Extraction of unpolarized TMDs from SIDIS and Drell-Yan processes. Filippo Delcarro

Transcription

1 Extraction of unpolarized TMDs from SIDIS and Drell-Yan processes Filippo Delcarro

2 What is the structure of the nucleons?!

3 Is this structure explained by QCD?!!"#$%&' () *+,-. /0

4 Where does the spin of the nucleon come from?!!"#$%&' () *+,-. /0

5 We need to map the structure of nucleons x Monday, 8 April 14. m 6

6 !"#$ TMD distributions!"#$% &'() * +,!"#$% &'() * +, -".(/'- &'() * , 0 1, 3 1, 1 4 1, < 1 = 1,56789:,;<7 Amsterdam Notation!"# '()*+, #-$*)-./*-+, 0/,1*-+,$!"# '#0$3!"# 0)(456,*(*-+, 0/,1*-+,$!"# 00$3 Monday, 8 April 14!"#$ -,.7(18 $/)9-96 *)(,$96)$6:5+56,*/5 -,*64)(*-+,!"#$ -, )6; ()6!:+;; "/7;6)$:!(,46)5(,CDE'?DFG%DHG3?+6):"/7;6)$CD'I#DJKDH&3 L?CD#-6<7CDM+686CD"6*ACD"/7;6)$CD>1<76467CDNOP'QHRDQK3D %&

7 !"#$ TMD distributions -".(/'- &'() *9!"#$% &'() * +, * , 0 1, 3 1, 1 4 1, <+6)="/8>6)$!"#$% &'() * +, < 1 = 1 ;-:6)$ A+)5=46(),56789:,;<7 *)(,$:6)$-*9!"# '()*+, #-$*)-./*-+, 0/,1*-+,$!"# '#0$3?)6*@68+$-*9!"# 0)(456,*(*-+, 0/,1*-+,$!"# 00$3 %&!"#$%&' () *+,-. /0

8 TMD distributions! * * 0 1 * < 1!5#678 ()9: ;-)<(9%&*=4>?!"# $%&'() #*+'&*,-'*().-)/'*()+ 0!"# $#.+1!"#.&%34)'%'*().-)/'*()+ 0!"#..+1

9 Semi-inclusive DIS m h N(x, z, P ht,q )= dσh N /(dxdzdp ht dq ) dσ DIS /(dxdq ) π F UU,T(x, z, P ht,q ) F T (x, Q )

10 Semi-inclusive DIS!"#$#% $ %! % % '()&*!&#$#% "

11 Semi-inclusive DIS!"#$#% $ %! % % '()&*!&#$#% "!"# $#%&

12 Semi-inclusive DIS!"#$%& " # " #& " '% '!%(%& $ %! % % )*"$+ '$%(%& "!"# $#%&

13 Semi-inclusive DIS!"# $$%!"#$%& " # " #& " '% '!%(%& $ %! % % )*"$+ '$%(%& "!"# &#$%

14 Structure functions and TMDs hadron P h P ht P zk photon p k q k quark k proton TMD Parton Distribution Functions P TMD Parton Fragmentation Functions F UU,T (x, z, P ht,q )= a dk dp f a 1 x, k D a h 1 z,p δ zk P ht + P + O M /Q Parton model or Phase 1 e.g., Pavia 014, Torino 014

15 Structure functions and TMDs hadron P h P ht P zk photon p k q k quark k proton TMD Parton Distribution Functions P TMD Parton Fragmentation Functions F UU,T (x, z, P ht,q )= a H a UU,T(Q ; µ ) dk dp f a 1 x, k ; µ D1 a h z,p ; µ δ zk P ht + P + Y UU,T Q, P ht + O M /Q With QCD corrections or Phase e.g., DEMS 014 for D-Y

16 TMD evolution f a 1 (x, k ; µ )= 1 π d b e ib k f a 1 (x, b ; µ ) see, e.g., Rogers, Aybat, PRD 83 (11) Collins, Foundations of Perturbative QCD (11) Collins, Soper, Sterman, NPB50 (85)

17 TMD evolution f a 1 (x, k ; µ )= 1 π d b e ib k f a 1 (x, b ; µ ) f a 1 (x, b T ; µ )= i Ca/i f1 i (x, b ; µ b )e S(b ;µ b,µ) e g K(b T )ln µ µ 0 a ˆf NP (x, b T ) collinear PDF pqcd nonperturbative part of evolution nonperturbative part of TMD see, e.g., Rogers, Aybat, PRD 83 (11) Collins, Foundations of Perturbative QCD (11) Collins, Soper, Sterman, NPB50 (85)

18 Drell-Yan processes TMD PDF!" #! # q $! %! " q $ %!" % TMD PDF

19 Drell-Yan processes TMD PDF!" #! # q &' %! " q $ %!" $ Analogous process for Z boson production TMD PDF

20 µn SIDIS en!"#$"%

21 Z CDF pn DRELL-YAN pp ϒ* E88 E605

22 Available data vailable data Z production Drell-Yan@ 10 3 Q GeV $ % &%&'()*+ $!"!!(#$!(#)!$#*!+#%!(#$!(#'!$#'!$#)!+#(!(#(!(#*!(#'!$#(!!&#'!)#'!"#"!(#%!$#%!$#"!"#"!"#%!&#$!(#(!" #$!" #! Fig. : Event distribution in the inclusive variables Q and x Bj and the 3 bins of the hadron cross section analysis. Within each bin, the fraction of events contained is indicated in %.! "# x hermes & / & % $!"# '( ' %' '( %& '( ) '! " # $!"#. )! " # $!"# Fig. 3: Hadron acceptances A h and A h + determined with the Monte Carlo simulation for Q > 1 (GeV/c) as a function of lab p T and lab η for negative hadrons h (left) and positive hadrons h + (right). The acceptances have been smoothed in order to reduce the granularity from the binning. ' (*- (*, (*+ (*$ (*# (*" (*! (*& (*' ( future data of EIC? small-x, high Q 4

23 Published and soon available fits Framework HERMES COMPASS DY Z production N of points KN 006 hep-ph/05065 Pavia 013 (+Amsterdam,Bilbao) arxiv: Torino 014 (+JLab) arxiv: DEMS 014 arxiv: EIKV 014 arxiv: NLL!! " " 98 No evo "!!! 1538 No evo " (separately) " (separately)!! 576 (H) 684 (C) NNLL!! " " 3 NLL 1 (x,q ) bin 1 (x,q ) bin " " 500 (?) Pavia 016 NLL " " " " 8156

24 8000 data points Pavia 016 TMD Eight-thousander fit Nanga Parbat, Pakistan, 816 m

25 HERMES (some selected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

26 Compass (some selected bins) 3"#$##45 $ % "$ % 3"#$#5 $ % "$/ 6 +7 % 3"#$#05 $ % "%$ 6 +7 % 3"#$#05 $ % "&$ 6 +7 % / / / / !"#$%&'())*+,"-.!"#$%/'())*+,"0.!"#$&&'())*+,"1.!"#$&/'())*+,"& !"#$10'())*+,"%.!"#$00'())*+,".!"#$-0'())*+,"#. % % % % #?+(<9#9,%+@?+(<9#9,%+@?+(<9#9,%+@?+(<9#9,%+@ # #$# #$% #$1 #$- #$/ $# #$# #$% #$1 #$- #$/ $# #$# #$% #$1 #$- #$/ $# #$# #$% #$1 #$- #$/ $# # #! "#! "#! "#! "#!"#$%&& '()*(+", -./ 0 1'" &* $"9,*& %+(,"* 9**(': ;)* )&(' %&,"+#%<9=%*9", *" %>"9' $+";<(#& +(<%*(' *" '%*%,"+#%<9=%*9",

27 Drell-Yan data,- 0/) # 6 $ / % 78. 9&'(. 3 & ".*$# &'(,- 0/% # &'(. 3 $ / % & "./$+ &'(,- 0/% # &'(. 3 $ / % & ",1$# &':,- 0/) 4)-%5 # &'(. 3 $ / % & "/+$+ &'(!"#$%&'(!"%$%&'(!")$%&'(!"*$%&'(!"+$%&'(!",,$-&'(!",,$%&'(!",.$%&'(!",/$%&'(,- 0/*,- 0/+,- 0/1,- 0#-,- 0/),- 0/),- 0/*,- 0/*,- 0/*,- 0/+,- 0/+,- 0/+,- / / /1 / / $- -$%,$-,$%.$-.$% /$- -$- -$%,$-,$%.$-.$% /$- -$- -$%,$-,$%.$-.$% /$- -$- -$%,$-,$%.$-.$% /$-! " &'(3! " &'(3! " &'(3! " &'(3! "#$% & '()*! "#$% & +(,-! "#$% & +(,!! "#$% & +(.*

28 Z Boson production data * *! " %+,-&'(). # /#01 4'( (Q MZ) * *! " %+,-&'(). # /#013 4'( $! $! 567 6! #" #! #" #! " " -./ / !! " #! #" $!!! " #! #" $!! " %&'()! " %&'()! "#$% & '()*! "#$% & '(''! "#$% &!(++! "#$% & '(,)

29 Conclusions 9

30 Conclusions We showed how useful is to fit the TMD FFs and PDFs to different different processes to test their universality. 9

31 Conclusions We showed how useful is to fit the TMD FFs and PDFs to different different processes to test their universality. We demonstrated for the first time that it is possible to fit simultaneously SIDIS, DY, and Z boson data 9

32 Conclusions We showed how useful is to fit the TMD FFs and PDFs to different different processes to test their universality. We demonstrated for the first time that it is possible to fit simultaneously SIDIS, DY, and Z boson data We extracted unpolarized TMDs using several thousand data points. 9

33 Conclusions We showed how useful is to fit the TMD FFs and PDFs to different different processes to test their universality. We demonstrated for the first time that it is possible to fit simultaneously SIDIS, DY, and Z boson data We extracted unpolarized TMDs using several thousand data points. We are working on uncertainty studies and Y terms still to be implemented. 9

34

35 BACKUP

36 μ and b prescriptions f a 1 (x, b T ; µ )= i Ca/i f1 i (x, b ; µ b )e S(b ;µ b,µ) e g K(b T )ln µ µ 0 a ˆf NP (x, b T ) 3

37 μ and b prescriptions Choice Choice f a 1 (x, b T ; µ )= i Ca/i f1 i (x, b ; µ b )e S(b ;µ b,µ) e g K(b T )ln µ µ 0 a ˆf NP (x, b T ) 3

38 μ and b prescriptions Choice Choice f a 1 (x, b T ; µ )= i Ca/i f1 i (x, b ; µ b )e S(b ;µ b,µ) e g K(b T )ln µ µ 0 a ˆf NP (x, b T ) µ b =e γ E /b b b T 1+b T /b max Collins, Soper, Sterman, NPB50 (85) µ b =e γ E /b b b max 1 e b 4 T b 4 max 1/4 Bacchetta, Echevarria, Mulders, Radici, Signori arxiv: µ b = Q 0 + q T b = b T DEMS 014 3

39 μ and b prescriptions Choice Choice f a 1 (x, b T ; µ )= i Ca/i f1 i (x, b ; µ b )e S(b ;µ b,µ) e g K(b T )ln µ µ 0 a ˆf NP (x, b T ) µ b =e γ E /b b b T 1+b T /b max Collins, Soper, Sterman, NPB50 (85) µ b =e γ E /b b b max 1 e b 4 T b 4 max 1/4 Bacchetta, Echevarria, Mulders, Radici, Signori arxiv: µ b = Q 0 + q T b = b T DEMS 014 Complex-b prescription Laenen, Sterman, Vogelsang, PRL 84 (00) 3

40 Nonperturbative ingredients 1 f a 1 (x, b T ; µ )= i Ca/i f1 i (x, b ; µ b )e S(b ;µ b,µ) e g K(b T )ln µ µ 0 a ˆf NP (x, b T ) 33

41 Nonperturbative ingredients 1 Choice f a 1 (x, b T ; µ )= i Ca/i f1 i (x, b ; µ b )e S(b ;µ b,µ) e g K(b T )ln µ µ 0 a ˆf NP (x, b T ) 33

42 Nonperturbative ingredients 1 Choice f a 1 (x, b T ; µ )= i Ca/i f1 i (x, b ; µ b )e S(b ;µ b,µ) e g K(b T )ln µ µ 0 a ˆf NP (x, b T ) e b T b T almost everybody e b T b T (x) a Pavia 013, KN 006 e λ ( 1b T 1+λ b ) T DEMS

43 Nonperturbative ingredients f a 1 (x, b T ; µ )= i Ca/i f1 i (x, b ; µ b )e S(b ;µ b,µ) e g K(b T )ln µ µ 0 a ˆf NP (x, b T ) 34

44 Nonperturbative ingredients Choice f a 1 (x, b T ; µ )= i Ca/i f1 i (x, b ; µ b )e S(b ;µ b,µ) e g K(b T )ln µ µ 0 a ˆf NP (x, b T ) 34

45 Nonperturbative ingredients Choice f a 1 (x, b T ; µ )= i Ca/i f1 i (x, b ; µ b )e S(b ;µ b,µ) e g K(b T )ln µ µ 0 a ˆf NP (x, b T ) g b T g ln 1+ b T 4 Collins, Soper, Sterman, NPB50 (85) Aidala, Field, Gamberg, Rogers arxiv: g 0 (b max ) 1 exp C F α s (µ b )b T πg 0 (b max )b max Collins, Rogers arxiv:

46 Low-bT modifications log Q b T log Q b T +1 see, e.g., Bozzi, Catani, De Florian, Grazzini hep-ph/ see talks by Collins, Boglione, (Rogers?) 35

47 Low-bT modifications log Q b T log Q b T +1 see, e.g., Bozzi, Catani, De Florian, Grazzini hep-ph/ b (b c (b T )) = b T + b 0 /(C 5 Q ) 1+b T /b max + b 0 /(C 5 Q b max) b min b (b c (0)) = b 0 C 5 Q 1 1+b 0 /(C 5 Q b max ). Collins et al. arxiv: see talks by Collins, Boglione, (Rogers?) 35

48 Data selection Q > 1.4 GeV 0. <z<0.7 P ht,q T < 0. Q +0.5 GeV P ht < 0.8 GeV(ifz<0.3) 36

49 Data selection Q > 1.4 GeV 0. <z<0.7 P ht,q T < 0. Q +0.5 GeV P ht < 0.8 GeV(ifz<0.3) Total number of data points: 8156 Total χ /dof = 1.45 Preliminary 36

50 Pavia 016 perturbative ingredients f a 1 (x, b T ; µ )= i Ca/i f1 i (x, b ; µ b )e S(b ;µ b,µ) e g K(b T )ln µ µ 0 a ˆf NP (x, b T ) A 1 1 S ) A S ) A 3 3 S )... B 1 1 S ) B S )... C 0 0 S ) C 1 1 S ) C S )... H 0 0 S ) H 1 1 S ) H S )... Y 1 1 S ) Y S )... 37

51 Pavia 016 other ingredients f a 1 (x, b T ; µ )= i Ca/i f1 i (x, b ; µ b )e S( b ;µ b,µ) e g K(b T )ln µ µ 0 a ˆf NP (x, b T ) 38

52 Pavia 016 other ingredients f a 1 (x, b T ; µ )= i Ca/i f1 i (x, b ; µ b )e S( b ;µ b,µ) e g K(b T )ln µ µ 0 a ˆf NP (x, b T ) µ b =e γ E 1 e b4 T /b4 max /b b b max 1 e b4 T /b4 min 1/4 b max =e γ E b min = e γ E Q 38

53 Pavia 016 other ingredients f a 1 (x, b T ; µ )= i Ca/i f1 i (x, b ; µ b )e S( b ;µ b,µ) e g K(b T )ln µ µ 0 a ˆf NP (x, b T ) µ b =e γ E 1 e b4 T /b4 max /b b b max 1 e b4 T /b4 min 1/4 b max =e γ E b min = e γ E Q g K = g b T µ 0 =1GeV 38

54 Pavia 016 other ingredients f a 1 (x, b T ; µ )= i Ca/i f1 i (x, b ; µ b )e S( b ;µ b,µ) e g K(b T )ln µ µ 0 a ˆf NP (x, b T ) µ b =e γ E 1 e b4 T /b4 max /b b b max 1 e b4 T /b4 min 1/4 b max =e γ E b min = e γ E Q g K = g b T µ 0 =1GeV g =0.14 GeV from fit results 38

55 Pavia 016 other ingredients f a 1 (x, b T ; µ )= i Ca/i f1 i (x, b ; µ b )e S( b ;µ b,µ) e g K(b T )ln µ µ 0 a ˆf NP (x, b T ) µ b =e γ E 1 e b4 T /b4 max /b b b max 1 e b4 T /b4 min 1/4 b max =e γ E b min = e γ E Q g K = g b T µ 0 =1GeV g =0.14 GeV from fit results ˆf NP a = e b T b T (x) a 38

56 Pavia 016 other ingredients f a 1 (x, b T ; µ )= i Ca/i f1 i (x, b ; µ b )e S( b ;µ b,µ) e g K(b T )ln µ µ 0 a ˆf NP (x, b T ) µ b =e γ E 1 e b4 T /b4 max /b b b max 1 e b4 T /b4 min 1/4 b max =e γ E b min = e γ E Q g K = g b T ˆf NP a = e b T b T (x) a µ 0 =1GeV ˆf a NP = F.T. of e P P (z) a g =0.14 GeV For fragmentation functions + λ P e P P (z) a from fit results + λ P e 4 P P (z) a 38

57 Effects of b prescription %"! $"# $"!!"#!! "!!!!! "#$ " " " #!""#$%$#&#!"!!"!!"# $"! $"# %"!!!!&'(!! " &"! %"# %"! $"#!!!! "!!! "!!!"# #! " " "##!$%$!&" $"!!"!!"# $"! $"# %"!!!!'()!! " 39

58 Pavia 013 (no TMD evo) Global χ /dof = 1.63±0.1 mx,z,p ht,q, proton target 1.80±0.7 Π 10 1 x0.15 Q.9 GeV Π 0.10z z z z ± K K 0.78± ± P ht P ht FIG. 3. Data points: Hermes multiplicities m h p(x, z, PhT ; Q ) for pions and kaons off a proton target as functions of PhT for one selected x and Q bin and few selected z bins. Shaded bands: 68% confidence intervals obtained from fitting 00 replicas of the original data points in the scenario of the default fit. The bands include also the uncertainty on the collinear fragmentation functions. The lowest PhT bin has not been included in the fit. 40

59 Pavia 013 (no TMD evo) Global χ /dof = 1.63±0.1 Without flavor dep.: global χ /dof = 1.7±0.11 mx,z,p ht,q, proton target 1.80±0.7 Π 10 1 x0.15 Q.9 GeV Π 0.10z z z z ± ± ± K K 0.78± ± ± ± P ht P ht FIG. 3. Data points: Hermes multiplicities m h p(x, z, PhT ; Q ) for pions and kaons off a proton target as functions of PhT for one selected x and Q bin and few selected z bins. Shaded bands: 68% confidence intervals obtained from fitting 00 replicas of the original data points in the scenario of the default fit. The bands include also the uncertainty on the collinear fragmentation functions. The lowest PhT bin has not been included in the fit. 40

60 Pavia 013 (no TMD evo) Global χ /dof = 1.63±0.1 Without flavor dep.: global χ /dof = 1.7±0.11 mx,z,p ht,q, proton target 1.80±0.7 Π 10 1 x0.15 Q.9 GeV Π 0.10z z z z ± ± ± K K 0.78± ± ± ± P ht P ht first PhT excluded from fit FIG. 3. Data points: Hermes multiplicities m h p(x, z, PhT ; Q ) for pions and kaons off a proton target as functions of PhT for one selected x and Q bin and few selected z bins. Shaded bands: 68% confidence intervals obtained from fitting 00 replicas of the original data points in the scenario of the default fit. The bands include also the uncertainty on the collinear fragmentation functions. The lowest PhT bin has not been included in the fit. 40

61 Pavia 013 (no TMD evo) Global χ /dof = 1.63±0.1 Without flavor dep.: global χ /dof = 1.7±0.11 mx,z,p ht,q, proton target not so low χ 1.80±0.7 Π 10 1 x0.15 Q.9 GeV Π 0.10z z z z ± ± ± K K 0.78± ± ± ± P ht P ht first PhT excluded from fit FIG. 3. Data points: Hermes multiplicities m h p(x, z, PhT ; Q ) for pions and kaons off a proton target as functions of PhT for one selected x and Q bin and few selected z bins. Shaded bands: 68% confidence intervals obtained from fitting 00 replicas of the original data points in the scenario of the default fit. The bands include also the uncertainty on the collinear fragmentation functions. The lowest PhT bin has not been included in the fit. 40

62 KN 006 perturbative ingredients f a 1 (x, b T ; µ )= i Ca/i f1 i (x, b ; µ b )e S(b ;µ b,µ) e g K(b T )ln µ µ 0 a ˆf NP (x, b T ) A 1 1 S ) A S ) A 3 3 S )... B 1 1 S ) B S )... C 0 0 S ) C 1 1 S ) C S )... H 0 0 S ) H 1 1 S ) H S )... Y 1 1 S ) Y S )... 41

63 DEMS 014 NLL f a 1 (x, b T ; µ )= i Ca/i f1 i (x, b ; µ b )e S(b ;µ b,µ) e g K(b T )ln µ µ 0 a ˆf NP (x, b T ) A 1 1 S ) A S ) A 3 3 S )... B 1 1 S ) B S )... C 0 0 S ) C 1 1 S ) C S )... H 0 0 S ) H 1 1 S ) H S )... Y 1 1 S ) Y S )... 4

64 DEMS 014 NNLL f a 1 (x, b T ; µ )= i Ca/i f1 i (x, b ; µ b )e S(b ;µ b,µ) e g K(b T )ln µ µ 0 a ˆf NP (x, b T ) A 1 1 S ) A S ) A 3 3 S )... B 1 1 S ) B S )... C 0 0 S ) C 1 1 S ) C S )... H 0 0 S ) H 1 1 S ) H S )... Y 1 1 S ) Y S )... 43