 TeV

BN: “IR safe” observables do not exist!

QED BN:

EW BN: all observables, even including W, Z emission depend on

P. CiafaloniM. CiafaloniD. Comelli

Noncancellation mechanism

• QCD confines color average infrared safe !• EW: average over e , senseless• Symmetry breaking BN

M. Ciafaloni, P. Ciafaloni, D. Comelli 2000-2005

E

)()( eee asymptotically

A 1 TeV 14 % 8 %

P. CiafaloniM. CiafaloniD. Comelli ‘05

U. Baur (2006)

as a function of “inclusivity” x

Heavy quarks productionP. Ciafaloni, D. Comelli ’06

Conclusions

Why don’t we begin taking seriously into account weak gauge bosons emissions at ILC, LHC?

Conclusions

• High energy EW dominated by log^2(E) of IR origin

• W,Z emission HAVE to be considered for ILC but also for LHC

• Final prediction (sign) very much dependent on observable definition

Correzioni elettrodeboli alla scala del TeV

• Precisione < 1%

higher orders• 1 loop, leading 2 loops,

risommazioni

predizioni sotto controllo

• Precisione inferiore• Non necessariamente

dominato da QCD• Osservabili inclusive

effetti spettacolari

- Dominate da struttura IR, non UV - O(20 %) a 1 TeV