Interference Effects in Medium Induced Gluon Radiation Jorge Casalderrey Solana (in collaboration with E. Iancu) arXiv:1105.1760
Motivation X X X • When partons propagate through the QGP they radiates gluons. What happens when two partons propagate simultaneously? • Is there interference between more than one propagating source? In vacuum, interference is important ⇒ angular ordering Are in-medium showers angular ordered? Interesting angular distribution in N=1 opacity (Mehtar-Tani, Salgado, Tywoniuk 10) Is there a restriction on in-medium large angle emissions? important for the description of di-jet asymmetries
BDMPS-Z Radiation s = ˆ qL θ 2 ω 2 � s L • Gluons are emitted with a typical angle Θ s
BDMPS-Z Radiation s = ˆ qL θ 2 ω 2 ω ≪ ω c ≡ 1 qL 2 2 ˆ � s L • Gluons are emitted with a typical angle Θ s
BDMPS-Z Radiation s = ˆ qL θ 2 ω 2 ω ≪ ω c ≡ 1 qL 2 2 ˆ � s � s L L • Gluons are emitted with a typical angle Θ s
BDMPS-Z Radiation s = ˆ qL θ 2 ω 2 ω ≪ ω c ≡ 1 qL 2 2 ˆ � s � s � s L L L • Gluons are emitted with a typical angle Θ s
BDMPS-Z Radiation s = ˆ qL θ 2 ω 2 ω ≪ ω c ≡ 1 qL 2 2 ˆ � s � s � s L L L • Gluons are emitted with a typical angle Θ s • Emissions occur all along the medium: dN ∝ L
BDMPS-Z Radiation s = ˆ qL θ 2 ω 2 ω ≪ ω c ≡ 1 qL 2 2 ˆ � s � s � s � s � 2 ω � f τ f = q ˆ � f � q ˆ θ 2 f = ω 3 L L L L • Gluons are emitted with a typical angle Θ s • Emissions occur all along the medium: dN ∝ L • Soft gluons are formed (decohered) at a short time τ f
BDMPS-Z Radiation s = ˆ qL θ 2 ω 2 ω ≪ ω c ≡ 1 � f qL 2 2 ˆ � s � s � s � s � 2 ω � f τ f = � c q ˆ � f � q ˆ θ 2 f = ω 3 1 � f θ 2 c = qL 3 ˆ L L L L • Gluons are emitted with a typical angle Θ s • Emissions occur all along the medium: dN ∝ L • Soft gluons are formed (decohered) at a short time τ f • There is a minimum value for emissions Θ C
Two Partons: Very Large Angles � s � qq • Radiation from two sources propagating in plasma. • Θ qq >> Θ s the two fronts do not overlap No interference between BDMPS gluons
Two Partons: Very Large Angles � s � qq • Radiation from two sources propagating in plasma. • Θ qq >> Θ s the two fronts do not overlap No interference between BDMPS gluons
Two Partons: Very Large Angles � s � qq • Radiation from two sources propagating in plasma. • Θ qq >> Θ s the two fronts do not overlap No interference between BDMPS gluons • “Vacuum-Medium” interference is possible
Two Partons: Very Large Angles (quantum coherence) � s 2 τ int = { ωθ 2 q ¯ q � qq • Radiation from two sources propagating in plasma. • Θ qq >> Θ s the two fronts do not overlap No interference between BDMPS gluons • “Vacuum-Medium” interference is possible • Interference contribution scales with dI ∝ τ int
Two Partons: Large Angles � s � qq L • The two fronts overlap when Θ qq ≤ Θ s . Can they interfere?
Two Partons: Large Angles � f � s � s � qq � qq � f L L • The two fronts overlap when Θ qq ≤ Θ s . Can they interfere? No! at formation the fronts do not overlap
Two Partons: Large Angles � f � s � s � qq � qq � f L L • The two fronts overlap when Θ qq ≤ Θ s . Can they interfere? No! at formation the fronts do not overlap • “Vacuum-medium” interference is still possible • Interference contribution scales with dI ∝ τ int
Two Partons: Small Angles � s θ f � qq � f L • The two fronts overlap at formation: they can interfere.
Two Partons: Small Angles � s τ coh θ f (color coherence) � qq � f L • The two fronts overlap at formation: they can interfere. • The qq pair rotates color before emission. At � θ c � 2 / 3 τ coh = L θ q ¯ q The color of each quark is randomized ⇒ No interference • Interference contribution scales with dI ∝ τ coh
Two Partons: Very Small Angles � f � c � qq � f • Interference is possible. Antenna color remains almost constant • Interference occurs as in vacuum up to corrections Θ 2qq / Θ 2C The dipole interacts as a single charge • The corrections Θ 2qq / Θ 2C may lead to non-trivial distribution Natural limit for connecting to N=1 opacity (Mehtar-Tani, Salgado, Tywoniuk 10, see Hao Ma’s talk)
Summary p p + L + P ( ω , k ⊥ ) L I ( ω , k ⊥ ) q + q k x + x + k gg y + qg + y + k gg qg qq k 0 0 qq q p p • Medium induced radiation scales with the medium L − ( k ⊥ − k + u L ) 2 � � f L + ω P ( ω , k ⊥ ) ∝ α s C F θ 2 exp . Q 2 Q 2 s s • Large angles Θ f < Θ qq “vacuum medium” interference leads to: � ω � 1 / 2 R = |I| P = τ int Interference is suppressed (quantum coherence) L < ω c • Small angles Θ c << Θ qq < Θ f “medium-medium” interference : R = |I| P = τ coh (color coherence) Interference is suppressed ≪ 1 L • Very small angles Θ qq < Θ c the medium interacts with the whole dipole charge
⇒ Conclusions • Unless Θ qq is very small Each source induces gluons independently from each other • Typical sources for in-medium antennas In-medium radiations ⇒ θ qq ~ θ f Vacuum splittings (QCD evolution) ⇒ θ qq takes any value but ( ) q ∼ 10 GeV 2 / fm θ c ∼ 0 . 005 ˆ ω c ∼ 900 GeV L ∼ 6 fm BDMPS-Z gluons are NOT angular ordered • In addition to BDMPS-Z gluons, color decoherence of the antenna leads to additional gluon radiation! (see Y. Mehtar-Tani’s talk)
⇒ Conclusions • Unless Θ qq is very small Each source induces gluons independently from each other • Typical sources for in-medium antennas In-medium radiations ⇒ θ qq ~ θ f Vacuum splittings (QCD evolution) ⇒ θ qq takes any value but ( ) q ∼ 10 GeV 2 / fm θ c ∼ 0 . 005 ˆ ω c ∼ 900 GeV L ∼ 6 fm BDMPS-Z gluons are NOT angular ordered (but vacuum-like ones are) • In addition to BDMPS-Z gluons, color decoherence of the antenna leads to additional gluon radiation! (see Y. Mehtar-Tani’s talk)
Back-up
Parameter Definition Parametric estimate Physical meaning � 2 � θ f 2 ω vacuum formation time τ q τ f k 2 θ q ⊥ � � 2 ω ω ω c L in–medium formation time τ f q ˆ � 1 / 4 � � 3 / 4 2ˆ q � ω c formation angle θ f θ c ω 3 ω √ ˆ qL θ c ω c saturation angle θ s ω ω � θ f � 2 2 interference time τ int τ f ωθ 2 θ q ¯ q q ¯ q θ f 1 transverse resolution time τ λ τ f q ) 1 / 4 θ q ¯ q ( ω ˆ θ q ¯ q � θ f � 2 / 3 2 color decoherence time τ coh τ f q θ 2 q ) 1 / 3 θ q ¯ (ˆ q q ¯
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