Energy Evolution for the SiversAsymmetries in Hard Processes

Peng Sun

LBNL in collaboration with F YuanarXiv: 1304.5037

Outlines TMD factorization Energy evolution Fit the sivers function with SIDIS

experiments Implement the TMD evolution from low Q

SIDIS to Drell-Yan Collins asymmetries

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TMD factorization TMD factorization is an extension and

simplification to the collinear factorization

Simplifies the kinematicsPower counting, correction 1/Q neglected

(PT,Q)=H(Q) f1(x1,k1T,Q) f2(x2,k2T, Q) S(T)There is no x- and kT-dependence in the hard

factor

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Energy evolution

At the leading order of ɑs

By solving CSS evolution equations

There is no Landau pole singularity in the integral

Almost parameter-freeNo Q-dependent non-perturbative form factorGaussian assumption at lower scale Q0

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SIDIS

SIDIS at HERMES

g0=0.1, gh=0.045

Q2=3.14GeV2, x=0.16

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Q2=3.14GeV2

X=0.16

SIDIS at COMPASS, Q2=7.75, x=0.1

Drell-Yan

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Fit to Sivers asymmetries

With the evolution effects taken into account. Not so large Q difference

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Uncertainties in the Sivers functions: moments

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Up quark most constrained in the moderate xLarge uncertainties in small-x region and sea quark

Predictions at RHIC

About a factor of 2 reduction, as compared to previous order of magnitude difference

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Collins asymmetries in e+e- →hh

The collins effect is porprotianal to cos(2ɸ0)

Collins asymmetries

Ec.m.≈10GeV, di-hadron azimuthal asymmetric correlation in e+e- annihilation

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Test the evolution at BEPC

Ec.m.=4.6GeV, di-hadron in e+e- annihilation BEPC-(Beijing electron-positron collider)

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Conclusion We evaluate the energy dependence for

Sivers asymmetries in hard processes, from HERMES/COMPASS to typical Drell-Yan process

The same evolution procedure consistently describes the Collins asymmetries from HERMES/COMPASS and BELLE

Further tests are needed to nail down this issue

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Thank you very much!

Ji Ma Yuan scheme, in SIDIS

Structure function is

It depends on ρ

Collins scheme

This version is much simpler than that of Ji Ma Yuan

In Aybat-Collins-Qiu-Rogers framework

And then

Here gK(b) is gc×b2

Energy Evolution in TMD factorization scheme

Aybat-Collins-Qiu-Rogers, 2011

Q2-dependence Aybat-Prokudin-Rogers, 2011

23/4/21 25Needs a cross check!

Collins asymmetries in SIDIS

asd

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Energy evolution

In our framework

At the leading order of ɑs