**Next message:**Vladyslav Shtabovenko: "Re: Infinite Tadpoles"**Previous message:**Vladyslav Shtabovenko: "Re: Difficult clearing arguments to PaVe functions"**In reply to:**Jongping Hsu: "F_0(0,0,p^2,....)?"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Mail actions:**[ respond to this message ] [ mail a new topic ]

Hi Jongping,

essentially (see attachment),

Subscript[F,

0](0,0,p^2,0,0,p^2,0,p^2,p^2,0,p^2,p^2,p^2,p^2,p^2,0,0,0,0,0,0)==((D-10)

(D-8) (D-5) (D-3) Subscript[B, 0](p^2,0,0))/(4 p^8)

Your use case is actually quite interesting. Essentially, one needs

something like an inverse of ToPaVe in order to convert scalar

Passarino-Veltman functions back into FAD-integrals, so that one can

apply IBP-reduction. I will think of an implementation for that.

Cheers,

Vladyslav

Am 21.12.2016 um 02:27 schrieb Jongping Hsu:

*> Hi,Vladyslav,
*

*> What is the relation between
*

*> p^4 F_0(0,0,p^2,0,0,p^2,0,p^2,p^2,0,p^2,p^2,p^2,p^2,p^2,0,0,0,0,0,0)and
*

*> B_0(p^2,0,0)?
*

*> Thanks. JP
*

*>
*

*> HSU Jongping,
*

*> Chancellor Professor
*

*> Department of Physics
*

*> Univ. of Massachusetts Dartmouth,
*

*> North Dartmouth, MA 02747. FAX (508)999-9115
*

*> http://www.umassd.edu/engineering/phy/people/facultyandstaff/jong-pinghsu/
*

*> recent monograph: Space-Time Symmetry and Quantum Yangâ€“Mills Gravity
*

*> (https://sites.google.com/site/yangmillsgravity123/)
*

*>
*

*> ------------------------------------------------------------------------
*

*> *From: *"Vladyslav Shtabovenko" <noreply@feyncalc.org>
*

*> *To: *feyncalc@feyncalc.org
*

*> *Sent: *Monday, December 19, 2016 10:05:46 AM
*

*> *Subject: *Re: Possible bug in OneLoop
*

*>
*

*> Dear both,
*

*>
*

*> with the current stable version the issue does not apper anymore.
*

*> This
*

*>
*

*> S1 = OneLoop[k,
*

*> FVD[k, \[Mu]] SPD[k, p] SPD[
*

*> k] FAD[{k + p - q, mw}, {k + p + q, mw}, {k, my}]];
*

*> S2 = OneLoop[k,
*

*> FVD[k, \[Mu]] SPD[k, p] SPD[
*

*> k] FAD[{k + p - q, mw}, {k + p + q, mw}, {k, mu}]];
*

*> NewM = S1 - S2;
*

*> Simplify[PaVeReduce[NewM /. mu -> my]]
*

*>
*

*>
*

*> gives zero, as well as
*

*>
*

*> ampy = SP[k] SP[k, p] FourVector[k,
*

*> a] FAD[{k + p - q, mw}, {k + p + q, mw}, {k, my}] // FCI //
*

*> ChangeDimension[#, D] &
*

*> ty = PaVeReduce[OneLoop[k, ampy]];
*

*> ampy1 = FDS[ampy];
*

*> ty1 = PaVeReduce[OneLoop[k, ampy1]];
*

*> ty - ty1
*

*>
*

*> and
*

*>
*

*> T1 = OneLoop[k,
*

*> FVD[k, a] SPD[k, p] SPD[
*

*> k] FAD[{k, my}, {k + p - q, mw}, {k + p + q, mw}],
*

*> DenominatorOrder -> False];
*

*> T2 = OneLoop[k,
*

*> FVD[k, a] SPD[k, p] SPD[
*

*> k] FAD[{k, my}, {k + p - q, mw}, {k + p + q, mw}],
*

*> DenominatorOrder -> True];
*

*> Simplify[PaVeReduce[T1 - T2]]
*

*>
*

*> I will nevertheless add your examples to our testsuite.
*

*>
*

*> Cheers,
*

*> Vladyslav
*

*>
*

*>
*

*>> I don't have an answer to your question. Howver, I agree
*

*>> that there is a bug, or at least a terrible inconsistency, in how
*

*>> OneLoop handles this kind of UV divergent integral. This concerns me
*

*>> because I've been using FeynCalc to manipulate some integrals whose
*

*>> sum is finite, but with individual terms that are UV divergent.
*

*>>
*

*>> In fact, one does not have to rename the mass variable to reveal a
*

*> problem.
*

*>> The answer depends on the order of the propagators.
*

*>>
*

*>> ==========================
*

*>>
*

*>> SetOptions[OneLoop,Prefactor->1/(I Pi^2)];
*

*>>
*

*>> First we define, as you did:
*

*>>
*

*>> ampy = SP[k] SP[k,p] FourVector[k,a]
*

*> FAD[{k+p-q,mw},{k+p+q,mw},{k,my}]//FCI;
*

*>>
*

*>> k^2 k.p k[a]
*

*>> ampy = ----------------------------------------------------------
*

*>> ((k + p - q)^2 - mw^2) ((k + p + q)^2 - mw^2) (k^2 - my^2)
*

*>>
*

*>> The one loop integral is:
*

*>>
*

*>> ty = PaVeReduce[OneLoop[k,ampy]];
*

*>>
*

*>> Now instead put it in standard order using FeynAmpDenominatorSimplify:
*

*>>
*

*>> ampy1 = FDS[ampy];
*

*>>
*

*>> k^2 k.p k[a]
*

*>> ampy1 = ----------------------------------------------------------
*

*>> (k^2 - my^2) ((k + p - q)^2 - mw^2) ((k + p + q)^2 - mw^2)
*

*>>
*

*>> ty1 = PaVeReduce[OneLoop[k,ampy1]];
*

*>>
*

*>> ty is not equal to ty1. The difference, after simplifying B0[0,m0,m1] is
*

*>>
*

*>> -(2 mw^2 + 4 my^2 - p^2 - q^2 - 2 p.q) (p[a] + q[a])
*

*>> ty-ty1 = ----------------------------------------------------
*

*>> 48
*

*>>
*

*>> If we now change the mass my -> mu, and so define ampu = ampy/.my->mu,
*

*>> and ampu1 = ampy1/.my->mu, then the analogous tu and tu1 ARE in fact
*

*>> equal. However, as you discovered, tu does not equal ty
*

*>> (after replacing mu->my), with the difference being
*

*>>
*

*>> (3 mw^2 - 2 q^2) q[a]
*

*>> tu-ty = ---------------------
*

*>> 6
*

*>>
*

*>> Going back to the ampy amplitude, if we apply ScalarProductCancel we find
*

*>> (equivalent to regrouping k^2 -> k^2-my^2 + my^2 and cancelling
*

*> propagators):
*

*>>
*

*>> SPC[ampy]
*

*>>
*

*>> k.p k[a]
*

*>> = --------------------------------------------- +
*

*>> ((k + p - q)^2 - mw^2) ((k + p + q)^2 - mw^2)
*

*>>
*

*>> my^2 k.p k[a]
*

*>> ----------------------------------------------------------
*

*>> ((k + p + q)^2 - mw^2) (k^2 - my^2) ((k + p - q)^2 - mw^2)
*

*>>
*

*>> Here the one loop integral gives the same result as the standard ordered
*

*>> result ty1. Interestingly, evaluating the one loop integral of SPC[ampu]
*

*>> also gives the SAME result as ty1 (after replacing mu->my). That this
*

*>> should happen is clear from the form of the amplitude above, since the
*

*>> first term is independent of my^2, and the second is explicitly
*

*>> multiplied by my^2. So I suspect that this form gives the "correct"
*

*>> answer (or perhaps the "preferred" answer).
*

*>
*

*>
*

- application/mathematica attachment: F0.nb

**Next message:**Vladyslav Shtabovenko: "Re: Infinite Tadpoles"**Previous message:**Vladyslav Shtabovenko: "Re: Difficult clearing arguments to PaVe functions"**In reply to:**Jongping Hsu: "F_0(0,0,p^2,....)?"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Mail actions:**[ respond to this message ] [ mail a new topic ]

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