Hadron single spin asymmetry and polarization relation in reactions involving photons

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1 STARS and SMFNS 2017 Habana Varadero, Cuba Hadron single sin asymmetry and olarization relation in reactions involving hotons Carlos Javier Solano Salinas Facultad de Ciencias UNI, Lima, Perú Cooeration with V. Guta CINVESTAV Mérida, México

2 MOTIVATION SOME PROTON CONUNDRUMS:

3 SIZE OF THE PROTON BEFORE: Proton s radius was about 0,88 femtometers (10-15 m) LAST MEASUREMENTS: Bernauer, MAMI article accelerator in Mainz, Germany, using electron scattering: roton s radius ~ 0,88 fm Randolf Pohl, Max Planck Institute of Quantum Otics in Garching, Germany, a new more recise method. They created muonic hydrogen and studied the muon transitions: roton s radius ~ 0,841 fm NEW PHYSICS???

4 LIFE-TIME OF THE PROTON t=0 Big Bang t < 106 seconds Quarks and gluons roam freely t = 106 seconds Protons and neutrons form t = 10 s atomic nuclei Protons and neutrons begin to form t = 13.8 billion years In today s universe, atoms have formed into stars, lanets and intelligent life. t = 1034 years or later A substantial ortion of rotons may have decayed.

5 LIFE-TIME OF THE PROTON (cont.) Unification theories???

6 PROTON CONFINEMENT Much bigger gluon density intensity close to border DIVISION OF PROTON ENERGY

7 SPIN OF THE PROTON SPIN CRISIS (1997)

8 SPIN OF THE PROTON (cont.) Contributions to Proton Sin: Sin of valence quarks Orbital motion of valence quarks Contribution of gluons Contribution of sea quarks??? Rojo et al, RHIC-Brookhaven: gluons (35%), valence quarks (25%), unaccounted (40%) KehFei Liu, Lattice QCD: gluons (25%), valence quarks (25%), orbital valence quarks motion (50%)

9 Alternative studies Hadron single sin (Left-Right) asymmetry and olarization relation in reactions involving hotons

10 Introduction Discovery of hyeron olarization in inclusive roduction at high energies Left-right asymmetries in single-sin hadron-hadron collisions A. Exerimental results B. Theoretical models A N ( x F,T,h s ) N L ( x F, T,h s, )N L ( x F,T,h s, ) N L ( x F, T,h s, )+N L (x F,T,h s, ) N L ( x F, T,h s, )N R (x F,T,h s, ) A N ( x F,T,h s ) N L ( x F, T,h s, )+N R ( x F, T,h s, )

11 AN exerimental results

12 Theoretical Models A. QCD based hard scattering models: 1- Incoming hadron arton distributions: fia(xa,q2) 2- q q roduction from artons σ^ ij ( c,q 2 ) Calculable? by QCD 3- q q hadronization (fragmentation) into hadrons: Incalculable by QCD

13 A. QCD based hard scattering models (cont.): In order to describe the observed large asymmetries we can make use of one these ossibilities: 1- Look for higher order in the elementary rocesses which may lead to larger asymmetries 2- Introduce asymmetric intrinsic transverse momentum distributions for the transversely olarized quarks in a transversely olarized nucleon 3- Introduce asymmetric transverse momentum distribution in the fragmentation functions for the transversely olarized quarks, which lead to the observed hadrons The cross sections of the elementary rocesses are result of theoretical calculations. Probabilities 2- and 3- can only be robed exerimentally because those asymmetric momentum distributions are introduced by hand.

14 B. Non-erturbative quark-antiquark fusion models: Orbiting Valence Quark Model based in the Static (constituent) Quark Model. Basic elementary rocess is quark-antiquark fusion (incalculable by QCD). The fusion is of 1(2) valence quark(s) of Projectile with suitable sea quark/antiquark(s) from the Target. Existence of orbital motion of the valence quarks in transversely olarized nucleons. Existence of surface effect in single sin hadron-hadron collisions.

15 B. Non-erturbative quark-antiquark fusion models (cont.): The number density of roduced h s is given by N ( x F,T,h s ) N 0 ( x F,T,h s )+D ( x F,T,h s ) where N 0 (x F,T,h s ) is the contribution for non-direct formation and D( x F,T,h s ) T the number density of h s roduced through direct formation rocess q P + q h v The left-right asymmetry is dominated by ΔN ( x F,T,h s,tr ) C ΔD( x F,T,h s,tr ) exerimentally C ~ 0.6 dx P dx T q v ( x P ) q s ( xt )K ( x P,q v ;xt, q s x F,h,s ) D( x F,h s )= qv, q s D( x F,h s ) k h q v ( x F ) q s ( where x = 0 m 2h s In fragmentation region x0 xf ) N ( x F,h s ) D (x F,h s ) q v ( x F ) s

16 B. Non-erturbative quark-antiquark fusion models (cont.): The olarization of the valence quarks inside a olarized nucleon is determined by the wave function of the model (Static (constituent) Quark Model). This imlies that, for roton, 5/3 of the 2 u valence quarks are olarized in the same, and 1/3 in the oosite, direction as the roton. For d, they are 1/3 and 2/3 resectively. It should be emhasized that q (x F,tr ) q (x F,l) The simlest ansatz is 5 u+v ( x F,tr )= u v ( x F ) 1 uv ( x F,tr )= u v ( x F ) 6 1 d +v (x F,tr )= d v ( x F ) 3 2 dv ( x F,tr )= d v ( x F ) 3 6

17 Proerties of ±, or in ± 0 ( )+(0 ) π ( π,η )+X

18 Proerties of ±, or in ( )+(0 ) π ±( π 0,η )+X

19 Pion and leton air roduction

20 Proosed Reactions ± A. Left-right asymmetry in e +( ) e +π +X We consider the hoton from the ee - vertex. The effective interaction is γ+ ( ) π± +X The left-right asymmetry is π Aγ ( x F,Q s )= 2 γ γ 2 C γ k π [ Δu v ( x,q )] d ( x,q ) + 2 γ γ 2 N 0 ( x F s )+2 k π u v ( x,q ) d ( x,q ) N0 is significant only for small xf. Then for xf > π Aγ C γ This redicts π + ositive Aγ 2 Δu v ( x,q ) 2 Cγ 2 u v ( x,q2 ) 3 for large xf and similar + π+ to A N seen + in ( )+ π +X and A π to be smaller than A π but negative and similar to A πn γ γ

21 A. Left-right asymmetry in ± ± γ+ ( ) π +X and ( )+ π +X (using PDFs of CTEQ for roton and GRSV for hoton)

22 B. Transverse olarization of hyeron (H) in e + e +H+X - Here the effective interaction is γ+ H+X where is unolarized and H =,,, etc. - Kinematics is like case A, but here the hyeron tranverse olarization P(H) is measured. Denote transverse olarization of a valence quark, in the unolarized roton, by - Assume a quark with uward ( ) ( ) (downward ( ) ) olarization referentially scatter to the left (right) in the roduction lane with resect to the beam direction. - This quark will combine with a two quark state (qq) from the hoton to form hyeron H. It is also ossible that two quarks from the roton combine with a quark from the hoton to to give the olarized H.

23 Some examles for transverse olarization of hyeron (H) in e + e +H+X 1- When H = -(dds) (d v ) is common with those in -. Only valence d-quark from the roton - Let robability of d v ( )(d v ( )) from the roton to move to left (right) be. Then the robability to move to right (left) will be (1- ) - The unolarized roton has equal robability of having d v ( ) or Σ Σ d v ( )(d v ( )) Σ ( ) d v ( ) - But the robability of - We exect N ( Σ ( )), number of Σ ( ) formed by left moving d v ( ) ord v ( ) 5 1 will be roortional to α+ (1α ), while N ( Σ ( )) to 1 α+ 5 (1α ) is 5/6 (1/6). 6 - in a Thus, one exects that the olarization N ( Σ ( ))N ( Σ ( )) 2 P( Σ )= = (2 α1) N ( Σ ( ))+N ( Σ ( )) 3 - As exected, this is zero if = 1/2. Since, it is assumed 1/2, the model redicts 0 P( Σ ) 2 3

24 Other examles: 2- H = -(dss) and 0(uss) The u v and d v will contribute to their roduction by combining with (ss)γ - state from the hoton. One exects 1 1 P(Ξ )=P(Ξ )= (12 α )= P( Σ ) H = +(uus) 0 There are two formation mechanisms: (1) u v +(us )γ and (2)(uu)v +(s )γ. One exects that at low xf the non-direct formation dominates, at middle xf ( ) the + mechanism (1) will dominate (then P( Σ ) P (Σ ) or smaller), and a large x F the mechanism (2). 4- H = 0(uds) There are 3 formation mechanisms: (1) u v +(ds )γ, (2) d v +(us )γ and (3) (ud )v +(s)γ If the valence diquark mechanism is negligible one may exect 0 P( Σ ) P (Σ ) 5- H = 0(uds) Here the olarization comes only from the s-quark. The mechanism suggested is the + 0 associated roduction of K (uv s γ ) or K (d v s γ ). One exects P( Λ0 )=(2 α1)

25 C. Left-right asymmetry in ( )+ γ+x : ( )+ l + l +X It has a larger cross section than In this reaction the rojectile roton is olarized, so one exect a A N left-right asymmetry of the emitted hoton very small (exer. results comatible with zero). q s γ+gluon The rocess at the quark level is q v ( tr )+ where q Pv =u,d and q s is from the sea of the other roton. Formation of through u u is 4 times larger than through d d The model gives the asymmetry γ P T T T T T C k [ 4 Δu ( x ) u ( x )+Δd (x ) d ( x )] γ γ v s v s γ γ A N ( x F )= N 0 ( x γf )+k γ [ 4 u v ( x ) uts ( x T )+d v ( x ) d Ts ( xt )] γ For large x >0. 5 one exects C 8u ( x )+d ( x ) v v AγN ( x γf ) γ 3 4 uv ( x )+d v ( x )

26 ( )+ γ+x

27 D. Effects of Sea Polarization: Exerimental studies of g1 structure function (J.Ashman et.al.) led to the ossibility that the sea of the roton is strongly olarized (Goshtasbour, Ramsey). This could lead to a ossible observable asymmetry in the target fragmentation region (xf < 0). Consider the rection ± ( )+ π +X where the rojectile is olarized A πn ( x F,s)= π AN T T C s kπ Δ d s ( x )u v ( x ) + N 0 ( x F )+k π d s ( x ) utv ( x T ) is obtained by u d. Note that xt+xp=- xf and xpxt =mπ2/s One can also rove the sea olarization with reaction γ + π Aγ ( x F,s)= π+ Aγ is obtained by Estimates of ± γ+ ( ) π +X γ C s k π Δ u s ( x ) d γ ( x ) γ N 0 ( x F )+k π u s ( x ) d γ ( x ) u d Δ u s have been extracted (Goshtasbour-Ramsey) from data giving Δ u s (0.1)us

28 ( )+ π± +X and γ+ ( ) π± +X

29 Conclusions In this reliminar work, test of a articular henomenological model are given for some new rocesses. 0 In articular, relations like P( Σ )=2 P (Ξ ) for rocess B and π+ 2 Aγ C γ 3 in B, rovide new and simle tests of the model. The rocesses which rovide these tests would rove small x-region of the roton (C) and hoton (A). Further, the ossibility of a left-right asymmetry in the target fragmentagion due to a olarized sea is suggested. We exect that the new generation of exeriments (maybe at Jefferson Lab?), will be able to measure the effects discussed above.