Transverse Spin Physics

by Barone, Vincenzo; Ratcliffe, Philip G.

• ISBN13: 9789812381019
• ISBN10: 9812381015
• Format: Hardcover
• Copyright: 2003-03-01
• Publisher: World Scientific Pub Co Inc

Summary

This book is devoted to the theory and phenomenology of transverse-spin effects in high-energy hadronic physics. Contrary to common past belief, it is now rather clear that such effects are far from irrelevant. A decade or so of intense theoretical work has shed much light on the subject and brought to surface an entire class of new phenomena, which now await thorough experimental investigation. Over the next few years a number of experiments world-wide (at BNL, CERN, DESY and JLAB) will run with transversely polarised beams and targets, providing data that will enrich our knowledge of the transverse-spin structure of hadrons. It is therefore timely to assess the state of the art, and this is the principal aim of the volume.An outline of the book is as follows. After a few introductory remarks (Chapter 1), attention is directed in Chapter 2 to transversely polarised deeply-inelastic scattering (DIS), which probes the transverse spin structure function g2. This existing data are reviewed and discussed (for completeness, a brief presentation of longitudinally polarised DIS is also provided). In Chapter 3 the transverse-spin structure of the proton is illustrated in detail, with emphasis on the transversity distribution and the twist-three parton distribution contributing to g2. Model calculations of these quantities are also presented. In Chapter 4, the QCD evolution of transversity is studied at leading and next-to-leading order. Chapter 5 illustrates the g2 structure function and its related sum rules within the framework of perturbative QCD. The last three chapters are devoted to the phenomenology of transversity, in the context of DrellYan processes (Chapter 6), inclusiveleptoproduction (Chapter 7) and inclusive hadroproduction (Chapter 8). The interpretation of some recent single-spin asymmetry data is discussed and the prospects for future measurements are reviewed.

Table of Contents

Preface	vii
Introduction	1	(12)
The transverse-spin structure function and the transversity distributions	2	(1)
A first look at g2	3	(2)
A prelude to transversity	5	(4)
Notation and terminology	9	(2)
Conventions	11	(2)
Polarised deeply-inelastic scattering	13	(44)
Basics of DIS	14	(3)
The unpolarised cross-section	17	(2)
Polarised cross-sections	19	(3)
Target polarisation	22	(2)
Forward virtual Compton scattering	24	(2)
Spin asymmetries	26	(2)
The partonic content of structure functions	28	(11)
Unpolarised structure functions	31	(2)
The longitudinal spin structure function	33	(1)
The transverse-spin structure function	34	(5)
Mellin moments of polarised structure functions	39	(7)
The first moment of g1	40	(2)
The Bjorken sum rule	42	(1)
The Wandzura--Wilczek relation	43	(1)
The Burkhardt--Cottingham sum rule	44	(2)
The Efremov--Leader--Teryaev sum rule	46	(1)
Experimental results on polarised structure functions	46	(7)
Transverse spin in electroweak DIS	53	(4)
The transverse-spin structure of the proton	57	(46)
The quark-quark correlation matrix	57	(2)
Leading-twist distribution functions	59	(3)
Probabilistic interpretation of distribution functions	62	(3)
Vector, axial and tensor charges	65	(1)
Quark-nucleon helicity amplitudes	66	(2)
The Soffer inequality	68	(2)
Transverse motion of quarks	70	(5)
Twist-three distributions	75	(6)
Sum rules for ΔTf and gT	81	(2)
T-odd distributions	83	(4)
Model calculations	87	(16)
Models for the transversity distributions	88	(8)
Calculations of the tensor charges	96	(2)
Models for g2	98	(5)
The QCD evolution of transversity	103	(34)
The renormalisation-group equation	104	(5)
QCD evolution at leading order	109	(6)
QCD evolution at next-to-leading order	115	(8)
Fragmentation functions at next-to-leading order	123	(3)
Evolution of the transversity distributions	126	(5)
Evolution of the Soffer inequality and positivity constraints	131	(4)
The low-x behaviour of h1	135	(2)
The g2 structure function in QCD	137	(20)
The operator-product expansion---non-singlet	139	(4)
Ladder-diagram summation	143	(3)
Singlet g2 in LO	146	(1)
Non-singlet and singlet coefficients g2 in NLO	146	(1)
Sum rules for g2 in QCD	147	(3)
The Burkhardt--Cottingham sum rule in QCD	147	(2)
The Wandzura--Wilczek relation in QCD	149	(1)
The Efremov--Leader--Teryaev sum rule in QCD	150	(1)
Low-x behaviour of g2	150	(1)
Twist-three evolution equations in the large-Nc limit	151	(3)
Evolution of the g2 fragmentation function	154	(3)
Transversity in Drell--Yan production	157	(26)
Double transverse-spin asymmetries	157	(1)
The Drell--Yan process	158	(7)
Z0-mediated Drell--Yan processes	165	(1)
Factorisation in Drell--Yan processes	165	(6)
Twist-three contributions to the Drell--Yan process	171	(5)
Predictions for Drell--Yan double transverse-spin asymmetries	176	(3)
Transversity at RHIC	179	(4)
Transversity in inclusive leptoproduction	183	(62)
Single-particle leptoproduction: definitions and kinematics	183	(4)
The partonic description of semi-inclusive DIS	187	(3)
The fragmentation matrix	190	(2)
Time reversal and transverse polarisation	192	(2)
Leading-twist fragmentation functions	194	(6)
KT-dependent fragmentation functions	197	(3)
The Collins fragmentation function	200	(3)
Cross-sections and asymmetries of inclusive leptoproduction	203	(8)
Integrated cross-sections	205	(1)
Single-spin azimuthal asymmetries	205	(6)
Factorisation in semi-inclusive DIS	211	(8)
The collinear case	211	(5)
The non-collinear case	216	(2)
Sudakov form factors	218	(1)
Inclusive leptoproduction at twist three	219	(1)
Two-particle leptoproduction	220	(9)
Leptoproduction of spin-one hadrons	229	(2)
Transversity in exclusive leptoproduction processes	231	(1)
Phenomenological analyses and experimental results	232	(10)
Λ0 hyperon polarimetry	232	(2)
Azimuthal asymmetries in pion leptoproduction	234	(7)
Transverse polarisation in e+e- collisions	241	(1)
Experimental perspectives	242	(3)
Hermes	242	(1)
Compass	243	(1)
Elfe	244	(1)
Tesla-N	244	(1)
Transversity in inclusive hadroproduction	245	(12)
Inclusive hadroproduction with a transversely polarised target	245	(3)
Transverse motion of quarks and single-spin asymmetries	248	(3)
Single-spin asymmetries at twist three	251	(6)
Experimental results and phenomenology	252	(5)
Appendix A Polarisation of a Dirac particle	257	(6)
A.1 The polarisation operator and spin vector	257	(2)
A.2 Longitudinal polarisation	259	(1)
A.3 Transverse polarisation	260	(1)
A.4 The spin density matrix	261	(2)
Appendix B Sudakov decomposition of yectors	263	(2)
Appendix C Projectors for structure functions	265	(2)
Appendix D Reference frames	267	(4)
D.1 The γ*N collinear frames	267	(1)
D.2 The hN collinear frames	268	(3)
Appendix E Dimensional regularisation and minimal subtraction	271	(4)
Appendix F Mellin-moment identities	275	(2)
Bibliography	277	(14)
Index	291