pedro d. ruiz-femenía · international workshop on heavy quarkonium, desy, hamburg, oct 17th p....
TRANSCRIPT
photonphoton spectrumspectrum in in thethe softsoft--energyenergy regionregionPedro D. Ruiz-Femenía
Talk at the Talk at the International Workshop on Heavy QuarkoniumInternational Workshop on Heavy Quarkonium17-20 October 2007, DESY, Hamburg
Nucl.Phys.BNucl.Phys.B (2007),(2007),doidoi:10.1016/:10.1016/j.nuclphysbj.nuclphysb.2007.07.013.2007.07.013
________________________________________________________International Workshop on Heavy Quarkonium, DESY, Hamburg, Oct 17th P. Ruiz-Femenía - 2
Motivation
The oPs decay spectrum for
The soft-radiation loop momentum region
spectrum for
Summary
OutlineOutline
NRQED calculation
QED spectrum in the soft-energy region
________________________________________________________International Workshop on Heavy Quarkonium, DESY, Hamburg, Oct 17th P. Ruiz-Femenía - 3
MotivationMotivation
NRQED, includes binding effects
satisfies Low´s theorem for[ Manohar, RF ’03 ]
valid for the whole region ?
new NR mode? is the NREFT calculation missing something?
orthopositronium (o-Ps) decay spectrum for
________________________________________________________International Workshop on Heavy Quarkonium, DESY, Hamburg, Oct 17th P. Ruiz-Femenía - 4
NRQED NRQED computationcomputation ofof thethe oPsoPs spectrumspectrum
there is a long-distance part in the decay when one ofthe photons in the final state is not hard
long-distance part
short-distance parthard photons
Coulomb Hamiltonian
________________________________________________________International Workshop on Heavy Quarkonium, DESY, Hamburg, Oct 17th P. Ruiz-Femenía - 5
DipoleDipole approximationapproximation
dipole approx.Atomic transitions in Ps Multipole expansion
valid for
o-Ps → 3γ decay with one small-energy photon
[ Voloshin ’04 ]
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oPs calculation without multipole expanding the e.m. field
dipole approx.
________________________________________________________International Workshop on Heavy Quarkonium, DESY, Hamburg, Oct 17th P. Ruiz-Femenía - 7
EFT EFT oPsoPs spectrumspectrum: : resultsresults
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EFT EFT oPsoPs spectrumspectrum: :
________________________________________________________International Workshop on Heavy Quarkonium, DESY, Hamburg, Oct 17th P. Ruiz-Femenía - 9
QED QED computationcomputation
from the NRQED computation in the region
exact phase-space distribution at one-loop is known [ Adkins ’05 ]
________________________________________________________International Workshop on Heavy Quarkonium, DESY, Hamburg, Oct 17th P. Ruiz-Femenía - 10
Threshold Threshold expansionexpansion ofof QED 1QED 1--looploop diagramsdiagramsBeneke, Smirnov ‘98
asymptotic expansion of loop integrals involving heavy massiveparticles close to threshold
separation of regions achieved by expanding loop momentaaccording to the v-scaling above (each region contributes to a single power of v)
________________________________________________________International Workshop on Heavy Quarkonium, DESY, Hamburg, Oct 17th P. Ruiz-Femenía - 11
LadderLadder graphgraph
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11--looploop QED QED resultresult forfor
agrees with NLO term of NRQED calculation
________________________________________________________International Workshop on Heavy Quarkonium, DESY, Hamburg, Oct 17th P. Ruiz-Femenía - 13
RelevanceRelevance forfor Heavy Heavy QuarkoniumQuarkonium
photon spectrum can be writtenas a sum of a direct contrib. anda fragmentation contrib.
________________________________________________________International Workshop on Heavy Quarkonium, DESY, Hamburg, Oct 17th P. Ruiz-Femenía - 14
11--looploop QCD QCD correctioncorrection forfor
________________________________________________________International Workshop on Heavy Quarkonium, DESY, Hamburg, Oct 17th P. Ruiz-Femenía - 15
ResultsResults forfor thethe directdirect UpsilonUpsilon decaydecay spectrumspectrum
Krämer ‘99
Catani, Hautmann ’95Maltoni, Petrelli ‘99
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SummarySummary
Application to the soft-energy direct photon spectrum inUpsilon decays is straightforward
Threshold expansion of 1-loop diagrams
NRQED calculation of the photon spectrumvalid for all