Low Q^2 Jet Production at HERA in Next-to-Leading Order QCD

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DESY 98–046ISSN 0418–9833hep–ph/9804352April 1998Low Q 2Jet Production at HERA in Next-to-Leading Order QCD G.Kramer,B.P¨o tter II.Institut f¨u r Theoretische Physik ?,Universit¨a t Hamburg Luruper Chaussee 149,D-22761Hamburg,Germany e-mail:kramer@mail.desy.de,poetter@mail.desy.de Abstract We present next-to-leading order calculations of one-and two-jet production in eP collisions at HERA for photon virtualities in the range 1

have equal transverse momenta.

1Introduction

Recently jet production in electron-proton scattering in the transition region between photoproduction and deep-inelastic scattering(DIS)has received very much attention both from the experimental[1,2,3]and the theoretical[4,5,6,7]side.

In the photoproduction of jets,i.e.,in eP collisions at HERA for photon virtualities in the region0～

This approach can easily be extended to the case of jet production in eP collisions with a?xed Q2=0,as long as Q2is small enough compared to the hard scattering scale μ2[4,5,6,7].For this case the parton distributions of the photon depend on x and the scaleμ2,as in real photoproduction(Q2=0),and in addition on the virtuality Q2. Several models exist for describing theμ2evolution of these parton distribution functions (PDF’s)with changing Q2[4,8,9],but very little data from deep-inelastic eγ?scattering with photonsγ?of virtuality Q2=0[10]exist,where they could be tested.Experimental data from jet production in the region Q2?μ2～E2T could help to gain information on the Q2evolution of these photon structure functions.Parton densities of the virtual photon are suppressed[4,9,11]with increasing Q2and are,in the usual LO de?nition, assumed to vanish like ln(μ2/Q2)for Q2→μ2,so that in the region Q2～μ2the direct process dominates.Therefore,in the LO framework,it depends very much on the choice of scaleμ2in relation to E2T,whether a resolved contribution is present in the region Q2≥E2T.This has been observed recently in a study of the dijet rate in DIS in the region5E2T. Of course,for a smaller scaleμ2,as for exampleμ2=E2T,the resolved contribution was in fact small for the region Q2≥E2T,as to be expected.In this approach the resolved contribution may be considered as a NLO correction to the direct cross section, which is evaluated in the leading-logarithm approximation.This interpretation of the H1measurements is not very satisfactory for the following reasons.First the sum of the LO direct and resolved cross section su?ers from an appreciable scale dependence.

Second in the region Q2≥E2T power like terms∝(Q2/E2T)n are more important than the logarithmic ones∝ln(μ2/Q2)which are summed by using the parton PDF’s of the virtual photon.To account correctly for the power behaved terms one must include the complete NLO corrections to the leading(inαs)direct-photon contributions.So,if one wishes to cover the whole range from Q2?E2T to Q2>E2T,one must still include the resolved contribution(i.e.those involving the PDF’s of the virtual photon),however,in such a way that these are matched with the NLO direct photon contributions by subtracting from the latter those terms which are already included through the PDF’s of the virtual photon.Such a subtraction has been worked out in our earlier work with M.Klasen[7] by separating the collinear photon initial state singularities from the NLO corrections to the direct cross section.There we studied inclusive one-and two-jet production with virtual photons in the region Q2?E2T by transforming to the HERA laboratory system. In this system the results were compared to the photoproduction cross sections and the unsubtracted direct-photon cross section up to NLO.The dependence of the cross section on Q2had been investigated for some cases up to Q2=9GeV2(please note that in[7] we used P2for the variable Q2).We found that with increasing Q2the sum of the NLO resolved and the NLO direct cross section,in which the terms already contained in the resolved part were subtracted,approached the unsubtracted direct photon cross section. However,some di?erence remained even at the highest studied Q2.

In this paper we want to extend this work in several directions.First we calculate the two cross sections,the resolved and the subtracted direct cross section over a larger range of Q2,namely1≤Q2≤100GeV2,including NLO corrections for both cross sections.We compare this cross section with the unsubtracted direct cross section as a function of Q2. Following essentially the analysis of the dijet rate of the H1collaboration[12]we divide the Q2range into seven subsequent Q2intervals which we specify later.In the intervals with the larger Q2the longitudinal cross section is not negligible anymore.Therefore this cross section had to be included in the subtracted direct as well as in the unsubtracted direct cross section.Second we present our results in the photon-proton center-of-mass system as was used in the analysis of the experimental data[3,12].For this purpose we had to calculate the resolved cross section,usually given in the HERA laboratory system also in the virtual photon-proton center-of-mass system.

We have calculated various inclusive one-jet cross sections either as a function of the rapidityηintegrated over E T>E T min or as a function of E T integrated over the whole accessibleηrange.The dijet rate needs some extra discussion,since experimentally this rate is de?ned with cuts on the transverse energies of both jets.In addition to the two-jet rate,which we have calculated,applying all the experimental cuts on various kinematical variables,we have computed also the usual inclusive dijet cross section as a function of E T with the rapiditiesη1andη2of the two-jets integrated out.

The outline of our work is as follows.In section2we describe how the direct,the subtracted direct and the resolved cross section are calculated.Furthermore we describe the input PDF’s of the proton and the photon.The results for the inclusive single-jet, inclusive dijet and the two-jet rate are presented in section3.Here we discuss also some of the subtleties concerning the de?nition of the dijet rate and?nally we compare with the

dijet data from H1[12].Section4contains a summary and an outlook to future studies in the transition region between photoproduction and the deep inelastic collision region. 2Inclusive Single-and Dijet Cross Sections

2.1General Structure of Cross Sections

In order to de?ne the general structure of the cross sections,which we want to calculate, we write for the inclusive production of two jets in electron-proton scattering

e(k)+P(p)→e(k′)+jet1(E T

1,η1)+jet2(E T

2

,η2)+X(1)

Here,k and p are the momenta of the incoming electron and proton,respectively.k′is the momentum of the outgoing electron.The two jets in the?nal state are characterized

by their transverse momenta E T

i and rapiditiesηi,which are the observables also in the

experiment.The four-momentum transfer of the electron is q=k?k′and Q2=?q2. The phase space of the electron is parametrized by the invariants y=pq/pk and Q2.In

the case of very small virtualities Q2?q20,where q0is the energy of the virtual photon,y gives the momentum fraction of the initial electron energy k0,carried away by the virtual

photon and y=q0/k0.However,in this work we do not use this approximation,since we will consider also the range of larger Q2.The total energy in the eP center-of-mass system is

√

4S H x b

4πα

16π2dφ

Q2

(5)

Hereφis the azimuthal angle of the outgoing electron,which we integrate out with the

result dφ

2y2H g+

4(1?y)+1+(1?y)2

(S H y)2

pμpνHμνgives the contribution propor-

tional to the cross section for longitudinal polarized virtual photons.With H g and H L we de?ne the corresponding cross sections for the scattering of unpolarized transversal and longitudinal polarized virtual photons on the parton b:

dσUγb=1

4x b S H y

H U d PS(n)(7)

dσLγb=

1

σeb=α

y

dσUγb+

2(1?y)

Q2

(9)

In the limit Q2→0one obtains the familiar formula for the absorption of photons with small virtuality,where dσLγb is neglected and the transversely unpolarized cross section dσUγb is multiplied with the di?erential Weizs¨a cker-Williams spectrum[13]

d fγ/e

2π

1+(1?y)2

σH(S H) can be written as a convolution of the hard scattering cross section dσab for the reaction

a+b→jet1+jet2+X with the PDF’s of the photon f U,L

a/γ(x a)and the proton f b/P(x b)in

the following form

dσH(S H)

2πQ2 1+(1?y)2y f L a/γ(x a)dσab (11)

Of course,for the direct photon interaction f U,L

a/γdσab=δ(1?x a)dσU,L

γb

.

The phase space factor in(7)and(8)depends on the number of particles in the?nal states.In our case we have either two or three jets in the?nal state.For describing the?nal state in terms of the relevant variables we adopt the center-of-mass system of the virtual photon and the proton.In the case of two jets in the?nal state,we express the respective four-momenta p1and p2by their rapiditiesη1andη2and their transverse

energies E T

1=E T

2

=E T in the center-of-mass system:

p1=E T(coshη1,1,0,sinhη1),

p2=E T(coshη2,?1,0,sinhη2).(12)

From energy-momentum conservation we obtain in the case of direct production(x a=1)

W=E T(e?η1+e?η2),(13)

y=

W2+Q2

W2+Q2

E T(sinhη1+sinhη2).(15) Here,the rapidities are de?ned with respect to the proton momentum direction as positive z direction.The phase space d PS(2)together with dydx b can be expressed either by E T,

η1and y

d PS(2)dydx b=1

W2+Q2

1

W2+Q2 Q2W?E T e?η1 (17)

or by E T,η1andη2

d PS(2)dydx b=1

W2+Q2

dη1dη2E T dE T(18)

In this case x b is given by the formula(15).The phase space with three partons or jets in the?nal state is more complicated and will not be written down.

As is well known the higher order(inαs)contributions to the direct and resolved cross sections have infrared and collinear singularities.To cancel them we use the familiar techniques.The singularities in the virtual and real contributions are regularized by

going to d dimensions.In the real contributions the singular regions are separated with the phase-space slicing method based on invariant mass slicing.This way,we have for both,the direct and the resolved cross section,a set of two-body contributions and a set of three-body contributions.Each set is completely?nite,as all singularities have been canceled or absorbed into PDF’s.Each part depends separately on the phase-space slicing parameter y s.The analytic calculations are valid only for very small y s,since terms O(y s) have been neglected in the analytic integrations.For very small y s,the two separate pieces have no physical meaning.The y s is just a technical parameter which must be chosen su?ciently small and serves the purpose to distinguish the phase space regions,where the integrations are done analytically,from those,where they are performed numerically. The?nal result must be independent of the parameter y s.In the real corrections for the direct cross section there are?nal state singularities and contributions from parton initial state singularities(from the proton side).They have been calculated by Graudenz[14] in connection with NLO corrections for jet production in deep-inelastic eP scattering. Since he used the same phase-space slicing method they can be taken over together with the virtual corrections up to O(αα2s).To these results,which were given only for the H g matrix element,we added the NLO contributions to H L,so that together with the LO contributions we have both cross sections dσUγb and dσLγb in(9)available up to NLO.This describes the calculation of the full cross section,which is valid for general Q2.

The resulting NLO corrections to the direct process become singular in the limit Q2→0,i.e.direct production with real photons.For Q2=0these photon initial state singularities are usually also evaluated with the dimensional regularization method.Then the singular contributions appear as poles in?=(4?d)/2multiplied with the splitting

function P q

i←γ[15].These singular contributions are absorbed into PDF’s f a/γ(x a)of the

real photon.For Q2=0the corresponding contributions appear as terms ln(s/Q2),√

MS factorization in the real photon case.Of course,this has

consequences concerning the selection of the PDF of the virtual photon.The details for this subtraction of the initial state singularities can be found in[7].The cross section with these subtractions in the NLO corrections to the direct process will be denoted the subtracted direct cross section.It is clear that this cross section alone has no physical meaning.Only with the resolved cross section added it can be compared with experimental data.

In the general formula(9)for the deep-inelastic scattering cross section,we have two contributions,the transverse(dσUγb)and the longitudinal part(dσLγb).Since only the transverse part has the initial-state collinear singularity we have performed the subtraction only in the matrix element H g which contributes to dσUγb.Therefore we do not need f L

a/γin(11).It is also well known that dσLγb vanishes for Q2→0.The calculation of the resolved cross section including NLO corrections proceeds as for real photoproduction at Q2=0[16],except that the cross section is calculated also for?nal state variables in the virtual photon-proton center-of-mass system.The kinematic relation between initial and ?nal state variables are similar to those for direct production except that x a=1and an additional integration over x a in(11)has to be performed.

2.2Jet De?nition

The invariant mass resolution introduced in the last subsection is not suitable to distin-guish two and three jets in the?nal state.With the enforced small values for y s the two-jet cross section would be negative in NLO,i.e.unphysical.Therefore we must choose a jet de?nition that enables us to de?ne much broader jets.We do this in accordance with the jet de?nition in the experimental analysis and choose the jet de?nition of the Snowmass meeting[17].According to this de?nition,two partons i and j are recombined if for both partons i and j the condition R i,J

2.3Numerical Input

For the computation of the direct and resolved components in the one-and two-jet cross

sections we need the PDF’s of the proton f b/P(x b)and of the photon f U

a/γ(x a)in(11)at

the respective factorization scales M P and Mγ.Since we perform the subtraction only

in the transversal part of the NLO direct contribution,we only use f U

a/γand set f L aγ=0

in(11).For the proton PDF’s we have chosen the CTEQ4M version[18],which is a

NLO parametrization with

MS =204MeV.We include N f=5

?avours.TheΛvalue of the proton PDF is also used to calculateαs from the two-loop formula at the scaleμ.The factorization scales are put equal to the renormalization scaleμ(Mγ=M P=μ),whereμwill be speci?ed later.For f a/γ,the PDF of the virtual photon(we skip the upper index U in the following),we have chosen one of the parametrizations of Sj¨o strand and Schuler[9].These sets are given in parametrized form for all scales Mγ,so that they can be applied without repeating the computation of the evolution.Unfortunately,these sets are given only in LO,i.e.the boundary conditions for Q2=M2γand the evolution equations are in LO.In[8]PDF’s for virtual photons have been constructed in LO and NLO.However,parametrizations of the Mγevolution have not been worked out.Second,these PDF’s are only for N f=3?avours,so that the charm and bottom contributions must be added as an extra contribution,which is inconvenient for us.Therefore we have selected a SaS version which includes charm and bottom as massless?avours.As explained in the previous section,we de?ne the subtraction of the collinear singularities for the NLO direct cross section in the

MS factorization.In[9]such PDF’s in the

MS type PDF’s of the photon the authors of[9]have presented both types of PDF’s.Unfortunately,the

MS subtraction as we have used it in[7].Therefore we start with the SaS1D parametrization in[9], which is of the DIS type with no?nite term in Fγ2(x,M2γ)and transform it with the well-known formulas to the usual

MS

=200MeV has been adopted.In addition to the distinction DIS versus

starting scale Q0,which is Q0=600MeV for the u,d,s quarks and the gluon and related

to the c and b quark masses,respectively.

2.4Numerical Tests

The separation of the two-body and three-body contributions with the slicing parameter y s is a purely technical device als already mentioned in section2.1.The sum of the two-

and three-body contributions for physical cross sections must be independent of y s.The parameter has to be quite small to guarantee that the approximations in the analytical

calculations are valid.Typically,y s=10?3,forcing the two-body contributions to become

negative,whereas the three-body cross sections are large and positive.We have already checked in connection with our earlier work[7]that by varying y s between10?4and

10?3the superimposed two-and three-body contributions are independent of y s for the

inclusive single-and dijet cross sections.Furthermore,we have explicitly checked that the direct one-and two-jet cross sections for virtual photons are in perfect agreement with

the ones from real photoproduction given in[15,16]by integrating the virtuality over the region of small Q2with Q2min≤Q2≤4GeV2.In this case the main contribution to the cross section comes from the lower integration boundary,where the dependence

of the matrix elements on Q2is small.The NLO calculations are implemented in the computer program JETVIP[20].Several other programs for calculating jet cross sections

in deep-inelastic eP scattering are available,although without considering the resolved

photon component.The eP→n jets event generator MEPJET[21]is also based on the phase-space slicing method.Two other NLO programs DISENT[22]and DISASTER [23]use the subtraction method.To check our cross sections away from Q2?0,we have compared JETVIP with results obtained with DISENT and found the programs to agree within5%for all Q2considered in this work.

3Results

In this section we shall present our numerical results in the form that we show?rst the full direct cross section including the transversal and the longitudinal part.Second,we have calculated the subtracted direct cross section and the resolved cross section which we superimpose to give the cross section which we compare with the full direct cross section. These results are presented and discussed in the following subsections for three cases,the inclusive one-jet cross section,the inclusive two-jet cross section and the exclusive two-jet rate with three separate versions of E T cuts.The exclusive two-jet rates will be compared with recent H1data[12].For the comparison with these data we have considered the Q2bins as shown in Tab.1.In the experimental analysis only the bins II to VII are considered.We have added the bin I in order to have results for cross sections of rather small virtuality,where the resolved part is more important than for all other bins.The bins chosen for the two-jet analysis of H1involve some further cuts on the scattering angle and the energy of the electron in the?nal state.These are taken into account in

Table1:The seven subsequent bins of photon virtuality,Q2,considered in this work.

Bin number II IV VI Q2-range in GeV2[5,11][15,20][30,50]

= dE T d2σ1jet

dη

d σ1j

e t /d η [n b ](a) Q 2=[1,5] GeV 20

1

234

5

6

-3-2.5-2-1.5-1-0.50DIR RES-NLO DIRS RES-LO SUM (b) Q 2=[5,11] GeV 200.51

1.5

22.53-3-2.5-2-1.5-1-0.50ηd σ1j e t /d η [n b ](c) Q 2=[20,30] GeV 200.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-3-2.5-2-1.5-1-0.50η(d) Q 2=[50,100] GeV 200.10.20.30.40.50.60.70.80.91-3-2.5-2-1.5-1-0.50

Figure 1:Inclusive single-jet cross section dσ1jet /dηintegrated over E T >5GeV as a function of η.In (a):1

section obtained from the sum of DIRS and the NLO resolved cross section.Near the maximum of the cross sections they di?er by approximately 25%in bin I and by 20%in the other bins.This means,at the respective Q 2characterizing these bins,the summed cross section is always larger than the pure direct cross section.This di?erence originates essentially from the NLO corrections to the resolved cross section,as is obvious when we add the LO resolved curve to the DIRS contribution in Figs.1a,b,c and d.If we study this in more detail,we see that the sum of the LO resolved (lower full curve)and the subtracted direct cross section is somewhat below the DIR curve for η?2in case of bin I,below the DIR curve for all η<0in bin II,only slightly below the DIR curve in bin V and above the DIR curve for η?1in bin VII.In the largest Q 2bin the di?erence is approximately 5%near the maximum of the two curves.Near η??3the di?erence is larger since the LO resolved cross section

d σ1j

e t /d η [n b ](a) Q 2=[1,5] GeV 20

1

234

5

6

-3-2.5-2-1.5-1-0.50σD =σL +σT σL σT (b) Q 2=[5,11] GeV 200.51

1.5

22.53-3-2.5-2-1.5-1-0.50ηd σ1j e t /d η [n b ](c) Q 2=[20,30] GeV 200.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-3-2.5-2-1.5-1-0.50η(d) Q 2=[50,100] GeV 200.10.20.30.40.50.60.70.80.91-3-2.5-2-1.5-1-0.5

Figure 2:Transverse and longitudinal parts of the direct part of the direct inclusive single-jet cross section dσ1jet /dηintegrated over E T >5GeV as a function of η,for the Q 2bins (a)–(d)as in Fig.1.σT (dotted),σL (dashed),σT +σL (full).

increases stronger towards smaller η’s than the DIRS cross section decreases.So,up to a few percent the full DIR cross section and the LO resolved plus subtracted direct cross section section are equal.This means that the term subtracted in the direct cross section is replaced to a very large extent by the LO resolved cross section.Di?erences between these two stem from the evolution of the subtraction term to the scale μ=

MS subtraction scheme,which is the case in our analysis.Another

reason for the agreement of the NLO DIR with the sum of the subtracted direct and the LO resolved cross sections is that all contributions are of the same order in αs ,i.e.of

d σ1j

e t

/d E T [n b /G e V ](a) Q 2=[1,5] GeV 210

-210-1110

46810121416DIR RES DIRS SUM (b) Q 2=[5,11] GeV 210-210

-1

11046810121416d σ1j e t

/d E T [n b /G e V ]E T (c) Q 2=[20,30] GeV 210-3

10-210-11

46810121416E T (d) Q 2=[50,100] GeV 210-310-2

10-1

146810121416

Figure 3:Inclusive single-jet cross section dσ1jet /dE T integrated over ηas a function of the transverse momentum E T ,for the Q 2bins (a)–(d)and labeling of curves as in Fig.1.

O (αα2s ).This also explains that the inclusion of the NLO corrections to the resolved cross section brings in additional terms and that the sum of DIRS and the NLO resolved part lies above the pure direct cross section.We conclude that except for the lowest two Q 2bins,the NLO direct cross section gives the same results as SUM,if we restrict ourselves to the LO contributions of the resolved cross section.

We mentioned already that in the medium Q 2range the longitudinal cross section is not negligible.To see this more explicitly we have calculated the two contributions present in (9)separately.First we write analogous to (7)and (8)dσU γb =(dσg γb +dσL γb )/2,where dσg γb only contains the contribution of H g =?g μνH μνto dσU γb .By substituting this decomposition into (9)we have calculated ?rst the cross section d

d.Here we have selected the same bins as in Fig.1,namely bin I,II,V and VII.In these ?gures we also showσD=σT+σL,which must agree with the DIR cross section in Fig. 1a,b,c and d.We see thatσL is small compared toσT in the?rst two bins,but still non-negligibl

e.With increasing Q2the cross sectionσL increases and it is comparable to σT near the maximum of the cross section in bin V.In the last binσL even dominates overσT belowη=?1.5.This shows that the longitudinal partσL must be taken into account for Q2>1GeV2.We emphasize that theσL plotted in Fig.2includes the NLO corrections.In our earlier work[7]we have considered onlyσT,which is justi?ed in the region Q2<1GeV2.We observe in Fig.2a,b,c and d,thatσT andσL have a di?erent behaviour as a function ofη.σT is?atter,i.e.σL decreases much faster towardsη=0.

Next we considered the di?erent components to the E T distribution

dσ1jet

dE T dη

(21)

of the inclusive one-jet cross section.Here we integrated over the kinematically allowed ηrange.The results of this cross section for the bins I,II,V and VII are shown in Fig. 3a,b,c and d.The four cross sections DIR,DIRS,NLO resolved cross section(RES) and the sum of DIRS and the resolved cross section(SUM)are plotted.We observe in these?gures a similar pattern as in theηdistributions in Fig.1a,b,c and d.The cross section SUM is always larger than the NLO direct cross section DIR in all seven bins.The di?erence is approximately30%and originates from the NLO corrections to the resolved cross section.The relation of the resolved cross section to the subtracted direct cross section DIRS changes drastically with increasing Q2.Whereas in the?rst bin(Fig.3a) the NLO resolved cross section is much larger than the DIRS cross section(this is similar as in photoproduction where Q2=0),the resolved cross section is smaller than DIRS in bin VII,in particular at larger E T.But at this larger Q2bin the resolved cross section is still essential and can not be neglected,compared to DIRS.

3.2Inclusive Two-Jet Cross Sections

We now present results for the inclusive dijet cross section.The di?erential cross section d3σ/dE T dη1dη2yields the maximum of information possible on the parton distributions and is better suited to constrain them than with measurements of inclusive single jets. Since dijet production is a more exclusive process than one-jet production,the cross sections are smaller.

The selection of the variables E T,η1,η2is as for the dijet cross section in photoproduc-tion,except that we work now in the virtual photon-proton center-of-mass system and not in the HERA laboratory system as in our previous work[7].The variable E T is de?ned to be the transverse energy of the measured(or trigger)jet,which has rapidityη1.The second rapidityη2is associated with the second jet such that in the three-jet sample these

two measured jets have the largest E T,i.e.E T

1,E T

2

>E T

3

.A subtlety arises since at

leading order the transverse energies of the two observed jets balance(E T

1=E T

2

=E T).

In the three-parton events present at next-to-leading order this equality is approached in

d σ2j

e t

/d E T [n b /G e V ](a) Q 2=[1,5] GeV 210

-210-1110

6810121416DIR RES DIRS SUM (b) Q 2=[5,11] GeV 210-310-2

10

-116810121416d σ2j e t

/d E T [n b /G e V ]E T (c) Q 2=[20,30] GeV 210-3

10-210-11

681012

1416E T (d) Q 2=[50,100] GeV 210-310-2

10-1

16810121416

Figure 4(a)-(d):Inclusive dijet cross section dσ2jet /dE T integrated over the kinematically possible η1?and η2?range as a function of the transverse momentum E T ,for the Q 2bins (a)–(d)and labeling of curves as in Fig.1.RES is NLO resolved.

events containing two large E T jets while the third jet has E T 3=0.To obtain an infrared

safe cross section the E T of the third jet must vary away from E T 3=0.Therefore the

region E T 1=E T 2can not be ?xed and the trigger E T assigned above can not be de?ned as the jet with the largest E T .We shall come back to this point when we consider the dijet rate as measured by H1[12].Similar to the inclusive single-jet cross section we could predict distributions in η1and η2for ?xed E T or distributions in E T for various values or intervals of the two rapidities η1and η2in the same way as was done for Q 2=0[15,16].Since such detailed information is not expected from experiment in the near future we calculated only the distribution with the two rapidities η1and η2integrated over the kinematically allowed region.Concerning the variation with Q 2we have done the computation again for the seven Q 2bins de?ned at the beginning of this section,but we present results only for the bins I,II,V and VII.These dijet cross sections dσ/dE T for the four Q 2bins are plotted in Fig.4a,b,c and d.We show again the full direct cross section (DIR),the NLO resolved cross section (RES),

the subtracted direct cross section(DIRS)and the sum of the latter two(SUM).The pattern of these cross sections as a function of E T is similar as we have obtained it in

Fig.3a,b,c and d for the one-jet cross section.The sum of NLO resolved and DIRS is always larger than the DIR cross section.The di?erence is again approximately30% almost independent of Q2and E T.We remark that all the components which we plotted

have the same dependence and di?er only in the normalization.Furthermore,similar as for the one-jet cross sections shown in Fig.3a,b,c and d the cross section SUM is dominated by the NLO resolved cross section in the?rst Q2bin(see Fig.4a)whereas

the NLO resolved component and the DIRS component contribute almost equally in the last Q2bin.We emphasize that the sum of NLO resolved and DIRS cross section is still

larger than the DIR cross section even in the highest Q2bin.Of course,this di?erence should gradually diminish with larger Q2,since thenμ2/Q2→1and the PDF of the virtual photon approaches zero.For the Q2bins considered here the di?erence with the

DIR prediction is a NLO e?ect,as we have checked explicitly.This has some bearing on the determination of the strong coupling constantαs from the inclusive single-and dijet

cross sections in the Q2range considered in this work.

3.3Dijet Rate and Comparison with H1Data

In[3]preliminary data for the dijet rate R2as a function of Q2have been reported.R2

measures the cross section for two-jet production normalized to the total eP scattering cross section in the respective Q2bin.The data were obtained in the bins II to VII by requiring for both jets E T>5GeV in the hadronic center-of-mass frame with the additional constraints y>0.05,k′0>11GeV(k′0is the?nal state electron energy), 156?<θe<173?and integrated overη1andη2with?η=|η1?η2|

subsection the experimental cuts E T

1,E T

2≥5GeV are problematic from the theoretical

viewpoint since the so de?ned cross section is infrared sensitive.With this same cut on the transverse energy of both jets there remains no transverse energy of the third jet,so that there is very little or no contribution from the three-body processes.Through the phase space slicing,needed to cancel infrared and collinear singularities in NLO,3-body processes are always included inside the cuto?y s,which,however,are counted in the

E T

1=E T

2

contribution.For these contributions the y s cut acts as a physical cut.In

order to avoid this sensitivity on y s one needs constraints on E T

1,E T

2

or E T

3

which avoids

the problematic region E T

1=E T

2

.This problem was encountered already two years ago in

the calculation of the inclusive two-jet cross section in photon-proton collisions[25].The comparison with data from ZEUS required the handling of a lower E T cut on both jets in the HERA laboratory system.To avoid the cuto?(y s)dependence it was suggested in

[25]to arrange the two-and three-jet contributions in such a way that contributions with

E T

3<1GeV are included in the two-jet cross section and the contribution with E T

3

>1

GeV in the three-jet cross section.With this additional constraint on the three-jet part

one can demand E T

1,E T

2

>5GeV.Unfortunately the constraint on E T

3

is very di?cult

to realize experimentally,because transverse energies of such low value for E T

3

can not be measured with su?cient accuracy.Furthermore,it is clear that in the experimental

analysis the constraint E T

1,E T

2

>5GeV is satis?ed only inside some measurement errors

on the transverse energies,which are not very well known,so that the constraints on E T

1 and E T

2

are not https://www.doczj.com/doc/142885056.html,st,uncontrolled hadronization e?ects produce shifts between the measured jet energies and the jet energies de?ned in our NLO analysis.

Another possibility to remove the infrared sensitivity is to require di?erent lower limits

on E T

1and E T

2

,as for example,E T

1

>7GeV,E T

2

>5GeV,if E T

1

>E T

2

or E T

1

and E T

2

interchanged if E T

2>E T

1

.This possibility was also considered in[25]in connection with

the photoproduction of two jets.Then,the third jet can have enough transverse energy to avoid the infrared sensitivity.Of course,the size of the dijet cross section depends on

the way the cuts on E T

1and E T

2

are introduced.Therefore,it is important,that the same

cuts are applied in the theoretical calculation and in the experimental analysis.

In the following we shall consider three possibilities for de?ning the two-jet rate R2:

(i)?mode:E T

1,E T

2

>5GeV,and if E T

1

>E T

2

(E T

2

>E T

1

)then E T

1

>7GeV

(E T

2

>7GeV)

(ii)Σmode:E T

1,E T

2

>5GeV together with E T

1

+E T

2

>13GeV

(iii)E T

3mode:E T

1

,E T

2

>5GeV with the additional cut on E T

3

,so that contributions

with E T

3

<1GeV are included in the two-jet cross section

The modes?andΣhave been applied also in the measurements of R2[12],so that for these two modes our results can be compared directly to the data.We give results also for the E T

3

mode,so one can see the di?erences resulting from the constraints on the R2 rate.The?mode has been considered also recently in connection with inclusive two-jet photoproduction in the HERA system[26].It is clear that the theoretical problems with the E T cut on both jets appear equally in connection with NLO corrections to the direct as well as to the resolved cross section.

We start with the?mode.In Fig.5a we compare results for the direct cross section in LO(DIR-LO)and NLO(DIR-NLO)for three di?erent scalesμ=M/2,M,2M where M=

R 2Q 2

00.01

0.02

0.03

0.04

0.050.06

0.07

0.08

10102Q 2

00.010.020.030.040.050.060.070.0810102

Figure 5:Dijet rate R 2=σ2jet /σtot with E T min =5GeV for the ?mode compared to

H1-data.(a)The full line corresponds to the NLO deep-inelastic dijet rate (DIR-NLO),the dashed curve gives the LO deep-inelastic dijet rate (DIR-LO).The dotted lines show the scale variation for the NLO direct,where the upper dotted curve corresponds to the smaller scale.(b)The dash-dotted curve gives the NLO direct (DIR-NLO),the dashed is NLO resolved (RES-NLO),the dotted is NLO DIRS and the full is SUM.

bins.In addition,we show the contribution of the two components (DIRS and RES-NLO)in the sum separately,similar as we have done it in the previous two subsections.In the ?rst Q 2bin,DIRS and the NLO resolved cross section are almost equal,the cross section in the largest Q 2bin is dominated by DIRS.In this bin the unsubtracted direct cross section DIR is almost equal to the sum of DIRS and NLO resolved.In the ?rst Q 2bin this cross section is 50%larger than the NLO direct cross section.We also compare with the H1data [12].In the smaller Q 2bins the sum of DIRS and NLO resolved agrees better with the experimental data than the DIR cross section.In the two largest Q 2bins the di?erence of the cross sections DIR and SUM is small and it can not be decided which of these cross sections agrees better with the data due to the experimental errors.This is in contrast to the 30%di?erence between the DIR and SUM found for the inclusive single-and dijet cross sections which we attributed to the NLO corrections of the resolved contributions.This di?erence is reduced in the dijet rate R 2due to the speci?c cuts on the transverse energies of the two jets in the de?nition of the dijet rate.These cuts suppress the resolved component stronger than the direct one,which leads to the observed behaviour of the dijet rate at the large Q 2bins.We emphasize that the theoretical cross sections are calculated on parton level whereas the experimental two-jet rate is based on hadron jets.Corrections due to hadronization e?ects are estimated to be typically around 5%and at most 20%[12].The experimental errors for R 2consist of the combination of statistical and bin-by-bin systematic errors.An additional overall 10%systematic error connected with hadron-energy measurements is not shown and can be seen in [12].

The corresponding results in the Σmode are plotted in Fig.6a and b.In Fig.6b

R 2Q 2

00.01

0.02

0.03

0.04

0.050.06

0.07

0.08

10102Q 2

00.010.020.030.040.050.060.070.0810102

Figure 6:Dijet rate R 2=σ2jet /σtot with E T,min =5

GeV for the Σmode compared to H1-data.The curves in a and b are labeled as in Fig.5.

R 2Q 20

0.02

0.04

0.06

0.080.1

0.12

0.14

10102

Figure 7:Dijet rate R 2=σ2jet /σtot with E T,min =5GeV for the E T 3mode compared to

H1-data.The curves are labeled as in Fig.5b.

we compare with the H1data for R 2obtained in the same mode.We observe that the theoretical results for R 2on one side and the experimental data on the other side are very similar for the two modes.Therefore,most of the remarks made in connection with the ?mode apply as well to the results in the Σmode.

As the third possibility to de?ne the exclusive two-jet rate R 2,we consider the E T 3mode with the cut E T 3<1GeV .Our results for R 2in this mode are plotted in Fig.7,again for the four cross sections,DIR,DIRS,NLO resolved (RES-NLO)and the sum of DIRS and NLO resolved cross section (SUM).One should compare this summed cross section with the direct cross section DIR.They are more or less equal except in the ?rst Q 2bin,where they di?er by approximately 35%.By comparing with the results in Fig.5b and 6b we notice that the R 2in the E T 3mode is larger than in the other two modes.

In the ?rst Q 2bin they di?er almost by a factor of two.This shows that the way how the two-jet rate is de?ned theoretically or experimentally is very important.This problem

暗黑破坏神资料迪克方块

暗黑破坏神资料迪克方块 赫拉迪克方块[Cube] 可以通过完成第II场景任务获得,并且帮助你完成后面的一些任务. 同时它还提供了额外的储物空间和合成装备等新的功能. 赫拉迪克方块在你的物品栏中提供了12 格的空间. 但是它本身只占用2x2 的空间. 当你拣起物品后,可以将它们直接放入Cube ,当物品放入时,会有声音提示.如果你要取出其中的物品,可以鼠标右键点击,然后取出物品.一些物品在Cube 中是可以直接使用的,例如城镇传送之书. 当凯恩鉴定未鉴定物品时,会连同Cube 内的物品一同鉴定,所以当你有想保持未鉴定状态的物品时,请不要放在Cube 内. [ 点击查看大图- 116 KB ] 你不能将一个Cube 放进另一个Cube 中, 如此循环的话...

可以将一些带有抗性的戒指项链等小物品放在Cube 内,当你面对某种元素攻击的头目时,拿出使用可以起到很好的作用. 转换物品 你可以通过Cube 特有的神奇能量来创造出新的物品,将需要符合条件的物品放个入,然后点击转换按钮即可. Cube 可以用来制作合成物品. 转换公式 下面列出了Cube 目前可以使用的转换公式. 英文版资料 3 个相同符文(符文1-9#) = 1 个更高级别符文 3 艾尔-> 1 艾德 3 艾德-> 1 特尔 3 特尔-> 1 那夫 3 那夫-> 1 爱斯 3 爱斯-> 1 伊司 3 伊司-> 1 塔尔 3 塔尔-> 1 拉尔 3 拉尔-> 1 欧特 3 欧特-> 1 书尔

这个规律只能到9#. 3 完美的骷髅+ 1 杰出物品+ 乔丹之石= 给该杰出物品增加1 凹槽 杰出物品只能有一个凹槽. 当它以有凹槽时,你无法增加新的凹槽. 你只能应用在没有凹槽的杰出物品上. 1 完美的骷髅+ 1 杰出物品+ 乔丹之石= 1 同类型更高品质的杰出物品 这个公式可以用来合成更高品质的随机物品. ilvl = int(.66 * clvl) + int(.66 * ilvl). 也就是物品的ilvl 等于66 乘以你的clvl 加上66 乘以ilvl, 物品的ilvl 要取整数. 6 完美的骷髅+ 1 杰出物品= 1 随机新的同类型杰出物品 你不能用这个公式去改变杰出物品的类型. ilvl = int(.4 * clvl) + int(.4 * ilvl) . 这个公式无法作用在占用空间大于3x2 的物品上. 4 治疗药剂(任何类型) + 红宝石(任何类型) + 魔法剑= 吸血属性的魔法剑 你可以通过这个公式获得一把吸血剑. ilvl = 30. 合成的剑始终为"巫妖的" 后缀(4-5% 击中偷取生命) 并且有可能得到好的前缀. 剑的类型不会改变. 例如, 放入双手剑后仍然得到的是有了吸血属性的双手剑.

暗黑破坏神2合成公式

暗黑破坏神2合成公式 合成公式 以下的是当前赫拉迪克方块的所有合成公式 1.09 及 1.10 通用公式 3 同类型的神符 (低于 10 级) = 1 高一级别的神符 3 El Runes -> 1 Eld Rune 3 Eld Runes -> 1 Tir Rune 3 Tir Runes -> 1 Nef Rune 3 Nef Runes -> 1 Eth Rune 3 Eth Runes -> 1 Ith Rune 3 Ith Runes -> 1 Tal Rune 3 Tal Runes -> 1 Ral Rune 3 Ral Runes -> 1 Ort Rune 3 Ort Runes -> 1 Thul Rune 对于高于10 级的神符无效 3 完美骷髅 + 1 亮金装备 + 乔丹之石(Stone of Jordan) = 为此装备打一孔亮金装备最多只能有 2 个孔，你无法为一个已经有孔的装备打孔 1 完美骷髅 + 1 亮金装备 + 乔丹之石(Stone of Jordan) = 随机的此亮金装备(同时提高此装备的等级) 提高装备等级依照公式: final ilvl = int(.66 * clvl) + int(.66 * ilvl) 也就是说，最终的装备等级(final ilvl) 为你的角色等级 (clvl) 乘以 0.66 (取整)，加上装备原来的等级 (ilvl) 乘以 0.66 (同样取整)

6 完美骷髅 + 1 亮金装备 = 1 随机的此亮金装备(同时降低此装备的等级) 你可以用这个公式为亮金装备产生新的属性。final ilvl = int(.4 * clvl) + int(.4 * ilvl) 此公式对大于 3x2 的装备无效 4 生命药剂 (同类型) + 红宝石 (同类型) + 魔法剑 = 有偷取生命属性的魔 法剑你可以用此公式产生有偷取生命属性的魔法剑 ilvl = 30 剑上会一直有 "of the Leech" 后缀 (4-5% Life Stolen Per Hit) 同时也有得到前缀的机会，剑的类型同时也会保留。 3 魔法戒指 = 1 随机的魔法项链 用 3 个不想要的魔法戒指生成一个低等级的魔法项链。ilvl = int(.75 * clvl) 既一个 65 级的角色，ilvl = 48。所有 48 级的词缀都可以获得。+2 所有技能的词缀等级为 90，也就是说无法产生 +2 所有技能的项链 3 魔法项链 = 1 随机的魔法戒指 用 3 个不想要的魔法项链生成一个低等级的魔法戒指。ilvl = int(.75 * clvl) 既一个 65 级的角色，ilvl = 48。所有低于 51 等级的词缀都是可以获得的 3 小回复药剂 = 1 全面回复药剂 3 同类型同等级的宝石(低于完美级) = 1 同类型的高一级宝石 此公式经常用于为宝石升级 2 十字弓弹 = 1 箭矢 2 箭矢 = 1 十字弓弹 1 长矛 + 1 箭矢 = 1 标枪 任何类型/等级的长矛都可以使用 1 斧子 + 1 匕首 = 飞斧

给暗金物品打孔

给暗金物品打孔，一般到第5幕铁匠那完成打孔任务。还有用公式打孔，不是富人别用！ 暗黑版本必须一样 局域网 如果线已经做好在2台电脑上设置下IP 我的电脑→控制面板→网络连接→本地链接→属性→常规里的internet协议（TCP/IP)→使用下面的ip地址→ ip地址192.168.0.1 字码掩码255.255.255.0 其他空出然后确定。 第二台机子如上只不过ip设置为 192.168.0.2 字码掩码255.255.255.0 默认网关192.168.0.1 首选DSN服务器 192.168.0.1 如有更多就是IP192.168.0.3~~~~~192.168.0.255 IP设置好后插入网线，进入游戏→其他多人游戏→tcp/ip游戏其中一人主控游戏，另一人加入游戏，加入时要输入的IP地址就是刚才设置的，如不记得在主机进入游戏后按TAB会在右上角显示IP 输入即可 双绞线如是直接链接2台电脑 2端布线顺序 白绿、绿、白橙、蓝、白蓝、橙、白棕、棕 白橙、橙、白绿、蓝、白蓝、绿、白棕、棕 如是通过路由器 则2端布线顺序一致 白绿、绿、白橙、蓝、白蓝、橙、白棕、棕 白绿、绿、白橙、蓝、白蓝、橙、白棕、棕 或白橙、橙、白绿、蓝、白蓝、绿、白棕、棕 白橙、橙、白绿、蓝、白蓝、绿、白棕、棕 如果是上战网，正版的话点击BATTLE NET 就可以了盗版的上网上搜下暗黑战网下个注册表就可以了 更简单的就是用QQ对战平台或者浩方

如果你不连英特网是局域网的话，请设置你们的IP，比如你是192.168.25.44另一位192.168.25.45，子网掩码都为255.255.255.0 然后进游戏，点击【其他多人连线】→【TCP/IP游戏】→【主控游戏】然后在选择你要使用的角色，选择难度就可以了。这是主控游戏，支持主机的MOD。 如果你是在局域网跟另一位朋友玩让他进你建的游戏就点【进入游戏】。 进去后点P邀请你朋友跟你组队。 完了。不知道的你追问吧。 装备合成公式 关于一些赫拉迪克方块合成公式(适用于1.10以后版本) 宝石类 三个低级宝石合成出一个更高一级的宝石 宝石级别:裂碎- 裂开- 宝石(钻石) - 无暇的- 完美 符文类 1# - 10#符文都是由三个低级的合成出一个更高一级的符文. 符文11#以上（包括11#）的合成公式: 3 符文10 + 1 碎裂的黄宝石= 符文11 3 符文11 + 1 碎裂的紫宝石= 符文12 3 符文12 + 1 碎裂的蓝宝石= 符文13 3 符文13 + 1 碎裂的红宝石= 符文14 3 符文1 4 + 1 碎裂的绿宝石= 符文15 3 符文15 + 1 碎裂的白宝石= 符文16 3 符文16 + 1 裂开的黄宝石= 符文17 3 符文17 + 1 裂开的紫宝石= 符文18 3 符文18 + 1 裂开的蓝宝石= 符文19 3 符文19 + 1 裂开的红宝石= 符文20 3 符文20 + 1 裂开的绿宝石= 符文21 2 符文21 + 1 裂开的白宝石= 符文22 2 符文22 + 1 普通的黄宝石= 符文23 2 符文32 + 1 无暇的绿宝石= 符文33 物品装备类 3 完美的宝石+ 1 魔法物品= 随机属性魔法物品 6 完美的骷髅+ 1 黄金物品= 低等级黄金物品 1 完美的骷髅+ 1 黄金物品+ 乔丹之石= 高等级金物品 3 完美的骷髅+ 1 黄金物品+ 乔丹之石= 给黄金物品打1个孔 符文07 + 符文10 + 1 完美的黄宝石+ 普通盔甲= 有孔的盔甲 符文08 + 符文11 + 1 完美的紫宝石+ 普通武器= 有孔的武器 符文08 + 符文10 + 1 完美的蓝宝石+ 普通头盔= 有孔的头盔

暗黑2赫拉迪克方块的所有合成公式

转自https://www.doczj.com/doc/142885056.html,/暗黑3战网 D2 赫拉迪克方块－所有合成公式 1.09 及 1.10 通用公式 3 同类型的神符 (低于 10 级) = 1 高一级别的神符 3 El Runes -> 1 Eld Rune 3 Eld Runes -> 1 Tir Rune 3 Tir Runes -> 1 Nef Rune 3 Nef Runes -> 1 Eth Rune 3 Eth Runes -> 1 Ith Rune 3 Ith Runes -> 1 Tal Rune 3 完美骷髅 + 1 亮金装备 + 乔丹之石(Stone of Jordan) = 为此装备打一孔 亮金装备最多只能有 2 个孔，你无法为一个已经有孔的装备打孔 1 完美骷髅 + 1 亮金装备 + 乔丹之石(Stone of Jordan) = 随机的此亮金装备(同时提高此装备的等级) 提高装备等级依照公式: final ilvl = int(.66 * clvl) + int(.66 * ilvl) 也就是说，最终的装备等级(final ilvl) 为你的角色等级 (clvl) 乘以 0.66 (取整)，加上装备原来的等级 (ilvl) 乘以 0.66 (同样取整) 6 完美骷髅 + 1 亮金装备 = 1 随机的此亮金装备(同时降低此装备的等级) 你可以用这个公式为亮金装备产生新的属性。final ilvl = int(.4 * clvl) + int(.4 * ilvl) 此公式对大于 3x2 的装备无效 (此公式可用于洗亮金投缳) 4 生命药剂 (同类型) + 红宝石 (同类型) + 魔法剑 = 有偷取生命属性的魔法剑 你可以用此公式产生有偷取生命属性的魔法剑 ilvl = 30 剑上会一直有 "of the Leech" 后缀(4-5% Life Stolen Per Hit) 同时也有得到前缀的机会，剑的类型同时也会保留。

角色基本术语

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赫拉迪克方块合成公式大全

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关于一些赫拉迪克方块合成公式

关于一些赫拉迪克方块合成公式(适用于1.10以后版本)宝石类 三个低级宝石合成出一个更高一级的宝石 宝石级别:裂碎 - 裂开 - 宝石(钻石) - 无暇的 - 完美 符文类 1# - 10#符文都是由三个低级的合成出一个更高一级的符文. 11符文以上符文的合成公式: 3 符文10 + 1 碎裂的黄宝石 = 符文11 3 符文11 + 1 碎裂的紫宝石 = 符文12 3 符文12 + 1 碎裂的蓝宝石 = 符文13 3 符文13 + 1 碎裂的红宝石 = 符文14 3 符文1 4 + 1 碎裂的绿宝石 = 符文15 3 符文15 + 1 碎裂的白宝石 = 符文16 3 符文16 + 1 裂开的黄宝石 = 符文17 3 符文17 + 1 裂开的紫宝石 = 符文18 3 符文18 + 1 裂开的蓝宝石 = 符文19 3 符文19 + 1 裂开的红宝石 = 符文20 3 符文20 + 1 裂开的绿宝石 = 符文21 2 符文21 + 1 裂开的白宝石 = 符文22 2 符文22 + 1 普通的黄宝石 = 符文2 2 符文32 + 1 无暇的绿宝石 = 符文33 物品装备类 3 完美的宝石 + 1 魔法物品 = 随机属性魔法物品 6 完美的骷髅 + 1 黄金物品 = 低等级黄金物品 1 完美的骷髅 + 1 黄金物品 + 乔丹之石 = 高等级金物品 3 完美的骷髅 + 1 黄金物品 + 乔丹之石 = 给黄金物品打1个孔 符文07 + 符文10 + 1 完美的黄宝石 + 普通盔甲 = 有孔的盔甲 符文08 + 符文11 + 1 完美的紫宝石 + 普通武器 = 有孔的武器 符文08 + 符文10 + 1 完美的蓝宝石 + 普通头盔 = 有孔的头盔 符文07 + 符文11 + 1 完美的红宝石 + 普通盾牌 = 有孔的盾牌 符文09 + 武器 -> 完全修好 符文08 + 盔甲 -> 完全修好 符文15 + 回城卷轴 + 任何镶嵌过的物品 = 未镶嵌宝石的物品 (宝石或神符消失) 6个不同的完美宝石 + 1 项链 = 多彩的(加4抗) 项链 1 戒指 + 1 完美的红宝石 + 1 爆炸药剂 = 深红的戒指(+抗火) 1 戒指 + 1 完美的蓝宝石 + 1 融解药剂 = 深蓝的戒指(+抗冰) 1 戒指 + 1 完美的黄宝石 + 1 耐力药剂 = 珊瑚的戒指(+抗电) 1 戒指 + 1 绿宝石 + 1 解毒药剂 = 碧玉的戒指(+抗毒) 1 斧头 + 1 匕首 = 投掷斧 1 长矛 + 1 箭袋 = 标枪 3 戒指 = 随机属性项链 3 项链 = 随机戒指 1个怀特的脚＋ 1个回城书 = 秘密奶牛关卡 3 生命药剂 + 3魔法药剂 + 1 普通的宝石 = 全面恢复药剂（大紫）

Gczbjc暗黑破坏神赫拉迪克宝盒合成公式

|_ ~ 吾尝终日而思矣，不如须臾之所学也；吾尝而望矣，不如登高之博见也。 －－《荀子·劝学》 合成公式 克莱姆的连枷 + 克莱姆之心 + 克莱姆之眼 + 克莱姆之脑 -> 超级克莱姆连枷1个怀特的脚＋ 1个回城书 -> 通往奶牛关的门 (你必须已经杀死该难度的DIABLO。每个难度一次。注意，如果你把牛都引到入口处并在那里被杀，你就无法再杀进去了。逃跑时应在远离入口的地方用时空门逃跑 ) 3 生命药剂 + 3 魔法药剂 + 1 普通的宝石 -> 全面恢复药剂(大紫) 3 生命药剂 + 3 魔法药剂 + 1 碎裂的宝石 -> 恢复药剂(小紫) 3 小紫 -> 1 大紫 6个不同的完美宝石 + 1 项链 -> 多彩的(加4抗) 项链 1 戒指 + 1 完美的红宝石 + 1 爆炸药剂 -> 深红的戒指 (+抗火) 1 戒指 + 1 完美的蓝宝石 + 1 融解药剂-> 深蓝的戒指 (+抗冰) 1 戒指 + 1 完美的黄宝石 + 1 耐力药剂 -> 珊瑚色的戒指 (+抗电) 1 戒指 + 1 绿宝石 + 1 解毒药剂 -> 碧玉的戒指 (+抗毒) 1任何戒指+1任何绿宝石+4解毒瓶=1绿戒指此公式可制造出加毒防御力的戒指。戒指的毒防御力是随机的。 1任何戒指+1任何红宝石+4爆炸瓶=1红戒指同上，制造防火戒指。 1任何戒指+2任何黄宝石=1珊瑚戒指同上，制造防电戒指。 1任何戒指+2任何蓝宝石+4冷冻瓶=1珊瑚戒指同上，制造防冰戒指。 1 斧头 + 1 匕首 -> 投掷斧 1 长矛 + 1 箭袋 -> 标枪 3 戒指 -> 项链 3 项链 -> 戒指 ================================================================== 魔法武器合成公式,重要. 3 普通宝石 + 1 带孔武器 (任何类型) = 1 带孔魔法武器 (同一类型) 这个公式会随机生成一个新带孔武器，武器类型与原来相同，孔数随机生成，属性也将会改变。最大的作用是把例如一把黑色带孔武器变为蓝色武器。 ------------------------------------------------------------------ 3 无瑕疵宝石 + 1 魔法武器 = 带孔魔法武器 给普通蓝色武器打孔，孔数方面没有具体的说明确定方法，应该是随机生成。属性将会完全改变。. ----------------------------------------------------------------- 1 魔法小盾 + 1 钉头棒 + 2 骷髅 -> 刺盾 四个医疗药水(任何类型)+一个红宝石(任何类型)+蓝色魔法物品类/绿色套装类/亮黄色杰出装备类的剑->一把同样类型的可以吸取生命值的剑 1 钻石 + 1 短剑 + 1 长杖 + 1 腰带 -> 野蛮的长棍 1 窒息药剂 + 1 生命药剂 -> 解毒药剂

暗黑破坏神赫拉迪克方块合成公式 十

暗黑破坏神赫拉迪克方块合成公式十 110合成公式 克莱姆的连枷+ 克莱姆之心+ 克莱姆之眼+ 克莱姆之脑-> 超级克莱姆连枷 1个怀特的脚＋1个回城书-> 通往奶牛关的门 3 生命药剂+ 3 魔法药剂+ 1 普通的宝石-> 全面恢复药剂(大紫) 3 生命药剂+ 3 魔法药剂+ 1 碎裂的宝石-> 恢复药剂(小紫) 3 小紫-> 1 大紫 6个不同的完美宝石+ 1 项链-> 多彩的(加4抗) 项链 1 戒指+ 1 完美的红宝石+ 1 爆炸药剂-> 深红的戒指

(+抗火) 1 戒指+ 1 完美的蓝宝石+ 1 融解药剂-> 深蓝的戒指(+抗冰) 1 戒指+ 1 完美的黄宝石+ 1 耐力药剂-> 珊瑚色的戒指(+抗电) 1 戒指+ 1 绿宝石+ 1 解毒药剂-> 碧玉的戒指(+抗毒) 1 斧头+ 1 匕首-> 投掷斧 1 长矛+ 1 箭袋-> 标枪 3 戒指-> 项链 3 项链-> 戒指 1.10新增的魔法武器合成公式,用于替代3CG公式,重要. 3 普通宝石+ 1 带孔武器(任何类型) = 1 带孔魔法武器

(同一类型) 这个公式会随机生成一个新带孔武器，武器类型与原来相同，孔数随机生成，属性也将会改变。最大的作用是把例如一把黑色带孔武器变为蓝色武器。 3 无瑕疵宝石+ 1 魔法武器= 带孔魔法武器给普通蓝色武器打孔，孔数方面没有具体的说明确定方法，应该是随机生成。属性将会完全改变。. 1 魔法小盾+ 1 钉头棒+ 2 骷髅-> 刺盾 4 生命药剂+ 1 红宝石+ 1 魔法剑-> 吸血的剑 1 钻石+ 1 短剑+ 1 长杖+ 1 腰带-> 野蛮的长棍 1 窒息药剂+ 1 生命药剂-> 解毒药剂 2 箭袋-> 矢袋 2 矢袋-> 箭袋

暗黑 赫拉迪克方块的所有合成公式

转自暗黑3战网 D2 赫拉迪克方块－所有合成公式 及通用公式 3 同类型的神符 (低于 10 级) = 1 高一级别的神符 3 El Runes -> 1 Eld Rune 3 Eld Runes -> 1 Tir Rune 3 Tir Runes -> 1 Nef Rune 3 Nef Runes -> 1 Eth Rune 3 Eth Runes -> 1 Ith Rune 3 Ith Runes -> 1 Tal Rune 3 完美骷髅 + 1 亮金装备 + 乔丹之石(Stone of Jordan) = 为此装备打一孔 亮金装备最多只能有 2 个孔，你无法为一个已经有孔的装备打孔 1 完美骷髅 + 1 亮金装备 + 乔丹之石(Stone of Jordan) = 随机的此亮金装备(同时提高此装备的等级) 提高装备等级依照公式: final ilvl = int(.66 * clvl) + int(.66 * ilvl) 也就是说，最终的装备等级(final ilvl) 为你的角色等级 (clvl) 乘以 (取整)，加上装备原来的等级 (ilvl) 乘以 (同样取整)

6 完美骷髅 + 1 亮金装备 = 1 随机的此亮金装备(同时降低此装备的等级) 你可以用这个公式为亮金装备产生新的属性。final ilvl = int(.4 * clvl) + int(.4 * ilvl) 此公式对大于 3x2 的装备无效 (此公式可用于洗亮金投缳) 4 生命药剂 (同类型) + 红宝石 (同类型) + 魔法剑 = 有偷取生命属性的魔法剑你可以用此公式产生有偷取生命属性的魔法剑 ilvl = 30 剑上会一直有 "of the Leech" 后缀 (4-5% Life Stolen Per Hit) 同时也有得到前缀的机会，剑的类型同时也会保留。 3 Tal Runes -> 1 Ral Rune 3 Ral Runes -> 1 Ort Rune 3 Ort Runes -> 1 Thul Rune 对于高于10 级的神符无效 3 魔法戒指 = 1 随机的魔法项链 用 3 个不想要的魔法戒指生成一个低等级的魔法项链。ilvl = int(.75 * clvl) 既一个 65 级的角色，ilvl = 48。所有 48 级的词缀都可以获得。+2 所有技能的词缀等级为 90，也就是说无法产生 +2 所有技能的项链 3 魔法项链 = 1 随机的魔法戒指 用 3 个不想要的魔法项链生成一个低等级的魔法戒指。ilvl = int(.75 * clvl) 既一个 65 级的角色，ilvl = 48。所有低于 51 等级的词缀都是可以获得的

赫拉迪克方块的合成公式

赫拉迪克方块的合成公式 克莱姆的连枷 + 克莱姆之心 + 克莱姆之眼 + 克莱姆之脑 -> 超级克莱姆连枷 1个怀特的脚＋ 1个回城书 -> 通往奶牛关的门 3 生命药剂 + 3 魔法药剂 + 1 普通的宝石 -> 全面恢复药剂（大紫） 3 生命药剂 + 3 魔法药剂 + 1 碎裂的宝石 -> 恢复药剂（小紫） 3 小紫 -> 1 大紫 6个不同的完美宝石 + 1 项链 -> 多彩的(加4抗) 项链 1 戒指 + 1 完美的红宝石 + 1 爆炸药剂 -> 深红的戒指 (+抗火) 1 戒指 + 1 完美的蓝宝石 + 1 融解药剂-> 深蓝的戒指 (+抗冰) 1 戒指 + 1 完美的黄宝石 + 1 耐力药剂 -> 珊瑚色的戒指 (+抗电) 1 戒指 + 1 绿宝石 + 1 解毒药剂 -> 碧玉的戒指 (+抗毒) 1 斧头 + 1 匕首 -> 投掷斧 1 长矛 + 1 箭袋 -> 标枪 3 戒指 -> 项链 3 项链 -> 戒指 3 普通宝石 + 1 带孔武器 (任何类型) = 1 带孔魔法武器 (同一类型) 这个公式会随机生成一个新带孔武器，武器类型与原来相同，孔数随机生成，属性也将会改变。最大的作用是把例如一把黑色带孔武器变为蓝色武器。 3 无瑕疵宝石 + 1 魔法武器 = 带孔魔法武器给普通蓝色武器打孔，孔数方面没有具体的说明确定方法，应该是随机生成。属性将会完全改变。. 1 魔法小盾 + 1 钉头棒 + 2 骷髅 -> 刺盾 4 生命药剂 + 1 红宝石 + 1 魔法剑 -> 吸血的剑 1 钻石 + 1 短剑 + 1 长杖 + 1 腰带 -> 野蛮的长棍 1 窒息药剂 + 1 生命药剂 -> 解毒药剂 2 箭袋 -> 矢袋 2 矢袋 -> 箭袋 宝石的合成公式,没有变化. 3 碎裂的红宝石 -> 裂开的红宝石 3 裂开的红宝石 -> 普通的红宝石 3 普通的红宝石 -> 无暇的红宝石 3 无暇的红宝石 -> 完美的红宝石 10符文以前符文的合成公式,没有变化. 3 符文01 -> 符文02 3 符文02 -> 符文03 3 符文03 -> 符文04 3 符文0 4 -> 符文05 3 符文05 -> 符文06 3 符文06 -> 符文07 3 符文07 -> 符文08 3 符文08 -> 符文09 3 符文09 -> 符文10

Udietoo详细图文教程(汇编)

一、首先介绍修改器的基本界面和菜单双击Udietoo运行程序后，会出现一个英文界面如图01，和暗黑II游戏的选角色界面有点像，这里面的角色就是你暗黑安装文件夹save里面的角色，所以建议修改前备份save文件夹，以免出现不能挽回的错误。 要注意的是，Udietoo读取存档不是用户本人指定的，它直接读取注册表中注明的存档文件位置，所以本机上未安装暗黑II游戏时运行Udietoo可能会出错。 选择要修改的角色进入，界面也和暗黑游戏很像。以下快捷键可以快速地打开各种界面： A（或ctrl+a）→储存箱 I(或ctrl+i) →物品栏 C（或ctrl+c）→人物属性 S（或ctrl+s）→项目保存（实际上是自带装备材料栏，想要编辑什么东西，可以在这里找） U（或ctrl+u）→赫拉迪克方块 T（或ctrl+t）→技能树 Q（或ctrl+q）→任务栏 W（或ctrl+w）→传送点栏 H（或ctrl+h）→雇佣兵 以下的不常用： P（或ctrl+p）→游戏信息 B（或ctrl+b）→死亡人物栏 K（或ctrl+k）→技能快捷键 N（或ctrl+n）→NPC修改 在物品栏状态时，在物品栏空白处点击鼠标右键，有以下提示（图02或图03）：

或 左上角第一个菜单如图11： 左右对照，可得各英文菜单表达的意思。 二、人物技能、属性、传送点的修改按照以下图示说明就可以修改了。

这里作一些说明。在图07中，需要注意的是，你用鼠标点一个别的任务，下面那一串代码中绿色就会换位置，如图，08、09中，08中选的是第二个任务，09中选的是第三个任务，绿色代码的位置就变了。这个绿色代码就是你所选任务的状态代码，白色的是其他任务的状态代码。这一串代码中如果有1，那么任务处于激活状态，如果全是0，那么任务未激活。任务激活状态下，一般代码的倒数第三个位置是1，如图中鼠标选定的位置。如果最后一个数字是0，表示任务未完成，如果最后一个数字是1，表示任务完成。可以利用方向键移动光标到相应位置来修改。未完成任务是彩色显示，完成任务是灰色显示，这和游戏中一样。 要说明一下，改这个的目的是提高掉宝率。BOSS 首次死亡的时候掉宝率会高于再次死亡，也就是首次完成任务时，BOSS 会更容易掉好的装备。 可能不同版本的Udietoo 在这一项修改上稍有差别，提供图07的教程，从图中就可以看到它不用修改代码，直接点击鼠标就可以修改。我本人用的这个Udietoo 点击不能修改，只好修改代码了。但结果应该是一样的。该教程中提到，ACT5的最后一个任务杀巴尔（Baal ）不能重复激活，其他都可以。我个人试了一下也不能辨别出真假，但我想对多数玩家来说，这是无关紧要的。

赫拉迪克方块合成公式

1.10所有合成公式(中文版) 克莱姆的连枷+克莱姆之心+克莱姆之眼+克莱姆之脑->超级克莱姆连枷 1个怀特的脚＋1个回城书->通往奶牛关的门 3生命药剂+3魔法药剂+1普通的宝石->全面恢复药剂(大紫) 3生命药剂+3魔法药剂+1碎裂的宝石->恢复药剂(小紫) 3小紫->1大紫 6个不同的完美宝石+1项链->多彩的(加4抗)项链 1戒指+1完美的红宝石+1爆炸药剂->深红的戒指(+抗火) 1戒指+1完美的蓝宝石+1融解药剂->深蓝的戒指(+抗冰) 1戒指+1完美的黄宝石+1耐力药剂->珊瑚色的戒指(+抗电) 1戒指+1绿宝石+1解毒药剂->碧玉的戒指(+抗毒) 1斧头+1匕首->投掷斧 1长矛+1箭袋->标枪 3戒指->项链 3项链->戒指 1.10新增的魔法武器合成公式,用于替代3CG公式,重要. 3普通宝石+1带孔武器(任何类型)=1带孔魔法武器(同一类型) 这个公式会随机生成一个新带孔武器，武器类型与原来相同，孔数随机生成，属性也将会改变。最大的作用是把例如一把黑色带孔武器变为蓝色武器。 3无瑕疵宝石+1魔法武器=带孔魔法武器给普通蓝色武器打孔，孔数方面没有具体的说明确定方法，应该是随机生成。属性将会完全改变。. 1魔法小盾+1钉头棒+2骷髅->刺盾 4生命药剂+1红宝石+1魔法剑->吸血的剑 1钻石+1短剑+1长杖+1腰带->野蛮的长棍 1窒息药剂+1生命药剂->解毒药剂 2箭袋->矢袋 2矢袋->箭袋 宝石的合成公式,没有变化. 3碎裂的红宝石->裂开的红宝石 3裂开的红宝石->普通的红宝石 3普通的红宝石->无暇的红宝石 3无暇的红宝石->完美的红宝石 其他宝石的合成方法同上 10符文以前符文的合成公式,没有变化. 3符文01 El ->符文02 Eld 3符文02->符文03 3符文03->符文04 3符文04->符文05 3符文05->符文06 3符文06->符文07 Tal 3符文07->符文08 Ral 3符文08->符文09 Ort 3符文09->符文10 Thul 09魔法的经典合成公式,3PG仍有效,3CG被取消.