Zhongbo Kang UCLA. The 7 th Workshop of the APS Topical Group on Hadronic Physics

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1 Probing collinear and TMD fragmentation functions through hadron distribution inside the jet Zhongbo Kang UCLA The 7 th Workshop of the APS Topical Group on Hadronic Physics February 1-3, 2017

2 Jets are abundantly produced at the LHC They are most common at the LHC 2

3 Jets and its internal substructure as new tools Jesse Thaler,

4 Hadron distribution inside the jet Study a hadron distribution inside a fully reconstructed jet F (z h ; p T )= F (z h,j T ; p T )= z h = p h T /p jet T d h. dp T d dz h p + p! jet (h)+x d dp T d d h. dp T d dz h d 2 j T d dp T d j T : hadron transverse momentum with respect to the jet direction R! αi = { Ti, ηi, φi} The 1 st observable is like collinear fragmentation function, while the 2 nd observable is more like a TMD fragmentation function LHC did a great deal of all kinds of measurements, and compared with Pythia simulation h jet 4

5 Collinear z-dependence: light hadron ATLAS measurements at 7 TeV and 2.76 TeV , ATLAS-CONF Light hadron 5

6 Collinear z-dependence: heavy meson D meson production inside a jet ATLAS, arxiv:

7 Relative momentum j T dependence j T shape does not change much: how to link to TMD evolution

8 Relative momentum j T dependence j T shape does not change much: how to link to TMD evolution

9 RHIC measurements Hadron azimuthal distribution inside the jet in transversely polarized p+p collisions: spin dynamics h i p " S? ( S ) + p! [jet h( H )] + X STAR, in arxiv: ) - φ H S sin(φ A UT 0.06 ± STAR, P P (jet π ) X s = 500 (GeV), P = 31 (GeV) T s = 200 (GeV), P = 12.9 (GeV) + T π, s = 500 (GeV) - π, s = 500 (GeV) + π, s = 200 (GeV) - π, s = 200 (GeV) z See Prokudin s talk on Wednesday Kang, Prokudin, Ringer, Yuan, to appear 9

10 Questions How does the factorization formalism look like? How is the collinear z-distribution of hadrons in the jet related to the standard collinear fragmentation function? How is the transverse momentum dependent j T -distribution of hadrons in the jet related to the usual TMD fragmentation function as measured in SIDIS and e+e-? Lots of work have been performed along these directions recently, and very active developments e.g., Kaufmann, Mukherjee, Vogelsang; Bain, Makris, Mehen, Leibovich; Kang, Ringer, Vitev; Neill, Scimenmi, Waalewijn;

11 A further re-factorization for jet and jet substructure For cross section or substructure of single inclusive jet production h p a c p a c p b p b d pp!hx dp T d = X a,b,c f a f b H ab!c D h c d pp!jet(v)x dp T d dv = X a,b,c f a f b H ab!c G c (µ p T R, v) Fragmentation function Semi-inclusive jet function D h c ) G c (µ p T R, v) Kang, Ringer, Vitev, arxiv: , , JHEP 11

12 Recall single hadron production Illustration of single hadron production: h p + p! h + X p a c p b d pp!hx dp T d = X a,b,c f a f b H ab!c D h c QCD factorization can be reviewed from the spirit of the effective field theory: physics at very different scales do not affect each other Hard collision happens at scale ~ pt Hadronization/fragmentation happens at a much lower scale ~ mh The interference between these two scales should be suppressed by mh/pt 12

13 QCD factorization makes things simple Think of QCD factorization using the spirit of effective field theory What are the relevant scales for single jet production? Two momenta: (1) hard collision: pt (2) jet radius can build one: pt*r In the small-r limit, one can actually factorizes the jet cross section into two steps, just like single hadron production jet jet R! αi = { Ti, ηi, φi} e e + (a) (b) d pp!jetx dp T d = X a,b,c f a f b H ab!c J c (µ p T R) Good thing: semi-inclusive jet function J q,g (z, R, w) are purely perturbative Kang, Ringer, Vitev, arxiv: , Dai, Kim, Leibovich, , see also, Kaufmann, Mukherjee, Vogelsang,

14 Semi-inclusive jet function Describe how a parton (q or g) is transformed into a jet (with a jet radius R) and energy fraction z J q (z,! J,µ)= z 2N c Tr apple n/ 2 h0 (! n P) n(0) JXihJX n(0) 0i z =! J /! Semi-inclusive quark/gluon jets follow DGLAP evolution equation, just like hadron fragmentation functions Z 1 µ d dµ J i(z,! J,µ)= s(µ) X j z dz 0 z 0 P ji z z 0,µ J j (z 0,! J,µ) Kang, Ringer, Vitev, arxiv: , JHEP 14

15 Collinear hadron distribution inside the jet First produce a jet, and then further look for a hadron inside the jet h R! αi = { Ti, ηi, φi} F (z h,p T )= z h = p h T /p T Kang, Ringer, Vitev, arxiv: , JHEP d h. dp T d dz h d dp T d c Just like the single inclusive jet production, we have Semi-inclusive fragmenting jet function d dp T d dz h / X a,b,c z = p T /p c T f a f b H ab!c G h c (z,z h,µ) 15

16 Two DGLAPs Parton-to-jet part: evolution is for variable z µ d dµ Gh i (z,z h,µ)= s(µ) X j Z 1 z dz 0 z z 0 P ji z 0 Gj h (z 0,z h,µ) Substructure of the jet: collinear hadron distribution in the jet, relevant to variable z h G h i (z,z h,µ)= X j Z 1 z h dz 0 h z 0 h J ij (z,z 0 h,µ) D h j zh z 0 h,µ µ p T Resum ln(r) µ J p T R µ D 1 GeV Evolve standard FFs from 1 GeV to pt*r 16

17 Great probe for collinear FFs Works pretty well in comparison with experimental data ), p F(z T h [400,500] [3,400] [260,3] [2,260] [160,2] [1,160] [80,1] [60,80] 4 [40,60] 2 [25,40] p+p s = 7 TeV anti-k T R=0.6 η < 1.2 ), p F(z T h ± h p+p s = 2.76 TeV anti-kt ATLAS R=0.4 η < 1.6 CMS R= < η < 2 [2,260] [160,2] [1,160] [80,1] [60,80] [45,60] [0,300] z h z h Could be used for better constraining gluon-to-hadron FFs, large-z region and etc Kang, Ringer, Vitev, arxiv:

18 What about TMD FFs? TMD hadron distribution inside the jet d h. d F (z h,j T ; p T )= dp T d dz h d 2 j T dp T d h jet R! αi = { Ti, ηi, φi} z h = p h T /p jet T j T : hadron transverse momentum with respect to the jet direction Factorization formalism Kang, Liu, Ringer, Xing, in preparation d dp T d dz h d 2 / X f a f b H ab!c Gc h (z,z h,j T,µ) j T a,b,c Re-factorization of semi-inclusive fragmenting jet function Z Gc h (z,z h,j T,µ) = C c!d (z,r) d 2 T d 2 k T 2 (j T T k T )S( T,R)D h d (z h,k T ) 18

19 A couple of main points One soft function + one TMD FFs How do the rapidity divergences cancel between them? Recall: standard TMD factorization for SIDIS, DY, e+e-, which always involve one soft function + TWO TMDs What sets the scale for the TMD evolution of TMD FFs? 19

20 TMD factorization for DY: p + p! [! `+` ]+X Factorized form and mimic parton model d dq 2 dyd 2 q? / = = Z Z Z d 2 k 1? d 2 k 2? d 2? H(Q)f(x 1,k 1? )f(x 2,k 2? )S(? ) 2 (k 1? + k 2? +? q? ) d 2 b (2 ) 2 eiq? b H(Q)f(x 1,b)f(x 2,b)S(b) F (x, b) =f(x, b) p S(b) d 2 b (2 ) 2 eiq? b H(Q)F (x 1,b)F (x 2,b) Rapidity divergences cancel between f(x 1,k 1? ) F (x, b) =f(x, b) p S(b) H(Q) S(? ) f(x 2,k 2? ) 20

21 Quark TMD at one loop ( apple f q/q (x, b) = s C F +lnµ2 µ 2 b 1 + ln µ2 µ 2 P qq (x) b + apple2ln µ2 µ 2 ln b p µ2 ln 2 µ 2 b Soft factor S(b) = s 2 C F apple + ( 4 1 2ln µ2 µ 2 ln 2 b µ 2 b Interesting features Rapidity divergence cancels in TMDs in b-space at NLO + 2 ln p ln µ2 µ b ln µ2 µ 2 b ) +ln 2 µ 2 µ 2 b (1 x)+(1 x) ln 2 µ 2 b (1 x) ) F sub q/q (x, b) =f q/q(x, b) p S(b) µ b =2e E /b f q/q (x, b) and S(b) lives in the same μ ~ μ b, but different rapidity scale ν ~ p +, μ b Kang, Spin 2016 conference 21

22 Quark TMD at one loop ( apple f q/q (x, b) = s C F +lnµ2 µ 2 b 1 + ln µ2 µ 2 P qq (x) b + apple2ln µ2 µ 2 ln b p µ2 ln 2 µ 2 b Soft factor S(b) = s 2 C F apple + ( 4 1 2ln µ2 µ 2 ln 2 b µ 2 b Interesting features Rapidity divergence cancels in TMDs in b-space at NLO + 2 ln p ln µ2 µ b ln µ2 µ 2 b ) +ln 2 µ 2 µ 2 b (1 x)+(1 x) ln 2 µ 2 b (1 x) ) F sub q/q (x, b) =f q/q(x, b) p S(b) µ b =2e E /b f q/q (x, b) and S(b) lives in the same μ ~ μ b, but different rapidity scale ν ~ p +, μ b Kang, Spin 2016 conference 22

23 What s different for hadron in the jet? Soft radiation has to happen inside the jet For single inclusive jet production, first we produce a high-pt jet This process only involves hard-collinear factorization, and such a process is not sensitive to any soft radiation This is the usual standard collinear factorization Z 1 0 `+ y ` dy y ) Z tan 2 R 2 0 dy y Once such a high-pt jet is produced, we further observe a hadron inside the jet At this step, we measure the relative transverse momentum of hadron w.r.t the jet. For such a step, soft radiation matters However, only those soft radiation that happens inside the jet matters Restricts soft radiation to be within the jet: cuts half of the rapidity divergence Rapidity divergence cancel between restricted soft factor and TMD FFs At least up to this order, the combined evolution is the same as the usual TMD evolution in SIDIS, DY, e+e-; justify the use of same TMD evolution here p p a b c p S(b)D h c (z h,b) e+ e )S(b, R)D h c (z h,b) pp 23

24 Collins function: universal Collins function: unpolarized hadron from a transversely polarized quark D h/q (z,p? )=D q 1 (z,p2?)+ 1 H?q 1 zm (z,p2?)s q ˆk h S q k h p? Spin-independent Spin-dependent p? 2002: A. Metz studied the universality property of Collins function in a modeldependent way very subtle finally found it is universal between SIDIS and e+e- ü ü ü ü ü 2004: Collins and Metz have general arguments 2008: Yuan generalizes to pp Collins function is universal: concern on collinear gauge link (unsubtracted TMDs) Now soft function seems to be fine, too h H?SIDIS 1 (z,p 2?)=H?e+ e 1 (z,p 2?)=H?pp 1 (z,p 2?) Metz 02, Collins, Metz 04, Yuan 08, Gamberg, Mulders,, Boer, Kang, Vogelsang, Yuan,, 24

25 Evolution structure TMD + DGLAP evolution DGLAP evolution z µ p T µ J p T R Resum ln(r) TMD evolution (z h,j T ) µ b 1/b Evolve TMD FFs from μ b to pt*r TMD FFs thus are related to the usual TMD FFs in SIDIS at scale pt*r Thus hadron TMD distribution inside the jet could be used to test the universality of TMD FFs from SIDIS, e+e- processes 25

26 Summary jet cross section and jet substructure for inclusive jet production follow a two-step factorization First step: parton-to-jet production Second step: jet internal substructure The hard function associated with the 1 st step is the same as that for single inclusive hadron production For jet substructure, one could then concentrate on the 2 nd step Collinear and TMD distribution of hadron in a jet are great processes to probe collinear and/or TMD FFs Factorization seems to be okay 26

27 Summary jet cross section and jet substructure for inclusive jet production follow a two-step factorization First step: parton-to-jet production Second step: jet internal substructure The hard function associated with the 1 st step is the same as that for single inclusive hadron production For jet substructure, one could then concentrate on the 2 nd step Collinear and TMD distribution of hadron in a jet are great processes to probe collinear and/or TMD FFs Factorization seems to be okay Thank you! 27