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Doubly charged Higgsino contribution to the decays mu--e photon and mu--3e and to the anoma

a r X i v :h e p -p h /9704306v 1 12 A p r 1997

UQAM-PHE-97/03CUMQ/HEP 96February 1,2008

DOUBLY CHARGED HIGGSINO CONTRIBUTION TO THE DECAYS μ→eγAND μ→3e AND TO THE ANOMALOUS MAGNETIC MOMENT OF THE MUON ?a μWITHIN THE LEFT-RIGHT SUPERSYMMETRIC

MODEL

G.Couture a ,M.Frank b and H.K¨o nig a ,b

D′e partement de Physique,Universit′e du Qu′e bec `a Montr′e al

C.P.8888,Succ.Centre Ville,Montreal,Qu′e bec,Canada,H3C 3P8b

Department of Physics,Concordia University,1455De Maisonneuve Blvd.W.

Montreal,Quebec,Canada,H3G 1M8

Abstract

We present a detailed and complete calculation of the doubly charged Higgsino contri-bution to the decays μ→eγand μ→3e and to the anomalous magnetic moment of the muon ?a μwithin the left-right supersymmetric model.We include the mixing of the scalar partners of the left and right handed leptons,and show that it leads to a strong enhance-ment of the decay modes in certain scenarios.We ?nd that the contribution of the doubly charged Higgsino can be close to the known experimental values and are reachable by future experiments.

1Introduction

The quest for a supersymmetric grand uni?ed theory is plagued by lack of direct signals which would distinguish such a theory from supersymmetry in general.Supersymmetry,in particular the Minimal Supersymmetric Model(MSSM)[1],can be probed experimentally through the high energy production of superpartners.However,the MSSM,while?lling in some of the theoretical gaps of the Standard Model,fails to explain other phenomena such as the weak mixing angle,the small mass(or masslessness)of the known neutrinos,the origin of CP violation,to quote a few.Extended gauge structures such as grand uni?ed theories, introduced to provide an elegant framework for uni?cation of forces[2],would connect the standard model with more fundamental structures such as superstrings,and also resolve the puzzles of the electroweak theory.

Phenomenologically,grand uni?ed theories would either predict relationships between otherwise independent parameters of the standard model,or new interactions(i.e.interac-tions forbidden or highly suppressed in the standard model).

Among supersymmetric grand uni?ed theories,SO(10)[3]and SU(5)[4]have received signi?cant attention.In this aricle we shall study a model based on the left-right symmetric extension of the MSSM,based on SU(2)L×SU(2)R×U(1)B?L.Its attraction is that on one hand the Left-Right Supersymmetric Model(LRSUSY)is an extension of the Minimal Supersymmetric Standard Model based on left-right symmetry and on the other hand it could be viewed as a low-energy realization of certain SUSY?GUT s,such as SO(10).

LRSUSY shares some of the attractive properties of the MSSM,like providing a natural solution for the gauge hierarchy problem.LRSUSY also supresses naturally rapid proton decay,by disallowing terms in the Lagrangian that explicitly violate either baryon or lepton numbers[5].It gauges the only quantum number left ungauged,B?L.The LRSUSY model also shares some of the attractive features of the original left-right symmetric model[6],such as providing a possible explanation for the smallness of the neutrino mass and for the origin of parity violation.Recently,this model has received a lot of attention,because it could o?er a framework for solving both the strong and the weak CP problem[7].Furthermore it has the very attractive feature of automatically conserving R-parity.

So far,there is no experimental evidence for the right-handed interactions predicted by the SU(2)L×SU(2)R×U(1)B?L theory,let alone by supersymmetry.Yet the foundation of

LRSUSY has so many attractive features that the model deserves some experimental and theoretical investigation.The next generation of linear colliders will provide an excellent opportunity for such a study.The theoretical and experimental challenge lies in?nding distinctive features for the left-right supersymmetric model,which allow it to be distinguished from both the SUSY version of the Standard Model and from the non-supersymmetric version of the left-right theory[8].Lepton-?avor violation decays are just the right type of such phenomena.The LRSUSY model provides a natural framework for large lepton?avor-violating e?ects through two mechanisms:on one hand it can give rise to a leptonic decay width of the Z-boson through both left-handed and right-handed scalar lepton mixing[9], on the other hand it contains lepton-?avor-blind higgsinos which couple to leptons only and enhance lepton-?avor violation.

In a recent paper[10]we analysed the lepton?avor-violating decayμ→eγ,whose signature can be reliably calculated and,by the structure of the model,showed to be greatly enhanced over the MSSM,and already accessible at the current experimental accuracy.

The contribution of the doubly charged Higgs boson to lepton-?avor violation decays were considered in[11]and quite strong constraints to its mass and its Yukawa coupling to the leptons were presented.Here we will study a new source of enhancement coming from the existence,in the supersymmetric sector,of a doubly-charged higgsino.Since the measurement ofμ→eγhas a very precise bound B(μ→eγ)<4.9×10?11and B(μ→3e)<1.0×10?12[12],we are able to obtain values close to the experimental bound and restrict some of the parameters in the theory.

A similar contribution from the doubly-charged higgsino(with di?erent mass parameters) appears in the calculation of another accurately measured quantity,the anomalous magnetic moment of the muon(AMMM)aμ=(g?2)/2.Its experimental value is a expμ=1165922(9)×10?9[12].The measured deviation of the AMMM lies within a range of?2×10?8≤?a expμ≤2.6×10?8[13]

Experiment E821,under way at the Brookhaven National Laboratory(BNL),is designed to improve the existent data on the AMMM by a factor of10?20.When completed,it would be possible to test deviations from the1-loop predictions of the Minimal Supersymmetric Standard Model,believed to arise most likely from supersymmetric contibutions.For com-pleteness,we also investigate the e?ect of the contribution of the doubly-charged higgsino to the AMMM.We then restrict the parameter space of the left-right supersymmetric model

by combining these e?ects.

Our paper is organized as follows:in section2we give a brief description of the model, followed by the numerical analysis of the decayμ→eγin section3and the AMMM in section4.Our conclusions are reached in section5.In addition,Appendices A and B will present the detailed analytical calculations.

2The Left-Right Supersymmetric Model

The LRSUSY model,based on SU(2)L×SU(2)R×U(1)B?L,has matter doublets for both left-and right-handed fermions and the corresponding left-and right-handed scalar partners (sleptons and squarks)[8].In the gauge sector,corresponding to SU(2)L and SU(2)R, there are triplet gauge bosons(W+,?,W0)L,(W+,?,W0)R and a singlet gauge boson V corresponding to U(1)B?L,together with their superpartners.The Higgs sector of this

model consists of two Higgs bi-doublets,Φu(1

2,0)andΦd(1

,0),which are required to give

masses to both the up and down quarks.In addition,the spontaneous symmetry breaking of the group SU(2)R×U(1)B?L to the hypercharge symmetry group U(1)Y is accomplished by introducing the Higgs triplet?elds?L(1,0,2)and?R(0,1,2).The choice of the triplets (versus four doublets)is preferred because with this choice a large Majorana mass can be generated for the right-handed neutrino and a small one for the left-handed neutrino[6]. In addition to the triplets?L,R,the model must contain two additional tripletsδL(1,0,?2) andδR(0,1,?2),with quantum number B?L=?2to insure cancellation of the anomalies that would otherwise occur in the fermionic sector.Given their strange quantum numbers, theδL andδR do not couple to any of the particles in the theory so their contribution is negligible for any phenomenological studies.

As in the standard model,in order to preserve U(1)EM gauge invariance,only the neutral Higgs?elds aquire non-zero vacuum expectation values(V EV′s).These values are:

?L = 00v L0 , ?R = 00v R0 and Φ = κ00κ′e iω .

Φ causes the mixing of W L and W R bosons with CP-violating phaseω.In order to simplify, we will take the V EV′s of the Higgs?elds as: ?L =0and

?R = 00v R0 , Φu = κu000 and Φd = 000κd .

Choosing v L=κ′=0satis?es the more loosely required hierarchy v R?max(κ,κ′)?v L and also the required cancellation of?avor-changing neutral currents.The Higgs?elds aquire non-zero V EV′s to break both parity and SU(2)R.In the?rst stage of breaking the right-handed gauge bosons,W R and Z R aquire masses proportional to v R and become much heavier than the usual(left-handed)neutral gauge bosons W L and Z L,which pick up masses proportional toκu andκd at the second stage of breaking.[5]

The supersymmetric sector of the model,while preserving left-right symmetry,has four singly-charged charginos(corresponding to?λL,?λR,?φu,and?φd),in addition to???L,???R,?δ?

and?δ?R.The model also has eleven neutralinos,corresponding to?λZ,?λZ′,?λV,?φ01u,?φ02u L

,?φ01d,?φ02d,??0L,??0R?δ0L,and?δ0R.It has been shown that in the scalar sector,the left-triplet ?L couplings can be neglected in phenomenological analyses of muon and tau decays[14]. Although?L is not necessary for symmetry breaking[15],it is introduced only for preserving left-right symmetry,we will not neglect the couplings of?L in the fermionic sector,which leads to important consequences as shown later.

The doubly charged???R is however very important:it carries quantum number B?L of2and couples only to leptons,therefore breaking lepton-quark universality.It and its supersymmetric partner could,as will be seen in the next section,play an important role in ?avor-violating leptonic decays.

In the scalar matter sector,the LRSUSY contains two left-handed and two right-handed scalar fermions as partners of the ordinary leptons and quarks,which themselves come in left-and right-handed doublets.In general the left-and right-handed scalar leptons will mix together.Some of the e?ects of this mixings,such as enhancement of the AMMM,have been discussed elsewhere[5].Only global lepton-family-number violation would prevent?e,?μand ?τto mix arbitrarily.Permitting this mixing to occur,we could expect small e?ects to occur in the non-supersymmetric sector,such as radiative muon or tau decays,in addition to other nonstandard e?ects such as massive neutrino oscillations and violation of lepton number itself.But,in general,allowing for the mixing,we have six charged-scalar lepton states (involving15real angles and10complex phases)and six scalar neutrinos(also involving15 real angles and10complex phases).In order to reduce the(large)number of parameters we shall assume in what folows that only two generations of scalar leptons(the lightest)mix signi?cantly1.

The mixings are as follows:?μL,R and?e L,R with angleθL,R;?νμ

L,R and?νe

L,R

with angle

αL,R;so that,for example:

=?μL cosθL+?e L sinθL,(1)

=??μL sinθL+?e L cosθL,(2)

and similar for?l R

1,2and?νL

1,2

and?νR

1,2

Furthermore we include the mixing of the scalar partners to the left and right handed leptons;that is,we take?e L=cosθ?e?e1?sinθ?e?e2and?e R=sinθ?e?e1+cosθ?e?e2,and similiar for the other generations,where we express the mixings by the matrix?K a mn in Appendix A.

The physical mass eigenstates are then given by eq.(1-2).

Next we consider the implications of the above-mixing in the LRSUSY in lepton-?avor violating decayμ→eγ.

3The Decayμ→eγ

To obtain the contributions of the doubly charged higgsino to the decay rate ofμ→eγwe have to calculate the diagrams of?g.(1).

The detailed calculations are shown in the Appenix A.The matrix element given in eq.(14)leads to the following result:

iM=+eh2LR

m2?

mμ

cθ

sθ

(

cθ

sθ

)

B R?

l =s2θ

+c2θ

cθ

sθ

mixing of all generations via a supersymmetric version of the Kobayashi-Maskawa matrix.

~μ

~e, μ

Figure 1:The penguin diagrams with scalar leptons and doubly charged Higgsinos within

the loop.In the left-right model without SUSY the same diagrams occur with ??

?l and ?l ??L,R

?rst and second generation in the mixing angles c θL,R ,eq.(1-2).c θ?l is the mixing angle of the scalar partners of the left and right handed leptons.Note that if we would include the mixing of all 3generations the expression is far more complicated,in particular for the Higgsino mass term.Since m ???m l the mixing of the scalar leptons can not be neglected.If we

exclude the contribution of the left handed Higgsino then B L ?l

and,as can be easily seen from eq.(14)(all ?K

a m 1

set to be 0),the term proportional to the Higgsino mass are absent 2.A matrix element of the form iM =e

α2

m 2e

νe )=

G 2F

384πs 4W

m μ

8π3

h 4LR m ?

? 4

c 2θL s 2θL (B L

e ?

B L ?μ)

c 2θR s 2θR (B R

e ?

B R ?μ)

(4)

Simliar for B(μ→3e).It isΓ(μ→3e)

3π[log m2μ

If we neglect the mixing of the scalar partners of the left and right handed leptons,that is,setting sinθ?

=0eq.(4)leads to:

B(μ→eγ)=3s4W

α m W

4π3

h4LR

4c2θs2θ 7m?

4(6)

Eq.(6)leads to B(μ→eγ)≈2.97×10?16h4LR c2θs2θfor m?

=100GeV and thus far smaller

than the experimental limit.

However the situation is changed when the mixing of the scalar partners of the right and

left handed leptons is included.Since m l?m?

the mixing angle is given by

sinθ?

l ～m l(A l?μtanβ)/m2?

～m l/m?

with(A l?μtanβ)～m?

,where A l is the trilinear

scalar interaction,μthe mixing mass terms of the Higgs bosons and tanβ=v2/v1the ratio

of their vacuum expectation values(vev’s).This leads to B L?

l ≈B?

+m??

mμ

(?B?

??B?

)where

we assumed that after left-right symmetry breaking the relations cθ

L /cθ

～sθ

/sθ

～1still

hold.

If the left-right symmetry is conserved we have?B?

l1=?B?

and eq.(5)is recovered.However

after breaking,the mass di?erence between the scalar partners of the left handed and right handed leptons is much larger than the mass di?erence between the generations.We expect

1?m2?

(?Bμ

??Bμ

)～5

4The Anomalous Magnetic Moment of the Muon

The calculations to the AMMM are similiar as to theμ→eγdecay.From eq.(15)we obtain the following result:

?aμ=?2h2LR

2 B L?μ+B R?μ (7)

B L?μand B R?μas given in eq.(3).Again B L?μis absent when we exclude the contribution of the left handed higgsino.

Eq.(7)leads to

?aμ=?2h2LR

2(B?μ1+B?μ2)(8)

Eq.(8)leads to?aμ≈?3.49×10?9h2LR for m?

～m?μ=100GeV,thus already very

close to the experimental lower limit of?a expμ,leading to the constraint h2LR<5·10?4m2?

?(GeV).

5Conclusions

We presented the results of the contribution of the doubly charged Higgsino to the decays μ→eγandμ→3e and to the anomalous magnetic moment of the muon?aμ.It was shown that when mixing of the scalar partners of the left and right handed leptons are neglected the contribution to the decay modes is far below the experimental limits.However for the anomalous magnetic moment it is within the reach of the future BNL experiments.When mixing of the scalar leptons is included we obtain a constrain for the lepton-scalar lepton-

doubly charged Higgsino coupling h LR in the order of less than10?4m?

(GeV)if maximal electron-muon mixing is assumed(not to be confused with the upper mixing of the scalar leptons).The e?ect of this mixing on?aμis negligible.

6Acknowledgements

We want to thank M.Pospelov for fruitful discussions.This work was funded by NSERC of Canada and les Fonds FCAR du Qu′e bec.

A Appendix:The matrix elements

In this Appendix we present the ?nal results of the calculations of the Feynman diagrams as shown in Fig.1with ?avor non diagonal couplings of the doubly charged Higgsino to the left and right handed leptons and their scalar partners.We de?ne the following matrix:

iM =+

eh 2LR

u p 2(q 2γμ?/q q μ)(T aL 11P L +T aR

22P R )u p 1

u p 2iσμνq ν

m ??(1?α1)(T aL 12P L +T aR 12P R )

D ???

iM S

dα1e ?l

α31

(11)

α21(1

?α1)

??μ

D ???

(12)

D ???

l SE =m 2???(m 2???m 2

?l a

)α1T aL 11:=K ?L ae,μK L aμ?K a 2

m 1T aR 22:=K ?R ae,μK R aμ?K a 2

m 2

T aL 12:=K ?R ae,μK L aμ?K a m 1?K a

m 2

T aR 12:=K ?L ae,μK R aμ?K a m 1?K a

m 2

where e ??=?2,e ?l =+1and e μ=?1.We have to sum over the generation indices a =1?3and over the eigenstates of the scalar partners of the left and right handed leptons m =1,2.The divergencies cancel after the summation of all diagrams e ??+e ?l ?e μ≡0.

Due to this equation many more terms like terms proportional to m ??α1(1?α1)(p 1+p 2)

μdrop out after summation and are not explicitely written down in eqs.(10-12).Furthermore

we made use of eqs.(A.5)-(A.8)in[16]and eqs.(A.6)+(A.7)in[17].After summation of eqs.(10-12)the?nal matrix element is given by:

iM=+eh2LR

m2?

u p

iσμνqν m??(T aL12P L+T aR12P R)[e???B G(x???l a m)+eμ?B F(x???l a m)]

[m e,μ(T aL11P L+T aR22P R)+mμ(T aL11P R+T aR22P L)]

[e??[?B G(x???

l a m

)+B F(x???

l a m

)]+e?

B F(x???

l a m

)] u p1 ??μq

The?nal functions after Feynman integration are shown in Appendix B.Since we are not interested in CP violation we can skip the?in T aL,R

3.Furthermore for a photon on mass shell we have q2=0and due to gauge invariance??μq qμ=0.

Neglecting the electron mass the matrix element for the decayμ→eγis then given by:

iM=+eh2LR

m2?

2mμ

F(q2)

(4π)2 mμ

mμ

K R a2K L a2?K a m1?K a m2[e?

(x???

l a m

)+eμ?B F(x???

l a m

)]

As above after summation over all mass eigenstates and generations of the leptons eq.(15)

leads to the result as given in eq.(7).

B Appendix:The ?nal functions

A G (x ?

?l a

)=1

(1?x ?

?l a

(1+2x ???l a m

)log(x ?

?l a

)}A F (x ?

?l a

)=1

(1?x ?

?l a

dα1α1(1?α1)/D ???l a m (18)

{1?x ?

?l a

+2x ?

??l a m

log(x ?

??l a m

)}B F (x ?

?l a

)=1

(1?x ?

?l a

(1?x ?

?l a

{1?x ??

?l a

+x ???l a m

log(x ?

??l a m

)}?B F (x ???l a m

2B G (x ??

?l a m

)(21)

D ???l a m =1?(1?x ?

?l a

)α1x ?

?l a m

m 2?l a m

m 2??

B F =G ′/6,

m μ

m 2??

(B G ?B F )=F ′/12and

m μ

m ?

?G =(2G ′+F ′)/3.

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暗黑2装备合成公式

暗黑2单机专用的宝盒公式: 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**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.............................................................................. .......... 1.10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 .............................................................................. ....... 1.09魔法的经典合成公式,3PG仍有效,3CG被取消. 3 完美的宝石 + 1 魔法物品 -> 魔法物品.............................................................................. ........ 1.09黄金的相关合成公式,未变. 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.............................................................................. ... 1.09以后的所有橙色物品合成公式仍然有效,未有新增公式. 具体请见:手工橙色物品公式..............................................................................

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

暗黑2赫拉迪克方块的所有合成公式

转自https://www.sodocs.net/doc/df1591310.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。

《暗黑破坏神2 》全部合成公式

《暗黑破坏神2 》全部合成公式核心提示：暗黑破坏神2游戏攻略。霍拉瑞克宝盒（Horadric Cube）霍拉瑞克宝盒在《黑暗破坏神２》中并非一件普通的道具，它属于“情节道具”中的一种，是游戏进行必不可缺的物品。你将在ＡＣＴ２“干涸的山”（Dry Hills）场景中“亡灵大厅”（Halls of the Dead）第三层发现霍拉瑞克宝盒，它可以用来组合ＡＣＴ２中的Horadric Staff和ＡＣＴ３中的Khalim's Flail外还具有其它多种特殊的用途。霍拉瑞克宝盒最常用的用途是存储物品。霍拉瑞克宝盒本身只占据４个空格（２Ｘ２），但宝盒内部能够提供１２个单元的存储空间（４Ｘ３），也就是说一个宝盒能够多提供８个单元的存储空间。另外，霍拉瑞克宝盒还可以为玩家提供用品的“转化”功能。转化的方式如下：（１）３瓶治疗药水＋３瓶魔法药水＝１瓶恢复药水（可使用任何等级的药水）（２）３瓶治疗药水＋３瓶魔法药水＋１颗宝石＝１瓶全恢复药水（可使用任何等级的药水和宝石）（３）３瓶治疗药水＋１瓶Strangling Gas药水＝１瓶解毒药水（可使用任何等级的药水）（４）３颗同类同等级宝石＝１颗高等级宝石（主要用于升级宝石。３颗缺损的宝石可以生成１颗裂开的宝石；３颗裂开的宝石可以生成１颗普通的宝石；３颗普通的宝石可以生成１颗无瑕疵的宝石；３颗无暇疵的宝石可以生成１颗完美的宝石，如果要这样生成一颗完美的宝石的话要８１颗缺损的宝石，还不如直接去碰运气找宝石祭坛的好……）

（５）３颗完美的头骨宝石＋１枚护身符＝１个可以将角色技能等级提升１至２级的护身符（也可以使用任意类型的３颗完美宝石，但头骨宝石的向率更高，几乎可以达到１００％）（６）３颗完美的宝石＋１件物品（武器或盔甲）＝１件同类的魔法物品（对金色、黄色和绿色装备无效，转化后的物品属性可能提高也可能降低）（７）１件斧类武器＋２件匕首类武器＝１捆飞斧（可以使用任意的斧类武器和匕首类武器，只能转化出普通的飞斧）（８）１枚戒指＋１枚绿宝石＋４瓶解毒药水＝１枚绿戒指（２１－３０抗毒性，与宝石的质量和戒指的成分无关）（９）１枚戒指＋１枚红宝石＋４瓶爆炸药水＝１枚红戒指（２１－３０抗火性，与宝石的质量和戒指的成分无关）（１０）１枚戒指＋１枚蓝宝石＋４瓶解冻药水＝１枚蓝戒指（２１－３０抗寒性，与宝石的质量和戒指的成分无关）（１１）１枚戒指＋２枚黄宝石＝１枚黄戒指（２１－３０抗电性，与宝石的质量和戒指的成分无关）（１２）３枚护身符＝１枚戒指（戒指的属性与护身符的属性大致相同）（１３）３枚戒指＝１枚护身符（护身符的属性与戒指的属性大致相同）

DIABLO2——暗黑破坏神2装备顶级合成

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 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..................................................................................... 09魔法的经典合成公式,3PG仍有效,3CG被取消. 3 完美的宝石+ 1 魔法物品-> 魔法物品...................................................................................... 09黄金的相关合成公式,未变. 6 完美的骷髅+ 1 黄金物品-> 低等级黄金物品

暗黑破坏神2套装与暗金装备

普通套装天上的衣服阿卡娜的诡计- 法师套装北极装置- 亚马逊套装狂战士的军火库- 野蛮人套装卡珊的陷阱- 法师套装希弗伯的法衣克雷得劳的支柱死亡的伪装哈斯拉柏的防御地狱的工具- 死灵法师套装依雷撒的精洗炉依森哈德的武器室米拉伯佳的雪茄- 圣骑士套装西刚的全套刀剑坦克雷的战斗工具维达拉的配备- 亚马逊套装毁灭之王: 普通/扩展/精华套装艾尔多的守卫－德鲁依套装布尔凯索的孩子- 野蛮人套装牛魔王之皮甲门徒格瑞斯华尔德的传奇- 圣骑士套装天堂的信徒华宁的威严不朽之王- 野蛮人套装马维娜之战斗诗歌- 亚马逊套装娜塔亚的非难- 刺客套装娜吉的古代遗迹- 法师套装孤儿的呼唤山德的愚行沙撒璧的雄伟贡品塔拉夏的外袍- 法师套装塔格奥的化身- 死灵法师套装艾尔多的守卫－德鲁依套装部分套装奖励 150% 额外的攻击准确率加成(2 套装物品) 50% 更佳的机会取得魔法装备(3 套装物品) 全部套装奖励

+3 德鲁依技能 +350% 增强伤害* 150% 额外的攻击准确率加成 50% 更佳的机会取得魔法装备 10% 击中偷取法力所有抗性+50 +150 防御 +150 法力显示光环艾尔多的冷酷凝视猎人的伪装防御: 157-171 (可变) (基础防御: 67-81) 须要等级: 36 须要力量: 56 耐久度: 20 (限德鲁依) +90 防御 25% 快速再度攻击法力重生17% 抗寒+40-50% (可变) 凹槽(2) +5 照亮范围 +15 精力(2 套装物品) +15 精力(3 套装物品) +15 精力(完全装备) 艾尔多的成长战场之靴防御: 39-47 (可变) 须要等级: 45 须要力量: 95 刺客踢伤害: 37-64 无法破坏 40% 高速跑步/行走 +180 耐力最大值 10% 受损的生命移至法力耐力恢复速度+32% +50 生命抗火+40-50% (可变) +15 敏捷(2 套装物品) +15 敏捷(3 套装物品) +15 敏捷(完全装备)

暗黑2装备合成公式

暗黑2单机专用合成公式时间:2009-07-10 00:45 点击:次最近发现很多朋友是单机的,那么网上提供的公式将有很多不适合你,所以收集了D2的合成公式单机版. 暗黑2单机专用的宝盒公式: 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**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

暗黑2赫拉迪克方块的所有合成公式

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暗黑破坏神2橙色物品合成公式图解

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+(10-20) To Life ,+(10-20)生命点数图示形状的鞋子+5号符文+完美红宝石+珠宝 Crushing Blow (5-10)% ,(5-10)%机会击中使怪物失去一半生命, (1-3)% Life Stolen Per Hit ,+(1-3)%生命每次击中吸取, +(10-20) To Life ,+(10-20)生命点数, 图示形状的手套+4号符文+完美红宝石+珠宝 Open Wounds (5-10)% ,(5-10)%造成伤口, (1-3)% Life Stolen Per Hit ,+(1-3)%生命每次击中吸取,

+(10-20) To Life ,+(10-20)生命点数, 图示形状的腰带+7号符文+完美红宝石+珠宝 Attacker Takes Damage of (4-7) ,攻击反弹(4-7), (1-3)% Life Stolen Per Hit ,+(1-3)%生命每次击中吸取, +(10-20) To Life ,+(10-20)生命点数, 图示形状的盾牌+6号符文+完美红宝石+珠宝 + (1-3) Life Per Demon Kill ,+(1-3)生命每杀死一个恶魔, (1-3)% Life Stolen Per Hit ,+(1-3)%生命每次击中吸取,

暗黑2合成公式1.11版

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百度文库- 让每个人平等地提升自我！ 11 提醒一下：全部Cube合成活动与进行Cube合成时的盒子级别、游戏场景、难度、以及同一游戏的玩家数量等均无关系。 ◆洗GC/SC 洗GC/SC的原理都是基于与人物等级无关的3PG公式即与宝石类型、人物级别、游戏难度等均无要求一、洗GC 合成方法：三个完美宝石（任何类型）+ 超大型护身符固定属性：无固定属性，完全随机。期望目标：45life技能GC、12FHR技能GC等一般要求：1.GC级别≥91，用DGC（暗黑破坏神掉的GC，Lv94）、NGC（尼拉塞克掉的GC，Lv95）、BGC（巴尔掉的GC，Lv99）均符合要求。二、洗SC 合成方法：三个完美宝石（任何类型）+ 小护身符固定属性：无固定属性，完全随机。期望目标：JP451PD、3max/20ar/20Life、20Life/4r5等一般要求：1.SC级别≥94，用DSC（暗黑破坏神掉的SC，Lv94）、NSC（尼拉塞克掉的SC，Lv95）、BSC（巴尔掉的SC，Lv99）均符合要求。 ◆洗橙色装备（手工艺品Crafted Items）橙色装备具有几个固定属性，同时还会具有若干随机属性。两者共同决定了成果的好坏。同时要注意：与洗GC/SC不同的是，手工艺品的成色与所用的人物级别有关。一、洗戒指合成方法：蓝色魔法戒指 + Sol(12#) + 完美红宝石 + 魔法珠宝固定属性：+(1-5)强壮+(1-3)%每次击中吸取生命(LL) +(10-20)生命期望目标：11LL并有若干其他好属性，如6LM、4r11、单抗30等一般要求：1.戒指等级≥86，最好用Lv99的。一般可用高级别人物赌博得到2.人物级别：如果用Lv99的戒指，人物级别要≥74；如果用Lv90的戒指，人物级别要≥82；如果用Lv86的戒指，人物级别要≥86。二、洗项链(一)Blood类合成方法：蓝色魔法项链 + Amn(11#) + 完美红宝石 + 魔法珠宝固定属性：(5-10)% 快速奔跑/行走(FRW)+(1-4)%偷取生命(LL) +(10-20)生命期望目标：+2人物技能、+10FRW、+Life、+Str等一般要求：1.项链等级≥90，最好用Lv99的。一般可用高级别人物赌博得到2.人物级别：如果用Lv99的项链，人物级别要≥82；如果用Lv94的项链，人物级别要≥86；如果用Lv90的项链，人物级别要≥90。

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