Light flavor asymmetry of polarized quark distributions in thermodynamical bag model

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1 Inian Jornal of Pre & Applie Physics Vol. 5, April 014, pp Light flavor asymmetry of polarize qark istribtions in thermoynamical bag moel K Ganesamrthy a & S Mrganantham b* a Department of Physics, Urm Dhanalakshmi College, Trichy , Tamil Na, Inia b Department of Physics, National College, Trichy , Tamil Na, Inia * smrga_physics@yahoo.in, ckgm@sify.com Receive 13 September 013; accepte 1 Febrary 014 The polarize qark istribtions x ( x), x ( x) an x[ ( x) ( x)] are evalate in the kinematic range 0.01<x<1.0 at an average vale of the sqare of the for momentm transfer Q =10 GeV sing Thermoynamical Bag Moel(TBM). Flavor ecomposition of polarize qark istribtion are evalate as a fnction of x for p ( + ) / ( + ) an own ( + ) / ( + ) flavor in the kinematic range 0.033<x<0.6 at Q =.5 GeV sing TBM. The calclate vales are compare with the theoretical preictions of the Chiral Qark Soliton Moel (CQSM) an experimental reslts of J Lab E99117 an HERMES Collaboration. Keywors: Polarize istribtion fnctions, Flavor ecomposition, Bag moel 1 Introction The Fermi istribtion fnction is for the noninteracting Fermi particles, we make it to correspon to the interacting qarks emitting glons an qarkantiqark pairs (sea qarks). The reslting qark istribtion fnction is epenent on both x an Q which etermine the invariant mass of the final haronic state. Semi-inclsive Deep Inelastic Scattering (SIDIS) is a powerfl tool to etermine the separate contribtions q f of the qarks an antiqarks of flavor f to the total spin of the ncleon. The featre 1, of the CQSM as compare with many other effective moels like the MIT bag moel is that it can give reasonable preictions. This TBM moel 3,4 offers a clear insight into the transition of static properties of ncleon into its ynamical properties, as observe in DIS of lepton, is highly sccessfl in explaining the wealth of experimental ata of both npolarize an polarize ncleon strctre fnctions. The TBM is se Carlitz-Kar moel 5 only to obtain the qark istribtion fnctions which incle the effect of qark interactions. The thermal eqilibrim envisage in the TBM is only for the prpose of ecing the qark istribtion fnctions an not for explaining the mechanism of lepton interaction with the ncleon. For the latter, we still retain the original parton moel an the Deep Inelastic Scattering (DIS) of lepton on ncleon is treate as the incoherent sm of elastic scattering of lepton on qarks. In an inelastic event, this allows the energy transfer to a single qark which eventally haronizes to form a jet or more than one jet if it emits glons. The spin asymmetries of semi-inclsive cross-sections for the proction of positively an negatively charge harons have been measre in eep-inelastic scattering. The polarize qark an antiqark istribtion is extracte as a fnction of x for p an own flavors 6. The highly polarize beam an high pressre polarize 3 He target at Jefferson Lab Hall A to investigate the internal spin strctre of the netron in the pertrbative an the strong regimes of Qantm Chromo Dynamics (QCD). Thermoynamical Bag Moel preictions for spin epenent nclear qark istribtions an the polarize EMC effect for nclear meia sch as Li 7 an Al 7 are evalate 7, similarly the EMC ratio of iron to eterim has been performe in or earlier work by sing Nachtman variable 8. Thermoynamical Bag Moel The DIS of leptons on ncleons inicates that ncleon consists of three valence qarks, sea qarks an glons, confine within a small volme. Base on this observation, TBM as a moifie form of MIT bag moel treats qarks an glons as fermions an bosons. The invariant mass (W) of the final haron an the eqations of state 3 are: [ ] ε ( T ) V BV W M Mν Q + = = + (1)

2 0 INDIAN J PURE & APPL PHYS, VOL 5, APRIL 014 µ = + () 3 6( n n ) µ T µ = + (3) 3 6( n n ) µ T where ε(t) is energy ensity of the system at a temperatre T, V volme of bag, B bag constant, W mass of excite ncleon at temperatre T, v energy transfer, Q sqare of for momentm transfer, M ncleon mass at gron state, ( n n ) nmber ensity of -qark, ( n n ) nmber ensity of -qark, µ chemical potential of -qark an µ chemical potential of -qark. ε(t) is obtaine energy ensities of -qark an -qark an glon as follows: 1 1 T 7 ε T + ε = µ + µ ε ε µ µ = + T + T (4) (5) 4 T ε g = (6) 30 The chemical potentials of an qarks 9 are enote by µ an µ an the temperatre of the system by T. Since each flavor of qark an antiqark has 6 egrees of freeom an the glon has 16 egrees of freeom, the energy of the system consisting of,, an glons. The total energy ensity ε(t) of the bag comprise of qarks an glon can be written in terms of the energy ensities of the constitents as given by: ε ( T ) = 6( ε + ε ) + 6( ε + ε ) + 16ε (7) g The pressre balance conition or the energy minimization conition with respect to the ncleon volme taken into consieration. Eq. (1) relates the invariant mass of the ncleon obtaine from DIS kinematic variables an TBM. The invariant mass in TBM is obtaine by consiering the energy transfer to the ncleon reslts in heating p the constitents of the ncleon. The temperatre an two chemical potentials are not free parameters rather they are evalate in accorance with x an Q either with fixe Q or with fixe x. At very low Q, i.e. as Q tens to zero, temperatre of the bag T also tens to zero an only the valence qarks ominates. When T 0 MeV, the invariant mass is eqal to the mass of the ncleon at rest. As Q increases, temperatre of the bag increases an in trn more an more sea qarks an glons are generate an hence the invariant mass correspons to the excite state of ncleon for T>0 MeV. The npolarize p an own qark istribtion fnctions 4 are expresse in terms of temperatre an chemical potential. 6V 1 Mx ( x, Q ) = M Txln 1 exp µ + T (8) 6V 1 Mx ( x, Q ) = M Txln 1 exp µ + T (9) The anti-qark istribtion can be obtaine by ptting µ µ 6V 1 Mx ( x, Q ) = M Txln 1 exp µ + T (10) 6V 1 Mx ( x, Q ) = M Txln 1 exp µ + T (11) µ is the chemical potential of a qark with flavor. (x,q ) an (x,q ) incle both valence an intrinsic sea qarks which are ientical an not istingishable in or approach. 3 Polarize Qark Distribtions Fnctions The ncleon spin strctre, it is now wiely accepte that the intrinsic qark spin contribtes only a small fraction of the total ncleon spin. The spin sm rle inicates that the remaining part is carrie by the sea qarks, glons an orbital anglar momentm. Here we present in the kinematic region 0.01<x<1.0 where the Bjorken Scaling variable x is large. For these kinematics, the valence qark is ominant an ratio s of strctre fnction can be estimate base on or theoretical moel calclations. Let q(x) enotes the ifference between the probability of fining a qark or antiqark with positive helicity an the corresponing probability of fining a qark or antiqark with negative helicity.

3 GANESAMURTHY & MURUGANANTHAM: LIGHT FLAVOR ASYMMETRY OF POLARIZED QUARK 1 q( x) = q ( x) + q ( x) q ( x) q ( x) (1) The polarize istribtion fnctions an which can be obtaine by mltiplying the npolarize istribtions 10. ( x) = [ ( x) ( x)] [ ( x) ( x)] cos θ ( x) 3 (13) 1 ( x) = [ ( x) ( x)] cos θ ( x) 3 Polarize antiqark istribtion is obtaine by: ( x) = ( x) [ ( x)] cos θ ( x) 3 1 ( x) = [ ( x)] cos θ ( x) 3 (14) (15) (16) 1 where cos θ ( x) = is known as H0 1 + ( )(1 x) x spin iltion factor which vanishes as x0 an becomes nity as x1 characterizing the valence qark helicity contribtion to the proton. Since the spin iltion factor is not erive from first principles it is ajste to satisfy the Bjorken sm rle, which is consiere as the fnamental test of QCD, this enables to etermine the valence qark istribtions explicitly. Here H 0 is the only free parameter which is se to satisfy the Bjorken sm rle. The spin iltion is a factorization process in which it has an inbilt property of qarks, glons an sea qarks insie the ncleon. In the low x region, sea qarks varies of the orer of reciprocal of Bjorken variable an at higher x region the istribtion is proportional to the power vales of x. The polarize antiqark sea in the ncleon is also flavor asymmetry 11. We are consiering a bag which contains non-interacting valence qarks, sea qarks in a sea of glons moving at a thermoynamical temperatre T. The exchange of glons between the constitent qarks may affect qarks helicities an orbital anglar momentm. The glon istribtion can be written as : 16V Mx G( x) = M Txln 1 exp + T (17) The effect of the glon contribtion increases as the temperatre increases. Glons carry large amont of spin than the valence qarks an the sea qarks. At low excitation, the proton contains only valence qarks. The spin carrie by the glons g is obtaine by sing x for the spin iltion fnction for the glons is: g = xg( x) (18) The Bjorken sm rle 1 is given by: α ( Q ) (19) 1 p n 1 g A s g1 ( x, Q ) g1 ( x, Q ) x = 1 6 g 0 V where g A an g V are axial vector an vector copling constants of weak interactions an Bjorken sm rle is of fnamental importance for the nerstaning of elementary particles. The gage-copling constant 13 is expresse as: Q α s = ln 11 ( N f / 3) Λ (0) The strong interactions have a typical energy scale Λ QCD =50 MeV at which the copling constant becomes of orer one. The one glon exchange potential has been stie in etail sing semirelativistic qark moel calclations 14. In a formal way, the ncleon s total spin of 1 / can be ecompose into constitents. 1 1 < SN >= = + G + L 1 = ( + + q ) + G + L + L v v s q G (1) where the three terms are the contribtions for the qark an glon spins an from their orbital anglar momentm. The total qark helicity Σ is efine as the sm of the helicity istribtions of p, own an strange qarks an antiqarks. The polarize qark an antiqark istribtion is extracte as a fnction of x for p an own flavors. The flavor asymmetry of the polarize qark istribtions are evalate within the range 0.01<x1.0 at an average Q =10 GeV by sing TBM an reslts have been compare to the preictions 15 of the CQSM.

4 INDIAN J PURE & APPL PHYS, VOL 5, APRIL Flavor Decomposition The DIS of polarize leptons on polarize proton reveale that the spin carrie by the qarks is very small an consierable excitement starte on EMC spin crisis 16 an the inclsive eep inelastic scattering that only a fraction of the ncleon spin can be attribte to the qark spins an that the strange qark sea seems to be negatively polarize. These conclsions follow from the extraction of the first moments of p, own an strange qark spin istribtions from the inclsive ata by assming SU(3) f flavor asymmetry. These Parton istribtion fnctions (PDFs) epen on whether the Parton s helicity is eqal or opposite to that of the ncleon. The flavor ecomposition of polarize -qark istribtions are evalate by sing the relation ( + )/( + ) an similarly for -qarks, the flavor ecomposition is ( + ) /( + ) where an are the npolarize p an own qark istribtion fnctions, an are the polarize istribtion fnctions. We se the p-qark an own-qark istribtions 17 obtaine in J Lab E99117 along with preliminary reslts of the HERMES semiinclsive measrements Reslts an Discssion In the present work, the flavor asymmetry has been evalate by qark istribtions base on TBM. Using the qark istribtion fnctions (obtaine by transforming the Fermi istribtion fnction to the infinite momentm frame an sbstitting the bag variables) the ncleon strctre fnctions are calclate. Figre 1 shows similar behavior in the positive x omain while comparing or evalate vales with CQSM preictions. However, in the negative x omain or estimate vales are negative in whole x region. TBM reslts shows that the x ( x) is positive in whole x region an x ( x) is negative region in 0.15<x0.8 an also almost positive for x>0.8. Ths, or preiction matches well with CQSM preictions. Figre shows x[ ( x) ( x)] is positive in the entire x region which is similar to the CQSM preiction. At very low vales of x, the ominance of sea qarks is a natral conseqence of this moel. In evalating spin strctre fnction, or efforts to satisfy Bjorken sm rle as efine by Eq. (19). The momentm fraction carrie by polarize qarks in nclear meim. The charge carrie by -qark is positive an hence polarize -qark istribtion is positive istribtion. In case of -qark Fig. 1 Polarize spin istribtion fnction x ( x) an x ( x) as a fnction of Bjorken variable x at Q =.5 GeV Fig. Polarize spin istribtion fnction x[ ( x) ( x)] as a fnction of Bjorken variable x at Q =10 GeV istribtion is ownwar negative istribtion. As expecte, the helicity ensity of the -qark is fon to be positive an large at x>0.1 an that of the qark is negative, while the helicity ensities of the light sea qarks are fon to be compatible with zero. Accoring to scaling process, the valence qarks ominate more in the higher x region than in the low x region. Since the polarization occrs only in the low x region, the p an own qarks are flippe by the sea qarks an glon in that region. The istribtion fnctions of the an qarks for the proton -qarks ominate over the -qarks whereas for the antiqarks the opposite featre is observe. The

5 GANESAMURTHY & MURUGANANTHAM: LIGHT FLAVOR ASYMMETRY OF POLARIZED QUARK 3 Fig. 3 Flavor ecomposition of the qark polarization as a fnction of x at Q =.5 GeV TBM (soli line), J Lab E99117 ata (fille circles) an The HERMES Collaboration ata (open circles) Fig. 4 Flavor ecomposition of the qark polarization as a fnction of x at Q =.5 GeV TBM (soli line), J Lab E99117 ata (fille circles) an The HERMES Collaboration ata (open circles) ominance of the -qarks over the -qarks is observe becase the chemical potential µ is greater than µ as a conseqence of two valence -qarks an one valence -qarks for the proton. The flavor ecomposition of the an qark polarization as a fnction of x has been stie sing TBM an is shown in Figs 3 an 4, respectively. The stanar eviation 19 can be carrie ot for or theoretical calclation with corresponing experimental observations. In the case of inclsive DIS that only a fraction of the ncleon spin can be attribte to the qark spins an that the strange qark sea seems to be negatively polarize. Bt in the semiinclsive polarize eep inelastic scattering which separates spin contribtions of qark an antiqark flavor to the total spin of the ncleon can be etermine as a fnction of the Bjorken scaling variable x. It is evient that the flavor ecomposition of polarize qark istribtion in the ncleon in the range 0.033<x0.6 at Q =.5 GeV by sing TBM. The calclate vales show close agreement with the experimental ata from The J Lab E99117 an HERMES Collaboration in the mile region. References 1 Diakonov D I, Petrov V Y, Pobylitsa P V, Polyakov M V & Weiss C, Ncl Phys B, 480 (1996) 341. Diakonov D I, Petrov V Y, Pobylitsa P V, Polyakov M V & Weiss C, Ncl Phys D 56 (1997) Ganesamrthy K, Devanathan V & Karthiyayini S, Mo Phys Lett A 9 (1994) Ganesamrthy K, Devanathan V & Rajasekaran M, Z Phys C 5 (1991) Carlitz R, Phys Lett B 58 (1975) 345; Kar J, Ncl Phys B, 18 (1977) Zein-Eine Meziani, Braz J Phys, 34 (004) Ganesamrthy K, Sambasivam R, Braz J Phys, 39 (009) Ganesamrthy K, Sambasivam R, Trk J Phys, 3 (008) Mac E & Ugaz E, Z Phys C, 43 (1989) Carlitz R & Kaer J, Phys Rev Lett, 38 (1997) Ganesamrthy K, & Kolangi Kannan S, Ncl Phys A,861 (011) Bjorken J D, Phys Rev, 148 (1996) 1467; D1 (1970) Boyanovsky D, arxive:hep-ph/ Antony Prakash Monteiro & Vijaya Kmar K.B, Inian J Pre & Appl Phys. 48 (010) Wakamats M, arxiv: hep-ph/ v1. 16 Ashman J, et al., EM Collaboration, Phys Lett B,06 (1988) Gao J, American Physical Society, 9 (004) Galmian P et al., arxiv: hep-exp/ v. 19 Santhosh KP, Bij RK& Antony Joseph, J Phys G: Ncl Part Phys, 35 (008)

Hadron Structure Theory I. Alexei Prokudin

Hadron Structure Theory I. Alexei Prokudin Haron Strctre Theory I Alexei Prokin The plan: l Lectre I: Strctre of the ncleon l Lectre II Transverse Momentm Depenent istribtions (TMDs) Semi Inclsive Deep Inelastic Scattering (SIDIS) l Ttorial Calclations