physics in pa collisions - ustcpnp.ustc.edu.cn/groupnew/xueshuhuodong/document/... · physics in pa...

Physics in pA collisions:Opportunities and Challenges in Saturation Physics

Bo-Wen Xiao

Institute of Particle Physics, Central China Normal University

A. Mueller, BX, F. Yuan, Phys. Rev. Lett. 110, 082301 (2013).

G. Chirilli, BX and F. Yuan, Phys. Rev. Lett. 108, 122301 (2012).

F. Dominguez, BX and F. Yuan, Phys.Rev.Lett. 106, 022301 (2011).

F. Dominguez, C.Marquet, BX and F. Yuan, Phys.Rev.D83, 105005 (2011).

May 30, 2013 at USTC

1 / 38

Introduction

1 Introduction

2 One-loop Calculation for Forward Hadron Productions in pA Collisions

3 Gluon Distributions and LO dijet productions

4 One-loop Calculation for Dijet and Higgs Productions

5 Conclusion

2 / 38

Introduction

高能极限下的核子结构

Gluon splitting functions (胶子劈裂函数) have 1/z singularities→Splitting of small-x gluon is favored→ Gluon density rises at low x ≡ Q2

s .

3 / 38

Introduction

高能极限下的核子内胶子的饱和现象

Saturation Phenomenon (Color Glass Condensate)

Gluon Splitting

Gluon Recombination

Resummation of the αs ln 1x ⇒ BFKL equation.

When too many gluons squeezed in a confined hadron, gluons start to overlap andrecombine (重叠并再结合)⇒ Non-linear dynamics⇒ BK equation

Introduce the saturation momentum Qs(x) (引入饱和动量)to separate the saturated dense regime x < 10−2 from the dilute regime.

4 / 38

Introduction

Dual Descriptions of Deep Inelastic Scattering

Bjorken frame Dipole frame

...

Bjorken frameF2(x,Q2) =

∑q

e2qx[fq(x,Q2) + fq(x,Q2)

].

Dipole frame [A. Mueller, 01; Parton Saturation-An Overview]

F2(x,Q2) =∑

f

e2f

Q2

4π2αem

∫ 1

0dz∫

d2x⊥d2y⊥[|ψT (z, r⊥,Q)|2 + |ψL (z, r⊥,Q)|2

]×[1− S(2) (x⊥, y⊥)

], with r⊥ = x⊥ − y⊥.

Bjorken: the partonic picture of a hadron is manifest. Saturation shows upas a limit on the occupation number of quarks and gluons.Dipole: the partonic picture is no longer manifest. Saturation appears as the unitaritylimit for scattering. Convenient to resum the multiple gluon interactions.

5 / 38

Introduction

高能极限下的核子内胶子的饱和现象

Saturation physics describes the high density parton distributions in the high energy limit.

Unitarity of S-matrix⇔ Gluon Saturation. (散射矩阵的幺正性⇔胶子饱和现象)Scatterings involving heavy ions reach saturation faster than proton scatterings.Gluon Saturation itself is a very interesting QCD phenomenon, also it provides importantinformation for the initial condition of heavy ion collisions.How to identify the smoking guns? 寻找胶子饱和现象的确凿证据！

6 / 38

Introduction

Recent pA run at the LHC and the ALICE Data

0 2 4 6 8 10 12 14 16 18 200.4

0.6

0.8

1

1.2

1.4

1.6

1.8 = 5.02 TeVNN

spPb

| < 0.3cms

ηALICE, NSD, charged particles, |

Saturation (CGC), rcBKMCSaturation (CGC), rcBK

Saturation (CGC), IPSat

0 2 4 6 8 10 12 14 16 18 20

pP

bR

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8 )0πShadowing, EPS09s (

LO pQCD + cold nuclear matter

(GeV/c)T

p

0 2 4 6 8 10 12 14 16 18 200.4

0.6

0.8

1

1.2

1.4

1.6

1.8 HIJING 2.1=0.28gs

=0.28g

DHC, s

DHC, no shad.

DHC, no shad., indep. frag.

Unprecedented opportunities to study saturation physics. A lot of rich physics for us toexplore both experimentally and theoretically.

Most saturation models employ LO formula or only part of NLO calculation.Large uncertainty!

Serious challenges: Factorization issue and NLO correction!

7 / 38

Introduction

Challenges

kt factorization formula for the single inclusive gluon productions in hadron-hadron collision:

3

atic error in the comparison of theory and experiment.Explicitly noticing such problems can be an importantmotivation for topics for further research that are impor-tant for the success of a field.

The kT -factorization formula that we discuss, Eq. (1)below, is intended to be valid for single inclusive jet pro-duction in hadron-hadron collisions. It is widely usedin phenomenological applications to study the particlemultiplicity observed at hadron colliders. (For some ex-amples see [4–12] and references therein. A comparisonof some phenomenological predictions to LHC data forthe particle multiplicities in both proton-proton and lead-lead collisions was presented by the ALICE collaboration[13].)

The kT -factorization formula used in this area is (see,e.g., Ref. [8, Eq. (1)]):

d!

d2pT dy=

2"s

CF p2T

!

!!

d2kA,T fA(xA, kA,T ) fB(xB , pT " kA,T ). (1)

Here fA and fB are TMD densities of gluons in theirparent hadrons, and the two gluons combine to give anoutgoing gluon of transverse momentum pT which givesrise to an observed jet in the final state. In the formula,CF = (N2

c " 1)/2Nc with Nc = 3 for QCD, y is therapidity of the final-state jet, and xA,B = (pT /

#s)e±y.

The incoming hadrons A and B can be protons or nuclei.Questions that now naturally arise are: Where does

this formula originate from? Where can a proper deriva-tion be found, and under what conditions and to whataccuracy is the derivation valid? What are the explicitdefinitions of the unintegrated distributions fA,B, and dothese definitions overcome the subtleties that are foundin constructing definitions of TMD distributions in QCDin the non-small-x regime [2, Chs. 13 & 14]? In an idealworld, we could say that in order for the requirements(T1)–(T4) to be fulfilled, it is absolutely necessary thatthese questions be answered, and that a person who readsa paper which makes use of this formula can, if needed,go back to the original source and himself/herself repro-duce and verify the derivations. But we must recognizethat in the real world some of these issues are very deepand di!cult, and that therefore complete answers to thequestions do not (yet) all exist. Nevertheless, in thissubject, we should expect some kind of derivation, withthe accompanying possibility of an outsider being ableto identify, for example, possible gaps in the logic wherefurther work is needed.

However, as we will explain below, we tried to find anykind of a derivation of the formula by following citationsgiven for it, but were unable to do so. Our findings canbe visualized in Fig. 1, which shows the chain of refer-ences that one needs to follow to arrive at the nearestpossible source(s), starting from a selection of recent pa-pers. Coming to those sources we find that the formula isnever derived but essentially asserted. Moreover, the ba-sic concepts involved are never defined in a clear enough

way to make it understandable what exactly it is thatis being done. We therefore find it impossible that (1)can be satisfactorily re-derived from sources referencedin the literature, contrary to what should be the case ifprinciples (T1)–(T4) hold.

A clear symptom that these are not merely abstractdi!culties but are problems with practical impact is thatthe overall normalization factor di"ers dramatically be-tween the references. See, for example, Eq. (40) in [14]and Eq. (4.3) in [15] — and notice that this di"erence innormalization does not appear to be commented on, letalone explained. The di"erence in normalization factorsdemonstrates that at least one of the presented factor-ization formulas is definitively wrong. (In the two ap-pendices of the present paper, we will show that in factthe normalizations of both formulas appear to be wrong.)There are a number of di!cult physical and mathemati-cal issues that need to be addressed if one is to provide afully satisfactory proof of a factorization formula. Theseissues go far beyond a mere normalization factor. Butthe existence of problems with the normalization factoris a diagnostic: it provides a clear and easily verifiablesymptom that something has gone wrong. A minimumcriterion for a satisfactory derivation is that it should beexplicit enough to allow us to debug how the normaliza-tion factor arises.

At the top of our chart of references, Fig. 1, we havechosen some of the recent phenomenological applications[8–11] that make use of (1). We also include some earlierhighly cited phenomenological applications [5, 6]. Thereexist a very great number of papers which make use of(1), so we include here only a representative few. As isindicated in the top part of Fig. 1, a central source thatis given for (1) is the highly cited Ref. [14]. We thus askwhether we then can find a derivation of (1) in [14].

That paper performs a calculation in a quasi-classicalapproximation of particle production in DIS using thedipole formalism (see the reference for the exact calcu-lations that define this “quasi-classical” approximation).There actually is an implicit assumption of a factorizedstructure from the very start in this formalism (see Eqs.(1) and (7) in the reference). For our purposes it is im-portant to notice what the exact statement is regarding(1), which can be found as Eq. (40) in [14]. (An unimpor-tant di"erence is that in [14], the f ’s in (1) are insteadwritten as f/k2

T .) Prior to this equation, an equation forthe production of gluons in DIS is derived, Eq. (39) in[14]. The exact statement just prior to stating (1) in theform of Eq. (40) in [14] reads

The form of the cross section in Eq. (39) sug-gests that in a certain gauge or in some gaugeinvariant way it could be written in a fac-torized form involving two unintegrated gluondistributions merged by an e!ective Lipatovvertex.

There is no derivation of Eq. (1). Rather, this equation isstated as being the “usual form of the factorized inclusive

Factorization and NLO calculation? Gluon distribution?Difficulties: 1. LO, resumming the past and future gauge links;2. NLO, removing divergences.Alternative solution: the effective hybrid factorization in pA collisions.

8 / 38

Introduction

Dilute-Dense (Hybrid) factorizations

The effective Dilute-Dense factorization

x1 ∼ p⊥√se+y ∼ 1

x2 ∼ p⊥√se−y � 1

Jan 8, 2013 Zhongbo Kang, LANL

Observation at high energy

! The spin asymmetry becomes the largest at forward rapidity region, corresponding to! The partons in the projectile (the polarized proton) have very large momentum

fraction x: dominated by the valence quarks (spin effects are valence effects)! The partons in the target (the unpolarized proton or nucleus) have very small

momentum fraction x: dominated by the small-x gluons

! Thus spin asymmetry in the forward region could probe both! The transverse spin effect from the valence quarks in the projectile: Sivers

effect, Collins effect, and etc! The small-x gluon saturation physics in the target

4

projectile:

target:

valence

gluon

√s

Tuesday, January 8, 2013

Protons and virtual photons are dilute probes of the dense gluons inside target hadrons.

For dijet productions in pA collisions (2→ 2), there is an effective kt factorization.

dσpA→ggX

d2P⊥d2q⊥dy1dy2=xpg(xp, µ)xAg(xA, q⊥)

1π

dσdt.

For dijet processes in pp, AA collisions, there is no kt factorization[Collins, Qiu,08],[Rogers, Mulders; 10].

9 / 38

Introduction

Some relevant experiments

Operation in 2013 and future operations.

Forward rapidity physics at RHIC and the LHC(LHCf and TOTEM, etc.) 5 TeV

Cosmic ray events can have incoming particles with energy up to 1012 GeV.

Future EIC or LHeC experiments.

10 / 38

One-loop Calculation for Forward Hadron Productions in pA Collisions

1 Introduction




5 Conclusion

11 / 38


Factorization

In a physical process, in order to probe the dense nuclear matter precisely, the properfactorization is required.

Factorization is about separation of short distant physics (perturbatively calculable hardfactor) from large distant physics (parton distributions and fragmentation functions).

σ ∼ xf (x)⊗H⊗ Dh(z)

xf (x) and Dh(z) should be universal.NLO calculation always contains various kinds of divergences.

Some divergences can be absorbed into xf (x) or Dh(z) following evolution equations.The rest of divergences should be cancelled.

Hard factorH = H(0)

LO +αs

2πH(1)

NLO + · · ·

should always be finite and free of divergence of any kind.

12 / 38


Forward hadron production in pA collisions

Consider the inclusive production of inclusive forward hadrons in pA collisions, i.e., in theprocess: [Dumitru, Jalilian-Marian, 02]

x1 ∼ p⊥√se+y ∼ 1

x2 ∼ p⊥√se−y � 1

Jan 8, 2013 Zhongbo Kang, LANL

Observation at high energy

! The spin asymmetry becomes the largest at forward rapidity region, corresponding to! The partons in the projectile (the polarized proton) have very large momentum

fraction x: dominated by the valence quarks (spin effects are valence effects)! The partons in the target (the unpolarized proton or nucleus) have very small

momentum fraction x: dominated by the small-x gluons

! Thus spin asymmetry in the forward region could probe both! The transverse spin effect from the valence quarks in the projectile: Sivers

effect, Collins effect, and etc! The small-x gluon saturation physics in the target

4

projectile:

target:

valence

gluon

√s

Tuesday, January 8, 2013

The leading order result for producing a hadron with transverse momentum p⊥ at rapidity yh

dσpA→hXLO

d2p⊥dyh=

∫ 1

τ

dzz2

∑f

xpqf (xp)F(k⊥)Dh/q(z) + xpg(xp)F(k⊥)Dh/g(z)

.

· · ·

The origin of the transverse momentum of the forward parton is from multiple scatterings.13 / 38


The overall picture of the NLO calculation

[G. Chirilli, BX and F. Yuan, Phys. Rev. Lett. 108, 122301 (2012)] Why is NLO important?

NLO correction opens up a new channel (parton kt now can come from hard interaction),therefore it is not small.

Consistency check of the LO factorization formula.

Three types of divergences.

· · ·

H

Cp Cf

R

A X

PhP

Compare to earlier works: [A. Dumitru, A. Hayashigaki, J. Jalilian-Marian; 2006], [T.Altinoluk, A. Kovner; 2011]. Divergences and Virtual Diagrams!

14 / 38


NLO calculation for the q → q channel

[G. Chirilli, BX and F. Yuan, Phys. Rev. Lett. 108, 122301 (2012)]

(a) (b)

(d)(c)

(a) (b)

The rapidity divergence (y = 12 ln l+

l− → −∞ light-cone) does not cancel betweenreal and virtual graphs for k⊥ dependent observables.Subtractions of the divergences via renormalization group equations: BK and DGLAP.

15 / 38


Factorization for single inclusive hadron productions

Obtain a systematic factorization for the p + A→ H + X process by systematicallyremove all the divergences!

Gluons in different kinematical region give different divergences. 1.soft, collinear to thetarget nucleus; 2. collinear to the initial quark; 3. collinear to the final quark.

k+ ≃ 0

P+

A≃ 0

P−p ≃ 0

Rapidity Divergence Collinear Divergence (F)Collinear Divergence (P)

All the rapidity divergence is absorbed into the UGD F(k⊥) while collinear divergencesare either factorized into collinear parton distributions or fragmentation functions.

Consistent check: take the dilute limit, k2⊥ � Q2

s , the result is consistent with the leadingorder collinear factorization formula.

16 / 38


Numerical implementation of the NLO result

Consistent implementation should include all the αs (NLL) corrections.[A. Stasto, BX, D. Zaslavsky, in preparation] State of the Art Calculation in the small-xformalism.

NLO parton distributions. (Choose your favorite one, CTEQ or MSTW)

NLO fragmentation function. (DSS or other FFs.)

Use NLO hard factors.

Use the one-loop approximation for the running coupling which is sufficient in thiscalculation.

rcBK evolution equation for the dipole gluon distribution.

Looking at about 30− 50 percent uncertainty. Large Nc limit gives about 10 percent.

Large NLO correction !

17 / 38

Gluon Distributions and LO dijet productions

1 Introduction




5 Conclusion

18 / 38


kt dependent parton distributions

The unintegrated quark distribution

fq(x, k⊥) =

∫dξ−d2ξ⊥4π(2π)2 eixP+ξ−+iξ⊥·k⊥〈P

∣∣∣ψ(0)L†(0)γ+L(ξ−, ξ⊥)ψ(ξ⊥, ξ−)∣∣∣P〉

as compared to the integrated quark distribution

fq(x) =

∫dξ−

4πeixP+ξ−〈P

∣∣ψ(0)γ+L(ξ−)ψ(0, ξ−)∣∣P〉

The dependence of ξ⊥ in the definition.Gauge invariant definition.Light-cone gauge together with proper boundary condition⇒ parton densityinterpretation.The gauge links come from the resummation of multiple gluon interactions.Gauge links may vary among different processes.

19 / 38


A Tale of Twin Gluon Distributions—-绝代双“胶”

For many years, we have know that there are two different gluon distributions:I. Weizsacker Williams gluon distribution [Kovchegov, Mueller, 98]

xG(1)

II. Color Dipole gluon distribution [known since early 90s]

xG(2)

Puzzle: Why there are two gluon distributions?How to distinguish them in experiment? · · ·[F. Dominguez, BX and F. Yuan, Phys.Rev.Lett. 106, 022301 (2011)]

Quadrupole⇒Weizsacker Williams gluon distribution;

Dipole⇒ Color Dipole gluon distribution.

20 / 38



[F. Dominguez, BX and F. Yuan, Phys.Rev.Lett. 106, 022301 (2011)]Gauge Invariant definitions (规范不变定义): I. Weizsacker Williams gluon distribution:

xG(1) = 2∫

dξ−dξ⊥(2π)3P+

eixP+ξ−−ik⊥·ξ⊥Tr〈P|F+i(ξ−, ξ⊥)U [+]†F+i(0)U [+]|P〉.

II. Color Dipole gluon distributions:

xG(2) = 2∫


eixP+ξ−−ik⊥·ξ⊥Tr〈P|F+i(ξ−, ξ⊥)U [−]†F+i(0)U [+]|P〉.

ξ−

ξT

ξ−

ξT

U [−] U [+]

Remarks:

All physical observable in QCD must be gauge invariant. Both are observables.

The WW has probabilistic interpretation. ⇒ gluon density (胶子的密度分布).

Both are fundamental gluon distributions. 绝代双“胶”

21 / 38



I. Weizsacker Williams gluon distribution:

xG(1) = 2∫


eixP+ξ−−ik⊥·ξ⊥Tr〈P|F+i(ξ−, ξ⊥)U [+]†F+i(0)U [+]|P〉.

II. Color Dipole gluon distributions:

xG(2) = 2∫


eixP+ξ−−ik⊥·ξ⊥Tr〈P|F+i(ξ−, ξ⊥)U [−]†F+i(0)U [+]|P〉.

k⊥ = 0 k⊥ 6= 0

Questions:

Can we distinguish these two gluon distributions experimentally?

How to measure xG(1) directly? DIS dijet. Important measurement EIC and LHeC.

How to measure xG(2) directly? Direct γ+Jet in pA collisions and inclusive processes.

22 / 38


DIS dijet

[F. Dominguez, C. Marquet, BX and F. Yuan, 11]

x1 x!1

x2 x!2

x1

x2

x!2

x!1

dσγ∗T A→qq+X

dP.S. ∝ Ncαeme2q

∫d2x1

(2π)2

d2x′1(2π)2

d2x2

(2π)2

d2x′2(2π)2 e−ik1⊥·(x1−x′1)

×e−ik2⊥·(x2−x′2)∑

ψ∗T (x1 − x2)ψT(x′1 − x′2)[1 + S(4)

xg (x1, x2; x′2, x′1)− S(2)

xg (x1, x2)− S(2)xg (x′2, x

′1)]

︸︷︷︸−uiu′j

1Nc〈Tr[∂iU(v)]U†(v′)[∂jU(v′)]U†(v)〉xg⇒Operator Def

,

In the dijet correlation limit, where u = x1 − x2 � v = zx1 + (1− z)x2

S(4)xg (x1, x2; x′2, x

′1) = 1

Nc

⟨TrU(x1)U†(x′1)U(x′2)U†(x2)

⟩xg6= S(2)

xg (x1, x2)S(2)xg (x′2, x

′1)

Quadrupoles are generically different objects and only appear in dijet processes.23 / 38


DIS dijet—-深度非弹性散射中的双喷注过程

The dijet production in DIS.

⇒

Remarks:

Dijet in DIS is the unique physical process which can measure Weizsacker Williams gluondistributions.

Golden measurement for the Weizsacker Williams gluon distributions of nuclei at small-x.The cross section is directly related to the WW gluon distribution.

EIC(美国) and LHeC(欧洲核子中心) will provide us perfect machines to study the stronggluon fields in nuclei. Important part in EIC and LHeC physics design.[arXiv:1212.1701; J.Phys. G39 (2012) 075001.]

24 / 38


Di-Hadron correlations in DIS—-深度非弹性散射中的双π介子产生

Di-pion correlations at EIC

C(∆φ) =

∫|p1⊥|,|p2⊥|

dσeA→h1h2

dy1dy2d2p1⊥d2p2⊥∫|p1⊥|

dσeA→h1

dy1d2p1⊥

Forward di-hadron correlations in

d+Au collisions at RHIC

!"=0

(near side)!"=#

(away side)

(rad)

! “Coincidence probability” at measured by STAR Coll. at forward rapidities:

CP (∆φ) =1

Ntrig

dNpair

d∆φ∆φ

trigger

! Absence of away particle in d+Au coll.

“monojets”! Away peak is present in p+p coll.

d+Au central

p+p

trigger

associated

(k1, y1)(k2, y2) xA =

|k1| e−y1 + |k2| e−y2

√s

20

2 2.5 3 3.5 4 4.50

0.020.040.060.08

0.10.120.140.160.18

eAueAu - sat

eAu - nosateCa

pTtrigger > 2 GeV/c

1 < pTassoc < pT

trigger

|!|<4

ep Q2 = 1 GeV2

!"!"

C(!"

)

C eAu

(!"

)2 2.5 3 3.5 4 4.50

0.05

0.1

0.15

0.2EIC stage-II# Ldt = 10 fb-1/A

Figure 3.21: Left: Saturation model prediction of the coincidence signal versus azimuthal angledifference ∆ϕ between two hadrons in ep, eCa, and eA collisions [165, 166]. Right: Comparisonof saturation model prediction for eA collisions with calculations from conventional non-saturatedmodel for EIC stage-II energies. Statistical error bars correspond to 10 fb−1/A integratedluminosity.

There are several advantages to studying di-hadron correlations in eA collisions ver-2105

sus dAu. Directly using a point-like electron probe, as opposed to a quark bound in a2106

proton or deuteron, is extremely beneficial. It is experimentally much cleaner as there is2107

no “spectator” background to subtract from the correlation function. The access to the2108

exact kinematics of the DIS process at EIC would allow for more accurate extraction of2109

the physics than possible at RHIC or LHC. Because there is such a clear correspondence2110

between the physics of this particular final state in eA collisions to the same in pA collisions,2111

this measurement is an excellent testing ground for universality of multi-gluon correlations.2112

The left plot in Fig. 3.21 shows prediction in the CGC framework for dihadron ∆ϕ2113

correlations in deep inelastic ep, eCa, and eAu collisions at stage-II energies [165, 166].2114

The calculations are made for Q2 = 1 GeV2. The highest transverse momentum hadron in2115

the di-hadron correlation function is called the “trigger” hadron, while the other hadron is2116

referred to as the “associate” hadron. The “trigger” hadrons have transverse momenta of2117

ptrigT > 2 GeV/c and the “associate” hadrons were selected with 1 GeV/c < passoc

T < ptrigT .2118

The CGC based calculations show a dramatic “melting” of the back-to-back correlation2119

peak with increasing ion mass. The right plot in Fig. 3.21 compares the prediction for2120

eA with a conventional non-saturated correlation function. The latter was generated by a2121

hybrid Monte Carlo generator, consisting of PYTHIA [169] for parton generation, showering2122

and fragmentation and DPMJetIII [170] for the nuclear geometry. The EPS09 [150] nuclear2123

parton distributions were used to include leading twist shadowing. The shaded region2124

reflects uncertainties in the CGC predictions due to uncertainties in the knowledge of the2125

saturation scale, Qs. This comparison nicely demonstrates the discrimination power of these2126

measurement. In fact, already with a fraction of the statistics used here one will be able to2127

exclude one of the scenarios conclusively.2128

The left panel of Fig. 3.22 depicts the predicted suppression through JeAu, the relativeyield of correlated back-to-back hadron pairs in eAu collisions compared to ep collisions

76

[E. Aschenauer, J. H. Lee and L. Zheng, BX, for EIC white paper]

EIC stage II energy 30× 100GeV.C(∆φ)能够反映双喷注产生的概率

Physical picture: 核内稠密的胶子会压低双喷注的产生。25 / 38


Lepton-pair-Hadron correlations in dAu collisions at RHIC

[A. Stasto, BX, D. Zaslavsky, 12]

0 π2

π 3π2

2π0

0.002

0.004

σDYF/σDYSIF

GBW

BK

rcBK

0 π2

π 3π2

2π0

0.001

0.002

0.003

∆φ

σDYF/σDYSIF

GBW

BK

rcBK

M = 0.5GeV, 4GeV and Y = 2.5.Direct measurement of the dipole gluon distribution.

26 / 38


STAR measurement on di-hadron correlation in dA collisions

There is no sign of suppression in the p + p and d + Au peripheral data.

The suppression and broadening of the away side jet in d + Au central collisions is due tothe multiple interactions between partons and dense nuclear matter (CGC).

Probably the best evidence for saturation. Smoking Gun ?

27 / 38


Dijet processes in the large Nc limit in pA collisions

The Fierz identity:

= 12

− 12Nc and

= 12

−12

Graphical representation of dijet processes

g→ qq:

x2

x1

x�’2

x�’1v=zx1+(1 z)x2 v�’=zx�’1+(1 z)x�’2

⇒= 1

2! 1

2Nc

q→ qgb

x

b�’

x�’

v=zx+(1 z)b v�’=zx�’+(1 z)b�’

⇒

2= = 1

2− 1

2Nc

g→ ggx1 x�’1v=zx1+(1 z)x2 v�’=zx�’1+(1 z)x�’2

x2 x�’2

⇒= !

= !

The Octupole and the Sextupole are suppressed.28 / 38


Comparing to STAR and PHENIX data measured in dAu collisions

Physics predicted by C. Marquet. Further calculated in[A. Stasto, BX, F. Yuan, 11]For away side peak in both peripheral (less dense) and central (more saturation) dAu collisions

C(∆φ) =

∫|p1⊥|,|p2⊥|

dσpA→h1h2

dy1dy2d2p1⊥d2p2⊥∫|p1⊥|

dσpA→h1

dy1d2p1⊥

JdA =1〈Ncoll〉

σpairdA /σdA

σpairpp /σpp

⇒ 310 210

110

1

peripheral

central

fragAux

dAuJ

1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.00.006

0.008

0.010

0.012

0.014

0.016

Peripheral dAu CorrelationC( )

1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.00.012

0.014

0.016

0.018

0.020

0.022

Central dAu CorrelationC( )

29 / 38

One-loop Calculation for Dijet and Higgs Productions

1 Introduction




5 Conclusion

30 / 38


Motivation for Higgs production in pA collisions

Consider the forward Higgs productions in pA collisions: p + A→ H(MH, k⊥) + X

Comments:

One-loop calculation allows us to do resummations (Small-x[αsNc

2π ln 1x

]n resummation and

Sudakov (CSS)[αsCR

2π ln2 Q21

Q22

]n) together with multiple scatterings.

Perform an exact calculation for the leading power contribution for Higgs production.

The one-loop calculation between Higgs productions and dijet productions arevery similar since both MH � k⊥ and MJ � k⊥.

This calculation can be generalized to the calculation of the heavy quarkoniumΥ, J/Ψ productions.

31 / 38


LO calculation

Gluons couples to the massive scalar through the effective Lagrangian:[A. Mueller, BX, F. Yuan, Phys. Rev. Lett. 110, 082301 (2013).]

Leff = −14

gφΦFaµνFaµν

dσ(LO)

dyd2k⊥= σ0

∫d2x⊥d2x′⊥

(2π)2 eik⊥·(x⊥−x′⊥)xgp(x)SWWY (x⊥, x

′⊥) ,

Only initial state interaction is present. ⇒WW gluon distribution.SWW

Y (x⊥, y⊥) = −⟨

Tr[∂β⊥U(x⊥)U†(y⊥)∂β⊥U(y⊥)U†(x⊥)

]⟩Y

32 / 38


Some Technical Details

Typical diagrams (5 different types in total): [A. Mueller, BX, F. Yuan, Phys. Rev. Lett. 110,082301 (2013).]

Power counting analysis: take the leading power contribution in terms of k2⊥

Q2 .Subtraction of the rapidity divergence: ⇒ small-x evolution equation

xgp(x)

∫dξξ

KDMMX ⊗ SWW(x⊥, y⊥)

Subtraction of the collinear divergence and choose µ2 =c2

0r2⊥

:(−1ε

)SWW(x⊥, y⊥)Pg/g ⊗ xg(x)

Subtraction of the UV-divergence: (αs/π)Ncβ0(−1/εUV + ln(Q2/µ2)

).

(Color charge renormalization)33 / 38


Some Technical Details

Typical diagrams (5 different types in total): Q2 = M2H

Real diagrams⇒

+αs

πNc

[1ε2 −

1ε

lnQ2

µ2 +12

(ln

Q2

µ2

)2

− 12

(ln

c20

Q2r2⊥

)2

− π2

12

].

Virtual graphs⇒

αs

πNc

[− 1ε2 +

1ε

lnQ2

µ2 −12

ln2 Q2

µ2 +π2

2+π2

12+ β0 ln

Q2

µ2

]

34 / 38


Sudakov factor

For pA→ H(Q, k⊥) + X: Ssud(Q2, r2⊥) = αsNc

π

[12 ln2 Q2r2

⊥c2 − β0 ln Q2r2

⊥c2

]

dσ(resum)

dyd2k⊥|k⊥�Q = σ0

∫d2x⊥d2x′⊥

(2π)2 eik⊥·r⊥e−Ssud(Q2,r2⊥)SWW

Y=ln 1/xg (x⊥, x′⊥)

×xgp(x, µ2 = c20/r2⊥)

[1 +

αs

π

π2

2Nc

].

Mismatch between rapidity and collinear divergence between graphs⇒ Ssud(Q2, r2⊥).

Higher loop calculation⇒ exponentiation of Ssud(Q2, r2⊥).

35 / 38


Sudakov factor for dijet productions in pA collisions and DIS

Consider the dijet productions in pA collisions: [A. H. Mueller, BX, F. Yuan, in preparation.]

k⊥

k⊥ − P⊥

P⊥

P⊥ ≫ k⊥

Cqq = Nc

2 Cq! = Nc

2 + CF

2 Cg!qq = Nc

Comments:

Two scale problem : Q21 = M2

H and Q22 ' k2

⊥

Q21 � Q2

2 ⇒αsC2π

ln2 Q21

Q22

For back-to-back dijet processes, replace M2H(Q2

1) by M2J ∼ P2

⊥.

What is different for different channels are just the color factor C.

Empirical formula for C: C =∑

iCi2 , where Ci is the color factor of the incoming particles.

Ci = CF for incoming quarks, Ci = Nc for gluons.

Obtain complete agreement with the collinear factorization calculation.

Competition between Sudakov and Saturation suppressions.36 / 38

Conclusion

1 Introduction




5 Conclusion

37 / 38

Conclusion

Conclusion

总结:

NLO inclusive forward hadron productions in pA collisions at LHC. (More precise)

Two fundamental gluon distributions. 绝代双“胶”

DIS dijet provides direct information of the WW gluon distributions.

Important study at EIC and LHeC.

One-loop Calculation for dijet processes (Sudakov Factors)⇒ The quest for more precisetest of the saturation phenomena. [A. H. Mueller, BX, F. Yuan, in preparation.]

A lot of interesting physics especially in the era of LHC and future EIC.

38 / 38

physics in pa collisions - ustcpnp.ustc.edu.cn/groupnew/xueshuhuodong/document/... · physics in pa...

Documents