Transcript Zhou
TMDs in nuclei
Jian Zhou Temple University Based on paper: Phys.Rev.D77:125010,2008. e-Print: arXiv:0801.0434 [hep-ph] by Liang, Wang and JZ.
Outline:
Brief review on k T broadening phenomena Nuclear TMDs and k T broadening Nuclear dependent azimuthal asymmetry Summary
nuclear dependent effect
Inclusive process (not too small x) weak dependence on target size single hard scattering ( the nuclear PDF) coherent multiple scattering power suppression 1/Q 2 A 1/3 In order to explore strong nuclear dependence effect, there are few ways to go .
strong nuclear effect: small x region, multiple scales process, no power suppression energy loss, k T broadening
k
T
broadening and higher-twist collinear approach
Transverse momentum distribution at low p T in fixed order perturbative calculation is ill-defined Moment of p T -distribution is less sensitive to low p T region: Momentum broadening: sensitive to the medium properties It turns out that k T Moreover, broadening is proportional to gluon distribution in the medium.
Baier, Dokshitzer, Mueller, Peign and Schiff
k
T
broadening in Drell-Yan
First considered in a QED model.
Bodwin, Brodsky and Lepage k T broadening calculated in the collinear factorization, in the covariant gauge, longitudinal gluon carry small transverse momentum. Guo in the light cone gauge, transverse gluon with collinear momentum. Fries In the collinear factorization, Double scattering contribute to kt broadening
k
T
broadening in various processes
1 Di-jet(photon-quark) imbalance Luo, Qiu and Sterman 2 Single jet in SIDIS G uo 3 heavy quarkonia in d+A kang and Qiu A lot of models for twist-4 collinear correlations are available, Guo; Qiu and Vitev; Fries; Osborne and Wang Assume nucleon is weakly bounded, gluon and quark come from the different nucleon, Conclusion:
Resummation
Multiple scattering resummed in the collinear factorization: Majumder and Muller Such resummation is also achieved in the Wilson line approach Kovner and Wiedemann , SCET Idilbi and Majumder; D ’ Eramo, Liu and Rajagopal TMD factorization Liang, Wang and JZ
Nuclear TMDs
Our starting point: where, Ji, Ma, Yuan Belitsky, Ji and Yuan In the light cone gauge(A + =0), L || =1 These gauge links not only make the TMDs gauge invariant but also lead to physical consequences such as single-spin asymmetry and nuclear dependent effect.
k
T
broadening and nuclear TMD
Partial integration: In the light cone gauge A + =0,
k
T
broadening and nuclear TMD
To isolate the leading nuclear effect, we neglect
d y
A
( 0)
D
Integrate over k T
A
Weakly bound approximation Strong nuclear size dependent effect , where
k
T
distribution and nuclear TMD
Infinite multiple scattering effect have been encoded in the gauge link, one should be able to reach resummation formula by manipulating the gauge link.
Using this relation again,
k
T
distribution and nuclear TMD
Transport operator: Expand the exponential factor, neglect covariant derivative
d y
A
( 0) ( )
A
Odd power of the operator vanish under the parity invariance, we are left only with the even-power terms of the expansion, weakly bound approximation
Maximal two-gluon correlation approximation
The combinatorial factor for grouping 2n number of gluon field operators into n pairs, Courtesy of Gao each gluon pair attaching to different nucleon in nuclei, so that we have the maximum nuclear size enhancement
Gaussian distribution
Inserting this expression into nuclear TMD, one ends up with, Replace the delta function with , and integrate over where Taking into account intrinsic transverse momentum in a nucleon, nuclear TMD modified as,
Azimuthal asymmetry in SIDIS
Unpolarized cross section, High p T , gluon radiation Georgi and Politzer Low p T , parton intrinsic transverse momentum Cahn
Nuclear dependent effect: jet production in SIDIS
Gao, Liang and Wang Twist-3 TMD distribution free partons g=0, using equation of motion, Reproduce the well known Cahn effect result (due to the finite k T ) Cahn
Nuclear dependent effect: jet production in SIDIS Gao, Liang and Wang Nuclear TMDs: with given twist-2 and twist-3 TMDs in a nucleon, one can then calculate nuclear dependence of the azimuthal asymmetry.
To illustrate it qualitatively, using an ansatz of the Gaussian Conclusion: the azimuthal asymmetry is suppressed by the k T broadening.
Nuclear dependent effect: direct photon production in SIDIS As long as l T < Nuclear dependent effect: direct photon production in SIDIS Fragmentation functions are perturbative calculable in QED . Transverse momentum conservation: When, expand structure functions with respect to k T around p T =l T Finally, structure functions take form, Nuclear dependent effect: direct photon production in SIDIS At High l T , twist-4 collinear factorization apply, l T < Courtesy of Gao One may expect TMD factorization and Collinear factorization yield the same result in the overlap region Λ QCD < We demonstrate that the leading nuclear effect comes from the gauge link in the nuclear TMDs. Azimuthal asymmetry is suppressed due to the k T broadening. The scale evolution of k T broadening.Summary:
Outlook: