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Azimuthal Spin Asymmetries

in

Light-Cone Quark model

Barbara Pasquini Pavia U. & INFN, Pavia (Italy)

In questo manuale sono illustrate le regole base per la corretta applicazione del marchio Università di Pavia. Il logo, i caratteri tipografici e i colori scelti sono infatti gli elementi che partecipano alla costruzione dell’identità visiva di qualsiasi attore che voglia presentarsi al mercato, sia esso un prodotto mass market, un’Istituzione o un ateneo. Sono il suo volto commerciale ma anche istituzionale, quello che permetterà all’Università di Pavia di essere riconoscibile nel tempo agli occhi del suo pubblico interno, ma anche esterno. Proprio per il ruolo centrale che rivestono, tali elementi devono essere rappresentati e utilizzati

secondo regole precise e inderogabili, al fine di garantire la coerenza e l’efficacia dell’intero sistema di identità visiva. Per questo è importante che il manuale, nella sua forma cartacea o digitale, venga trasmesso a tutti coloro che in futuro si occuperanno di progettare elementi di comunicazione per l’Università di Pavia.

INTRODUZIONE: L’IMMAGINE UNIVERSITÀ DI PAVIA

UNIVERSITÀ DI PAVIA

!TMDs from Light-Cone Quark Model for proton and pion

!Model results for Drell-Yan asymmetry

!Conclusions

Outline

!Drell-Yan at COMPASS with pion beam and transversely polarized target

‣asymmetry with convolution of proton pretzelosity and pion Boer-Mulders

‣physical content of proton pretzelosity ‣transverse-spin structure of quarks in the pion

Polarized Drell-Yan at COMPASS

Azimuthal spin asymmetries in light-cone constituent quark models

S. Boffi∗,1, 2 A. V. Efremov∗,3 B. Pasquini,1, 2 P. Schweitzer,4 and F. Yuan∗5, 6

1Dipartimento di Fisica Nucleare e Teorica, Università degli Studi di Pavia, Pavia, Italy 2Istituto Nazionale di Fisica Nucleare, Sezione di Pavia, Pavia, Italy

3Joint Institute for Nuclear Research, Dubna, 141980 Russia 4Department of Physics, University of Connecticut, Storrs, CT 06269, USA

5RIKEN BNL Research Center, Building 510A, BNL, Upton, NY 11973, U.S.A. 6Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, U.S.A.

(Dated: Spring 2010)

First notes on azimuthal and/or spin asymmetries due to T-odd TMDs in the Drell-Yan process (DY) and possibly (at a later stage) also semi-inclusive deeply inelastic scattering (SIDIS) (?). The purpose is to prepare practical predictions, most practically for COMPASS meeting 26 April 2010, on the basis of results from light-cone quark models for TMDs in nucleon [1], and pion(!) [2]. The “∗” marks not-informed authors, who might be interested and could become prospective informed-co-authors, upon agreement.

PACS numbers: 12.38.Bx, 12.39.St, 13.85.Qk Keywords:

I. INTRODUCTION

We study DY, see Fig. 1. This Figure and its caption are shamelessly borrowed from [3]. We will work in the Collins-Soper frame (CS) which is a particular dilepton rest frame, see [3] for a nice and pedagogical review.

X

H

H

X l

l a

b

+

−

q q

a

b −

X

H

H

X l

l a

b

+

−

a

b

q− q

FIG. 1: Amplitude for dilepton production in parton model approximation. Both diagrams have to be taken into account. The spectator systems Xa and Xb of the two hadrons are not detected.

The kinematical variables are s = (p1 + p2)2, the dilepton invariant mass Q2 = (k1 + k2)2 with p1/2 (and k1/2) indicating the momenta of the incoming proton and hadron h (and the outgoing lepton pair), and the rapidity

y = 1

2 ln

p1(k1 + k2)

p2(k1 + k2) . (1)

The parton momenta x1/2 in the TMDs are fixed in terms of s, Q 2 and y as follows

xa/b =

√

Q2

s e±y , (2)

and typically the observables are presented as functions of y. Below we will have COMPASS in mind, where the kinematics is s ≈ 400 GeV2 and Q2 = 20 GeV2.

Alternatively, one can use xF = xa − xb with xaxb = Q2/s.

a

b µ+

µ-

dσ

d4qdΩ =

α2

Fq2 σ̂U

�� 1 +D[sin2 θ]A

cos 2φ U cos 2φ

�

+|�ST | � D[sin2 θ]

� Asin(2φ+φS)T sin(2φ+ φS) +A

sin(2φ−φS) T sin(2φ− φS)

�

+ AsinφST sinφS ��

! DY cross section at leading-twist for transversely polarized target:

Ha : proton target

Hb : pion beam

Asin(2φ+φS)T

Acos 2φU Boer-Mulders functions of incoming hadrons

Boer-Mulders functions of pion beam and pretzelosity of nucleon target

AsinφST unpolarized TMD of pion beam and Sivers function of nucleon target

Asin(2φ−φS)T Boer-Mulders functions of pion beam and transversity of nucleon target

talk of C. Quintans

Polarized Drell-Yan at COMPASS

Azimuthal spin asymmetries in light-cone constituent quark models

S. Boffi∗,1, 2 A. V. Efremov∗,3 B. Pasquini,1, 2 P. Schweitzer,4 and F. Yuan∗5, 6

1Dipartimento di Fisica Nucleare e Teorica, Università degli Studi di Pavia, Pavia, Italy 2Istituto Nazionale di Fisica Nucleare, Sezione di Pavia, Pavia, Italy

3Joint Institute for Nuclear Research, Dubna, 141980 Russia 4Department of Physics, University of Connecticut, Storrs, CT 06269, USA

5RIKEN BNL Research Center, Building 510A, BNL, Upton, NY 11973, U.S.A. 6Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, U.S.A.

(Dated: Spring 2010)

First notes on azimuthal and/or spin asymmetries due to T-odd TMDs in the Drell-Yan process (DY) and possibly (at a later stage) also semi-inclusive deeply inelastic scattering (SIDIS) (?). The purpose is to prepare practical predictions, most practically for COMPASS meeting 26 April 2010, on the basis of results from light-cone quark models for TMDs in nucleon [1], and pion(!) [2]. The “∗” marks not-informed authors, who might be interested and could become prospective informed-co-authors, upon agreement.

PACS numbers: 12.38.Bx, 12.39.St, 13.85.Qk Keywords:

I. INTRODUCTION

We study DY, see Fig. 1. This Figure and its caption are shamelessly borrowed from [3]. We will work in the Collins-Soper frame (CS) which is a particular dilepton rest frame, see [3] for a nice and pedagogical review.

X

H

H

X l

l a

b

+

−

q q

a

b −

X

H

H

X l

l a

b

+

−

a

b

q− q

FIG. 1: Amplitude for dilepton production in parton model approximation. Both diagrams have to be taken into account. The spectator systems Xa and Xb of the two hadrons are not detected.

The kinematical variables are s = (p1 + p2)2, the dilepton invariant mass Q2 = (k1 + k2)2 with p1/2 (and k1/2) indicating the momenta of the incoming proton and hadron h (and the outgoing lepton pair), and the rapidity

y = 1

2 ln

p1(k1 + k2)

p2(k1 + k2) . (1)

The parton momenta x1/2 in the TMDs are fixed in terms of s, Q 2 and y as follows

xa/b =

√

Q2

s e±y , (2)

and typically the observables are presented as functions of y. Below we will have COMPASS in mind, where the kinematics is s ≈ 400 GeV2 and Q2 = 20 GeV2.

Alternatively, one can use xF = xa − xb with xaxb = Q2/s.

a

b µ+

µ-

dσ

d4qdΩ =

α2

Fq2 σ̂U

�� 1 +D[sin2 θ]A

cos 2φ U cos 2φ

�

+|�ST | � D[sin2 θ]

� Asin(2φ+φS)T sin(2φ+ φS) +A

sin(2φ−φS) T sin(2φ− φS)

�

+ AsinφST sinφS ��

! DY cross section at leading-twist for transversely polarized target:

Ha : proton target

Hb : pion beam

Asin(2φ+φS)T

Acos 2φU Boer-Mulders functions of incoming hadrons

Boer-Mulders functions of pion beam and pretzelosity of nucleon target

AsinφST unpolarized TMD of pion beam and Sivers function of nucleon target

Asin(2φ−φS)T Boer-Mulders functions of pion beam and transversity of nucleon target

talk of C. Quintans

Table 9: Expected statistical errors for various asymmetries assuming two years of data taking and a beam momentum of 190 GeV/c.

Asymmetry Dimuon mass (GeV/c2) 2 < Mµµ < 2.5 J/ψ region 4 < Mµµ < 9

δ A cos 2φ U

0.0020 0.0013 0.0045

δ A sin φS T

0.0062 0.0040 0.0142

δ A sin(2φ+φS) T

0.0123 0.008 0.0285

δ A sin(2φ−φS) T

0.0123 0.008 0.0285

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