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Electro not-so-weak interactions Paolo Ciafaloni INFN – Sezione di Lecce

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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

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How the story begins on a day of last century......

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RGE 1 loop Why not RGE-driven? σ10 %@ TeV higher orders LEP: leading terms in m t, (log E)

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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 log 2 μ (EW: μ M) Asymptotic behaviour dictated by IR (not UV) Emission probability ~ log 2 (E/M) (non ) p p+k k

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Asymptotic expansion IRUV LHC, LC LEP n loops: Unusual situation! QED, QCD (α log) Dependence on IR cutoff M for any E LLNLLNNLL

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2 fermions B. Jantzen V.A. Smirnov hep-ph/0603133 2 loops SU(2)

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

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Inclusive observables P P 2 j + X W,Z X hard: E > 1 TeV soft: 100 GeV < E << 1 TeV

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BN: IR safe observables do not exist! QED BN : EW BN: all observables, even including W, Z emission depend on P. Ciafaloni M. Ciafaloni D. Comelli

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Noncancellation mechanism QCD confines color average infrared safe ! EW: average over e, senseless Symmetry breaking BN M. Ciafaloni, P. Ciafaloni, D. Comelli 2000-2005

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E asymptotically

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A 1 TeV 14 % 8 % P. Ciafaloni M. Ciafaloni D. Comelli 05

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U. Baur (2006)

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as a function of inclusivity x

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Heavy quarks production P. Ciafaloni, D. Comelli 06

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Conclusions Why dont we begin taking seriously into account weak gauge bosons emissions at ILC, LHC?

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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

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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

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