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On the Frozen QCD Coupling
Moscow, 28 August 2013

M a rio G re co U n ive rsity a n d IN FN - R o m a T re


Motivation

· The frozen QCD coupling is often used as an effective fixed coupling. · Supposed to mimic running coupling effects and/or the lack of knowledge of alfa(s) in the infrared region. · Usually its value is fixed from the analysis of the experimental data, for a given process. Scale of alfa(s) is unknown a-priori.



Quick history - infrared region
· e+e- annihilation, QCD and duality.



QCD:

Duality: compare moments

E.Etim,M.G.,1975


"Frozen alfa(s)": contin. of alfa(s) at low energy. M.G., Penso, Srivastava, Phys.Rev.D,1980.


Quick history - infrared region
· e+e- annihilation, QCD and duality. · P t - d istrib u tio n s fro m Q C D r e su m m a tio n .
Curci, M.G., Srivastava, Phys.Rev.Lett. 1979




Quick history - infrared region
· e+e- annihilation, QCD and duality. · Pt -distribution from QCD resummation. · P o w e r-b e h a ve d c o n trib s. to h a rd p ro ce sse s in Q C D fro m n o n p e rtu rb a tive e ffe cts.
Dokshitzer, Marchesini and Webber, Nucl.Phys. 1996

· .....


Quick history - perturb. region
· C o m p lica te d c a lcs . --> a lfa ( s) fixe d W h ich sca le ? · L e a d in g L o g . A p p ro xim a tio n s · S u m m in g d o u b le /sin g le lo g s · S m a ll x, D G L A P , B FK L


Recent analysis -

E.P.J.Plus 128(2013)

Ermolaev,M.G.,Troyan

· N o ve l w a y to d e fin e fro ze n co u p lin g s, in d e p e n d e n tly fro m e xp e rim e n ts. · Th re e kin d s o f co u p lin g s: DLA - spacelike arguments DLA - timelike arguments SLA (ex. BFKL) · O u r e stim a te s a g re e w ith re su lts a va ila b le in lite ra tu re .


Simple mathematical argum.
· C o n sid e r: (A ) f(x) va rie s m u ch fa ste r th a n g (x)

(B ) f(x) a n d g (x) va ry sim ila rly


DIS structure functs. from evolution equations

Leading DL contribs. at small x

---->
Ermolaev, Troyan,PL 2008

Which scale?


P rin cip le o f m in im a l se n sitivity

Stevenson 1981

· (i) Fa cto rize d g lu o n t im e like ( D IS )

· (ii) Factorized gluon spacelike (e+e- , DY)

- Agrees with previous e+e- estimates


Further check with intercepts in DIS
· Regge asymptotics calculated in DLA w ith fixe d a lfa ( s) fo r
Ermolaev,Manaenkov,Ryskin,Bartels 1996

· S a m e ca lcu la tio n ta kin g in to a cco u n t ru n n in g a lfa ( s) e ffe cts
Ermolaev,M.G.,Troyan 2000-'01-'04

· Tw o re su lts a g re e w ith in 1 0 -1 5 % Fro ze n co u p lin g - -> la rg e r in te rce p ts


Frozen coupling for SLA
· Well-known ex. BFKL Pomeron (LO, NLO). Scale fixed a posteriori Brodsky,Fadin,Kim,Lipatov 1999 -(i) Apply PMS (ii) Define averaged coupling --> -- Agrees with previous estimates -->


Conclusions
· N o ve l w a y to d e fin e t h e fro ze n Q C D co u p lin g s a n d fix th e ir va lu e . · It d e p e n d s o n th e typ e o f le a d in g lo g s. DLA/SLA, and space-/time-like argums. · In sig h t in th e in fra re d re g io n . · O u r e stim a te s, b a se d o n P M S , a g re e w ith p re vio u s re su lts w ith in a fe w % , w ith n o u se o f e xp e rim e n ta l d a ta .


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