Longitudinal double spin asymmetries in single hadron quasi-real photoproduction at high pT

(1)

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Longitudinal

double

spin

asymmetries

in

single

hadron

quasi-real

photoproduction

at

high

p

_T

C. Adolph

i

,

R. Akhunzyanov

h

,

M.G. Alexeev

ab

,

G.D. Alexeev

h

,

A. Amoroso

ab

,

ac

,

V. Andrieux

v

,

V. Anosov

h

,

W. Augustyniak

ae

,

A. Austregesilo

q

,

C.D.R. Azevedo

b

,

B. Badełek

af

,

F. Balestra

ab

,

ac

,

J. Barth

e

,

R. Beck

d

,

Y. Bedfer

v

,

k

,

J. Bernhard

n

,

k

,

K. Bicker

q

,

k

,

E.R. Bielert

k

,

R. Birsa

z

,

J. Bisplinghoff

d

,

M. Bodlak

s

,

M. Boer

v

,

P. Bordalo

m

,

2

,

F. Bradamante

y

,

z

,

C. Braun

i

,

A. Bressan

y

,

z

,

M. Büchele

j

,

E. Burtin

v

,

W.-C. Chang

w

,

M. Chiosso

ab

,

ac

,

I. Choi

ad

,

S.-U. Chung

q

,

3

,

A. Cicuttin

aa

,

z

,

M.L. Crespo

aa

,

z

,

Q. Curiel

v

,

S. Dalla Torre

z

,

S.S. Dasgupta

g

,

S. Dasgupta

y

,

z

,

O.Yu. Denisov

ac

,

∗

,

L. Dhara

g

,

S.V. Donskov

u

,

N. Doshita

ah

,

V. Duic

y

,

W. Dünnweber

4

,

M. Dziewiecki

ag

,

A. Efremov

h

,

P.D. Eversheim

d

,

W. Eyrich

i

,

M. Faessler

4

,

A. Ferrero

v

,

M. Finger

s

,

M. Finger Jr.

s

,

H. Fischer

j

,

C. Franco

m

,

N. du Fresne von Hohenesche

n

,

J.M. Friedrich

q

,

V. Frolov

h

,

k

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E. Fuchey

v

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F. Gautheron

c

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O.P. Gavrichtchouk

h

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S. Gerassimov

p

,

q

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F. Giordano

ad

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I. Gnesi

ab

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ac

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M. Gorzellik

j

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S. Grabmüller

q

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A. Grasso

ab

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ac

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M. Grosse Perdekamp

ad

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B. Grube

q

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T. Grussenmeyer

j

,

A. Guskov

h

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F. Haas

q

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D. Hahne

e

,

D. von Harrach

n

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R. Hashimoto

ah

,

F.H. Heinsius

j

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F. Herrmann

j

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F. Hinterberger

d

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N. Horikawa

r

,

5

,

N. d’Hose

v

,

C.-Y. Hsieh

w

,

S. Huber

q

,

S. Ishimoto

ah

,

6

_,

_{A. Ivanov}

ab

,

ac

_,

_{Yu. Ivanshin}

h

_,

T. Iwata

ah

,

R. Jahn

d

,

V. Jary

t

,

R. Joosten

d

,

P. Jörg

j

,

E. Kabuß

n

,

B. Ketzer

d

,

q

,

G.V. Khaustov

u

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Yu.A. Khokhlov

u

,

7

,

8

,

Yu. Kisselev

h

,

F. Klein

e

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K. Klimaszewski

ae

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J.H. Koivuniemi

c

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V.N. Kolosov

u

,

K. Kondo

ah

,

K. Königsmann

j

,

I. Konorov

p

,

q

,

*

Correspondingauthors.

E-mailaddresses:oleg.denisov@cern.ch(O.Yu. Denisov),gerhard.mallot@cern.ch(G.K. Mallot),claude.marchand@cea.fr(C. Marchand). 1 _Deceased.

2 _Also_at_Instituto_Superior_Técnico,_Universidade_de_Lisboa,_Lisbon,_Portugal.

3 _Also_at_Department_of_Physics,_Pusan_National_University,_Busan_609-735,_Republic_of_Korea_and_at_Physics_Department,_Brookhaven_National_Laboratory,_Upton,_NY_11973, USA.

4 _Supported_by_the_DFG_cluster_of_excellence_‘Origin_and_Structure_of_the_Universe’_{(www.universe-cluster.de).} 5 _Also_at_Chubu_University,_Kasugai,_Aichi_{487-8501, Japan.}

6 _Also_at_KEK,_1-1_Oho,_Tsukuba,_Ibaraki_{305-0801, Japan.}

7 _Also_at_Moscow_Institute_of_Physics_and_Technology,_Moscow_Region,_141700,_Russia. 8 _Supported_by_Presidential_grant_{NSh-999.2014.2.}

9 _Present_address:_Typesafe_AB,_Dag_{Hammarskjölds}_väg_13,₇₅₂₃₇_Uppsala,_Sweden. 10 _Present_address:_RWTH_Aachen_University,_III._{Physikalisches}_Institut,₅₂₀₅₆_Aachen,_Germany. 11 _Supported_by_the_DFG_Research_Training_Group_Programme₁₁₀₂_“Physics_at_Hadron_{Accelerators”.} 12 _Present_address:_Uppsala_University,_Box_516,_SE-75120_Uppsala,_Sweden.

13 _Supported_by_the_German_{Bundesministerium}_für_Bildung_und_Forschung. 14 _Supported_by_EU_FP7_{(HadronPhysics3,}_Grant_Agreement_number_283286). 15 _Supported_by_Czech_Republic_MEYS_Grant_LG13031.

16 _Supported_by_SAIL_(CSR),_Govt._of_India. 17 _Supported_by_CERN-RFBR_Grant_12-02-91500.

18 _Supported_by_the_Portuguese_FCT_–_Fundação_para_a_Ciência_e_Tecnologia,_COMPETE_and_QREN,_Grants_CERN/FP_109323/2009,_116376/2010,_123600/2011_and CERN/FIS-NUC/0017/2015.

19 _Supported_by_the_MEXT_and_the_JSPS_under_the_Grants_No._18002006,_No._20540299_and_No._18540281;_Daiko_Foundation_and_Yamada_Foundation. 20 _Supported_by_the_Israel_Academy_of_Sciences_and_Humanities.

21 _Supported_by_the_Polish_NCN_Grant_{DEC-2011/01/M/ST2/02350.}

http://dx.doi.org/10.1016/j.physletb.2015.12.035

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V.F. Konstantinov

u

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A.M. Kotzinian

ab

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ac

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O. Kouznetsov

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M. Krämer

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P. Kremser

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F. Krinner

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Z.V. Kroumchtein

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N. Kuchinski

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R.P. Kurjata

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R. Longo

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A. Magnon

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G.K. Mallot

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∗

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C. Marchand

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∗

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B. Marianski

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A. Martin

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J. Marzec

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J. Matoušek

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H. Matsuda

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T. Matsuda

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G. Meshcheryakov

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W. Meyer

c

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T. Michigami

ah

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Yu.V. Mikhailov

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Y. Miyachi

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P. Montuenga

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A. Nagaytsev

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F. Nerling

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D. Neyret

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V.I. Nikolaenko

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J. Nový

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,

k

,

W.-D. Nowak

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G. Nukazuka

ah

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A.S. Nunes

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A.G. Olshevsky

h

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I. Orlov

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M. Ostrick

n

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D. Panzieri

a

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ac

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B. Parsamyan

ab

,

ac

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S. Paul

q

,

J.-C. Peng

ad

,

F. Pereira

b

,

M. Pešek

s

,

D.V. Peshekhonov

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,

S. Platchkov

v

,

J. Pochodzalla

n

,

V.A. Polyakov

u

,

J. Pretz

e

,

10

,

M. Quaresma

m

,

C. Quintans

m

,

S. Ramos

m

,

2

_,

_{C. Regali}

j

_,

_{G. Reicherz}

c

_,

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ad

_,

N.S. Rossiyskaya

h

,

D.I. Ryabchikov

u

,

8

,

A. Rychter

ag

,

V.D. Samoylenko

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,

A. Sandacz

ae

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C. Santos

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,

S. Sarkar

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,

I.A. Savin

h

,

G. Sbrizzai

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,

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P. Schiavon

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K. Schmidt

j

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11

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H. Schmieden

e

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K. Schönning

k

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12

,

S. Schopferer

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A. Selyunin

h

,

O.Yu. Shevchenko

h

,

1

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L. Silva

m

,

L. Sinha

g

,

S. Sirtl

j

,

M. Slunecka

h

,

F. Sozzi

z

,

A. Srnka

f

,

M. Stolarski

m

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M. Sulc

l

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H. Suzuki

ah

,

5

,

A. Szabelski

ae

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T. Szameitat

j

,

11

,

P. Sznajder

ae

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S. Takekawa

ab

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ac

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S. Tessaro

z

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F. Tessarotto

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F. Thibaud

v

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F. Tosello

ac

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V. Tskhay

p

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S. Uhl

q

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J. Veloso

b

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M. Virius

t

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T. Weisrock

n

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M. Wilfert

n

,

J. ter Wolbeek

j

,

11

_,

_{K. Zaremba}

ag

_,

_{M. Zavertyaev}

p

_,

E. Zemlyanichkina

h

,

M. Ziembicki

ag

,

A. Zink

i a_University_of_Eastern_Piedmont,₁₅₁₀₀_Alessandria,_Italy

b_University_of_Aveiro,_Department_of_Physics,_3810-193_Aveiro,_Portugal

c_Universität_Bochum,_Institut_für_{Experimentalphysik,}₄₄₇₈₀_Bochum,_Germany13,14

d_Universität_Bonn,_{Helmholtz-Institut}_für_{Strahlen- und}_Kernphysik,₅₃₁₁₅_Bonn,_Germany13

e_Universität_Bonn,_{Physikalisches}_Institut,₅₃₁₁₅_Bonn,_Germany13

f_Institute_of_Scientiﬁc_Instruments,_AS_CR,₆₁₂₆₄_Brno,_Czech_Republic13

g_Matrivani_Institute_of_Experimental_Research_&_Education,_Calcutta₇₀₀_030,_India16

h_Joint_Institute_for_Nuclear_Research,₁₄₁₉₈₀_Dubna,_Moscow_region,_Russia17

i_Universität_{Erlangen–Nürnberg,}_{Physikalisches}_Institut,₉₁₀₅₄_Erlangen,_Germany13

j_Universität_Freiburg,_{Physikalisches}_Institut,₇₉₁₀₄_Freiburg,_Germany13,14

k_CERN,₁₂₁₁_Geneva_23,_Switzerland

l_Technical_University_in_Liberec,₄₆₁₁₇_Liberec,_Czech_Republic15

m_LIP,_1000-149_Lisbon,_Portugal18

n_Universität_Mainz,_Institut_für_Kernphysik,₅₅₀₉₉_Mainz,_Germany13

o_University_of_Miyazaki,_Miyazaki_889-2192,_Japan19

p_Lebedev_Physical_Institute,₁₁₉₉₉₁_Moscow,_Russia

q_Technische_Universität_München,_Physik_Department,₈₅₇₄₈_Garching,_Germany13,4

r_Nagoya_University,₄₆₄_Nagoya,_Japan19

s_Charles_University_in_Prague,_Faculty_of_Mathematics_and_Physics,₁₈₀₀₀_Prague,_Czech_Republic15

t_Czech_Technical_University_in_Prague,₁₆₆₃₆_Prague,_Czech_Republic15

u_State_Scientiﬁc_Center_Institute_for_High_Energy_Physics_of_National_Research_Center_‘Kurchatov_{Institute’,}₁₄₂₂₈₁_Protvino,_Russia v_CEA_IRFU/SPhN_Saclay,₉₁₁₉₁_{Gif-sur-Yvette,}_France14

w_Academia_Sinica,_Institute_of_Physics,_Taipei_{11529, Taiwan}

x_Tel_Aviv_University,_School_of_Physics_and_Astronomy,₆₉₉₇₈_Tel_Aviv,_Israel20

y_University_of_Trieste,_Department_of_Physics,₃₄₁₂₇_Trieste,_Italy z_Trieste_Section_of_INFN,₃₄₁₂₇_Trieste,_Italy

aa_Abdus_Salam_ICTP,₃₄₁₅₁_Trieste,_Italy

ab_University_of_Turin,_Department_of_Physics,₁₀₁₂₅_Turin,_Italy ac_Torino_Section_of_INFN,₁₀₁₂₅_Turin,_Italy

ad_University_of_Illinois_at_{Urbana-Champaign,}_Department_of_Physics,_Urbana,_IL_61801-3080,_USA ae_National_Centre_for_Nuclear_Research,_00-681_Warsaw,_Poland21

af_University_of_Warsaw,_Faculty_of_Physics,_02-093_Warsaw,_Poland21

ag_Warsaw_University_of_Technology,_Institute_of_{Radioelectronics,}_00-665_Warsaw,_Poland21

ah_Yamagata_University,_Yamagata_{992-8510, Japan}19

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Articlehistory:

Received11September2015

Receivedinrevisedform17November2015 Accepted11December2015

Availableonline21December2015 Editor:M.Doser

Keywords: COMPASS

Deepinelasticscattering Doublespinasymmetry

WemeasuredthelongitudinaldoublespinasymmetriesALLforsinglehadronmuoproductionoffprotons

and deuteronsatphoton virtuality Q2_<₁ _(GeV/_c₎2 _for_transverse _hadron_momenta _p

T intherange

1 GeV/c to4 GeV/c.They weredeterminedusingCOMPASSdata takenwithapolarisedmuonbeam of160 GeV/c or200 GeV/c impingingonpolarised6_LiD_or_NH

3targets.Theexperimentalasymmetries

arecomparedtonext-to-leadingorderpQCDcalculations,andaresensitivetothegluonpolarisationG

(3)

HighpT G

Fig. 1. Contributionstothesingle-inclusivecrosssection forquasi-realphotoproductionofahadronh intodirect (left)andresolved(right)subprocessesaccordingto Ref.[14].Theinternallinesrepresentthephotona=γ∗(left)andpartons{a,b,c}= {q,q¯,g}.Thecentralblobdescribesthehardscatteringcrosssectionσˆ.Theperipheral blobsdescribethenon-perturbativeobjects:partondistributionsofthenucleon, fN

b,andofthephoton,f γ∗

a ,andthefragmentationfunctionsoftheproducedhadron,Dhc.

1. Introduction

The spin structure of the nucleon is one of the major unre-solvedissues inhadronicphysics.While thequark spin contribu-tionto the nucleon spin, denotedas

, hasbeen measured to beabout30%

[1]

,thegluonspincontributionisstillinsuﬃciently constrainedaftermorethan twodecades ofintense study.Inthe

frameworkofperturbativeQuantumChromodynamics(pQCD),

in-clusiveDeep InelasticScattering (DIS)issensitivetogluon contri-butionsonlythroughhigher-ordercorrectionstothecrosssection. Thespin-averagedgluon densityg

(

xg

)

,wherexg denotesthe

nu-cleonmomentum fraction carried by gluons, is well constrained byDISexperimentswithunpolarisedbeamandtargetbecauseof theirhighstatistics andlargekinematiccoverage. Thefewer data fromDIS experiments with polarised beam and target, however, cannot suﬃcientlyconstrainthegluonhelicitydistribution

g

(

xg

)

.

Thisaffectsdirectlyourknowledgeofthecontributionofthegluon spintothespinofthenucleon,knownas

G

=

g

(

xg

)

dxg,and

to a lesserextent that of the quarks [2]. In order tobetter con-strain

g

(

xg

)

,one hastoresorttoprocesseswherecontributions

fromgluonsappearatleadingorder,suchashadronproductionat hightransversemomentaorproductionofopencharminpolarised lepton–nucleon[3–7]orhadron–hadroninteractions[8–11].

The COMPASS collaboration hasalready investigated asymme-triesofhadronsathightransverse momenta pT,inboth the DIS

andthe quasi-realphotoproductionregimes [4,6,12]. Here, trans-verse means transverse withrespect to the direction of the vir-tualphoton

γ

∗ thatisexchanged inthescatteringprocess.Using a Lund Monte Carlosimulation, these measurements were inter-pretedonthehadronlevel,therebysimultaneouslyextractingthe gluonhelicityonthepartonlevel.Suchananalysisisrestrictedto leadingorder(LO)inthestrongcouplingconstant

α

s,aspresently

there exists no next-to-leading order (NLO) Monte Carlo simula-tionforleptoproduction.Duetothelimitationofneglectinggluon contributionsatNLO,suchresultscannot beusedinrecentglobal ﬁtsatNLOofpolarisedPartonDistributionFunctions(PDFs)[13].

InthisLetter,we presenta newanalysisofCOMPASSdatafor single-inclusive hadron quasi-real photoproduction at high pT,22

which differs from our previous analysis in that all measured hadronswithinagivenpT binareincludedintheanalysis,andnot

onlythehadron(s)withhighestpT.Moreover,theinterpretationof

22 _Note_that_also_inclusive_quasi-real_{photoproduction}_of_hadron_pairs_can_be con-sidered[15].

theresults isbasedona collinearpQCD framework thatwas de-velopeduptoNLO[14],thebasicconceptbeingtheapplicationof the factorisationtheoremto calculatethecross section of single-inclusivehadron production. The authors ofRef. [14] discuss the sensitivityof COMPASS data to

g

(

xg

)

interms ofcontributions

from“direct-photon”,

γ

∗g

→

qq (Photon

¯

Gluon Fusion),andfrom “resolved-photon”subprocesses,qg andgg,wherethephotonacts as a source of partons. Similarly, they consider direct

γ

∗q

→

qg

(QCD Compton) as well as resolved qq and gq subprocesses for

thebackground.These contributionsto thecrosssection are rep-resented schematically in Fig. 1. In the framework of collinear fragmentation, photo-absorption on quarks,

γ

∗q

→

q,is not con-tributingtohighpT hadronproduction.

In order to gain conﬁdence in the applicability of this pQCD framework to single-hadron production with longitudinally po-larisedbeamandtarget, an importantstepisto compare predic-tionsofthismodeltomeasurementswithbeamandtarget unpo-larised,forwhichthePDFsarewellknown.Whilegoodagreement

was found by RHIC experiments on the production of high-pT

hadrons in pp collisions at

√

s

200 GeV [16,17], complications arisewhenhardscatteringsubprocessesareprobedinthe “thresh-old” regime, in which large logarithmic contributions from soft and collinear gluons play a signiﬁcant role [18]. Such contribu-tionsbecomedominantattheCOMPASScentre-of-massenergyof

√

s

18 GeV.Whentakenintoaccount byatechnique knownas “threshold resummation”at next-to-leadinglogarithm (NLL)[18], the calculations reproduce the COMPASS cross section measure-ments[19]withintheoreticaluncertainties.

In thisLetter, we analyse the quasi-realphotoproduction data

collected by COMPASS from 2002 to 2011 on longitudinally

po-larised deuteron and proton targets. In Sec. 2, we give a brief descriptionoftheexperimentalsetup,anddetailsonthedata se-lectioncan be foundin Sec.3.The procedure fortheasymmetry determinationisdescribedinSec.4.InSec.5,wepresentthe cor-responding double spin asymmetries for single-inclusive hadron production asa function of their transverse momenta pT. These

asymmetriesarecomparedtocalculationsthatwereperformed us-ingthecodeofRef.[14],whichdoesnotincludetheresummation ofthresholdlogarithms.

2. Experimentalsetup

The measurements were performed with the COMPASS setup

using positive muons from the M2 beam line of the CERN SPS.

(4)

Ref.[20],withupdatesvalidsince2006describedinRef.[21].The

muon beamhada nominalmomentumof 160 GeV

/

c, exceptfor

2011wherethe momentumwas 200 GeV

/

c.On average,its

mo-mentumspreadwas5% anditspolarisationwas Pb

≈

0

.

8.

Momen-tumandtrajectoryofincident muonswere measuredby aset of scintillatorhodoscopes,scintillatingﬁbreandsiliconmicrostrip de-tectors.Thebeamwasscatteredoffasolidstatedeuteratedlithium (6_LiD) _target _from₂₀₀₂ _to ₂₀₀₆_and _off _an _ammonia _(NH

3)

tar-getin2007and2011,providinglongitudinallypolariseddeuterons andprotons,respectively.The targetmaterial wasplaced insidea largeaperture superconducting solenoid, andbydynamic nuclear polarisationit was polarised toa value of Pt

≈

0

.

5 for6LiD and

Pt

≈

0

.

85 for NH3.Until 2004, thetarget material was contained

intwocontiguous60 cm longcellsthatwereoppositelypolarised. From2006onwards,threecontiguoustargetcellsoflength30 cm, 60 cm and30 cm wereusedtominimisesystematiceffects,with the polarisation in the outer cells being opposite to that in the centralone. Thedirectionofthe targetpolarisationwas regularly flipped by reversing the solenoidfield to compensate for accep-tancedifferencesbetweenthe differenttarget cells.At leastonce peryear,thedirectionofthepolarisationwasreversedrelativeto thatofthesolenoidfield.Thedilutionfactor f ,whichaccountsfor thepresenceofunpolarisablematerial,amountstotypically0.4for thedeuteratedlithiumtargetandto0.16fortheammoniaone.Itis calculatedastheratioofthecrosssectiononpolarisabledeuteron orprotonto thaton all targetnuclei, corrected forunpolarised x

andy dependentelectromagneticradiativeeffects[22],wherex is

theBjorkenscalingvariableand y therelativemuonenergy trans-fer. No further radiative effects are taken into account. The mo-mentaandanglesofscatteredmuonsandproducedhadronswere measuredinthetwo-stageopenforwardspectrometer,whereeach

stage includes a dipole magnet with upstream and downstream

trackingdetectors. 3. Dataselection

In order to be selected, an event must have an interaction

vertex that contains both incoming and scattered muons and

at least one hadron candidate track. The measured beam

mo-mentum is required to be in a

±

20 GeV interval around the

nominal value (

±

15 GeV in 2011). In order to equalise the ﬂux through each target cell,the extrapolatedbeam trackisrequired to pass all target cells. Cuts on the position of the vertex al-low the selection of the target cell, in which the scattering oc-curred. Only events with photon virtuality Q2

<

1

(

GeV

/

c

)

2 are accepted.Thiskinematic regionis referred toin thefollowing as quasi-realphotoproductionregion.Inaddition, y isrequiredtobe within 0.1 and 0.9, where the lower limit removes events that are diﬃcult to reconstruct and the upper limit removes the re-gionwhereelectromagneticradiativeeffectsarelarge.These kine-matic cutsresult ina range of 10−5

_<

_x

_<

₀

_.

_{02 and} _a _minimum

mass squared of the hadronic ﬁnal state, W2_, _of ₂₅

₍

_GeV

_/

_c2

₎

2_.

Thehadron candidatetrackmust have pT

>

0

.

7GeV

/

c.The

frac-tion z of the virtual photon energy carried by the hadron is

required to be in the range 0

.

2

<

z

<

0

.

8, where the lower limit is imposed to suppress the contribution from target rem-nant hadronisation and the upper limit to reject badly recon-structed hadrons. The anglebetweenthe directionofthe hadron and that of the virtual photon is restricted to be in the range 10 mrad

< θ <

120 mrad, which corresponds to 2

.

4

>

η

>

−

0

.

1, where

η

is the pseudo-rapidity in the

γ

∗N centre-of-mass sys-tem. Afterall selections, the ﬁnal sample consistsof140 million eventsforthedeuterontargetand105millionfortheproton tar-get.

4. Asymmetrycalculation

The double-spin asymmetry of the cross sections for single hadron quasi-real photoproduction is deﬁned as ALL

= (

σ

−

σ

⇔

)/(

σ

+

σ

⇔

)

=

σ

/

σ

,wherethesymbols

and

⇔

denote anti-paralleland parallelspin directions,respectively, ofthe inci-dent muonandthetarget deuteronorproton.Thisasymmetry is evaluated usingthesamemethodasinourpreviousanalyses [6]. The number of hadrons produced in a target cell is related to

ALL and to the spin independent cross section

σ

=

σ

+

σ

⇔:

Ni

=

ai

φ

ini

σ

(

1

+

fiPbPtiALL

)

,wherei

=

u1

,

d1

,

u2

,

d2.Atargetcell (u or d) withagivendirectionofthe targetpolarisation (1or2) hastheacceptanceai,theincomingmuonﬂux

φ

iandthenumber

oftargetnucleonsni.Forthetwo-celltarget,u andd denotes

up-streamanddownstreamcell, respectively,whileforthethree-cell target,u denotesthesumoftheoutercellsanddthecentralcell. The asymmetry ALL isextracted fromthe second orderequation

that isobtainedfromthe quantity

(

Nu1

·

Nd2

)/(

Nd1

·

Nu2

)

.Inthis

relation,ﬂuxesandacceptancescancel,provided that theratioof acceptances ofthe twosets ofcells is equalforthe two orienta-tionsofthesolenoidﬁeld.

Inordertominimisestatisticaluncertainties,allquantities

en-tering the asymmetry are calculated for each hadron using a

weight factor wi

=

fiPb [23].The muon beampolarisation Pb is

obtained from a parametrisation as a function of the beam mo-mentum.The targetpolarisation Pti isnotincludedintheweight

wi asitchangeswithtime andcouldgeneratefalseasymmetries.

Inordertoreducesystematicuncertainties,dataaregroupedinto periods that are close in time and hence have the same detec-torconditions,andtheweightedaverageoverallperiodsistaken. The asymmetries determined for a given target from data taken in different years were found to be consistent and hence com-bined. The asymmetriesare obtainedforboth positive and nega-tive unidentiﬁedhadronsinbinsof pT intherange0

.

7 GeV

/

c to

4 GeV

/

c andinbinsof

η

intherange

−

0

.

1 to2

.

4 inorderto fa-cilitatea detailedcomparisontotheory (see Sec.5). Thedatafor

pT

<

1

.

0 GeV

/

c areonlyusedtoinvestigatesystematic

uncertain-ties as the pQCD framework is commonly applied only for hard

scales

μ

2

_p2

T

≥

1

.

0

(

GeV

/

c

)

2,andtheyareshowngreyedoutin

alltheﬁgureswheretheyappearin.

Thesystematicuncertaintieson ALLarecalculatedasthesquare

rootofthesumofsquaresofmultiplicativeandadditive contribu-tions. The uncertainties on the dilution factor (

≈

5%), the beam (

≈

5%)andthetarget(

≈

5%)polarisationscontribute toatotalof

≈

8% of multiplicative uncertainties, i.e. thosebeing proportional totheasymmetryitself.Additivecontributionsoriginatefrom ﬂuc-tuations of the detector performance, which may lead to false asymmetries. Their possible occurrence is investigated by divid-ingthedatasampleintodifferentsubsets.Asymmetriescalculated with hadrons detected in left and right (top and bottom) parts of the spectrometers are found to be compatiblewithin statisti-caluncertainties,aswell asthoseforthetworelativeorientations of the solenoid ﬁeld and the target spin vectors. No systematic uncertaintyisthusattributedtotheseeffects.Possiblefalse asym-metriesbetweendatasetshavingthesamepolarisationstatesare also foundto be compatiblewithzero.Foreach pT bin,the

sta-tisticaldistributionoftheasymmetriescalculatedbytime periods closelyfollowsanormaldistribution.Theobserveddeviationsfrom a Gaussian allow usto quantify thelevel of overall additive sys-tematicuncertaintiesasafractionofthestatisticalones,whichon averageamounts toaboutone half.Theseadditive systematic un-certaintieslargelydominateoverthemultiplicativeones.

5. Resultsandinterpretation

Theﬁnalasymmetriesarecalculatedusingalldataaccumulated withthedeuterontarget intheyears2002to 2006andwiththe

(5)

Fig. 2. TheasymmetryALLasafunctionofpT forchargedhadronquasi-realphotoproductionontheprotonforthreerapiditybins.Thebandsatthebottomindicatethe systematicuncertainties,whicharedominatedbytimedependentﬂuctuations(seeSec.4). Top:positivehadronproduction;bottom:negativehadronproduction.

Fig. 3. Same asFig. 2, but for the deuteron.

proton target in the years 2007 and2011. Their pT-dependence

in three rapidity bins spanning the full interval

−

0

.

1

<

η

<

2

.

4 (

[−

0

.

1

,

0

.

45

]

,

[

0

.

45

,

0

.

9

]

, and

[

0

.

9

,

2

.

4

]

) is shown in Fig. 2 and

Fig. 3foreachtargettypeandhadroncharge.

We compareour asymmetries with theoretical calculationsat

NLOwithoutthresholdresummationbasedontheframework

de-scribed in Ref. [14] andsummarised in the following. Using the code of Ref. [14], the asymmetries are computed in bins of pT

and

η

as theratio of polarised to unpolarised hadron cross sec-tions,whereacrosssectionisaconvolutionofthe“muon–parton distributionfunction” faμ, thenucleon PDFs fbN,the perturbative

partoniccrosssections

σ

ˆ

a+b→c+X,andthefragmentationfunctions

(FF)Dhc: ALL

(

pT

,

η

)

=

d

σ

h d

σ

h

(

pT

,

η

)

=

a,b,c

f μ a

⊗

f_bN

⊗

d

σ

ˆ

a+b→c+X

⊗

Dhc

a,b,c f μ a

⊗

f_bN

⊗

d

σ

ˆ

a+b→c+X

⊗

Dhc

.

(1)

Hereandbelow,spin-dependentquantitiesaredenotedby the symbol

andwillbe referredtoaspolarisedonesintherestof the Letter (spin-independentones asunpolarised). The processes involved in Eq. (1) can be classified into “direct” ones that are initiated by aquasi-real photonand“resolved” onesthatare ini-tiatedbyitsfluctuationintopartons.Thisclassificationisdenoted by the subscript a (see Fig. 1). For direct processes, subscript a

refers to

γ

∗,and

()

f_γμ∗ istheprobability fora muonto emita

quasi-realphoton. Forresolved processes, subscript a refersto q,

¯

q or g,and

()

faμ is the convolution of thisprobability witha

non-perturbative parton distribution of the photon,

()

faγ∗. The

polarised version of the latter is not known experimentally and hence taken to range between the positive andnegative magni-tude of theunpolarised one. This induces a small uncertainty in thetheoreticalcalculations.

Thevaluesoftheasymmetriesarecomputedhereusingthe fol-lowinginputdistributions:theunpolarisedpartondistributionsof thephoton faγ∗ fromGRS

[24]

,theunpolarisednucleon PDFs fbN

(6)

Fig. 4. Contributionsofthesixsubprocessesa+b→c+X describedinSec.1tothefullNLOunpolarised(left)andpolarised(right)photoproductioncrosssectionsfora deuterontarget.ThepolarisedcrosssectionsarecomputedusingthepolarisedPDFsetofRef.[13].

Fig. 5. COMPASSasymmetriesALLforaprotontargetasafunctionofpTandinthreerapiditybins,comparedtoNLOcalculationsbasedonRef.[14]fordifferentchoicesfor thepolarisedPDFs(seetext).Onlystatisticaluncertaintiesareshown.Errorbandsonthetheorycurvesrepresenttheuncertaintiesduetothepolarisedpartondistribution ofthephoton.Top:positivehadronproduction;bottom:negativehadronproduction.

inRef. [14] (the “standard” setandthe two sets for“maximum” [

g

(

x

)

=

g

(

x

)

] and “minimum” [

g

(

x

)

= −

g

(

x

)

] gluon distribu-tionfunctionsatinputscale),aswellasthemostrecentpolarised PDFsetDSSV14fromRef.[13].ForthepolarisedPDFsetsused,the integrationovertherange0

.

05

<

xg

<

0

.

2,whichischaracteristic

forthe kinematiccoverage ofCOMPASS in thegluon momentum

fraction, yields thefollowing “truncated”valuesof

G at ascale of3

(

GeV

/

c

)

2

:

GGRSVmin

≈ −

0

.

6,

GDSSV14

≈

0

.

1,

GGRSVstd

≈

0

.

2,

GGRSVmax

≈

0

.

7.Theotherinputsthatwechangedwithrespectto Ref.[14]arethefragmentationfunctionsDh_c,forwhichweusethe mostrecent parton-to-pion fragmentation setof Ref. [27], which bestﬁtstherecentCOMPASSpionmultiplicities[28].Wechecked, asitwasdone inRef.[14],thatasymmetriesforhadronandpion productionarealmostindistinguishable,sothat itissafeto com-pare ourexperimental data totheoretical asymmetries computed withaparton-to-pionFFset.Thefractionsofthetotalunpolarised (respectively polarised) cross section for the various individual subprocesses are shown in Fig. 4 as a function of pT. Although

theunpolarisedcrosssectionsforprocessesinvolvinggluonsfrom thenucleonarenotthedominantones,thepolarisedcrosssection forthe

γ

g subprocessislargeinmagnitudeforhadronproduction athigh pT,which makesthe studyofsuch asymmetriesrelevant

intheCOMPASSkinematicregion.

Thecomputationsof ALL

(

pT

)

are performedatCOMPASS

kine-matics using the same cuts as in the present data analysis, i.e., pT

>

1 GeV

/

c, Q2

<

1

(

GeV

/

c

)

2,0

.

1

<

y

<

0

.

9,0

.

2

<

z

<

0

.

8.For

consistency, we veriﬁed that when using the same inputs as in Ref.[14],wereproducetheasymmetrycalculatedthere.The com-putations are done separately forthe production of positive and negative hadrons, and for three distinct bins in

η

:

[−

0

.

1

,

0

.

45

]

,

[

0

.

45

,

0

.

9

]

, and

[

0

.

9

,

2

.

4

]

. The results of these computations are comparedtotheexperimentalasymmetriesin

Fig. 5

and

Fig. 6

.

ThedataareseentobeconsistentwiththeNLOcalculationsof Ref.[14]usingthemostrecentpolarisedPDF[13]andFF[27]sets, except forpositive hadron productionfromthe protoninthe ra-pidity range

−

0

.

1

<

η

<

0

.

9.Ourdataarealsocomparedin

Fig. 5

and Fig. 6to calculationsusing earlierGRSV polarised PDFs[26]

togive animpressionoftheirsensitivityto

G,whichseems en-hancedathighervaluesof

η

.Apossiblereasonforthediscrepancy seenatlow

η

inpositivehadronproductionfromtheprotonmay be that themodelcalculationshadtobe done withoutthreshold resummation at NLL, as the formalism for the polarised case is not yet fullyavailable.However, contrary tothe unpolarisedcase

where data can only be described by pQCD if threshold

resum-mation is included [18],23 spin asymmetries are expected to be

23 _In_Ref._[19],_the_validity_of_the_formalism_[18]_was_veriﬁed_in_the_full_η_and pT rangecovered byCOMPASSkinematics. Thisstatement doesnotsuffer from slightlylargery andQ2_cuts_used_in_the_present_analysis_to_enhance_statistics,_as wecheckedthattheasymmetriesobtainedforthetwosetsofcutsarecompatible withinstatisticaluncertainties.

(7)

Fig. 6. Same asFig. 5, but for a deuteron target.

less affected [29]. A ﬁrst estimation of the impact of threshold resummation onourdoublespinasymmetriesincludingsofaronly the direct processes [30] indicates a substantial dilution of the asymmetries,whichmayexplainpartofthediscrepancybetween experimentandtheoryforpositivehadronproductiononthe pro-tonatlowvaluesof

η

.

6. Summary

Insummary, we have presented inthis Letter a newanalysis of COMPASS data on polarised single-inclusive hadron quasi-real photoproduction,which in principle is well suited foran extrac-tion of the gluon polarisation

G in the framework of collinear pQCD.Resultsforthelongitudinalspinasymmetry ALL

(

pT

)

on

po-larised protons and deuterons are given separately for positively andnegatively charged hadrons, andin three rapidity bins.They arecomparedtotheoreticalcalculationsatNLO withoutthreshold resummationandoverallagreementisfoundwiththecalculations based on earlier GRSVstd and recent DSSV14 polarised PDF sets,

andusingthemostrecentFFset.Nevertheless,calculations includ-ingfullthresholdresummationatNLLareneededbeforea mean-ingfulresulton

G canbeextractedquantitativelyfromourdata. Acknowledgements

We thank Werner Vogelsang and Marco Stratmann for many

useful discussions and for providing us the codes for the NLO pQCD calculation. We gratefully acknowledge the support of the CERNmanagementandstaffandtheskillandeffortofthe techni-ciansofourcollaboratinginstitutes.Thisworkwasmadepossible bytheﬁnancialsupportofourfundingagencies.

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