Fractional momentum correlations in multiple production of W bosons and of b b pairs in high energy pp collisions

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1 SMR Fift International Conference on PERSPECTIVES IN HARONIC PHYSICS Particle-Nucleus and Nucleus-Nucleus Scattering at Relativistic Energies May 26 Fractional momentum correlations in multiple production of w bosons and of bb pairs in ig energy pp collisions Enrico CATTARUZZA Universita' degli Studi di Trieste ipartimento di Fisica Via A. Valerio Trieste ITALY Tese are preliminary lecture notes, intended only for distribution to participants

2 Fractional momentum correlations in multiple production of W bosons and of b b pairs in ig energy pp collisions 1 E. Cattaruzza, A. el Fabbro and. Treleani 1 epartment of Pysics of University of Trieste (INFN) 2 epartment of Teoretical Pysics of University of Trieste 1 2 Fift International Conference on Perspectives in Hadronic Pysics

3 Outline Importance of multiparton scattering at new collider energies isconnected collisions double parton scattering and double parton distribution; ouble parton distribution in te LLA of pqc numerical results for te violation to te factorization ansatz of double parton distributions; Multiple production of b bpairs and W bosons in pp-collisions numerical results wit and witout correlation corrections; Conclusions E. Cattaruzza, A. el Fabbro and. Treleani TRIESTE 25/5/26 p.1

4 Introduction RHIC and LHC ig energy colliders Regime of very sort distances and ig momentum transfer asymptotic freedom and validity of perturbative metods small Bjorken x => growing flux of of partons being adrons extended objects, more tan one pair of partons is expected to interact A in different points in transverse space, wit large transverse b momentum excanged => pqc B b E. Cattaruzza, A. el Fabbro and. Treleani TRIESTE 25/5/26 p.2

5 isconnected collisions double parton scattering ouble-parton scattering simplest case of multiparton interaction Presence of two different scales j A i 1) ard perturbative scale 2) inverse of distance in transverse space b b of te interacting partons l k factorization of perturbative and non-perturbative component of te process B 1 2 (A,B) = m 2 i,j,k,l jl(x 1,x 2,b) ik (x 1,x 2 ;b) ˆAij(x 1,x 1 ) ˆBkl(x 2,x 2 ) ouble parton distribution non-perturbative ingredient providing correct dimensionality, related to two body correlations E. Cattaruzza, A. el Fabbro and. Treleani TRIESTE 25/5/26 p.3

6 isconnected collisions double parton scattering ik (x 1,x 2 ;b)= G i (x 1 )G k (x 2 )F ik (b) correlation in transverse space and fractional momenta are neglected te dimensionality of te two body distribution leads to te introduction of a non-perturbative scale factor, effective cross section eff = d 2 bf (b) 2 1 (A,B) = m 2 A S B S eff Inclusive cross-section factorized into te product of inclusive single scattering cross-section of pqc parton model CF collaboration eff = (14.5± 1.7)mb E. Cattaruzza, A. el Fabbro and. Treleani TRIESTE 25/5/26 p.4

7 ouble Parton istribution in LLA of pqc Tis symplified ypotesis of factorization in contrast wit leading logaritm approximation of pqc [1] If two parton distribution is factorized at reference scale, it becomes dinamically correlated at any different scale of a ard process egree of violation of factorization ansatz can be estimated by solution of te generalized LAP equation for two parton distribution were j d dt = P j1 j 1 + P j2 j 2 + j P j j1 j 2 t= 1 2 b ln 1+ g2 (µ 2 ) bln and b= 33 2n f 4 µ 12 satisfies te evolution equation d j dt = j P j j [1] A. M. Snigirev, Pys. Rev. 68, (23) (ep-p/34172); V.L. Korotkik, A.M. Snigirev, Pys. Lett. B 594, (24) (ep-p/44155). E. Cattaruzza, A. el Fabbro and. Treleani TRIESTE 25/5/26 p.5

8 ouble Parton istribution in LLA of pqc If te following initial condition is taken (x 1,x 2 ;t= ) = j 1 (x 1;) j 2 (x 2;) (1 x 1 x 2 ) (x 1,x 2 ;t) = j 1 (x 1;t) j 2 (x 2;t) (1 x 1 x 2 )+ (x 1,x 2 ;t) te non-factorized contribution is expressed in terms of initial single j parton densities and te distribution functions i (x;t),corr,1 (x 1,x 2 ;t) = (1 x 1 x 2 ) j 1 (t = ) j 1 j 1 (t) j 2 (t = ) j 2 j 2 (t),corr,2 (x 1,x 2 ;t) = t dt j (t ) P j j 1 j 2 j 1 j 1 (t t) j 2 j 2 (t t) E. Cattaruzza, A. el Fabbro and. Treleani TRIESTE 25/5/26 p.6

9 ouble Parton istribution in LLA of pqc j i (x;t) represents te probability to find a parton j witin a parton i; it satisfies te evolution equation d j i dt (x;t) = j i P j j j wit te initial condition i (x;t = ) = ij (1 x). Te equation is solved by introducing te Mellin transforms 1 j i (n;t) = dx x n j i (x;t), wic lead to a system of ordinary differential equations at first order. j i (x;t) = dn 2 ı x n j i (n;t) = L 1 ( j i (n;t), ln(x)). E. Cattaruzza, A. el Fabbro and. Treleani TRIESTE 25/5/26 p.7

10 ouble Parton istribution in LLA of pqc j Once i (x;t) as been determined, te integral of te LAP equation as performed using MRS99 as parametrization for parton distribution and Vegas algoritm for numerical integration. In te kinematical regime of interest (x never exceeds ),corr,1 is negligible; j 1 (x;t) j 2 (x;t) d dt = P j1 j 1 + P j2 j 2 Effect of correlation induced by evolution is estimated by te ratio R (x 1,x 2 ;t) = plotted as a function of,corr,1 (x 1,x 2 ;t)+,corr,2 (x 1,x 2 ;t) j 1 (x 1;t) j 2 (x, 2;t) x= x 1 =x 2 E. Cattaruzza, A. el Fabbro and. Treleani TRIESTE 25/5/26 p.8

11 Numerical Results for te Correlation Ratio Factorization scale coice Ratio R gg (x;t).3 Q fct = m b Q fct = m w µ= 1.2GeV n f =4 K = 5.7 Q fct =M W =8GeV R gg 35% forx R gg 8 1% forx.1 R gg (x) R gg 2% forx.1 Q fct =M b =4.6GeV R gg 1 12% forx R gg 5% forx.1 R gg 2% forx x E. Cattaruzza, A. el Fabbro and. Treleani TRIESTE 25/5/26 p.9

12 Numerical Results for te Correlation Ratio R ud (x) R cd (x).3 Q fct = m b Q fct = m W.1.1 x _ cd correlation.3 Q fct = m b Q fct = m W _ ud correlation R us (x) R cs (x).3 K = x _ cs correlation.3 Q fct = m b Q fct = m W _ us correlation Q fct = m b µ= 1.2GeV Q fct = m W Ratio R qq (x;t) Q fct =M W =8GeV R qq 35% forx R qq 2% forx.1 R qq 1% forx.1 Q fct =M b =4.6GeV R qq 23% forx R qq 1% forx.1 R qq 5% forx x.1.1 x E. Cattaruzza, A. el Fabbro and. Treleani TRIESTE 25/5/26 p.1

13 Numerical Results for te Correlation Ratio!#$%%& ()*$+ Q fct = 8 GeV Q fct = 8 GeV x2 x1 Q fct = 8 GeV K = Ratio.5.3 x2.3, 1,,2,3 1,,2,3,4#),,,,,,5,4#),,,,,,5!#$%%& ()*$+!!! x1,,,-.!#$%%& ()*$ Q fct = 8 GeV.5 Ratio.3 Ratio Ratio.5.3 x2 x ,,2,3 1,,2,3,4#),,,,,,5,4#),,,,,,5 x1,, -/!#$%%& ()*$+ x2,,-#!#$%%& ()*$ E. Cattaruzza, A. el Fabbro and. Treleani TRIESTE 25/5/26 p.11

14 ouble Parton istribution in LLA of pqc Remark Te non-perturbative input of double-parton scattering cross section j is not represented by te distribution functions 1 j 2 (x;t), were te transverse variables ave been integrated; ouble parton scattering cross section depends on relative separation of partons in transverse space => outside control of pqc; Given te different origin of te terms in (x;t), it is not unnatural to ave different non-perturbative scales for te transverse separation of te factorized and of te correlated terms; Assumption j 1) in and 1 j 2,corr,1 => CF low resolution scale process 2) in => scale related to size of gluon cloud of a valence quark,fact,corr,2 E. Cattaruzza, A. el Fabbro and. Treleani TRIESTE 25/5/26 p.12

15 ouble Parton istribution in LLA of pqc (x 1,x 2,b;t) were te parton pair densities satisfy,fact (x 1,x 2 ;t)+,corr,1 (x 1,x 2 ;t) F ef f (b) +,corr,2 (x 1,x 2 ;t)f r (b) d 2 bf i (b) = 1 d 2 bf i (b) 2 = 1 i wit i= eff, r. r eff r F ef f transverse density of partons at resolution scale leading to scale factor eff =14.5m b; F r transverse density for partons correlated in fractional momenta, important at iger resolution scale; r [ r, eff ], wit r =2.8m b related to te size [3] of te gluon cloud of a valence quark in te adron. [3] B. Pov, Nucl. Pys. A 699, 226 (22) E. Cattaruzza, A. el Fabbro and. Treleani TRIESTE 25/5/26 p.13

16 Multiple Production of b b pairs Multiple production of b bpairs and W bosons in pp-collisions 1) pp b bb b iger order corrections in S are very important ; te wole effect of iger order corrections is reduced to a single numerical value, K factor K = (q q) LO (q q) Our assumption is tat iger order corrections in double b bb b production can be taken into account by multiplying te cross section of eac connected process by te same K factor In addition to usual factorized contribution, scaling wit eff, double cross section includes not factorized contributions jl related to te couplings of bot wit and ik,corr,2,fact 1 jl,corr,2 E. Cattaruzza, A. el Fabbro and. Treleani TRIESTE 25/5/26 p.14

17 Numerical Results at LHC b b production cross-section and correlation effect [4] E. Cattaruzza, A. el Fabbro and. Treleani, Pys. Rev. 7, 3422 [arxivep-p/44177]. # fact & # corr (!b) # fact pp!bbbb K = 5.7 pp!bbbb # corr /# fact, r = r eff, r = r # corr, r = r eff, r = r # corr /# fact, r < r < r eff # corr, r < r < r eff r = r r = r eff # corr /# fact.3 r = r 1) K factor =5.3 2) MRS99for PF 3) Scale coices Q fct =Q rn =m b F ef f [4] 4) Gaussian distrib. for and F r.1 1 1!s (GeV) ifr [r eff,r ] (12 2)% at s= 1TeV && (3.5 6)% at s= 14TeV r = r eff !s (GeV) 1/ eff 2/( eff + r ) scale factors Effect of correlations decreases increasing c.m; te decrease is faster as s 5TeV for larger c.m x becomes smaller tan.1were R gg.3 E. Cattaruzza, A. el Fabbro and. Treleani TRIESTE 25/5/26 p.15

18 Multiple Production of W pairs 2) pp W + W +,W W te cross-sections of like-sign W pair ave been evaluated at te leading order, including only quark initiated processes in te elementary interaction (q q W ) iger order corrections are taken into account multiplying te lowest order correction by te K factor [5] K s(m 2 W ) [5] V.. Barger, R. J. N. Pillips, Collider Pysics (updated edition), Addison- Wesley Publising Company, Inc. (1996), p.247. E. Cattaruzza, A. el Fabbro and. Treleani TRIESTE 25/5/26 p.16

19 Numerical Results at LHC production cross-section and correlation effect # fact & # corr (nb).1.1 1e-5 1e-6 1e-7.6 pp!w + W + pp!w + W + r = r # fact r = r eff # corr, r = r eff, r = r # corr, r < r < r eff K = !s (GeV) # corr /# fact x [,6] 1 2 as s [1.,14]T ev.5.3 r = r eff r = r # corr /# fact, r = r eff, r = r # corr /# fact, r < r < r eff !s (GeV) corr fact corr fact [27 45%,7.5 13% ]for W + [23 4%,12 2% ]for W 1) MRS99for PF 2) Scale coices Q fct =Q rn =M W 3) Gaussian distrib. for and F r F ef f 2/ eff 2/( eff + r ) scale factors E. Cattaruzza, A. el Fabbro and. Treleani TRIESTE 25/5/26 p.17

20 Numerical Results at LHC production cross-section and correlation effect # fact & # corr (nb).1.1 1e-5 1e-6 1e-7 1e-8 # fact.6 pp!w - W - pp!w - W - r = r r = r eff # corr, r = r eff, r = r # corr, r < r < r eff 5 1!s (GeV) K = 5.7 # corr /# fact x [,6] 1 2 as s [1.,14]T ev !s (GeV) corr fact corr fact r = r eff r = r # corr /# fact, r = r eff, r = r # corr /# fact, r < r < r eff [27 45%,7.5 13% ]for W + [23 4%,12 2% ]for W 1) MRS99for PF 2) Scale coices Q fct =Q rn =M W 3) Gaussian distrib. for and F r F ef f 2/ eff 2/( eff + r ) scale factors E. Cattaruzza, A. el Fabbro and. Treleani TRIESTE 25/5/26 p.18

21 Conclusions As an effect of evolution, te multiparton distributions are expected to become strongly correlated in momentum fraction at large Q 2 and finite x ; Hig resolution scale multiparton process (equal sign W pair production) and a smaller resolution scale process ( b bb b production) in pp collisions in te energy range s [1,14]TeV ave been considered; isconnected contributions to te cross-section, after evolving multiparton distribution at desired resolution scale, ave been evaluated; Terms wit correlation, in equal sign W pair production, are at most 4% of te cross-section at 1 TeV and a 2% effect at LHC Te effect is muc smaller in b bb b production, were corrections are of te order of 5%. E. Cattaruzza, A. el Fabbro and. Treleani TRIESTE 25/5/26 p.19