Zhongbo KangUCLA

QCD multiple scattering in cold nuclear matter

2017 Meeting of APS Division of Particles and FieldsFermilab

July 31 – August 4, 2017

Perturbative QCD

§ Perturbative QCD is very successful in describing and interpreting experimental data at e+e-, e-p, and p-p collisions

2p+p➝h+X p+p➝jet+X

QCD factorization at leading-twist

§ Such a success relies on QCD factorization theorems at leading-twist, which is based on “single scattering picture”

3

p

p

h

a

b

c

d�pp!hX

dpT d⌘=

X

a,b,c

fa ⌦ fb ⌦Hab!c ⌦Dhc

Proton to nucleus

§ What do we expect when a proton is replaced by a heavy nucleus in high energy collisions?§ Nuclear binding energy is about 8 MeV/nucleon << typical energy exchange in

hard collisions

§ Should one expect a simple sum/superposition of individual nucleons?

§ However, large and non-trivial nuclear dependence have been observed in almost all processes involving nuclear targets

4

RF2 =1AF

A2 (x,Q2

12F

D2 (x,Q2)

6= 1

Nuclear broadening: nuclear size dependence

§ Nuclear broadening of average transverse momentum of produced particles in p+A vs p+p

5

hp2T ipA = hp2T ipp + bA1/3

0

0.2

0.4

0.6

10 102

J/ψϒDY

A

∆⟨p

⊥2 ⟩ (G

eV2 )

0

0.02

0.04

∆<P T2 >

[GeV

2 ] π+

0

0.02

0.04π-

0

0.02

0.04

10 102A

K+

HERMES Fermilab, SPS ALICE

Single vs multiple scattering

§ Single scattering is localized in space and cannot have size dependence, it is “multiple scattering” that plays an important role

§ Generic structure of cross section for particle production

6

leading twist

twist-3

twist-4

perturbative expansion

power expansion

�

hphys =

h↵

0sC

(0)2 + ↵

1sC

(1)2 + ↵

2sC

(2)2 + . . .

i⌦ T2(x)

+1

Q

h↵

0sC

(0)3 + ↵

1sC

(1)3 + ↵

2sC

(2)3 + . . .

i⌦ T3(x)

+1

Q

2

h↵

0sC

(0)4 + ↵

1sC

(1)4 + ↵

2sC

(2)4 + . . .

i⌦ T4(x)

+ . . .

Generalized QCD factorization

§ Framework to compute the contributions of multiple scattering§ A generalized QCD factorization framework was developed by Qiu and Sterman

in 1990s

§ Over the years, we have improved for fast/efficient implementation and for generic kinematic regions

§ Example diagrams

7

x1P (x1 + x3)P

x′P ′

pc

pd

k′gkg

(M)

kg

x1P

k′g

(x1 + x3)P

x′P ′

pc

pd

(L)

x1P (x1 + x3)P

x′P ′

pc

pd

kg k′g

(R)

kg = x2P + k? k

0g = (x2 � x3)P + k?

Ehd�(D)

d3Ph/Z

dz

z2Dc!h(z)

Zdx0

x0 fa/p(x0)

⇥Z

dx1dx2dx3T (x1, x2, x3)

✓�1

2g�⇥

◆1

2

⇥2

⇥k�?⇥k⇥?H(x1, x2, x3, k?)

�

k?!0

Incoherent vs coherent multiple scattering

§ The nature of the multiple scattering (incoherent vs coherent) depends on the probing length of the probe§ At small-x region (forward region):

coherent ➝ suppression

§ At large-x region (backward region):

incoherent ➝ enhancement

8

1

Q

⇠ 1

xP

� 2R

✓m

p

◆

1

Q

⇠ 1

xP

< 2R

✓m

p

◆

e−

e−

Heavy meson production in backward region

§ Both initial-state and final-state double scattering contributions

9

0

0.5

1

1.5

2

2.5

0 1 2 3 4 5 6 7 8 9 10

TheoryPHENIX -2.0 < y < -1.4

Heavy-flavor muons in d+Au min. bias, √s=200 GeV

pT (GeV)

RdA

u

0

0.5

1

1.5

2

2.5

0 2 4 6 8 10 12 14 16 18 20

TheoryALICE -4.0 < y < -2.96 (preliminary)

Heavy-flavor muons in p+Pb min. bias, √s=5020 GeV

pT (GeV)

RpP

b

Kang, Vitev, Xing, PLB 15

Dihadron correlation in forward region

§ In p+p collisions, at LO, two hadrons are produced back-to-back in transverse plane

§ However, in p+A/d+Au collisions, initial-state and final-state multiple scattering will lead to imbalance

§ Nuclear broadening of dihadronimbalance

10

0π

K +

0π

K +

�hq2?i = hq2?ipA � hq2?ipp

~q? = ~Ph1? + ~Ph2

?

0.20.40.60.8

11.2

h±-h±

3< pT,trig<5 GeV|y1,2|<0.35σ

F (ra

d)

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5

π±-h±

π0-h±

5< pT,trig<10 GeV

pT,assoc (GeV)

Kang, Vitev, Xing, PRD 2012

Dihadron suppression in forward region

§ Combine suppression and nuclear broadening, one can predict the azimuthal decorrelation

11

0.005

0.01

0.015

0.02

0.025

0.03

-1 0 1 2 3 4 5

shadowing+e-lossshadowing

d+Au central

∆φ

CP(∆φ)

STAR

Kang, Vitev, Xing, PRD, 12

Explore multiple scattering in more channels

§ Transverse momentum broadening also happens in other processes such as SIDIS, DY, J/𝜓 production§ Comparing the theoretical computations and experimental data can validate

our theoretical framework

12

µ−

q

µ−

µ+

q

q

g

g

Q

Q

e+A ! e+ h+X p+A ! µ+µ� +X p+A ! J/� +X

SIDIS DY J/ψ

Final-state Initial-state Both

Works pretty well

§ Description of the data using single set of correlation functions

13

0

0.2

0.4

0.6

10 102

J/ψϒDY

A

∆⟨p

⊥2 ⟩ (G

eV2 )

0

0.02

0.04

∆<P T2 >

[GeV

2 ] π+

0

0.02

0.04π-

0

0.02

0.04

10 102A

K+

HERMES Fermilab, SPS ALICE

Kang, Qiu, 08, 12

Kang, Xing, 16

Going beyond: radiative corrections

§ It would be highly desirable to carry out the multiple scattering computations to next-to-leading order (NLO)§ Verify the factorization theorem at NLO and at next-to-leading power (twist-4)

§ Derive the evolution equations for the relevant correlation functions

§ Reduce the theoretical uncertainties

§ We recently took this step, performed the NLO computations for SIDIS and DY processes

14

q

x1p (x1 + x3)pkg k′g

qµν

ℓ

(a)

T-4 q-g correlation

Double scattering in SIDIS at NLO

§ Virtual diagrams (7)

§ Real diagrams (69)

15

Kang, Wang, Wang, Xing, PRL 13, PRD 17

SIDIS: TMB at NLO

§ Logic: make sense of all sorts of divergence§ UV divergence: taken care by renormalization

§ Soft divergence: cancel between real+virtual

§ Collinear divergence: long-distance physics, part of PDFs/FFs, leads to DGLAP evolution of these functions

16

k ! 1k ! 0

k//P

T

qg

(xB

, 0, 0, µ2f

) = T

qg

(xB

, 0, 0)� ↵

s

2⇡

1

✏

+ lnµ

2

µ

2f

!Z 1

xB

dx

x

hPqg!qg

⌦ T

qg

+ P

qg

(x)Tgg

(x, 0, 0)i

New splitting kernel

�1

✏

�(1� z)Pqg!qg(x)⌦ TqgDh/q(z)

collinear to FScollinear to IS

�1

✏

�(1� x)Tqg(x, 0, 0)Pqq(z)

µ2 @Dh/q(zh, µ2)

@µ2=

↵s

2⇡

Zdz

zPqq(z)Dh/q(z, µ

2)

New evolution equation

§ Evolution equation for quark-gluon correlation function

§ Perform the same calculation for DY production in p+A collisions§ Same renormalized result at NLO for quark-gluon correlation function,

indicating the universality of the function, independent of the hard process

17

SIDIS vs DYFinal-state vs initial-state

Kang, Qiu, Wang, Xing, PRD 16

A full NLO calculation

§ Factorization

18

dh`2hT�idzh

/ Dq/h(z, µ2)⌦HLO(x, z)⌦ Tqg(x, 0, 0, µ

2)

+↵s

2⇡Dq/h(z, µ

2)⌦HNLO(x, z, µ2)⌦ Tqg(gg)(x, 0, 0, µ2)

nonperturbative

perturbative

nonperturbative

Though quite involved, (1) the evolution equation can be derived; at the same time, (2) multiple scattering hard part (short-distance physics) can be rigorously computed

Summary

§ Multiple scattering in high energy nuclear collisions are very important sources of nuclear dependence

§ The effects of multiple scattering can be systematically calculated in a high-twist formalism

§ QCD NLO computations for double scattering have been performed for the first time for SIDIS and DY processes § Looking forward to the precision analysis of p+A data in the future

19

Thank you!