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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