The transverse momentum distribution of hadrons inside jets

Transcription

1 The transverse momentum distribution of hadrons inside jets Felix Ringer Lawrence Berkeley National Laboratory INT, Seattle 09/13/17

2 Outline Introduction In-jet TMDs Collins asymmetries Conclusions Kang, Liu, FR, Xing `17 Kang, Prokudin, FR, Yuan `17 2

3 Outline Introduction In-jet TMDs Collins asymmetries Conclusions Kang, Liu, FR, Xing `17 Kang, Prokudin, FR, Yuan `17 3

4 Accessing Transverse Momentum Distributions SIDIS: JLab, HERMES, COMPASS Drell-Yan Electron-positron: BELLE, BABAR TMD extractions in global fits Bacchetta et al. `17, Kang et al. `16, Factorization Boglione et al. `17 Test of universality TMD evolution Collins FF Kang et al. `16 4

5 Introduction In-Jet TMDs Collins Asymmetries Conclusions Jets in proton-proton collisions PDFs and s are constrained by collider jet data Inclusive jet pt spectrum High pt jets are a promising observable for the search of BSM physics at the LHC Baseline for jet quenching in heavy-ion collisions!! Extending the high pt limit beyond Tevatr Jet substructure!! Accessing the low pt part using different Jets from scattering of partons jet reconstruction algorithms d Knowledge mbined HT O QCD (Vogelsang) Systematic Uncertainty Theory Scale Uncertainty p y JET < y 1.1< y JET 1.6< y pt [GeV/c] <0.1 (" 106 ) JET -14 jet JET 0.1< y JET (b) 11 CMS preliminary, 60 nb Tevatron pjet [GeV/c] T section: data and theory agree over many orders of magnitude 5 underlying interaction c p trig LHC <1.1 <1.6 (" 10-3 ) <2.1 (" 10-6) 300 <0.7 (" 103 ) s = 7 TeV y <0.5 ("1024) 0.5# y <1.0 ("256) 1.0# y <1.5 ("64) 1.5# y <2.0 ("16) 2.0# y <2.5 ("4) 2.5# y <3.0 ("1) T JET d2! / dy mbined MB CDF data ( L = 1.0 fb ) Systematic uncertainties NLO: JETRAD CTEQ6.1M corrected to hadron level µr = µf = max pjet / 2 = µ0 T PDF uncertainties JET RHIC K T D=0.7-1 dpt jet p+p g jet + X s=200 GeV midpoint-cone rcone = <η<0.8 [nb/(gev/c)] unavoidable at hadron(a) STAR, PRL 97 (2006), e.g. from parton scatstar 1010 d2!/dydp (pb/gev)!! Good agreement with NLO predictions NLO pqcd+np Exp. uncertainty Anti-kT R=0.5 PF p (GeV) T exper uncer by je res lumino

6 Hadron distributions inside jets Study hadron distributions inside a reconstructed jet F (z h,j?,p T )= d pp!(jeth)x dp T d dz h d 2 j? z h = p h T /p T pp! (jet h)+x j? : hadron transverse momentum with respect to the (standard) jet axis Longitudinal momentum distribution probes collinear FFs Transverse momentum distribution probes TMD FFs Collins azimuthal asymmetries 6

7 Recent measurements at the LHC and RHIC ATLAS Eur. Phys. J. C71 (2011) 1795 arxiv: STAR Collaboration, arxiv:

8 Analogy of hadron and jet cross sections Factorization Evolution Jet d pp!jetx dp T d = X a,b,c f a f b H c ab J c µ d dµ J i = X j P ji J j Hadron d pp!hx dp T d = X a,b,c f a f b H c ab D h c µ d dµ Dh i = X j P ji D h j 8 Kang, FR, Vitev `16

9 Semi-inclusive jet function in SCET The sijfs describe how a parton is transformed into a jet with radius R and carrying an energy fraction z jet! J =!! J 6=! initiating parton!! LO NLO where z =! J /! momentum sum rule: 9 see also: Kaufmann, Mukherjee, Vogelsang `15 Dai, Kim, Leibovich `16

10 Semi-inclusive jet function in SCET NLO result = s 2 UV 1 +ln µ 2 p 2 T R2 [P qq (z)+p gq (z)] MS scheme µ = p T RG equation timelike DGLAP for semi-inclusive jet function µ d dµ J i = X j P ji J j µ J = p T R resummation of n s ln n R 10 see also: Dasgupta, Dreyer, Salam, Soyez `16

11 Comparison to LHC data R =0.2 R =0.3 R =0.4 p T CMS Phys.Rev. C (2017) 11

12 The jet fragmentation function pp! (jeth)x l First reconstruct a jet and then identify hadrons inside that jet h z h = p h T /p T z = p T /p c T Similar factorization to inclusive jet production d pp!(jet h)x dp T d dz h = X a,b,c f a (x a,µ) f b (x b,µ) H c ab(x a,x b,,p T /z, µ) G h c (z,z h,! J,µ) Semi-inclusive fragmenting jet function 12 Procura, Stewart `10, Liu `11, Jain, Procura, Waalewijn `11, Arleo, Fontannaz, Guillet, Nguyen `14, Kaufmann, Mukherjee, Vogelsang `15, Kang, FR, Vitev `16,

13 Semi-inclusive fragmenting jet function Fragmenting parton! h 6=! J! h =! J z h =! h /! J Jet! J =!! J 6=! z =! J /! Initiating parton!! 13

14 Semi-inclusive fragmenting jet function Fragmenting parton! h 6=! J! h =! J z h =! h /! J Jet! J =!! J 6=! z =! J /! Initiating parton!! Matching G h i (z,z h,! J,µ)= X j Z 1 z h dz h z 0 h J ij (z,z 0 h,! J,µ)D h j zh z 0 h,µ ln R resummation µ d dµ Gh i (z,z h,! J,µ)= s(µ) X j Z 1 z dz 0 z z 0 P ji z 0 Gj h (z 0,z h,! J,µ) 14

15 Semi-inclusive fragmenting jet function Fragmenting parton! h 6=! J! h =! J z h =! h /! J Jet! J =!! J 6=! z =! J /! Initiating parton!! H i ab µ = p T Matching G h i (z,z h,! J,µ)= X j Z 1 z h dz h z 0 h J ij (z,z 0 h,! J,µ)D h j zh z 0 h,µ G h i µ J = p T R D h i 1 GeV ln R resummation µ d dµ Gh i (z,z h,! J,µ)= s(µ) X j Z 1 z dz 0 z z 0 P ji z 0 Gj h (z 0,z h,! J,µ) 2 DGLAPs now 15

16 The JFF is an ideal observable to constrain in particular gluon FFs 16 Slide courtesy of Tom Kaufmann

17 Phenomenology Light charged hadrons Arleo, Fontannaz, Guillet, Nguyen `14 Kaufmann, Mukherjee, Vogelsang `15 Kang, FR, Vitev `16 Neill, Scimemi, Waalewijn `16 Photons Kaufmann, Mukherjee, Vogelsang `16 Heavy flavor mesons Chien, Kang, FR, Vitev, Xing `15 Bain, Dai, Hornig, Leibovich, Makris, Mehen `16 Anderle, Kaufmann, Stratmann, FR, Vitev `17 Quarkonia Baumgart, Leibovich, Mehen, Rothstein `14 Bain, Dai, Hornig, Leibovich, Makris, Mehen `16 Kang, Qiu, FR, Xing, Zhang `17 Bain, Dai, Leibovich, Makris, Mehen `17 17 Kang, FR, Vitev `16

18 Phenomenology Light charged hadrons Arleo, Fontannaz, Guillet, Nguyen `14 Kaufmann, Mukherjee, Vogelsang `15 Kang, FR, Vitev `16 Neill, Scimemi, Waalewijn `16 Photons Kaufmann, Mukherjee, Vogelsang `16 Heavy flavor mesons Chien, Kang, FR, Vitev, Xing `15 Bain, Dai, Hornig, Leibovich, Makris, Mehen `16 Anderle, Kaufmann, Stratmann, FR, Vitev `17 Quarkonia Baumgart, Leibovich, Mehen, Rothstein `14 Bain, Dai, Hornig, Leibovich, Makris, Mehen `16 Kang, Qiu, FR, Xing, Zhang `17 Bain, Dai, Leibovich, Makris, Mehen `17 18 Chien, Kang, FR, Vitev, Xing `15

19 Phenomenology pp! (jet D )X Light charged hadrons Arleo, Fontannaz, Guillet, Nguyen `14 Kaufmann, Mukherjee, Vogelsang `15 Kang, FR, Vitev `16 Neill, Scimemi, Waalewijn `16 Photons Kaufmann, Mukherjee, Vogelsang `16 Heavy flavor mesons Chien, Kang, FR, Vitev, Xing `15 Bain, Dai, Hornig, Leibovich, Makris, Mehen `16 Anderle, Kaufmann, Stratmann, FR, Vitev `17 Quarkonia Baumgart, Leibovich, Mehen, Rothstein `14 Bain, Dai, Hornig, Leibovich, Makris, Mehen `16 Kang, Qiu, FR, Xing, Zhang `17 Bain, Dai, Leibovich, Makris, Mehen `17 19 New global D*-meson FF fit Anderle, Kaufmann, Stratmann, FR, Vitev `17

20 Light charged hadrons Arleo, Fontannaz, Guillet, Nguyen `14 Kaufmann, Mukherjee, Vogelsang `15 Kang, FR, Vitev `16 Neill, Scimemi, Waalewijn `16 Phenomenology e + e! D X Photons Kaufmann, Mukherjee, Vogelsang `16 Heavy flavor mesons Chien, Kang, FR, Vitev, Xing `15 Bain, Dai, Hornig, Leibovich, Makris, Mehen `16 Anderle, Kaufmann, Stratmann, FR, Vitev `17 pp! D X Quarkonia Baumgart, Leibovich, Mehen, Rothstein `14 Bain, Dai, Hornig, Leibovich, Makris, Mehen `16 Kang, Qiu, FR, Xing, Zhang `17 Bain, Dai, Leibovich, Makris, Mehen `17 20 New global D*-meson FF fit Anderle, Kaufmann, Stratmann, FR, Vitev `17

21 Phenomenology Light charged hadrons Arleo, Fontannaz, Guillet, Nguyen `14 Kaufmann, Mukherjee, Vogelsang `15 Kang, FR, Vitev `16 Neill, Scimemi, Waalewijn `16 Photons Kaufmann, Mukherjee, Vogelsang `16 Heavy flavor mesons Chien, Kang, FR, Vitev, Xing `15 Bain, Dai, Hornig, Leibovich, Makris, Mehen `16 Anderle, Kaufmann, Stratmann, FR, Vitev `17 Quarkonia Baumgart, Leibovich, Mehen, Rothstein `14 Bain, Dai, Hornig, Leibovich, Makris, Mehen `16 Kang, Qiu, FR, Xing, Zhang `17 Bain, Dai, Leibovich, Makris, Mehen `17 21 Kang, Qiu, FR, Xing, Zhang `17

22 Phenomenology Light charged hadrons Arleo, Fontannaz, Guillet, Nguyen `14 Kaufmann, Mukherjee, Vogelsang `15 Kang, FR, Vitev `16 Neill, Scimemi, Waalewijn `16 Photons Kaufmann, Mukherjee, Vogelsang `16 Heavy flavor mesons Chien, Kang, FR, Vitev, Xing `15 Bain, Dai, Hornig, Leibovich, Makris, Mehen `16 Anderle, Kaufmann, Stratmann, FR, Vitev `17 Quarkonia Baumgart, Leibovich, Mehen, Rothstein `14 Bain, Dai, Hornig, Leibovich, Makris, Mehen `16 Kang, Qiu, FR, Xing, Zhang `17 Bain, Dai, Leibovich, Makris, Mehen `17 22 Kang, Qiu, FR, Xing, Zhang `17

23 Introduction In-Jet e + TMDs e Collins Asymmetries Conclusions Outline Introduction In-jet TMDs Collins asymmetries Conclusions Kang, Liu, FR, Xing `17 Kang, Prokudin, FR, Yuan `17 23

24 Introduction In-Jet e + TMDs e Collins Asymmetries Conclusions TMD sensitive jet substructure observables Measure in addition the relative transverse momentum of the hadron wrt. to the (standard) jet axis Kang, Liu, FR, Xing `17 pp!(jet h)x d dp T d dz h d 2 = X f a (x a,µ) f b (x b,µ) H j ab(x c a,x b,,p T /z, µ)? a,b,c G h c (z,z h, j?,! J,µ) momentum fraction z h transverse momentum j? Standard jet axis Inclusive jet sample Relation to usual TMD evolution and fits Light charged hadrons 24 See also: Bain, Makris, Mehen `16 Neill, Scimemi, Waalewijn `17

25 Introduction In-Jet e + TMDs e Collins Asymmetries Conclusions Drell-Yan pp! [! 1`+` ]X Parton model interpretation 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) d 2 b (2 ) 2 eiq? b H(Q)F (x 1, b) F (x 2, b) f(x 1,k 1? ) Rapidity divergences cancel in redefined TMD F (x, b) =f(x, b) p S(b) H(Q) S(? ) f(x 2,k 2? ) 25

26 Introduction In-Jet e + TMDs e Collins Asymmetries Conclusions Jet fragmentation function pp! (jeth)x l Factorization formalism pp!(jet h)x d dp T d dz h d 2 = X f a (x a,µ) f b (x b,µ) H j ab(x c a,x b,,p T /z, µ) Gc h (z,z h, j?,! J,µ)? a,b,c where for j? p T R hard matching function Z Gc h (z,z h, j?,! J,µ)=H c!i (z,! J,µ) d 2 k? d 2? 2 (z h? + k? j? ) D h i (z h, k?,µ, ) S i (?,R,µ, ) TMD FF Soft function 26

27 Introduction In-Jet e + TMDs e Collins Asymmetries Conclusions Jet fragmentation function pp! (jeth)x l Hard matching functions Evolution: modified DGLAP µ 2 L =ln p 2 T R2 where 4 coupled equations with double logarithms. Characteristic scale µ H = p T R see also: Kang, FR, Waalewijn `17 27

28 Introduction In-Jet e + TMDs e Collins Asymmetries Conclusions Jet fragmentation function pp! (jeth)x l Rapidity regulator, scale Chiu, Jain, Neill, Rothstein `12 (In-jet) quark TMD D q q(z h, k?,µ, ) = (1 z h ) 2 (k? )+ s 2 2 C F (1 + )e E 1 µ 2 apple 2z h (1 z h ) 1+! J +(1 )(1 z h ) µ 2 k 2? 1+ 28

29 Introduction In-Jet e + TMDs e Collins Asymmetries Conclusions Jet fragmentation function pp! (jeth)x l Rapidity regulator, scale Chiu, Jain, Neill, Rothstein `12 (In-jet) quark TMD D q q(z h, k?,µ, ) = (1 z h ) 2 (k? )+ s 2 2 C F (1 + )e E 1 µ 2 apple 2z h (1 z h ) 1+! J +(1 )(1 z h ) µ 2 k 2? 1+ b-space and expansion in, : D q q(z h, b,µ, ) µ b = 2e E b 29

30 Introduction In-Jet e + TMDs e Collins Asymmetries Conclusions Jet fragmentation function pp! (jeth)x l Rapidity regulator (In-jet) quark TMD, scale Chiu, Jain, Neill, Rothstein `12 D q q(z h, b,µ, ) In-jet soft function S q (b,r,µ, ) = Z d 2?e i? b S q (?,R,µ, ) " =1+ s 2 C 2 1 µ 2 F +ln µ b 2 ln tan 2 (R/2) µ 2 µ 2 2 tan 2 (R/2) ln ln + 12 # µ 2 2 ln2 12 µ 2 b µ 2 b µ 2 b 30

31 Introduction In-Jet e + TMDs e Collins Asymmetries Conclusions Jet fragmentation function pp! (jeth)x l Rapidity regulator (In-jet) quark TMD, scale Chiu, Jain, Neill, Rothstein `12 D q q(z h, b,µ, ) In-jet soft function S q (b,r,µ, ) = Z d 2?e i? b S q (?,R,µ, ) " =1+ s 2 C 2 1 µ 2 F +ln µ b 2 ln tan 2 (R/2) µ 2 µ 2 2 tan 2 (R/2) ln ln + 12 # µ 2 2 ln2 12 µ 2 b µ 2 b µ 2 b 31

32 Introduction In-Jet e + TMDs e Collins Asymmetries Conclusions Jet fragmentation function pp! (jeth)x l Renormalization D i,bare (z h, b,µ, ) =Z D i (b,µ, ) D i,ren (z h, b,µ, ) S i,bare (b,r,µ, ) =Z S i (b,r,µ, ) S i,ren (b,r,µ, ) Evolution µ d dµ S i(b,r,µ, ) = S i,µ(r, µ, ) S i (b,r,µ, ) µ d dµ D i(z h, b,µ, ) = D i,µ(! J, ) D i (z h, b,µ, ) d d S i(b,r,µ, ) = d d D i(z h, b,µ, ) = S i, (b,µ) S i (b,r,µ, ) D i, (b,µ) D i (z h, b,µ, ) anomalous dimensions: S q,µ(r, µ, ) = D q,µ(! J, ) = s C F s C F ln 2 tan 2 (R/2) µ 2 apple 2 ln! J D q, (b,µ)= S q, (b,µ)= s µ 2 C F ln µ 2 b 32

33 Introduction In-Jet e + TMDs e Collins Asymmetries Conclusions Evolution Jet fragmentation function pp! (jeth)x l redefined TMD Dh/i R and evolution to a common scale µ µ 0 0 Collins, Soper, Sterman `85 standard TMD at extra evolution factor µ J! µ µ J 33

34 Introduction In-Jet e + TMDs e Collins Asymmetries Conclusions Evolution I. H c ab µ = p T using modified DGLAP for H c!i H c!i µ = p T R µ d dµ H c!i = ck H ki D h i µ = µ b 2. H c ab µ = p T using DGLAP for sifjfs G h c D h i G h c = H c!i D µ = p T R µ d dµ Gh c = P ic G h i D h i µ = µ b i ii + i,µ S + i,µ D =0 34

35 Introduction In-Jet e + TMDs e Collins Asymmetries Conclusions b* prescription perturbative Sudakov factor: where: b = b/ p 1+b 2 /b 2 max, µ b =2e E /b, b max < 1/ QCD Collins, Soper, Sterman `85 non-perturbative Sudakov factor: quark TMD S q b µ NP = g 2 ln ln b µ 0 + g h zh 2 b 2 Sun, Isaacson, Yuan, Yuan `14 gluon TMD S g NP = C A b µ g 2 ln ln + g h C F b µ 0 zh 2 b 2 Balazs, Berger, Mrenna, Yuan `14 Balazs, Berger, Nadolsky, Yuan `14 Consistent with the fits of e.g. Sun, Kang, Prokudin, Yuan `16 35

36 Introduction In-Jet e + TMDs e Collins Asymmetries Conclusions Comparison to ATLAS data 2j F (zh,pt,j ) s =7TeV, η < 1.2, R =0.6 p T [25, 40], <z h >=0.08 sitmdff ATLAS 2j F (zh,pt,j ) s =7TeV, η < 1.2, R =0.6 p T [400, 500], <z h >=0.032 sitmdff ATLAS j [GeV] j [GeV] Varying µ, µ J by factors of 2 Still need to include NGLs Gluon contribution dominates at low p T 36

37 Introduction In-Jet TMDs Collins Asymmetries e W + e ± Conclusions Outline Introduction In-jet TMDs Collins asymmetries Conclusions Kang, Liu, FR, Xing `17 Kang, Prokudin, FR, Yuan `17 37

38 Introduction In-Jet TMDs Collins Asymmetries e W + e ± Conclusions Collins azimuthal asymmetries inside jets Transversely polarized pp collisions Test of the universality of the Collins FF as currently extracted in global fits to SIDIS and electron-positron data Test of TMD evolution effects Collins azimuthal spin asymmetry Yuan `08 38

39 Introduction In-Jet TMDs Collins Asymmetries e W + e ± Conclusions Collins azimuthal asymmetries inside jets where quark transversity distribution Collins FF Global fits used for our numerical studies with TMD evolution without Kang, Prokudin, Sun, Yuan `16 Anselmino, Boglione, D Alesio, Hernandez, Melis, Murgia, Prokudin `15 see also: generalized parton model D Alesio, Murgia, Pisano `11, `17 39

40 Introduction In-Jet TMDs Collins Asymmetries e W + e ± Conclusions Comparison to RHIC data with TMD evolution without pp! (jet ± )X 40

41 Outline Introduction In-jet TMDs Collins asymmetries Conclusions Kang, Liu, FR, Xing `17 Kang, Prokudin, FR, Yuan `17 41

42 Conclusions Inclusive jets and their substructure Identified hadrons within jets: light hardrons, photons, open heavy flavor, quarkonia TMD FFs within jets Y-term, non-global logarithms, global fits le + e! (jeth)x 42