Electro not-so-weak interactions at the TeV scale Paolo Ciafaloni INFN – Sezione di Lecce

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

RGE 1 loop

L unp R



Z

What is x? x=  no exp P.Ciafaloni,D. Comelli 2000 x=kt exp Fadin et al 2000 non abelian theory + Sym. br + Z,  mixing Sudakov EW form factor

Fixed order, resummations Accomando, Denner, Hollik, Kuehn, Fadin,Lipatov, Melles, Smirnov, Ciafaloni, Comelli, Beenakker, Dittmaier, Moretti, Ross, Verzegnassi,..... Pozzorini 2004: Sudakov EW f.f. LL, exp[QED] exp[SU(2) True for all observables at all orders? Maybe, however... no NNLL, no ext. gauge bosons nobody did the “real thing” why kt?? Kuehn,Penin, Melles, NNLL “QCD-like”

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

Why Consider Fully incl? Expect exp[-L^2]->1 P. Ciafaloni,M. Ciafaloni,D. Comelli: BN violation Even fully incl. obs. sensible to IR cutoff ~Log^2[M] Any observable with weak charges in initial leg has strong dependence on M at any energy, even when E>>>>M NO “IR safe” observables can be defined for EW interactions

IR theorems? A simple argument e e W W

BN only applies to QED KLN:include also states degenerate with initial ones QCD: color averaging -> log^2 cancellation EW: nonabelian charges in initial state

Resummation Final state divergencies cancel out – one relevant L=log(E/M) 2 11’ 2‘

 e+ e-e+

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

Exotica New SM Physics

BN in abelian theories Just an academic exercise? Not really.....

Inclusive processes sensitive to MH Long ~Goldstones No tree level dependence Rad corr  Log MH ? j j’

Why consider W,Z emission? relevant for ILC LHC: against commonlore; however emission enhanced by L^2 and...

Thorne 2007 (MRST) on PDFs uncertaintes:

as a function of “inclusivity” x >0 <0 exclusive inclusive

W,Z emission relevant for some LHC observables as they are defined now and should be taken into account One can define “new”, all-inclusive, observables. Then effects can be spectacular...

Heavy quarks production P. Ciafaloni, D. Comelli ’06

Conclusions Any EW observable at TeV scale and beyond dominated by Log^2 of IR origin. ILC: majority of observables W,Z radiation relevant for ILC. Resummation needed, effects can be bigger than QCD LHC: effects can be ~ 30 % for high pt. W,Z radiation relevant for some observables. Relative effect crucially depends on observable definition. Let us start taking seriously into account weak bosons emission Interesting physics for theory & experiment!

U. Baur (2006)

Osservabili inclusive in QCD Confinamento  media sul colore  infrared safe ! EW: q -> e, q -> non ha senso media su e, Rottura di simmetria BN M. Ciafaloni, P. Ciafaloni, D. Comelli

Ad alte energie Z,W sono simili a g,  P. Ciafaloni, D. Comelli ‘98 Singolarità per k → 0, k ~ p  log 2 μ (EW: μ → M) Andamento asintotico determinato da dinamica IR (non UV) Probabilitá di emissione ~  log 2 (E/M) (non  ) p p+k k

In questo talk Qual’è l’andamento asintotico delle sezioni d’urto? Qual’ è la rilevanza per LHC, LC? Modello Standard delle int. deb. E>>Mw,Mz,mt~M~100 GeV Unica scala del processo

Espansione asintotica IRUV LHC, LC LEP n loops: Situazione inusuale! QED, QCD (α log)ⁿ Dipendenza da IR cutoff M per E qualsiasi LLNLLNNLL

2 fermioni → 2 fermioni B. Jantzen V.A. Smirnov hep-ph/ loops SU(2)

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

BN: non è possibile definire osservabili “IR safe” QED BN : EW BN: osservabili inclusive di emissione di W, Z dipendono da P. Ciafaloni M. Ciafaloni D. Comelli